Last modified on 25 July 2008, at 17:56

Fundamentals of Transportation/Grade/Problem

TProblem
Problem:

It has been estimated that a Tour-de-France champion could generate a sustained 510 Watts of power while a healthy young human male (HYHM) can generate about 310 Watts of power. The bicycling champion and HYHM are going to race (on bicycles) up a hill with a 6% upgrade, that is five miles long, and the elevation at the top of the hill is 5000 feet. Both rider/bicycle combinations weigh 170 lbs, with frontal area 0.4m2 and coefficient of drag 0.9 (values being typical of bicyclists in crouched racing positions). The coefficient of rolling resistance for both bicycles is 0.01. Assume \rho is 1.0567 kg/cubic-m. Remember, power equals the product of force and velocity. (1) Who gets to the top first? (2) How much longer does it take the loser to make it to the top?