Calculating Speed from Skid Marks.

I have always loved watching television shows which involve some sort of forensics.  CSI and all its variations including NCIS captured my attention because of solving a mystery based only on evidence.

One topic they don't usually discuss is determining the speed of a vehicle based on the length of the skid marks left behind.

I have a friend who was driving home from church one day.  He came around the curve, just across the train tracks, when he hit a street sweeper that was making a U-turn in the middle of the road.  What's worse, there was a sign posted before the curve advising people to look for the flagman who was absent.

He was issued a ticket for speeding.  He came back as soon as he got a tape measure to determine the length of the marks.  He brought the information to me so I could check the officer's conclusion.  So after a bit of research and calculations, I discovered he was only going about 36.5 mph in a 35 zone. 
I used the calculation S = sqrt(30*D*f*n).  S means speed, 30 is a constant, D is the distance of the drag marks, f refers to the drag factor based on type of road, and n is the breaking efficiency in a percent.

The officer was notified of his calculation error.  I thought that would be the end of it but the officer came back with a charge of reckless driving, a charge that could result in my friend spending time in jail and loosing his license.   Add injury to insult, no lawyer would touch the case because they said the case was too absurd to be prosecuted.

The city refused to provide photos of the damage to the street cleaner.  They would not talk to the insurance company, or do much at all.  He supplied everything he could from my calculations to photos of the damage to his car, to drawings and anything else he could think of.  The insurance company was using my calculations, his pictures but the city refused to discuss it at all.

He finally went in to talk to a District Attorney to discuss his plea of not guilty with the damaged bumper in his hand. Fortunately, the D.A. had a enough classes in physics to understand my friends argument on why he was not recklessly driving.  The DA basically threw the charges out due.

This is my real life example of how my use of math in real life saved a friend from getting convicted of a fairly serious charge to being freed.  Mathematical equations do work within a real life context.  I am going to have fun having students do this in class in the fall.

Let me know what you think.  Have a good day.