Yes, there is a mathematic relationship between torque and horsepower. But remember that the critical point is physical limitations. If you had a motor that redlines at 4000rpm with X amount of torque, versus a motor that redlines at 12,000rpm with the same amount of torque, the horsepower curves work out differently. When people talk about having a lot of torque they usually refer to usable torque, like off the line. There are often times when a motor has very little torque, but because it's designed to rotate to a higher rpm value, it will do more work (horsepower). So you can say that a motor has very little torque but can do a lot of work. If everything was flat surfaces with no wind forces and whatnot to slow things down, like say a track on the moon, you can use a single gear and a motor that can spin to any speed without blowing apart-- that motor can get to any speed or horsepower it felt like going with almost no torque. It just takes a while. The real world does impose physical limitations... like, if you had a motor with very little torque, and you tried to make it do a lot of work, eventually an opposing force will build up to cancel the torque (acceleration). (say an incline or wind drag or whatever).. so eventually your horsepower will top off. So being that we live in the real world, very often you need tremendous amounts of torque to get tremendous amounts of horsepower.

Hmm.. I'm kind of thinking about that electric motor example I gave before. Unlike gas motors, electric motors have the interesting property that if you tried to *oppose* torque it is producing, the motor will *increase* torque output. But if you didn't try to oppose the torque they have a flat curve all the way to redline. Theoretically, if the motor is made to not burn up, and you applied a brake to an electric motor it will give you infinite torque at near 0 rpm. I've heard stories of electric cars wasting Vipers off the line, well, for a little while anyway. :-)

Calvin