| As I recall, the formula for air friction is 1/2 rho*v^2 * Cd ...or something. Rho is the air density and Cd is the drag coefficient of the car, which won't change. The equations become P = E/t + friction loss I'm just assuming the friction loss is the same average loss for both before and after the hypothetical HP change. P = 1/2 m*v^2/t + 1/2 rho*v^2 * Cd
P = const/t + f t = const/(P-f) Now we have two unknown constants in the equation, which will mess up the nice relationship I had. But if we assume that the power lost to air friction f is very small compared to available horsepower P, we can use the "binomial expansion"
(P-f)^-1 = P^-1 + P^-2*f + P^-3*f^2 + ...
so
(P-f)^-1 ~ P^-1 ...which gets back our original answer after all. At 60mph, this should be true. At 100mph it probably isn't, so use one of those internet drag race simulators if you want 1/4 mile times. Those things use a whole bunch of real world data, computed much like we are computing our single constant. They just calibrate with data and give you a parameterized answer.
- John
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11:04:41 06/09/04
