# ITE Journal - March 2020 - 38

```Note that stopping vehicles will reach the limit line after the
signal has changed to red and, for these vehicles, the length of the
yellow interval is irrelevant.

1.	 The methodology for determining the length of the yellow
change interval described by both the classic and extended
kinematic equations incorporates the following presumptions:
a)	 The vehicle travels in free-flow conditions (unimpeded
movement, no queue, etc.).
b)	 The yellow indication illuminates at the moment the vehicle
arrives at the critical distance.
c)	 When the yellow illuminates, the vehicle's initial approach
velocity (v0) is the actual or estimated 85th percentile speed
or the posted limit, whichever is higher.
2.	 The extended kinematic equation presented here yields the
minimum yellow interval for a level intersection approach.
As with the kinematic equation for through movements,
3.	 The assumed intersection entry velocity should be determined
using engineering judgment. Generally, drivers entering an
intersection to conduct a left turn, do so at approximately 20 miles
per hour (mph) (32 kilometers per hour [km/hr]) depending on
the intersection radius. Right-turning drivers generally negotiate
the turn at approximately 12 mph (19 km/hr). An entry speed
can also be estimated based on the curve design speed published
by ITE.6 For a full explanation of this calculation, see "Yellow
Change Intervals for Turning Movements Using Basic Kinematic
Principles," available at www.ite.org/technical-resources/topics/
traffic-engineering/traffic-signal-change-and-clearance-intervals.
4.	 Calculating tolerance is standard engineering practice and
should be employed in calculations of the minimum yellow
change interval. Perception-reaction time, deceleration, approach
velocity, and entry velocity are not constants. A reasonable range
of values for each of these parameters is applicable for every
driver-vehicle complex approaching a signalized intersection.
Driver-vehicles whose metrics fall within a reasonable range
but do not strictly match the parameters typically chosen by the
traffic engineer should be accommodated.
For example, research shows that the 85th percentile PRT
is closer to 1.5 seconds (sec.) rather than the traditionally
accepted PRT of 1.0 sec.7 Likewise, some drivers, as well as
larger vehicles, cannot safely and comfortably decelerate at 10
ft./s2 (3.05 m/s2) and employ a deceleration of 8.0 ft./s2 (2.44 m/s2)
or less.8 Therefore, engineering tolerances should be employed
within signal timing protocols to accommodate all reasonable
driver-vehicle combinations, especially where the rate of
red-light violations is higher than acceptable.
38

Ma rch 2020

ite j o u rn al

5.	 The benefit of the extended kinematic equation is to provide
a sufficient yellow change interval for all driver-vehicle
movements to eliminate the dilemma zone and reduce red-light
violations. Practitioners should be aware that red-light
violations may increase in turning lanes if the available green
time is reduced to accommodate longer yellow intervals. This is
especially true where the green interval is insufficient to clear
the queue. Rather than reducing the green interval, practitioners
may consider increasing the cycle length instead.
6.	 Practitioners may have concerns about yellow intervals that are
"excessive," resulting in drivers stopped at the signal still viewing
a yellow indication. However, yellow intervals calculated using
the extended solution do not exceed the minimum time required
for a vehicle to come to a safe and comfortable STOP (Equation
13). Therefore the circumstance of a stopped driver facing a stale
yellow light should typically not occur. itej

References
1.	 "Traffic Lights Invented by William L. Potts," Mark Traffic. http://www.
marktraffic.com/traffic-lights-invented-by-william-l-potts.php. (Accessed
January 26, 2020).
2.	 D. Gazis, R. Herman and A. A. Maradudin, "The Problem of the Amber Signal
Light in Traffic Flow," Operations Research, vol. 8, no. 1, pp. 112-132, 1960.
3.	 J. E. Baerwald, "Traffic Signalization, Yellow Interval," in Traffic Engineering
Handbook, Washington, DC, Institute of Traffic Engineers (ITE), 1965.
4.	 M. Järlström, "An Extended Kinematic Equation," http://jarlstrom.com/
PDF/An Extended Kinematic Equation.pdf. (Accessed January 26, 2020).
5.	 A. A. Maradudin to the Institute of Transportation Engineers, July
29, 2015. Letter. https://www.thenewspaper.com/rlc/docs/2015/
6.	 Traffic Engineering Handbook, 6th Edition. Washington, DC: Institute of
Transportation Engineers, 2009.
7.	 McGee, H., et al. NCHRP Report 731: Guidelines for Timing Yellow and AllRed Intervals at Signalized Intersections. Washington, DC: Transportation
Research Board of the National Academies, 2012.
8.	 Harwood, DW., et al. NCHRP Report 505: Review of Truck Characteristics
as Factors in Roadway Design. Washington, DC: Transportation Research
Board of the National Academies, 2003.

Jay Beeber (M) is executive director of Safer Streets
L.A., a public policy and research organization
dedicated to the adoption of scientifically sound and
sensible transportation practices. He has authored
numerous research reports on transportation safety
issues and was a featured presenter at the ITE's Annual Meeting in
2016. He has served on a number of transportation related working
groups including subcommittees on Statewide Traffic Signal Timing
for the California Traffic Control Devices Committee and the

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# ITE Journal - March 2020

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