Rex Beck Asks … Does Horsepower Needed to Reach a Given Top Speed Increase With the Square or the Cube of Velocity?

Q: Doesn’t the horsepower requirement to reach a given speed actually increase with the square of the velocity, not the cube, as you indicated in a Feb. 2019 Pit Stop answer to Paul Simmons (“Why Is my 1989 Mustang Engine So Noisy?”)?

A: Nope. Sorry, but this is a common misconception, if only because at hundreds of mph, the huge power increase needed to get there is pretty hard to wrap your head around. Nevertheless, here’s the deal: Critical aero forces go up with the square of the speed, but the horsepower required to reach a given speed does, in fact, go up with the cube of the velocity.

Let’s start at the beginning: Aerodynamic forces acting on a vehicle become a major factor above 120 mph, so they don’t play a significant role for most dual-purpose hot rods or even Sportsman-level drag cars. But if ultimate top speed is the goal, aero forces become extremely important. The basic theories of fluid dynamics date back to at least 1800, developed by George Cayley. His ideas were refined and tested throughout the 19th century by those who followed, including Lord Rayleigh. Then came the Wright brothers, and the rest, as they say, is history. The formulas as they are used today are pretty straightforward,