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?
Y = t + v / [2(a + Gg)]
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
Biggest Error - A middle school student with a basic knowledge of the laws of motion will get this.