All the talk about the Koenigsegg One:1 and its bonkers 1 BHP/kg power to weight ratio got me thinking. First of all, the mixed unit systems in "BHP" and "kg" grates on me for aesthetic reasons, and the fact that the number is "1" is a happy accident but ultimately meaningless. Even deeper than that, however, is the fact that dimensional analysis reveals that it is not immediately obvious how to massage this metric into a dimensionless number that can be used as a figure of merit for automotive performance. Airplanes have a thrust, T, (dimensions of force), and a weight, W, (mass * g, also dimensions of force), which makes it easy to determine if the craft is "ballistic," T/W>1 or not, and how much so.

Horsepower is, in dimensional terms, power, which is energy per unit time. Reducing to SI base units, 1hp = 745.7 Watts = 745.7 kg*m^2/s^3. Dividing by the "weight" (actually, mass) of 1 kg gives the quantity 745.7 m^2/s^3. Whatever that quantity is, the Koenigsegg One:1 has it.

So what is that quantity? Well, its units of m^2/s^3 could be interpreted as a squared velocity per unit time, but that has no immediate applicability. How about a velocity times an acceleration? 745.7 (m/s)(m/s^2). What is another relevant physical quantity we can bring into play that will help unravel this? How about the acceleration due to gravity, 9.8 m/s^2?

If we take this power/weight ratio and divide by g=9.8 m/s^2, we get 76.1 m/s, or 170 mph. Ok, this is a velocity, and a fast one, but it's not the top speed of the One:1, or anything like that, so what is it?

It is the speed at which the One:1 could theoretically still spin its tires under acceleration if their coefficient of friction was 1, marking the speed at which the car goes from friction-limited to power-limited. This is, of course, in the absence of aerodynamic effects such as downforce that would prevent wheelspin even at lower speeds than this. It also neglects the number of drive wheels and the F/R weight distribution, but I think it still has a notional value.