In the comments of my last car post, ECooperZone asked an excellent question that I didn’t even address. I have given myself a literal slap on the wrist for that, because it’s bad thought-experiment etiquette.
The issue is horsepower. I listed the horsepower of my Toyota Yaris’s engine several times, and then just sort of tossed it out, because it didn’t factor into my equations. After reading ECooperZone’s comment, I got that nagging feeling that we nerds get when an equation comes out a little too perfect, and we have to go back and pick through the steps one-by-one to see if we forgot to multiply by pi or something like that.
Luckily, the issue of horsepower doesn’t invalidate my whole thought experiment, because, as I mentioned in my response to the comment, horsepower and torque are intimately related. I found a concise summary of the relation here. The equation is shockingly, pleasantly simple:
horsepower = torque * rotation speed (in radians per second)
Remember the scene from the Arnold Scwharzenegger Conan the Barbarian where Conan becomes a musclebound superhero because some evil bastards make him push a grinding wheel for ten years?
Let’s say Conan has to apply 50 pounds of force. That’s 222 newtons. That lever-arm looks to be about 2 meters long, for 444 newton-meters of torque at the axle. The wheel isn’t turning very fast: I’d judge about 1 rotation per minute, which is 2 * pi radians divided by 60 seconds, or 0.1 radians per second. 444 newton-meters * 0.1 per second (radians isn’t an actual unit, so we can drop it) means 44.4 Watts total power, or a pathetic 0.06 horsepower (Hey, it’s a kid pushing a grindstone. What did you expect?)
That’s the relationship between horsepower and torque as I understand it. If I’ve gotten anything wrong, I’ll slap myself on the wrist again and tell y’all about it.