Horse power = force*distance/time. Torque is cross product(Force, radius vector to point of contact). For our purpose just force. Since horse power has a force component in it, it can be used interchangeably with toque for the above purposes. I cant imagine an engine with zero horse power capable of producing any torque.
Again: It is plain wrong to say "you don't need horsepower to get uphill, you need torque". If you do not have horse power you cannot produce any torque. Horse power is the cause and torque is the effect. And torque is the cause, and uphill motion is the effect. So Horse power is the ultimate cause.
If we are going to nitpick with definitions, let us do it properly. Unless it is painfully obvious that I am hurting civil conversation here, a downmod is to be followed by a line of clarification.
Notice we have a pedal in the car called acceleration. We do not have 2 pedals one saying "horse power" and one saying "torque".
Increasing the torque of an engine at a particular RPM is the same as increasing the power output at the same RPM.
If you have experience with a stick shift, you notice that we shift to a lower gear to go uphill. We are simply changing the gear ratio. Now why do we do that? We want to make sure that all the hard work the engine is doing is transformed into something that moves us up the hill. If we do not lower the gear ratio, the tire will skid and some of that power will be transformed into heat and go useless (besides the real possibility of skidding into this side of the valley!) .
So we are not trading horse power for torque, rather we are making sure that we get all the power to convert into torque by using a low gear ratio. power --> torque ---> uphill. The thing that is causing the confusion is the low gear ratio, which has to do with Friction that the tire has with the road. Friction is the crucial component that transforms engine power capacity into torque. That's why we have treads in the tire. That is one of the reasons Army tanks and Bulldozers have continuous tracks, to increase friction.
