# Trying to find the error in my logic or math. Deceleration of a car.

1. Aug 8, 2011

### mrspeedybob

So I got a ticket a few days ago for running a red light, the yellow light was very short, I'm trying to figure out if the city set the yellow light too short to be reasonable.

The speed limit at that location is 50 mph, the yellow light is 4 seconds.
Federal motor vehical safety standards specify that a vehical must be able to stop from 62 mph in 230 feet.

Stopping distance = Average speed during stop x time spent stopping
At constant deceleration average speed during stop = 1/2 initial speed
62 mph = 91 fps
so...
230=(1/2)*91*t
230=45.5*t
t=5 seconds

Stopping from 50 mph instead of 62 should take 50/62 of the time, or 4 seconds. This is exactly the duration of the yellow light so stopping in time would require instant reaction to the light turning yellow. Instant reaction is impossible for a human so the light is unreasonably short.

On the other hand...

50 mph = 73 1/3 fps
73 1/3 fps * 4 seconds = 293 1/3 feet so I should have been at least that far from the light when it turned yellow. Since my stopping distance from 50 mph is shorter then my stopping distance from 62 mph I should have had > 63 feet to react to the light.

I don't see a flaw in either line of reasoning but they obviously contradict each other. Where is my error?

2. Aug 8, 2011

### Staff: Mentor

147 feet - the distance is time times average speed. Their calculation is fine. What matters is your distance when you start to apply the brake.

3. Aug 8, 2011

### bp_psy

Did you decide to not stop and just drive full speed?
By using your previous argument the stopping distance should be [(73 1/3 fps) / 2] * 4 seconds .

4. Aug 8, 2011

### xts

There is no contradiction. You may drive those a bit more than 63 feet at the full speed, then push brake. You start decelerating, and deceleration lasts for 4s. Meanwhile the light changes to red, but you are still in front of the lights. Finally you stop at the lights as it is red for 2s or so already.

So you had over 1s to make a decision.

Other issue is that regulation for stopping distance applies to emergency braking. Street lights shouldn't force people to brake with maximum possible deceleration.
I have several streetlights on 80km/h (50 mph) road I drive every day. They allow for comfortable smooth stopping. I'll check what's their yellow light duration.

5. Aug 8, 2011

### mrspeedybob

Ok, I see what I did. If I'm 4 seconds away from the light when I hit the brakes my reduced speed actually gives me 8 seconds to stop. That's an obvious error, I feel silly now.
I was towing a trailer that I had just borrowed from someone and I was unfamiliar with it. I decided it was safer to go through the yellow then perform what I felt would have been aggressive braking with an unfamiliar trailer. The light was shorter then I expected and turned red just as I got to it.

So when I do the math correctly I had 1 second to make a decission and 6 seconds to stop, or 2 seconds to decide and 4 to stop. While this is certainly possible it does seem a little aggressive. No sweat in a car but in a truck with trailer it's white-knuckles.

I am currious to know if a 4 second yellow in a 50 mph zone is normal or shorter then normal.

6. Aug 8, 2011

### xts

For me it seemed also too short. I just imaginated that in winter conditions. So I've checked the streetlights on a road to my house.
The speed limit is 80km/h (almost the same as 50 mph), if the conditions are good most people drive 90-100 km/h (everyone knows that traffic cameras have 20km/h margin ). Yellow light lasts for 9.7s, which allows for smooth, relaxed stopping even at 100km/h. The lights have different programmes for rush hours and for relaxed time, so I may believe the cycle gets even longer in winter.

Last edited: Aug 8, 2011
7. Aug 8, 2011

### Drakkith

Staff Emeritus
Speedybob, I think your only chance is to argue that you felt it unsafe to attempt a stop with a trailer. However I don't think you are going to have much luck. Sorry!

8. Aug 8, 2011

### rcgldr

See if you can find out what the "codes" are in your country / state / city. In the USA, the normal duration of a yellow light is at least 1 second for every 10 mph. This is to allows for about 3/4 second reaction time, and about 1/2 g of braking deceleration, with some margin of time window to continue through or stop. For faster speeds (50 mph or more) usually the yellow lights add another 1/2 to 1 second of time (like 5.5 seconds for a 50 mph street).