Yellow Light Means Go Very Fast

In the movie Starman (1984), Jeff Bridges plays the role of an alien. The alien watches the earthling Jenny Hayden (played by Karen Allen) drive. When Jenny needs to take a rest, she allows him to drive. And so he drives. When he sees a traffic signal turn yellow, he speeds up and causes a crash. Jenny gets mad and tells him, "You told me you know how to drive!" He responds, "I do. I watched you closely. "Red light means stop. Green light -- go. Yellow light -- go very fast."

This is exactly, mathematically speaking, what the yellow light means. Traffic engineers use a math equation to set the yellow light duration. The equation does in fact cause drivers to beat the light. The equation does cause drivers to run red lights. The equation does cause crashes. The equation is the sole source of money for the red-light camera industry.

Below is the "ITE yellow change interval equation" which traffic engineers have been misusing since 1965. There are 5 math and physics errors in it. Without these errors, there would no red-light camera industry. Can you spot the errors?

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Y = t + v / [2(a + Gg)]

Where:

• Y = yellow change interval (yellow light duration)

• t = the time it takes the 50th percentile driver to perceive a light turning yellow and put his foot on the brake

• v = approach speed (typically the speed limit, but engineers typically fix it to 23 mph for left-turn lanes)

• a = comfortable stopping deceleration for the 50th percentile passenger sedan driving on dry pavement

• G = grade of road

• g = the earth's gravity acceleration constant

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Errors

Biggest Error - A middle school student with a basic knowledge of the laws of motion will get this.

. . . is the 2 in the denominator. ( v / a ) is the time to stop. ( v / 2a ) is half the time to stop. The yellow light gives you half the time to stop. How did the 2 get in there? What does ( v / 2a ) mean?

Let S = ( [v * v] / 2a ) is the distance to stop. S / v = ( v / 2a ) is the time it takes you traverse the stopping distance driving at constant speed v. In other words, from the point upstream from the intersection where you can no longer stop, it will take you Y seconds to drive toward and enter the intersection. However, you must go the speed limit or faster.

The "2" is why we beat the light. We neither know exactly how long is the yellow nor exactly what what distance it takes us to stop. Therefore, we beat the light because it increases our chances of entering the intersection before the light turns red. We beat the light in order to not break the law. You can see the Catch-22 in this.

What is the problem with (v / 2a) for turning motions?

Hint: When you turn, do you travel toward the intersection at constant speed?

Also consider what traffic engineers do for left turns. Engineers set the yellow to 3 seconds regardless of speed limit.

• What do traffic assume?

• If the speed limit is 45 mph, the comfortable stopping distance is 300 ft for the 50th percentile driver. If you are 299 ft from the intersection, to what speed must you accelerate in order to arrive at the intersection before the light turns red?

Other Errors

There are 4 more errors. Add a comment and identify them.

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