The power that the car engine makes has to overcome aerodynamic drag on the interstate in order to maintain a?

Question

constant speed. Assume the power required of a car’s engine to overcome aerodynamic drag is proportional to the velocity in meters per second cubed. How much is the drag reduced if you slow from 80 miles per hour on the Interstate to 55 miles per hour? Would this save gas? If so, would it improve your fuel economy? why or why not? (100 words please) Given the cost of gas, this might be important. Also, underinflated tires waste gas.

Answer 1

I'm not a physicist.  But generally, power consumed is a cube function of speed.  Meaning that if you double an object's speed (an electric motor, for example) it consumes eight times the power.  This is not entirely true with automobiles, as there are waaay too many forces in play.  Aerodynamic drag is also exponential: meaning that a Corvette doubling it's speed incurs less of a drag increase than a Mack truck.  Then there is gearing and engine efficiency: how a car is geared and what RPM it turns at highway speed makes a huge difference (thus the debut of the CVT).

Answer 2

If drag is a cubic function of speed then in going from 80 down to 55 mph, drag will be reduced to 55^3/80*3 = 32.5% of its value at 80. The reduction is 67.5%. To keep a car moving at a constant speed requires enough power to overcome rolling resistance and aerodynamic drag. Reducing either of these will lessen the power required.This will (obviously) save gas and improve fuel economy.