The intergreen period of a phase consists of both the yellow (amber) indication and the all-red indication (if applicable. This phase is governed by three separate concepts: stopping distance, intersection clearance time, and pedestrian crossing time, if there are no pedestrian signals. 

The yellow signal indication serves as a warning to drivers that another phase will soon be receiving the right-of-way. The intergreen interval, therefore, should be long enough to allow cars that are greater than the stopping distance away from the stop-bar to brake easily to a stop. The intergreen interval should also allow vehicles that are already beyond the point-of-no-return to continue through the intersection safely. 

This issue is called the"dilemma zone" concept. If the intergreen time is too short, only those vehicles that are close to the intersection will be able to continue through the intersection safely. In addition, only vehicles that are reasonably distant will have adequate time to react to the signal and stop. Those who are in between will be caught in the "dilemma zone," and won’t have enough time to stop or safely cross the intersection. Figure 1 shows this situation graphically.

Figure 1:  Dilemma Zone

The only responsible thing to do, it seems, is to eliminate the dilemma zone. This would allow any vehicle, regardless of its location, to be able to safely stop or, alternatively, safely proceed during the intergreen period. This is done by making sure that any vehicle closer to the intersection than its minimum braking distance can safely proceed through the intersection without accelerating or speeding.

First, we calculate the minimum safe stopping distance. The equation for this distance is given below and a more detailed discussion of this distance can be found in the geometric design portion of this website.

Minimum Safe Stopping Distance:

SD = 1.47*Vo*tr + (1.47*Vo)2/(30*[f ± G])

Where:
SD = Min. safe stopping dist. (ft)
Vo = Initial velocity (mph)
tr = Perception/Reaction time (sec)
f  = Coefficient of friction
G = Grade, as a percentage

Next, we calculate the time required for a vehicle to travel the minimum safe stopping distance and to clear the intersection. This is simple kinematics as well.

Intersection Clearance Time:

T = (SD + L + W)/(1.47*Vo)

Where:
T = Intersection clearance time (sec)
Vo = Initial velocity (mph)
L = Length of the vehicle (ft)
SD = Min. safe stopping dist. (ft)
W = Width of the intersection (ft)

Now that you’ve determined the first two elements of the intergreen period length—stopping distance and intersection clearance time—you need to consider the pedestrians. The intergreen time for intersections that have signalized pedestrian movements is the same as the intersection clearance time. 

If you have an intersection where the pedestrian movements are not regulated by a separate pedestrian signal, you need to protect these movements by providing enough intergreen time for a pedestrian to cross the intersection. In other words, if a pedestrian begins to cross the street just as the signal turns yellow for the vehicular traffic, he/she must be able to cross the street safely before the next phase of the cycle begins. The formula for this calculation is shown below.

Pedestrian Crossing Time:

PCT = W/V

Where:
PCT = Pedestrian crossing time (sec)
W = Width of the intersection (feet)
V = Velocity of the pedestrian (usually 4 ft/sec)

Once you have considered the safety of both the vehicular traffic and the pedestrian traffic for the given phase, you can choose the intergreen time. The intergreen time is equal to whichever is larger, the pedestrian crossing time or the intersection clearance time.