Citation
Development of a capacity analysis procedure for U.S. roundabouts based on Vail, Colorado's Vail Rd./I-70 South roundabout

Material Information

Title:
Development of a capacity analysis procedure for U.S. roundabouts based on Vail, Colorado's Vail Rd./I-70 South roundabout
Creator:
Kramer, James H
Publication Date:
Language:
English
Physical Description:
xii, 178 leaves : illustrations ; 29 cm

Subjects

Subjects / Keywords:
Traffic circles -- United States ( lcsh )
Traffic flow -- United States ( lcsh )
Highway capacity -- United States ( lcsh )
Highway capacity ( fast )
Traffic circles ( fast )
Traffic flow ( fast )
United States ( fast )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Bibliography:
Includes bibliographical references (leaves 177-178).
General Note:
Submitted in partial fulfillment of the requirements for the degree, Master of Science, Civil Engineering.
General Note:
Department of Civil Engineering
Statement of Responsibility:
by James H. Kramer.

Record Information

Source Institution:
|University of Colorado Denver
Holding Location:
Auraria Library
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
39694092 ( OCLC )
ocm39694092
Classification:
LD1190.E53 1997m .K73 ( lcc )

Downloads

This item has the following downloads:


Full Text
DEVELOPMENT OF A CAPACITY ANALYSIS PROCEDURE FOR U.S.
ROUNDABOUTS BASED ON VAIL, COLORADOS VAIL RD./I-70 SOUTH
ROUNDABOUT
by
James H. Kramer, P.E.
B.S.C.E., University of Wisconsin, 1977
M.B.A., Regis University, 1992
A thesis submitted to the
University of Colorado at Denver
in partial fulfillment
of the requirements for the degree of
Master of Science
Civil Engineering
1997
AL


This thesis for the Master of Science
degree by
James H. Kramer
has been approved
by
Sarosh I. Khan
/(t/fe
Date


Kramer, James H. (M.S., Civil Engineering)
Development of a Capacity Analysis Procedure For U.S. Roundabouts,
Based on Vail Colorados Vail Rd./I-70 South Roundabout
Thesis directed by Dr. Bruce N. Janson
ABSTRACT
This paper develops an American procedure to calculate the capacity for the Vail
Rd./I-70 south roundabout at Vail, Colorado. In Britain, a study has previously been
made of the entry capacities of roundabouts at eighty-six locations, and a unified
formula for capacity prediction developed. The traffic flow entering a roundabout
from a saturated approach was found to be linearly dependent on the circulating flow
crossing the entry point to the roundabout. The entry angle and radius was found to
have small but significant effects. The inscribed circle diameter, used as a simple
measure of overall size, was found to be effective as a predictive variable for the
capacity. The American Highway Capacity Manual (HCM) currently has no analysis
methodology for roundabouts, but the Transportation Research Board Committee
on Highway Capacity and Quality of Service, Unsignalized Intersections
Subcommittee is now preparing the addition of material to HCM Chapter 10 to
come out in 1998. This thesis demonstrates a new procedure which can be used to
correct the British capacity procedure for an American roundabout at Vail, Colorado.
With opposing flow located on the X axis, capacity on the Y axis, and a linear
relationship, the American Roundabout capacity procedure for the Vail, Colorado
m


roundabout requires the Y intercept to change but the slope of the linear
entry/circulating flow relationship remains the same. This new procedure calculates
a capacity 17% lower than the British procedure for the roundabout. The only
explainable reason for the difference between the British capacity procedure on
British roundabouts and this new American procedure is American driver familiarity
with negotiating a roundabout.
This abstract accurately represents the content of the candidates thesis. I
recommend its publication.
Signe
Bruce N. Janson
IV
v


ACKNOWLEDGEMENT
Acknowledgment is gratefully given to Dr. Bruce Janson of the University of
Colorado at Denver for providing direction and input on the composition of this
paper. I would also like to thank Leif Ourston, P.E., and Peter Doctors, P.E., of
Ourston and Doctors, and Barry Crown of Britain, author of the British software
program RODEL, for their direction and input in the preparation of this thesis. Their
patience with my questions and enthusiasm to help me in this endeavor will always
be remembered and appreciated.


CONTENTS
Chapter Page
1. Introduction..................................................... 1
1.1 Background and Problem Identification............................ 1
1.2 Problem Approach................................................. 5
2. Intersection Control Alternatives................................ 7
2.1 Traffic Signals.................................................. 7
2.2 Two-Way Stop Control............................................. 8
2.3 All-Way Stop Control............................................. 8
2.4 The Roundabout................................................... 9
2.5 Comparison of Alternative Control Modes.............................. 11
2.6 Justification Categories............................................. 16
3. Accidents at Roundabouts............................................. 18
3.1 U.S.A. Research...................................................... 18
3.2 British Research..................................................... 18
3.3 Accidents Fall as Roundabouts Spread to Other Countries.............. 21
3.4 Safety of Roundabouts for Pedestrians and Bicyclists................. 23
3.5 Accident Investigation in France..................................... 24
4. Theories of Capacity and Delay................................... 27
4.1 Introduction......................................................... 27
4.2 Statistical Theories................................................. 28
4.3 Probabilistic Theories Gap Acceptance............................ 29
4.4 Simulation Methods................................................... 31
5. History in the Development of the Capacity Formula................... 33
5.1 Introduction......................................................... 33
5.2 Capacity Estimation of Roundabout Weaving Sections Before 1966... 35
vi


Chapter
Page
5.3 Test-Track Weaving Experiments..................................... 38
5.4 Experiments After the Change in Priority Rule, 1966................ 41
5.5 Further Developments of Capacity Formula After 1966................ 43
5.6 The Search for a New Capacity Formula.............................. 46
5.7 Improved Capacity Formula.......................................... 51
5.8 Development of a Unified Capacity Formula.......................... 58
5.9 Roundabout Capacity Design Current Practice...................... 61
6. Pedestrians, Equestrians, and Cyclists............................. 68
6.1 Introduction....................................................... 68
6.2 Current Design Guidance Pedestrians.............................. 69
6.3 Current Design Guidance Equestrians.............................. 71
6.4 Current Design Guidance Cyclists................................. 71
6.5 Safety Studies of Pedestrians and Cyclists......................... 75
6.6 Pedestrians and Cyclists........................................... 81
6.7 International Developments......................................... 83
7. Traffic Models for Roundabout Analysis............................. 87
7.1 Introduction....................................................... 87
7.2 Rodel.............................................................. 91
7.3 Sidra.............................................................. 93
7.4 Arcady............................................................. 94
7.5 Other Traffic Models............................................... 95
7.6 Capacity Estimation Tools.......................................... 95
8. British Capacity Analysis Procedure Using Rodel................... 104
8.1 Introduction...................................................... 104
8.2 Capacity Six Regression Equations................................. 105
VI1


Chapter
Page
9. Interpreting Rodels Printouts.................................. 107
9.1 Introduction.................................................... 107
10. Vail South Roundabout Configuration............................. 115
10.1 Background...................................................... 115
11. Data Collection and Summary.........................................130
11.1 Location........................................................... 130
11.2 Data Summary....................................................... 131
12. Data Analysis...................................................... 147
12.1 Introduction....................................................... 147
12.2 Linearity.......................................................... 148
13. American Proposed Procedure........................................ 163
13.1 Introduction....................................................... 163
14. Theory Mean Capacity of Each Individual Leg...................... 171
14.1 Introduction....................................................... 171
14.2 Hypothesis Test Mean Capacity of Each Individual Leg............. 171
14.3 Solution........................................................... 171
15. Conclusions........................................................ 175
viii
References
177


FIGURES
Figure Page
1- 1 Basic Roundabout.................................................... 2
2- 1 Volume vs Delay Single Lane Approaches........................... 13
2- 2 Volume vs Delay Two-Lane Roundabouts............................. 13
3- 1 Estimated Number of Accidents at Intersections and Roundabouts for
Specific Average Daily Traffic.................................... 26
5-1 Dimensions and Flows................................................47
5-2 Sample Comparison Between Revised-Wardrop and Laboratory
Report 773 Formula............................................... 49
5-3 Observed vs Estimated Capacities................................... 52
5-4 Geometric Parameters............................................... 56
5-5 Geometric Parameters of Entry...................................... 57
5- 6 Entry / Circulating Flow Relationship...............................60
6- 1 Pedestrian Crossing Locations at a Roundabout...................... 70
6- 2 Exclusive Bicycle Lane at a Roundabout............................. 74
7- 1 Roundabout Capacity Single Lane vs Multi-Lane Circulating Flow...96
IX


Figure
Page
7-2 Average Queueing Delay to Vehicles Entering Single Single Lane
Circulating Flow Roundabouts........................................ 97
7-3 Average Queueing Delay to Vehicles Entering Multi-Lane
Circulating Flow Roundabouts........................................ 98
7-4 Roundabout Capacity Analysis Worksheet...............................99
7-5 Turning Widths Required For Normal Roundabout...................... 101
7-6 Typical Signing and Striping....................................... 102
7-7 Capacity / Geometry Relationships.................................. 103
9- 1 RODEL Printouts.................................................... Ill
10- 1 Construction Plan Geometry Layout of Vail South Roundabout......... 118
10-2 RODEL Output Original Design Analysis 85% Confidence Level
Flow Factor LOO Existing Traffic Counts August 1994............. 119
10-3 RODEL Output Original Design Analysis 85% Confidence Level
Flow Factor 1.50 Existing Traffic Counts August 1994............ 120
10- 4 RODEL Output Original Design Analysis 85% Confidence Level
Flow Factor 1.56 Existing Traffic Counts August 1994............ 121
11- 1 Measured Entry Flows vs Circulating Flows.......................... 136
11- 2 Graph of Circulating Flow vs Entry Capacity Based on Geometry and
RODEL Equations..................................................... 142
12- 1 Entry Capacity Qe, and Circulating Flow Qc at a Roundabout Entry.... 150


Figure Page
12-2 Mean Values of the Residuals In Entry Capacity Qe Left by the
Linear Representation In Successive 300 pcu/hr Bands of the
Circulating Flow Qe.......................................................150
12- 3 Graph of Circulating Flow vs Entry Capacity Comparison Between
Measured and RODEL................................................ 157
13- 1 RODEL Results Based on Actual Field Counts Capacity = 5004
Vehicles Per Hour 50% Confidence Level...........................167
13-2 RODEL Results At Capacity Average Delay = 0.50 Minutes
(Definition of Capacity) Capacity = 6026 Vehicles / Hour 50%
Confidence Level....................................................168
13-3 RODEL Results At Capacity Average Delay = 0.50 Minutes
(Definition of Capacity) Capacity = 5598 Vehicles / Hour 85%
Confidence Level.......................................................169
13- 4 The Average Queue Length L As A Function Of The Traffic Intensity
p According To The Co-Ordinate Transformation Method...................170
14- 1 Graph of Critical Region For Test Statistic Capacity of Each Leg...... 173
XI


TABLES
Table Page
2- 1 Roundabout Selection Categories and Justification Conditions....... 17
3- 1 Numbers of Roundabouts in the Sample by Intersection Category...... 19
3-2 Causes of Roundabout Accidents in France........................... 25
5- 1 Measured and Practical Ranges of Entry Capacity Parameters......... 66
6- 1 Bicycle Accident Types at a Sample of 84 4-Arm Roundabouts......... 79
6-2 95 Percentile Queue Lengths in Vehicle Numbers..................... 83
6-3 Other Traffic Models............................................... 95
11-1 Actual Field Counts Flowing Through Roundabout at Capacity......... 132
11- 2 RODEL 6 Regression Equations Solved for Each leg, Based on
Geometry...........................................................141
12- 1 Data Analysis for Each Leg.........................................152
12-2 Descriptive Statistics Analysis of Measured Data for Each Leg......153
12-3 Corrected Y-Intercept Based on Field Measurements................. 156
12- 4 Analysis of Measured vs Expected Values, t-test: Paired Two Sample
For Means Pearson Correlation....................................162
13- 1 Procedure For Correcting Y-Intercept Based on Field Measurements.... 166
14- 1 Hypothesis Test Data Analysis......................................174
xii


1. Introduction
1.1 Background and Problem Identification
The modem roundabout, which dates from 1963 in England, finally arrived in the
United States in 1990 in a major Las Vegas residential subdivision. When the first
snow country roundabouts in the nation were built in 1995 (the Montpelier
roundabout and two at the 1-70 exit in Vail, Colorado), roundabouts in the United
States numbered 12. Today, about 3 years later, the number has jumped to 50. In
Vermont, four new roundabouts are entering or are in final design with construction
likely in 1997 and 1998. In the November 1996 election, Avon, Colorado, the exit
after Vail, approved a $3.5 million, 20-year bond issue for five roundabouts from the
1-70 interchange to the Beaver Creek Mountain ski resort. The roundabout
community anticipates that roundabouts will be built in the United States annually by
the hundreds in a year or so and by the thousands annually early in the next century,
duplicating the trends first in Britain and Australia during the 1970s and 1980s and
now being repeated throughout western Europe. For example, the Paris newspaper
Le Monde (October 3, 1996) reported France with over 12,000 roundabouts. Most
have been built since the mid 1970s.
A roundabout has three major characteristics compared to its predecessors, traffic
circles, and rotaries. First, the roundabout gives vehicles in the circular travel way
the right-of-way. This change on a national basis in England in 1963 marked the
roundabout era beginning. Second, roundabouts are small, generally from 70 to 160
1


Basic roundabout
Figure 1-1
2


feet in diameter compared to 300 to 400 feet and more for traffic circles and rotaries.
Third, roundabouts have an entry splitter island that slows down or constrains
speed just before entry, duplicating in a way the curvature the driver will experience
within the roundabout itself.
In technical and non-technical performance, the roundabout as an intersection control
device far surpasses traditional stop sign and yield techniques, and the traffic signal.
Roundabouts feature approximately half the collisions and a third of the injuries of
signalized or unsignalized intersections. One Netherlands study of 181 new modem
roundabout installations before and after performance shows roundabouts cut car
occupant injuries by 95%, pedestrian injuries 89%, and bicycle injuries 30%. When
injuries do occur at roundabouts, they tend to be less severe than those at traffic
lights and signed intersections. The roundabout accident performance in the study
was uniformly superior in urban, suburban, and rural locations. The most
conservative estimate from reviewing data from several nations concludes
roundabouts cut collisions by 50 percent.
Roundabouts self-police vehicle speeds and traffic calm about 100 yards in each
direction, unlike signal systems they require no electricity, cost less, use less land,
enable U-tums, save energy, reduce pollution, and introduce beauty to intersections.
In terms of peak hour volumes, delay per car at the Montpelier Vermont roundabout
is 2.7 seconds compared to 6.3 seconds for the old signed intersection. At
moderately high volume four-way intersections, roundabouts cut average delay of
signalized intersections by two thirds.
3


The theory explored in this paper is that the measured mean capacity at the Vail
south roundabout for each entry leg into the roundabout as well as the combined
measured mean capacity will be less than the capacity calculated by the British
capacity program RODEL, presumably because of the unfamiliarity of American
drivers using roundabouts. This hypothesis is found to be true based on the
statistical tests performed in this thesis.
The focus of this paper is to demonstrate a new capacity procedure which can be
used to calculate the capacity of an American roundabout negotiated by American
drivers at Vail, Colorado.
4


1.2 Problem Approach
This effort involved collecting and reducing 1-minute traffic data samples at each
approach to the south Vail roundabout. Traffic count data in the south Vail
roundabout was obtained on July 4, 1997. Approach number 1 was the Vail Road
approach from the north into the south roundabout. On approach number 3 (south
frontage road approach from west), the outside lane was coned off so the approach
was 8.67 meters as originally analyzed. This outside lane only lasts for a short
distance from a driveway. On approach number 5 (south frontage road from east) the
bypass lane was coned off so the traffic had to enter the roundabout. Traffic on any
approach which did not have at least 5 vehicles queued was stopped until the queues
on that approach was a minimum of 5 vehicles. Then the traffic at the east frontage
road entry, which had the longest queue was allowed to enter the roundabout
followed by the other sequential approaches. One minute counts of the total inflow
from the entry and the corresponding circulating flow across the entry were obtained
at each entry to the roundabout. This was repeated 15 times between the P.M. hours
of 2:30 and 7:00. One person was located at each approach to count the traffic. Only
15 one minute counts were obtained during this time period because of the time for
setup and concern regarding the stopping of traffic. Counts were taken with hand
held counters at each entry to the roundabout.
The collected data was compared to the capacity as calculated by the British program
RODEL to determine the differences between measured and RODEL calculated for
each entry leg into the roundabout.
5


To restate the hypothesis, the measured mean capacity at the Vail south roundabout
for each entry leg as well as the combined roundabout measured mean capacity will
be less than the capacity calculated by the British capacity program RODEL,
presumably because of the unfamiliarity of American drivers using roundabouts.
Hence, with opposing circular flow located on the X axis, entry capacity on the Y
axis, and using a linear relationship, the American roundabout capacity procedure for
the Vail, Colorado roundabout requires the Y intercept to be lowered downward
while the slope of the linear entry/circulating flow relationship remains the same.
This results in an approximately 17 % reduction in the actual capacity for each leg
into the roundabout.
6


2. Intersection Control Alternatives
There are three alternatives to roundabouts for intersection control. Each has
significant operational limitations in comparison with a roundabout. Each alternative
will be discussed separately:
2.1 Traffic Signals Roundabouts can efficiently handle particular intersections
with decreased delay and greater efficiency than traffic signals. This is particularly
true where traffic volumes entering the roundabout are roughly similar and where
there are a high number of left turning vehicles.
Traffic signals cause unnecessary delay for many reasons:
The need to provide a minimum green time to each movement in every cycle
creates time intervals in which no vehicles are entering the intersection.
The need to provide for the most critical of two or more movements that proceed
simultaneously results in an ineffective use of green time by non-critical
movements.
The "lost time" associated with startup and termination of a green phase detracts
further from the amount of time that is available for moving traffic.
Left turns that take place from shared lanes impede the other movements in
7


the shared lanes unnecessarily. This results in a very inefficient utilization of
the available roadway space.
Heavy left turns, even from exclusive lanes, require dedicated phases that rob
time from the major movements and increase the total time lost due to startup and
termination of traffic movements.
Signals are mechanical devices that not only require maintenance but also
periodically malfunction. They are also dependent upon electrical power, and do
not, therefore, provide any control during power failures.
Many signal violations occur at higher speeds so that the severity of accidents is
often high.
Permitted left turns and right turns on red introduce additional conflicts.
2.2 Two-Way Stop Control (TWSC) can accommodate low traffic volumes with
much less delay than traffic signals, but this control mode favors the (major) street
(unstopped) movements at the expense of the minor street (stopped) movement.
When the major street traffic volumes are heavy (typically 1400 vph or more) there is
little or no opportunity for cross street access. This places a definite limit on the
application of TWSC. Even when TWSC capacity is not exceeded, there is often
public pressure to install signals at TWSC intersection.
2.3 All-Way Stop Control (AWSC) treats the cross street movements more
favorably, without the wasted time associated with traffic signals. However, the rate
8


at which vehicles may enter an intersection (i.e. headway) under AWSC is relatively
low and, therefore, the total intersection capacity is somewhat limited.
2.4 The roundabout, on the other hand, overcomes all of these disadvantages. There
is no sequential assignment of right-of-way and therefore no wasted time. Left turns
are not subordinated to through traffic. Vehicles enter under yield control instead of
stop control and therefore have lower headways and higher capacities. There are no
electrical components to malfunction.
Roundabouts, on the other hand, have their own limitations:
Steady-state entry headways are shorter at traffic signals because of the positive
assignment of right-of-way. By using long cycle times to minimize the effects of
start-up lost time, it is possible under most conditions to achieve higher approach
capacities.
For very low volume applications, TWSC and AWSC are easier and less
expensive to implement.
Since roundabout operation is not periodic, it is not possible to coordinate the
operation of roundabouts on an arterial route to provide smooth progression for
arterial flows.
Roundabouts offer the least positive form of control. Each vehicle entering the
intersection must yield to all traffic that has already entered.
9


Roundabouts impose a new form of traffic control that is not familiar to most
American motorists.
Therefore, roundabouts are not the solution to all traffic problems at all locations.
Careful study is required to identify the most appropriate control mode at any given
location. The studies required to justify the installation of traffic signal control and
all-way stop control are based on the warrants and requirements set forth in the
Manual of Uniform Traffic Control Devices (MUTCD). No such warrants and
requirements exist for roundabouts.
Three general questions must be answered to justify a roundabout as the most
appropriate form of control at any intersection:
Will a roundabout be expected to perform better than other alternative control
modes? In other words, will it reduce delay, improve safety or solve some other
operational problem?
Are there factors present to suggest that a roundabout would be a more
appropriate control, even if delays with a roundabout are slightly higher?
If any contradicting factors exist, can they be resolved satisfactorily?
If these questions may be answered favorably, then a roundabout may be considered
as a logical candidate control mode.
10


2.5 Comparison of Alternative Control Modes
Using hypothetical data, consider a very simple hypothetical example involving a
roundabout with four right-angle approaches. Each approach has one lane and there
is one circulating lane. The central island diameter is 16 meters. The volume
distribution is such that the east-west approaches carry 30 percent of the total
entering traffic, and the north-south approaches each carry 20 percent. This gives a
60-40 split between the major and minor streets. The northbound and southbound
volumes are equal, as are the eastbound and westbound volumes. All approaches
have 10 percent right turns and 20 percent left turns. Trucks account for 2 percent of
the traffic on all movements.
This example reflects a typical volume distribution, and its symmetry provides an
excellent base for examining the effect of the total volume on the performance of the
intersection as a whole. It also lends itself to comparison with other control modes.
One parameter of particular importance is the practical capacity of the roundabout.
The default value is 85 % of the possible capacity (2500 vph single lane entry). The
SIDRA (Australian Capacity Procedure) documentation points out that roundabout
operation at near capacity levels is less predictable than signal operation. This is
because signal control is more positive, and therefore less dependent on driver
behavior. Therefore, more caution is urged in dealing with roundabouts that operate
above the practical capacity, especially when implementation decisions are involved.
The default value of 85 percent for practical capacity will be used in this analysis.
Another feature of roundabout delay modeling is the concept of geometric delay, i.e.,
the delay experienced by drivers within the roundabout due to a negotiation speed
11


that is slower than the approach speed. Geometric delay must be added to queuing
delay to arrive at the total estimated delay for each approach. SIDRA offers the
option to include or exclude the geometric delay from the computations. Technically,
a delay estimate that includes geometric delay provides a more realistic assessment
of roundabout performance. However, the HCM methodology for signalized and
unsignalized intersection analysis deals only in the queue delay. Therefore,
roundabout delay estimates that exclude geometric delay are more appropriate for
comparison with these other control alternatives.
Figure 2-1 shows the average delay per vehicle as a function of the total entering
volume for all of the control alternatives. The nature of the relationship is similar
among all control modes; i.e., low delays are experienced at low volumes and a more
or less exponential increase in delay occurs with increasing volume. The curve
becomes very steep as the volumes approach capacity. The volume vs. delay
relationships are shown for both one lane and two lane roundabouts. These two
configurations will be discussed separately.
The single lane comparison shown in Figure 2.1 includes TWSC, AWSC and signal
control alternatives. In all cases, single shared lane approaches are examined. For
signal control, the addition of exclusive left turn bays was treated as a separate case.
This would require a widening of the intersection. Since the construction of a
roundabout would also require widening, this configuration provides the most
reasonable performance comparison between traffic signal and roundabout control.
Exclusive left turn bays introduce the option for protected left turn phasing. Since
protected left turn phases introduce additional lost time which reduces the efficiency
of the signal operation, they may be expected to produce higher overall delays.
12


Figure 2-1
Example
Data
30% major street
40% minor street
20% left turns
10% right turns
1000 2000 3000 4000
Total Entering Volume (vph)
Single lane roundabouts.
Figure 2-2
70_
source (5)
50
a40
o
Volume vs. Delay
La h e A p proaches
^P^ssibie roundabout
(4000 vph)
t; 1 Practica I rounds bout
capacity (3700 vph)
ixample Data
-0% major street
0% minor street
:0% left turns
0% right turns
4jgnal
t 'Jj&U
,
15 *
Sv- 'j. ^ <£?.
5 -- UW.. >*f;
r r-.
.if*
2000 4000 6000
Total Entering Volume (vph)
Two-lane roundabouts.
13


Therefore, they have been used in this exercise only when they are necessary to
provide adequate capacity for the left turns. This produces a discontinuous
relationship between total volume and delay for signals with exclusive left turn bays
in Figure 2-1. Note that the two- phase operation creates the lowest delay per vehicle
up to the point where one movement (in this case the heaviest left turn) exceeds its
capacity. The three phase operation, which provides protection for the major street
left turns only, is able to accommodate a higher total entering volume than the two
phase operation, but with an increased delay per vehicle. The four phase operation,
which provides protection for all left turns, is able to accommodate the highest
entering volume of all the single lane alternatives, but the delay near capacity
becomes excessive.
Protected left turn phases may be implemented with or without permitted left turn
movements on the phases that accommodate the through movements. The addition of
the permitted phase generally reduces delay to left turns. In this exercise, left turns
were permitted on the through phases in addition to the protected turning phases. The
signal timing plans were determined by the HCM Chapter 9 planning method which
does not rely on the capacity of the permitted phase (except for two sneakers per
cycle) in determining the time required for the protected phase. This provides a more
conservative approach.
A number of observations may be made about the single lane analysis on Figure 2-1.
First, the roundabout exhibits clearly superior performance (i.e., lower delay per
vehicle) in comparison to all other modes up to a total entering volume of
approximately 2000vph. Roundabout delays remain below 10 seconds per vehicle up
to this point. The TWSC choice is clearly the least attractive (1300 vph capacity) in
this example, but this should come as no surprise, since TWSC is not well suited to
14


situations with heavy cross street volumes. For stop-sign control, higher capacities
(up to 1800 vph) can be achieved with AWSC than TWSC. Note that the roundabout
delays are always lower than AWSC delays, indicating that AWSC performance is
never superior to a roundabout at any volume level.
The signal without left turn bays offers performance similar to AWSC. The signal
delays are slightly higher at low volumes and slightly lower at high volumes, with
the crossover point at about 1100 vph. Roundabout delays are always lower in
comparison to signals without left turn bays.
The signal with exclusive left turn bays offers the most logical alternative to the
roundabout in terms of space requirements. At volumes below 2000 vph the
roundabout exhibits substantially lower delays. Above 2000 vph, the roundabout
delays exceed the signal delays and increase rapidly up to the capacity of about 2400
vph. The two phase signal also reaches its capacity (i.e., one left turn becomes
saturated) in the same 2400 vph range. Above this point, the signal offers the only
alternative that will operate within its capacity. This, of course, requires left turn
protection which increases the unit delay. Three phase operation is shown to function
within capacity up to about 3000 vph and four phase operation finally breaks down at
about 3500 vph with delays in excess of 70 seconds per vehicle.
The comparison shown in Figure 2-2 for the two lane case is simpler because there
are only two alternatives to examine. In this case the signal configuration most
comparable with the space required by a two lane roundabout is one in which each
approach has two through lanes and an exclusive left turn bay. Because of the higher
traffic volumes to be accommodated, all left turns will be assumed to have protected
plus permitted phasing.
15


The comparison of delays for the two lane case closely parallels the single lane case.
The roundabout offers substantially reduced delays up to its practical capacity, in this
case about 3700 vph. Between the practical capacity and the possible capacity (4000
vph) the unit delay nearly doubles. The single delay even at the lowest volumes is
greater than the roundabout delay at the practical capacity.
The signal delay is approximately the same as the roundabout delay (about 20
seconds per vehicle) at the possible capacity of the roundabout (i.e., 4000 vph). The
signal continues to function within its capacity up to 5800 vph, although the total
delays approach 70 seconds per vehicle. The equivalent stopped delay corresponding
to 70 seconds per vehicle total delay is approximately 54 seconds per vehicle. This
corresponds to the upper range of level of service E, which is consistent with the
expectation for a signal operating at capacity.
2.6 Justification Categories
Seven reasons to select a roundabout as the most appropriate form of traffic control.
To provide an organized approach to the justification process, a series of categories
has been developed, each of which represents a good reason to install a roundabout.
These categories are summarized in Table 2-1 in terms of their anticipated
relationships to warrants contained in the MUTCD and Highway Capacity Manual
(HCM) levels of service.
16


TABLE 2-1
ROUNDABOUT SELECTION CATEGORIES AND JUSTIFICATION CONDITIONS
CATEGORY AND DESCRIPTION AWSC WARRANT MET AWSC LOS SIGNAL WARRANT MET SIGNAL LOS NUMBER OF LANES CONDITIONS FOR JUSTIFICATION
COMMUNITY ENHANCEMENT N/A N/A N/A N/A 1 Typically applied in commercial and civic districts. Aesthetics are Important
TRAFFIC CALMING NO A NO A 1 Primarily a residential application. Demonstrated need for traffic calming.
SAFETY IMPROVEMENT N/A N/A N/A N/A N/A Existence of safety problem which would be aleviated by use of a roundabout intersection treatment
ALL-WAY STOP ALTERNATIVE YES B-D NO A-B 1 Delays should compare favorably with AWSC.
LOW VOLUME SIGNAL ALTERNATIVE YES D-F YES A-C 1 Delays should compare favorably with signal.
MEDIUM VOLUME SIGNAL ALTERNATIVE YES F YES B-D 2 Delays should compare favorable with signal. Other justifying factors required.
SPECIAL CONDITIONS such as unusual geometries, high volumes, right-of- way limitations, etc.) Y/N N/A Y/N N/A 1-3+ Site specific justification required.
source (5)
17


3. Accidents at Roundabouts
3.1 U.S.A. Research
Aimee Flannery, a research assistant at Pennsylvania State University has conducted
a recent accident study by collecting traffic and crash data for existing roundabouts
in the U.S.A. She then performed a statistical analysis to determine the
effectiveness of roundabouts as a treatment for intersecting roadways. (17)
General information regarding thirteen roundabouts located in Maryland, Florida,
Nevada and California was collected. In addition, six retro-fitted roundabout sites
with accident data ranging from 1 to 3 years before and after were analyzed. In all
but one case, the reduction in accidents for roundabout sites was in the range of 60%
to 70%. A chi-squared test and a normal approximation test were performed using
the accident data from these six roundabout sites. Both of these tests indicated a
significant difference in the frequency and mean of accidents at 95% and 99%
confidence levels, respectively, between pre-roundabout and post-roundabout
periods. (17)
3.2 British Research
A very important study dealing with personal injury accidents at 4-arm roundabouts
was reported by Britains Maycock and Hall (1984) in Laboratory Report (LR) 1120.
Data for a sample of 84 roundabouts in six categories were assembled by
Southampton University, as shown in the following Table 3-1.
18


Table 3-1
Numbers Of Roundabouts In The Sample By Intersection Category
Junction Category Speed Limit Group
30-40 mph 50-70 mph
Small island roundabout >4m 25 11
Conventional roundabout 11 11
Conventional dual-roadway roundabout 14 12
TOTAL 84
During the course of the accident sampling period (six years 1974-79), some 67
roundabouts remained unchanged in design. Data from Police accident reports of
accidents within 20 m of each roundabout was used. Traffic flow data was mainly
16 hour classified turning counts at each site. Nearly all those in the 30-40 mph
category included pedestrian flows. Detailed layout data and the characteristics of
each approach were recorded for all roundabouts in the sample, and included
inscribed circle diameter, central island diameter, road class, roadway type, gradient,
approach speed limit. Arm-specific data included, entry path curvature, entry width
and flare dimensions. (12-p.45)
The data and results of analysis are presented in Britains LR (Lab Report) 1120 in 24
tables. These include accident frequencies, and severities and rates by roundabout
type. The accidents were further analyzed by type and by road user involvement
(bicyclist, motorcyclist, pedestrian, etc.) The accident frequencies by type were
related to traffic flow and roundabout geometry, using regression methods.
Equations were also developed to enable roundabout accidents to be predicted for use
in design and appraisal. Only the chief influences on design are shown below.
19


Some of the main findings were:
1. The distribution in time of the accidents in the sample generally reflected the
Britain national pattern.
2. The average accident frequency (of the sample) was 3.31 personal injury
accidents per year, 16% of which were fatal or serious.
3. The average accident rate per 100 million vehicles passing through the
intersection was 27.5.
4. Small roundabouts in 30-40 mph zones, had both higher frequencies and rates
than other roundabouts.
5. The analyses of accidents by type, showed that the pattern at small roundabouts
was different from that at conventional roundabouts. More than 2/3rds (71%) of
accidents at the former were entering/circulating but those at the latter were
divided evenly between entering/circulating, approaching and single vehicle
accidents.
6. All roundabouts had high involvement rates for two wheeled vehicles. The rates
per 100 million road user class were about 10-15 times that of car occupants. At
small roundabouts, bicyclists were particularly (14 times) more vulnerable than
cars.
20


3.3 Accidents Fall As Roundabouts Spread To Other Countries
Around the world, accident rates are falling as roundabouts spread. The Netherlands
achieved a 95-percent reduction in injuries to vehicle occupants as many
conventional intersections were replaced by modem roundabouts. (12-p.48)
The fatality rate in the Unites Kingdom is about half the rate in France 5000 in the
United Kingdom compared to 10,000 in France. The difference is partially attributed
to the use of roundabouts since the French and British population and their number
of motor vehicles are about the same. (12-p.48)
In France, where roundabouts were installed mostly in urban areas and their suburbs
including residential areas, the safety of roundabouts was generally superior to
signalized intersections, except where the roundabouts were large with wide entries
or where there was extensive bicycle traffic. The accident rate on rural roads was
clearly better for roundabouts than for major/minor intersections regulated by stop or
yield signs. The average rate of reported injury accidents per 100 million vehicles
entering major/minor intersections was 12. This was three times higher than the rate
for roundabouts where there were only four accidents per 100 million vehicles. (12-
p.48)
Numerous one or two lane roundabouts have been built recently in Germany, but
several large old style traffic circles remain. Researchers investigated 14 circular
intersections and 14 non-circular intersections. The number of accidents per million
vehicles were:
21


Old Traffic Circles 6.58
Signalized Intersections 3.35
Smaller Roundabouts 1.24
The most extensive roundabout accident analysis in Norway was conducted in 1990.
Accident records from 1985 to 1988 at 59 roundabouts and 124 signalized
intersections were examined. The comparative accident rates, in numbers of reported
accidents per hundred million vehicles, are given below:
Number of Legs Roundabouts Signalized Intersections
3 3 5
4 5 10
Besides safety benefits, other advantages to roundabouts were demonstrated. Speed
reduction, moderation of traffic flows in favor of through traffic, use of the central
island to mark the transition from one class of road to another, and improved
capacity are products of roundabouts. (12-p.50)
Studies of British mini-roundabouts, which often have two-or three-lane entries even
though the central islands are less than 4 m in diameter, indicate that larger
roundabouts are generally safer. However, recent studies of mostly one-lane mini-
roundabouts in continental Europe found a lower accident rate at mini-roundabouts
than at larger roundabouts. (12-p.50)
Studies in Switzerland and France identified the following benefits of mini-
22


roundabouts:
Flow improvements.
Reduction of conflicts/accidents.
Reduction of speeds upstream, through, and downstream of mini-roundabouts.
Adherence to the yield-at-entry requirement.
Reduction of noise (as a result of the reduction of speed).
Heightened awareness of drivers as they were forced to reduce speed.
3.4 Safety Of Roundabouts For Pedestrians And Bicyclists
While modem roundabouts have long been considered safe for pedestrians, the
record for bicycles and motorcycles has been mixed.
According to one study in the United Kingdom, 15 percent of all intersection
accidents in 1984 involved at least one bicyclist, but 22 percent of all roundabout
accidents involved at least one bicyclist. (12-p.51)
In contrast, British mini-roundabouts do not appear to be particularly dangerous for
bicyclists. A survey in 1989 of mini-roundabouts in England, Scotland, and Wales,
found that the crash involvement rates of motorcycles and bicycles in 50-km/h speed
zones was about the same for four-leg signalized intersections. However, the rate for
cars at the mini-roundabouts was much lower than at the intersections: (12-p.51)
23


Crash Involvement Rates (per 10 million of vehicle type)
Bicycle Motorcycle Car
Signalized Intersection 175 240 48
Mini-roundabout 189 237 27
Contrary to the British experience, a recent study in the Netherlands of 181 mini-
roundabouts that were converted from three- and four-leg intersections found injuries
to bicyclists decreased on average from 1.30 casualties per year to 0.37 casualties per
year a 72 percent reduction. (12-p.53)
In Europe, bicyclists at roundabouts were handled in one of three ways: bicyclists
mix with motor vehicles, bicyclists have a separate lane, or bicyclists have a separate
bike road. The bike road provided the best protection for cyclists, and perhaps
surprisingly, the bike lane was the least safe option because this design requires the
motorists and bicyclists to cross paths. (12-p.53)
3.5 Accident Investigation in France
In 1990, 202 accidents were investigated at 179 urban roundabouts in France. The
following table shows the relative frequency of the different causes of these
accidents.
24


Table 3-2
Causes Of Roundabout Accidents In France
Cause of Accident Percent of
Accidents
Entering traffic failing to yield to Circulating traffic 36.6%
Loss of control inside the circulatory roadway 16.3%
Loss of control at entries 10.0%
Rear-end accidents at entries 7.4%
Sideswipe, mostly at two-lane exits with bicyclists (two of three) 5.9%
Running over pedestrians at marked crosswalks, mostly at two 5.9%
lane entries
Pedestrians on the circulatory roadway 3.5%
Loss of control at exits 2.5%
Head-on collision at exits 2.5%
Weaving inside the circulatory roadway 2.5%
The major design recommendations derived from the above study are:
Ensure motorists recognize the approach to the roundabout
Avoid entries and exits with two or more lanes except for capacity requirements
Separate the exit and entry by a splitter (ghost) island
Avoid perpendicular entries or very large radii
Avoid very tight exit radii
Avoid oval-shaped roundabouts
25


A study of roundabout lighting in France found that nighttime accidents are
relatively rare and most accidents involve property damage only. The study
recommends that lighting design should be based on a perception process: remote
perception at about 250 m, approaching perception at about 100 m, and entry
perception at the entry. Figure 3-1 below shows the estimated number of accidents at
X-intersections and roundabouts for specific average daily traffic. (12-p.55)
Figure 3-1
Estimated number of accidents at X-intersections and
roundabouts for specific average daily traffic.
source (15)
26


4. Theories of Capacity and Delay
4.1 Introduction
Apart from the application of personal experience, theories of capacity and delay fall
into four groups:
Deterministic
Statistics
Probabilities
Simulation
Whatever theories underlie the basis of roundabout design, the results will be judged
on whether they offer a practical design tool to the highway or traffic engineer, and
whether the resultant roundabout layouts operate safely as predicted, within a
reasonable range.
Deterministic ideas are not of great importance. These may simply be the opinions of
practitioners laid down as rules, for example roundabouts, should be used only on
routes of certain traffic flow and be of a certain minimum size, roadway width, etc.
These rules may involve invalid assumptions of traffic behavior, but can be useful in
the absence of a theory based on systematic collection of data, and validated by
measured observation. However, in the design process, many details which cannot
be satisfactorily modeled are often determined by what is reasonable, or
appearance.
27


In Great Britain early rules of roundabout design for which there was no proof
were:
1) A large roundabout will carry more traffic than a small one of similar
shape;
2) The capacity depends on but is not proportional to, the minimum width of
the roadway around the central island;
3) The greater the weaving length or the smaller the angle of approach of
weaving traffic streams, the greater is the capacity.
As there was no entry priority and roundabouts were previously designed for the
weaving movements of vehicles on the circulatory roadway, these assumptions were
not unreasonable.
4.2 Statistical Theories
The development of statistical theories depends on a pre-existing stock of
roundabouts from which satisfactory sample data can be drawn (It is notable that in
countries where large samples are not available, more reliance is placed on other
theories). The statistical approach consists in measuring some variables on a sample
of intersections so as to relate one variable to others, and then to use this relationship
as a predictor. The variable to be explained is usually capacity, but waiting times,
delays or queue lengths and accident frequency can also be estimated in the same
way. This approach to roundabout capacity estimation is used notably in Great
Britain, but is also currently used or being investigated in; France, Germany, Israel.
Norway, and Switzerland.
28


4.3 Probabilistic Theories Gap Acceptance
Both gap-acceptance and simulation techniques were mainly applied to non-
roundabout intersections but more recently, have been applied to roundabouts.
When the gap acceptance theory is applied at roundabouts, the major flow is the
circulating flow, in which randomly spaced gaps occur. If these gaps exceed a
certain minimum value (usually fixed, although more comprehensive theories allow
for a frequency distribution of minimum acceptable gaps) they are entered by one or
more vehicles from the waiting minor flow on the approaches. Theories of gap
acceptance are intrinsically passive in the sense that circulating traffic is assumed not
to react in the presence of entering traffic. At roundabouts, (unlike other
intersections, except possibly during periods of congestion) the entry process is
somewhat more interactive than gap-acceptance assumptions allow, with gap forcing
and priority reversal aspects, and it is difficult to say whether the gaps are naturally
accuring or are modified for, or by, the entering vehicle. Therefore, although gap-
acceptance is an important element, it is unlikely to be a complete and sufficient
determinate of capacity.
The theoretical gap acceptance model of capacity for roundabouts have been
developed from those for other intersections. These require two parameters:
a critical gap in the major flow (also s, t, or tg).
This is the useful minimum gap.
29


f follow-up (move-up) time or headway (also tfP). The gap required
behind a minor departing vehicle (and the next major vehicle) for a vehicle
waiting second in a queue. This is usually assumed to be constant and often
estimated as 0.6a.
Critical-gap values vary, depending on the maneuver to be made ie. left-turn, right-
turn, through, and the size of the intersection. They also vary with size of urban-area
or rural conditions, gradient, traffic flow and the psycho-physical state of drivers.
Heavy vehicles need greater critical gaps and headway. Corrections (and pcu
equivalents) are made to represent these and averages can be found for these
corrections which are applicable to local areas. Assumptions are gap-acceptance and
distribution of headways; results are capacity, waiting times and various
probabilities.
The critical gap for various maneuvers (and the average minimum headway,) is also
influenced by; vehicle type dimensions, weight, engine capacity and acceleration
ability. There will be national and local differences, for example, in Czechoslovakia,
where passenger cars were small low powered and with relatively slow acceleration,
both parameters will be large, (typically 5 to 10.5 seconds), and this would result in a
generally lower capacity for a given layout than in say Great Britain. There will
also be variations over time which can affect all capacity measurements. Gap-
acceptance methods of roundabout capacity estimation, delay, (and in some cases
risk analysis) are used in Australia and Sweden. They are used, or have been
30


investigated, in others including; Czechoslovakia, France, Israel, Germany, and
Great Britain.
4.4 Simulation Methods
In an attempt to overcome the multiplicity of theoretical problems inherent in gap-
acceptance approaches simulation methods of capacity evaluation are becoming
more popular to model traffic streams and driver behavior at intersections. A
comprehensive vehicle by vehicle model of the entry/circulating flow relationship
should include all of the various mechanisms of vehicle-vehicle interaction,
separately identified. In 1980 Kimber thought it was not feasible in practice to
construct such a model because of the complexity of (1) separating the mechanisms
observationally, 2) determining their relative importance from site to site and 3)
relating a parametric description of each to geometric details of layout.
Simulation techniques, involving complex computer programs have been developed
in the last decade, which require considerable computing power. These are used in a
number of countries to model behavior at non-signalized intersections but only some
have been adapted to roundabouts. With the general availability of powerful micro
computers, the earlier role of simulation models of entry capacity, delay and accident
risk, is changing from an instrument of scientific research, towards a practical tool
for the traffic engineer. However, there is considerable potential for refinement and
simplification of these models for roundabouts, and they are likely to be applied in
new or exceptional circumstances rather than routine ones. Simulation models have
31


been developed or investigated in Australia, France, Germany, Great Britain, and
Switzerland.
32


5. History In The Development of the Capacity Formula
5.1 Introduction
In Great Britain the roundabout has been a popular form of road intersection for
many years and has also long been recognized as the safest of intersection types.
Roundabouts have a wide range of application both in rural and urban areas, and can
be found on all classes of road from highway intersections to private accesses, often
being used to replace major/minor intersections and sometimes replacing traffic
signal controlled intersections. They range in size from minis with a painted center
spot of 1 meter diameter to those with central island diameters well in excess of 100
meters. There must be several thousands of roundabouts in Great Britain but it is
impossible to give a precise figure. The number on rural trunk and principal roads in
England is in excess of 1000. A survey of mini roundabouts was conducted in 1988-
89, from which it is estimated that there were 1600 of that type on public roads in
Great Britain. Design practices (including efficiency, user cost and safety), have
been subject to much scrutiny for some three decades, and the methods now used
incorporate the results of a continued program of major research studies. These have
been aimed at producing sound practical design methodologies for practicing traffic
engineers, as opposed to academic models that are difficult to apply. Many of the
research reports include design procedures and interpretation advice.
Prior to 1966 in Great Britain there was no defined priority at roundabouts between
entering and traffic already on the circulation roadway. The basis of roundabout
33


operation at that time was that entering traffic merged with circulating traffic along a
weaving section downstream of the entry and capacity was governed by its
limiting flow. Pre-war rural and suburban arterial road designs for roundabouts
were circular. Size was determined solely by experience of the authority and the
circular roadway was generally as wide as the entering road. An early example of
the empirical approach used in Great Britain for the estimation of roundabout
capacity was given by Clayton in 1941. In a further paper in 1945, taking account of
additional data, he observed that insufficient data were available upon which to base
a scientific analysis but some empirical rules could be devised. These had
minimum support from experimental observations and therefore, were only
deterministic assumptions. Claytons formula for roundabout capacity estimation
was superseded by Wardrops, which was based on sufficient data from full scale
tests of traffic capacity on experimental weaving sections in 1955-56. (l-p.62)
Subsequently to the introduction of the give-way rule for entry to roundabouts in
Great Britain in 1966, roundabout entries functioned in some respects like one-way
T-junctions. By removing the problem of instability, the rule enabled smaller and
more efficient roundabouts to be developed. This made it feasible to use
roundabouts much more extensively. Changes were initiated to typical entry
geometry such as, having strongly deflected traffic paths, oblique entry, and often
extra lanes at entry, (l-p.62)
Capacity estimation became a two stage process.
34


1) entry capacity was to be determined as a function of the flow in the
priority stream crossing each entry
2) the inflow from each entry must be calculated. Since this depends on the
priority flow, which in turn comes from the previous entries, the problem
of predicting the average balance of inflows from all the entries is an
interactive one.
Intensive studies were conducted at the Transport and Road Research Laboratory in
the late 1960s to determine by observation of at-capacity operation with queueing in
the approach, the relation between intersection layout and the entry capacity
expressed as a function of the priority stream flow. In all, 122 intersections were
studied on the public road and about 40 on the test track. The public road capacity
data amount to some 1700 minutes and include observations on about 0.75 meter
vehicles. The current Great Britain approach to roundabout design is strongly
empirical, and rests on the primacy of directly measured quantities-capacity, delay,
accident rate-and the importance of ensuring that models and relations stand in clear
correspondence to them, (l-p.63)
5.2 Capacity Estimation of Roundabout Weaving Sections Before 1966
Standard circular roundabouts were recommended in 1937. In 1941 Clayton
suggested empirical values for a weaving factor for roundabout capacity design,
derived from traffic signal theory and saturation density for a weaving section. He
conceded that the difficulty of checking these with actual traffic densities, was that
few if any roundabouts were working to capacity, except perhaps Trafalgar Square.
35


In 1945 Clayton commented on the difficulty of applying standard designs at actual
intersections which varied considerably in size and shape, and that non standard
amendments sometimes suffered operational difficulties. To resolve this problem, he
developed a formula for the capacity prediction of a weaving section, of smaller 4
arm roundabouts using the contemporary empirical formula available for traffic
signals, and data from roundabouts in London. An arbitrary measure maximum
weaving angle was related to circulating traffic density as a weaving factor. The
results were adapted for roundabouts of various sizes:
T = S { L 790 ( L 4/3 ) }
where S = the saturation density of traffic, taken as 1200 veh / hr / lane.
L = the number of entry traffic lanes
a = the maximum weaving angle
or T = Fw L S
where Fw is the weaving factor
This was applicable to a roundabout with any number of entries and shape, the total
capacity of the roundabout being double that of the shortest side. It was taken from
this that, within limits, and if the most suitable roadway width was used, the
capacity of a roundabout was roughly proportional to its size. Clayton suggested that
an upper limit to capacity of a roundabout (however large) was 7,500 veh / hr (plus
bicycles), or little more than the pre-war volume at Hyde Park comer, (l-p.64)
36


Tables produced from the application of Claytons formula were subsequently
incorporated in the advisory manual Design and Layout of roads in Built Up Areas
of 1946, as the basis of the recommended Design procedure for roundabouts. The
capacities of 4-arm roundabouts were given but where there were alternatives, a
larger island was preferred. The capacity to be provided was to be 1.33 the estimated
volume. In addition to the benefits of long weaving lengths, a virtue was made of
asymmetrical designs that fitted into whatever shape of site was available. Although
the ideal shape of a (rural) roundabout prior to this time was considered to be
circular, designs were forced into square or rectangular shapes which appeared to be
very suitable for urban sites. Later Clayton refined this formula to extend its
theoretical validity and tested it with additional data. The weaving factor Fw was
expressed as a function of the proportion of weaving traffic ( p-ratio of smaller
weaving stream to total traffic), the angle of convergence a (degrees) and the width
of the weaving section w (ft) giving: (l-p.64)
F m = 1 k a/90 ( 1 40/3w )
where k = 2/3 ( l+2p ) in the original version based on US data,
but 8/9 ( l+p/2 ) in a revised version taking account of tests carried out at in
1947 at the then Road Research Laboratory.
While there were still insufficient observations to establish a definite relationship,
nevertheless Clayton felt that those available did appear to support his quas-
37


theoretical rule. This was the basis of roundabout design in Great Britain until the
late 1950s. (l-p.64)
5.3 Test-Track Weaving Experiments
In 1947 the Road Research Board Laboratory of the Department of Scientific and
Industrial Research (DSIR) (subsequently to become the Road Research Laboratory,
and later the Transport Research Laboratory), began a study of weaving sections,
using the large surface area available at Norholt Airport. 45 vehicles were used,
running at pre-determined speeds in two or three columns which weaved across one
another on a section 250 ft (76 meters) long by 24 ft (7.3 meters) wide. By the mid
1950s, other research had been carried out leading to disagreement on the maximum
capacity of a weaving section. Opinion varied from 1500 veh/hr to over 5000 veh/hr.
Claytons results conflicted with the information from the US Highway Research
Board, and Shrope where the effects of some important factors had not been
measured. Wynn, Gourlay and Strickland, had obtained useful data on weaving and
merging traffic but these had not been related to roundabout capacity. Friedrich and
Grabe had given some semi-theoretical values for roundabout capacity, but their
assumptions about behavior in the weaving section were very arbitrary, (l-p.64)
In 1955 in the absence of reliable information further large scale experiments were
carried out at Northolt using 130 vehicles circulating continuously through a single
weaving section up to 300 ft long and 50 ft wide. It was thought to be the first such
full scale test-track experiment to investigate traffic behavior. The vehicles included
double decker buses, medium and heavy commercial vehicles, light vans, cars,
38


motor-cycles and taxis. Groups were formed to interweave from different directions
with sufficient numbers circulating to constitute moving queues at entry. Whatever
the value of the mean flow its standard deviation was found to be 120 veh/hr. The
dimensions of the section, traffic mix and weaving properties were varied for each
test of 10-12 minutes over four days, during which the weather also varied.
Observations included filming from a tower wagon. It was found in wet weather that
the maximum flow through the weaving section was reduced by about 10%. In
further track experiments in 1956, varying the number of vehicles taking part, the
maximum flow in the weaving section increased by about 5% up to 3250 veh/hr
which was considered an ultimate capacity. A major difference from real
roundabout operation was that since the test-track section was open ended there was
no danger of blocking back from an adjoining weaving section, and this was to prove
critical, (l-p.65)
Taking the results from the test-track experiments Wardrop used a method of
successive approximation to establish a mathematical relationship between the
capacity, and the traffic and geometric variables.
Comparison with existing roundabouts showed reasonable agreement and the results
were published in 1957. The formula was further modified expressing the maximum
flow in pcu and treating the ratio 2/1 in a more logical manner:
Qm = 108w (1 + e/wl (1 p/31 p.c.u. per hour
(1 + w/1)
39


where Qm = maximum flow through weaving section (dry weather no bicycles)
w = width of weaving section (ft.), range 20 60
e = average of entry widths (ft.), range (e/w) 0.4 -1.0
1 = length of weaving section (ft.), range (w/1) 0.12- < 0.4
p = proportion of weaving traffic to total traffic in weaving section, range 0.4
- 1.0
Its prediction was good compared with the data, but one difficulty was that in
practice the simple design used in the tests could rarely be applied and effective
dimensions were used. A further difference was that in practical roundabouts
interaction from other weaving sections caused blocking and therefore, the
comparisons with smaller roundabouts were not good. Since all roundabouts were in
danger of locking at the observed flows it was concluded that it was not necessarily
safe to use the results of the test-track experiments to determine the capacity of a
complete roundabout. It seemed a reasonable assumption that the maximum flows
would not be exceeded in a complete roundabout, and therefore, a practical capacity
was taken as 80% of the ultimate capacity given by the formula, ie. The term 108w
in the dividend of the above formula became 86w. However, as long as there was no
rule governing priorities at roundabouts, even this capacity could frequently not be
sustained in situations involving heavy traffic, and locking was prevalent, (l-p.66)
Wardrops work on the capacity of weaving sections was incorporated in the
Ministry of Transports Advisory Memoranda Urban Traffic Engineering
Techniques (UTET) 1965, and Roads in Urban Areas (RUA) 1966, for the
40


capacity design of roundabouts. The recommendations included the effects of
interaction between weaving sections and weighting for vehicles operating in
different circumstances and weaving sections could be designed from nomograms
based on the Wardrop formula. There were distinct differences in the effects of
two wheelers and goods vehicles on capacity at roundabouts and traffic signals.
Roundabout design was to be generous and the designer was not to be wedded to
geometrical shapes such as a circle for the central island, although it was recognized
that the dead areas on roundabouts was an indication of poor design. In effect this
continued the trend from 1945, producing great variation in the effectiveness of
designs but some, by chance favorably constrained by their sites, were later to be
easily improved to a modem layout, (l-p.67)
5.4 Experiments After The Change In Priority Rule, 1966
The introduction of the give way to traffic from the right rule at roundabouts made
a significant contribution to the efficiency of roundabouts in Great Britain and it was
evident that smaller roundabouts which previously had been prone to locking, were
working well. With offside priority operation, entry was controlled by the ability of
entering drivers to detect and utilize gaps in the circulatory flow round the island. It
meant that section length was no longer a significant factor in controlling capacity;
entry width was of paramount importance, since in theory the entry capacity of a
section increased with the number of entry lanes provided. This lead to a series of
experiments by TRL in the late 1960s to find ways of making better use of the area
available at junctions in order to increase their capacity. Full scale test-track
experiments, were reported by Blackmore in LR 356 1970. (l-p.67)
41


With any method of intersection control, the highest capacity in a given area was
achieved by layouts providing the greatest width for each movement, particularly at
the point of entry to the intersection. The highest capacity for roundabouts was
obtained by layouts with marked deflection to the left on entry, and a very small
central island. The deflection was found not only to improve circulation and reduce
congestion but also to control the speed of entry to a safe level. A simple maximum
capacity formula was found to apply generally to intersections regardless of shape,
layout and method of control. (Subsequently known as the Full Capacity
Blackmore Formula): (l-p.68)
q = k ( Z w + V"a" )
where: q, is the capacity in pcu/hr.;
k, is the efficiency coefficient;
Iw, is the sum of the roadway widths in meters, used by
traffic in both directions to and from the intersection;
a, is the area in square meters of widening ie. The area within
the intersection outline, including islands, lying outside the
area of the original roadway intersection.
The capacity given by the above formula with k = 100 can be regarded as the
potential capacity obtainable in a given sized of intersection under the almost ideal
42


conditions of the experiment and an optimum curb outline. At most intersections on
public roads the capacity to be expected would be appreciably lower, ie k < 100. In
H.7/71 : 1971 values of k were given for new layouts of roundabouts with average
site conditions, of: 80, for 3 way intersections; 70, for 4 way intersections and 65, for
5 or more way intersections. Capacity in normal peak conditions was to be taken as
80% of these. At mini roundabouts at constricted sites with central islands less than
4m (restricted to 3 way intersections), it was suggested that these factors may
overstate the capacity, and a k value of 70 was to be used, (l-p.68)
5.5 Further Developments of Capacity Formula After 1966
During the experimental period for roundabouts with new layouts, (approximately
1967 72), the method of calculation of capacity of roundabouts officially to be used
at that time (ie Wardrops), was contained in Urban Traffic Engineering Techniques
and in the design manual Roads in Urban Areas) then recently published. However,
many of the smaller roundabouts constructed after the 1966 change in the priority
rule for roundabouts, had geometric proportions outside the limits of that method.
The conventional design specified a maximum width/length ratio for the weaving
section, therefore, increasing the section width to increase capacity often required
an increase in section length. Thus the higher the traffic demand, the longer the
section length had to be. It was increasingly apparent to practitioners that this, and
the use of minimum radius to achieve longer effective weaving lengths within the
available land, was producing roundabouts that did not relate to the desired paths of
vehicles. The observed capacity of such roundabouts also did not meet the design
capacity, in some cases being only 3/4 of it. This was shown by dead areas or those
43


untrafficked surfaces of roadway which collected debris, and were particularly
obvious after a light fall of snow. These revealed that although bicyclists used them,
the flanking (ie. Left turning) traffic was not able to keep to the curblines, and
encroached on the weaving lane, constricting its effective width. Various
modifications of design were suggested by Bapat, incorporating transition curves,
leading to central islands more circular in shape. This reduced the weaving length,
which was supposed to be the key to roundabout capacity, but observations at
modified roundabouts showed that capacity actually increased, (l-p.69)
By 1970 it was clear that the experimental small island roundabouts on public roads
with central island diameters of about 14 m. were observed to have equal or even
higher traffic capacity than larger roundabouts with more conventional radii and
weaving lengths. It was suggested that it would be cost beneficial if these could be
provided initially as at-grade roundabouts on road schemes where eventual grade-
separation was likely. Further work by Ashworth and Field, and Murgatroyd,
reported in 1973, showed that the proportion of weaving traffic used in the Wardrop
formula had no influence on capacity under priority rule and an alternative design
procedure or revised formula was called for. Murgatroyd used linear regression
analysis to show that a new design capacity Qd, could be written: (l-p.69)
Od = 90w (T + e/wl 1100
(1 + w/1)
He also found that other effects such as pedestrian flows, poor signposting and the
absence of helpful road markings, could reduce roundabout capacity by up to 50%.
44


Other evidence from studies of roundabout modifications by local authorities, eg.
Teeside, Attwood 1973, suggested that long weaving lengths were not very effective
but concluded that a weaving formula design had not been made redundant by the
priority rule, (l-p.69)
In the early 1970s, further experimentation with new types of roundabout continued
on public roads. These initially concerned the reduction of central islands and
widening of approaches, but at some larger roundabouts many alternative layouts
were tested from 1972-74, which were described by Blackmore and Marlow in 1975.
The thrust of these experiments was to compare capacities of different layout types
and geometry including: different diameters of central island; circular roadway
width; and widening or flaring of approaches. In addition large roundabouts were
also converted to ring intersections using traffic signals or mini roundabouts. The
experiments had indicated that entry width might be more critical than weaving
length and also suggested the importance of geometrical features of roundabouts
concerning capacity and safety. In 1975 the Department of Transport (DOT)
Technical Memo. H.2/75 was issued, in which the full capacity Blackmore
formula, was to be used for small, mini and double roundabouts; but on the basis that
the proportion of weaving traffic made no significant contribution to accuracy
(although the concept of weaving at roundabouts was questioned), a Modified
Wardrop formula was to be applied to conventional, ie larger roundabouts: (1-
p.69)
Q P = 160 fl + e/wl veh/h
1 + wL
45


where w = width of weaving section (meters),
e = average width of entries to weaving section (meters),
L = length of weaving section (meters).
Weaving lengths were to be shorter and wider. The formula was based on
observations at actual roundabouts within the ranges:
w 9.1m to 18m; e/w 0.63 to 0.95m; w/L 0.16 to 0.38; e,/e2 0.34 to 1.14
It was considered that the formula would hold for variables lying a little outside the
above values, if the design could not be made 85% of Q P. Arbitrary deductions
were to be made to capacity for entry angles less than 30 % and for exit angles more
than 60 %, The conventional roundabout was recommended for larger new
intersections or major improvements, and was seen as appropriate for two or three
level, grade-separated non free-flow intersections, (l-p.70)
5.6 The Search For A New Capacity Formula
The result of the modified Wardrop formula (applied in H2/75), was to
substantially reduce the practical capacity for typical roundabouts, compared with the
previous formula. The recommended shape was no longer to be square with
minimum radius, but circular if possible. However, the approaches were not
widened, and with the limitations of width, the use of the modified formula still
forced larger(conventional) roundabouts into longer weaving lengths. It was not a
46


satisfactory replacement for the capacity of entries for larger conventional
roundabouts, and there was still a distinction from smaller (offside priority)
roundabouts in the approach to their design. At the time it was recognized as only an
interim measure, since Blackmores full capacity formula was too coarse a measure
for the purpose of engineering design and economic assessment. What was required
was an entry by entry assessment allowing for the effects of geometry. In 1976 full
scale track experiments were carried out by TRL to obtain data for a new capacity
formula for conventional roundabouts, (l-p.70)
The search for a completely new capacity formula was reported by Philbrick in 1977.
This centered around the fitting of a linear relationship between traffic entering a
roundabout from a saturated approach and that already in the circulating roadway.
Regression techniques were used to include geometric effects in the relationship.
Figure 5-1
Dimensions and flows (LR. 773)
source (2)
47


The most successful attempt was the simplest, with total entry capacity Qe being
related to the total circulating flow, Qc (in pcu/h). Over the observed flow ranges
this could be regarded as linear. Using regression techniques, the equations
predicted the weaving section capacity with less residual between-sections
variation than the original Wardrop formula and were much more successful at
predicting the within-sections variation of Qe and Qc. The equations were:
Entry Capacity, Qe = F fc Qc pcu/h
Where F = 233e, (1.5 1/ Vr^ ) 255 efu/h, (1 efu = 1 entering
pcu)
fc = 0.0449 (2e, w) + 0.282
Qc = circulating flow in pcu/h
The derived heavy vehicle pcu value was 2.00, and the ranges of the parameters in
the data used were: e, 4.0 to 12.5m; (2el -w) 2.5 to 9.5m;
e, / sr, 0.74 to 3.30; Qc 580 to 3890 pcu/h
This was applied to the design of conventional roundabouts in TE Design Note
No.l issued by the DOT in 1978 as an interim measure, pending a full revision of the
48


Technical Memorandum. However it was 1981 before this holding position could be
replaced.
0 1000 2000 3000 4000
Qc (peu/h)
Figure 5-2
Sample comparison between revised-Wardrop and LR 773", formula
During the same period other possible approaches were sponsored by TRL including
a gap acceptance method by Ashworth ad Laurence and that of McDonald and
Armitage at Univ. of Southampton, England. This also was similar to gap
acceptance method, but based on the concept of saturation flow and lost time, as
at traffic signals (which was also the starting point for Claytons ideas for roundabout
capacity formula in 1941). Theoretical formula were developed, the most useful
being:
49


where q2 = entering flow (veh/s)
q, = circulating flow (veh/s)
qs = saturation flow (veh/s)
L = lost time (s)
P = minimum headway of circulating vehicles (s)
Data for the study included the TRL 1976 test track and public road experiments.
Each site was described by 22 simple geometric factors, time-lapse and event
records. A series of empirical relationships were determined. The two parameters qs
and L were estimated together by the method of least squares. Each of the capacity
parameters was tested against the geometric factors using multiple regression
techniques and the following relationships were thought to be the best, both in terms
of statistical goodness of fit and conceptual validity, (l-p.72)
Saturation flow:
q s = 0.12EO + 0.04(E1-EO)
where, EO = approach width (m); El = entry width (m); FI = flared length
(m)
Lost time. The lost time (L) associated with each group of entering vehicles was
found to be related to the geometry of the approach of the circulating vehicles:
L = 2.3 + 0.006K1 0.04W2
where, K1 = entry curvature (km-1); W2 = previous weaving width (m);
Minimum circulating headway (P ,), proved to be difficult to predict but the best
estimator was determined as:
P,(i)=l/(0.12EO(j) + 0.04(El(j))
50


where, P ,(i) = mean minimum circulating headway at study entry (i) (s);
EO Q = approach width of previous entry (j)(m);
El (j) = entry width at previous entry (j)(m).
The relationships produced consistent results. Measured and predicted values of
entry capacity showed reasonable agreement. McDonald and Armitage concluded
from their study that a roundabout may be considered to operate as a series of linked
T intersections at which a saturation flow/lost time concept applies. This assumes
that weaving is not a controlling factor but rather a minor aspect of capacity
consideration. Since the geometric characteristics of the study sites covered a wide
range, from mini to large conventional roundabouts, for the latter, capacity may be
best assessed by entry rather than weaving relationships. Therefore, a uniform
approach to roundabout capacity design was possible, (l-p.73)
5.7 Improved Capacity Formula
It was decided to further the development of empirical models rather than pursue the
gap- acceptance models where there was no clear indication which of the parameters
would be the best predictors of capacity. Gap-acceptance models usually predict a
curvilinear relationship between entering and circulation flow but real data shows
that a straight line provides at least as good a fit over the observed range of data.
Great Britain observations indicate that the gap-acceptance assumption that
circulating traffic does not react to the presence of entering traffic; and that gap-
acceptance parameters are independent of the magnitude of the circulating flow, may
be false at high degrees of saturation. The approach was based on the linear
relationship suggested by Philbrick between each entry and its adjacent circulating
51


flow. The traffic performance of a roundabout could therefore be linked to the size
and shape of its entries by means of the constants fc and F. The problem was to
obtain predictive relationships whereby fc and F can be calculated from a knowledge
of entry geometry. Linear regression techniques were used to construct a framework
of predictive relationships for entry capacity. The experiments, analyses and
development of predictive equations are described in several TRL reports, mainly,
LR 773, SR 334, SR 436 and LR 942.
KEY-A TRRL data.
O Public road data.
Figure 5-3
Observed v estimated capacities
source (7)
52


When the new types of roundabouts were being developed, Blackmores work
showed a strong degree of mutual interaction, this was seen as desirable in itself
since it prevented over strict rules of entry from reducing the capacity. Kimber and
Semmens reported on further full scale track experiments carried out in 1976,
including both Mini and Small island roundabouts. The aim was to improve on the
full capacity Blackmore formula, to provide entry-by-entry, capacity calculations for
the purpose of engineering design and economic assessment. The track experiment
was used to investigate systematically the relationship between the capacity of a
roundabout entry and the geometric and traffic factors affecting it. The entry
capacity, Qe, was found to be linearly related to the flow of the circulating traffic,
Qc, across the entry, and equations of the type; (l-p.74)
Qe = F fcQc
accounted for approximately 90% of the variance of Qe, the residual variance
showed no systematic trend. The basic factors affecting the relationship were
identified as:
(i) the entry width, e;
(ii) the circulation width, u, and
(iii) the size factor, D.
The best predictive equation for the entry capacity was found by;
fc = 0.29 +0.116e
and F = 329e + 35u + 2.4D 135
where: e, u, and D are in meters and Qe and Qc, in vehicles per hour.
The entry width e, was found to be by far the most important parameter.
53


Entry flaring was found to provide sizeable traffic benefits, even for small circulating
flows, increasing capacity by up to 45%. The circulation width and overall size of
the roundabout had significant but small effects. The tests on entry paths on D = 15
meters roundabouts, 3 arm and 4 arm, indicated that the entry mechanism is
unaffected by the geometric paths anticipated by drivers waiting to enter the
intersection, (l-p.75)
The effect of flaring the approach width at entry was to raise the value of the
intercept F beyond the value expected for the equivalent unflared entry, but to leave
the slope unchanged for low and intermediate circulating flows. At higher
circulating flows entry capacity was the same as for an unflared entry of width e.
The maximum capacity for flared entries was obtained when the angular deflection (
0 ) of the outer curb was slight, 1 in 2 or less, but useful improvement could be
obtained with a 1 in 1 flares, (l-p.75)
As the circulating flow across one entry originates from previous entries a balancing
process is required to deal with a roundabout as a whole. This may be either a
simple iterative algorithm (Furness) or linear programming. A computer program
was developed to enable each entry to be considered in turn and to calculate all the
traffic flows both entering and within the roundabout, (l-p.75)
In order to calibrate these provisional results on public roads, initially in 1977,
twenty eight roundabout sites conforming with Technical Memoranda H7/71 and
H2/75, where continuous queueing occurred for 30 minutes or more, were studied.
54


This excluded large island roundabouts although a wide range of variation in
geometry and traffic flows was covered, enabling the effects of traffic composition to
be assessed. The study was described by Glen, Sumner and Kimber. The aim was to
check the Track Experiment results in everyday conditions and develop capacity
relationships suitable for design purposes. The main geometric characteristics were
refined from those used in the track experiments, as follows:
i) the entry width, e (m); range 4.5 16.5
ii) the circulation width, u (m), at the point of maximum entry deflection;
range 5.5 22.4
iii) the inscribed circle diameter, D (m); range 13.5-58.5
iv) the average effective length, l(m) over which the flare is developed;
v) the approach road half width, v(m); range 1.9 6.9
vi) the sharpness of flare, S = (e-v)l; range 0.05 -1.98
vii) the entry radius, r (m).
55


Since entry capacity is affected by variations in composition of flow, pcu values
were derived. The greatest variation was shown by two wheelers.
56


Mean pcu Values (rounded)
Entry
Circulation
Heavy Vehicles 1-9(2) 1-7(2)
Other Vehicles 0.2 (zero) 0.8(1)
The main difference between traffic behavior on the track and on public roads, was a
more efficient use of entry width on public road sites.
A Point of maximum entry
deflections at left hand
of yeild line
e Entry width
v Approach half width
r Entry radius
D Inscribed circle
Diameter
I' Average effective flare length
Figure 5-5
Geometric parameters of entry
57


The intercept F and slope fc of the entry capacity relationship:
Qe = F fcQc,
were determined by the average number of queues at the give-way line, which was in
turn determined by the entry geometry. The track experiment equations gave correct
capacity predictions provided that the average number of queues at entry was
predicted correctly. Simplified versions were calibrated to allow for the effects of
partial entry saturation in public road conditions. The best predictive equation were
given by:
F = 224(v + (e- v) / (1 + S)) + 35u + 2.4D 135
and fc = 0.063 (v + (e v) / (1 + S)) + 0.29 (pcu/h)
The analysis confirmed the main findings of the Track Experiment. The most
important factors determining the capacity of an entry are the entry width e, and flare
S. Since v is fixed by the approach road geometry, and the effects of u and D are
slight, only e and S should be treated as the primary design parameters, (l-p.89)
5.8 Development of A Unified Capacity Formula
The period from 1978 to 1980 was one of further study of public road roundabouts,
particularly of conventional larger types of roundabout. The design rules of
H.2/75 still tended to produce weaving lengths and some that were modified
allowed increased approach speeds which increased accidents. A unified capacity
formula was in sight, but it was evident that new comprehensive guidelines were also
urgently needed. The capacity studies were further consolidated and in 1980 Kimber
described the development of a unified capacity formula that would be applicable to
58


both smaller roundabouts, designed for offside priority, and the larger
conventional ones, produced from the previous design assumptions of
weaving/merging behavior. A total data base was accumulated from eighty-six
public road roundabout sites in five major studies and statistically weighted for
analysis. The analyses of the combined data and the subsequent development of a
unified formula provided a general capacity prediction procedure for all at-grade
single-island roundabouts. Account was taken of local site conditions and an
iterative design procedure was suggested. The range of the geometric variables
included a minimum inscribed circle diameter of 13.5 m. This diameter was
equivalent to a Mini roundabout conversion of a intersection comprising road widths
of approximately 6.5 meters roadways and therefore the unified formula would be
applicable to most normal urban mini roundabout installations. The geometric
characteristics were identical with those previously used, with the additions:
the angle of entry (degrees);
the alternative average effective flare length 1 (m) ; and for the inclusion
of larger conventional roundabouts in the studies;
the width of the weaving section w (m)
the length of the weaving section L (m)
The empirical approach described previously was pursued further by regression
analysis. The larger data base showed that a single linear relationship between traffic
entering a roundabout from a saturated approach and the circulating flow crossing the
entry, was applicable to all sizes of roundabouts with inscribed circle diameters from
13.5 to 171.6 metres. A pcu value of 2 for heavy vehicles at roundabouts had been
obtained previously and that was the value used in establishing the pcu values for
59


entiy flow Qe and circulating flow Qc in the analysis. The possibility of non-
linearity was thoroughly tested with a second order model. Non-linearity might arise
from the fact that in practice it is difficult to suppress the entry flow entirely, even
when the circulating flow is very large. No significant non-linearity was detected.
The analysis suggested that the operation of roundabouts on public roads does not
normally reach this region and it would be highly undesirable for roundabouts to be
designed to operate in this way. The linear relationship Qe = F fcQc will ensure
that designs are conservative for abnormally high values of circulating flow. For
models based on pooled data from many sites, the effect of unexplained within-sites
and between-sites variation, on the accuracy of a prediction of the mean capacity
value for a single site is very small. The first, of the order of a few pcu/h, and for the
second, the standard error is about 200 pcu. (l-p.80)
Figure 5-6
Entry/circulating flow relationship
source (8)
60


5.9 Roundabout Capacity Design Current Practice
Intersection design calls for many decisions and choices and is a complex task. By
choosing too elaborate a design, the engineer may unnecessarily redirect resources.
In capacity provision it will seem less risky to over-provide but it will rarely be
economic to avoid transient overload altogether, (l-p.101)
The procedure for the design roundabouts in GB is currently covered in two main
documents:
1) Department of Transport Advice Note TA.23/81 : 1981
2) Department of Transport Design Manual for Roads and Bridges (DMRB)
Vol. 6, Section 2, Part 3, TD.16/93 Geometric Design of Roundabouts,
issued in Sept: 1984 .
Other documents which are used include: Guidelines on Highway Link Design; the
Department of Transport Traffic Appraisal Manual (TAM); and The Economic
Appraisal (COBA) Manual (These procedures are now used generally by all
highway authorities in the UK), (l-p.101)
Guidance on the most appropriate form of intersection is also given in TA.30/82
(DMRB 5.1). Methods of assessment and economic appraisal for major (trunk) road
schemes are described in great detail in the DOT manuals, TAM (Traffic Appraisal
Manual), COBA (Cost Benefit Appraisal) Manual, and more recently, the
Environmental Appraisal Manual. TA.23/81 refers to the first two of these including
61


the evaluation of design flows from traffic counts; and the use of growth factors
derived from national/local statistics. TD. 16/93 refers to both of these Manuals. (1-
p.102)
TA.23/81 : 1981, recommended that ARCADY (which was also released in 1981)
should be used for the estimation of capacity, delays and queues. A procedure for
manual calculation is provided in TA.23/81, however, roundabout design will
normally involve a number of trials, and it is not realistic to calculate these manually
(particularly for queue lengths and delays). It is generally accepted that the need for
manual calculation has been supplanted by the later availability of micro computer
versions of ARCADY and the universal access to micro computers now available to
designers. However, the description and examples of the calculation of roundabout
capacities in Annex 1 of the 1993 design guidelines, virtually renders current
reference to TA.23/81 unnecessary, (l-p.102)
Design Reference Flows TA.23/81 and subsequently TD. 16/93 give guidance on
determining the size of roundabouts and the procedures for deriving the Design
Reference Flows. These are the adjusted hourly traffic flow rates for the detail
design of intersections. For urban roads with little seasonal variation the 30th highest
(annual) hourly flow, and for inter-urban roads, the 50th highest, are generally used.
For the purpose of DOT economic assessment procedures (COBA), they are taken
as a range (the turning flows should also have a range), to allow various options for a
junction to be considered, to arrive at an operationally economical optimum. (1-
p. 102)
62


The equation for the prediction of entry flow into a roundabout as a function of the
circulating flow and entry geometry, can be applied to all types of single at-grade
roundabout whether mini or normal types. Having developed a range of Reference
Traffic Flows, a designer should use the equations for roundabout entry capacity
(manually or by computer) to produce trial designs for assessment, (l-p.102)
The Ratio of Flow to Capacity For the assessment of different options, the
reference-flow/capacity or RFC ratio, is used as the indicator of the likely
performance of an intersection under a future year loading. It should be calculated
for each trial design. Thus if an entry RFC of 85% occurs queueing will theoretically
be avoided in the chosen design year peak hour in 5 out of 6 peak hour periods or
sites. Similarly, if an entry RFC of 70% occurs, queueing will theoretically be
avoided in 39 out of 40 peak hour periods or sites. The general use of designs with
an RFC of about 85% is likely to result in a level of provision which will be
economically justified. There will be cases, however, where the adoption of a lower
figure will be justified: for example, where the cost of a higher level of provision is
low in both economic and environmental terms, or where space for enlargement is
unlikely to be available in the future at a reasonable cost and thus the cost of being
wrong becomes unreasonably high. On the other hand, if there are cost or
environmental implications in providing higher capacity, for instance in urban areas,
then even the 85% ratio may be unsuitable and a higher ratio with consequent
queueing, will have to be accepted (to an extent assessed by the reduction of
economic or environmental impact), (l-p.102)
63


Circumstances will vary and it may often not be possible to provide the same RPC
on all approaches, but the aim should be to achieve a reasonable design in this
respect. On the other hand, ratios higher than 85% could be used at some less
important entries if exceptionally low ratios are unavoidable at others, though the
possibility of excessive queueing at any entry should be avoided. Designers should
not strive to obtain a unique value. A range of situations must be considered and the
advantages and disadvantages of each one assessed, (l-p.103)
Variation It must be stressed that the calculated capacities, queues and delays are
average values of very broad distributions. The formula used are based on multiple
regression analyses from observations from a large number of sites. Actual values
can vary about the average due to:
1) Site to site variation; and
2) Day to day to day variation.
As far as day to day variation is concerned this will manifest itself in practice as
variations in the queue lengths and delays at any given time in the peak period. The
formula merely calculate the average values over many days. ARCADY/3 offers
calculations for daily variability as well as averages.
TD. 16/93 records, that the best predictive equation for the capacity of a roundabout
entry (except those at grade separated interchanges, see below), found by research up
64


to 1993, is:
Qe = k (F fcQc) when fcQc is less or equal to F,
or Qe = 0 when fcQc is greater than F.
where: Qe = entry flow in pcu/hour (1 HGV = 2pcu)
Qc = circulating flow across the entry in pcu/hour
k = 1 .00347 ( 30) .978 {(1/r) .05}
F = .21 t (1 + .2 x2)
fc = 1 + .5 / (1 + M)
M = exp {(D-60)/10}
x2 = v + (e v) / (1 + 2S)
S = 1.6 (e-v)/l
The above equations apply to all roundabouts except those at grade separated
interchanges. For all entries at very large and grade separated roundabouts:
Qe = 1.004F 0.036SEP 0.232Qc + 14.35 FcQc (2.14 0.023 Qc)
where SEP = separation of exit and entry for grade separated approaches,
Qc = mean circular flow for central 30 minutes.
For manual calculations the RFC should be calculated using the above formula. The
design Reference Flows should be multiplied by 1.125 to allow for short term
variation in traffic flows. Short term variation is included inARCADY/3.
For computerized calculation a computer program such as ARCADY/3 should be
used. The appraisal can be based on either an RFC of 85% or, in certain cases, a
higher or lower ratio as described previously. In calculating this, a time segment
length of not less than 5 minutes should be used to build up the flow pattern during
65


the peaks (which can also be synthesized in ARCADY/3 from hourly flows if
necessary). The program prints out the RFC (labeled Demand/Capacity in the
output), queue lengths and delays at each entry for each time segment. An inspection
can therefore be made, for each arm in turn, of the queue length and delay if the RFC
reaches 85% or (70%). (1-p. 104)
Layout Factors The trial design should be adjusted where necessary to obtain
operational efficiency or increased safety by adjusting the entry widths, the length of
flares, etc. The list below gives the normal practical limits of parameters for new
design, compared with the range measured at roundabouts on which the capacity
formula are based. (1-p. 104)
Table 5-1
MEASURED AND PRACTICAL RANGES OF ENTRY CAPACITY
PARAMETERS Parameter Practical Range Measured Range
e entry width 4.0- 15.0 m 3.6- 16.5 m
V approach half-width 2.0-7.3 m 1.9- 12.5 m
1 effective length of flare 10.0- 100.0 m 1 -30.0 m
S sharpness of flare 0 2.9 m
r entry radius 6.0- 100.0 m 3.4 infinity
0 entry angle 10 I/2 60 Vi 0 l/2 77 54
D inscribed circle 15.0- 100.0 m 13.5 171.6m
66


Circulatory roadway width, should be kept constant, ie, (inscribed circle diam. -
central island diam.) /2, at 1 to 1.2 times the greatest e, up to a maximum of 15 m.
(l-p.105)
67


6. Pedestrians, Equestrians and Cyclists
6.1 Introduction
The introduction of smaller roundabouts with flared approaches in lieu of traffic
signals would emphasize the need for crossing facilities for pedestrians. Generally
with flared approaches the crossing should be sited as far back from the intersection
as pedestrian convenience will allow. Crossing provision are preferred to be
included in the deflection islands, either, as an unmarked crossing place with lowered
curbs, or incorporated into a marked or signal controlled pedestrian crossing. Where
justified by pedestrian flow, underpasses or overpasses could be considered, but the
more compact style of roundabout serves to reduce the length of pedestrian detour
and therefore the apparent justification for grade separated pedestrian facilities.
The introduction of a roundabout at an intersection might adversely affect the pattern
and safety of pedestrian movement, and require that appropriate measures be taken
such that the pedestrian route is located away from roundabout intersections if
possible. Crossings located before the give-way line should allow 2 to 3 cars to
queue in each lane, between the give-way markings and the pedestrian crossing. If
used, deflection island refuges should be at least 1.2m wide. A signal controlled
crossing should normally be sited before (although not too far) the flared approach.
It should be noted that this might be helpful in interrupting the dominant traffic
stream to allow the entry of a minor flow.
The 1984 Britain design guidelines TA. 16/84 suggested that as a general rule
pedestrians should be discouraged from crossing the circular roadway on
roundabouts. Guard rails may be required to channel pedestrians movements away
68


from the roundabout to safer crossing points. The length of detour should be
minimized if dangerous alternatives used by some pedestrians are to be avoided. (1-
p.212)
6.2 Current Design Guidance Pedestrians
The current Britain guidelines TD. 16/93, Advice on pedestrian facilities, is that
separate routes with crossings away from the flared entries to roundabouts are
preferable. Here the roadway widths are less and vehicular movements are more
straightforward. When this is not practical, the following should be considered;
a. Unmarked crossing place (ie dropped curbs), with a central refuge if
possible.
b. Zebra crossing with or without central refuge.
c. Some form of controlled crossing with or without a central refuge
which includes for cyclists.
d. Underpass or overpass.
The type of facility selected will depend upon the expected volumes and movements
of both pedestrians and traffic, and should be designed in accordance with the
current recommendations and requirements (DMRB 2.2; 6.2; 8.5). The use of
different types of facility at the same intersection is not recommended as this could
lead to confusion by pedestrians and drivers. Crossings should not be placed across
multi-lane entries. They should be located away from the intersection where the
roadway is relatively narrow. (1 -p.213)
69


con mo. lne E
* STREET CEN7ERLWE
- CONTROL UK D
CONTROL UK CROVW
planted landscape _____
(LANDSCAPING SY OTHERS)
CNO CONTROL UK C
ENO CONTROL L*C H
RAISED IgpAH
COLORED, PATTEW<£D
CONCRETE PAVEMENT
(TYPICAL ALL KDUN5)
CONTROL LME H
OUTFALL VERTICAL CURB
AMO CUTTER. TYPICAL ALL
KDIAMS AK> ISLANDS.
EXCEPT AS NOTED PARALLEL
TO CROWN LNC.
VERTICAL CURB CUTTER (FTP)
Figure 6-1
Pedestrian Crossing Locations At A Roundabout
70


In urban areas, where large numbers of pedestrians are present, guard rails or other
means of deterring pedestrians from crossing should be used to prevent
indiscriminate crossing of the roadway. The design of guard rails should not obstruct
drivers visibility to pedestrians through them, and vice-versa, are available, but
should be checked in case spots do occur, (l-p.213)
6.3 Current Design Guidance Equestrians
Where there is expected to be regular use of the roundabout approaches by ridden
horses, of the order of more than 20 horses a week, consideration should be given to
the provision of crossing places where the roundabout arms have to be crossed.
These should preferably be crossed at some distance from the roundabout to permit
suitable visibility to the roundabout by the rider. The principles are set out in DOT
TA.57/87:1989 (DMRB 6.3). Segregated routes at the roundabout are to preferred.
Ridden horses could share cycle tracks where these are distant from the circulatory
roadway but should not be expected to use pedestrian facilities, (l-p.213)
6.4 Current Design Guidance Cyclists
The current Britain guidelines TD. 16/93:1993 state the safety implications for two
wheeled vehicles at roundabouts. It also gives advice on facilities for cyclists and
therefore allows designers to determine what measures to employ to safeguard two
wheelers in circumstances relating to the particular site under investigation, (l-p.213)
Roundabouts have an impressive overall safety record for most vehicle types but this
does not apply equally to two wheeled vehicles. Research has shown that on four-
armed roundabouts on class A roads, injury accidents involving two-wheeled
vehicles constitute about half of all those reported. The proportion of accidents
71


involving bicyclists is about 15%, although they typically constitute less that 2% of
the traffic flow. The accident involvement rates for two-wheeled vehicles, expressed
in terms of accidents per road user movement, are 10 to 15 times those of cars; with
bicyclists having slightly higher accident rates than two-wheeled motor vehicle
riders.
The study at four-arm roundabouts, has shown for example that, in 30 and 40 mph
speed limit areas, there are differences in bicyclists involvement rates for different
categories of roundabouts. Designers should be aware of the following:
a. Normal roundabouts with small central islands and flared entries have
accident rates which are about twice those of normal roundabouts with
large central islands and unflared entries.
b. 70 per cent of bicyclist accidents at smaller normal roundabouts are of the
circulating type.
c. At dual roadway roundabouts the accident involvement rate for cyclists is
about two to three greater than that at dual roadway traffic signals but for
cars, the opposite is true.
Data for bicycle involvement rates in 50 to 70 mph speed limits were less reliable
due to low bicycle flows and few bicycle accidents, and did not show any significant
differences between types of roundabout. The rates observed were similar to those
for smaller normal roundabouts in 30 to 40 mph speed limits. Comparable data for
bicycle accidents at mini roundabouts, three-arm roundabouts and single roadway
72


traffic signals are reported in TRL CR. 161:1989 which shows involvement rates for
bicycles at mini-roundabouts that are respectively 8 and 9.5 times that for cars.
Guidelines on the geometric design of roundabouts TD. 16/93 observes that
roundabouts are a particular hazard for bicycles as outlined in above. The
operational performance and safety factors have been monitored at a number of
experimental schemes aimed at improving cyclists safety at roundabouts. These
have included the use of with flow cycles lanes around circulatory roadway,
conversion of peripheral walkways to joint cyclist/pedestrian facilities, shared use of
pedestrian underpasses and signposting alternative bicycle routes away from the
roundabout. Evaluation of these, has concluded that once a bicyclist has entered a
roundabout it is difficult to reduce the risk, and that the use of shared facilities have
limited use depending on the volume of pedestrians and bicyclist. Nevertheless
bearing in mind the practicalities and economics, it is important to consider facilities
which take bicyclists out of the circulatory roadway at roundabouts by application of
the following:
a. Shared use by pedestrians and bicyclists of a peripheral cycle/walkway;
b. A signposted alternative route away from the roundabout;
c. Full grade separation for bicyclist and pedestrians, eg by a combined
pedestrian/cyclist underpass system.
Failing these, then greater emphasis should be placed by the designer on the safety
aspects of the design of the roundabout layout, rather than high capacity, by careful
attention to the entries and flares, (l-p.214)
73


Figure 6-2
Exclusive Bicycle Lane At A Roundabout
source (9)
74


If the volume of bicyclists is significant but high enough economically to justify
segregated facilities then consideration should be given to signalizing the roundabout
or to an alternative form of intersection with traffic signals. Signalized bicycle
crossings should be given to bicyclists at segregated left turn lanes, (l-p.215)
The study report 1990 on the Britain 1984 guidelines, refers to experimental schemes
aimed at improving safety of bicyclists at roundabouts. The report recommended
that, local authorities should be further encouraged to consider the provision of
facilities which take cyclists out of the circulatory roadway at roundabouts or, if this
is not feasible, consideration be given to an alternative form of junction, such as
traffic signals, (l-p.215)
A further recommendation for revision referred to low profile deflection islands
recommended in TA.42/84. Experience of these indicated that the use of minimal
height subsidiary deflection islands could be a danger to both bicyclists and
pedestrians. In the current Britain guidelines these islands are now to be delineated
only by white reflective paint and reflective markers. Pedestrians should not be
expected to cross left turn lanes which are segregated only by road markings. If a
safer crossing cannot be provided, curbed islands of sufficient width with refuges
should be used, (l-p.215)
6.5 Safety Studies Of Pedestrians and Cyclists
Comparative studies of pedestrian and bicyclist safety at mini-roundabouts and
traffic signal controlled junctions in Avon were reported by Davies in 1984. Results
from a 1977 study of 12 mini roundabouts in Avon gave a 22% reduction in all
accidents and a 64% reduction in fatal and serious accidents (although neither were
75


significant at the 10% level). In a later study of small and mini roundabouts,
formerly priority controlled, all injury accidents were reduced by 34%. This
reduction was reflected in all accident categories examined, although the numbers of
pedestrian and bicyclist accidents were very low. In the comparative study with
traffic signals, mini and small roundabouts showed a slightly lower percentages of
pedestrian and bicyclist accidents, (l-p.215)
Maycock and Hall showed that roundabout entering/circulating accidents were
particularly sensitive to entry path curvature and entry width. It would appear that,
although bicyclist circulating accidents are dependent to some degree on deflection,
they are not as sensitive to this parameter as total accidents. The analyses indicated
that cycle accidents are related to cyclist flow and therefore an ideal treatment
would; reduce accidents, be inexpensive and be capable of widespread application.
A number of experimental layouts had been installed, for example:
a) with-flow bicycle lanes on the roundabout roadway, but the
improvement in accidents, if any, was slight and more compact
roundabouts with flared entries would limit this solution.
b) two-way bicycle tracks around the perimeter, but the need to give way
to traffic when crossing the arms of the roundabout make high traffic
flow sites unattractive to bicyclists and this approach would be
difficult at restricted urban sites.
Combined cyclist/pedestrian underpass systems offer complete segregation.
Conversion of existing pedestrian underpasses may be possible where pedestrian
flows allow. The suitability of these would depend on existing site conditions in
76


order to avoid potential pedestrian/bicyclist accidents. Results from experimental
conversion schemes suggest that a barrier to maintain pedestrian/bicyclist
segregation is effective, (l-p.216)
Findings in the Britain County Surveyors Society (CSS) Report No. 1/4, 1987 which
are given as indications needing substantiation by further work included:
1. Small and mini roundabouts are no less safe for pedestrians than other
forms of intersection control.
2. The proportion of accidents involving two wheeled vehicles at Small
and Mini roundabouts is no different to that for Conventional
roundabouts.
3. Small roundabouts may be more dangerous for bicyclists than traffic
signals.
The Britain CSS Report No. 1/3 Pedestrian Crossing Facilities, also summarizes the
results of prior studies. Harper reported in 1985 on a study of 63 signal controlled
pedestrian crossings in Wiltshire, over the period 1979-1984. This study showed that
accident rates for sites including Mini roundabouts, were lower with a 40 mph speed
limit than in a 30 mph area. Bramwell reported in 1986 that in Buckinghamshire
marked (Zebra) crossings on the immediate approaches to roundabouts showed
similar accident rates to those more distantly sited, (l-p.217)
Layfield and Maycock reported in 1986 that, at roundabouts, of accidents involving
bicyclists, 15% are fatal or serious, significantly lower than the general value (at
mini-roundabouts 18%). These lower severity ratios at roundabouts are offset by the
fact that a higher proportion (8%) of bicycle accidents occur at roundabouts
77


(including mini), than the proportion (4%) of non-bicycle accidents which occur at
roundabouts. Remedial treatment aimed at bringing the ratio in line with non-
bicyclists would, if successful, reduce bicycle accidents at roundabouts by about 40%
(at 1984 data and prices equivalent to savings of £3.5m per year). Studies of hospital
records indicate that a very high proportion of bicyclist injury accidents, most of
which do not involve any other vehicle, are unreported. Geographical study of
reported accidents to bicyclists indicate that a majority of accidents might be
generated at relatively few roundabout sites where clusters of bicyclist accidents
occur. This suggests that bicycle accidents at roundabouts could be substantially
reduced by accident countermeasures aimed at relatively few sites, (l-p.217)
Roundabouts are perceived by bicyclists as hazardous sites that should be avoided.
At large roundabouts many bicyclists are prepared to alter their route or get off and
walk to avoid hazard. The Britain Highway Code recommends bicyclists to
dismount whenever they feel unable to cope with the traffic conditions. A study of
accidents at 84 (4-arm) roundabouts showed that 68% of bicycle accidents involved
circulating bicyclists. Bicyclists approaching the roundabout accounted for 14% of
bicycle accidents and bicyclists entering and leaving the roundabout each accounted
for 7% of bicycle accidents. The findings confirmed that as far as the largest group
(68%) of bicycle accidents are concerned (ie. circulating bicyclists being struck by
entering vehicles), the design of entry geometry is an important consideration for
safety. Where deficiencies of roundabout deflection can be improved, safety benefits
to all road-users including bicyclists and motorcyclists should result, (l-p.217)
78


Table 6-1
FROM LAYFIELD & MAYCOCK, Bicycle Accident Types At A Sample Of
84 4-Arm Roundabouts
Accident type Number of accidents Percentage
Entering/circulation
Cyclist circulation/motor vehicle entering 104 50
Motor vehicle circulating/cyclist entering 15 7
Approaching
Rear-end shunt (bicycle hit) 20 10
Rear-end shunt (motor vehicle hit) 9 4
Single vehicle 3 1
Other
Cyclist circulating/motor vehicle exiting 20 10
Motor vehicle circulating/cyclist exiting 5 2
Leaving roundabout 11 5
Circulating on roundabout 16 8
Unclassified 7 3
Total 210 100
source (1)
79


A number of experimental schemes involving special facilities for bicyclists, at
roundabouts were described in detail by Layfield and Maycock in 1986. However,
none of the schemes showed great potential for accident reduction and a substantial
reduction in risk to bicyclists by introducing special facilities on the roadway or by
delivering bicyclists on to the walkway did not seem likely at the time. (1 l-p.39)
A significant hazard to bicyclists, which is not directly attributable to the roundabout
itself (but the accidents are sometimes assigned to the intersection), can occur when
auto traffic enters and leaves grade-separated roundabouts via slip-ramps. In 1987
Williams and Layfield reported that slip-ramps on all-purpose dual-roadways,
connecting with roundabouts and other grade-separated intersections, were found to
be a source of particular danger to bicyclists. Bicyclists using the dual-roadway have
to cross obliquely, the path of fast moving diverging and merging auto traffic.
Although bicyclist casualties from slip-ramp accidents formed only a small
proportion (1%) of all reported bicyclist casualties in 1985, 40% of them suffered
fatal or serious injury which was well above the average for bicyclists, different types
of facilities provided for bicyclists at roundabouts. (1 l-p.39)
Remedial measures aimed at reducing the accident risk had been developed by the
Britain Berkshire County Council. These consisted of a bicycle lane, diverting
bicyclists from the main roadway to a right-angle crossing of the slip-ramp at a safer
location. This arrangement gave bicyclists greater control of their own safety but
removed their priority and made a less direct route. The initial usage by bicyclists in
80


an experimental period was two thirds. The arrangement has since become the
standard treatment for dual roadway slip roads. (1 l-p.39)
6.6 Pedestrian Crossings At Roundabouts
Design considerations for Zebra crossings are covered in TA. 10/80 (233). If a
crossing giving pedestrian priority is located close to the entry/exit points of a
roundabout there will be inevitable consequences for the operation of the roundabout
and possibly for safety. In some cases the safety effects may be positive as speeds
will be reduced. (10-p. 12)
Where a crossing must be provided within the intersection layout, a zebra crossing is
preferred. If a signalized crossing is provided, it should preferably be of the divided
crossing type to avoid excessive delays at the exit points, because the blocking
back mechanism causes queues to extend onto the circulatory roadway. (10-p. 12)
A requirement was introduced in TA.42/84:1984 and is mandatory in TD. 16/93:
1993, for drivers at the give-way line to have unobstructed visibility of the full width
of a pedestrian crossing across the next exit. If the crossing is within 50m of the
roundabout (there may be difficulty in meeting this criterion in some restricted urban
sites). (10-p. 12)
Marlow and Maycock quantified the reduction of intersection capacity from the
siting of uncontrolled marked (Zebra) crossings close to intersection, including the
effect of blocking-back by queues on exit. (10-p. 12)
The theoretical approach is based on random arrivals at two servers in series, using
the vehicular real and virtual capacity of a Zebra crossing derived by Griffiths,
and roundabout entry capacity derived by Kimber. The application is limited to
81


ratios of real crossing capacity to entry capacity greater than 1. If this is <1 the real
crossing capacity will dominate and segregation of pedestrians would be needed.
The Reduction in capacity due to the blocking effect was found to be similar (or
greater) than the approach crossing/entry effect. It emphasizes the need to take this
additional factor into account when considering the location of pedestrian crossings
near to roundabouts (or other intersections). In many cases, a crossing to intersection
queue of 4 to 5 spaces, reduces the crossing interaction on the entry side of the
intersection to quite a small effect, and allows a flow rate of about 50 to 60% of the
capacity of the crossing on the roundabout exit, before the 5% blocking criterion is
reached.(10-p. 13)
In 1987 Marlow looked into the question of traffic signal pedestrian crossings at or
near to entries to mini roundabouts, and the effect on the traffic operation of the
roundabout, including resulting queues blocking back into the junction. DOT
Advice Note TA. 10/80 1980, suggested that a pedestrian crossing should be sited at
least 20m from the intersection, to avoid this interaction. Any confusion that mini-
roundabouts might appear to be signaled seemed unlikely, but close proximity can
affect the traffic operation of the intersection. Also, the requirements conflict, since
the diversion may be unattractive to pedestrians. In order to assist in siting decisions
for the crossing, the general guidelines were quantified by Marlow more
comprehensively. Using a capacity relationship and the recommended settings. The
general operating capacity for fixed time Pedestrian signals of this type was
established at 1,300 to 1,400 vph and pedestrian flows >400/h. Typical small
roundabouts had entry capacities in the range of 600 to 1,300 vph with a circulating
flow of 500 to 1,000 vph. Marlow used Poisson probabilities for the arrival of
82


vehicles during the pedestrian stage, for six levels of flow and three road widths, to
derive estimates of 95 percentile queue lengths in vehicle numbers.
Table 6-2
95 Percentile Queue Lengths In Vehicle Numbers
Road width Flow (vehicles/hour)
(metres) 250 500 750 1,000 1,250 1,500
7.3 2 3 5 6 7 8
9.0 2 4 5 7 8 9
11.0 3 5 6 8 9 11
Similar considerations apply to both entry and existing. An indication of the siting
of crossing (for an unflared entry), can be obtained assuming an average vehicle
space of approximately 5m giving a range of 10 to 40 m for a 7.3 road and from 15
to 55m for an 1 lm road. (10-p.l5)
Generally, any entry flaring to more than two lanes should occur between the
crossing and the roundabout. This applies to both Zebra and Pedestrian crossings.
6.7 International Developments
In the French report by Alphand, a study of pedestrian accidents at roundabouts had
been made but the numbers were too small to produce reliable statistics; however,
some common points could be inferred. The majority of accidents took place on
83


two-lane entries, but the same number (7) occurred on pedestrian crossings adjoining
the give-way line. The balance of accidents occurred within the roundabout. An
element of entrapment by barriers etc. of pedestrians entering the roundabout is
suggested in the latter. Other common characteristics included children and old
people, high traffic flows (> 20,00 vpd), towncenters and peak-hour traffic. The
French suggest locating pedestrian crossings 4 to 5m before the give-way line and
staggered to bring the exit crossing nearer to the roundabout. (This might improve
visibility to exiting traffic but could increase the probability of queues blocking
back). (10-p.l6)
An analysis of accidents involving bicycles and mopeds at French urban
roundabouts, shows a major cause of accidents (50.6%) as the refusal of priority to
bicycles and mopeds. This is more prevalent (33.4%) on larger roundabouts of >30m
diameter but also on oval shaped (19%), high entry speed and possible masking by
other traffic are suggested causes. The accident rate increases with traffic flow and
more than half of the accidents occur during peak periods. (10-p.l6)
The German experience of pedestrian and cyclist safety at roundabouts was reported
by Brilon and Stuwe in 1992. Deflection islands are recommended with refuges for
pedestrians. Traffic safety for pedestrians at single lane German roundabouts is
generally very high, since there are only very narrow conflict zones with the
motorized traffic which, moreover passes these zones at very low speed. In most
cases pedestrians cross without noticeable delay, in only a few cases is it likely to be
critical (It was noted that at a German roundabout (Munster, Lundgeriplatz) with
high volumes of pedestrians, bicyclists and motorized vehicles, the reduction in
capacity was smaller than that predicted by Marlow and Maycock). In critical cases
84


to avoid blocking-back from crossing pedestrians exits, the distance of the crossing
from the roundabout should be more than 6m. (10-p. 17)
The German experience is that bicycle traffic at roundabouts requires special
attention. Different solutions may be required depending on the site.
a) At small roundabouts (diameter up to 35-40m), bicyclists indicate
their required direction by cycling either on the right side or in the
middle of the circulatory roadway. In these roundabouts bicyclists get
along well with the motorized traffic without risk, since cars and
bicycles proceed at almost the same speed and there is no overtaking
in the roundabout.
b) If roads leading to the roundabout have separate bicycle paths, these
can also be continued around the roundabout and they may be two-
way. Bicyclists then cross entries and on paths on the inner side of
pedestrian crossings. The bicycle traffic often splits up into cyclists
needing protection, eg children, who use the separate bicycle paths
and fast, sporty bicyclists who stay in the circulatory roadways.
c) Fixed track, or marked bicycle lanes, sometimes with a colored
surface, at the outer side of the circulatory roadway. This solution
seems not to be favorable and observations show that bicyclists often
have to stretch out their arm to prevent motorized vehicles from
cutting in front of them. Moreover the fixed track systematically
leads the bicyclists to the problematic conflict zones at the entries.
Therefore, solution c) is not recommended by Brilon and Stuwe. If the approaching
lanes are provided with bicycle tracks, these should end 20 to 30m in front of the
85


roundabout, which should then used by cyclists according to b) above. It was
concluded that the problem of bicyclists in roundabouts demands more extensive
investigation. (10-p. 18)
86


7. Traffic Models For Roundabout Analysis
7.1 Introduction
A roundabout must generally be considered as an alternative to two-way stop
control (TWSC), all-way stop control (AWSC) or traffic signal control. The
performance analysis methodology for these alternative control modes is described
in detail in the Highway Capacity Manual (HCM). The current HCM offers
procedures that produce comparable estimates of entry capacity (vph) and delay
(seconds per vehicle) for each approach to a stop sign or signal controlled
intersection. The HCM procedures have been adopted by many State Department
of Transportations for assessing the level of service (LOS) on state roadways.
Software is available for the productive application of these procedures.
Unfortunately, the HCM does not provide a similar model for the evaluation of
roundabouts. Therefore, a different analysis model must be adopted. This model
should produce results that are comparable with the results of the HCM models for
the alternative control modes. It should also be readily implemented in software
within the same computational structure as the HCM models.
Several methods of roundabout modeling have been developed, most of them in
other countries where roundabouts are common intersection treatments. The
Australian methods are most comparable with HCM methods, and are implemented
in software that is most compatible with the computational structure that has been
developed in Florida for comparing other control modes. For example, the
Signalized and Unsignalized Intersection and Design Research Aid (SIDRA)
87


program offers an option to implement the HCM procedures for many
computations.
In addition, the Australian method is based on analytical models while other
methods, such as the British method, tend to be more empirical in nature. In
general, analytical models are more transportable internationally because they
depend more on mathematical relationships and less on observed driver behavior.
The details of the Australian analysis methodology are covered thoroughly in four
significant documents.
Evaluating the performance of a Roundabout presents the basic theory that
applies to roundabout modeling.
Austroads Guide to Traffic Engineering Practice: Part 6, Roundabouts
contains the full set of guidelines that govern the design, evaluation and
operation of roundabouts in Australia.
Capacity and Design of Traffic Circles in Australia presents a technical,
but readable summary of the roundabout modeling process and offers some
updates to the information presented in the previous references.
The SIDRA 4.1 program documentation describes the way in which the
theory contained in all of the references was implemented in SIDRA. It also
explains departures from the theory that were introduced for practical
88


Full Text

PAGE 1

DEVELOPMENT OF A CAPACITY ANALYSIS PROCEDURE FOR U.S. ROUNDABOUTS BASED ON VAIL, COLORADO'S VAIL RD./l-70 SOUTH ROUNDABOUT by James H. Kramer, P.E. B.S.C.E., University ofWisconsin, 1977 M.B.A., Regis University, 1992 A thesis submitted to the University of Colorado at Denver in partial fulfillment of the requirements for the degree of Master of Science Civil Engineering 1997 @

PAGE 2

This thesis for the Master of Science degree by James H. Kramer has been approved by Date

PAGE 3

Kramer, James H. (M.S., Civil Engineering) Development of a Capacity Analysis Procedure For U.S. Roundabouts, Based on Vail Colorado's Vail Rd./1-70 South Roundabout Thesis directed by Dr. Bruce N. Janson ABSTRACT This paper develops an American procedure to calculate the capacity for the Vail Rd./1 -70 south roundabout at Vail, Colorado. In Britain, a study has previously been made ofthe entry capacities of roundabouts at eighty-six locations, and a unified formula for capacity prediction developed. The traffic flow entering a roundabout from a saturated approach was found to be linearly dependent on the circulating flow crossing the entry point to the roundabout. The entry angle and radius was found to have small but significant effects. The inscribed circle diameter, used as a simple measure of overall size, was found to be effective as a predictive variable for the capacity. The American Highway Capacity Manual (HCM) currently has no analysis methodology for roundabouts, but the "Transportation Research Board Committee on Highway Capacity and Quality of Service, Unsignalized Intersections Subcommittee" is now preparing the addition of material to HCM Chapter 10 to come out in 1998. This thesis demonstrates a new procedure which can be used to correct the British capacity procedure for an American roundabout at Vail, Colorado. With opposing flow located on the X axis, capacity on the Y axis, and a linear relationship, the American Roundabout capacity procedure for the Vail, Colorado iii

PAGE 4

roundabout requires the Y intercept to change but the slope of the linear entry/circulating flow relationship remains the same. This new procedure calculates a capacity 17% lower than the British procedure for the roundabout. The only explainable reason for the difference between the British capacity procedure on British roundabouts and this new American procedure is American driver familiarity with negotiating a roundabout. This abstract accurately represents the content of the candidate's thesis. I recommend its publication. Si Bruce N. Janson iv

PAGE 5

ACKNOWLEDGEMENT Acknowledgment is gratefully given to Dr. Bruce Janson of the University of Colorado at Denver for providing direction and input on the composition of this paper. I would also like to thank Leif Ourston, P.E., and Peter Doctors, P.E., of Ourston and Doctors, and Barry Crown of Britain, author of the British software program RODEL, for their direction and input in the preparation of this thesis Their patience with my questions and enthusiasm to help me in this endeavor will always be remembered and appreciated.

PAGE 6

CONTENTS Chapter 1. Introduction ......................................................................................... 1.1 Background and Problem Identification.................................... 1 1.2 Problem Approach.............................................................................. 5 2. Intersection Control Alternatives............................................. 7 2.1 Traffic Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Two-Way Stop Control......................................................... 8 2.3 All-Way Stop Control.......................................................... 8 2.4 The Roundabout................................................................. 9 2.5 Comparison of Alternative Control Modes................................... 11 2.6 Justification Categories........................................................ 16 3. Accidents at Roundabouts.................................................... 18 3.1 U.S.A. Research................................................................. 18 3.2 British Research................................................................. 18 3.3 Accidents Fall as Roundabouts Spread to Other Countries............. 21 3.4 Safety of Roundabouts for Pedestrians and Bicyclists.................... 23 3.5 Accident Investigation in France............................................. 24 4. Theories of Capacity and Delay................................................ 27 4.1 Introduction....................................................................... 27 4.2 Statistical Theories............................................................... 28 4.3 Probabilistic Theories "Gap Acceptance"................................... 29 4.4 Simulation Methods.............................................................. 31 5. History in the Development of the Capacity Formula....................... 33 5.1 Introduction..................................................................... 33 5.2 Capacity Estimation of Roundabout Weaving Sections Before 1966... 35 vi

PAGE 7

Chapter 5.3 Test-Track Weaving Experiments.......................................... 38 5.4 Experiments After the Change in Priority Rule, 1966.. .. .. .. . . .. . 41 5.5 Further Developments of Capacity Formula After 1966.. .. ....... .. ..... 43 5.6 The Search for a New Capacity Formula................................. 46 5.7 Improved Capacity Formula................................................. 51 5.8 Development of a Unified Capacity Formula............................. 58 5.9 Roundabout Capacity DesignCurrent Practice......................... 61 6. Pedestrians, Equestrians, and Cyclists....................................... 68 6.1 Introduction..................................................................... 68 6.2 Current Design Guidance-Pedestrians.................................... 69 6.3 Current Design Guidance-Equestrians.................................... 71 6.4 Current Design Guidance -Cyclists.......................................... 71 6.5 Safety Studies of Pedestrians and Cyclists................................. 75 6.6 Pedestrians and Cyclists...................................................... 81 6. 7 International Developments................................................... 83 7. Traffic Models for Roundabout Analysis.................................... 87 7.1 Introduction..................................................................... 87 7.2 Rodel..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 7.3 Sidra.............................................................................. 93 7.4 Arcady..... .. .. . . .. .. .. .. .. .. .. . .. .. .. .. . . .. .. .. .. . . . . . . . 94 7.5 Other Traffic Models......................................................... 95 7.6 Capacity Estimation Tools................................................... 95 8. British Capacity Analysis Procedure Using Rodel.... .... .. .. . . .. .. . 104 8.1 Introduction..................................................................... 104 8.2 Capacity Six Regression Equations.......................................... 105 vii

PAGE 8

Chapter 9. Interpreting Rodel's Printouts................................................ 107 9.1 Introduction..................................................................... 107 10. Vail South Roundabout Configuration....................................... 115 10.1 Background.................................................................... 115 11. Data Collection and Summary .................................................................... 130 11.1 Location........................................................................ 130 11.2 Data Summary............................................................... 131 12. Data Analysis............................................................................................. 14 7 12.1 Introduction..................................................................... 14 7 12.2 Linearity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 13. American Proposed Procedure................................................................... 163 13.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 14. Theory-Mean Capacity of Each Individual Leg........................... 171 14.1 Introduction..................................................................... 171 14.2 Hypothesis Test-Mean Capacity of Each Individual Leg............... 171 14.3 Solution......................................................................... 171 15. Conclusions.................................................................. 175 References............................................................................... 177 viii

PAGE 9

FIGURES Figure 1-1 Basic Roundabout.................................................... . . . . . . . . 2 2-1 Volume vs DelaySingle Lane Approaches ....................................... 13 2-2 Volume vs DelayTwo-Lane Roundabouts..................................... 13 3-1 Estimated Number of Accidents at Intersections and Roundabouts for Specific Average Daily Traffic......................................................... 26 5-1 Dimensions and Flows ................................................................... 47 5-2 Sample Comparison Between "Revised-Wardrop" and "Laboratory Report 773" Formula..................................................................... 49 5-3 Observed vs Estimated Capacities................................................. 52 5-4 Geometric Parameters..................................................................... 56 5-5 Geometric Parameters of Entry ......................................................... 57 5-6 Entry I Circulating Flow Relationship ................................................ 60 6-1 Pedestrian Crossing Locations at a Roundabout................................ 70 6-2 Exclusive Bicycle Lane at a Roundabout......................................... 74 7-1 Roundabout CapacitySingle Lane vs Multi-Lane Circulating Flow ...... 96 ix

PAGE 10

Figure Page 7-2 Average Queueing Delay to Vehicles Entering Single Single Lane Circulating Flow Roundabouts......................................................... 97 7-3 Average Queueing Delay to Vehicles Entering Multi-Lane Circulating Flow Roundabouts ......................................................... 98 7-4 Roundabout Capacity Analysis Worksheet .......................................... 99 7-5 Turning Widths Required For Normal Roundabout.. .......................... 101 7-6 Typical Signing and Striping.......................................................... 102 7-7 Capacity I Geometry Relationships .................................................. 103 9-1 RODEL Printouts......................................................................... 111 10-1 Construction Plan Geometry Layout of Vail South Roundabout............ 118 10-2 RODEL Output Original Design Analysis 85% Confidence Level Flow Factor 1.00Existing Traffic Counts-August 1994 .................. 119 10-3 RODEL Output Original Design Analysis 85% Confidence Level Flow Factor 1.50 Existing Traffic Counts -August 1994 .................. 120 10-4 RODEL Output-Original Design Analysis85% Confidence Level Flow Factor 1.56 Existing Traffic Counts -August 1994 .................. 121 11-1 Measured Entry Flows vs Circulating Flows.................................... 136 11-2 Graph of Circulating Flow vs Entry Capacity Based on Geometry and RODEL Equations ........................................................................ 142 12-1 Entry Capacity Qe, and Circulating Flow Qc at a Roundabout Entry .... 150 X

PAGE 11

Figure Page 12-2 Mean Values of the Residuals In Entry Capacity Qe Left by the Linear Representation In Successive 300 pculhr Bands of the Circulating Flow Qe ....................................................................... 150 12-3 Graph of Circulating Flow vs Entry Capacity Comparison Between Measured and RODEL.............. .. .. . . . .. .. .. .. .. . . .. . . . . . . .. .. . 157 13-1 RODEL Results Based on Actual Field Counts Capacity = 5004 Vehicles Per Hour 50% Confidence Level.. ..................................... 167 13-2 RODEL Results At Capacity Average Delay = 0.50 Minutes (Definition of Capacity) Capacity = 6026 Vehicles I Hour50% Confidence Level. .......................................................................... 168 13-3 RODEL Results At Capacity Average Delay = 0.50 Minutes (Definition of Capacity)Capacity = 5598 Vehicles I Hour-85% Confidence Level. .......................................................................... 169 13-4 The Average Queue Length LAs A Function Of The Traffic Intensity p According To The Co-Ordinate Transformation Method ................... 170 14-1 Graph of Critical Region For Test Statistic Capacity of Each Leg ...... 173 xi

PAGE 12

TABLES Table Page 2-1 Roundabout Selection Categories and Justification Conditions............... 17 3-1 Numbers of Roundabouts in the Sample by Intersection Category......... 19 3-2 Causes of Roundabout Accidents in France....................................... 25 5-1 Measured and Practical Ranges of Entry Capacity Parameters ............... 66 6-1 Bicycle Accident Types at a Sample of 84 4-Arm Roundabouts............ 79 6-2 95 Percentile Queue Lengths in Vehicle Numbers.............................. 83 6-3 Other Traffic Models..................................................................... 95 11-1 Actual Field Counts Flowing Through Roundabout at Capacity........... 132 11-2 RODEL 6 Regression Equations Solved for Each leg, Based on Geometry ...................................................................................... 141 12-1 Data Analysis for Each Leg ............................................................. 152 12-2 Descriptive Statistics Analysis of Measured Data for Each Leg ............. 153 12-3 Corrected Y -Intercept Based on Field Measurements......................... 156 12-4 Analysis of Measured vs Expected Values, t-test: Paired Two Sample For Means Pearson Correlation ...................................................... 162 13-1 Procedure For Correcting YIntercept Based on Field Measurements.... 166 14-1 Hypothesis Test Data Analysis ......................................................... 174 xii

PAGE 13

1. Introduction 1.1 Background and Problem Identification The modern roundabout, which dates from 1963 in England, finally arrived in the United States in 1990 in a major Las Vegas residential subdivision. When the first snow country roundabouts in the nation were built in 1995 (the Montpelier roundabout and two at the I -70 exit in Vail, Colorado), roundabouts in the United States numbered 12. Today, about 3 years later, the number has jumped to 50. In Vermont, four new roundabouts are entering or are in final design with construction likely in 1997 and 1998. In the November 1996 election, A von, Colorado, the exit after Vail, approved a $3.5 million, 20-year bond issue for five roundabouts from the I-70 interchange to the Beaver Creek Mountain ski resort. The roundabout community anticipates that roundabouts will be built in the United States annually by the hundreds in a year or so and by the thousands annually early in the next century, duplicating the trends first in Britain and Australia during the 1970s and 1980s and now being repeated throughout western Europe. For example, the Paris newspaper Le Monde (October 3, 1996) reported France with over 12,000 roundabouts. Most have been built since the mid 1970s. A roundabout has three major characteristics compared to its predecessors, traffic circles, and rotaries. First, the roundabout gives vehicles in the circular travel way the right-of-way. This change on a national basis in England in 1963 marked the roundabout era beginning. Second, roundabouts are small, generally from 70 to 160

PAGE 14

Truck Apron Exit Curve\ Yield Line Inscribed Circle Diameter Splitter Island Departure width Exit width Entry Width Raised Central Island Diameter Central Island Diameter Circulating Roadway Width Basic roundabout. Figure 1-1 2

PAGE 15

feet in diameter compared to 300 to 400 feet and more for traffic circles and rotaries. Third, roundabouts have an entry "splitter" island that slows down or constrains speed just before entry, duplicating in a way the curvature the driver will experience within the roundabout itself. In technical and non-technical performance, the roundabout as an intersection control device far surpasses traditional stop sign and yield techniques, and the traffic signal. Roundabouts feature approximately half the collisions and a third of the injuries of signalized or unsignalized intersections. One Netherlands study of 181 new modem roundabout installations before and after performance shows roundabouts cut car occupant injuries by 95%, pedestrian injuries 89%, and bicycle injuries 30%. When injuries do occur at roundabouts, they tend to be less severe than those at traffic lights and signed intersections. The roundabout accident performance in the study was uniformly superior in urban, suburban, and rural locations. The most conservative estimate from reviewing data from several nations concludes roundabouts cut collisions by 50 percent. Roundabouts self-police vehicle speeds and traffic calm about 100 yards in each direction, unlike signal systems they require no electricity, cost less, use less land, enable U-tums, save energy, reduce pollution, and introduce beauty to intersections. In terms of peak hour volumes, delay per car at the Montpelier Vermont roundabout is 2.7 seconds compared to 6.3 seconds for the old signed intersection. At moderately high volume four-way intersections, roundabouts cut average delay of signalized intersections by two thirds. 3

PAGE 16

The theory explored in this paper is that the measured mean capacity at the Vail south roundabout for each entry leg into the roundabout as well as the combined measured mean capacity will be less than the capacity calculated by the British capacity program RODEL, presumably because of the unfamiliarity of American drivers using roundabouts. This hypothesis is found to be true based on the statistical tests performed in this thesis. The focus of this paper is to demonstrate a new capacity procedure which can be used to calculate the capacity of an American roundabout negotiated by American drivers at Vail, Colorado. 4

PAGE 17

1.2 Problem Approach This effort involved collecting and reducing 1-minute traffic data samples at each approach to the south Vail roundabout. Traffic count data in the south Vail roundabout was obtained on July 4, 1997. Approach number 1 was the Vail Road approach from the north into the south roundabout. On approach number 3 (south frontage road approach from west), the outside lane was coned off so the approach was 8.67 meters as originally analyzed. This outside lane only lasts for a short distance from a driveway. On approach number 5 (south frontage road from east) the bypass lane was coned off so the traffic had to enter the roundabout. Traffic on any approach which did not have at least 5 vehicles queued was stopped until the queues on that approach was a minimum of 5 vehicles. Then the traffic at the east frontage road entry, which had the longest queue was allowed to enter the roundabout followed by the other sequential approaches. One minute counts of the total inflow from the entry and the corresponding circulating flow across the entry were obtained at each entry to the roundabout. This was repeated 15 times between the P.M. hours of2:30 and 7:00. One person was located at each approach to count the traffic. Only 15 one minute counts were obtained during this time period because of the time for setup and concern regarding the stopping of traffic. Counts were taken with hand held counters at each entry to the roundabout. The collected data was compared to the capacity as calculated by the British program RODEL to determine the differences between measured and RODEL calculated for each entry leg into the roundabout. 5

PAGE 18

To restate the hypothesis, the measured mean capacity at the Vail south roundabout for each entry leg as well as the combined roundabout measured mean capacity will be less than the capacity calculated by the British capacity program RODEL, presumably because of the unfamiliarity of American drivers using roundabouts. Hence, with opposing circular flow located on the X axis, entry capacity on the Y axis, and using a linear relationship, the American roundabout capacity procedure for the Vail, Colorado roundabout requires the Y intercept to be lowered downward while the slope of the linear entry/circulating flow relationship remains the same. This results in an approximately 17 %reduction in the actual capacity for each leg into the roundabout. 6

PAGE 19

2. Intersection Control Alternatives There are three alternatives to roundabouts for intersection control. Each has significant operational limitations in comparison with a roundabout. Each alternative will be discussed separately: 2.1 Traffic Signals-Roundabouts can efficiently handle particular intersections with decreased delay and greater efficiency than traffic signals. This is particularly true where traffic volumes entering the roundabout are roughly similar and where there are a high number of left turning vehicles. Traffic signals cause unnecessary delay for many reasons: The need to provide a minimum green time to each movement in every cycle creates time intervals in which no vehicles are entering the intersection. The need to provide for the most critical of two or more movements that proceed simultaneously results in an ineffective use of green time by non-critical movements. The "lost time" associated with startup and termination of a green phase detracts further from the amount of time that is available for moving traffic. Left turns that take place from shared lanes impede the other movements in 7

PAGE 20

the shared lanes unnecessarily. This results in a very inefficient utilization of the available roadway space. Heavy left turns, even from exclusive lanes, require dedicated phases that rob time from the major movements and increase the total time lost due to startup and termination of traffic movements. Signals are mechanical devices that not only require maintenance but also periodically malfunction. They are also dependent upon electrical power, and do not, therefore, provide any control during power failures. Many signal violations occur at higher speeds so that the severity of accidents is often high. Permitted left turns and right turns on red introduce additional conflicts. 2.2 Two-Way Stop Control (TWSC) can accommodate low traffic volumes with much less delay than traffic signals, but this control mode favors the (major) street (unstopped) movements at the expense of the minor street (stopped) movement. When the major street traffic volumes are heavy (typically 1400 vph or more) there is little or no opportunity for cross street access. This places a definite limit on the application ofTWSC. Even when TWSC capacity is not exceeded, there is often public pressure to install signals at TWSC intersection. 2.3 All-Way Stop Control (AWSC) treats the cross street movements more favorably, without the wasted time associated with traffic signals. However, the rate 8

PAGE 21

at which vehicles may enter an intersection (i.e. headway) under A WSC is relatively low and, therefore, the total intersection capacity is somewhat limited. 2.4 The roundabout, on the other hand, overcomes all of these disadvantages. There is no sequential assignment of right-of-way and therefore no wasted time. Left turns are not subordinated to through traffic. Vehicles enter under yield control instead of stop control and therefore have lower headways and higher capacities. There are no electrical components to malfunction. Roundabouts, on the other hand, have their own limitations: Steady-state entry headways are shorter at traffic signals because of the positive assignment of right-of-way. By using long cycle times to minimize the effects of start-up lost time, it is possible under most conditions to achieve higher approach capacities. For very low volume applications, TWSC and A WSC are easier and less expensive to implement. Since roundabout operation is not periodic, it is not possible to coordinate the operation of roundabouts on an arterial route to provide smooth progression for arterial flows. Roundabouts offer the least positive form of control. Each vehicle entering the intersection must yield to all traffic that has already entered. 9

PAGE 22

Roundabouts impose a new form of traffic control that is not familiar to most American motorists. Therefore, roundabouts are not the solution to all traffic problems at all locations. Careful study is required to identify the most appropriate control mode at any given location. The studies required to justify the installation of traffic signal control and all-way stop control are based on the warrants and requirements set forth in the Manual of Uniform Traffic Control Devices (MUTCD). No such warrants and requirements exist for roundabouts. Three general questions must be answered to justify a roundabout as the most appropriate form of control at any intersection: Will a roundabout be expected to perform better than other alternative control modes? In other words, will it reduce delay, improve safety or solve some other operational problem? Are there factors present to suggest that a roundabout would be a more appropriate control, even if delays with a roundabout are slightly higher? If any contradicting factors exist, can they be resolved satisfactorily? If these questions may be answered favorably, then a roundabout may be considered as a logical candidate control mode. 10

PAGE 23

2.5 Comparison of Alternative Control Modes Using hypothetical data, consider a very simple hypothetical example involving a roundabout with four right-angle approaches. Each approach has one lane and there is one circulating lane. The central island diameter is 16 meters. The volume distribution is such that the east-west approaches carry 30 percent of the total entering traffic, and the north-south approaches each carry 20 percent. This gives a 60-40 split between the major and minor streets. The northbound and southbound volumes are equal, as are the eastbound and westbound volumes. All approaches have 10 percent right turns and 20 percent left turns. Trucks account for 2 percent of the traffic on all movements. This example reflects a typical volume distribution, and its symmetry provides an excellent base for examining the effect of the total volume on the performance of the intersection as a whole. It also lends itself to comparison with other control modes. One parameter of particular importance is the practical capacity of the roundabout. The default value is 85 % of the possible capacity (2500 vph single lane entry). The SIDRA (Australian Capacity Procedure) documentation points out that roundabout operation at near capacity levels is less predictable than signal operation. This is because signal control is more positive, and therefore less dependent on driver behavior. Therefore, more caution is urged in dealing with roundabouts that operate above the practical capacity, especially when implementation decisions are involved. The default value of 85 percent for practical capacity will be used in this analysis. Another feature of roundabout delay modeling is the concept of geometric delay, i.e., the delay experienced by drivers within the roundabout due to a negotiation speed 11

PAGE 24

that is slower than the approach speed. Geometric delay must be added to queuing delay to arrive at the total estimated delay for each approach. SIDRA offers the option to include or exclude the geometric delay from the computations. Technically, a delay estimate that includes geometric delay provides a more realistic assessment of roundabout performance. However, the HCM methodology for signalized and unsignalized intersection analysis deals only in the queue delay. Therefore, roundabout delay estimates that exclude geometric delay are more appropriate for comparison with these other control alternatives. Figure 2-1 shows the average delay per vehicle as a function of the total entering volume for all ofthe control alternatives. The nature of the relationship is similar among all control modes; i.e., low delays are experienced at low volumes and a more or less exponential increase in delay occurs with increasing volume. The curve becomes very steep as the volumes approach capacity. The volume vs. delay relationships are shown for both one lane and two lane roundabouts. These two configurations will be discussed separately. The single lane comparison shown in Figure 2.1 includes TWSC, A WSC and signal control alternatives. In all cases, single shared lane approaches are examined. For signal control, the addition of exclusive left tum bays was treated as a separate case. This would require a widening of the intersection. Since the construction of a roundabout would also require widening, this configuration provides the most reasonable performance comparison between traffic signal and roundabout control. Exclusive left tum bays introduce the option for protected left tum phasing. Since protected left tum phases introduce additional lost time which reduces the efficiency of the signal operation, they may be expected to produce higher overall delays. 12

PAGE 25

Figure 2-1 >o (i) :xample ,!! Jata 30% major street 40% minor street 20% left turns 10% right turns Figure 2-2 :xample Data rO% major street 0% minor street '0% left turns 0% right turns 1000 2000 3000 4000 Total Entering Volume (vph) Single lane roundabouts. source (5) 2000 4000 6000 Total Entering Volume (vph) Two-lane roundabouts. 13

PAGE 26

Therefore, they have been used in this exercise only when they are necessary to provide adequate capacity for the left turns. This produces a discontinuous relationship between total volume and delay for signals with exclusive left tum bays in Figure 2-1. Note that the twophase operation creates the lowest delay per vehicle up to the point where one movement (in this case the heaviest left turn) exceeds its capacity. The three phase operation, which provides protection for the major street left turns only, is able to accommodate a higher total entering volume than the two phase operation, but with an increased delay per vehicle. The four phase operation, which provides protection for all left turns, is able to accommodate the highest entering volume of all the single lane alternatives, but the delay near capacity becomes excessive. Protected left turn phases may be implemented with or without permitted left tum movements on the phases that accommodate the through movements. The addition of the permitted phase generally reduces delay to left turns. In this exercise, left turns were permitted on the through phases in addition to the protected turning phases. The signal timing plans were determined by the HCM Chapter 9 planning method which does not rely on the capacity of the permitted phase (except for two sneakers per cycle) in determining the time required for the protected phase. This provides a more conservative approach. A number of observations may be made about the single lane analysis on Figure 2-1. First, the roundabout exhibits clearly superior performance (i.e., lower delay per vehicle) in comparison to all other modes up to a total entering volume of approximately 2000vph. Roundabout delays remain below 10 seconds per vehicle up to this point. The TWSC choice is clearly the least attractive (1300 vph capacity) in this example, but this should come as no surprise, since TWSC is not well suited to 14

PAGE 27

situations with heavy cross street volumes. For stop-sign control, higher capacities (up to 1800 vph) can be achieved with A WSC than TWSC. Note that the roundabout delays are always lower than A WSC delays, indicating that A WSC performance is never superior to a roundabout at any volume level. The signal without left turn bays offers performance similar to A WSC. The signal delays are slightly higher at low volumes and slightly lower at high volumes, with the crossover point at about 1100 vph. Roundabout delays are always lower in comparison to signals without left turn bays. The signal with exclusive left tum bays offers the most logical alternative to the roundabout in terms of space requirements. At volumes below 2000 vph the roundabout exhibits substantially lower delays. Above 2000 vph, the roundabout delays exceed the signal delays and increase rapidly up to the capacity of about 2400 vph. The two phase signal also reaches its capacity (i.e., one left tum becomes saturated) in the same 2400 vph range. Above this point, the signal offers the only alternative that will operate within its capacity. This, of course, requires left tum protection which increases the unit delay. Three phase operation is shown to function within capacity up to about 3000 vph and four phase operation finally breaks down at about 3500 vph with delays in excess of 70 seconds per vehicle. The comparison shown in Figure 2-2 for the two lane case is simpler because there are only two alternatives to examine. In this case the signal configuration most comparable with the space required by a two lane roundabout is one in which each approach has two through lanes and an exclusive left tum bay. Because of the higher traffic volumes to be accommodated, all left turns will be assumed to have protected plus permitted phasing. 15

PAGE 28

The comparison of delays for the two lane case closely parallels the single lane case. The roundabout offers substantially reduced delays up to its practical capacity, in this case about 3700 vph. Between the practical capacity and the possible capacity (4000 vph) the unit delay nearly doubles. The single delay even at the lowest volumes is greater than the roundabout delay at the practical capacity. The signal delay is approximately the same as the roundabout delay (about 20 seconds per vehicle) at the possible capacity of the roundabout (i.e., 4000 vph). The signal continues to function within its capacity up to 5800 vph, although the total delays approach 70 seconds per vehicle. The equivalent stopped delay corresponding to 70 seconds per vehicle total delay is approximately 54 seconds per vehicle. This corresponds to the upper range of level of service E, which is consistent with the expectation for a signal operating at capacity. 2.6 Justification Categories Seven reasons to select a roundabout as the most appropriate form of traffic control. To provide an organized approach to the justification process, a series of categories has been developed, each of which represents a good reason to install a roundabout. These categories are summarized in Table 2-1 in terms of their anticipated relationships to warrants contained in the MUTCD and Highway Capacity Manual (HCM) levels of service. 16

PAGE 29

TABLE 2-1 ROUNDABOUT SELECTION CATEGORIES AND JUSTIFICATION CONDITIONS CATEGORY AND AWSC AWSC SIGNAL SIGNAL NUMBER CONDITIONS FOR DESCRIPTION WARRANT LOS WARRANT LOS OF LANES JUSTIFICATION MET MET COMMUNITY Typically applied In commercial ENHANCEMENT NIA N/A N/A N/A 1 and civic districts. Aesthetics are Important Primarily a residential application. TRAFFIC CALMING NO A NO A 1 Demonstrated need for traffic calming. Existence of safety problem SAFETY NIA N/A NJA NIA NIA which would be aleviated by use IMPROVEMENT of a roundabout intersection treatment AJ...L-WAY STOP YES B-0 NO A-B 1 Delays should compare favorably AJ...TERNATIVE with AWSC. LOW VOLUME Delays should compare favorably SIGNA!. YES 0-F YES A-C 1 AJ...TERNATIVE with signal. MEDIUM VOLUME Delays should compare favorable SIGNAL YES F YES 8-D 2 with signal. Other justifying AJ...TERNATIVE factors required. SPECIAL CONDITIONS such as unusual geometries, YIN NIA YIN NIA 1-3+ Site specific justification required. high volumes, right-
PAGE 30

3. Accidents at Roundabouts 3.1 U.S.A. Research Aimee Flannery, a research assistant at Pennsylvania State University has conducted a recent accident study by collecting traffic and crash data for existing roundabouts in the U.S.A. She then performed a statistical analysis to determine the effectiveness of roundabouts as a treatment for intersecting roadways. ( 17) General information regarding thirteen roundabouts located in Maryland, Florida, Nevada and California was collected. In addition, six retro-fitted roundabout sites with accident data ranging from 1 to 3 years before and after were analyzed. In all but one case, the reduction in accidents for roundabout sites was in the range of 60% to 70%. A chi-squared test and a normal approximation test were performed using the accident data from these six roundabout sites. Both of these tests indicated a significant difference in the frequency and mean of accidents at 95% and 99% confidence levels, respectively, between pre-roundabout and post-roundabout periods. (17) 3.2 British Research A very important study dealing with personal injury accidents at 4-arm roundabouts was reported by Britains Maycock and Hall (1984) in Laboratory Report (LR) 1120. Data for a sample of 84 roundabouts in six categories were assembled by Southampton University, as shown in the following Table 3-1. 18

PAGE 31

Table 3-1 Numbers Of Roundabouts In The Sample By Intersection Category Junction Category Small island roundabout >4m Conventional roundabout Conventional dual-roadway roundabout TOTAL Speed Limit Group 30-40 mph 50-70 mph 25 11 11 14 84 11 12 During the course of the accident sampling period (six years 1974-79), some 67 roundabouts remained unchanged in design. Data from Police accident reports of accidents within 20 m of each roundabout was used. Traffic flow data was mainly 16 hour classified turning counts at each site. Nearly all those in the 30-40 mph category included pedestrian flows. Detailed layout data and the characteristics of each approach were recorded for all roundabouts in the sample, and included inscribed circle diameter, central island diameter, road class, roadway type, gradient, approach speed limit. Arm-specific data included, entry path curvature, entry width and flare dimensions. (12-p.45) The data and results of analysis are presented in Britains LR (Lab Report) 1120 in 24 tables. These include accident frequencies, and severities and rates by roundabout type. The accidents were further analyzed by type and by road user involvement (bicyclist, motorcyclist, pedestrian, etc.) The accident frequencies by type were related to traffic flow and roundabout geometry, using regression methods. Equations were also developed to enable roundabout accidents to be predicted for use in design and appraisal. Only the chief influences on design are shown below. 19

PAGE 32

Some of the main findings were: 1. The distribution in time of the accidents in the sample generally reflected the Britain national pattern. 2. The average accident frequency (ofthe sample) was 3.31 personal injury accidents per year, 16% of which were fatal or serious. 3. The average accident rate per 100 million vehicles passing through the intersection was 27.5. 4. Small roundabouts in 30-40 mph zones, had both higher frequencies and rates than other roundabouts. 5. The analyses of accidents by type, showed that the pattern at small roundabouts was different from that at conventional roundabouts. More than 2/3rds (71 %) of accidents at the former were entering/circulating but those at the latter were divided evenly between entering/circulating, approaching and single vehicle accidents. 6. All roundabouts had high involvement rates for two wheeled vehicles. The rates per 100 million road user class were about 10-15 times that of car occupants. At small roundabouts, bicyclists were particularly (14 times) more vulnerable than cars. 20

PAGE 33

3.3 Accidents Fall As Roundabouts Spread To Other Countries Around the world, accident rates are falling as roundabouts spread. The Netherlands achieved a 95-percent reduction in injuries to vehicle occupants as many conventional intersections were replaced by modem roundabouts. (12-p.48) The fatality rate in the Unites Kingdom is about half the rate in France 5000 in the United Kingdom compared to 10,000 in France. The difference is partially attributed to the use of roundabouts since the French and British population and their number of motor vehicles are about the same. (12-p.48) In France, where roundabouts were installed mostly in urban areas and their suburbs including residential areas, the safety of roundabouts was generally superior to signalized intersections, except where the roundabouts were large with wide entries or where there was extensive bicycle traffic. The accident rate on rural roads was clearly better for roundabouts than for major/minor intersections regulated by stop or yield signs. The average rate of reported injury accidents per 100 million vehicles entering major/minor intersections was 12. This was three times higher than the rate for roundabouts where there were only four accidents per 1 00 million vehicles. ( 12-p.48) Numerous one or two lane roundabouts have been built recently in Germany, but several large old style traffic circles remain. Researchers investigated 14 circular intersections and 14 non-circular intersections. The number of accidents per million vehicles were: 21

PAGE 34

Old Traffic Circles Signalized Intersections Smaller Roundabouts 6.58 3.35 1.24 The most extensive roundabout accident analysis in Norway was conducted in 1990. Accident records from 1985 to 1988 at 59 roundabouts and 124 signalized intersections were examined. The comparative accident rates, in numbers of reported accidents per hundred million vehicles, are given below: Number of Legs 3 4 Roundabouts 3 5 Signalized Intersections 5 10 Besides safety benefits, other advantages to roundabouts were demonstrated. Speed reduction, moderation of traffic flows in favor of through traffic, use of the central island to mark the transition from one class of road to another, and improved capacity are "products" of roundabouts. (12-p.SO) Studies of British mini-roundabouts, which often have two-or three-lane entries even though the central islands are less than 4 m in diameter, indicate that larger roundabouts are generally safer. However, recent studies of mostly one-lane mini roundabouts in continental Europe found a lower accident rate at mini-roundabouts than at larger roundabouts. (12-p.SO) Studies in Switzerland and France identified the following benefits of mini-22

PAGE 35

roundabouts: Flow improvements. Reduction of conflicts/accidents. Reduction of speeds upstream, through, and downstream ofmini-roundabouts. Adherence to the yield-at-entry requirement. Reduction of noise (as a result of the reduction of speed). Heightened awareness of drivers as they were forced to reduce speed. 3.4 Safety Of Roundabouts For Pedestrians And Bicyclists While modern roundabouts have long been considered safe for pedestrians, the record for bicycles and motorcycles has been mixed. According to one study in the United Kingdom, 15 percent of all intersection accidents in 1984 involved at least one bicyclist, but 22 percent of all roundabout accidents involved at least one bicyclist. (12-p.51) In contrast, British mini-roundabouts do not appear to be particularly dangerous for bicyclists. A survey in 1989 of mini-roundabouts in England, Scotland, and Wales, found that the crash involvement rates of motorcycles and bicycles in 50-km/h speed zones was about the same for four-leg signalized intersections. However, the rate for cars at the mini-roundabouts was much lower than at the intersections: ( 12-p.51) 23

PAGE 36

Crash Involvement Rates (per 10 million of vehicle type) Signalized Intersection Mini-roundabout Bicycle 175 189 Motorcycle 240 237 Car 48 27 Contrary to the British experience, a recent study in the Netherlands of 181 mini roundabouts that were converted from threeand four-leg intersections found injuries to bicyclists decreased on average from 1.30 casualties per year to 0.37 casualties per year-a 72 percent reduction. (12-p.53) In Europe, bicyclists at roundabouts were handled in one of three ways: bicyclists mix with motor vehicles, bicyclists have a separate lane, or bicyclists have a separate bike road. The bike road provided the best protection for cyclists, and perhaps surprisingly, the bike lane was the least safe option because this design requires the motorists and bicyclists to cross paths. (12-p.53) 3.5 Accident Investigation in France In 1990, 202 accidents were investigated at 1 79 urban roundabouts in France. The following table shows the relative frequency of the different causes of these accidents. 24

PAGE 37

Table 3-2 Causes Of Roundabout Accidents In France Cause of Accident Entering traffic failing to yield to Circulating traffic Loss of control inside the circulatory roadway Loss of control at entries Rear-end accidents at entries Sideswipe, mostly at two-lane exits with bicyclists (two of three) Running over pedestrians at marked crosswalks, mostly at two lane entries Pedestrians on the circulatory roadway Loss of control at exits Head-on collision at exits Weaving inside the circulatory roadway Percent of Accidents 36.6% 16.3% 10.0% 7.4% 5.9% 5.9% 3.5% 2.5% 2.5% 2.5% The major design recommendations derived from the above study are: Ensure motorists recognize the approach to the roundabout Avoid entries and exits with two or more lanes except for capacity requirements Separate the exit and entry by a splitter (ghost) island A void perpendicular entries or very large radii A void very tight exit radii A void oval-shaped roundabouts 25

PAGE 38

A study of roundabout lighting in France found that nighttime accidents are relatively rare and most accidents involve property damage only. The study recommends that lighting design should be based on a perception process: remote perception at about 250 m, approaching perception at about 100 m, and entry perception at the entry. Figure 3-1 below shows the estimated number of accidents at X-intersections and roundabouts for specific average daily traffic. (12-p.55) c.: c !:3 c OJ -o ;::; u <( >.. L :::1 'C' -o c ... :'1 ... u.. .... 0 L OJ ..0 E ::J z Figure 3-1 2.5 30k Total entering ADT 2 1.5 Stop Control -----8.2k Total entering ADT 0.5 0 0.1 0.2 0.3 0.4 ADT Ratio (MinorfTotal) 1-+-X-lntemction 4Estimated number of accidents at X-intersections and roundabouts for specific average daily traffic. source (15) 26 0.5

PAGE 39

4. Theories of Capacity and Delay 4.1 Introduction Apart from the application of personal experience, theories of capacity and delay fall into four groups: Deterministic Statistics Probabilities Simulation Whatever theories underlie the basis of roundabout design, the results will be judged on whether they offer a practical design tool to the highway or traffic engineer, and whether the resultant roundabout layouts operate safely as predicted, within a reasonable range. Deterministic ideas are not of great importance. These may simply be the opinions of practitioners laid down as rules, for example roundabouts, should be used only on routes of certain traffic flow and be of a certain minimum size, roadway width, etc. These rules may involve invalid assumptions of traffic behavior, but can be useful in the absence of a theory based on systematic collection of data, and validated by measured observation. However, in the design process, many details which cannot be satisfactorily modeled are often determined by "what is reasonable", or appearance. 27

PAGE 40

In Great Britain early "rules" of roundabout design for which there was no proof were: 1) A large roundabout will cany more traffic than a small one of similar shape; 2) The capacity depends on but is not proportional to, the minimum width of the roadway around the central island; 3) The greater the "weaving length" or the smaller the angle of approach of weaving traffic streams, the greater is the capacity. As there was no entry priority and roundabouts were previously designed for the weaving movements of vehicles on the circulatory roadway, these assumptions were not unreasonable. 4.2 Statistical Theories The development of statistical theories depends on a pre-existing stock of roundabouts from which satisfactory sample data can be drawn (It is notable that in countries where large samples are not available, more reliance is placed on other theories). The statistical approach consists in measuring some variables on a sample of intersections so as to relate one variable to others, and then to use this relationship as a predictor. The variable to be explained is usually capacity, but waiting times, delays or queue lengths and accident frequency can also be estimated in the same way. This approach to roundabout capacity estimation is used notably in Great Britain, but is also currently used or being investigated in; France, Germany, Israel. Norway, and Switzerland. 28

PAGE 41

4.3 Probabilistic Theories -"Gap Acceptance" Both gap-acceptance and simulation techniques were mainly applied to non roundabout intersections but more recently, have been applied to roundabouts. When the "gap acceptance" theory is applied at roundabouts, the major flow is the circulating flow, in which randomly spaced gaps occur. If these gaps exceed a certain minimum value (usually fixed, although more comprehensive theories allow for a frequency distribution of minimum acceptable gaps) they are entered by one or more vehicles from the waiting minor flow on the approaches. Theories of gap acceptance are intrinsically passive in the sense that circulating traffic is assumed not to react in the presence of entering traffic. At roundabouts, (unlike other intersections, except possibly during periods of congestion) the entry process is somewhat more interactive than gap-acceptance assumptions allow, with gap forcing and priority reversal aspects, and it is difficult to say whether the gaps are naturally accuring or are modified for, or by, the entering vehicle. Therefore, although gap acceptance is an important element, it is unlikely to be a complete and sufficient determinate of capacity. The theoretical gap acceptance model of capacity for roundabouts have been developed from those for other intersections. These require two parameters: "a" critical gap in the major flow (also "s", "t", or "tg"). This is the useful minimum gap. 29

PAGE 42

"f' follow-up (move-up) time or headway (also "tf', "P"). The gap required behind a minor departing vehicle (and the next major vehicle) for a vehicle waiting second in a queue. This is usually assumed to be constant and often estimated as 0.6a. Critical-gap values vary, depending on the maneuver to be made ie. left-tum, right tum, through, and the size of the intersection. They also vary with size of urban-area or rural conditions, gradient, traffic flow and the psycho-physical state of drivers. Heavy vehicles need greater critical gaps and headway. Corrections (and pcu equivalents) are made to represent these and averages can be found for these corrections which are applicable to local areas. Assumptions are gap-acceptance and distribution ofheadways; results are capacity, waiting times and various probabilities. The critical gap for various maneuvers (and the average minimum headway,) is also influenced by; vehicle type dimensions, weight, engine capacity and acceleration ability. There will be national and local differences, for example, in Czechoslovakia, where passenger cars were small low powered and with relatively slow acceleration, both parameters will be large, (typically 5 to 10.5 seconds), and this would result in a generally lower capacity for a given layout than in, say Great Britain. There will also be variations over time which can affect all capacity measurements. Gap acceptance methods of roundabout capacity estimation, delay, (and in some cases risk analysis) are used in Australia and Sweden. They are used, or have been 30

PAGE 43

investigated, in others including; Czechoslovakia, France, Israel, Germany, and Great Britain. 4.4 Simulation Methods In an attempt to overcome the multiplicity of theoretical problems inherent in gap acceptance approaches "simulation" methods of capacity evaluation are becoming more popular to model traffic streams and driver behavior at intersections. A comprehensive vehicle by vehicle "model" of the entry/circulating flow relationship should include all ofthe various mechanisms ofvehicle-vehicle interaction, separately identified. In 1980 Kimber thought it was not feasible in practice to construct such a model because of the complexity of ( 1) separating the mechanisms observationally, 2) determining their relative importance from site to site and 3) relating a parametric description of each to geometric details of layout. Simulation techniques, involving complex computer programs have been developed in the last decade, which require considerable computing power. These are used in a number of countries to model behavior at non-signalized intersections but only some have been adapted to roundabouts. With the general availability of powerful micro computers, the earlier role of simulation models of entry capacity, delay and accident risk, is changing from an instrument of scientific research, towards a practical tool for the traffic engineer. However, there is considerable potential for refinement and simplification of these models for roundabouts, and they are likely to be applied in new or exceptional circumstances rather than routine ones. Simulation models have 31

PAGE 44

been developed or investigated in Australia, France, Germany, Great Britain, and Switzerland. 32

PAGE 45

5. History In The Development of the Capacity Formula 5.1 Introduction In Great Britain the roundabout has been a popular form of road intersection for many years and has also long been recognized as the safest of intersection types. Roundabouts have a wide range of application both in rural and urban areas, and can be found on all classes of road from highway intersections to private accesses, often being used to replace major/minor intersections and sometimes replacing traffic signal controlled intersections. They range in size from mini's with a painted center spot of 1 meter diameter to those with central island diameters well in excess of 100 meters. There must be several thousands of roundabouts in Great Britain but it is impossible to give a precise figure. The number on rural trunk and principal roads in England is in excess of 1000. A survey of mini roundabouts was conducted in 198889, from which it is estimated that there were 1600 ofthat type on public roads in Great Britain. Design practices (including efficiency, user cost and safety), have been subject to much scrutiny for some three decades, and the methods now used incorporate the results of a continued program of major research studies. These have been aimed at producing sound practical design methodologies for practicing traffic engineers, as opposed to academic models that are difficult to apply. Many of the research reports include design procedures and interpretation advice. Prior to 1966 in Great Britain there was no defined priority at roundabouts between entering and traffic already on the circulation roadway. The basis of roundabout 33

PAGE 46

operation at that time was that entering traffic merged with circulating traffic along a "weaving section" downstream of the entry and capacity was governed by its limiting flow. Pre-war rural and suburban "arterial" road designs for roundabouts were circular. Size was determined solely by experience of the authority and the circular roadway was generally as wide as the entering road. An early example of the empirical approach used in Great Britain for the estimation of roundabout capacity was given by Clayton in 1941. In a further paper in 1945, taking account of additional data, he observed that "insufficient data were available upon which to base a scientific analysis but some empirical rules could be devised". These had minimum support from experimental observations and therefore, were only deterministic assumptions. Clayton's formula for roundabout capacity estimation was superseded by Wardrop's, which was based on sufficient data from full scale tests oftraffic capacity on experimental ''weaving sections" in 1955-56. (1-p.62) Subsequently to the introduction of the give-way rule for entry to roundabouts in Great Britain in 1966, roundabout entries functioned in some respects like one-way T-junctions. By removing the problem of instability, the rule enabled smaller and more efficient roundabouts to be developed. This made it feasible to use roundabouts much more extensively. Changes were initiated to typical entry geometry such as, having strongly deflected traffic paths, oblique entry, and often extra lanes at entry. (1-p.62) Capacity estimation became a two stage process. 34

PAGE 47

1) entry capacity was to be determined as a function of the flow in the priority stream crossing each entry 2) the inflow from each entry must be calculated. Since this depends on the priority flow, which in tum comes from the previous entries, the problem of predicting the average balance of inflows from all the entries is an interactive one. Intensive studies were conducted at the Transport and Road Research Laboratory in the late 1960s to determine by observation of at-capacity operation with queueing in the approach, the relation between intersection layout and the entry capacity expressed as a function of the priority stream flow. In all, 122 intersections were studied on the public road and about 40 on the test track. The public road capacity data amount to some 1700 minutes and include observations on about 0.75 meter vehicles. The current Great Britain approach to roundabout design is strongly empirical, and rests on the primacy of directly measured quantities-capacity, delay, accident rate-and the importance of ensuring that models and relations stand in clear correspondence to them. (1-p.63) 5.2 Capacity Estimation of Roundabout Weaving Sections Before 1966 Standard circular roundabouts were recommended in 193 7. In 1941 Clayton suggested empirical values for a "weaving factor" for roundabout capacity design, derived from traffic signal theory and saturation density for a weaving section. He conceded that the difficulty of checking these with actual traffic densities, was that few if any roundabouts were working to capacity, except perhaps Trafalgar Square. 35

PAGE 48

In 1945 Clayton commented on the difficulty of applying standard designs at actual intersections which varied considerably in size and shape, and that non standard amendments sometimes suffered operational difficulties. To resolve this problem, he developed a formula for the capacity prediction of a weaving section, of smaller 4 arm roundabouts using the contemporary empirical formula available for traffic signals, and data from roundabouts in London. An arbitrary measure "maximum weaving angle" was related to circulating traffic density as a "weaving factor". The results were adapted for roundabouts of various sizes: T = S { La190 ( L-413 ) } where S =the saturation density of traffic, taken as 1200 veh I hr I lane. L = the number of entry traffic lanes a = the maximum weaving angle or T = Fw L S where F w is the weaving factor This was applicable to a roundabout with any number of entries and shape, the total capacity of the roundabout being double that of the shortest side. It was taken from this that, within limits, and if the most suitable roadway width was used, the capacity of a roundabout was roughly proportional to its size. Clayton suggested that an upper limit to capacity of a roundabout (however large) was 7,500 veh I hr (plus bicycles), or little more than the pre-war volume at Hyde Park comer. (1-p.64) 36

PAGE 49

Tables produced from the application of Clayton's formula were subsequently incorporated in the advisory manual "Design and Layout of roads in Built Up Areas" of 1946, as the basis of the recommended Design procedure for roundabouts. The capacities of 4-arm roundabouts were given but where there were alternatives, a larger island was preferred. The capacity to be provided was to be 1.33 the estimated volume. In addition to the benefits of long weaving lengths, a virtue was made of asymmetrical designs that fitted into whatever shape of site was available. Although the "ideal" shape of a (rural) roundabout prior to this time was considered to be circular, designs were forced into square or rectangular shapes which appeared to be very suitable for urban sites. Later Clayton refined this formula to extend its theoretical validity and tested it with additional data. The weaving factor F w was expressed as a function of the proportion of weaving traffic ( p-ratio of smaller weaving stream to total traffic), the angle of convergence a (degrees) and the width ofthe weaving section w (ft) giving: (1-p.64) F"' = 1 -k a/90 ( 1 40/3w) where k = 2/3 ( 1 + 2p ) in the original version based on US data, but 8/9 ( 1 +p/2 ) in a revised version taking account of tests carried out at in 194 7 at the then Road Research Laboratory. While there were still insufficient observations to establish a definite relationship, nevertheless Clayton felt that those available did appear to support his quas-37

PAGE 50

theoretical rule. This was the basis of roundabout design in Great Britain until the late 1950s. (1-p.64) 5.3 Test-Track Weaving Experiments In 1947 the Road Research Board Laboratory of the Department of Scientific and Industrial Research (DSIR) (subsequently to become the Road Research Laboratory, and later the Transport Research Laboratory), began a study of weaving sections, using the large surface area available at Norholt Airport. 45 vehicles were used, running at pre-determined speeds in two or three columns which weaved across one another on a section 250 ft (76 meters) long by 24 ft (7.3 meters) wide. By the mid 1950s, other research had been carried out leading to disagreement on the maximum capacity of a weaving section. Opinion varied from 1500 vehlhr to over 5000 vehlhr. Clayton's results conflicted with the information from the US Highway Research Board, and Shrope where the effects of some important factors had not been measured. Wynn, Gourlay and Strickland, had obtained useful data on weaving and merging traffic but these had not been related to roundabout capacity. Friedrich and Grabe had given some semi-theoretical values for roundabout capacity, but their assumptions about behavior in the weaving section were very arbitrary. (1-p.64) In 1955 in the absence of reliable information further large scale experiments were carried out at Northolt using 130 vehicles circulating continuously through a single weaving section up to 300 ft long and 50 ft wide. It was thought to be the first such full scale test-track experiment to investigate traffic behavior. The vehicles included double decker buses, medium and heavy commercial vehicles, light vans, cars, 38

PAGE 51

motor-cycles and taxis. Groups were formed to interweave from different directions with sufficient numbers circulating to constitute moving queues at entry. Whatever the value of the mean flow its standard deviation was found to be 120 vehlhr. The dimensions of the section, traffic mix and weaving properties were varied for each test of 1 0-12 minutes over four days, during which the weather also varied. Observations included filming from a tower wagon. It was found in wet weather that the maximum flow through the weaving section was reduced by about 1 0%. In further track experiments in 1956, varying the number of vehicles taking part, the maximum flow in the weaving section increased by about 5% up to 3250 vehlhr which was considered an "ultimate capacity". A major difference from real roundabout operation was that since the test-track section was open ended there was no danger of blocking back from an adjoining weaving section, and this was to prove critical. ( 1-p.65) Taking the results from the test-track experiments Wardrop used a method of successive approximation to establish a mathematical relationship between the capacity, and the traffic and geometric variables. Comparison with existing roundabouts showed reasonable agreement and the results were published in 1957. The formula was further modified expressing the maximum flow in pcu and treating the ratio 211 in a more logical manner: Qm = 1 08w (1 + e/w) (1 -p/3) p.c.u. per hour (1 +w/1) 39

PAGE 52

where Qm = maximum flow through weaving section (dry weather no bicycles) w =width of weaving section (ft.), range 20-60 e =average of entry widths (ft.), range (e/w) 0.4-1.0 1 =length ofweaving section (ft.), range (w/1) 0.12< 0.4 p =proportion of weaving traffic to total traffic in weaving section, range 0.4 1.0 Its prediction was good compared with the data, but one difficulty was that in practice the simple design used in the tests could rarely be applied and "effective dimensions" were used. A further difference was that in practical roundabouts interaction from other weaving sections caused blocking and therefore, the comparisons with smaller roundabouts were not good. Since all roundabouts were in danger of locking at the observed flows it was concluded that it was not necessarily safe to use the results of the test-track experiments to determine the capacity of a complete roundabout. It seemed a reasonable assumption that the maximum flows would not be exceeded in a complete roundabout, and therefore, a practical capacity was taken as 80% of the "ultimate capacity given by the formula, ie. The term 1 08w in the dividend of the above formula became 86w. However, as long as there was no rule governing priorities at roundabouts, even this capacity could frequently not be sustained in situations involving heavy traffic, and "locking" was prevalent. (l-p.66) Wardrop's work on the capacity of weaving sections was incorporated in the Ministry of Transport's Advisory Memoranda "Urban Traffic Engineering Techniques" (UTET) 1965, and "Roads in Urban Areas" (RUA) 1966, for the 40

PAGE 53

capacity design of roundabouts. The recommendations included the effects of interaction between weaving sections and weighting for vehicles operating m different circumstances and weaving sections could be designed from nomograms based on the "Wardrop" formula. There were distinct differences in the effects of two wheelers and goods vehicles on capacity at roundabouts and traffic signals. Roundabout design was to be "generous" and the designer was not to be "wedded to geometrical shapes such as a circle for the central island", although it was recognized that the "dead areas" on roundabouts was an indication of poor design. In effect this continued the trend from 1945, producing great variation in the effectiveness of designs but some, by chance favorably constrained by their sites, were later to be easily improved to a modern layout. (1-p.67) 5.4 Experiments After The Change In Priority Rule, 1966 The introduction of the "give way to traffic from the right" rule at roundabouts made a significant contribution to the efficiency of roundabouts in Great Britain and it was evident that smaller roundabouts which previously had been prone to locking, were working well. With offside priority operation, entry was controlled by the ability of entering drivers to detect and utilize gaps in the circulatory flow round the island. It meant that section length was no longer a significant factor in controlling capacity; entry width was of paramount importance, since in theory the entry capacity of a section increased with the number of entry lanes provided. This lead to a series of experiments by TRL in the late 1960's to find ways of making better use of the area available at junctions in order to increase their capacity. Full scale test-track experiments, were reported by Blackmore in LR 356 1970. ( 1-p.67) 41

PAGE 54

With any method of intersection control, the highest capacity in a given area was achieved by layouts providing the greatest width for each movement, particularly at the point of entry to the intersection. The highest capacity for roundabouts was obtained by layouts with marked deflection to the left on entry, and a very small central island. The deflection was found not only to improve circulation and reduce congestion but also to control the speed of entry to a safe level. A simple maximum capacity formula was found to apply generally to intersections regardless of shape, layout and method of control. (Subsequently known as the Full Capacity "Blackmore" Formula): (1-p.68) q=k(2:w+ -fa) where: q, is the capacity in pculhr.; k, is the efficiency coefficient; 2:w, is the sum of the roadway widths in meters, used by traffic in both directions to and from the intersection; a, is the area in square meters of widening ie. The area within the intersection outline, including islands, lying outside the area of the original roadway intersection. The capacity given by the above formula with k = 100 can be regarded as the potential capacity obtainable in a given sized of intersection under the almost ideal 42

PAGE 55

conditions of the experiment and an optimum curb outline. At most intersections on public roads the capacity to be expected would be appreciably lower, ie k < 100. In H. 7/71 : 1971 values of k were given for new layouts of roundabouts with average site conditions, of: 80, for 3 way intersections; 70, for 4 way intersections and 65, for 5 or more way intersections. Capacity in normal peak conditions was to be taken as 80% of these. At mini roundabouts at constricted sites with central islands less than 4m (restricted to 3 way intersections), it was suggested that these factors may overstate the capacity, and a k value of70 was to be used. (1-p.68) 5.5 Further Developments of Capacity Formula After 1966 During the experimental period for roundabouts with new layouts, (approximately 1967 72), the method of calculation of capacity of roundabouts officially to be used at that time (ie Wardrop's), was contained in Urban Traffic Engineering Techniques and in the design manual Roads in Urban Areas) then recently published. However, many of the smaller roundabouts constructed after the 1966 change in the priority rule for roundabouts, had geometric proportions outside the limits of that method. The conventional design specified a maximum width/length ratio for the "weaving section", therefore, increasing the section width to increase capacity often required an increase in section length. Thus the higher the traffic demand, the longer the section length had to be. It was increasingly apparent to practitioners that this, and the use of minimum radius to achieve longer effective weaving lengths within the available land, was producing roundabouts that did not relate to the desired paths of vehicles. The observed capacity of such roundabouts also did not meet the design capacity, in some cases being only 1'4 of it. This was shown by "dead areas' or those 43

PAGE 56

untrafficked surfaces of roadway which collected debris, and were particularly obvious after a light fall of snow. These revealed that although bicyclists used them, the flanking (ie. Left turning) traffic was not able to keep to the curblines, and encroached on the "weaving" lane, constricting its effective width. Various modifications of design were suggested by Bapat, incorporating transition curves, leading to central islands more circular in shape. This reduced the "weaving length", which was supposed to be the key to roundabout capacity, but observations at modified roundabouts showed that capacity actually increased. (1-p.69) By 1970 it was clear that the experimental small island roundabouts on public roads with central island diameters of about 14 m. were observed to have equal or even higher traffic capacity than larger roundabouts with more conventional radii and weaving lengths. It was suggested that it would be cost beneficial if these could be provided initially as at-grade roundabouts on road schemes where eventual grade separation was likely. Further work by Ashworth and Field, and Murgatroyd, reported in 1973, showed that the proportion of weaving traffic used in the Wardrop formula had no influence on capacity under priority rule and an alternative design procedure or revised formula was called for. Murgatroyd used linear regression analysis to show that a new design capacity Qd, could be written: (1-p.69) Qd = 90w (1 + e/w)1100 (1 + w/1) He also found that other effects such as pedestrian flows, poor signposting and the absence of helpful road markings, could reduce roundabout capacity by up to 50%. 44

PAGE 57

Other evidence from studies of roundabout modifications by local authorities, eg. Teeside, Attwood 1973, suggested that long weaving lengths were not very effective but concluded that a weaving formula design had not been made redundant by the priority rule. ( 1-p.69) In the early 1970's, further experimentation with new types of roundabout continued on public roads. These initially concerned the reduction of central islands and widening of approaches, but at some larger roundabouts many alternative layouts were tested from 1972-74, which were described by Blackmore and Marlow in 1975. The thrust of these experiments was to compare capacities of different layout types and geometry including: different diameters of central island; circular roadway width; and widening or flaring of approaches. In addition large roundabouts were also converted to "ring" intersections using traffic signals or mini roundabouts. The experiments had indicated that entry width might be more critical than "weaving length" and also suggested the importance of geometrical features of roundabouts concerning capacity and safety. In 1975 the Department of Transport (DOT) Technical Memo. H.2/75 was issued, in which the full capacity "Blackmore" formula, was to be used for small, mini and double roundabouts; but on the basis that the proportion of weaving traffic made no significant contribution to accuracy (although the concept of weaving at roundabouts was questioned), a "Modified Wardrop" formula was to be applied to "conventional", ie larger roundabouts: (1p.69) Q r = 160 (1 + e/w) veh/h 1 +wL 45

PAGE 58

where w =width of weaving section (meters), e =average width of entries to weaving section (meters), L =length ofweaving section (meters). Weaving lengths were to be shorter and wider. The formula was based on observations at actual roundabouts within the ranges: w-9.1m to 18m; e/w0.63 to 0.95m; w/L0.16 to 0.38; e1/e2 0.34 to 1.14 It was considered that the formula would hold for variables lying a little outside the above values, if the design could not be made 85% of Q P Arbitrary deductions were to be made to capacity for entry angles less than 30 Y2 and for exit angles more than 60 Yz, The "conventional roundabout was recommended for larger new intersections or major improvements, and was seen as appropriate for two or three level, grade-separated non free-flow intersections. (1-p.70) 5.6 The Search For A New Capacity Formula The result of the modified "Wardrop" formula (applied in H2/75), was to substantially reduce the practical capacity for typical roundabouts, compared with the previous formula. The recommended shape was no longer to be square with minimum radius, but circular if possible. However, the approaches were not widened, and with the limitations of width, the use of the modified formula still forced larger( conventional) roundabouts into longer weaving lengths. It was not a 46

PAGE 59

satisfactory replacement for the capacity of entries for larger conventional roundabouts, and there was still a distinction from smaller ("offside priority") roundabouts in the approach to their design. At the time it was recognized as only an interim measure, since Blackmore's full capacity formula was too coarse a measure for the purpose of engineering design and economic assessment. What was required was an entry by entry assessment allowing for the effects of geometry. In 1976 full scale track experiments were carried out by TRL to obtain data for a new capacity formula for "conventional' roundabouts. ( 1-p. 70) The search for a completely new capacity formula was reported by Philbrick in 1977. This centered around the fitting of a linear relationship between traffic entering a roundabout from a saturated approach and that already in the circulating roadway. Regression techniques were used to include geometric effects in the relationship .... 'it> I I I Figure 5-l Dimensions and flows (LR. 773) source (2) 47

PAGE 60

The most successful attempt was the simplest, with total entry capacity Qe being related to the total circulating flow, Qc (in pcu/h). Over the observed flow ranges this could be regarded as linear. Using regressiOn techniques, the equations predicted the "weaving" section capacity with less residual between-sections variation than the original Wardrop formula and were much more successful at predicting the within-sections variation of Qe and Qc. The equations were: Entry Capacity, Qe = F-fc Qc pcu/h Where F = 233e1 (1.5 11 ) 255 efu!h, pcu) fc = 0.0449 (2e1 -w) + 0.282 Qc = circulating flow in pcu/h (1 efu = 1 entering The derived heavy vehicle pcu value was 2.00, and the ranges of the parameters in the data used were: e1 4.0 to 12.5m; (2el -w)-2.5 to 9.5m; e1 I sr1 0.74 to 3.30; Qc 580 to 3890 pcu/h This was applied to the design of "conventional' roundabouts in TE Design Note No.1 issued by the DOT in 1978 as an interim measure, pending a full revision of the 48

PAGE 61

Technical Memorandum. However it was 1981 before this holding position could be replaced. source (6) 4000 ,....., ... SECTION M ...... ... 3000 ..c ...._ :::J u a. 2000 QJ a 1000 ........... -----Revised .. ... -New formulae Regression line to observed data ..... .............. .........___ .............. ....... t-. '-..... ........... .. ....... ...... ....... 0 ...... 0 1000 2000 3000 4000 Oc (pcu/h) Figure 5-2 Sample comparison between "revisedWardrop" and "LR 773 ",formula During the same period other possible approaches were sponsored by TRL including a gap acceptance method by Ashworth ad Laurence and that of McDonald and Armitage at Univ. of Southampton, England. This also was similar to gap acceptance method, but based on the concept of "saturation flow" and "lost time", as at traffic signals (which was also the starting point for Clayton's ideas for roundabout capacity formula in 1941). Theoretical formula were developed, the most useful being: 49

PAGE 62

where q2 =entering flow (veh/s) q1 =circulating flow (veh/s) qs =saturation flow (veh/s) L =lost time (s) p 1 =minimum headway of circulating vehicles (s) Data for the study included the TRL 1976 test track and public road experiments. Each site was described by 22 simple geometric factors, time-lapse and event records. A series of empirical relationships were determined. The two parameters qs and L were estimated together by the method of least squares. Each of the capacity parameters was tested against the geometric factors using multiple regression techniques and the following relationships were thought to be the best, both in terms of statistical "goodness offit" and conceptual validity. (l-p.72) Saturation flow: q s = 0.12EO + 0.04(E1-EO) where, EO= approach width (m); E1 =entry width (m); F1 = flared length (m) Lost time. The lost time (L) associated with each group of entering vehicles was found to be related to the geometry of the approach of the circulating vehicles: L = 2.3 + 0.006K1 0.04W2 where, K1 =entry curvature (km-1); W2 =previous weaving width (m); Minimum circulating headway (p 1), proved to be difficult to predict but the best estimator was determined as: p 1(i) = 11(0.12EO() + 0.04(E1(i)) 50

PAGE 63

where, P 1(i) =mean minimum circulating headway at study entry (i) (s); EO = approach width of previous entry (j)(m); E 1 (i) = entry width at previous entry (j)(m). The relationships produced consistent results. Measured and predicted values of entry capacity showed reasonable agreement. McDonald and Armitage concluded from their study that a roundabout may be considered to operate as a series of linked T intersections at which a saturation flow/lost time concept applies. This assumes that "weaving" is not a controlling factor but rather a minor aspect of capacity consideration. Since the geometric characteristics of the study sites covered a wide range, from mini to large "conventional" roundabouts, for the latter, capacity may be best assessed by entry rather than weaving relationships. Therefore, a uniform approach to roundabout capacity design was possible. (l-p.73) 5. 7 Improved Capacity Formula It was decided to further the development of empirical models rather than pursue the gapacceptance models where there was no clear indication which of the parameters would be the best predictors of capacity. Gap-acceptance models usually predict a curvilinear relationship between entering and circulation flow but real data shows that a straight line provides at least as good a fit over the observed range of data. Great Britain observations indicate that the gap-acceptance assumption that circulating traffic does not react to the presence of entering traffic; and that gap acceptance parameters are independent of the magnitude of the circulating flow, may be false at high degrees of saturation. The approach was based on the linear relationship suggested by Philbrick between each entry and its adjacent circulating 51

PAGE 64

flow. The traffic performance of a roundabout could therefore be linked to the size and shape of its entries by means of the constants fc and F. The problem was to obtain predictive relationships whereby fc and F can be calculated from a knowledge of entry geometry. Linear regression techniques were used to construct a framework of predictive relationships for entry capacity. The experiments, analyses and development of predictive equations are described in several TRL reports, mainly, LR 773, SR 334, SR 436 and LR 942. KEY:-6 TRRL data 3000 .r:. ci. :> >-..... u ro 0.2000 ro u -a Cll > .... Cll "' .D 0 1000 0 Public road data. iOOO 2000 JlOO t.OOO Estimated capacity (v.p.h.) Figure 5-3 Observed v estimated capacities source (7) 52

PAGE 65

When the new types of roundabouts were being developed, Blackmore's work showed a strong degree of mutual interaction, this was seen as desirable in itself since it prevented over strict rules of entry from reducing the capacity. Kimber and Semmens reported on further full scale track experiments carried out in 1976, including both Mini and Small island roundabouts. The aim was to improve on the full capacity Blackmore formula, to provide entry-by-entry, capacity calculations for the purpose of engineering design and economic assessment. The track experiment was used to investigate systematically the relationship between the capacity of a roundabout entry and the geometric and traffic factors affecting it. The entry capacity, Qe, was found to be linearly related to the flow of the circulating traffic, Qc, across the entry, and equations ofthe type; (1-p.74) Qe = F-fcQc accounted for approximately 90% of the vanance of Qe, the residual vanance showed no systematic trend. The basic factors affecting the relationship were identified as: (i) the entry width, e; (ii) the circulation width, u, and (iii) the size factor, D. The best predictive equation for the entry capacity was found by; fc = 0.29 + 0.116e and F = 329e + 35u + 2.4D-135 where: e, u, and D are in meters and Qe and Qc, in vehicles per hour. The entry width e, was found to be by far the most important parameter. 53

PAGE 66

Entry flaring was found to provide sizeable traffic benefits, even for small circulating flows, increasing capacity by up to 45%. The circulation width and overall size of the roundabout had significant but small effects. The tests on entry paths on D = 15 meters roundabouts, 3 arm and 4 arm, indicated that the entry mechanism is unaffected by the geometric paths anticipated by drivers waiting to enter the intersection. ( 1-p. 75) The effect of flaring the approach width at entry was to raise the value of the intercept F beyond the value expected for the equivalent unflared entry, but to leave the slope unchanged for low and intermediate circulating flows. At higher circulating flows entry capacity was the same as for an unflared entry of width e. The maximum capacity for flared entries was obtained when the angular deflection ( 8 ) of the outer curb was slight, 1 in 2 or less, but useful improvement could be obtained with a 1 in 1 flares. (1-p.75) As the circulating flow across one entry originates from previous entries a balancing process is required to deal with a roundabout as a whole. This may be either a simple iterative algorithm (Furness) or linear programming. A computer program was developed to enable each entry to be considered in tum and to calculate all the traffic flows both entering and within the roundabout. (1-p. 75) In order to calibrate these provisional results on public roads, initially in 1977, twenty eight roundabout sites conforming with Technical Memoranda H7171 and H2175, where continuous queueing occurred for 30 minutes or more, were studied. 54

PAGE 67

This excluded large island roundabouts although a wide range of variation in geometry and traffic flows was covered, enabling the effects of traffic composition to be assessed. The study was described by Glen, Sumner and Kimber. The aim was to check the Track Experiment results in everyday conditions and develop capacity relationships suitable for design purposes. The main geometric characteristics were refined from those used in the track experiments, as follows: i) the entry width, e (m); range 4.5 -16.5 ii) the circulation width, u (m), at the point of maximum entry deflection; range 5.5 22.4 iii) the inscribed circle diameter, D (m); range 13.5 -5 8.5 iv) the average effective length, l(m) over which the flare is developed; v) the approach road half width, v(m); range 1.9-6.9 vi) the sharpness of flare, S = (e-v)l; range 0.051.98 vii) the entry radius, r (m). 55

PAGE 68

---c:::st] I I .I .I ..... 0 0 Figure 5-4 I l/2D .. : Geometric parameters Since entry capacity is affected by variations in composition of flow, pcu values were derived. The greatest variation was shown by two wheelers. 56

PAGE 69

Heavy V chicles Other V chicles Mean pcu Values (rounded) Entry 1.9 (2) 0.2 (zero) Circulation 1.7 (2) 0.8 (1) The main difference between traffic behavior on the track and on public roads, was a more efficient use of entry width on public road sites. LEGEND A Point of maximum entry r Entry radius deflections at left hand 0 Inscribed circle of yeild line Diameter e Entry width v Approach half width Figure 5-S I' Average effective flare length Geometric parameters of entry 57

PAGE 70

The intercept F and slope fc of the entry capacity relationship: Qe = F-fcQc, were determined by the average number of queues at the give-way line, which was in tum determined by the entry geometry. The track experiment equations gave correct capacity predictions provided that the average number of queues at entry was predicted correctly. Simplified versions were calibrated to allow for the effects of partial entry saturation in public road conditions. The best predictive equation were given by: F = 224(v + (e-v) I (I + S)) + 35u + 2.4D-135 and fc = 0.063 (v + (e-v) I (1 + S)) + 0.29 (pculh) The analysis confirmed the main findings of the Track Experiment. The most important factors determining the capacity of an entry are the entry width e, and flare S. Since v is fixed by the approach road geometry, and the effects of u and D are slight, only e and S should be treated as the primary design parameters. (1-p.89) 5.8 Development of A Unified Capacity Formula The period from 1978 to 1980 was one of further study of public road roundabouts, particularly of "conventional" larger types of roundabout. The design rules of H.2/75 still tended to produce ''weaving lengths" and some that were modified allowed increased approach speeds which increased accidents. A unified capacity formula was in sight, but it was evident that new comprehensive guidelines were also urgently needed. The capacity studies were further consolidated and in 1980 Kimber described the development of a unified capacity formula that would be applicable to 58

PAGE 71

both smaller roundabouts, designed for "offside priority", and the larger "conventional" ones, produced from the previous design assumptions of weaving/merging behavior. A total data base was accumulated from eighty-six public road roundabout sites in five major studies and statistically weighted for analysis. The analyses of the combined data and the subsequent development of a unified formula provided a general capacity prediction procedure for all at-grade single-island roundabouts. Account was taken of local site conditions and an iterative design procedure was suggested. The range of the geometric variables included a minimum inscribed circle diameter of 13.5 m. This diameter was equivalent to a Mini roundabout conversion of a intersection comprising road widths of approximately 6.5 meters roadways and therefore the unified formula would be applicable to most normal urban mini roundabout installations. The geometric characteristics were identical with those previously used, with the additions: the angle of entry$ (degrees); the alternative average effective flare length I (m) ; and for the inclusion of larger "conventional" roundabouts in the studies; the width of the weaving section w (m) the length of the weaving section L (m) The empirical approach described previously was pursued further by regression analysis. The larger data base showed that a single linear relationship between traffic entering a roundabout from a saturated approach and the circulating flow crossing the entry, was applicable to all sizes ofroundabouts with inscribed circle diameters from 13.5 to 171.6 metres. A pcu value of 2 for heavy vehicles at roundabouts had been obtained previously and that was the value used in establishing the pcu values for 59

PAGE 72

entry flow Qe and circulating flow Qc in the analysis. The possibility of nonlinearity was thoroughly tested with a second order model. Non-linearity might arise from the fact that in practice it is difficult to suppress the entry flow entirely, even when the circulating flow is very large. No significant non-linearity was detected. The analysis suggested that the operation of roundabouts on public roads does not normally reach this region and it would be highly undesirable for roundabouts to be designed to operate in this way. The linear relationship Qe = F fcQc will ensure that designs are conservative for abnormally high values of circulating flow. For models based on pooled data from many sites, the effect of unexplained within-sites and between-sites variation, on the accuracy of a prediction of the mean capacity value for a single site is very small. The first, of the order of a few pcu/h, and for the second, the standard error is about 200 pcu. (1-p.80) c AB: Linear representation (first order empirical model) CD: Second order empirical model D B Figure 5-6 Ent1ylcirculating flow relationship source (8) 60

PAGE 73

5.9 Roundabout Capacity Design -Current Practice Intersection design calls for many decisions and choices and is a complex task. By choosing too elaborate a design, the engineer may unnecessarily redirect resources. In capacity provision it will seem less risky to over-provide but it will rarely be economic to avoid transient overload altogether. ( 1-p.1 01) The procedure for the design roundabouts in GB is currently covered in two main documents: 1) Department of Transport Advice Note T A.23/81 : 1981 2) Department of Transport Design Manual for Roads and Bridges (DMRB) Vol. 6, Section 2, Part 3, TD.16/93 Geometric Design of Roundabouts, issued in Sept: 1984 Other documents which are used include: Guidelines on Highway Link Design; the Department of Transport Traffic Appraisal Manual (TAM); and The Economic Appraisal (COBA) Manual {These procedures are now used generally by all highway authorities in the UK). (1-p.101) Guidance on the most appropriate form of intersection is also given in T A.30/82 (DMRB 5.1). Methods of assessment and economic appraisal for major (trunk) road schemes are described in great detail in the DOT manuals, TAM (Traffic Appraisal Manual), COBA (Cost Benefit Appraisal) Manual, and more recently, the Environmental Appraisal Manual. T A.23/81 refers to the first two of these including 61

PAGE 74

the evaluation of design flows from traffic counts; and the use of' growth factors" derived from nationaVlocal statistics. TD .16/93 refers to both of these Manuals. ( l p.102) TA.23/81 : 1981, recommended that ARCADY (which was also released in 1981) should be used for the estimation of capacity, delays and queues. A procedure for manual calculation is provided in T A.23/81, however, roundabout design will normally involve a number of trials, and it is not realistic to calculate these manually (particularly for queue lengths and delays). It is generally accepted that the need for manual calculation has been supplanted by the later availability of micro computer versions of ARCADY and the universal access to micro computers now available to designers. However, the description and examples of the calculation of roundabout capacities in Annex 1 of the 1993 design guidelines, virtually renders current reference to TA.23/81 unnecessary. (1-p.102) Design Reference Flows-TA.23/81 and subsequently TD.16/93 give guidance on determining the size of roundabouts and the procedures for deriving the "Design Reference Flows". These are the adjusted hourly traffic flow rates for the detail design of intersections. For urban roads with little seasonal variation the 30th highest (annual) hourly flow, and for inter-urban roads, the 50th highest, are generally used. For the purpose of DOT economic assessment procedures ("COBA''), they are taken as a range (the turning flows should also have a range), to allow various options for a junction to be considered, to arrive at an operationally economical optimum. (l p.102) 62

PAGE 75

The equation for the prediction of entry flow into a roundabout as a function of the circulating flow and entry geometry, can be applied to all types of single at-grade roundabout whether mini or normal types. Having developed a range of Reference Traffic Flows, a designer should use the equations for roundabout entry capacity (manually or by computer) to produce trial designs for assessment. ( 1-p.l 02) The Ratio of Flow to Capacity For the assessment of different options, the reference-flow/capacity or RFC ratio, is used as the indicator of the likely performance of an intersection under a future year loading. It should be calculated for each trial design. Thus if an entry RFC of 85% occurs queueing will theoretically be avoided in the chosen design year peak hour in 5 out of 6 peak hour periods or sites. Similarly, if an entry RFC of 70% occurs, queueing will theoretically be avoided in 39 out of 40 peak hour periods or sites. The general use of designs with an RFC of about 85% is likely to result in a level of provision which will be economically justified. There will be cases, however, where the adoption of a lower figure will be justified: for example, where the cost of a higher level of provision is low in both economic and environmental terms, or where space for enlargement is unlikely to be available in the future at a reasonable cost and thus the cost of being wrong becomes unreasonably high. On the other hand, if there are cost or environmental implications in providing higher capacity, for instance in urban areas, then even the 85% ratio may be unsuitable and a higher ratio with consequent queueing, will have to be accepted (to an extent assessed by the reduction of economic or environmental impact). (1-p.102) 63

PAGE 76

Circumstances will vary and it may often not be possible to provide the same RFC on all approaches, but the aim should be to achieve a reasonable design in this respect. On the other hand, ratios higher than 85% could be used at some less important entries if exceptionally low ratios are unavoidable at others, though the possibility of excessive queueing at any entry should be avoided. Designers should not strive to obtain a unique value. A range of situations must be considered and the advantages and disadvantages of each one assessed. (1-p.1 03) Variation -It must be stressed that the calculated capacities, queues and delays are average values of very broad distributions. The formula used are based on multiple regression analyses from observations from a large number of sites. Actual values can vary about the average due to: 1) Site to site variation; and 2) Day to day to day variation. As far as day to day variation is concerned this will manifest itself in practice as variations in the queue lengths and delays at any given time in the peak period. The formula merely calculate the average values over many days. ARCADY/3 offers calculations for daily variability as well as averages. TD.16/93 records, that the best predictive equation for the capacity of a roundabout entry (except those at grade separated interchanges, see below), found by research up 64

PAGE 77

to 1993, is: Qe = k (F fcQc) when fcQc is less or equal to F, or Qe = 0 when fcQc is greater than F. where: Qe =entry flow in pculhour (1 HGV = 2pcu) Qc = circulating flow across the entry in pculhour k = 1 .00347 30)-.978 {(1/r).05} F=.21t;, (1+.2x2 ) fc = 1 + 5 I ( 1 + M) M=exp {(D-60)/ 10} x2=v+(e-v)/(1 +2S) S=l.6(e-v)/1' The above equations apply to all roundabouts except those at grade separated interchanges. For all entries at very large and grade separated roundabouts: Qe = 1.004F0.036SEP0.232Qc + 14.35 FcQc (2.140.023 Qc) where SEP = separation of exit and entry for grade separated approaches, Qc = mean circular flow for central 30 minutes. For manual calculations the RFC should be calculated using the above formula. The design Reference Flows should be multiplied by 1.125 to allow for short term variation in traffic flows. Short term variation is included inARCADY/3. For computerized calculation a computer program such as ARCADY/3 should be used. The appraisal can be based on either an RFC of 85% or, in certain cases, a higher or lower ratio as described previously. In calculating this, a time segment length of not less than 5 minutes should be used to build up the flow pattern during 65

PAGE 78

the peaks (which can also be synthesized in ARCADY/3 from hourly flows if necessary). The program prints out the RFC (labeled Demand/Capacity in the output), queue lengths and delays at each entry for each time segment. An inspection can therefore be made, for each arm in tum, of the queue length and delay if the RFC reaches 85% or (70%). (1-p.104) Layout Factors The trial design should be adjusted where necessary to obtain operational efficiency or increased safety by adjusting the entry widths, the length of flares, etc. The list below gives the normal practical limits of parameters for new design, compared with the range measured at roundabouts on which the capacity formula are based. (1-p.104) Table 5-l MEASURED AND PRACTICAL RANGES OF ENTRY CAPACITY PARAMETERS e v s r 0 D Parameter entry width approach half-width effective length of flare sharpness of flare entry radius entry angle inscribed circle Practical Range 4.0-15.0 m 2.0-7.3 m 10.0-100.0 m 6.0-100.0 m 10 Y2-60 Y2 15.0-100.0 m 66 Measured Range 3.6-16.5 m 1.9-12.5 m 1-30.0 m 0-2.9 m 3.4-infinity 0 y2-77 Y2 13.5 171.6 m

PAGE 79

Circulatory roadway width, should be kept constant, ie, (inscribed circle diam. central island diam.) /2, at 1 to 1.2 times the greatest e, up to a maximum of 15 m. (1-p.105) 67

PAGE 80

6. Pedestrians, Equestrians and Cyclists 6.1 Introduction The introduction of smaller roundabouts with flared approaches in lieu of traffic signals would emphasize the need for crossing facilities for pedestrians. Generally with flared approaches the crossing should be sited as far back from the intersection as pedestrian convenience will allow. Crossing provision are preferred to be included in the deflection islands, either, as an unmarked crossing place with lowered curbs, or incorporated into a marked or signal controlled pedestrian crossing. Where justified by pedestrian flow, underpasses or overpasses could be considered, but the more compact style of roundabout serves to reduce the length of pedestrian detour and therefore the apparent justification for grade separated pedestrian facilities. The introduction of a roundabout at an intersection might adversely affect the pattern and safety of pedestrian movement, and require that appropriate measures be taken such that the pedestrian route is located away from roundabout intersections if possible. Crossings located before the give-way line should allow 2 to 3 cars to queue in each lane, between the give-way markings and the pedestrian crossing. If used, deflection island refuges should be at least 1.2m wide. A signal controlled crossing should normally be sited before (although not too far) the flared approach. It should be noted that this might be helpful in interrupting the dominant traffic stream to allow the entry of a minor flow. The 1984 Britain design guidelines T A.l6/84 suggested that as a general rule pedestrians should be discouraged from crossing the circular roadway on roundabouts. Guard rails may be required to channel pedestrians movements away 68

PAGE 81

from the roundabout to safer crossing points. The length of detour should be minimized if dangerous alternatives used by some pedestrians are to be avoided. (lp.212) 6.2 Current Design GuidancePedestrians The current Britain guidelines TD.16/93, Advice on pedestrian facilities, is that separate routes with crossings away from the flared entries to roundabouts are preferable. Here the roadway widths are less and vehicular movements are more straightforward. When this is not practical, the following should be considered; a. Unmarked crossing place (ie dropped curbs), with a central refuge if possible. b. Zebra crossing with or without central refuge. c. Some form of controlled crossing with or without a central refuge which includes for cyclists. d. Underpass or overpass. The type of facility selected will depend upon the expected volumes and movements ofboth pedestrians and traffic, and should be designed in accordance with the current recommendations and requirements (DMRB 2.2; 6.2; 8.5). The use of different types of facility at the same intersection is not recommended as this could lead to confusion by pedestrians and drivers. Crossings should not be placed across multi-lane entries. They should be located away from the intersection where the roadway is relatively narrow. (1-p.213) 69

PAGE 82

SCAL[ 1&' IIAIS(D CCJ.OIIm, PA 1"TIJIN(l) COfoiCliW; I[ I' A II[W(N T (T't?ICAI. AU. WEIIW
PAGE 83

In urban areas, where large numbers of pedestrians are present, guard rails or other means of deterring pedestrians from crossing should be used to prevent indiscriminate crossing of the roadway. The design of guard rails should not obstruct drivers' visibility to pedestrians through them, and vice-versa, are available, but should be checked in case spots do occur. (1-p.213) 6.3 Current Design Guidance Equestrians Where there is expected to be regular use of the roundabout approaches by ridden horses, of the order of more than 20 horses a week, consideration should be given to the provision of crossing places where the roundabout arms have to be crossed. These should preferably be crossed at some distance from the roundabout to permit suitable visibility to the roundabout by the rider. The principles are set out in DOT TA.57/87:1989 (DMRB 6.3). Segregated routes at the roundabout are to preferred. Ridden horses could share cycle tracks where these are distant from the circulatory roadway but should not be expected to use pedestrian facilities. (1-p.213) 6.4 Current Design Guidance Cyclists The current Britain guidelines TD.16/93:1993 state the safety implications for two wheeled vehicles at roundabouts. It also gives advice on facilities for cyclists and therefore allows designers to determine what measures to employ to safeguard two wheelers in circumstances relating to the particular site under investigation. ( 1-p.213) Roundabouts have an impressive overall safety record for most vehicle types but this does not apply equally to two wheeled vehicles. Research has shown that on four armed roundabouts on class A roads, injury accidents involving two-wheeled vehicles constitute about half of all those reported. The proportion of accidents 71

PAGE 84

involving bicyclists is about 15%, although they typically constitute less that 2% of the traffic flow. The accident involvement rates for two-wheeled vehicles, expressed in terms of accidents per road user movement, are 10 to 15 times those of cars; with bicyclists having slightly higher accident rates than two-wheeled motor vehicle riders. The study at four-arm roundabouts, has shown for example that, in 30 and 40 mph speed limit areas, there are differences in bicyclists involvement rates for different categories of roundabouts. Designers should be aware ofthe following: a. Normal roundabouts with small central islands and flared entries have accident rates which are about twice those of normal roundabouts with large central islands and unflared entries. b. 70 per cent ofbicyclist accidents at smaller normal roundabouts are of the "circulating" type. c. At dual roadway roundabouts the accident involvement rate for cyclists is about two to three greater than that at dual roadway traffic signals but for cars, the opposite is true. Data for bicycle involvement rates in 50 to 70 mph speed limits were less reliable due to low bicycle flows and few bicycle accidents, and did not show any significant differences between types of roundabout. The rates observed were similar to those for smaller normal roundabouts in 30 to 40 mph speed limits. Comparable data for bicycle accidents at mini roundabouts, three-arm roundabouts and single roadway 72

PAGE 85

traffic signals are reported in TRL CR.l61: 1989 which shows involvement rates for bicycles at mini-roundabouts that are respectively 8 and 9.5 times that for cars. Guidelines on the geometric design of roundabouts TD.16/93 observes that roundabouts are a particular hazard for bicycles as outlined in above. The operational performance and safety factors have been monitored at a number of experimental schemes aimed at improving cyclists safety at roundabouts. These have included the use of with flow cycles lanes around circulatory roadway, conversion of peripheral walkways to joint cyclist/pedestrian facilities, shared use of pedestrian underpasses and signposting alternative bicycle routes away from the roundabout. Evaluation of these, has concluded that once a bicyclist has entered a roundabout it is difficult to reduce the risk, and that the use of shared facilities have limited use depending on the volume of pedestrians and bicyclist. Nevertheless bearing in mind the practicalities and economics, it is important to consider facilities which take bicyclists out of the circulatory roadway at roundabouts by application of the following: a. Shared use by pedestrians and bicyclists of a peripheral cycle/walkway; b. A signposted alternative route away from the roundabout; c. Full grade separation for bicyclist and pedestrians, eg by a combined pedestrian/cyclist underpass system. Failing these, then greater emphasis should be placed by the designer on the safety aspects of the design of the roundabout layout, rather than high capacity, by careful attention to the entries and flares. (l-p.214) 73

PAGE 86

Figure 6-2 Exclusive Bicycle Lane At A Roundabout source (9) 74

PAGE 87

If the volume of bicyclists is significant but high enough economically to justify segregated facilities then consideration should be given to signalizing the roundabout or to an alternative form of intersection with traffic signals. Signalized bicycle crossings should be given to bicyclists at segregated left tum lanes. ( 1-p.215) The study report 1990 on the Britain 1984 guidelines, refers to experimental schemes aimed at improving safety of bicyclists at roundabouts. The report recommended that, local authorities should be further encouraged to consider the provision of facilities which take cyclists out of the circulatory roadway at roundabouts or, if this is not feasible, consideration be given to an alternative form of junction, such as traffic signals. (1-p.215) A further recommendation for revision referred to low profile deflection islands recommended in T A.42/84. Experience of these indicated that the use of minimal height subsidiary deflection islands could be a danger to both bicyclists and pedestrians. In the current Britain guidelines these islands are now to be delineated only by white reflective paint and reflective markers. Pedestrians should not be expected to cross left tum lanes which are segregated only by road markings. If a safer crossing cannot be provided, curbed islands of sufficient width with refuges should be used. (1-p.215) 6.5 Safety Studies Of Pedestrians and Cyclists Comparative studies of pedestrian and bicyclist safety at mini-roundabouts and traffic signal controlled junctions in Avon were reported by Davies in 1984. Results from a 1977 study of 12 mini roundabouts in A von gave a 22% reduction in all accidents and a 64% reduction in fatal and serious accidents (although neither were 75

PAGE 88

significant at the 10% level). In a later study of small and mini roundabouts, formerly priority controlled, all injury accidents were reduced by 34%. This reduction was reflected in all accident categories examined, although the numbers of pedestrian and bicyclist accidents were very low. In the comparative study with traffic signals, mini and small roundabouts showed a slightly lower percentages of pedestrian and bicyclist accidents. (l-p.215) Maycock and Hall showed that roundabout entering/circulating accidents were particularly sensitive to entry path curvature and entry width. It would appear that, although bicyclist circulating accidents are dependent to some degree on deflection, they are not as sensitive to this parameter as total accidents. The analyses indicated that cycle accidents are related to cyclist flow and therefore an "ideal treatment" would; reduce accidents, be inexpensive and be capable ofwidespread application. A number of experimental layouts had been installed, for example: a) with-flow bicycle lanes on the roundabout roadway, but the improvement in accidents, if any, was slight and more compact roundabouts with flared entries would limit this solution. b) two-way bicycle tracks around the perimeter, but the need to give way to traffic when crossing the arms of the roundabout make high traffic flow sites unattractive to bicyclists and this approach would be difficult at restricted urban sites. Combined cyclist/pedestrian underpass systems offer complete segregation. Conversion of existing pedestrian underpasses may be possible where pedestrian flows allow. The suitability of these would depend on existing site conditions in 76

PAGE 89

order to avoid potential pedestrian/bicyclist accidents. Results from experimental conversion schemes suggest that a barrier to maintain pedestrian/bicyclist segregation is effective. ( 1-p.216) Findings in the Britain County Surveyors Society (CSS) Report No. 1/4, 1987 which are given as "indications" needing substantiation by further work included: 1. Small and mini roundabouts are no less safe for pedestrians than other forms of intersection control. 2. The proportion of accidents involving two wheeled vehicles at Small and Mini roundabouts is no different to that for "Conventional" roundabouts. 3. Small roundabouts may be more dangerous for bicyclists than traffic signals. The Britain CSS Report No.l/3 Pedestrian Crossing Facilities, also summarizes the results of prior studies. Harper reported in 1985 on a study of 63 signal controlled pedestrian crossings in Wiltshire, over the period 1979-1984. This study showed that accident rates for sites including Mini roundabouts, were lower with a 40 mph speed limit than in a 30 mph area. Bramwell reported in 1986 that in Buckinghamshire marked (Zebra) crossings on the immediate approaches to roundabouts showed similar accident rates to those more distantly sited. ( 1-p.217) Layfield and Maycock reported in 1986 that, at roundabouts, of accidents involving bicyclists, 15% are fatal or serious, significantly lower than the general value (at mini-roundabouts 18%). These lower severity ratios at roundabouts are offset by the fact that a higher proportion (8%) of bicycle accidents occur at roundabouts 77

PAGE 90

(including mini), than the proportion (4%) of non-bicycle accidents which occur at roundabouts. Remedial treatment aimed at bringing the ratio in line with non bicyclists would, if successful, reduce bicycle accidents at roundabouts by about 40% (at 1984 data and prices equivalent to savings of .5m per year). Studies of hospital records indicate that a very high proportion of bicyclist injury accidents, most of which do not involve any other vehicle, are unreported. Geographical study of reported accidents to bicyclists indicate that a majority of accidents might be generated at relatively few roundabout sites where clusters ofbicyclist accidents occur. This suggests that bicycle accidents at roundabouts could be substantially reduced by accident countermeasures aimed at relatively few sites. ( 1-p.217) Roundabouts are perceived by bicyclists as hazardous sites that should be avoided. At large roundabouts many bicyclists are prepared to alter their route or get off and walk to avoid hazard. The Britain Highway Code recommends bicyclists to dismount whenever they feel unable to cope with the traffic conditions. A study of accidents at 84 (4-arm) roundabouts showed that 68% ofbicycle accidents involved circulating bicyclists. Bicyclists approaching the roundabout accounted for 14% of bicycle accidents and bicyclists entering and leaving the roundabout each accounted for 7% of bicycle accidents. The findings confirmed that as far as the largest group (68%) ofbicycle accidents are concerned (ie. circulating bicyclists being struck by entering vehicles), the design of entry geometry is an important consideration for safety. Where deficiencies of roundabout deflection can be improved, safety benefits to all road-users including bicyclists and motorcyclists should result. ( 1-p.217) 78

PAGE 91

Table 6-1 FROM LAYFIELD & MAYCOCK, Bicycle Accident Types At A Sample Of 84 4-Arm Roundabouts Accident type Number of accidents Percentage Entering/circulation Cyclist circulation/motor vehicle entering 104 50 Motor vehicle circulating/cyclist entering 15 7 Approaching Rear-end shunt (bicycle hit) 20 10 Rear-end shunt (motor vehicle hit) 9 4 Single vehicle 3 1 "Other" Cyclist circulating/motor vehicle exiting 20 10 Motor vehicle circulating/cyclist exiting 5 2 Leaving roundabout 11 5 Circulating on roW1dabout 16 8 Unclassified 7 3 Total 210 100 source (1) 79

PAGE 92

A number of experimental schemes involving special facilities for bicyclists, at roundabouts were described in detail by Layfield and Maycock in 1986. However, none of the schemes showed great potential for accident reduction and a substantial reduction in risk to bicyclists by introducing special facilities on the roadway or by delivering bicyclists on to the walkway did not seem likely at the time. (11-p.39) A significant hazard to bicyclists, which is not directly attributable to the roundabout itself (but the accidents are sometimes assigned to the intersection), can occur when auto traffic enters and leaves grade-separated roundabouts via slip-ramps. In 1987 Williams and Layfield reported that slip-ramps on all-purpose dual-roadways, connecting with roundabouts and other grade-separated intersections, were found to be a source of particular danger to bicyclists. Bicyclists using the dual-roadway have to cross obliquely, the path of fast moving diverging and merging auto traffic. Although bicyclist casualties from slip-ramp accidents formed only a small proportion (1 %) of all reported bicyclist casualties in 1985,40% ofthem suffered fatal or serious injury which was well above the average for bicyclists, different types of facilities provided for bicyclists at roundabouts. (11-p.39) Remedial measures aimed at reducing the accident risk had been developed by the Britain Berkshire County Council. These consisted of a bicycle lane, diverting bicyclists from the main roadway to a right-angle crossing of the slip-ramp at a safer location. This arrangement gave bicyclists greater control of their own safety but removed their priority and made a less direct route. The initial usage by bicyclists in 80

PAGE 93

an experimental period was two thirds. The arrangement has since become the standard treatment for dual roadway slip roads. (11-p.39) 6.6 Pedestrian Crossings At Roundabouts Design considerations for Zebra crossings are covered in T A.1 0/80 (233). If a crossing giving pedestrian priority is located close to the entry/exit points of a roundabout there will be inevitable consequences for the operation of the roundabout and possibly for safety. In some cases the safety effects may be positive as speeds will be reduced. (10-p.12) Where a crossing must be provided within the intersection layout, a zebra crossing is preferred. If a signalized crossing is provided, it should preferably be of the divided crossing type to avoid excessive delays at the exit points, because the "blocking back" mechanism causes queues to extend onto the circulatory roadway. (10-p.12) A requirement was introduced in TA.42/84:1984 and is mandatory in TD.16/93: 1993, for drivers at the give-way line to have unobstructed visibility of the full width of a pedestrian crossing across the "next" exit. If the crossing is within 50m of the roundabout (there may be difficulty in meeting this criterion in some restricted urban sites). (10-p.12) Marlow and Maycock quantified the reduction of intersection capacity from the siting of uncontrolled marked (Zebra) crossings close to intersection, including the effect of "blocking-back" by queues on exit. ( 1 O-p.12) The theoretical approach is based on random arrivals at "two servers in series", using the vehicular "real" and "virtual" capacity of a Zebra crossing derived by Griffiths, and roundabout entry capacity derived by Kimber. The application is limited to 81

PAGE 94

ratios of real crossing capacity to entry capacity greater than 1. If this is <1 the real crossing capacity will dominate and segregation of pedestrians would be needed. The Reduction in capacity due to the blocking effect was found to be similar (or greater) than the approach crossing/entry effect. It emphasizes the need to take this additional factor into account when considering the location of pedestrian crossings near to roundabouts (or other intersections). In many cases, a crossing to intersection queue of 4 to 5 spaces, reduces the crossing interaction on the entry side of the intersection to quite a small effect, and allows a flow rate of about 50 to 60% of the capacity of the crossing on the roundabout exit, before the 5% "blocking" criterion is reached. (10-p.13) In 1987 Marlow looked into the question of traffic signal pedestrian crossings at or near to entries to mini roundabouts, and the effect on the traffic operation of the roundabout, including resulting queues "blocking back" into the junction. DOT Advice Note T A.1 0/80 1980, suggested that a pedestrian crossing should be sited at least 20m from the intersection, to avoid this interaction. Any confusion that mini roundabouts might appear to be signaled seemed unlikely, but close proximity can affect the traffic operation ofthe intersection. Also, the requirements conflict, since the diversion may be unattractive to pedestrians. In order to assist in siting decisions for the crossing, the general guidelines were quantified by Marlow more comprehensively. Using a capacity relationship and the recommended settings. The general operating capacity for fixed time Pedestrian signals of this type was established at 1,300 to 1,400 vph and pedestrian flows >400/h. Typical small roundabouts had entry capacities in the range of 600 to 1,300 vph with a circulating flow of 500 to 1,000 vph. Marlow used Poisson probabilities for the arrival of 82

PAGE 95

vehicles during the pedestrian stage, for six levels of flow and three road widths, to derive estimates of95 percentile queue lengths in vehicle numbers. Table 6-2 95 Percentile Queue Lengths In Vehicle Numbers Road width Flow (vehicles/hour) (metres) 250 500 750 1,000 1,250 1,500 7.3 2 3 5 6 7 8 9.0 2 4 5 7 8 9 11.0 3 5 6 8 9 11 Similar considerations apply to both entry and existing. An indication of the siting of crossing (for an unflared entry), can be obtained assuming an average vehicle space of approximately 5m giving a range of 10 to 40 m for a 7.3 road and from 15 to 55m for an 11m road. (10-p.15) Generally, any entry flaring to more than two lanes should occur between the crossing and the roundabout. This applies to both Zebra and Pedestrian crossings. 6.7 International Developments In the French report by Alphand, a study of pedestrian accidents at roundabouts had been made but the numbers were too small to produce reliable statistics; however, some common points could be inferred. The majority of accidents took place on 83

PAGE 96

two-lane entries, but the same number (7) occurred on pedestrian crossings adjoining the give-way line. The balance of accidents occurred within the roundabout. An element of entrapment by barriers etc. of pedestrians entering the roundabout is suggested in the latter. Other common characteristics included children and old people, high traffic flows(> 20,00 vpd), towncenters and peak-hour traffic. The French suggest locating pedestrian crossings 4 to 5m before the give-way line and staggered to bring the "exit" crossing nearer to the roundabout. (This might improve visibility to exiting traffic but could increase the probability of queues "blocking back"). (10-p.16) An analysis of accidents involving bicycles and mopeds at French urban roundabouts, shows a major cause of accidents (50.6%) as the refusal of priority to bicycles and mopeds. This is more prevalent (33.4%) on larger roundabouts of>30m diameter but also on oval shaped (19%), high entry speed and possible masking by other traffic are suggested causes. The accident rate increases with traffic flow and more than half of the accidents occur during peak periods. ( 1 O-p.16) The German experience of pedestrian and cyclist safety at roundabouts was reported by Brilon and Stuwe in 1992. Deflection islands are recommended with refuges for pedestrians. Traffic safety for pedestrians at single lane German roundabouts is generally very high, since there are only very narrow conflict zones with the motorized traffic which, moreover passes these zones at very low speed. In most cases pedestrians cross without noticeable delay, in only a few cases is it likely to be critical (It was noted that at a German roundabout (Munster, Lundgeriplatz) with high volumes of pedestrians, bicyclists and motorized vehicles, the reduction in capacity was smaller than that predicted by Marlow and Maycock). In critical cases 84

PAGE 97

to avoid blocking-back from crossing pedestrians exits, the distance of the crossing from the roundabout should be more than 6m. (10-p.17) The German experience is that bicycle traffic at roundabouts requires special attention. Different solutions may be required depending on the site. a) At small roundabouts (diameter up to 35-40m), bicyclists indicate their required direction by cycling either on the right side or in the middle of the circulatory roadway. In these roundabouts bicyclists get along well with the motorized traffic without risk, since cars and bicycles proceed at almost the same speed and there is no overtaking in the roundabout. b) If roads leading to the roundabout have separate bicycle paths, these can also be continued around the roundabout and they may be two way. Bicyclists then cross entries and on paths on the inner side of pedestrian crossings. The bicycle traffic often splits up into cyclists needing protection, eg children, who use the separate bicycle paths and fast, sporty bicyclists who stay in the circulatory roadways. c) Fixed track, or marked bicycle lanes, sometimes with a colored surface, at the outer side of the circulatory roadway. This solution seems not to be favorable and observations show that bicyclists often have to stretch out their arm to prevent motorized vehicles from cutting in front of them. Moreover the fixed track systematically leads the bicyclists to the problematic conflict zones at the entries. Therefore, solution c) is not recommended by Brilon and Stuwe. If the approaching lanes are provided with bicycle tracks, these should end 20 to 30m in front of the 85

PAGE 98

roundabout, which should then used by cyclists according to b) above. It was concluded that the problem of bicyclists in roundabouts demands more extensive investigation. ( 1 O-p.l8) 86

PAGE 99

7. Traffic Models For Roundabout Analysis 7.1 Introduction A roundabout must generally be considered as an alternative to two-way stop control (TWSC), all-way stop control (A WSC) or traffic signal control. The performance analysis methodology for these alternative control modes is described in detail in the Highway Capacity Manual (HCM). The current HCM offers procedures that produce comparable estimates of entry capacity (vph) and delay (seconds per vehicle) for each approach to a stop sign or signal controlled intersection. The HCM procedures have been adopted by many State Department of Transportation's for assessing the level of service (LOS) on state roadways. Software is available for the productive application of these procedures. Unfortunately, the HCM does not provide a similar model for the evaluation of roundabouts. Therefore, a different analysis model must be adopted. This model should produce results that are comparable with the results of the HCM models for the alternative control modes. It should also be readily implemented in software within the same computational structure as the H CM models. Several methods of roundabout modeling have been developed, most of them in other countries where roundabouts are common intersection treatments. The Australian methods are most comparable with HCM methods, and are implemented in software that is most compatible with the computational structure that has been developed in Florida for comparing other control modes. For example, the Signalized and Unsignalized Intersection and Design Research Aid (SIDRA) 87

PAGE 100

program offers an option to implement the HCM procedures for many computations. In addition, the Australian method is based on analytical models while other methods, such as the British method, tend to be more empirical in nature. In general, analytical models are more transportable internationally because they depend more on mathematical relationships and less on observed driver behavior. The details of the Australian analysis methodology are covered thoroughly in four significant documents. Evaluating the performance of a Roundabout presents the basic theory that applies to roundabout modeling. Austroads Guide to Traffic Engineering Practice: Part 6, Roundabouts contains the full set of guidelines that govern the design, evaluation and operation of roundabouts in Australia. Capacity and Design of Traffic Circles in Australia presents a technical, but readable summary of the roundabout modeling process and offers some updates to the information presented in the previous references. The SIDRA 4.1 program documentation describes the way in which the theory contained in all of the references was implemented in SIDRA. It also explains departures from the theory that were introduced for practical 88

PAGE 101

purposes, and provides guidelines for preparation of input data and the interpretation of results. These documents are very detailed and their contents will not be covered in detail here. They provide important information on the modeling of roundabout performance and should be studied by analysts who require a deeper understanding of the process. The weakness of early versions of ARCADY for practical (many iterations of designs) use in design offices, has encouraged the production of alternative "software design tools". A different approach, using Kimber's work in Laboratory Report (LR) 909 and LR 942 has been incorporated in the roundabout design program "RODEL", described by Crown in 1987. This re-orders the way in which output is presented, and entry width and flare length are replaced by an "entry factor" (presumably similar to x2 in LR 942). The queues and delays are displayed for this factor, estimated to a specified confidence level. The displays are interactive and show both input and output simultaneously. The manual shows the relationship of individual parameters to capacity. It is suggested that the ease and speed ofRODEL simplifies the continuous process of design optimization. However there are some differences between RODEL and ARCADY, eg the methods specified for measurement of entry and exit geometry, and there is scope for possible different results from the programs, particularly for small roundabouts, (it is advisable, particularly in the case of trunk road schemes, to 89

PAGE 102

check the final design using a current version of ARCADY, which is a requirement ofT A.23/81 ). ARCADY/3 does not consider exit geometry in capacity assessment, but the exit curb radius and exit angle are considered in the assessment of geometric delay. As in the case of circulating roadway width, the strictures on roundabout design contained in the Advice Notes are expected to ensure that capacity will not be affected, eg by applying the principle of"easy exits". Willumsen and Kay described the development of a computer system for the optimization of roundabout design. The system is based on high resolution graphics. A graphical layout is generated from initially specified (or default) parameters used in TRRL RR 35, and their treatment is consistent with LR's 909 and 942. It produces the smallest roundabout that fulfills the specified pattern of traffic and safety criteria. If these do not match, the program suggests modified values for certain geometric parameters. Other ARCADY parameters, eg delay, are also displayed. Iteration to redesign to different RFC values, by adjusting e and v parameters and the basic approach geometry until a satisfactory status returns, is fast on a suitable computer. The layout is screened to any scale and can be enhanced with a zoom facility before being sent to a plotter. The sequence of operations can be carried out with different degrees of intervention by the user. At the time of the report in 1988, automatic operation was only possible for unrestricted sites, but the treatment of site obstructions was being investigated. This promised to be a powerful design tool. Its greatest potential target would be urban roundabouts with restrained site conditions, which need frequent changes in the design process. 90

PAGE 103

The work on advanced computer assisted roundabout design has been subsequently developed (by Steer Davies Gleave) as "ROBOSIGN". Roundabout design with optimization to restricted sites is complex and usually requires iteration at many levels, ROBOSIGN is an attempt at full automation of the process. It is a computer aided design (CAD) program which incorporates geometric design and performance evaluation with drawing and plotting capabilities, and includes elements of an "expert system" for achieving optimum layouts. It is said to be capable of producing the final setting out details for a fully optimized roundabout, from basic data entry, in a matter of hours. Bearings and coordinates of sites can be incorporated from CAD programs and trial designs can be superimposed on the site plan indicating which changes to the default settings may be needed. The program includes rules and optimization procedures based on the knowledge of experienced highway engineers, but manual interaction can be required in fitting to site constraints. This should be considered as desirable, to allow the input of skill and experience. Design standards are held as external files which can be revised or adapted to local standards. Non standard designs can be produced with suitable warning messages. 7.2 RODEL RODEL is an interactive program developed for the evaluation and design of roundabouts. This program was developed in the Highways Department of Staffordshire County Council in England. RODEL is based on an empirical model developed by Kimber at the Transport and Road Research Lab (TRRL) in the UK. The empirical model was chosen over the gap acceptance model because it directly relates capacity to detailed geometric parameters. RODEL is an interactive 91

PAGE 104

program in which the simultaneous display of the both input and output data is shown in a single screen. There are two main modes of operation. In mode 1 the user specifies a target parameter for average delay, maximum delay, maximum queue, and maximum RFC factor (v/c ratio). RODEL generates several sets of entry geometries for each approach based on the given input. Depending on site specifics and constraints, the generated geometries can be used for design purposes. Mode 2 focuses more on performance evaluation using specified values of the geometric and traffic characteristics. One important data item for RODEL is the confidence level (CL) at which the analysis is being performed. RODEL is based on an empirically derived model which estimates expected values for the performance measures. Some degree of stochastic variation must be anticipated from site to site. The confidence level provides a way to recognize the stochastic component. For example, an 85% confidence level (the suggested default for RODEL) means the user can be 85% confident that the actual queues and delays will not be greater than the estimated values. RODEL is available from R.B. Crown, RODEL Software, Ltd. and Staffordshire County Council, 11 Carleton Close, Cheadle, Stoke-on Trent STlO lLB, United Kingdom. 92

PAGE 105

7.3 SIDRA Several methods of roundabout modeling have been developed, most of them in other countries where roundabouts are common intersection treatments. The Australian methods are most comparable with HCM methods, and are implemented in software that is most compatible with the computational structure that has been developed in Florida for comparing other control modes. For example, the Signalized and Unsignalized Intersection and Design Research Aid (SIDRA) program offers an option to implement the HCM procedures for many computations. SIDRA is used in the Florida Roundabout Guide as the primary model for evaluating roundabout performance. SIDRA generally adheres to the gap acceptance modeling that is used in the Australian analysis method described in the literature, but some departures have been introduced. Because it models signals and stop sign control in to roundabouts, it offers a convenient method of evaluating the performance of a roundabout in direct comparison to the alternative control modes. While SIDRA is a general intersection analysis program, this discussion will focus on its treatment of roundabouts. SIDRA will accommodate roundabouts with as many as eight approaches simultaneously. Like all of the other evaluation models, SIDRA has its own data entry and editing capability. Its user interface is graphics based, and is very well documented and user-friendly. It offers access to all of the advanced features of SIDRA, including a multiple rum mode that seeks out the practical capacity of a roundabout. Measures of effectiveness are also presented in a graphical format. 93

PAGE 106

SIDRA was developed by the Australian Road Research Board. It is available in the U.S.A. from the McTrans Center. 7.4 ARCADY ARCADY is another British roundabout analysis program which has the same theoretical background as RODEL. This program also incorporates Kimber's model which is based on the rule of circulating vehicles having priority over entry vehicles (off-side priority). Kimber used the idea of entry geometry affecting the capacity and related the equation to several site-specific parameters. The model also assumes a linear relationship between the circulating flow (Qc) and the maximum entry flow (Qe). The ARCADY input requirements are similar to RODEL since both programs follow the same methodology. The input parameters include entry width (E), inscribed circle diameter (D), flare length (L') approach road width (v), entry radius (R) and the entry angle (F). Like RODEL, ARCADY deals in the concept of confidence level. The main difference is that the confidence level may be specified for RODEL, but it is embedded in the ARCADY model at 50 percent. The ARCADY model utilizes a series of screen prompts guiding the user through the entry of all required geometric and traffic data. A graphical approximation of the geometries of each approach is displayed on the screen using simple text characters. ARCADY is available in the U.S.A. from George Hoyt and Associates, P.O. Box 313, Mt. Vernon, VA 22121. 94

PAGE 107

7.5 Other Traffic Models Table 7-1 Other Traffic Models Model Country Procedure SETRA France Empirical KREISEL Germany Statistical INSECT Australia Simulation KNOSIMO Germany Simulation SIMRO Britain Simulation HCM U.S.A. Statistical (Gap Acceptance) 7.6 Capacity Estimation Tools On the next few pages are capacity estimation tools one can use to estimate the capacity of a roundabout. 95

PAGE 108

L:' ..c. :c QJ 2:.. a 9 u.. z -' :::l 0 a: 0 CAPACITY FOR MULTI-LANE CIRCULATING FLOW ROUNDABOUTS CAPACITY FOR SINGLE LANE CIRCULATING FLOW ROUNDABOUTS 2600 2400 2200 2000 1800 1600 1400 1200 1000 800 600 400 200 Oemax = neOcexp(-qcT) 1 -e)(p ( -qc To) Oe.max = ne0ci1-QctdeKP(-qc(T-tc)] 1-e)(p (-qc T0 ) source (5) 1\ \ 1\ ./ Multi-lane circulating flow 1\ \ r\ .... \ \ \ 1\ 1\ f\ \ \ i\ '\ \ K [\ r-. \ Single lane _....I-" f'... 1'\ circulating flow I'\ f" "f'.... I'-....... t'-. 0 200 400 600 800 1000 1200 1400 1600 1800 CAPACITY PER ENTRY LANE Oc. mulnc (veh/hr) ROUNDABOUT CAPACITY Figure 7-1 source (5) 96

PAGE 109

50 40 30 20 (.) (I) en ?{ _J 10 w 0 9 C) 8 z w 7 :::> w 6 :::> a 5 w C) < 4 a: w 3 2 I 1/ I I l I 1/ I 1/ II 1/ rj 1 I I / I v I I I I j 1/ I I II Ill . I I I i/ /I/ 7 I II J I I I V:e/ I I I I Ill l/ (' .. I rl] i/ I i/ J v; v, Y AI v ; v v / / ,<>; 0 0 0 0 C\1 0 0 <") o o o oooo oooo o o o oooo oooo CIRCULATING FLOW a. (veh/hr) = Circulating llow (vehlh) -Entry volume per lane (veh/h) n.e T = Critical acceptance gap = 4 sees T0 -Follow -up headway = 2 sees tc = Minimum headway lor circulating traHic = 2 sees AVERAGE QUEUEING DELAY TO VEHICLES ENTERING SINGLE LANE CIRCULATING FLOW ROUNDABOUTS Figure 7-2 source (5) 97

PAGE 110

50 30 20 u Gl "' .....J w 10 0 g 8 w 7 :J 6 0 w 5 C) <( a: w 3 2 I II I 1 1/ J I I i/ 1/ I 1/ 1/ L I v 1/ 1/ 1/ I; v v v 1/ v j_ j_ 1/ I I I I J ;:.I I 1/ 1/ I $J 1/ I I <:".1 _L _L I II I II II ocy' L v II II J .. o;/ 0o r v 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 o o o oooooaooooo o <"of (") "''Il" V"'C),._CI
PAGE 111

ROUNDABOUT CAP A CITY ANALYSIS INTERSECTIONOF ___________ WITli _______ CITY DATI:. _______ PLAN NUMBER. _____________________ TRAFFIC VOLUMES !58 TRAFFIC '\.....__ I '19 _71 2..82 @ 4 ll i I[J211T(L)Lsi 318 L(L) Ul \.() \.n I B 'L( A) ...... t----f't\ -} 17S r(L) 1.8 l(L) ll'l T(L) 'lq L(A) 4 2 t.(L) -+-A BLOCKINGTRAFFIC t A' @2. L(A) B c. Approach Leg Ea1ly Volume AM PEAK HOUR I IS"B 2 618 3 35''-/ 5 PM PEAK HOUR I 2 3 5 Note 1: Entry Volume/Lane Capacityfl.ane Entry Ciladolin& Volwn:paVolum: .... 15E (f,3S 2.J/2 "19B 333 35'1 1-39 99 .]) :uncs.. 9t.o 1"0 /320 /200 :B:J) GJeAI'It. eq,..:or A.,. Sa ....... do:laypa-To
PAGE 112

ROUNDABOUT CAP A CITY ANALYSIS JNrERSECTIONOF ___________ WITH ________ CITY DATE. ________ ?LAN NUMBER TRAFFIC VOLUMES _j TRAFFIC 10 BLOCKING TRAFFIC Approach Leg Eniiy Volume AM PEAK HOUR I 2 3 4 s PM PEAK HOUR I 2 3 4 s Note I: Entry Volume/Lane Capacity/Lane L Eniiy Cilt:ulaliu& c.p.:aypcr Volum<:pcr Vohunc laDe Figure 7-4 100 PM PEAK Dq=of Avaage Sa\lntion delay per Tolai.Ddoy S..:oolc I 'l'
PAGE 113

/ \ Inscribed Circle Diameter f 91.4 85.3 79.2 73.2 67.1 61.0 57.9 54.9 51.8 48.8 45.7 42.7 39.6 36.6 33.5 30.5 29.0 "" \ LEGEND a Raised central island. b Low profile mountable apron. c Remaining circulatory roadway width, 1.0-1.2 times the maximum entry width. d Design vehicle. e 1 meter clearance minimum. f Inscribed circle diameter (lCD). g Width between curbs. NOTE: Splitter islands should not protrude into the inscribed circle if the roundabout is designed tightly as illustrated here, allowing only the minimum width g. Turning Widths Required for Normal Roundabouts Meters Feet ;; Design Vehicle Inscribed Circle Design Vehicle STAA Calif. Bus Diameter STAA Calif. Bus Min.g Min.g Min.g f Min.g Min.g Min.g 6.7 6.6 5.2 300 22.0 21.5 17.0 6.9 6.6 5.2 280 22.5 21.5 17.0 7.2 6.9 5.2 260 23.5 22.5 17.0 7.5 7.0 5.3 240 24.5 23.0 17.5 7.8 7.3 5.3 220 25.5 24.0 17.5 8.1 7.6 5.5 200 26.5 25.0 18.0 8.4 7.8 5.5 190 27.5 25.5 18.0 8.7 8.1 5.6 180 28.5 26.5 18.5 9.0 8.4 5.8 170 29.5 27.5 19.0 9.3 8.7 5.8 160 30.5 28.5 19.0 9.8 9.1 5.9 150 32.0 30.0 19.5 10.1 9.6 6.1 140 33.0 31.5 20.0 11.1 10.2 6.2 130 36.5 33.5 20.5 12.2 11.1 6.4 120 40.0 36.5 21.0 13.7 12.3 6.7 110 45.0 40.5 22.0 7.0 100 23.0 7.2 95 23.5 Design vehicle requues a larger ICD (mscnbed circle diameter). Figure 7-5 source (14) 1 01

PAGE 114

1,. .......... Signing and St . npmg Figure 7-6 102 i:,. .... .,.

PAGE 115

1800 -;;; 1600 :::> () eo >-11.00 "(3 "' n "' () 1200 1000 o, 11.00 -;;; 1200 :::> () ?: 1000 0 () ?: 1000 "(3 "' n "' () eoo 600 11.00 -;;; :::> () a. ?: 1200 "(3 () eo >-"(3 c:: n ct: () 1200 1000 eoo t. 5 6 7 B 9 10 11 Entry"Wtdth E (metres) 30 1.0 50 60 70 Inscribed Circle Diameter D 0 20 LO 60 eo Entry Angle Phi (deg) CAPACITYIGEOMETRY RELATIONSHIPS Figure 7-7 source (2) 103 eo (metres) 100

PAGE 116

8. British Capacity Analysis Procedure Using Rodel 8.1 Introduction Rode! is a computer application that predicts the traffic performance of modem roundabouts. Rodel estimates delay, queue length, and capacity as functions of roundabout geometry and flows. It was used to design Vail's modem roundabout interchanges. Rode! was developed by Barry Crown of the Staffordshire County Council in England. It applies research by the United Kingdom's Transport Research laboratory, which licenses its use. Rode! is faster and easier to use than a widely used program by the British Transport Research Laboratory, ARCADY. Insofar as the two programs overlap, their output is identical. Rode! works like a spreadsheet in which the designer answers what-if questions by changing one of the input parameters and running the program again. Because Rode! is fast and easy to use, the designer is likely to continue altering his design until a nearly optimal design is achieved. Rode! permits the designer to select the confidence level of his estimates of traffic performance. A confidence level of 50 percent is implicit in other traffic performance programs, like ARCADY or TRANSYT. Rodel's author recommends using a confidence level of 85 to 95 percent. This allows for inaccuracies in both the 104

PAGE 117

input design flows and the output capacity estimate. Often a small increase in roundabout entry width or flare length will greatly increase the probability that the roundabout will perform well at a high confidence level. 8.2 Capacity Six Regression Equations Capacity estimates ofRodel are based on research reported in Kimber, R.M., The Traffic Capacity of Roundabouts, TRRL Laboratory Report 942, 1980. Regression equations were developed from data taken at 86 roundabouts on public roads and 35 geometric variations on the TRRL study track. The capacity of each entry to a roundabout (Qe) was found to be a function of one flow variable, circulating flow, and six geometric parameters. The definitions of symbols are given below. PARAMETER SYMBOL 1. Capacity= maximum entering flow, pculh Qe 2. Circulating flow, pculh Qc 3. Entry width, m e 4. Approach half-width, m v 5. Length of flare, m 1, 6. Incribed circle diameter, m D 7. Entry angle, degrees 8. Entry radius, m r 105

PAGE 118

Capacity is estimated using the following six regression equations: PARAMETER EQUATION 1. Sharpness of flare 2. Entry width parameter 3. Function ofD 4. Adjustment factor, cap. Curve 5. Slope of capacity curve 6. Yintercept, pcu/min S = 1.6 (e-v) II' X2 = v + (e-v) I (1 +2 S) t0 = 1 + 0.5 I (1 + exp (( D-60) 110 )) k = 1 0.00347 ( 30)-0.978 ((1/r)-0.5) fc = 0.210 to ( 1+0.2 x2) F = 303 xz The best predictive equations of capacity are: Qe = k (F fc Qc ) Qe = 0 when fc Qc < = F, and when fc Qc > F Queues and delays are estimated by use of time-dependent queuing theory. This is reported in Kimber, R.M. and Erica M. Hollis, Traffic Queues and Delays at Road Junctions, TRRL Laboratory Report 909, 1979. Queue lengths are estimated in a series of small consecutive time intervals. Traffic demand and capacity are assumed to vary from interval to interval. 106

PAGE 119

9.0 Interpreting Rodel's Printouts 9.1 Introduction Rodel prints out traffic performance given a main screen, which has the following twelve fields. 1. TITLE In the title section of the main screen are the date, written the British way, day:month:year, the name of the roundabout, and the number of the computer run. This last nwnber corresponds to the number given in subsequent statistics screens. 2. GEOMETRY The user inputs seven geometric parameters. Distances are in meters. E Entry width L' v RAD PHI DIA GRAD SEP field Length of flare between V and E. Upstream roadway width before flaring begins. Curb return radius. Angle between entering traffic and circulating traffic. Incribed circle diameter of the roundabout. Grade separated, 0 or 1? The user inputs a one in this if the roundabout is very large, as at huge two-bridge British grade separated roundabouts that run over or under the freeway at some interchanges. 107

PAGE 120

3. TIME The user inputs the following seven parameters which set the periods over which traffic performance estimates are made. Times are in minutes. TIME PERIOD TIME SLICE RESULTS PERIOD TIME COST FLOW PERIOD FLOW TYPE FLOW PEAK The total period to be modeled. Equal pieces of the time period during which capacity and demand flow remain constant. Capacity and flow may change from slice to slice but not within each slice. The period over which results are computed. If the time period is minutes and the results period is from minute 15 to minute 75, then results for the middle 60 minutes are given. The value of driver's time in British pence per minute. The period over which the user inputs turning flows in field 5, explained below. If a 15 and 75 are given, the user inputs flows for the middle 60 minutes. Flows of field 5 may be entered in passenger car units (pcu's) or vehicles. A truck equals one vehicle or two pcu's. The peak hour being analyzed: a.m., off peak, or p.m. 108

PAGE 121

4. LEGNAME The user inputs an abbreviation of the name of each leg of the roundabout. The leg names are in the order of the direction that traffic flows around the roundabout. 5. PCU FACTOR This is the number of vehicles having more than four wheels divided by the total number of vehicles. 6. TURNING FLOWS For each leg, the user enters the number of vehicles exiting at the first exit, the second exit, and so on up to the final flow, which is the number ofU-tums exiting at the entry leg. 7. FLOW FACTOR (FLO F) The input flows are multiplied by this factor. With this factor the user can perform a sensitivity analysis to see what would happen if flows were to increase. 8. CONFIDENCE LEVEL (CL) Queues and delays are predicted at the input confidence level. If 85 is entered, we are 85 percent confident that the queues and delays will not be greater than predicted. 9. FLOWRATIOS To allow for peaking of traffic within the peak period, the turning flows are shaped into a flow profile. If the time period is 90 minutes and flow times are set at minute numbers 15 and 75, then RODEL shapes the flow profile into three rectangular steps: a beginning 15 minute step, a middle 60 minute step, and a final 15 minute step, the 109

PAGE 122

flow being constant within each step. Ifthe user inputs flow ratios of0.75, 1.125, and 0.75, then Rodel models the flow profile so that flows of the first and third step are 0.75 times the average input flows, and flows ofthe middle step are 1.125 times the average input flows. 10. FLOW TIMES The user inputs the flow times that are used with the flow ratios to produce the flow profile from the turning flows. 11. TRAFFIC PERFORMANCE Rodel outputs the traffic performance of each leg in this field, as follows. FLOW CAPACITY AVE DELAY MAX DELAY AVE QUEUE MAX QUEUE Entry flow, vehicles per results period. Capacity, vehicles per results period. Average delay, minutes per vehicle over results period. Maximum delay, minutes per vehicle over results period. Average vehicles in queue over results period. Maximum vehicles in queue over results period. 12. TOTAL DELAYS AND COSTS Rodel outputs the total vehicle delay in hours over the results period. It gives the cost of this delay in British pounds sterling. (3-p.1 0) 110

PAGE 123

RODEL RESULTS ORIGINAL DESIGN TRAFFIC COUNTS AUGUST 1994 5194 VEIUCLES PER HOUR 85"/o CONFIDENCE LEVEL FLOW FACTOR1.56 ************************************************************************* 24:9:97 MAIN VAIL SOUTH. 200 FOOT ROUNDABOUT 17 ******************************************************************************* E (m) 8.01 7.21 8.67 8.50 14.63 15.00 TIME PERIOD min 90 L' (m) 7.81 85.23 9.23 6.39 64.78 0.0 TIME SLICE min 15 v (m) 5.27 6.32 7.92 7.37 6.40 15.00 RESULTS PERIOD min 15 75 RAD (m) 42.67 23.32 21.34 19.81 15.85 15.00 TIME COST $/min 7.79 PHI (d) 14.00 39.00 14.50 22.00 17.00 0.0 FLOW PERIOD min 15 75 DIA (m) 60.96 60.96 60.96 60.96 60.96 60.96 FLOW TYPE pcu/veh VEH GRAD SEP 0 0 0 0 0 0 FLOW PEAK am/op/pm PM ******************************************************************************* *LEG NAME *PCU *FLOWS (1st exit 2nd etc ... U)*FLOF*CL* FLOW RATIO *FLOW TIME LEGl *1.03* LEG2 30/ *1.03* LEG312?Y *1.03* LEG4 (o75". *1.03* LEGS 17'1/ *1.03* LEG6 *1.03* 0 0 127 55 117 0 128 34 372 73 605 0 75 154 179 206 0 0 189 0 145 0 289 0 24 5 0 99 105 0 0 *1.56*85*0.75 1.125 0.75*15 45 75 0 *1.56*85*0.75 1.125 0.75*15 45 75 0 *1.56*85*0.75 1.125 0.75*15 45 75 0 *1.56*85*0.75 1.125 0.75*15 45 75 0 *1.56*85*0.75 1.125 0.75*15 45 75 0 *1.56*85*0.75 1.125 0.75*15 45 75 . . FLOW CAPACITY AVE DELAY MAX DELAY AVE QUEUE MAX QUEUE veh veh mins mins veh veh 725 1351 0.10 0.14 1 2 336 956 0.10 0. 14 1 1 1434 1669 0.46 0.98 11 22 754 1011 0.36 0.72 5 8 1945 2245 0.41 0.93 13 29 -= 5I
PAGE 124

******************************************************************************* 23:9:97 MAIN VAIL SOUTH. 200 FOOT ROUNDABOUT 16 ******************************************************************************* * MAX RFC 0.85 0.85 0.85 0.85 0.85 0.85 TIME PERIOD min 90 * TIME SLICE min 15 v (m) 5.27 6.32 7.92 7.37 6.40 15.00 RESULTS PERIOD min 15 75 RAD (m) 42.67 23.32 21.34 19.81 15.85 15.00 TIME COST $/min 7.79 PHI (d) 14.00 39.00 14 0 so 22.00 17.00 0.0 FLOW PERIOD min 15 75 DIA (m) 60.96 60.96 60.96 60.96 60.96 60.96 FLOW TYPE pcu/veh VEH GRAD SEP 0 0 0 0 0 0 FLOW PEAK am/op/pm PM ******************************************************************************* LEG NAME *PCU *FLOWS (1st exit 2nd etc ... U)*FLOF*CL* FLOW RATIO *FLOW TIME * * * LEGl *1.03* 0 128 75 189 24 0 *1.00*85*0.75 1.125 0.75*15 45 75 LEG2 *1.03* 0 34 154 0 5 0 *1.00*85*0.75 1.125 0.75*15 45 75 LEG3 *1.03* 127 372 179 145 0 0 *1.00*85*0.75 1.125 0.75*15 45 75 LEG4 *1.03* 55 73 206 0 99 0 *1.00*85*0.75 1.125 0.75*15 45 75 LEGS *1.03* 117 605 0 289 105 0 *1.00*85*0. 75 1.125 0.75*15 45 75 LEG6 *1.03* 0 0 0 0 0 0 *1.00*85*0.75 1.125 0.75*15 45 75 * * * ******************************************************************************* * MAX RFC 0.44 0.23 0.59 0.44 0.85 0.00 * AVE DELAY min 0.08 0.07 0.07 0.08 0.17 0.02 AVDEL s 6.5 MIN ENTRY E 5.27 6.32 7.92 7.37 8.34 15.00 L 0 s 8 MAX FLARE L' 0.00 0.00 0.00 0.00 100.00 0.00 VEH HRS 6.0 MAX ENTRY E 16.40 16.40 16.40 16.40 16.40 16.40 COST $ 2820.6 MIN FLARE L' 0.00 0.00 0.00 0.00 7.16 0.00 ******************************************************************************* 112

PAGE 125

******************************************************************************* 23:9:97 MAIN VAIL SOUTH. 200 FOOT ROUNDABOUT 17 ******************************************************************************* *MAX DELAY 1. 00 1.00 1.00 1. 00 1. 00 1. 00 TIME PERIOD min 90 TIME SLICE min 15 v (m) 5.27 6.32 7.92 7.37 6.40 15.00 RESULTS PERIOD min 15 75 RAD (m) 42.67 23.32 21.34 19.81 15.85 15.00 TIME COST $/min 7.79 PHI (d) 14.00 39.00 14.50 22.00 17.00 0.0 FLOW PERIOD min 15 75 DIA (m) 60.96 60.96 60.96 60.96 60.96 60.96 FLOW TYPE pcu/veh VEH GRAD SEP 0 0 0 0 0 0 FLOW PEAK am/op/pm PM ******************************************************************************* LEG NAME *PCU *FLOWS (1st exit 2nd etc ... U)*FLOF*CL* FLOW RATIO *FLOW TIME LEGl *1. 03. 0 128 75 189 24 0 *1.00*85*0.75 1.125 0.75*15 45 75 LEG2 *1.03* 0 34 154 0 5 0 *1.00*85*0.75 1.125 0.75*15 45 75 LEG3 *1.03* 127 372 179 145 0 0 *1.00*85*0.75 1.125 0.75*15 45 75 LEG4 *1.03* 55 73 206 0 99 0 *1.00*85*0.75 1.125 0.75*15 45 75 w LEGS *1.03* 117 605 0 289 105 0 *1.00*85*0.75 1.125 0.75*15 45 75 LEG6 *1.03* 0 0 0 0 0 0 *1.00*85*0.75 1.125 0.75*15 45 75 ******************************************************************************* MAX DELAY mins 0.11 0.09 0.10 0.11 1. 00 0.03 AVDEL s 13 .. 6 MIN ENTRY E 5.27 6.32 7.92 7.37 7.17 15.00 L 0 s B MAX FLARE L' 0.00 0.00 0.00 0.00 100.00 0.00 VEH HRS 12.6 MAX ENTRY E 16.40 16.40 16.40 16.40 16.40 16.40 COST $ 5876.4 MIN FLARE L' 0.00 0.00 0.00 0.00 2.61 0.00 * ******************************************************************************* 113

PAGE 126

******************************************************************************* * 23:9:97 MAIN VAIL SOUTH. 200 FOOT ROUNDABOUT 18 ******************************************************************************* * *MAX QUEUE 10 10 10 10 10 10 TIME PERIOD min 90 * TIME SLICE min 15 v (m) 5.27 6.32 7.92 7.37 6.40 15.00 RESULTS PERIOD min 15 75 RAD (m) 42.67 23.32 21.34 19.81 15.85 15.00 TIME COST $/min 7.79 PHI (d) 14.00 39.00 14.50 22.00 17.00 0.0 FLOW PERIOD min 15 75 DIA (m) 60.96 60.96 60.96 60.96 60.96 60.96 FLOW TYPE pcu/veh VEH GRAD SEP 0 0 0 0 0 0 FLOW PEAK am/op/pm PM * ******************************************************************************* LEG NAME *PCU *FLOWS (1st exit 2nd etc ... U)*FLOF*CL* FLOW RATIO *FLOW TIME * * * LEGl *1.03* 0 128 75 189 24 0 *1.00*85*0.75 1.125 0.75*15 45 75 LEG2 *1.03* 0 34 154 0 5 0 *1.00*85*0.75 1.125 0.75*15 45 75 LEG3 *1.03* 127 372 179 145 0 0 *1.00*85*0.75 1.125 0.75*15 45 75 LEG4 *1.03* 55 73 206 0 99 0 *1.00*85*0.75 1.125 0.75*15 45 75 LEGS *1.03* 117 605 0 289 105 0 *1.00*85*0.75 1.125 0.75*15 45 75 LEG6 *1.03* 0 0 0 0 0 0 *1.00*85*0.75 1.125 0.75*15 45 75 * * ******************************************************************************* * MAX QUEUE vehs 0.77 0.30 1. 41 0.79 10.00 0.00 * AVDEL s 9.0 MIN ENTRY E 5.27 6.32 7.92 7.37 7.58 15.00 L 0 s 8 MAX FLARE L' 0.00 0.00 0.00 0.00 100.00 0.00 VEH HRS 8.3 MAX ENTRY E 16.40 16.40 16.40 16.40 16.40 16.40 COST $ 3902.5 MIN FLARE L' 0.00 0.00 0.00 0.00 4.12 0.00 * ******************************************************************************* 114

PAGE 127

10. Vail South Roundabout Configuration 10.1 Background Following on the next pages are photographs and geometric construction plans for the south and north roundabouts. Also, the RODEL printouts used in the design of the south roundabout are shown for review. According to the roundabout analysis program RODEL, the following percent increases in existing (August 1994) traffic would be possible without exceeding average stopped delay of 30 seconds per vehicle on any leg (a measure of practical capacity), estimated at the 85th percentile. Table 10-1 Possible % Increase In Traffic To Reach Capacity ROUNDABOUT Main Vail North Main Vail South 115 A.M. 117% 52% P.M. 65% 56%

PAGE 128

source ( 15) 116

PAGE 129

/-70/VA/L ROAD Vail, Colorado September 11, 1995 source (13) 117 Scale: 1" = 1 00'

PAGE 130

... .. I. .,;j ... .... t:: 4 1;, .;;. ... ..,.,, . , ... ... ; ... ., t,.u ,,., .. ,.,'11 .. :. .... :',\ ..... 4 lo<.'t' ,.,. .. : NT 11. 1 .. H \IT::..)' Q 0 .00' 000' .. 4 64" .. ,,; ..... 22 29' ...rt_ Y J68J' {ig H: ..... 72 99' S'!l" 4:1 4 4 68. 6.1 ::;: I 1! 20.48' 14 21 2 lJ. lllr )6. W 11 ,_,)-j;:, 20.2,. 24.11' 1 }4. 9J" 65 1 J" 5-4 64 9' J8. 7 .611 27. 80' 52.01 10).41' I )9" 1 .62' !16.l.t 104 '1 )J21J 60.' 11. ,. 1 16' 12 4). 10. !10' .... 817' I K 15.JJ' JO.o-lo6. U 6!1. 69' 7 J,. M -f-----+-----------.::.. ":" .:..:-: .. --= ":" .::: .. -::: .. -:-...:: .... ..... -f------1 118 D ... zu: :I c( D D C1 a: m z a. c a D z W z Q ... :I ...... D c( :I a: ... Cl l: Ul D ... :I -o u. m m o a a :I IL U I ., ;;; ., .... 0 % Figure 10-1

PAGE 131

RODEL RESULTS ORIGINAL DESIGN TRAFFlC COUNTS AUGUST 1994 llll VEIDCLES PER HOUR 85% CONFIDENCE LEVEL FLOW FACTOR-1.00 ******************************************************************************* * 23:9:97 MAIN VAIL SOliTH. 200 FOOT ROUNDABOliT 3 ******************************************************************************* E {m) 8.01 7.21 8.67 8.50 14.63 15.00 TIME PERIOD min 90 L' {m) 7.81 85.23 9.23 6.39 64.78 0.0 TIME SLICE min 15 v {m) 5,27 6 ._32 7.92 7 .. 37 6.40 15.00 RESULTS PERIOD min 15 75 RAD {m) 42.67 23.32 21..34 19.81 15.85 15.00 TIME COST $/min 7.79 PHI {d) 14.00 39.00 14.50 22.00 17.00 0.0 FLOW PERIOD min 15 75 DIA {m) 60.96 60.96 60.96 60.96 60.96 60.96 FLOW TYPE pcu/veh VEH GRAD SEP 0 0 0 0 0 0 FLOW PEAK am/op/pm PM ******************************************************************************* LEG NAME *PCU *FLOWS {1st exit 2nd etc ... U)*FLOF*CL* FLOW RATIO *FLOW TIME * LEG1 -'1/b *1.03* 0 128 75 189 24 0 *1.00*85*0.75 1.125 0.75*15 45 75 LEG2 /'/3 *1.03* 0 34 154 0 5 0 *1.00*85*0.75 1.125 0.75*15 45 75 LEG3 8Z3 *1.03* 127 372 179 145 0 0 *1.00*85*0.75 1.125 0.75*15 45 75 )..EG4 '133 *1;03* 55 73 206' 0 99 0 *1.00*85*0.75 1.125 0.75*15 45 75 LEGS Ill(, *1.03* 117 605 0 289 105 0 *1.00*85*0.75 1.125 0.75*15 45 75 LEG6-*1.03* 0 0 0 0 0 0 *1.00*85*0.75 1.125 0.75*15 45 75 .. 29'61 * * ******************************************************************************* * FLOW veh 465 216 919 484 1247= 333/ 0 * CAPACITY veh 1527 1266 1909 1423 2618 2617 AVDEL s 3.2 AVE DELAY mins 0.06 0.06 0.06 0.06 0.04 0.00 L 0 s A MAX DELAY mins 0.07 0.08 0.09 0.09 0.06 0.00 VEH HRS 3.0 AVE QUEUE veh 0 0 1 1 1 0 COST $ 1395 0 3 MAX QUEUE veh 1 0 1 1 1 0 ******************************************************************************* Figure 10-2 119

PAGE 132

RODEL RESULTS ORIGINAL DESIGN TRAFF1 C COUNTS AUGUST 1994 4994 VEHICLES rER II OUR 85% CONFIDENCE LEVEL FLOW .SO ******************************************************************************* .. 24:9:97 MAIN VAIL SOUTH. 200 FOOT ROUNDABOUT 18 .. E (m) 8 .01 7.21 8.67 8 .50 14.63 15.00 TIME PERIOD min 90 L' (m) 7.81 85.23 9.23 6 .39 64.78 0.0 TIME SLICE min 15 v (m) 5 .27 6.32 7.92 7.37 6.40 15.00 RESULTS PERIOD min 15 75 RAD (m) 42.67 23.32 21.34 19.81 15.85 15.00 TIME COST $/min 7.79 PHI (d) 14.00 39.00 14.50 22.00 17.00 0.0 FLOW PERIOD min 15 75 DIA (m) 60.96 60.96 60.96 60.96 60.96 60.96 FLOW TYPE pcu/veh VEH GRAD SEP 0 0 0 0 0 0 FLOW PEAK am/op/pm PM ******************************************************************************* LEG NAME *PCU *FLOWS (1st exit 2nd etc . U)*FLOFCL FLOW RATIO *FLOW TIME * LEGl *1.03* 0 128 75 189 24 0 .50*85*0.75 1 .125 0.75*15 45 75 LEG2 *1.03* 0 34 154 0 5 0 *1.50*85*0.75 1.125 0.75*15 45 75 LEG3 *1.03* 127 372 179 145 0 0 *1.50*85*0.75 1.125 0.75*15 45 75 LEG4 *1.03* 55 73 206 0 99 0 *1.50*85*0.75 1.125 0.75*15 45 75 LEGS *1.03* 117 605 0 289 105 0 *1.50*85*0.75 1.125 0.75*15 45 75 LEG6 *1.03* 0 0 0 0 0 0 *1.50*85*0.75 1.125 0.75*15 45 75 .. .. .. .. .. ******************************************************************************* FLOW veh 697 323 1379 725 1870::: t.f99'(o CAPACITY veh 1:369 990 1694 1055 2285 1807 AVDEL s 12.8 AVE DELAY mins 0.09 0.09 0.27 0.24 0.22 0.00 L 0 s B MAX DELAY mins 0.13 0.13 0 .52 0.44 0.45 0.00 VEH HRS 17.7 AVE QUEUE veh 1 1 6 3 7 0 COST $ 8270.4 MAX QUEUE veh 1 1 11 5 13 0 .. .......................................................................... Figure 10-3 120

PAGE 133

RODEL RESULTS ORIGINAL DESIGN TRAFFIC COUNTS AUGUST1994 5194 VEHICLES PER HOUR 85% CONFIDENCE LEVEL FLOW FACTOR1.56 .............................................................................. 24:9:97 E L v RAD PHI DIA GRAD (m) (m) (m) (m) (d) (m) SEP 8 .01 7.81 S.27 42.67 14.00 60.96 0 MAIN VAIL SOUTH. 200 FOOT ROUNDABOUT 7.21 85.23 6 .32 23.32 39.00 60.96 0 8.67 9 .23 7.92 21.34 14 .so 60.96 0 8.SO 6 .39 7.37 19.81 22.00 60.96 0 14.63 64.78 6 .40 1S.85 17.00 60.96 0 15.00 0.0 15.00 15.00 0.0 60.96 0 TIME PERIOD min TIME SLICE min RESULTS PERIOD min TIME COST $/min FLOW PERIOD min FLOW TYPE p cu/veh PEAK am/op/pm 17 90 15 15 75 7.79 15 75 VEH PM ............................................................................. *LEG NAME *PCU *FLOWS (1st exit 2nd etc ... U)*FLOF*CL* FLOW RATIO *FLOW TIME LEGl *1.03* LEG230/ *1.03* LEG312.'i'l *1.03* LEG4 ,75: *1.03* LEGS 17'1/ *1.03* LEG6 *1.03* 0 0 127 55 117 0 128 34 372 73 605 0 75 154 179 206 0 0 189 0 145 0 289 0 24 5 0 99 lOS 0 * 0 *1.56*85*0.7S 1.125 0.75*15 45 75 0 *l.S6*8S*0.75 1.125 0.75*1S 4S 75 0 *1.56*85*0.75 1.125 0.75*15 45 75 0 *l.S6*8S*0.75 1 .125 0.75*15 45 75 0 *1.56*85*0.75 1.12S 0 .75*1S 45 75 0 *1.S6*85*0.75 1.125 0.75*1S 45 7S FLOW CAPACITY AVE DELAY MAX DELAY AVE QUEUE MAX QUEUE veh veh mins mins veh veh 725 1351 0.10 0.14 1 2 336 956 0.10 0.14 1 1 1434 1669 0 .46 0.98 11 22 754 1011 0.36 0. 72 5 8 1945 =51t:f 'lo 2245 1711 AVDEL s 0.41 0.00 L 0 s 0.93 0.00 VEH HRS 13 0 COST $ 29 0 21.1 c 30.4 14197.3 ............................................................................. Figure 10-4 121

PAGE 134

******************************************************************************* 23:9:97 MAIN VAIL SOUTH. 200 FOOT ROUNDABOUT 16 ******************************************************************************* * MAX RFC 0.85 0.85 0.85 0.85 0.85 0.85 TIME PERIOD min 90 * TIME SLICE min 15 v (m) 5.27 6.32 7.92 7.37 6.40 15.00 RESULTS PERIOD min 15 75 RAD (m) 42.67 23.32 21.34 19.81 15.85 15.00 TIME COST $/min 7.79 PHI (d) 14.00 39.00 14.50 22.00 17.00 0.0 FLOW PERIOD min 15 75 DIA (m) 60.96 60.96 60.96 60.96 60.96 60.96 FLOW TYPE pcu/veh VEH GRAD SEP 0 0 0 0 0 0 FLOW PEAK am/op/pm PM ******************************************************************************* LEG NAME *PCU *FLOWS (1st exit 2nd etc ... U)*FLOF*CL* FLOW RATIO *FLOW TIME LEGl *1.03* 0 128 75 189 24 0 *1.00*85*0.75 1.125 0.75*15 45 75 LEG2 *1.03* 0 34 154 0 5 0 *1.00*85*0.75 1.125 0.75*15 45 75 LEG3 *1.03* 127 372 179 145 0 0 *1.00*85*0.75 1.125 0.75*15 45 75 .LEG4 *1. 03* 55 73 206 0 99 0 *1.00*85*0.75 1.125 0.75*15 45 75 LEGS *1.03* 117 605 0 289 105 0 *1.00*85*0.75 1.125 0.75*15 45 75 LEG6 *1.03* 0 0 0 0 0 0 *1.00*85*0.75 1.125 0.75*15 45 75 * * ******************************************************************************* MAX RFC 0.44 0.23 0.59 0.44 0.85 0.00 AVE DELAY min 0.08 0.07 0.07 0.08 0.17 0.02 AVDEL s 6.5 MIN ENTRY E 5.27 6.32 7.92 7.37 8.34 15.00 L 0 s B MAX FLARE L' 0.00 0.00 0.00 0.00 100.00 0.00 VEH HRS 6.0 MAX ENTRY E 16.40 16.40 16.40 16.40 16.40 16.40 COST $ 2820.6 MIN FLARE L' 0.00 0.00 0.00 0.00 7.16 0.00 ******************************************************************************* 122

PAGE 135

************************* * 23:9:97 MAIN VAIL SOUTH. 200 FOOT ROUNDABOUT 17 ******************************************************************************* *MAX DELAY 1. 00 1. 00 1. 00 1. 00 1.00 1. 00 TIME PERIOD min 90 * TIME SLICE min 15 v (m) 5.27 6.32 7.92 7.37 6.40 15.00 RESULTS PERIOD min 15 75 RAD (m) 42.67 23.32 21.34 19.81 15.85 15.00 TIME COST $/min 7.79 PHI (d) 14.00 39.00 14.50 22.00 17.00 0.0 FLOW PERIOD min 15 75 DIA (m) 60.96 60.96 60.96 60.96 60.96 60.96 FLOW TYPE pcu/veh VEH GRAD SEP 0 0 0 0 0 0 FLOW PEAK am/op/pm PM ******************************************************************************* LEG NAME *PCU *FLOWS (1st exit 2nd etc ... U)*FLOF*CL* FLOW RATIO *FLOW TIME * * * LEGl 1. 03 0 128 75 189 24 0 *1.00*85*0.75 1.125 0.75*15 45 75 LEG2 *1.03* 0 34 154 0 5 0 *1.00*85*0.75 1.125 0.75*15 45 75 LEG3 *1.03* 127 372 179 145 0 0 *1.00*85*0.75 1.125 0.75*15 45 75 LEG4 1. 03* 55 73 206 0 99 0 *1.00*85*0.75 1.125 0.75*15 45 75 w LEGS *1.03* 117 605 0 289 105 0 *1.00*85*0.75 1.125 0.75*15 45 75 LEG6 1. 03* 0 0 0 0 0 0 *1.00*85*0.75 1.125 0.75*15 45 75 * * ******************************************************************************* * MAX DELAY mins 0.11 0.09 0.10 0.11 1. 00 0.03 AVDEL s 13 .. 6 MIN ENTRY E 5.27 6.32 7.92 7.37 7.17 15.00 L 0 s B MAX FLARE L' 0.00 0.00 0.00 0.00 100.00 0.00 VEH HRS 12.6 MAX ENTRY E 16.40 16.40 16.40 16.40 16.40 16.40 COST $ 5876.4 MIN FLARE L' 0.00 0.00 0.00 0.00 2.61 0.00 * ******************************************************************************* 123

PAGE 136

******************************************************************************* * 23:9:97 MAIN VAIL SOUTH. 200 FOOT ROUNDABOUT 18 ******************************************************************************* * *MAX QUEUE 10 10 10 10 10 10 TIME PERIOD min 90 * TIME SLICE min 15 v (m) 5.27 6.32 7.92 7.37 6.40 15.00 RESULTS PERIOD min 15 75 RAD (m) 42.67 23.32 21.34 19.81 15.85 15.00 TIME COST $/min 7.79 PHI (d) 14.00 39.00 14.50 22.00 17.00 0.0 FLOW PERIOD min 15 75 DIA (m) 60.96 60.96 60.96 60.96 60.96 60.96 FLOW TYPE pcu/veh VEH GRAD SEP 0 0 0 0 0 0 FLOW PEAK am/op/pm PM ******************************************************************************* LEG NAME *PCU *FLOWS (1st exit 2nd etc ... urFLOF*CL* FLOW RATIO *FLOW TIME * * LEG1 *1.03* 0 128 75 189 24 0 *1.00*85*0.75 1.125 0.75*15 45 75 LEG2 *1.03* 0 34 154 0 5 0 *1.00*85*0.75 1.125 0.75*15 45 75 LEG3 *1.03* 127 372 179 145 0 0 *1.00*85*0.75 1.125 0.75*15 45 75 .LEG4 *1.03* 55 73 206 0 99 0 *1.00*85*0.75 1.125 0.75*15 45 75 LEGS *1.03* 117 605 0 289 105 0 *1.00*85*0.75 1.125 0.75*15 45 75 LEG6 *1.03* 0 0 0 0 0 0 *1.00*85*0.75 1.125 0.75*15 45 75 * * * ******************************************************************************* * MAX QUEUE vehs 0.77 0.30 1. 41 0.79 10.00 0.00 * AVDEL s 9.0 MIN ENTRY E 5.27 6.32 7.92 7.37 7.58 15.00 L 0 s B MAX FLARE L' 0.00 0.00 0.00 0.00 100.00 0.00 VEH HRS 8.3 MAX ENTRY E 16.40 16.40 16.40 16.40 16.40 16.40 COST $ 3902.5 MIN FLARE L' 0.00 0.00 0.00 0.00 4.12 0.00 * ******************************************************************************* 124

PAGE 137

****************************************************************************** 23:9:97 MAIN VAIL SOUTH. 200 FOOT ROUNDABOU 5 ****************************************************************************** PM PEAK LEG NUMBER 1 LEG1 ****************************************************************************** * TIME *ARRIV FLOW* CAPACITY .. FLOW/CAP *END QUEUES*TOT DELAY *EXIT FLOW mins *vehs/slice*vehs/slice* (RFC) vehs mins *veh/slice 0 15 87.45 401.45 0.22 0.28 2.08 201.51 15 30 104.43 389.76 0.27 0.36 4.81 241.03 30 45 127.90 373.92 0.34 0.52 6.61 295.02 45 60 127.90 373.80 0.34 0.52 7.76 295.45 60 75 104.43 389.64 0.27 0.37 6.65 241.67 75 90 87.45 401.31 0.22 0.28 4.86 202.23 * * * * * * * * * * * * * * * ****************************************************************************** 125

PAGE 138

****************************************************************************** 23:9:97 MAIN VAIL SOUTH. 200 FOOT ROUNDABOU 5 ****************************************************************************** * PM PEAK LEG NUMBER 2 LEG2 ****************************************************************************** TIME mins 0 15 15 30 30 45 45 60 .. 60 75 75 90 *ARRIV FLOW* CAPACITY FLOW/CAP *END QUEUES*TOT DELAY *EXIT FLOW *vehs/slice*vehs/slice* (RFC) vehs mins veh/slice 40.57 351.06 48.45 330.58 59.34 .. 302.74 59.34 302.54 * 48.45 330.33 .. .. 40.57 350.72 .. .. .. .. .. * * 0.12 0.13 0.15 0.17 0.20 0.24 0.20 0.24 0.15 0.17 0.12 0.13 .. . * * 0.98 2.26 3.10 3.64 .. 3.12 2.28 * 0.00 0.00 0.00 0.00 0.00 0.00 ****************************************************************************** 126

PAGE 139

****************************************************************************** 23:9:97 MAIN VAIL SOUTH. 200 FOOT ROUNDABOU 5 ****************************************************************************** PM PEAK LEG NUMBER 3 LEG3 ********************** TIME mins 0 15 30 45 60 75 15 30 45 60 75 90 *ARRIV FLOW* CAPACITY vehs/slicevehs/slice 173.01 503.90 . 206.59 488.04 253.03 466.44 253.03 466.30 206.59 487.83 173.01 503.59 FLOW/CAP *END QUEUES*TOT DELAY *EXIT FLOW (RFC) vehs mins veh/slice 0. 34 0.52 3.90 108.19 0.42 0.73 9.38 129.42 0.54 1.17 14.28 158.42 0.54 1.18 17.66 158.64 0.42 0.74 14.39 129.74 0.34 0.53 9.49 108.58 ****************************************************************************** 127

PAGE 140

****************************************************************************** 23:9:97 MAIN VAIL SOUTH. 200 FOOT ROUNDABOU 10 ****************************************************************************** * PM PEAK LEG NUMBER 4 LEG4 ****************************************************************************** * * TIME *ARRIV FLOW* CAPACITY FLOW/CAP *END QUEUES*TOT DELAY *EXIT FLOW mins *vehs/slice*vehs/slice* (RFC) vehs mins *veh/slice * * 0 15 91.03 401.62 0.23 0.29 2.19 71.48 15 30 108.69 374.45 0.29 0.41 5.24 85.53 30 45 133.12 337.40 0.39 0.65 7.90 104.69 45 60 133.12 337.08 0.39 0.65 9.72 104.84 60 75 108.69 373.97 0.29 0.41 7.96 85.75 75 90 91.03 401.04 0.23 0.29 5.30 71.76 * * * * * * * * * * * * * * * * * * * * * * * * * * ****************************************************************************** 128

PAGE 141

****************************************************************************** * 23:9:97 MAIN VAIL SOUTH. 200 FOOT ROUNDABOU 10 ****************************************************************************** PM PEAK LEG NUMBER 5 LEGS ****************************************************************************** TIME *ARRIV FLOW* CAPACITY FLOW/CAP *END QUEUES*TOT DELAY *EXIT FLOW mins *vehs/slice*vehs/slice* (RFC) vehs mins *veh/slice * 0 15 234.61 696.08 0.34 0.51 3.80 161.37 15 30 280.14 671.45 0.42 0.71 9.15 193.11 30 45 343.11 .. 637.90 .. 0.54 .. 1.16 .. 14.01 236.37 45 60 343 .11 .. 637.58 0.54 .. 1.16 .. 17.37 236.73 60 75 280.14 670.98 0.42 0. 72 14.10 193.64 75 90 234.61 695.53 0.34 0.51 9.23 162.06 * * * * * * * * * * * * * * * * * * * ****************************************************************************** 129

PAGE 142

11. Data Collection and Summary 11.1 Location Traffic count data in the south Vail roundabout was obtained on July 4, 1997 when traffic entering the roundabout was at its highest since it was opened. Approach number 1 was the Vail Road approach from the north into the south roundabout. On approach number 3 (south frontage road approach from west) the outside lane was coned off so the approach was 8.67 meters as originally analyzed. This outside lane only lasts for a short distance from a driveway. On approach number 5 (south frontage road from east) the bypass lane was coned off so the traffic had to enter the roundabout. Traffic on any approach which did not have at least 5 vehicles queued was stopped until the queues on that approach was a minimum of 5 vehicles. Then the traffic at the east frontage road entry, which had the longest queue was allowed to enter the roundabout followed by the other sequential approaches. One minute counts of the total inflow from the entry and the corresponding circulating flow across the entry were obtained at each entry to the roundabout. This was repeated 15 times between the P.M. hours of2:30 and 7:00. One person was located at each approach to count the traffic. Only 15 one minute counts were obtained during this time period because of the time for setup and concern regarding the stopping of traffic. Counts were taken with hand held counters at each entry to the roundabout. 130

PAGE 143

11.2 Data Summary Table 11.1 summarizes all 15 of the one minute entry flows Qe and circulating flows Qc measured at each of the five entry approaches to the roundabout. The statistical analysis of each entry's data set is also shown on Table 11.1. The main value we need from the statistical analysis for each entry is the mean entry flow Qe and the mean circulating flow Qc for all of the saturated minutes together, both in pculh. The mean entry flow Qe and the mean circulating flow Qc for all the saturated minutes together, both in pculh were then multiplied times 60 to obtain the at capacity hourly entry flows Qe and the at capacity hourly circulating flow Qc. Table 11.2 summarizes calculations from the roundabout geometry calculating the slope of the entry I circulating flow relationship by means of the following equation: f c = k ( 0.210 t D ( 1 + 0.2 X 2) ) where k = 1 0.00347 ( 030)-0.978 ( ( 1 I r) -0.5))) Table 11.2 also summarizes the locally corrected intercept given by FL =Qe+fcQc and the entry I circulating flow line calculated is Qe L = F -fc Q c 1 31

PAGE 144

VAIL SOUTH ROUNDABOUT TABLE 11 JULY 4,1997 ACTUAL FIELD COUNTS FLOWING THROUGH ROUNDABOUT AT CAPACITY BY QUEUING UP TRAFFIC ON EACH APPROACH 2 :30P. M 7:00P.M. ENTRY FLOW 1 HR CIRCULATING FLOW 1 HR MEDIAN LEG COUNT 1 MINUTE ENTRY MEDIAN 1 MINUTE COUNT CIRCULATING CIRCULATING NUMBER COUNT FLOW ENTRY FLOW FLOW FLOW Pcu/Min Pcu/Hr Pcu/Hr Pcu/Min Pcu/Hr Pcu/Hr 1 17 1020 21 1260 LEG 1 ENTRY FLOW LEG 1 CIRCULATING FLOW 2 15 900 16 960 3 15 900 19 1140 Mean 1004 Mean 1120 4 16 960 18 1080 Standard Error 23.028 Standard Error 29 081 5 16 960 19 1140 Median 960 Median 1140 6 19 1140 21 1260 Mode 960 Mode 1140 7 15 900 20 1200 Standard Deviation 851. 187 Standard Deviation 112 631 8 19 1140 18 1080 Sample Variance 7954 .286 Sample Variance 12685.714 9 16 960 15 900 Kurtosis .222 Kurtosis .{) 426 10 18 1080 20 1200 Skewness 0 528 Skewness .{) 562 11 16 960 19 1140 Range 240 Range 360 12 19 1140 18 1080 Minimum 900 l\lllnlmum 900 13 16 960 16 960 Maximum 1140 Maximum 1260 -' 14 18 1080 19 1140 Sum 15060 Sum 16800 w 15 16 960 21 1260 Count 15 Count 15 N 1004 1120 Confidence Level(95.0%) 49.390 Conftdence Level(95.0%) 62. 373 CorT&Iadon Coefficient R Between a. and Qc 0 247 Std Error ol Predlc Cap s.sazl!td Error of Predlc Cap 7 041 2 1 9 540 37 2220 LEG 2 ENTRY FLOW LEG 2 CIRCULATING FLOW 2 8 4110 34 2040 3 8 480 40 2400 Mean 460 Mean 2120 4 10 600 35 2100 Standard Error 20 840 Standard Error 47 449 5 7 420 38 2260 Median 420 Median 2100 6 6 360 34 2040 Mode 420 Mode 2220 7 7 420 32 1920 Standard Deviation 80. 711 tandard Deviation 183 770 8 7 420 35 2100 Sample Variance 6514 286 mple Variance 33771.429 9 8 480 38 2280 Kurtosis .{) .756 Kurtoels .{) 789 10 6 360 30 1800 Skewness 0 504 Skewness .{) 106 11 7 420 37 2220 Range 240 Range 600 12 10 600 36 2160 Minimum 360 Minimum 1800 13 6 360 33 1980 Maximum 600 Maximum 2400 14 7 420 31 1860 Sum 6900 Sum 3 1 600 15 9 540 40 2400 Count 15 Count 15 460 2120 Confidence Level(95 .0%) 44 .696 Confidence Level(95 0%) 101. 769 CorT&Iation Coefficient R Between Qe and Qc 0 497 Sid Error of Predlc Cap 4 .052IStd Error of Predlc Cap 9.225

PAGE 145

ENTRY FLOW 1 HR CIRCULATING FLOW 1 HR MEDIAN LEG COUNT 1 MINUTE ENTRY MEDIAN 1 MINUTE COUNT CIRCULATING CIRCULATING NUMBER COUNT FLOW ENTRY FLOW FLOW FLOW Pcu/Min Pcu/Hr Pcu/Hr Pcu/Min Pcu/Hr Pcu/Hr 3 1 17 1020 29 1740 LEG 3 ENTRY FLOW LEG 3 CIRCULATING FLOW 2 18 1080 28 1880 3 20 1200 32 1920 Mean 1040 Mean 1636 4 15 900 29 1740 Slandard Error 25.298 Slandard Error 43.214 5 18 1080 25 1500 Median 1020 Median 1620 6 20 1200 27 1620 Mode 1020 Mode 1620 7 17 1020 22 1320 Slandard Oeviadon 97.980 Slandard Deviation 167.366 8 18 1080 26 1560 Sample Variance 9600.000 Sample Variance 28011.429 9 16 960 27 1620 Kurtosis .{1.651 Kurtosis .{1.272 10 17 1020 25 1500 Skewness 0.059 Skewness .{1.226 11 15 900 23 1380 Range 300 Range 600 12 17 1020 28 1680 Minimum 900 Minimum 1320 13 18 1080 27 1620 Maximum 1200 Maximum 1920 14 15 900 31 1860 Sum 15600 Sum 24540 15 19 1140 30 1800 Count 15 Count 15 1040 1636 Confidence Level(95.0%) 54.259 Confidence Level(95.0%) 92.684 Correlation Coellident R Between Qe and Qc 0.214 ...... Std Error of Predlc Cap 8232IStd Error of Predlc Cap 10.645 w w 4 1 10 600 36 2160 LEG 4 ENTRY FLOW LEG 4 C/RCULA TING FLOW 2 11 660 33 1980 3 10 600 34 2040 Mean 632 Mean 2192 4 12 720 42 2520 Slandard Error 18.393 Slandard Error 50.325 5 11 660 38 2280 Median 660 Median 2160 6 13 780 39 2340 Mode 880 Mode 2160 7 11 660 36 2160 Slandard Deviation 71.234 Slandard Deviation 194.907 8 9 540 34 2040 Sample Variance 5074.286 Sample Variance 37988.571 9 11 660 41 2460 Kurtosis 1.156 Kur1Dsls .208 10 10 600 39 2340 Skewness .{1.091 Skewness 0.369 11 11 860 32 1920 Range 300 Range 600 12 11 660 35 2100 Minimum 480 Minimum 1920 13 10 600 35 2100 Maximum 780 Maximum 2520 14 8 480 33 1980 Sum 9480 Sum 32880 15 10 600 41 2460 Count 15 Count 15 632 2192 Confidence Level(95.0%) 39.448 Confidence Levei(95.0%) 107.936 Correlation Coellicient R Between Qe and Qc 0.440 Sid Error of Predlc Cap 3.831IStd Error of Predic Cap 10.483

PAGE 146

ENTRY FLOW 1 HR CIRCULATING FLOW 1 HR MEDIAN LEG COUNT 1 MINUTE ENTRY MEDIAN 1 MINUTE COUNT CIRCULATING CIRCULATING NUMBER COUNT FLOW ENTRY FLOW FLOW FLOW Pcu/Min Pcu/Hr Pcu/Hr Pcu/Min Pcu/Hr Pcu/Hr 5 1 32 1920 25 1500 LEG 5 ENTRY R.OW LEG 5 C/RCULA TING FLOW 2 28 1680 23 1 380 3 31 1860 21 1260 Mean 1868 Mean 1384 4 34 2040 23 1380 Standard Error 30 910 Standard Error 40 .341 5 32 1920 22 1320 Median 1920 Median 1380 6 33 1980 26 1560 Mode 1920 Mode 1380 7 32 1920 27 1620 Standard DeviaUon 119 714 Standard Deviation 156 242 8 31 1860 19 1140 Sample Varlance 14331 429 Sample Variance 24411 429 9 28 1680 21 1260 Kurtosis 0 248 Kurtosis -{). 938 10 31 1860 24 14-40 Skewness -{).958 Skewness 0 000 11 32 1920 25 1500 Range 420 Range 480 12 33 1980 23 1380 Minimum 1820 Minimum 1140 13 32 1920 27 1620 Maximum 2040 Maximum 1620 14 27 1620 21 1260 Sum 28020 Sum 20760 15 31 1860 19 1140 Count 15 Count 15 1868 1384 Confidence Level(95 0%) 66 295 Confidence Level(95 0 % ) 86 524 Correlation Coellident R Between Qe and Qc 0 424 w Std Error of Predlc Cap S.5441Std Error of Predlc Cap 8 540 .t>.

PAGE 147

All measured data for entry flow and circulating flows have been graphed. Also, graphed is the linear entry capacity Q E vs circulating flow Q c relationship for each leg into the roundabout. 135

PAGE 148

&"" J: :3 (.) !!:.. 0 ...J 11. (!) w z 0"\ i= :3 :::1 (.) 0:: (.) ):: 0:: 1z w LEG 1 ENTRY FLOWS VS CIRCULATING FLOWS FIGURE 11-1 1400 -1200 1000 800 400 200 0 2 3 4 5 6 7 8 9 10 11 12 COUNT NUMBER 13 14 15

PAGE 149

J: 3 u !?;.. 0 ...J LL. w (!) -..J z i= :3 ::I u a: u ):: a: ..... z w LEG 2 ENTRY FLOWS VS CIRCULATING FLOWS FIGURE 11-1 2000 1500 1000 500 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 COUNT NUMBER

PAGE 150

w co ::1: ::; () !!:. ;: 0 ..J (!) z i= ::J () 0:: () ):: 0:: 1z w 2000 1800 1600 1400 1200 1000 800 600 400 200 0 2 3 4 LEG 3 ENTRY FLOWS VS CIRCULATING FLOWS FIGURE 11-1 5 6 7 8 9 10 11 12 13 COUNT NUMBER 14 15

PAGE 151

" J: 3 u !:. 0 ...J LL. (!) w z 1.0 i= :J u 0:: u ):: 0:: 1z UJ LEG 4 ENTRY FLOWS VS CIRCULATING FLOWS FIGURE 11-1 3000 -2500 2000 1500 1000 500 0 2 3 4 5 6 7 8 9 10 11 12 COUNT NUMBER 13 14 15

PAGE 152

J: 3 0 :: 0 ..J u... (!) """ z 0 f= :5 ::;:) 0 0:: 0 ): 0:: 1z w LEG 5 ENTRY FLOWS VS CIRCULATING FLOWS FIGURE 11-1 2500 -.. ... 2000 1500 1000 500 0 2 3 4 5 6 7 8 9 10 11 12 COUNT NUMBER 13 14 15

PAGE 153

VAIL SOUTH 200 FOOT DIAMETER ROUNDABOUT TABLE 11-2 -------CAPACITY USING SIX REGRESSION EQUATIONS --BASED ON GEOMETRY PARAMETER SYMBOL LEG 1 LEG2 LEG3 LEG4 LEGS ----1 CAPACITY=MAXIMUM ENTERING FLOW, PCUIH Qe 0 00 0 00 0.00 0.00 0.00 2 CIRCULATING FLOW, PCUIH Qc 0.00 0 00 0 00 0 00 0 00 3 ENTRY WIDTH, M e 8.01 7 .21 8.67 8 50 14. 63 4 LENGTH OF FLARE, M L 7.81 85 23 9.23 6 39 64.78 S APPROACH HALF-WIDTH, M v S.27 6 32 7.92 7 37 6 40 --6 INCRIBED CIRCLE DIAMETER, M 0 60.96 60 96 60.96 60.96 60. 96 7 ENTRY ANGLE DEGREES 0 14.00 39 00 14. 50 22 00 17. 00 II ENTRY RADIUS, M r 42.67 23 32 21.34 19.81 15.85 SIX REGRESSION EQUATIONS EQUATION LEG1 LEG2 LEG3 LEG4 LEGS 1 SHARPNESS OF FLARE 5 = 1.6 (e-v)/ L 0.561 0 017 0.130 0.283 0.203 2 ENTRY WIDTH PARAMETER Xz = v + (e-v) I (1 + 2 5) 6.561 7 .181 8.515 8.092 12.251 3 FUNCTION OF D lo = 1 + 0.5/ (1 + exp ((0-e()) /10 )) 1.238 1. 238 1.238 1.238 1.238 4 ADJUSTMENT FACTOR, CAP CURVE k = 1 0.00347 ( 0-30 ) 0 .978 ((1/r)-0.05) 1 .081 0 976 1 057 1. 027 1. 032 ..... 5 SLOPE OF CAPACITY CURVE fc = 0.210 to ( 1 +0.2 Xz ) 0.60112 0 63338 0.70274 0.68072 0 89700 6 Y INTERCEPT, PCUIMIN F = 303X2 1987 932 217S 910 2580 114 2451 766 3712 118 ..... PREDICTIVE EQUATIONS OF CAPACITY I 1 SLOPE OF ENTRY/CIRCULATING FLOW RELATION fc .. k (f .I 0.65011 0.61801 0.74270 0.69930 0.92598 2 ENTRY CAPACITY Qe = k (F-fc 0.:) when fc Oc<= F, and 2149.948 2123.105 2726.808 2518.677 3832.044 Qe =0 when fc 0.: > F ------f--------3 CIRCULATING FLOW Qc z (F -(Qa/k))lf. 3307.04 3435 40 3671.49 3601.74 4138 37 @ ENTRY CAPACITY ( Qe I= 0 f--------------------------. -----------------------------------: ____ -.. 1 :::=== ----------------------------------------. . I _____ -----------------------------------=--.--------------------------r---_-.. r =-=---= --------------------------I

PAGE 154

GRAPH OF CIRCULATING FLOW VS ENTRY CAPACITY OF LEG 1 BASED ON GEOMETRY VAIL SOUTH 200 FOOT DIAMETER ROUNDABOUT CIRCULATING FLOW Qc ENTRY CAPACITY Qe 3307.04 0 0 0 0 2149.948 0 0 FIGURE 11-2 DATA ORIGIN RODEL RODEL -----------------------------------------------------------------------------ENTRY CAPACITY Qe VS CIRCULATING FLOW Qc-LEG 1 ENTRY 2000 & 1500 Do. < u >-a: 1z w 500 0 500 1000 1500 2000 2500 3000 3500 CIRCULATING FLOW Qc 142

PAGE 155

GRAPH OF CIRCULATING FLOW VS ENTRY CAPACITY OF LEG 2 BASED ON GEOMETRY VAIL SOUTH 200 FOOT DIAMETER ROUNDABOUT CIRCULATING FLOW Qe ENTRY CAPACITY Qe 3435.4 0 0 0 0 2123.105 0 0 ENTRY CAPACITY Qe VS CIRCULATING FLOW Qc LEG 2 ENTRY 2000 a 1:: 1500 c:; : c( (.J >-a: 1000 ,_ z w 500 0 500 1000 1500 2000 2500 CIRCULATING FLOW Qc 143 FIGURE 11-2 3000 DATA ORIGIN RODEL RODEL 3500

PAGE 156

GRAPH OF CIRCULATING FLOW VS ENTRY CAPACITY OF LEG 3 BASED ON GEOMETRY VAIL SOUTH 200 FOOT DIAMETER ROUNDABOUT CIRCULATING FLOW Qc ENTRY CAPACITY Qe 3671.49 0 0 0 0 2726.808 0 0 ----------------------------------------------ENTRY CAPACITY Qe VS CIRCULATING FLOW Qc-LEG 3 ENTRY 3000 2500 2000 a r= f 1500 c( u > a: ... z 11.1 1000 500 0 0 500 1000 1500 2000 2500 3000 CIRCULATING FLOW Qe 144 FIGURE 11-2 DATA ORIGIN 3500 RODEL RODEL 4000

PAGE 157

GRAPH OF CIRCULATING FLOW VS ENTRY CAPACITY OF LEG 4 BASED ON GEOMETRY VAIL SOUTH 200 FOOT DIAMETER ROUNDABOUT CIRCULATING FLOW Qc ENTRY CAPACITY Qe 3601.74 0 0 0 0 2518.677 0 0 .------------------------------------------ENTRY CAPACITY Qe VS CIRCULATING FLOW Qc-LEG 4 ENTRY 2500 2000 a 0 <( ... 1500 <( u )a: 1z w 1000 500 0 0 500 1000 1500 2000 2500 3000 CIRCULATING FLOW Qc 145 FIGURE 11-2 DATA ORIGIN 3500 RODEL RODEL 4000

PAGE 158

GRAPH OF CIRCULATING FLOW VS ENTRY CAPACITY OF LEG 5 BASED ON GEOMETRY VAIL SOUTH 200 FOOT DIAMETER ROUNDABOUT & u o( .... o( u >-It: 1z w CIRCULATING FLOW Qc ENTRY CAPACITY Qe 4000 3500 3000 2500 2000 1500 1000 500 0 0 4138.37 0 0 0 500 0 3832.044 0 0 ENTRY CAPACITY Qe VS CIRCULATING FLOW Qc LEG 5 ENTRY 1000 1500 2000 2500 3000 CIRCULATING FLOW Qc 146 3500 FIGURE 11-2 DATA ORIGIN 4000 RODEL RODEL 4500

PAGE 159

12. Data Analysis 12.1 Introduction In this section, the data are more closely examined, and capacity comparisons are made between the collected data and the British Rodel computer model capacity regression equations. Table 12.1 shows the results of this comparative analysis. The results show that the measured capacity in the field was approximately 17% below the capacity level as calculated by the Rodel computer model using the six capacity regression equations. The confidence limits associated with the equations obtained in this way depend on the conditions of operation of the entry in question, but typically the standard error of the estimate near the mean should generally be less than 100 pcufhr. Table 12.1 shows an evaluation of this south Vail roundabout by calculating the standard deviation, cr (pcufhr), of the one-minute counts ofthe measured Qe entry flows, and the correlation coefficient, R, between the measured Qe and the Qc values. Then the standard error of the predicted capacity near the mean is calculated by the formula cr ( 1 -R2 ) IN where N is the number of one-minute counts. Table 12.1 shows the standard error of the predicted capacity ranges from 3.83 to 6.54 pcufhr for the entry flows, and from 7.05 to 10.65 pcufhr for the circulating flow. This standard error of the estimate near the mean is well within the expected range of 0 to 1 00 pcufhr. 147

PAGE 160

Descriptive statistics (table 12-2) were performed for each legs entry flow and circulating flow. Statistics calculated include: mean, standard error, median, mode, standard deviation, sample variance, kurtosis, skewness, range, minimum, maximum, sum, count, confidence level, correlation cofficient R between Q e and Q c, and standard error of the predicted capacity near the mean. Table 12-3 shows the calculations for the corrected Y-intercept and corrected entry/circulating flow line based on the field measurements obtained. Graphs are shown (see figure 12-3) for each leg showing the entry capacity and circulating flows based on RODEL calculations and measured flows. Table 12-4 shows the Pearson Correlation between the measured and expected values. Table 12-2 shown on the next page provides a statistical t test for a paired two sample for means related to the measured entry and circulating flows. The same test was performed for the expected entry and circulating flows. For the measured entry and circulating flows a pearson correlation was calculated showing a high degree of correlation at 0.9987. For the expected entry and circulating flows a Pearson Correlation was calculated also showing a high degree of correlation at 0. 9897. 12.2 Linearity The predictive equations of capacity are linear in the circulating flow. In previous studies it has not been possible to demonstrate any degree of non-linearity. In the Track Experiment by British engineers there was no measurable deviation from 148

PAGE 161

linearity in any test, and straight-line fits accounted for more than 90 per cent of the variance of Qe in most tests, with no systematic trend in the residual 10 per cent. The present analysis yields similar results. The problem is slightly more complicated for public road sites, where the variability of entry capacity measurements for a given site is rather higher than on the Test Track. The conclusion that there is no evidence for non-linearity in the data for sites considered separately might not then be sufficient in itself, since between-sites variation might, after geometric differences had been accounted for, provide evidence for residual non-linearity. The form ofnon-linearity sought is simple. As seen in Figure 12-1 ifnon-linearity is present it should result in a curve of the form concave upwards and with no oscillatory behavior. It is easiest to represent such a trend by means of a parabolic correction term in the entry capacity: Qe = Qe (p) + ( A + BQc + CQc 2 ) Where Qe (p) is the capacity predicted by the linear representation and A, B, and C are coefficients defining the parabolic term, and are determined by regression analysis. Formally, the above equation corresponds to a second order empirical model. However, the inclusion of such a parabolic term does not contribute significantly to the explained variance ofthe entry capacity. The result obtained, that A=+ 105 pculhr/, B =-0.1425, and C = + 0.0000405 (pculhr) -I contributes a non significant 0.6 per cent to the explained variance of Qe, and the parabolic term has a very low value over the range of circulating flow. 149

PAGE 162

..c c Figure 12-1 AB: Linear representation (first order empirical model) CD : Second order empirical model D B (b) ENTRY/CIRCULATING FLOW RELATIONSHIP ENTRY CAPACITY,
PAGE 163

The point is further illustrated by examining the residuals left by the linear representation. Figure 12-2 shows the means of residuals within successive 300 pculhr bands of circulating flow. Simple non-linearity would result in a trend from positive values of the mean residuals at low Qc to negative values at intermediate Qc, and to positive values again at high Qc. But the results shown do not justify such a conclusion. Apart from gap=acceptance considerations, non-linearity might in principle arise from the fact that in practice it is difficult to suppress the entry flow entirely, even when circulating flow is very large. As Qc increases the entry/circulating flow line is likely ultimately to become horizontal at some small but finite value of Qe. The present analysis suggests that the operation of roundabouts on the public roads does not normally reach this region. From the design point of view it would be highly undesireable for roundabouts to be designed to operate in such a manner. The linear/circulating flow relationship will ensure that designs are conservative for abnormally high values of circulating flow. 151

PAGE 164

--' V1 I\.) HYPOTHESIS TEST DATA ANALYSIS TABLE 12 Entry Flow Leg Entry Flow Standard Correlation Mean Deviation Coefficient -----X a R -----(Pcu/Hr) s 1 1004 89.187 0.247 -----2 460 80.711 0.497 3 1040 97.980 0.214 4 632 71.234 0.440 5 1868 119.714 0.424 --5004 TOTAL -------------------------r-----Calc Flow Standard Error RODEL 1< ... (14) 01Estlmate Calculated -----A a(1R2)/N Entry Flow (Pcu/Hr) (Pcu/Hr) 0.0610 5.582 1257 .35 r----------------------0.2470 4.052 479 -1.35 0.0458 6.232 1254 .35 .. 0.1936 3.831 755 .35 0.1798 6.544 2281 .35 6026 TOTAL 16.96% % OHierence -----------------------l I I I Hypothesis Test Circulating Flow I observed Acceptor Circulating Standard Correlation Standard Error ' X Calc Entry ReJect Null Flow Deviation Coefficient 01Estlmata S/15 Hypothesis Mean a A R a(1R2)/N Pcu/Hr s Pcu/Hr -10.987 Reject Null 1120 112.631 0.247 0.0610 7.049 --Hypolhesis Accept Null 2120 183.770 0.497 0.2470 9.225 Hypolhesls -8.459 Reject Null 1636 167.366 0.214 0.0458 10.645 Hypolhesis -8.687 Reject Null 2192 194.907 0.440 0.1936 10.483 Hypolhesls -13.361 Reject Null 1384 156.242 0.424 0.1798 8.54 Hypolhesls From Measured ------

PAGE 165

VAIL SOUTH ROUNDABOUT TABLE 12 JULY 4 1997 ACTUAL FIELD COUNTS FLOWING THROUGH ROUNDABOUT AT CAPACITY BY QUEUING UP TRAFFIC ON EACH APPROACH 2 :30P. M 7:00P.M. ENTRY FLOW 1 HR CIRCULATING FLOW 1 HR MEDIAN LEG COUNT 1 MINUTE ENTRY MEDIAN 1 MINUTE COUNT CIRCULATING CIRCULATING NUMBER COUNT FLOW ENTRY FLOW FLOW FLOW Pcu/Min PcuJHr PcuJHr Pcu/Min PcuJHr PcuJHr 17 1020 21 1260 LEG 1 ENTRY FLOW LEG 1 CIRCULATING FLOW 2 15 900 16 960 3 15 900 19 1140 Mean 1004 Mean 1120 4 16 960 18 1080 Stlndard Error 23 028 S1andard Error 29 .081 5 16 960 19 1HO Median 960 Median 1140 6 19 1140 21 1260 Mode 960 Mode 1140 7 15 900 20 1200 Stlndard Deviation 89.187 Stlndard Deviation 112 .631 8 19 1140 18 1080 Sample Variance 7954.286 Sample Variance 12685 .714 9 16 960 15 900 Kurtosis -1.222 Kurtosis 10 18 1080 20 1200 Skewness 0 528 Skewness 11 16 960 19 1140 Range 240 Range 360 12 19 1140 18 1080 Minimum 900 Minimum 900 13 16 960 16 960 Maximum 1140 Maximum 1260 14 18 1080 19 1140 Sum 15060 Sum 16800 __. 15 16 960 21 1260 Count 15 Count 15 IJ1 w 1004 1120 Confidence level( 95 0%) 49.390 Confidence level(95. 0%) 62 373 Coefficient R Between Qe and Qc 0 247 Std Error of Predlc Cap 5 5821Std Error of Predlc Cap 7.049 2 1 9 540 37 2220 LEG 2-ENTRY FLOW LEG 2CIRCULATING FLOW 2 8 480 34 2040 3 8 480 40 2400 Mean 460 Mean 2120 4 10 600 35 2100 Stlndard Error 20.840 Stlndard Error 47. 449 5 7 420 38 2280 Median 420 Median 2100 6 6 360 34 2040 Mode 420 Mode 2220 7 7 420 32 1920 Stlndard Deviation 80.711 Stlndard Devlalion 183. 770 8 7 420 35 2100 Sample Variance 6514 286 Sample Variance 33771. 429 9 8 480 38 2280 Kurtosis Kurtosis 10 6 360 30 1800 Skewness 0 504 Skewness 11 7 420 37 2220 Range 240 Range 600 12 10 600 36 2160 Minimum 360 Minimum 1800 13 6 360 33 1980 Maximum 600 Maximum 2400 14 7 420 31 1860 Sum 6900 Sum 31800 15 9 540 40 2400 Count 15 Count 15 460 2120 Confidence Level (95. 0%) 44. 696 Confidence level (95 0%) 101. 769 Correlation Coefficient R Between Qe and Qc 0 497 Std Error of Predlc Cap 4 052IStd Error of Predlc Cap 9 225

PAGE 166

ENTRY FLOW 1 HR CIRCULATING FLOW 1 HR MEDIAN LEG COUNT 1 MINUTE ENTRY MEDIAN 1 MINUTE COUNT CIRCULATING CIRCULATING NUMBER COUNT FLOW ENTRY FLOW FLOW FLOW Pcu/Min Pcu/Hr Pcu/Hr Pcu/Min Pcu/Hr Pcu/Hr 3 1 17 1020 29 1740 LEG 3 -ENTRY FLOW LEG 3CIRCULATING R.OW 2 18 1080 28 1680 3 20 1200 32 1920 Mean 1040 Mean 1636 4 15 900 29 1740 Standard Error 25 298 Standard Error 43.214 5 18 1080 25 1500 Median 1020 Median 1620 6 20 1200 27 1620 Mode 1020 Mode 1620 7 17 1020 22 1320 Standard Deviation 97 980 Standard Deviation 167. 366 8 18 1080 26 1560 Sample Variance 9600 000 Sample Variance 28011 429 9 16 960 27 1620 Kurtosis .0.651 Kurtosis .0. 272 10 17 1020 25 1500 Skewness 0 059 Skewness .0 226 11 15 900 23 1380 Range 300 Range 600 12 17 1020 28 1680 Minimum 900 Minimum 1320 13 18 1080 27 1620 Maximum 1200 Maximum 1920 14 15 900 31 1860 Sum 15600 Sum 24540 15 19 1140 30 1800 Count 15 Count 15 1040 1636 Confidence Level(95.0%) 54. 259 Confidence Level(95 0%) 92 684 Correlation Coefficient R Between Qe and Qc 0 214 Std Error of Predlc Cap 6 2321Std Error of Predle Cap 10.645 LT1 .t:. 4 1 10 600 36 2160 LEG 4ENTRY FLOW I LEG 4-CIRCULATING FLOW 2 11 660 33 1980 3 10 600 34 2040 Mean 632 Mean 2192 4 12 720 42 2520 Standard Error 18. 393 Standard Error 50 325 5 11 660 38 2280 Median 660 Median 2160 6 13 780 39 2340 Mode 660 Mode 2160 7 11 660 36 2160 Standard Deviation 71. 234 Standard Deviation 194.907 8 9 540 34 2040 Sample Variance 5074 286 Sample Variance 37988.571 9 11 660 41 2460 Kurtosis 1.156 Kurtosis -1. 208 10 10 600 39 2340 Skewness .0 .091 Skewness 0 369 11 11 660 32 1920 Range 300 Range 600 12 11 660 35 2100 Minimum 480 Minimum 1920 13 10 600 35 2100 Maximum 780 Maximum 2520 14 8 480 33 1980 Sum 9480 Sum 32880 15 10 600 41 2460 Count 15 Count 15 632 2192 Confidence Level(95.0%) 39 448 Confidence Levei(95 .0%J 107. 936 Correlation Coefficient R Between Qe and Qc 0 440 Sid Error of Predle Cap 3 .831IStd Error of Predlc Cap 10 483

PAGE 167

ENTRY FLOW 1 HR CIRCULATING FLOW 1 HR MEDIAN LEG COUNT 1 MINUTE ENTRY MEDIAN 1 MINUTE COUNT CIRCULATING CIRCULATING NUMBER COUNT FLOW ENTRY FLOW FLOW FLOW Pcu/Min Pcu/Hr Pcu/Hr Pcu/Min Pcu/Hr Pcu/Hr 5 1 32 1920 25 1500 LEG 5 -ENTRY FLOW LEG 5 CIRCULA T/NG FLOW 2 28 1680 23 1380 3 31 1860 21 1260 Mean 1868 Mean 1384 4 34 2040 23 1380 Standard Error 30.910 Standard Error 40.341 5 32 1920 22 1320 Median 1920 Median 1380 6 33 1980 26 1560 Mode 1920 Mode 1380 7 32 1920 27 1620 Standard Deviation 119.714 Standard Deviation 156.242 8 31 1860 19 1140 Sample Variance 14331.429 Sample Variance 24411.429 9 28 1680 21 1260 Kurtosis 0.248 Kurtosis .().938 10 31 1860 24 1440 Skewness .().958 Skewness 0.000 11 32 1920 25 1500 Range 420 Range 480 12 33 1980 23 1380 Minimum 1620 Minimum 1140 13 32 1920 27 1620 Maximum 2040 Maximum 1620 14 27 1620 21 1260 Sum 28020 Sum 20760 15 31 1860 19 1140 Count 15 Count 15 1868 1384 Confidence Level(95.0%) 66.295 Confidence Level(95.0%) 86.524 CorrelaUon Coefficient R Between Qe and Qc 0.424 Ul Std Error of Predlc Cap 11.5441Std Error of Predlc Cap 8.540 Ul

PAGE 168

LT1 0'1 CORRECTED INTERCEPT BASED ON FIELD MEASUREMENTS CORRECTED ENTRY/CIRCULATING FLOW UNE BASED ON FIELD MEASUREMENTS --TABLE 12-3 PARAMETER I SYMBOL LEG LEGZ 1 CAPACITYMAXJMUM ENTERING FLOW, PCUIH Qe 0 00 0 00 2 CIRCULAT ING FLOW, PCUIH Qc 0 .00 0 .00 3 ENTRY WIDTH, M e 8 0 1 7 .21 4 LENGTH OF FLARE, M L 7 .81 65.23 5 APPROACH HALF-WIDTH, M v 5 27 8.32 a iNCRiBED CIRCLE DIAMETER, M -------. o-----60 98 60.98 -7 ENTRY ANGLE, DEGREES ----------0-------14.00-39 00 8 ENTRY RADIUS, M r 42 67 23 32 SIX EQUATJQN LG1 LEG2 1 SHARPNESS OF FLARE s =1.6 v /L 0 .561 0 017 2 ENTRY WIDTH PARAMETER x, = v + (&-vi I (1 + 2 Sl 6 .561 7.181 3 FUNCTION OF D Ia = 1 + 0 .5/ (1 + exp ((0-601 /10 )) 1.238 1.238 4 ADJUSTMENT FACTOR, CAP CURVE k = 1 -0. 00347 ( 0-30 1-0 978 ((1/r)-0 .051 1 .081 0.976 5 SLOPE OF CAPACITY CURVE fc = 0.210 Ia C 1+0.2 x, I 0 60112 0 83338 6 Y -INTERCEPT, PCUIMIN F = 303 x, 1987 e32 2175 910 INTERCEP AND ENTRY/CIRCULA NG FLOW UNE BASED NGEOMEl RY 1 SLOPE OF ENTRY/CIRCULATING FLOW RELATIONSHIP r c k (f .I 0 65011 0.61801 2 ENTRY CAPACITY Qe =k(Ff.O.I when r. 0. F 3 CIRCULATING FLOW Qc (F (Qe/11))/f, 3307 04 3435 40 I@ ENTRY CAPACITY Qa 0 VAIL CORRECTED INTERCEP AND ENTRYICIRCULA1 N FLOW UNE """""" ON FIELD DA A I 1 RODEL CALCULATED ENTRY FLOW 1257 00 479 00 2 MEASURED MEAN ENTRY FLOW a .. 1004 .00 460 .00 % Difference between Radel end M11sured 20 13% 3 97% 3 RODEL CALCULATED CIRCULATING FLOW 1374 00 2660 00 ----2120.00 4 MEASURED MEAN CIRCULATING FLOW Qc 1120 00 --% Difference beiWeln Radel end Measured 18 49% 20 30% 5 --. . ------VAIL CORRECTED INTERCEPT FL Qe+lc:Qc 1732 .13 1770 .18 -6 ENTRY I CIRCULATING FLOW UNE ae fL.fQ 1004.00 460 .00 ------SLOPE .. -------------------------... ---------0 61801 7 ST--cF-ael ta, 0 65011 -. ------------------------------------------------------. ac-' -ca. /k))tr, _ -. --i : --8 CORRECTED CIRCULATING FLOW 1-!@ENTRY CAPACITY Qe) 0 -------LEG :I_ LEG4 LEG 5 0 .00 0 00 0 00 0 .00 0 .00 0 .00 8 67 8 50 14. 63 9 23 8 39 64 78 7 92 7.37 6.40 60 .98 60 .98 60.98 14. 50 22 00 17.00 21. 34 19 .81 15 65 LG3 LEG4 LGS 0 130 0 283 0 203 8 515 8 092 12.251 1 238 1 238 1.238 1 057 1 027 1 032 0 70274 0 68072 0 89700 2560 114 2451 766 3712.118 0 74270 0.69930 0.92598 2726 808 2518 677 3832 044 3671 .411 3601.74 4138.37 1254 00 755 00 2281.00 1040 .00 632 .00 1868 .00 17. 07% 18 .211% 18 11% 1982 00 2523 00 1675 00 1636 00 2192 00 1384.00 17. 48% 13 12% 17.37% 2255 06 2164 88 3149 56 1040 .00 832 00 1668 .00 ----0 74270 0 69930 0 92598 r------------------J----------------3036 30 3095 .77 j 3401.32 ---------..... --___________

PAGE 169

GRAPH OF CIRCULATING FLOW VS ENTRY CAPACITY OF LEG 1 BASED ON GEOMETRY VAIL SOUTH 200 FOOT DIAMETER ROUNDABOUT CIRCULATING FLOW Qc ENTRY CAPACITY Qe 3307.04 0 0 2149.948 2664.35 0 0 1732.13 FIGURE 12-3 DATA ORIGIN RODEL RODEL MEASURED MEASURED -----------------ENTRY CAPACITY Qe VS CIRCULATING FLOW Qc LEG 1 ENTRY 2000 ., 0 1500 0 o( ... o( 0 >-a: 1000 ... z w 500 0 500 1000 1500 2000 2500 3000 3500 CIRCULATING FLOW Qc 157

PAGE 170

GRAPH OF CIRCULATING FLOW VS ENTRY CAPACITY OF LEG 2 BASED ON GEOMETRY VAIL SOUTH 200 FOOT DIAMETER ROUNDABOUT CIRCULATING FLOW Qc ENTRY CAPACITY Qe 3435.4 0 2864.33 0 0 2123.105 0 1770.18 FIGURE 12-3 DATA ORIGIN RODEL RODEL MEASURED MEASURED ---------------------ENTRY CAPACITY Qe VS CIRCULATING FLOW Qc-LEG 2 ENTRY 2000 .. a 1500 i3 < ... < 0 >-It: 1000 fz w 500 0 500 1000 1500 2000 2500 3000 3500 CIRCULATING FLOW Qc I L_ ____ 158

PAGE 171

GRAPH OF CIRCULATING FLOW VS ENTRY CAPACITY OF LEG 3 BASED ON GEOMETRY VAIL SOUTH 200 FOOT DIAMETER ROUNDABOUT CIRCULATING FLOW Qc 3671.49 0 3036.30 0 ENTRY CAPACITY Qe 0 2726.808 0 2255.05 ENTRY CAPACITY Qe VS CIRCULATING FLOW Qc-LEG 3 ENTRY 3000 2500 .. 2000 0 u <( D. 1500 <( I.J > a: .... z w 1000 500 CIRCULATING FLOW Qc 159 FIGURE 12-3 DATA ORIGIN RODEL RODEL MEASURED MEASURED

PAGE 172

GRAPH OF CIRCULATING FLOW VS ENTRY CAPACITY OF LEG 4 BASED ON GEOMETRY VAIL SOUTH 200 FOOT DIAMETER ROUNDABOUT CIRCULATING FLOW Qc ENTRY CAPACITY Qe 3601.74 0 3095.77 0 0 2518.677 0 2164.86 ENTRY CAPACITY Qe VS CIRCULATING FLOW Qc-LEG 4 ENTRY 3000 2500 2000 0 0 < ... 1500 < u > a: .... z w 1000 500 0 0 500 1000 1500 2000 2500 3000 CIRCULATING FLOW Qc 160 FIGURE 12-3 DATA ORIGIN RODEL RODEL MEASURED MEASURED 3500 4000 _j

PAGE 173

GRAPH OF CIRCULATING FLOW VS ENTRY CAPACITY OF LEG 5 BASED ON GEOMETRY VAIL SOUTH 200 FOOT DIAMETER ROUNDABOUT CIRCULATING FLOW Qc ENTRY CAPACITY Qe 4138.37 0 3401.32 0 0 3832.044 0 3149.56 ENTRY CAPACITY Qe VS CIRCULATING FLOW Qc-LEG 5 ENTRY 4000 3500 3000 a 2500 u oC( a.. 2000 oC( u >-a: 1-1500 z w 1000 500 0 500 1000 1500 2000 2500 3000 3500 CIRCULATING FLOW Qc '---------------------------161 FIGURE 12-3 DATA ORIGIN RODEL RODEL MEASURED MEASURED 4000 4500

PAGE 174

0'\ ['...) VAIL SOUTH 200 FOOT DIAMETER ROUNDABOUT MEASURED VS EXPECTED VALUES TABLE 12-4 MEASURED (July 4, 1997, 2:30 :00PM) Leg Entry Flow Circulating Aow Number Pcu/Hr Pcu/Hr 1 1004 1120 2 480 2120 ____ 3 ___ -----w40-f-1636 --------------632-1----------2192' 4 ----51868 1384 Totals 5004 EXPECTED (As Calculated 'J'f Redel Regression Equations Wilh Avg Delay Per Yah 0.5 min Capacity) l Leg Entry Aow %Dm.rence Circulating Flow %Difference Number Pcu/Hr FromMusurecl Pcu/Hr From Measured 1 1257 20.13% 1374 18.49% 2 479 3.97% 2680 20.30% 3 1254 17.07% 1982 ----' 17.46% 4 755 16.29% 2523 -.. 1 13.12% 5 2281 18.11% 1675 ___ j 17.37% I Totals 8026 16.96% --------------------------------1--------------------------1-------Measured Enll}' Aow 1004 480 f----832 1868 Expected Entry Aow 1257 479 1254 755 2281 r-r------1--------r-----1--------r----f-----I Test Paired Two Sample for Means Measured Expected Musured Entry Row Entry Row Circulating Mean 1000.8 1205.2 Aow Vartance 295515.2 473114.2 Obserllations 5 5 1120 Pearson Comllation 0.9987 2120 Hypolheslzed Mean Dlffemnce 0 1636 df 4 2192 -----TSial' -3.0997 1384 P(T<-t) one-tall 0.0181 I Crilk:al one-tall 2.1318 P(T <-t) two-tall 0.0362 I CriUcal two-tail 2.7785 Expected 1-Tesl: Paired Two Sample for Means Circulating Me .. urecl Expected Aow CnulallllfiRow Circulating Row Mean 1690.4 2042.8 1374 Variance 214588.8 299448.7 2680 Obserllations 5 5 1982 Pearson Comllation 0.9897 2523 Hypothesized Mean Oiflerence 0 1675 df 4 I Stat -7.1090 P(T<-t) one-tall 0.0010 I Critical one-tail 2.1318 --1---P(T<"'l) two-tail 0.0021 I Critical two-tail 2.7765 ----------------------------------------------------------------------------------------------------------

PAGE 175

13. American Proposed Procedure 13.1 Introduction The following procedure can be used to correct the British Rodel capacity formula results to calculate roundabout capacity for local conditions at Vail, Colorado (USA) provided that the relevant entry is substantially overloaded during peak periods. 1. Make on-site counts of the total inflow from the entry and the corresponding circulating flow across the entry during successive minutes during which there is continuous queueing in all available lanes in the approach to the entry. Queuing should occur continuously for periods of twenty minutes or more during peak periods. The approach queues should be stable for at least five vehicle lengths (See Figure 13-4) upstream of any entry widening. At minimum a total of sixty minutes of saturation should be obtained. During peak periods if all approaches do not have at least five vehicle lengths upstream of any entry widening then traffic on that leg can be stopped until it queues up. Then that legs traffic can be released and on-site counts taken of the total inflow from the entry and the corresponding circulating flow across the entry during successive minutes during which there is continuous queueing in all available lanes in the approach to the entry at all entries. 163

PAGE 176

2. Calculate the mean entry flow Qe and mean circulating flow Qc for all of the saturated minutes together, both in pculh. 3. Calculate from the roundabout geometry the slope of the entry/circulating flow relationship by means of the following equation: where k = 1 0.00347 ( $ -30) 0.978 (( 1/r) 0.05 )) 4. Then the locally corrected intercept is given by and the entry I circulating flow line is The confidence limits associated with equations obtained in this way depend on the conditions of operation of the entry in question, but typically the standard error of estimate near the mean will be generally less than 100 pculhr. It can be evaluated for any given site simply by calculating the standard deviation, cr (pculhr), of the one minute counts of Qe and the correlation coefficient, R, between the Qe and the Qc values. Then the standard error of the predicted capacity near the mean will be cr ( 1 -R2 ) IN, where N is the number of one-minute counts. Both cr and R depend on the conditions of operation, and are thus site specific. 164

PAGE 177

5. The culmination ofthis procedure is to use the 6 regression equations from the British procedure to calculate capacity and then multiple the capacity times a multiplier factor of0.83 (17% less than the Britain capacity answer). This procedure will correct the British procedure for American roundabouts. The British procedure is generally considered the most accurate procedure for calculating the capacity of a roundabout. This multiplier factor may vary to some degree from one area of the United States to another. An example of this is that drivers in urban areas may be more aggressive than those in rural areas. Therefore, steps 1 through 4 above should be taken (to determine the multiplier factor) at a roundabout close to the vicinity of the designated roundabout. 165

PAGE 178

m m CORRECTED INTERCEPT BASED ON FIELD MEASUREMENTS --f--CORRECTED ENTRY/CIRCULATING FLOW UNE BASED ON FIELD MEASUREMENTS TABLE 13 PAIIAMETI:R SYMBOL LEG 1 1 CAPACITYMAXIMUM ENTERING FLOW, PCUIH Qe 0.00 2 CIRCULATING FLOW, PCUIH Qc 0 00 3 ENTRY WIDTH, M e 8 .01 ----4 LENGTH OF FLARE, M L 7 .81 5 APPROACH HALF-WIDTH, M v 5 27 6 INCRIBEO CIRCLE DIAMETER, M D 60.98 7 ENTRY ANGLE, DEGREES 0 14_00 8 ENTRY RADIUS, M r 42 67 I SIX REGRESSIC N EQUATIONS EQUATION LEG 1 1 SHARPNESS OF FLARE s = 1.8 (e-v) I L 0.561 2 ENTRY WIDTH PARAMETER x. = v + (e-v) I (1 + 2 S) 6_561 3 FUNCTION OF D lo = 1 + 0.51 (1 + exp ((Q..SO) /10 )) 1.238 4 ADJUSTMENT FACTOR, CAP. CURVE k = 1 0.00347 0 30 0.978 ((_llr)-{).05) LOBI 5 SLOPE OF CAPACITY CURVE fc = 0.210 lo ( 1+0_2 x.) 0.60112 6 Y INTERCEPT, PCUIMIN F 303X2 1987.932 INTERCEP AND ENTRY/CIRCULATING FLOW UNE BASED ON GEOMETRY 1 SlOPE OF ENTRY/CIRCULATING FLOW RELATIONSHIP fc k(l ,) 0.65011 2 ENTRY CAPACITY Qe =k(F-1,0.,) when f, 0. <= F, and 2149 948 Qe =0 when f, 0, > F ----------------3 CIRCULATING FLOW Qc (F (Qelk)) If, 3307.04 -I@ ENTRY CAPACITY ( Qe 0 I VAIL CORRECTED INTERCEPT AND ENTRY/CIRCULATING FLOW UNE BASED ON f'IEL.I:I DATA I 1 RODEL CALCULATED ENTRY FLOW 1257 00 ------2 MEASURED MEAN ENTRY FLOW ---_ _g._ __ 1004 00 %Difference betwHn Rodelnd Mured -.. ------------20.13% 3 RODEL CALCULATED CIRCULATING FLOW 1374 00 ------t---4 MEASURED MEAN CIRCULATING FLOW Qc 1120 00 -%Difference IMIWHn Rodelnd Me .. ured 18-49% -----------5 VAIL CORRECTED INTI:RCEPT F' Qe + fc Qc 1732 .13 -------------------6 ENTRY I CIRCULATING FLOW UNE ae' FL. 1. a. 1004 00 1 -1-----------------------7 SLOPE s' (F'Qe') IQ, 0.65011 ------------------------------ac' (F' (Qe' I k)) If, 8 CORRECTED CIRCULATING FLOW --------t_ 2664 35 IC!I ENTRY CAPACITY ( Qe) 0 --I ---------LEG2 LEG J LEG4 LEG 5 0 00 0.00 0.00 0 00 0 00 0.00 0.00 0 00 7 .21 8.67 8.50 14. 63 85 23 9 23 6 .311 64 78 8 32 7.92 7 37 8 40 60 98 60 .98 60 98 60 98 311_00 14.50 22.00 17.00 23 32 21.34 19.81 15. 85 LEG2 LEGJ LEG4 LEG 5 0_017 0.130 0.283 0 203 7 .181 8.515 8.092 12.251 1.238 1.238 1.238 1.238 0.078 1.057 1.027 1 032 0.83338 0.70274 0.68072 0 89700 2175_910 2560.114 2451.766 3712 118 I 0 61801 0 74270 0 69930 0 92598 2123 105 2728.608 2518 677 3832 044 3435 40 3671.49 3601.74 4138 .37 I 4711. 00 1254.00 755.00 2281 00 ----460 00 1040.00 632.00 --,66800 3 97% 17.07% 16.29% 18. 11% 2660 00 1982.00 2523 00 1675 00 2120 00 1638.00 2192.00 1384 00 20 30% 17_ 48% 13 12% -17_37%--1770 18 2255.05 2164 66 3149 55 ----460 00 1040.00 632 00 1668 00 -----0.61801 0.74270 0.69930 0 .112598 ----------3095.77 2864 33 3038.30 __ 3401 32 --=-------

PAGE 179

RODEL RESULTS ACTIJAL FIELD COUNTS CAPACITY-5004 VEHlCLES I HOUR 50 % CONFIDENCE LEVEL ******************************************************************************* * 4:11:97 MAIN VAIL SOUTH. ACTUAL FIELD COUNT 26 ******************************************************************************* * E (m) 8.01 7.21 8.67 8.50 14.63 15.00 TIME PERIOD min 90 L' (m) 7.81 85.23 9.23 6.39 64.78 0.0 TIME SLICE min 15 v (m) 5.27 6.32 7.92 7.37 6.40 15.00 RESULTS PERIOD min 15 75 RAD (m) 42.67 23.32 21.34 19.81 15.85 15.00 TIME COST $/min 7.79 PHI (d) 14.00 39.00 14.50 22.00 17.00 0.0 FLOW PERIOD min 15 75 DIA (m) 60.96 60.96 60.96 60.96 60.96 60.96 FLOW TYPE pcu/veh VEH GRAD SEP 0 0 0 0 0 0 FLOW PEAK am/op/pm PM ******************************************************************************* *LEG NAME *PCU *FLOWS (1st exit 2nd etc ... U)*FLOF*CL* FLOW RATIO *FLOW TIME * LEGl/dO'/ *1.03* LEG2 *1.03* LEG3/0Y0 *1.03* LEG4 t: JZ *1. 03* LEGS/b'<:;t: *1. 03 LEG6 ---*1.03* StJO
PAGE 180

RODEL RESULTS AT CAPACITY AVERAGE DELAY-0.50 MINUTES (DEFINITION OF CAPACITY) CAPACITY c 6026 VEHICLES I HOUR 50 % CONFIDENCE LEVEL ******************************************************************************* .. 11:10:97 MAIN VAIL SOliTH. CAPACITY SO% CL 73 ******************************************************************************* .. .. .. E (m) 8.01 7.21 8.67 8.SO 14.63 lS.OO TIME PERIOD min 90 L' (m) 7.81 8S.23 9.23 6.39 64.78 0.0 TIME SLICE min lS v (m) S.27 6.32 7.92 7.37 6.40 1S.OO RESULTS PERIOD min lS 7S .. RAD (m) 42.67 23.32 21.34 19.81 1S.8S lS.OO TIME COST $/min 7.79 PHI (d) 14 0 00 39.00 14.SO 22.00 17.00 0.0 FLOW PERIOD min lS 7S DIA (m) 60.96 60.96 60.96 60.96 60 0 96 60.96 FLOW TYPE pcu/veh VEH GRAD SEP 0 0 0 0 0 0 .. FLOW PEAK am/op/pm PM ******************************************************************************* *LEG NAME *PCU *FLOWS (1st exit 2nd etc ... U)*FLOF*CL* FLOW RATIO *FLOW TIME LEGl 1257 *1. 03* LEG2 '/79 *1.03* LEG3/2S'f*l.03* 'LEG4 7 1 0 3 ,EGS .2 2? I 1 0 3 LEG6 *1.03* .. (;OZ"(; .. 0 0 193 96 239 0 387 8S S67 127 1236 0 227 379 273 360 0 0 S70 0 221 0 S90 0 73 lS 0 172 216 0 * 0 *l.OO*S0*0.7S 0 *l.OO*S0*0.7S 0 *l.OO*S0*0.7S 0 *l.OO*S0*0.7S 0 *1.00*S0*0.7S 0 *l.OO*S0*0.7S * 1.12S 0.7S*1S 4S 7S 1.12S 0.7S*1S 4S 7S 1.12S 0.7S*1S 4S 7S 1.12S 0.7S*1S 4S 7S 1.12S 0.7S*1S 4S 7S 1.12S 0.7S*1S 4S 7S ******************************************************************************* * FLOW CAPACITY AVE DELAY MAX DELAY AVE QUEUE MAX QUEUE veh veh mins mins veh veh 12S7 14S2 0 0 49 1. OS 11 21 479 682 0 0 49 1. 04 4 8 12S4 1487 0.49 1.10 10 22 7SS 980 0.49 1. 07 6 13 * 2S73 162S AVDEL s 29.3 0.48 0.00 L 0 S D 1.13 0.00 VEH HRS 49.0 19 0 COST $ 22898.4 41 0 * ******************************************************************************* Figure 13-2 168

PAGE 181

RODEL RESULTS AT CAPACITY AVERAGE 050 MINUTES (DEFINITION OF CAPACITY) CAPACITY 5598 VEIUCLES /HOUR 85 % CONFIDENCE LEVEL ******************************************************************************* 11:10:97 MAIN VAIL SOUTH. CAPACITY 85% CL 24 ******************************************************************************* * E (m) 8.01 7.21 8.67 8.50 14.63 15.00 TIME PERIOD min 90 L' (m) 7.81 85.23 9.23 6.39 64.78 0.0 TIME SLICE min 15 v (m) 5.27 6.32 7.92 7.37 6.40 15.00 RESULTS PERIOD min 15 75 RAD (m) 42.67 23.32 21.34 19.81 15.85 15.00 TIME COST $/min 7.79 PHI (d) 14.00 39.00 14.50 22.00 17.00 0.0 FLOW PERIOD min 15 75 DIA (m) 60.96 60.96 60.96 60.96 60.96 60.96 FLOW TYPE pcu/veh VEH GRAD SEP 0 0 0 0 0 0 FLOW PEAK am/op/pm PM ******************************************************************************* *LEG NAME *PCU *FLOWS (1st exit 2nd etc ... U)*FLOF*CL* FLOW RATIO *FLOW TIME LEGl /027 *1.03* LEG2 '6"' *1.03* LEG3 /oti *1.03* LEG4 I'.Sh *1. 03 LEGS 15 *1.03* LEG6 *1.03* 5"0 IZ * 0 0 157 83 193 0 316 82 460 110 1003 0 185 368 221 313 0 0 466 0 180 0 478 0 60 14 0 150 173 0 0 *1.00*85*0. 75 0 *1. 00*85*0. 75 0 *1.00*85*0. 75 0 *1.00*85*0. 75 0 *1.00*85*0.75 0 *1.00*85*0.75 .. .. .. 1.125 1.125 1.125 1.125 1.125 1.125 0.75*15 45 75 0.75*15 45 75 0.75*15 45 75 0.75*15 45 75 0.75*15 45 75 0.75*15 45 75 .. ******************************************************************************* .. FLOW CAPACITY AVE DELAY MAX DELAY AVE QUEUE MAX QUEUE veh veh mins mins veh veh 1147 1330 0.49 1. 02 10 19 518 708 0. 49 1. 01 4 8 1137 1352 0.49 1. 09 10 20 733 941 0.49 l. 06 6 12 2063 -ss-M o 2330 1663 AVDEL s 29.3 0.49 0.00 L 0 S D 1.12 0.00 VEH HRS 45.6 17 0 COST $ 21321.1 37 0 * ******************************************************************************* Figure 13-3 169

PAGE 182

...J .<:: c. c ., :J ., :J 0 40r------------------------------------.--------------, .. a >-0 "0 0 .. ... E "'-;;. __ _i __ __j o.s o.al 0 0.2 0.4 1.0 1.2 1.4 Traffic intensity, p I Time evolution downwards Time evolution upwards THE AVERAGE QUEUE LENGTH L AS A FUNCTION OF THE .TRAFFIC INTENSITY p ACCORDING TO THE CO-ORDINATE TRANSFORMATION METHOD Figure 13-4 source (7) 170

PAGE 183

14. Theory 14.1 Introduction That the measured mean capacity at the Vail south roundabout for each entry leg into the roundabout will be less than the capacity calculated by the British capacity program RODEL, because of the unfamiliarity of American drivers in using American roundabouts. The six regression equations that are used to calculate the entry capacity in RODEL are based on the collection of data from 86 British roundabouts being used by British drivers who were very familiar with driving in and out of roundabouts. Also, the six regression equations in RODEL have been developed in such a manner that the standard error of the predicted capacity near the mean will generally be less than 100 vehicles per hour. 14.2 Hypothesis Test-Mean Capacity of Each Individual Leg 14.3 Solution: The null hypothesis Ho is that the mean for entry 1 is 11 = 1257 pcu/hr against the alternative hypothesis Ho = 11 < 1257 pcu/hr. This is to be performed for all 5 entries. a) t= X -Jlo S I -.Jn N = 15 a = 0.10 X = 1004 s =89.187 <-ta(n-1) 171

PAGE 184

t= X-1257 s;{TS < t10 ( 14) 1.35 b) With X= 1004 and S = 89.187 the observed value ofthe test statistic is: t = 1 004 1257 89.187 I ill -253.00 23.028 -10.97 c) Because-10.987 <-1.35, the test statistic falls in the critical region, and so you reject the null hypothesis. d) Looking under 14 degrees of freedom, you find that t =-10.987 falls below the values of t01 (14) =-2.62 and -t (14) = -1.35 .10 thus you find that p-value < .01 < .10 This procedure is repeated for all 5 entries and is summarized in table 14-1. At entries 1, 3, 4 and 5 you reject the null hypothesis at the a= 0.10 significance level and accept the alternative that H A < H o Only at entry number 2 do you accept the null hypothesis at the a= 0.10 significance level and reject the alternative that H A < H o It should be noted that the mean entry flow measured in the field for entry number 2 was also less than that calculated by Radel, but not by a significant amount. 172

PAGE 185

t = -10.97' Graph of Critical Region For Test Statistic Capacity of Each Leg 0 -1.1004) = -1.35 Figure 14-1 173 2 3

PAGE 186

HYPOTHESIS TEST o DATA ANALYSIS I I -+ --r TABLE 14o1 I I EiiiJYFioW Calc: Flow tHypolhesls Test I Clrc:ulailiigFiow LltQ I Entry Flow Standard Correlation Standard Error RODEL l
PAGE 187

15. Conclusions This analysis has shown that the British procedure using RODEL for calculating the capacity of a roundabout can be modified to calculate the capacity of modern American roundabouts (at Vail, Colorado) as measured in the field during actual operation.. The British procedure calculates the capacity of an American Roundabout (at Vail, Colorado) at approximately 17% greater capacity than measured in the field. It was found that this new procedure lowered the Y -intercept of the linear line on the entry capacity (y axis), and the circulating flow (x axis) graph, while the slope of the line remained the same. lfthe same Vail roundabout was located in Britain, the capacity procedure using RODEL and the capacity measured in the field would most likely be the same based on the field data collected from 86 British roundabouts used to develop the 6 regression equations used in the British RODEL capacity procedure. The only explanation can be U.S. driver unfamiliarity with roundabouts thus initial hesitation when negotiating the roundabout. It is assumed that drivers in Britain are more familiar with roundabouts, since they have experienced this type of intersection for a long time. While in the U.S. and elsewhere a roundabout is still an unusual solution. This unfamiliarity thus reduces the effective capacity of the roundabout than if the roundabout was constructed and operated in Britain where drivers are very familiar with driving through all kinds of roundabouts. A modified procedure to calculate capacity for modern American roundabouts (Vail, Colorado) was proposed in this paper. While the results presented in this paper are 175

PAGE 188

promising, it would be desirable for more research to validate these results. Additional data (at least 60 one minute counts) measuring the saturated entry and circulating flows as well as performing this procedure on another American roundabout to validate the results would be desireable. 176

PAGE 189

References: 1. Brown, M. (1995). The design ofroundabouts. Transport and Road Research Laboratory, Department ofTransport. 2. Crown, R. B. (October 1987). RODELAn alternative approach to roundabout design. Staffordshire County Council. 3. Crown, R. B. (1987). RODEL 1 Interactive roundabout design. Rodel Software Ltd. and Staffordshire County Council. 4. Essex County, Council Highways Department. (January 1986). Geometric design of roundabouts. Essex County, Council Highways Department. 5. Florida Department of Transportation. (1995). Florida roundabout design Florida Department of Transportation. 6. Kimber, R. M. (1980). TRRL Report LR 942, The traffic capacity of roundabouts. Transport and Road Research Laboratory, Department of Transport. 7. Kimber, R. M., and Hollis, E. M. (1979). TRRL Report LR 909, Traffic queues and delays at road intersections. Transport and Road Research Laboratory, Department ofTransport. 8. Kimber, R. M., Marlow, M., and Hollis, E. M. (1997). Flow/Delay Relationships For Major-Minor Priority Intersections. Transport and Road Research Laboratory, Department of Transport. 9. Layfield, R. E., and Maycock, G. (June 1986). Bicyclists at roundabouts. Transport and Road Research Laboratory, Department of Transport, Crowthome. 10. Marlow, M. (1987). TRL Working Paper TMN 136. Pedestrian crossings at roundabouts. Transport and Road Research Laboratory, Department of Transport, Crowthome. 177

PAGE 190

11. Marlow, M., and Maycock, G. (1982). TRRL Report SR.724. The effect of zebra crossings on intersection entry capacities. Transport and Road Research Laboratory, Department of Transport, Crowthorne. 12. Maycock, G., and Hall, R. D. (1984). TRRL Report LR 1120, Accidents at 4 arm roundabouts. Transport and Road Research Laboratory, Department of Transport, Crowthome. 13. Ourston, L., and Doctors, P. (September 1996). Desi&ns ofmodern american roundabouts. Ourston and Doctors. 14. Ourston, L., and Doctors, P. (September 1995). Roundabout desi&n guidelines. Ourston and Doctors. 15. TR News, (July-August 1997). Improving road safety and increasing capacity. Transportation Research Board. 16. Wardrop, J. G. (1957). The traffic capacity of weaving sections of roundabouts. Oxford, E.U.P. London. 17. Wilson, F. T. (1997). Modem roundabouts and traffic crash experience in the united states [WWW document]. URL http://www.aimee3@psu.edu 178