Answer Time

I’m once again teaching a First Year Seminar class at UC Davis on High Performance Driving. I just gave them a homework problem, so I thought I bring some of that here too. Here are my answers.

Questions

1. Two identical cars are traveling 60 mph. Car A has just the driver. Car B has 3 additional passengers. Which car stops first?
2. Two identical cars are traveling 60 mph. Car A has 195 width tires. Car B has 205 width tires.  Which car stops first?
3. Two identical cars are slowing down from speed by stomping on their brakes. Car A is going 60 mph. Car B is going 100 mph. Which driver feels more G-force?
4. Why do racecars have slick tires?

Answers

1. The laws say they stop at the same time. However, the coefficient of friction isn’t constant. The heavier car may heat up its tires quicker, leading to more friction. Up to a point when there is too much heat and it has less friction. In addition, the heavier car has  a lower coefficient of friction because tires don’t follow Amonton’s First Law: they provide less friction as load increases.
2. Again, the laws of friction don’t care about tire width. But tires care about load and a 205 tire spreads the load more than a 195. So Car B stops sooner. It may also have more aerodynamic drag (better for stopping) and more aerodynamic lift (worse for stopping).
3. Car B has more aerodynamic drag and probably more lift if these are street cars. Not sure which one of those wins. In addition, hysteresis is more effective at low speeds than high. So maybe Car B feels more G-force?
4. Load and heat. Wider tires distribute load better (less loss of friction with load). Tires with grooves may heat up too much and heat kills tires.

Summary

Tires are weird. You have to do a lot of testing to find out what’s optimal.