Running red lights and pushing yellows

I was waiting to pick up my wife from a work related meeting she had where neighbors of a certain area were complaining to city officials about a certain traffic light. As my wife recounted the story to me afterwards, the neighbors wanted the timing of the light to be slightly changed so that they could come out of a side street easier on to the main arterial street. The traffic engineer from the city tried to explain that changing timings can have devastating effects on driver behavior, especially on main roads. People are used to a certain amount of wait time at stop lights, if they are made to wait longer, they are likely to run red lights or push yellow lights in order to get to their destinations in time. Apparently there is a whole body of nationwide research to support such behavior change theories.

I don't doubt there is a lot  of research on such matters, but what bothers me is such data  or research conclusions are taken as the final word by government officials and bureaucrats. And not just in the case of traffic lights. Well, somebody did the research, they may be mistaken, their research may not apply universally or their research may just plain be old and outdated.

To talk of red and yellow lights, I think most people do not want to run red lights on purpose. The only reason they do it is because they are going too fast and they are too close to the stopping line to stop. So when they see the light turning from green to yellow to red, instead of braking, they accelerate. My premise is if the same driver saw the yellow light much sooner then they would have slowed down and halted instead of speeding up. I think all we need to stop red light running is an extended yellow light, one that will allow people to see it well in advance and slow down.

Let me present a scenario where we know the speed limit of a certain road and the margin by which someone is likely to exceed the limit. Can we from these two numbers arrive at a conclusion about how long a yellow light should be on for before turning red? Let's say the speed limit is thirty miles per hour (30 mph). Generally people drive five miles over limit but to accommodate the really aggressive ones, secretly we'll assume that the some drivers will drive ten miles over speed limit, or forty miles per hour (40 mph). If we assume an average car can go from 0 mph to 60 mph in 10 seconds, then we arrive at an acceleration value of 8.8 feet/second/second or 8.8 f/s/s. For those not used to the unit of acceleration, it is [feet per second] per second. This is because velocity is measured in feet per second and acceleration is the rate of change of velocity. The equation of motion is written: v = u + a*t , where v is the final velocity, u the initial velocity, a is the acceleration and t is the time to reach the final velocity from the initial velocity. Here, v is 60 mph, u is 0 mph, and t is 10 seconds. We also have to convert miles per hour, mph, to feet per second, f/s. A mile has 5280 feet and an hour has 3600 seconds.

8.8 f/s/s is about a quarter of the acceleration due to gravity. However, this value is often the best acceleration the car can muster. For normal, comfortable driving the real acceleration is probably half this value. However we'll use this same value for the maximum deceleration as well. This is not to say what the car is capable of, but what is comfortable to the driver and passenger. Since we are talking of regular street driving we'll also assume that the normal acceptable deceleration is half the maximum value as well. That gives us 4.4 f/s/s. For ease of calculation let's round it up to 5 f/s/s. Back to the street, so the person who is going 40 mph has to slow down comfortably and stop in such a way that their deceleration never goes beyond 5 f/s/s. Again using the equations of motion, we can find that the person needs at least 11.7 seconds to come to a complete stop and do it comfortably. Also we can find that the distance the car will have traveled in the process is 344.2 feet.

So what are our conclusions? In order to come to a complete stop the driver must be given about 12 seconds and about 344 feet. This example assumed that the wayward driver was going 40 mph on a 30 mph street. Most people won't go that fast, but some will and it is probably best to consider the worst case scenario when designing for safety. For a road with a higher speed limit the yellow light time should be even longer. But from experience I can tell you hardly any traffic light stays yellow for that long. As a result, the driver sees the yellow light too late and either brakes too suddenly or speeds up and runs through the red light. 

What can be done to mitigate this problem? For one, the light timings can be changed. It doesn't matter how long a light stays green or red: those things depend on traffic flow and are not critical to safety. The light that everyone ignores is the most important light for safety and its timing must be adjusted according to speed limit and expected or observed margin of over limit speeds. The other thing that can and should be done is to demarcate on the road the safety line. There should be a small sign on the side or it can be painted on the road itself where it says that if you are behind or at this line when the light turns yellow, start braking. People who are past that line should ignore the yellow light and drive through to the other side.

I agree with the traffic engineer in his argument against the neighbors who simply wanted to change the lights for reasons of their own convenience but I also wish the engineer, and his peers, were more analytical in their jobs and less reliant on government research from the past.