A Method For Estimating Right Turn Capacity
at Signalized Intersections With
Exclusive Right Turn Lanes
by
Richard R. Follmer, P E.
B.S., University of Colorado At Denver, 1993
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
2001
This thesis for a Master of Science
degree by
Richard R. Follmer
has been approved
by
Bruce N.'Janson
^61/ C 2 oo)
Date
Follmer, Richard R. (M.S., Civil Engineering)
A Method For Estimating Right Turn Capacity at Signalized Intersections With
Exclusive Right Turn Lanes.
Thesis directed by Associate Professor Bruce N. Janson
ABSTRACT
An essential component in evaluating the operation of a signalized intersection is the
saturation flow rate, the flow in vehicles per hour (vph) that can be accommodated by
a lane group. The Highway Capacity Manual (HCM 2000) analysis procedure
incorrectly calculates the average vehicle delay for right turns from an exclusive lane.
The HCM 2000 procedure estimates that the right turn capacity is 85% of the
capacity of a through lane during the signalized green phase. No allowance for right
turn capacity is given for the signalized red phase. The HCM 2000 procedure should
apply separate saturation flow rates for right turns made during both the red and
green intervals to properly calculate right turn delay.
This thesis tests the applicability of Equation 17-3 of the HCM 2000, Potential
Capacity of a Minor Traffic Movement at an Unsignalized Intersection, to evaluate the
saturation flow rate of an exclusive right turn movement at a signalized intersection.
The procedure is based on the premise that right-turns-on-red at a signalized
intersection are obstructed by conflicting flows during the signal red phase similarly to
the way in which conflicting flows obstruct right turns at an unsignalized intersection.
The evidence of this thesis would indicate that Equation 17-3 can represent the red
interval saturation flow rate after the base critical gap and base follow-up time values
of Exhibit 17-5 of the HCM 2000 are adjusted to more accurately reflect driver
behavior at signalized intersections. Based on further research and data analysis
resulting in an evaluation as described in this paper, it is recommended that the d.,
term of the uniform delay equation be modified to reflect right turn capacity during
both the red and green phase of a traffic signal.
This abstract accurately represents the content of the candidates thesis. I
recommend its publication.
Signed
Bruce N. Janson
IV
ACKNOWLEDGMENT
Acknowledgment is appreciatively given to Dr. Bruce N. Janson of the University of
Colorado at Denver for providing direction, guidance and input on the composition of this
paper. Without his assistance, the completion of this paper would not have been
achieved.
CONTENTS
Figures....................................................................viii
Tables.......................................................................ix
Chapter
1. Introduction...........................................................1
1.1 Background and Problem Identification .................................1
2. RTOR History...........................................................4
3. Project Approach ......................................................7
3.1 Modification of HCM Uniform Delay Equation ............................7
3.2 Calculation of Potential Right Turn On Red Saturation Flow Rate .......9
4. Data Collection.......................................................14
5. Data Analysis ........................................................18
5.1 Calculation of Conflicting Flow During Signal Red Phase ..............18
5.2 Calculation of Potential RTOR Saturation Flow Rate and Capacity......19
5.3 Relationship of Conflicting Flow Rate to Potential Capacity...........24
5.4 Comparison to Observed Right Turn Movements for RTOR,
Right Turn on Green (RTOG) and Total Right Turns ...................26
5.4.1 RTOR .................................................................26
5.4.2 Right Turn on Green (RTOG) and Total Right Turns .....................28
6. Recommendations ......................................................30
6.1 HCM 2000 Delay Equation Modification..................................30
6.2 Further Study ........................................................31
VI
Appendix
A. Data Collection Summary.................................................33
B. Conflicting Flow Calculations ..........................................39
C. Potential RTOR Saturation Flow Rate and Capacity .....................44
References ..................................................................49
VII
FIGURES
Figure
3.1 HCM 2000 Uniform Delay.................................................7
3.2 Modified Uniform Delay.................................................9
3.3 Minor Street Right Turn Conflicting Flows at Unsignalized Intersections 10
4.1 Data Collection Locations.............................................15
4.2 Data Collection Summary Sample .......................................17
5.1 Conflicting Flow Rate Versus Potential Capacity of an Unsignalized
Right Turn Minor Movement.............................................20
5.2 Conflicting Flow Rate Versus Potential Capacity of a Signalized
Right Turn Movement...................................................25
6.1 Modified Uniform Right Turn Delay.....................................31
TABLES
Table
5.1 Conflicting Flow Calculation -
Arapahoe Road/Dayton Street Intersection .................................18
5.2 Potential RTOR Saturation Flow Rate and Capacity -
Arapahoe Road/Dayton Street Intersection .................................21
5.3 Potential RTOR Capacity Versus Observed RTOR ..............................27
5.4 Potential Capacity Versus Observed RTOG and Total Right Turns..............29
IX
1.
Introduction
1.1 Background and Problem Identification
An essential component in evaluating the operation of a signalized intersection is the
saturation flow rate. The saturation flow rate of a signalized intersection is the flow in
vehicles per hour (vph) that can be accommodated by a lane group assuming that
the green phase is displayed 100 percent of the time. Recognizing that a green
indication is not displayed to that extent, a series of adjustment factors are used to
estimate the potential capacity of a movement given the prevailing physical and
operational characteristics of a lane group.
The Highway Capacity ManuaP (HCM 2000) estimates that the capacity of an
exclusive right turn lane during the signalized green phase is 85% of the capacity of a
through lane during the signalized green phase. The HCM 2000 also indicates that,
during the signal red phase, vehicles which turn right on a red signal indication
(RTOR) can be deducted from the right turn volume before analysis of lane group
capacity or level of service (LOS). However, if the number of RTOR is unknown or
the analysis is of future conditions, the HCM 2000 recommends that the right turn
volume be used without reduction for RTOR. These approaches will lead to an
incorrect calculation of average vehicle delay. Simply removing RTOR vehicles from
the analysis does not accurately quantify the delay that RTOR vehicles experience,
while using a capacity of 85% of a through lane for the entire traffic signal cycle does
1
not recognize the influence that conflicting traffic will have on the ability to complete a
RTOR maneuver.
A Right Turn Adjustment Factor of 0.85, when an exclusive right turn lane exists, is
only applicable during the green phase of the signal cycle. The HCM 2000 should
apply separate saturation flow rates for right turns made during the red and green
intervals. If the RTOR volume is known, and a RTOR queue generally exists for the
analysis period, then the RTOR volume is a good estimate of the RTOR saturation
flow rate. The HCM 2000 methodology can then be used to compute uniform delay
correctly with a modified formula.
If the red and green saturation flow rates are needed to evaluate alternative designs
such as changes to signal phasing, lane usage or intersection geometry, and the
actual RTOR volume is unknown, it is necessary to estimate this value to properly
evaluate an intersection. This thesis tests the applicability of Equation 17-3 of the
HCM 2000, Potential Capacity of a Minor Traffic Movement at an Unsignalized
Intersection, to the right turn movement at a signalized intersection.
The procedure is based on the concept of how conflicting flow (cross-street through
and right turn movements, and opposing left turns) during the signal red phase could
influence the ability to complete a RTOR maneuver similar to how conflicting flow
(cross-street through and right turn movements) influences the ability to complete a
right turn at an unsignalized intersection.
2
This thesis also shows how the HCM 2000 uniform delay equation should be
modified to include a RTOR saturation flow rate. Including RTOR in the uniform
delay equation would increase the capacity of the right turn movement; however, as
the level of conflicting vehicle flow increases during the red phase, the ability to
complete RTOR decreases, thereby reducing the overall benefit to capacity for the
right turn movement. This modified capacity and delay calculation is explained in the
main text of the thesis.
3
2.
RTOR History
As early as 1937, the State of California began allowing motorists to turn right on a
red signal indication. When this practice first began, a RTOR was permitted if only a
sign authorizing such a movement was present. In 1947, California changed its
policy to a permitted one, whereas, drivers facing a steady red signal indication could
turn right unless prohibited by a sign installation precluding such a movement.
Over the years, RTOR rules have been adopted in some form. There are four basic
policies used to enforce RTOR movements:
1. Totally prohibited.
2. Generally prohibited except where signed to allow it at selected intersections.
3. Generally permitted except where signed to prohibit it at selected
intersections.
4. Totally permitted2.
Surveys were conducted of state policies regarding prohibiting RTOR with the most
common factors being where five or more approaches exist at an intersection, where
there may be restrictive geometry or inadequate sight distance, or where there are
significant pedestrian volumes or high vehicle speeds through the intersection.
A study by Baumgaertner3 indicates that a relatively large number of motorists
4
(approximately 65%) did not comply with the stop provision of the law. Although such
a large percentage would seem to indicate that unsafe movements may be occurring
regularly, this study concluded that only about 2% did so unsafely, i.e., turning right on
red in the face of a real conflict. A more recent study4 found that approximately 60%
of motorists turning right on red came to a complete stop before executing the turn.
One of the first endeavors into estimating RTOR capacity was conducted by Luh and
Lu5. They proposed that, since the maneuver that drivers undertake when turning
right on a red signal indication is similar to that of motorists turning right from a minor
street onto a major street at a stop sign controlled intersection, the potential capacity
of these two turning maneuvers is also similar when both movements have similar
traffic conditions. The results of their work indicate that this approach is generally
true. Another approach is defined in the HCM whereby, if an exclusive right turn lane
exists, the number of right turn vehicles can be reduced by the number of shadowed
left turners, i.e., the right turn volume can be reduced by the number of non-
conflicting left turn movements that occur on the cross-street approach during the
signal phase when RTOR is permitted.
A study conducted by Virkler and Krishna6 compared the capacity methodology of the
HCM, SIDRA7 and the Luh and Lu approaches, and proposed an Adjusted Stop Sign
Analogy (ASSA) to account for the limited time of unsaturated conflicting traffic flow in
each phase. The ASSA added a second term to the unsignalized intersection
capacity equation, the results of which found that the ASSA tended to underestimate
5
gap capacity, while the basic Stop Sign Analogy (SSA) proposed by Luh and Lu
appeared to overestimate gap capacity.
Further research has been conducted into developing models to predict RTOR and
to calculate the resulting effect on vehicle delay,8,9'10. These models offer differing
approaches to predicting RTOR.
The issue of evaluating new methodologies for quantifying RTOR capacity at
signalized intersections is ongoing. This thesis provides additional information for
consideration.
6
3. Project Approach
3.1 Modification of HCM Uniform Delay Equation
The HCM 2000 equation for uniform delay is:
0.5C(1-g/C)2
where,
(3.1.1)
1-[min(1,X)g/C]
d., = uniform control delay assuming uniform arrivals (s/veh)
C = cycle length (s)
g = effective green time for lane group (s)
X = v/c ratio or degree of saturation for lane group
The uniform delay equation can be represented graphically as shown on Figure 3.1.
Saturation Flow Rate
During Green Interval
Time in Seconds
Figure 3.1
HCM 2000 Uniform Delay
7
As can be seen on Figure 3.1, the uniform delay equation does not provide allowance
for RTOR vehicles. As such, the capacity of the right turn movement would be
underestimated.
The HCM 2000 uniform delay equation for right turn movements is proposed to be
modified as follows:
(v-Sr)2
d1 = 0.5(C/v)(1-g/C)2[(v-Sr)+-----] where, (3.1.2)
Sg-v
d1 = uniform control delay assuming uniform arrivals (s/veh)
C = cycle length (s)
v = lane group volume (vph)
g = effective green time for lane group (s)
Sr = saturation flow rate during red interval (vph)
Sg = saturation flow rate during green interval (vph)
Equation 3.1.2 is graphically depicted on Figure 3.2. The next section explains the
method proposed by this thesis to estimate RTOR capacity based on the RTOR
saturation flow rate during red intervals.
8
/
/
/
Figure 3.2
Modified Uniform Delay
3.2 Calculation of Potential RTOR Saturation Flow Rate
Chapter 17 of the HCM 2000, on Unsignalized Intersections, documents a method of
estimating right turn capacity that is affected by the number of conflicting vehicles at
the intersection. For a minor street right turn movement, the HCM 2000 indicates that
The right turn movement... is in conflict with only the major-street through
movement in the right-hand lane into which right-turners will merge.1 The HCM 2000
formula for estimating conflicting flow for a minor right turn is:
Vc,9 = V^N + 0.5V3 + V14 + V15, where (3.2.1)
Vc9 = total conflicting volume for minor street right turn (vph)
V2/N = conflicting cross-street through vehicles per cycle divided by the number
9
of through lanes (vph)
V3 = conflicting cross-street right turn vehicles per cycle (vpc); this part of the
equation is used if right turns on the conflicting cross-street are from a
shared through/right lane and is removed from the equation if a separate
right turn lane exists on the conflicting cross-street.
V14 = conflicting pedestrian movements across the major street
V15 = conflicting pedestrian movements across the subject minor street
The conflicting movements are graphically depicted as follows:
A
2. !14
1 \..a i
9
Figure 3.3
Minor Street Right Turn Conflicting
Flows at Unsignalized Intersections
It is proposed that the conflicting flows of a signalized intersection can influence the
capacity of a signal-controlled right turn movement in a similar fashion as the
conflicting flows of an unsignalized intersection can influence the capacity of the stop
sign-controlled right turn movement. Pedestrian movements are not included in this
thesis since the HCM 2000 has developed a comprehensive methodology for the
treatment of pedestrians and their influence on capacity. One additional component
is included to this calculation, being the opposing left turn movement. Unlike an
10
unsignalized intersection, where a minor street right turn movement has the right-of-
way over a left turn on the opposing approach, a right turn movement at a signalized
intersection must yield to an opposing left turn movement when that movement is
provided a protected phase. The proposed procedure to calculate potential right turn
capacity is as follows:
Calculate Conflicting Volume During Signal Red Phase
Use a modified HCM 2000 Exhibit 17-4 Minor Right Turn equation for unsignalized
intersections:
Vc= (V2/N+V1o/Na+0.5V3)*3600/C, where (3.2.2)
Vc = total conflicting volume per hour (vph)
V2/N = conflicting cross-street through vehicles per cycle divided by the number
of through lanes (vpc)
V10/NA = conflicting opposing left turns per cycle divided by the number of left turn
lanes (vpc)
V3 = conflicting right turn vehicles per cycle (vpc); this part of the equation is
used if right turns on the conflicting cross-street are from a shared
through/right lane and is removed from the equation if a separate right turn
lane exists on the conflicting cross-street.
C = Cycle length (s)
3600/C= Conversion factor to an hourly conflicting volume
11
Calculate Potential RTOR Saturation Flow Rate
g(-Vc*Tc)/3600
Sr=Vc[-----------------], where (3.2.3)
1-e('Vc*Tf)/3600
Sr = Potential saturation flow rate of right turn during red interval (vph)
Vc = Conflicting vehicle flow rate (vph)
Tc = Critical gap for right turn movement (s)
Tf = Follow-up time for right turn movement (s)
Equation 3.2.3 is called potential capacity when applied to unsignalized
intersections but must be called potential saturation flow rate when applied to
signalized intersections since it assumes that RTOR can occur for the full hour.
Calculate Potential RTOR Capacity
Hence, equation 3.2.4 defines the RTOR capacity:
Cr=Sr(C-g), where (3.2.4)
Cr = Potential capacity of right turn during red interval (vph)
Sr = Saturation flow rate during red interval (vph)
C = Cycle length (s)
g = Effective green time for lane group (s)
12
Calculate Potential Right Turn on Green (RTOG) Capacity
The HCM 2000 defines the right turn on green saturation flow rate (Sg) as 85% of the
adjusted saturation flow rate for an exclusive right turn lane. The RTOG capacity is
defined by equation 3.2.5:
Cg = Sg(g/C), where (3.2.5)
Cg = Potential capacity of right turn during green interval (vph)
Sg = Saturation flow rate during green interval (vph)
g = Effective green time for lane group (s)
C = Cycle length (s)
Calculate Total Right Turn Capacity
Therefore, the total right turn capacity of an exclusive right turn lane is the sum of Cr
and Cg:
CT = Cr + Cg, where
(3.2.6)
CT = Total right turn capacity (vph)
Cr = Right turn capacity during red interval (vph)
Cg = Right turn capacity during green interval (vph)
Although this thesis focuses on Cr, ultimately comparing the potential Cr to observed
Cr, a comparison of potential versus observed Cg and CT is also included.
13
4.
Data Collection
To properly evaluate the objective of this thesis, it was determined that the following
information should be recorded:
Right turn volume during the right turn red and green phases
Conflicting cross-street through and right, and opposing left turn movements
during the right turn red phase
Intersection geometry
Intersection signal timing
The above data was collected at four intersections in the Denver metropolitan area
with data being collected twice at one of the intersections. See Figure 4.1 for a
representation of the data collection locations. Each of these locations are within, or
near, a region of the Denver metropolitan area known as the Denver Technological
Center, a relatively large area of mostly office uses. As a result, traffic flows during
the morning and evening peak hours are representative of most office buildings. In
addition, a reasonable amount of nearby commercial activity exists resulting in a
relatively high level of activity during the midday peak period, i.e., during the lunch
hour. The intersection locations and time of day when data was collected are:
14
15
Arapahoe Road/Dayton Street (AM peak hour)
Arapahoe Road/Syracuse Street (PM peak hour)
Arapahoe Road/Clinton Street/Boston Street (Midday peak hour)
Orchard Road/Greenwood Plaza Boulevard (PM peak hour)(twice)
Traffic flow data was collected on weekdays for numerous signal cycles during both
the morning, midday and evening peak hours of vehicle travel. Each of these
locations have varying lane geometry; however, each have three through lanes on the
conflicting cross-street and with one or two opposing left turn lanes. Only one
location, the Arapahoe Road/Clinton Street/Boston Street intersection had an
exclusive right turn lane on the conflicting cross-street. Each of the subject right turn
movements had exclusive right turn lanes. At the Orchard Road/Greenwood Plaza
Boulevard intersection, there was one exclusive right turn lane and a shared
through/right lane on the subject approach. Data was collected only for the exclusive
right turn lane.
Each of the right turn subject approaches is considered the minor street approach
given the relative comparison of traffic volumes between the subject approaches and
conflicting approaches. Adequate right turn demand and reasonable conflicting flow
existed during each time period that data was recorded. A sample of the collected
data (Figure 4.2) is on the following page. All of the collected data can be found in
Appendix A.
16
DATA COLLECTION SUMMARY
Intersection' Arapahoe Road / Dayton Street
GEOMETRY:
N
J
Subject Approach: SB Payton Street__________
Conflicting Approach: Wd Arapahoe Road
Opposing Approach: NB Payton Street
No. of Conflicting Lanes: T/R 5 I___________1
Time Period: _____________________
A-
Arapahoe
Road
SIGNAL TIMIMG:
120s
CYCLE LENGTH 1205
S = 0.1063 1 2 = 0.6917
c c
MINOR STREET Dayton Street
<3 = 96
Y+R = 56
G = 13e
Y+R = 56
MAJOR STREET Arapahoe Road
G = 66
Y+R = 56
6
G = 716
Y+R = 65
TRAFFIC VOLUMES:
Cycle No. Subject Approach RT Volume Conflicting Volume Cycle No. Subject Approach RT Volume Conflicting Volume
Adjacent Thru Adjacent RT Opposing LT Adjacent Thru Adjacent RT Opposing LT
Red Green Red Green
1 6 4 56 6 2
2 1 7 56 6 3
3 6 2 55 7 3
4 1 7 52 5 1
5 6 1 64 6 2
6 7 2 56 6 4
7 3 0 53 3 3
8 6 6 59 7 2
9 5 6 53 6 3
10 7 3 49 5 2 Figure 4.2
17
5.
Data Analysis
5.1 Calculation of Conflicting Flow During Signal Red Phase
Using Equation 3.2.2, Table 5.1 summarizes the calculation of conflicting flow at the
Arapahoe Road/Dayton Street intersection. Conflicting flow is shown in vph, while
conflicting vehicles are shown in vpc. Conflicting flow calculations for all
intersections are contained in Appendix B.
Table 5.1
Conflicting Flow Calculation Arapahoe Road/Dayton Street Intersection
Cycle No. RT Vol. During Red (vpc) Conflicting Vehicles (vpc) Number of Adjacent Through Lanes N Number of Opposing LT Lanes A/A Conflicting Flow vc (vph)
Cross- Street Through V, Opposing Left V,o Cross- Street Right V3
1 6 58 2 6 3 1 730
2 1 58 3 8 3 1 790
3 6 55 3 7 3 1 745
4 1 52 1 5 3 1 625
5 8 64 2 6 3 1 790
6 7 58 4 6 3 1 790
7 3 53 3 3 3 1 665
8 8 59 2 7 3 1 755
9 5 53 3 8 3 1 740
10 7 49 2 5 3 1 625
18
5.2 Calculation of Potential RTOR Saturation Flow Rate and Capacity
Chapter 17 of the HCM includes in Exhibit 17-5, Base Critical Gaps and Follow-Up
Times for TWSC (Two-Way Stop Controlled) Intersections, the base critical gap and
base follow-up time factors to use in calculating the potential capacity of a minor
movement at an unsignalized intersection. Chapter 17 continues to state that Base
factors for a six-lane major street are assumed to be the same as those for a four-
lane major street1. The potential capacity for a right turn minor movement at an
unsignalized intersection can be found on Exhibit 17-7, Potential Capacity for Four-
Lane Streets, and is represented on Figure 5.1.
Since each of the study intersections had three through lanes on the conflicting
through movement approach, a base critical gap (Tc) of 6.9 seconds and a base
follow-up time (Tf) of 3.3 seconds were used as suggested by the HCM 2000.
Using Equations 3.2.3 and 3.2.4, where,
g(-Vc*Tc)/3600
Sr=vc[----------------Land (3.2.3)
1 _e(-Vc*Tf)/3600
Cr= Sr(C-g) (3.2.4)
19
Potential Capacity, Cp, i (veh / h)
LEGEND
= RT Minor
HCM Exhibit 17-7
Conflicting Flow Rate. Vc, x (veh / h)
Figure 5.1
Conflicting Flow Rate Versus
Potential Capacity of an
Unsignalized Right Turn Minor Movement
Table 5.2 contains a sample calculation of the potential RTOR saturation flow rate
and potential capacity at the Arapahoe Road/Dayton Street intersection. Potential
RTOR saturation flow rate and potential RTOR capacity is shown in vph, while
conflicting flow is shown in vpc. The calculation of potential RTOR saturation flow
rate for all intersections can be found in Appendix C.
Table 5.2
Potential RTOR Saturation Flow Rate and Capacity -
Arapahoe Road/Dayton Street Intersection
Cycle No. Conflicting Flow (VJ (vpc) Potential RTOR Saturation Flow Rate (Sr)(vph) Cycle Length (s) Red Time (s) Potential RTOR Capacity (Cr) (vph)
1 66 369 120 107 329
2 69 337 II l 301
3 65 361 II l 322
4 58 433 I I 386
5 72 337 II 1 301
6 68 337 1 I 301
7 59 407 I I 363
8 68 356 11 I 317
9 64 364 i I 324
10 56 433 l II 386
Ave. 64.5 373 120 107 333
21
As can be seen in Table 5.2, as the conflicting flow of the intersection increases, the
potential RTOR saturation flow rate and potential RTOR capacity decreases as one
would expect.
There are several factors that can influence the potential RTOR saturation flow rate
and, ultimately, the RTOR capacity:
1. g/C Ratio There were three differing g/C ratios between the four
intersections. At those locations with less green time, the saturation flow
rate of the right turn movement was typically less, while those
intersections with more green time typically had a greater saturation flow
rate.
2. Number of Opposing Left Turn Lanes Each intersection had the same
number of cross-street through lanes (3) conflicting with the subject
approach; however, two intersections had only one opposing left turn lane,
one intersection had two opposing left turn lanes, while one intersection
had one exclusive left turn lane and one shared left/through lane on the
opposing approach. Although not evidenced in the collected data, it is
expected that those intersections with two opposing left turn lanes would
offer less opportunities for RTOR since the acceptance lanes would
typically be more occupied from a physical standpoint than when only one
opposing left turn lane exists given other intersection similarities.
22
3. Traffic Signal Phasing The type of signal phasing could influence data
collection. Of the four intersection locations, two had leading left turn
phasing on each approach, one had leading left turn phasing but with
more green time for left turn movements for two directions (overlap
phasing), and one had split phasing on the subject and opposing
approaches.
4. Exclusive Versus Non-Exclusive Right Turn Lane on Conflicting Cross-
Street Approach Only one of the four intersections had an exclusive right
turn lane on the conflicting cross-street approach. It would be anticipated
that, when an exclusive right turn lane exists, additional RTOR would
occur since driver expectancy of conflicting volume is more assured.
5. Right Turn Demand The number of vehicles waiting to complete a right
turn movement can influence capacity. As demand increases, the
number of vehicles being serviced during a traffic signal cycle will likely
increase due to driver impatience, thereby reducing vehicle headway.
6. Initial Queue The smaller the number of vehicles waiting in queue when
a new vehicle arrives, the shorter the time that vehicles need to wait
versus when a longer queue exists. Driver impatience will be reduced
and, as a result, headway could be increased.
7. Sight Distance Sight obstructions would likely influence the ability to
complete a RTOR maneuver and, therefore, would reduce right turn
capacity.
23
5.3 Relationship of Conflicting Flow Rate to Potential Capacity
Figure 5.2 presents a graph of calculated conflicting flow rate versus potential right
turn capacity using the data from the subject intersections. The Vc versus Cp graph
was calculated using the average 1-g/C ratio for the subject intersections and using
adjusted Tc and Tf values as will be discussed in Section 5.4. As can be seen in
Figure 5.2, the data points represent an exponential curve as can be expected when
using Equation 3.2.3. These data would suggest that Equation 3.2.3 can represent
potential right turn capacity at a signalized intersection as hypothesized. Of note, the
curve of Figure 5.2, when compared to the minor right turn curve of Exhibit 17-7 of
the HCM 2000, Potential Capacity for Four-Lane Streets, is lower.
24
Potential Capacity, Cp, i (veh / h)
1500
LEGEND
= RT Minor
HCM Exhibit 17-6
= Vc vs. Cp
Conflicting Flow Rate. Vc, x (veh / h)
Figure 5.2
Conflicting Flow Rate Versus
Potential Capacity of a
Signalized RightTurn Movement
5.4 Comparison to Observed Right Turn Movements for
RTOR, Right Turn on Green (RTOG) and Total Right Turns
A comparison of observed right turn movements to the potential capacity of right turn
movements was conducted. The methodology included:
a) Estimate the number of right turn movements per hour based on the
observed number of right turns during the several signal cycles by
prorating to an entire hour, and
b) Using the average potential capacity for the number of signal cycles
observed at each intersection.
5.4.1 RTOR
Table 5.3 contains the comparison of observed versus potential RTOR capacity for
each data set. As can be seen, each of the subject intersections had an observed
RTOR volume less than the potential RTOR capacity. Four of the intersections had
an estimated potential capacity approximately Vh to % greater than the observed
RTOR, while at one intersection, the estimated potential capacity was more than
twice the observed RTOR.
26
Table 5.3
Potential RTOR Capacity Versus Observed RTOR
Intersection Potential RTOR Capacity (Cr)(vph) Observed RTOR Volume (vph) Percent Difference
Arapahoe Road/ Dayton Street 333 156 +113.5%
Arapahoe Road/ Syracuse Street 305 197 +54.8%
Orchard Road/ Greenwood Plaza Boulevard -1 362 274 +32.1%
Arapahoe Road/ Clinton Street/ Boston Street 292 175 +66.9%
Orchard Road/ Greenwood Plaza Boulevard 2 340 202 +68.3%
The evidence of Table 5.3 would indicate that the base critical gap (Tc) and base
follow-up time (Tf) values of Exhibit 17-5 of the HCM 2000 (Tc = 6.9, Tf = 3.3) would
need to be adjusted to more accurately reflect driver behavior at signalized
intersections. By adjusting Tc and Tf for each intersection so that potential right turn
capacity equals observed RTOR movements, it was found that Tc and Tf would need
to range from 7.2 to 7.6, and 3.5 to 4.0, respectively. Each of these higher
parameters will lower the potential capacity of equation 3.2.4. As an example, the
potential capacity of Figure 5.2 was developed using the highest values of each of the
Tc and Tf parameters, being 7.6 and 4.0, respectively.
27
One reason why Cp may be lower for right turns at signalized intersections when
compared to right turns at unsignalized intersections can be attributed to the
difference in driver behavior at these intersections. At an unsignalized intersection, a
motorist recognizes that they must accept a gap in the through vehicle travel stream
at some point to be able to complete their maneuver; whereas, at a signalized
intersection, a motorist may choose to wait for a green indication instead of accepting
a RTOR gap. As a result, capacity for a RTOR movement would be lower than a
minor right turn at an unsignalized intersection.
5.4.2 Right Turn on Green (RTOG) and Total Right Turns
A comparison of potential capacity versus observed RTOG and total right turns was
also conducted. Table 5.4 shows that the percent difference for RTOG varies
considerable between intersections with one intersection even having a potential
capacity less than what was observed. For total right turns, four out of five
intersections are relatively close in percent difference for the comparison of potential
and observed total right turn movements, being approximately 25% to 39%. Only the
Arapahoe Road/Dayton Street intersection had a relatively large difference, possibly
attributable to relatively less right turn demand.
28
Table 5.4
Potential Capacity Versus Observed RTOG and Total Right Turns
Intersection Right Turn on Green (RTOG) Total Right Turns
Potential Capacity (CJfvph) Observed Volume (vph) Percent Difference Potential Capacity (C,)(vph) Observed Volume (vph) Percent Difference
Arapahoe Rd./ Dayton St. 175 126 +38.9% 508 282 +80.1%
Arapahoe Rd./ Syracuse St. 175 149 + 17.5% 479 345 +38.8%
Orchard Rd./ Greenwood Plaza Blvd. -1 363 290 +25.2% 726 556 +30.6%
Arapahoe Rd./ Clinton St./ Boston St. 210 226 -7.1% 502 401 +25.2%
Orchard Rd./ Greenwood Plaza Blvd. 2 363 307 + 18.2% 703 509 +38.1%
29
6.
Recommendations
6.1 HCM 2000 Delay Equation Modification
Based on further data analysis resulting in an evaluation as described in this paper, it
is recommended that the d, term of the uniform right turn delay equation be modified
to reflect right turn capacity during both the red and green phase of a traffic signal. It
is proposed that the uniform right turn delay calculation be modified as follows:
Average Uniform Right Turn Delay per Right Turn Vehicle =
(v-Sr)2
d, = 0.5(C/v)(1-g/C)2[(v-Sr)+-----] where, (6.1)
Sg-v
C = Cycle length (s)
v = Right turn volume (vph)
g/C = Green to cycle length ratio
Sr = Saturation flow rate during red phase (vph)
Sg = Saturation flow rate during green phase (vph)
Equation 6.1 is graphically represented on Figure 6.1:
30
/
Figure 6.1
Modified Uniform Right Turn Delay
The modification of the uniform right turn delay equation as proposed is anticipated to
more accurately reflect driver behavior when conducting a right turn movement at a
signalized intersection.
6.2 Further Study
The amount of data that was collected and used in the development of this paper is
not sufficient to enact the proposed recommendation. Further data must be collected
and analyzed to verify the initial findings of this paper. Some suggestions for further
data collection are:
1. Intersections with Differing Geometry As noted previously, each of the
intersections used for data collection for this paper had three through
31
lanes on the adjacent approach. Data should also be collected at
intersections with only one or two approach lanes. A separate left turn
lane(s) should exist on the cross-street approach, however, to simplify the
data analysis. Data collection at locations with one or two left turn lanes
on the opposing approach should be continued, as well as locations with
both exclusive and shared right turn lanes on the cross-street approach.
2. Signal Timing Continued data collection at locations with differing signal
cycle lengths, g/C ratios and phasing patterns should occur to assure that
the potential RTOR saturation flow rate is not dependent upon one
contributing factor.
3. Delay Data Vehicle queue data should be recorded during the same
traffic signal cycle as when right turn and conflicting volume is recorded to
assure an accurate comparison of calculated versus measured delay.
4. T and T, Further data must be collected for use in calibrating potential
capacity to determine appropriate values of Tc and Tf.
32
APPENDIX A
DATA COLLECTION SUMMARY
DATA COLLECTION SUMMARY
Intersection: Arapahoe Road / Payton Street
GEOMETRY:
JILL
Subject Approach: SB Payton Street_______
Conflicting Approach- WB Arapahoe Road___
Opposing Approach: NB Payton Street______
No. of Conflicting Lanes: T/R 5 I________1
Time Period: AM Peak_____________________
SIGNAL TIMIMG:
120s
CYCLE LENGTH 120^_______
2 = 0.1053 1 Â£ = 0.5917
c c
X-
'r
Arapahoe
Road
MINOR STREET Dayton Street
G = 9 s G = 13s
Y+R = 5s Y+R = 5s
MAJOR STREET Arapahoe Road
G = 6s G 71s
Y+R=5s Y+R=6s
TRAFFIC VOLUMES:
Cycle No. Subject Approach FIT Volume Conflicting Volume Cycle No. Subject Approach RT Volume Conflicting Volume
Adjacent Thru Adjacent RT Opposing LT Adjacent Thru Adjacent RT Opposing LT
Red Green Red Green
1 6 4 55 6 2
2 1 7 55 5 3
3 6 2 55 7 3
4 1 7 52 5 1
5 6 1 64 6 2
6 7 2 55 6 4
7 3 0 53 3 3
8 5 5 59 7 2
9 5 5 53 5 3
10 7 3 49 5 2
34
DATA COLLECTION SUMMARY
Ip'fgrsGCtion" Arapahoe t^oa^ / Syracuse Street-
GEOMETRY:
j
Subject Approach: SB Syracuse Street_______
Conflicting Approach- WB Arapahoe Road-----
Opposing Approach: NB Syracuse Street______
No. of Conflicting Lanes: T/R___5_____I---1
Time Period: l?M Peak______________________
"V
in
=>
o (0
to
i_ s_
>>-P
,tT)
X
'r
Arapahoe
Road
SIGNAL TIMIMG:
120s MINOR STREET Syracuse Street
TRAFFIC VOLUMES:
Cycle No. Subject Approach RT Volume Conflicting Volume Cycle No. Subject Approach RT Volume Conflicting Volume
Adjacent Thru Adjacent RT Opposing LT Adjacent Thru Adjacent RT Opposing LT
Red Green Red Green
1 4 6 49 5 3 11 5 6 67 7 3
2 4 4 76 9 4 12 9 7 61 6 3
3 9 5 52 4 3 13 4 7 72 9 2
4 7 1 69 3 3 14 6 6 72 6 2
5 5 2 56 4 2 15 9 4 55 6 2
6 7 1 65 7 2 16 6 7 56 3 2
7 5 6 64 5 2 17 6 3 59 5 1
8 7 3 69 7 1 18 10 7 53 3 1
9 7 7 67 4 3 19 6 4 62 6 4
10 3 & 71 6 2 20 6 1 67 5 3
35
DATA COLLECTION SUMMARY q
Intersection' Orchard Road / Greenwood Plaza 51 vd.
GEOMETRY:
Subject Approach: NB Greenwood Plaza 51 vd.
Conflicting Approach: Orchard road_________
Opposing Approach: SB Greenwood Plaza 51 vd.
No. of Conflicting Lanes: T/R 5 L ^1/2
Time Period: f?eak________________________
L
y
Orchard
Road
SIGNAL TIMIMG:
115s
MINOR STREET Greenwood Plaza Blvd.
G = 25s
Y+R = 5s
G = 27s
Y+R = 5s
MAJOR STREET Orchard Road
G = 13s G = 29s
Y+R = 5s Y+R = 6s
TRAFFIC VOLUMES:
Cycle No. Subject Approach RT Volume Conflicting Volume Cycle No. Subject Approach RT Volume Contlicting Volume
Adjacent Thru Adjacent RT Opposing LT Adjacent Thru Adjacent RT Opposing LT
Red Green Red Green
1 11 5 23 0 25 11 9 6 23 1 15
2 7 9 25 0 27 12 7 & 26 3 9
3 9 10 27 3 24
4 9 4 32 0 16
5 12 9 35 0 16
6 6 11 21 1 15
7 6 10 26 0 22
8 10 11 32 0 16
9 10 12 24 0 17
10 9 14 24 3 16
36
DATA COLLECTION SUMMARY
Intersection- Arapahoe Road / Clinton St. / Boston St.
Subject Approach: 5g Boston Street_________
Conflicting Approach: WBArapahoe Road______
Opposing Approach: NB Clinton Street_______
No. of Conflicting Lanes: T/R 5 L 2
Time Period: ________________________
SIGNAL TIMIMG:
GEOMETRY:
100s
MINOR STREET Boston / Clinton Street
,1: 4 A
?! JSs 31 1 8 T 8
G = 6s G = 6s (3 = 13s
Y+R = 5s Y+R = 5s
MAJOR STREET Arapahoe Road
Y+R = 5s
Y+R = 6s
TRAFFIC VOLUMES:
Cycle No. Subject Approach RT Volume Conflicting Volume Cycle No. Subject Approach RT Volume Conflicting Volume
Adjacent Thru Adjacent Thru Mjacpm Opposing
Red Green Red Green
1 2 6 47 14 11 6 5 53 21
2 2 7 42 11 12 4 6 41 16
3 5 13 36 13 13 3 6 43 17
4 5 6 35 11 14 6 5 45 19
5 7 7 51 13 15 3 5 46 14
6 6 5 43 10
7 7 5 43 14
8 9 3 49 14
9 3 6 43 14
10 5 7 67 9
37
DATA COLLECTION SUMMARY @
Intersection' Orchard Road / Greenwood Plaza 51 vd.
Subject Approach: NB Greenwood Plaza Blvd.
Conflicting Approach: EB Orchard road-------
Opposing Approach: SB Greenwood Plaza Blvd.
No. of Conflicting Lanes: T/R 5 I------11/2
Time Period: f?eak______________________
GEOMETRY:
~r
j/.
L
Orchard
Road
SIGNAL TIMIMG:
115s
MINOR STREET Greenwood Plaza Blvd.
G = 25e G = 27s
Y+P = 5s Y+P = 5s
MAJOR STREET Orchard Poad
G = 15s G = 29s
Y+R = 5s Y+R = 6s
TRAFFIC VOLUMES:
Cycle No. Subject Approach RT Volume Conflicting Volume Cycle No. Subject Approach RT Volume Conflicting Volume
Adjacent Thru Adjacent RT Opposing LT Adjacent Thru Adjacent RT Opposing LT
Red Green Red Green
1 4 15 55 1 50 11 4 5 16 1 16
2 7 7 52 0 27
3 & 7 26 0 14
4 9 11 21 0 20
5 9 6 16 2 12
6 6 12 28 0 16
7 & 14 52 1 25
8 2 14 54 0 22
9 7 10 57 1 22
10 7 9 54 2 19
38
APPENDIX B
CONFLICTING FLOW CALCULATIONS
Cycle No. RT Vol. During Red (vpc) Conflicting Vehicles (vpc) Number of Adjacent Through Lanes N Number of Opposing LT Lanes NA Conflicting Flow vc (vph)
Cross- Street Through V.? Opposing Left vw Cross- Street Right V,
Arapahoe Road/Dayton Street
1 6 58 2 6 3 1 730
2 1 58 3 8 3 1 790
3 6 55 3 7 3 1 745
4 1 52 1 5 3 1 625
5 8 64 2 6 3 1 790
6 7 58 4 6 3 1 790
7 3 53 3 3 3 1 665
8 8 59 2 7 3 1 755
9 5 53 3 8 3 1 740
10 7 49 2 5 3 1 625
39
CONFLICTING FLOW CALCULATIONS CONTD.
Cycle No. RT Vol. During Red (vpc) Conflicting Vehicles (vpc) Number of Adjacent Through Lanes N Number of Opposing LT Lanes NA Conflicting Flow Vc (vph)
Cross- Street Through V} Opposing Left v10 Cross- Street Right v3
Arapahoe Road/Syracuse Street
1 4 49 3 5 3 1 655
2 4 76 4 9 3 1 1015
3 9 52 3 4 3 1 670
4 7 69 3 3 3 1 825
5 5 58 2 4 3 1 700
6 7 65 2 7 3 1 815
7 5 64 2 5 3 1 775
8 7 69 1 7 3 1 825
9 7 67 3 4 3 1 820
10 3 71 2 8 3 1 890
11 5 67 3 7 3 1 865
12 9 61 3 6 3 1 790
13 4 72 2 9 3 1 915
14 8 72 2 6 3 1 870
15 9 55 2 6 3 1 700
16 8 58 2 3 3 1 685
17 6 59 1 5 3 1 695
18 10 53 1 3 3 1 605
19 6 62 4 6 3 1 830
20 8 67 3 5 3 1 835
40
CONFLICTING FLOW CALCULATIONS CONTD.
Cycle No. RT Vol. During Red (vpc) Conflicting Vehicles (vpc) Number of Adjacent Through Lanes N Number of Opposing LT Lanes A/A Conflicting Flow vc (vph)
Cross- Street Through v2 Opposing Left vn Cross- Street Right v
Orchard Road/Greenwood Plaza Boulevard -1
1 11 23 25 0 3 2 631
2 7 25 27 0 3 2 683
3 9 27 24 3 3 2 704
4 9 32 16 0 3 2 584
5 12 35 16 0 3 2 616
6 6 21 15 1 3 2 470
7 6 26 22 0 3 2 616
8 10 32 18 0 3 2 616
9 10 24 17 0 3 2 517
10 9 24 16 3 3 2 548
11 9 23 15 1 3 2 490
12 7 26 9 3 3 2 459
41
CONFLICTING FLOW CALCULATIONS CONTD.
Cycle No. RT Vol. During Red (vpc) Conflicting Vehicles (vpc) Number of Adjacent Through Lanes N Number of Opposing LT Lanes NA Conflicting Flow Vc (vph)
Cross- Street Through V, Opposing Left v10 Cross- Street Right v3
Arapahoe Road/Clinton Street/Boston Street
1 2 47 14 0 3 2 816
2 2 42 11 0 3 2 702
3 5 36 13 0 3 2 666
4 5 35 11 0 3 2 618
5 7 51 13 0 3 2 846
6 6 43 10 0 3 2 696
7 7 43 14 0 3 2 768
8 9 49 14 0 3 2 840
9 3 43 14 0 3 2 768
10 5 67 9 0 3 2 966
11 6 53 21 0 3 2 498
12 4 41 18 0 3 2 420
13 3 43 17 0 3 2 402
14 6 45 19 0 3 2 438
15 3 46 14 0 3 2 360
42
CONFLICTING FLOW CALCULATIONS CONTD.
Cycle No. RT Vol. During Red (vpc) Conflicting Vehicles (vpc) Number of Adjacent Through Lanes N Number of Opposing LT Lanes A/A Conflicting Flow Vc (vph)
Cross- Street Through v2 Opposing Left v10 Cross- Street Right v3
Orchard Road/Greenwood Plaza Boulevard 2
1 4 38 30 1 3 2 579
2 7 32 27 0 3 2 454
3 8 26 14 0 3 2 386
4 9 21 20 0 3 2 449
5 9 18 12 2 3 2 323
6 6 28 16 0 3 2 376
7 8 32 25 1 3 2 490
8 2 34 22 0 3 2 490
9 7 37 22 1 3 2 443
10 7 34 19 2 3 2 402
11 4 16 18 1 3 2 381
43
APPENDIX C
POTENTIAL RTOR SATURATION FLOW RATE AND CAPACITY
Cycle No. Conflicting Flow (VJ (vpc) Potential RTOR Saturation Flow Rate (Sr)(vph) Cycle Length (s) Red Time (s) Potential RTOR Capacity (Cr)
Arapahoe Road/Dayton Street
1 66 369 120 107 329
2 69 337 1 1 301
3 65 361 I 1 322
4 58 433 li 1 386
5 72 337 I I 301
6 68 337 I I 301
7 59 407 I li 363
8 68 356 I I 317
9 64 364 1 I 324
10 56 433 1 1 386
Ave. 64.5 373 120 107 333
44
POTENTIAL RTOR SATURATION FLOW RATE AND CAPACITY CONTD.
Cycle No. Conflicting Flow (VJ (vpc) Potential RTOR Saturation Flow Rate (Sr)(vph) Cycle Length (s) Red Time (s) Potential RTOR Capacity (Cr)
Arapahoe Road/Syracuse Street
1 57 413 120 107 369
2 89 240 1 U 214
3 59 404 11 ll 360
4 75 320 1 a 285
5 64 386 11 i 345
6 74 325 11 a 290
7 71 345 11 a 308
8 77 320 11 a 285
9 74 322 11 a 287
10 81 290 11 a 258
11 77 301 1 a 268
12 70 337 11 a 301
13 83 279 1 a 249
14 80 299 1 a 266
15 63 386 11 a 345
16 63 395 11 a 352
17 65 389 11 a 347
18 57 446 11 a 397
19 72 317 11 a 283
20 75 315 U a 281
Ave. 71.3 342 120 107 305
45
POTENTIAL RTOR SATURATION FLOW RATE AND CAPACITY CONTD.
Cycle No. Conflicting Flow (VJ (vpc) Potential RTOR Saturation Flow Rate (Sr)(vph) Cycle Length (s) Red Time (s) Potential RTOR Capacity (Cr)
Orchard Road/Greenwood Plaza Boulevard -1
1 48 428 115 88 332
2 52 396 1 1 307
3 54 384 I 1 297
4 48 460 1 356
5 51 439 1 340
6 37 546 1 11 423
7 48 439 1 1 340
8 50 439 l 1 340
9 41 509 l 1 394
10 43 486 l 11 376
11 39 529 l I 410
12 38 554 I I 430
Ave. 45.8 467 115 88 362
46
POTENTIAL RTOR SATURATION FLOW RATE AND CAPACITY CONTD.
Cycle No. Conflicting Flow (VJ (vpc) Potential RTOR Saturation Flow Rate (Sr)(vph) Cycle Length (s) Red Time (s) Potential RTOR Capacity (Cr)
Arapahoe Road/Clinton Street/Boston Street
1 61 324 100 87 282
2 53 385 I 1 335
3 49 407 II I 354
4 46 437 I i 380
5 64 310 I 1 270
6 53 389 I 1 338
7 57 349 I I 303
8 63 313 1 1 272
9 57 349 1 I 303
10 76 258 1 I 225
11 74 240 1 209
12 59 324 1 I 282
13 60 321 1 I 280
14 64 293 I 1 255
15 60 330 l 287
Ave. 59.7 335 100 87 292
47
POTENTIAL RTOR SATURATION FLOW RATE AND CAPACITY CONTD.
Cycle No. Conflicting Flow (VJ (vpc) Potential RTOR Saturation Flow Rate (Sr)(vph) Cycle Length (s) Red Time (s) Potential RTOR Capacity (Cr)
Orchard Road/Greenwood Plaza Boulevard 2
1 69 293 115 88 227
2 59 355 I l 275
3 40 529 1 410
4 41 497 1 I 385
5 32 599 1 I 464
6 44 489 II I 379
7 58 363 1 I 282
8 56 387 1 I 300
9 60 360 1 I 279
10 55 396 II I 307
11 35 550 I I 426
Ave. 49.9 438 115 88 340
48
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49
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