Brakes vs Engine

[Michiel van Wessem <jmvw@xxxxxxxxx>]

Hiya, 

A little while ago in the discussion about cars accelerating out of
control, I said that brakes have more force then the engine. I thought it
might be interesting to see how many hp you'd need to overpower your
brakes. Plus I get a chance to refresh high school physics.

In something I found on-line, called 49 Code of Federal Regulations
(10-1-1997 edition) Chapter V, paragraph 571.105 (I'm not sure what all
this means), I see that passenger cars in the US are required to be able to
stop in 673 feet from 100 mph in a first test. There probably are a number
of conditions under which this criteria must be met, but this two numbers
seem fine for my purposes.

I'll convert stuff to SI units and back, because I'm used to SI and
converting will probably reduce the chance of errors. 

673 feet = 221 m
100 mph = 161 km/h = 44.7 m/s

We'll use my car for this experiment. It weighs exactly 1500 kg with me and
my tool chest and stuff in it (because I just ate).

Speed goes from 44.7 m/s to 0 m/s in 221 m. Assuming that deceleration is
constant (which is good enough for my purposes) the average speed over this
distance will be 44.7 / 2 = 22.4 m/s so the time it takes to stop is 221 /
22.4 = 9.89 seconds.

The amount of kinetic energy converted into heat (and brake squeal etc)
while stopping is equal to the initial kinetic energy, which is 1/2 mv^2,
1/2 * 1.500 * 10^3 * 44.7^2 = 1.50 * 10^6 J

This conversion happens in 9.89 seconds, deceleration is constant, P = E/t
so the power is 1.50 * 10^6 / 9.89 = 1.52 * 10^5 W is 152 kW, which is
about 203 hp. 

So if the brakes on my car would have minimal required strength, the engine
could overpower the brakes if it could put more then 203 hp on the road
constantly during acceleration. My car doesn't have this much power, but
maybe a modified E30 M3 would. So it doesn't seem unlikely that certain
high-powered cars might overpower their brakes. 

Heavier cars have stronger brakes, so will need even bigger engines to
overpower those brakes. To see how much power any car needs to overpower
its crappy minimum US legal brakes, use any of the following formulas:

- - if weight in kg, the power in kW is weight / 9.90
- - if weight in US pounds, the power in hp is weight / 16.3

Have fun! :)

Michiel (87 325es with web page: http://www.vramp.net/~jmvw/cars/BMW )

PS: I had forgotten some of the stuff I needed to do these things. I found
help in a terrific site with high school physics, at
http://www.glenbrook.k12.il.us/gbssci/phys/Class/BBoard.html

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