this is the "engineering methods "In the current edition of ITE's Traffic Engineering Handbook (44), a standard kinematic equation is provided as a method to calculate the change interval length. The equation for calculating the change period, CP, is as follows:
The principal factors that are taken into account in the development of the change period are:

Perception-reaction time of the motorist, t, typically 1 sec.;
Speed of the approaching vehicle, V, expressed in ft./sec.;
Comfortable deceleration rate of the vehicle, a, typically 10 ft./sec.2;
Width of the intersection, W;
Length of vehicle, L, typically 20 ft.; and
Grade of the intersection approach, g, in percent divided by 100 (downhill is negative).
The equation allows time for the motorist to see the yellow signal indication and decide whether to stop or to enter the intersection. This time is the motorist's perception-reaction time, generally 1 sec. It then provides time for motorists further away from the signal to decelerate comfortably and motorists closer to the signal to continue through to the far side of the intersection. These times are dependent on the characteristics of the traffic and the roadway environment. If there is a grade on the approach to the intersection, the equation adjusts the time needed for the vehicle to decelerate.
this is from the fhwa's rules and regulationsThe FHWA also proposed in the NPA
to revise the second STANDARD
statement to indicate that the durations
of the yellow change interval and, when
used, the red clearance interval, shall be
determined using engineering practices,
and also proposed to add a new
SUPPORT statement to indicate that
engineering practices for determining
the durations of these intervals can be
found in two publications from the ITE.The FHWA proposed this to enhance
safety at signalized intersections by
requiring that accepted engineering
methods be used to determine the
durations of these critical intervals
rather than random or ‘‘rule of thumb’’
settings, and by recommending the
provision of a red clearance interval
when such accepted engineering
practices indicate that a red clearance
interval is needed. As documented in
the FHWA report ‘‘Signalized
Intersections: Informational Guide,’’ 171
a variety of studies from 1985 through
2002 have found significant safety
benefits from using accepted
engineering practices to determine the
durations of yellow change and red
clearance intervals. Recent safety
studies 172 have further documented
significant major reductions in crashes
when jurisdictions have revised the
durations of the yellow change and red
clearance intervals using the accepted
engineering practices. A State DOT and
two local DOTs opposed the revision
because their agencies have other
methods for calculating red intervals
and do not believe the ITE methods to
be superior. The FHWA disagrees
because the studies have shown
significant safety benefits when red
clearance times are provided per the ITE
methods and therefore, adopts in this
final rule the language as proposed in
the NPA
heres the pdf on the rules and reg and the time duration can be found on page 91http://edocket.access.gpo.gov/2009/pdf/E9-28322.pdf