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Horsepower and Torque
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Introduction

A frequently asked question is, "What's the difference between horsepower and torque?" A common answer is that "Torque gets you moving, Horsepower = MPH." But that's an oversimplification that hides a lot of information. In this article I attempt to present that information.

Mass, Velocity, and Force

Any object has mass and velocity. Velocity is how fast it's going and in what direction. If you're just sitting there, then relative to your desk, you have zero velocity. If you're on a motorcycle riding on a freeway going north then you have a velocity of 65MPH northbound.

To change an object's velocity, you need a force. What's interesting about masses is that they exert exactly that kind of force on other masses. We're close to the Earth (when I sit at my desk, my butt is about two feet away from the floor) so we feel its attractive force—gravity. We say how strong the Earth's gravity is by saying how fast something would accelerate if you dropped it: 32.2 ft/sec^2 (or 9.8 m/sec^2). That is, every second that something is falling, it will fall 32 ft/sec (or 9.8 m) faster.

Unit Analysis

32.2 ft/sec^2 and 9.8 m/sec^2 are shorthand ways of saying 32 feet per second per second. What's the second "per second" about? Consider the typical way that a vehicle's acceleration is specified: zero to sixty in six seconds. Well, the "sixty" really means 60 mile/hr.

Since a mile is 5280 feet and an hour is 3600 seconds, that's the same as 88.0 feet/sec. How did I get from 60 mile/hr to 88.0 ft/sec? 60 mile/hr multiplied by 5280 ft/mile gets us 316,800 mile/hr ft/mile and since a mile divided by a mile is 1, we can leave them out of the expression: 316,800 ft/hr. Now we divide that by 3600 sec/hr (which is the same as multiplying by 1/3600 hr/sec) and we get 88.0 ft/hr hr/sec. Again, an hour divided by an hour is 1, so those hours are out of there, leaving us with 88.0 ft/sec.

Here's the whole equation:

60 mile
5280 ft
1 hour
88 ft

X
X
= 60 x 5280 / 3600 x ft / second =
hour
mile
3600 second
second

Divide that by the six seconds it took and you get 14.7 feet / sec / sec.

88 ft
1
14.7 ft

X
= 88 / 6 * ft / sec / sec =
second
6 seconds
sec^2

It's just easier to write 14.7 ft/sec^2

Throughout all of this I've kept the units of measurement along with the numbers they belong to. The same rules of math apply to them as do to the numbers. That way, if your answer is in the right units, you stand a better chance of it being the right answer.

Work and Power

My chair is keeping me from accelerating toward the Earth. It is exerting an upward force on my butt of 130 lb to match the force of gravity that's trying to accelerate me downward, which is 130 lb.

So a force is something that can accelerate a mass. A mass is something that you need a force to accelerate. (And there are no immovable objects or irresistable forces in this universe.) With me so far?

Work is a force applied over a distance. If you lift an object that weighs one pound up one foot, you have done one foot-pound of work. If you did it in one second, you could calculate the power it took: one foot-pound per second. If you did it in half a second, the power would be two foot-pounds per second. But if it took you two, say, ten seconds, that would be 0.1 foot-pounds per second.

So now we have mass, force, work, and power. Mass just sits there. Force tries to move it. Work moves it over a certain distance. Power does that within a certain amount of time.

Let's turn to Torque.

Find a handy bolt sticking out of the wall. Slip a wrench over it and attach a weight to the end. If the wrench is one foot long and the weight is one pound, then it is exerting a torque of one pound-foot on the bolt. You multiply the length of the wrench (or "moment arm") by the amount of force applied to the end. So if you had a 6" wrench and a 2-pound weight, that would be the same torque. Or a 10' wrench and a tenth-pound weight, it would still be the same amount of torque. (My wrenches are magical. They don't weigh anything.)

Now none of this is doing any work: the wrenches aren't turning. If you turn the wrench through a whole circle by applying that pound of force, that's work. If it took you one second, that's power. Let's say that pushing that foot-long wrench around by applying one pound of force at the end took you one second. The work done is one pound-foot-second per revolution.

Let's say that bolt was on there good and tight and it took 60 pound-foot-seconds to turn it one full revolution. Well, it's 60 seconds per minute, so that's the same as one pound-foot-minute per revolution. And that is 1/5250 of a horsepower.

So now we have torque, work, and power. Torque is force around a circle. Work is torque over a full circle. Power does that within a certain amount of time.

Torque and Power

It takes force to accelerate a motorcycle. A little force will accelerate a motorcycle slowly; a lot will do it faster. Force on a wheel is best measured by torque. With the right gearing, the little motor that opens and closes the plastic tray on your computer's CD-ROM drive can apply as much torque as you want ... it just can't do it very fast. That's where power comes in: how fast the motor can do the work of accelerating the motorcycle.

Torque all by itself is not terribly useful as a number for an engine's ability. There's this gearbox and final drive that changes the torque to whatever range is needed. In first gear, any given engine speed can produce a lot more toque at the rear wheel than in top gear ... but more slowly. We have gearboxes because piston engines have this annoyingly nonlinear torque curve: they're better at making torque at some RPMs than others, and they don't make any at zero RPM. So as long as the gearbox has the right ratios, I don't really care what the peak torque is—I want the engine to have a more-or-less linear torque curve.

Accelerating and maintaining top speed both require force and power. At speed, there's no more acceleration to be done, but you have to push all that air out of the way. So "Torque gets you moving, Horsepower = MPH" isn't true either.

 
Home http://www.timberwoof.com/motorcycle/faq/hp-torque.html, updated 20050115