[Jeff Frigo]

Vehicle Top Speed vs Horsepower Requirements

From an article in December 1990 Motor Trend Magazine, Technologue Section by Ron Grable(p116)


Vehicle top speed is a subject of much debate, and more than a little mystique. >Interested in your vehicle’s acceleration or braking? Just find a deserted road and try it out; a stopwatch and a measuring tape are all that are need. Top speed, on the other hand, is much more difficult, requiring lots of controlled space and some way to measure triple-digit speeds, since most >speedometers are notoriously inaccurate. The Fast Five story in this issue examined, among other things, the top speed of some fairly exotic vehicles we tested at the Arizona Test Center. Questions arose during testing about what factors actually determine the top speed of a given vehicle

F=(0025) x Cd x A x V2

P=(.0027) x F x V


Formula 1 defines the force (F), or thrust, required to push an object (of frontal area A and drag coefficient Cd) through the air at speed V.

Formula 2 converts the force found in formula 1 into horsepower (P) for a given speed V.


Notice the required thrust is proportional to A and Cd, so a 10-percent decrease in frontal area or drag coefficient results in a 10-percent reduction in required thrust for the same speed. More important, thrust is proportional to the second power of speed V. This means a 50-percent increase in speed requires 2.25 times more thrust (1.5 x 1.5).


In formula 2, horsepower is F multiplied by V, but since F is already related to the second power of V, formula 2 shows that power is proportional to the third power of V. So, for that 50-percent increase in speed used in the example above, while thrust requirements double, needed power more than triples (1.5 x1.5 x 1.5 = 3.375).


To put all this in real-world numbers, if a vehicle’s Cd and frontal area are such that 100 horsepower is needed to push it through the air at 100 mph, increasing the speed 50 percent, to 150 mph, will require 338 horsepower (100 x 1.5 x 1.5 x 1.5). To double the speed from 100 to 200 mph would require 800 horsepower (100 x 2 x 2 x 2).