Greenshields’ Formula

We all recognize that there is a delay from when a green traffic signal is energized to when a vehicle actually rolls forward. The trick is to us an acceptable value when modeling this delay such as in a crash reconstruction. I prefer to use an accepted value, and then look at what happens if it varies a second or two one way or the other. This ‘sensitivity analysis’ helps when I am on cross examination regarding my assumed values.

Many decades ago Greenshields collected data on start-up times for vehicles. He found that 4 seconds was an appropriate value. As a matter of fact, this is still used today for most all green light traffic signal timing: T = 4 + 2N, where N is the number of cars in the queue. The 4 seconds is the start-up time to get the first car moving, and the 2 seconds is the time for each car to move into the intersection. As an example, if there was 100 feet of storage space we would use T = 4 + ((100/20) x 2) = 14 seconds of green. We do assume that a typical car is 20 feet long.

Over time we have seen drivers become more urbanized in their driving and start-up habits. And, we have also seen a reduction in the complexity of getting a vehicle moving. Old clutches and three-speed gearboxes have been replaced with automatic transmissions. Because of this I will typically use a shorter time, say 2 seconds, as an appropriate start-up value for cars. I’ll still use the 4 seconds for larger and heavier vehicles like trucks.

I always encourage my students to spend some time at an intersection in a non-obvious manner (leave the marked patrol car at the station!) and record start-up times themselves. My recent students tell me they are seeing 2.0 to 2.5ish as typical values for cars. I think that you doing your own research lends a lot of credibility to your reliance on published values when you are on cross.

Questions/comments? If so, please send me an email, and we’ll discuss it.
Daren

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