Energy, Power, and Torque

This article presents a brief description of energy, power, and torque, and shows how they are related. It's a lot like a chapter in a physics book.

The intent is to provide background information for discussions elsewhere relating to engine torque / horsepower curves, prop selection, and so forth.

The final section gives the relationship between horsepower, RPM, and torque, namely

Horsepower = Torque x RPM / 5252

1. Properties and Forms of Energy

Energy is a very real physical entity. It is as real as mud. However, nobody understands exactly what it is. It is not a material or substance made of atoms or molecules; it's a bit of a mystery.

An eighth-grade general science book defines energy as “the capacity for doing work.” But that doesn't explain a lot.

Even though the details are not understood, we can identify several forms in which energy appears:

    Kinetic -- the energy of motion. Anything that moves has kinetic energy.

    Potential - the stored energy associated with elevation or configuration. Anything lifted “up high” has potential energy. A stretched spring or a compressed gas does also.

    Chemical - the energy contained in chemicals such as gasoline, propane, sulfuric acid, and so forth.

    Thermal - the energy of heat; the collective kinetic energy of moving atoms and molecules. The higher the temperature, the faster the atoms move, and the faster they move, the more energy they have.

    Radiant - the energy associated with electromagnetic waves such as light, radio waves, radar waves, ultraviolet, infrared, and so forth.

    Acoustical - the energy associated with sound waves.

    Electrical - the energy associated with electrical charges. A charged capacitor contains electrical energy. (The energy stored in a battery is chemical energy that gets converted to electrical when a current flows through the battery.)

    Nuclear - the energy associated with mass as per E = mc2. There is an intimate relationship between mass and energy. One can be converted to the other, given the proper physical conditions.

Conservation of Energy

Energy can neither be created nor destroyed. It can only be converted or transformed from one form to another. This is a fundamental principle of physics.

Energy Transformations

Energy transformations can be observed all around us. When an object falls from a height, potential energy is converted to kinetic energy. When a plane dives, potential energy is converted to kinetic energy; it picks up speed as it loses altitude. The reverse happens when it zooms upward.

An engine converts chemical energy to kinetic energy. Brakes convert kinetic energy to thermal energy (heat) due to friction.

The energy expended in pushing a box across a floor is converted mostly to thermal energy due to the friction between the box and the floor.

In all cases, when a given amount of energy is converted to other forms, the total amount of energy remains the same. If a complete accounting is done, the sum of the energy appearing in the new forms will exactly equal the original energy. This is a consequence of the principle of the conservation of energy.

However, when chemical energy is used to power a vehicle, only a relatively small fraction of the original (fuel) energy is converted to a useful form. Most is wasted as heat flowing out the exhaust because the typical internal combustion engine is less than 40% efficient.

2. Work, Scientific Definition

In physics, work is done when a force pushes (or pulls) against an object and produces a displacement in the direction of the force. The formula for calculating work is simply

    Work = Force x Distance

If the force is measured in pounds and the distance moved is measured in feet, the resulting unit for work will be the foot-pound. For example, if a 2-pound object is lifted a distance of 4 feet, the work done is 8 ft-lbs.

If a force of 40 pounds is required to push a box across a level floor, 400 ft-lbs of work is done in pushing the box a distance of 10 ft.

Work and energy are related in that an energy transformation always occurs when work is done. It is impossible to have one without the other. It follows that work and energy are measured in the same units, namely ft-lbs, in this article.

3. Power

Power is the rate at which work is done or, equivalently, it is the rate at which energy is converted from one form to another. And here, “rate” means simply “how fast.” The formula for calculating power is

    Power = Work done / Time required to do the work
    Power = Energy transformed / Time

The most familiar unit of power measurement relating to engines is the horsepower (HP). One horsepower is the equivalent of 550 ft-lbs per second.

For example, a 1 HP motor can lift a 550 pound weight a distance of 1 foot in one second. On the other hand, a 2 HP motor would be able to lift the weight a distance of 2 feet in one second. (Assuming proper gearing, etc.)

Another unit of power used extensively in electrical applications is the watt. It is related to the horsepower by

    1 horsepower = 746 watts.

Here's a fact: A transmission, gearbox, belt drive, or whatever, cannot increase the power being transmitted from an engine or motor to a load. It can change the RPM, but not the horsepower, assuming the engine or motor puts out the same power in all cases.

This arises from the principle of conservation of energy. The gearbox does not contribute any energy to the system. It merely transmits the power from one place to another, perhaps changing the RPM in the process.

Now don't misunderstand this. It is true that a transmission can change RPM so that an engine is able to operate at an optimum RPM and generate more power than at a higher or lower RPM, but the additional power still comes from the engine and not the transmission. After all, you don't add fuel to a transmission.

Another example:

Suppose a person weighing 185 lbs takes 16 seconds to run up a long flight of steps, like may be found at a football stadium. If the vertical distance from bottom to top of the steps is 32 ft, what is the power output of the person as he runs up the steps?

    Work done = 185 lb x 32 ft = 5,920 ft-lbs

    Time required = 16 seconds

    Power = Work done / Time required

    = 5,920 ft-lbs / 16 seconds = 370 ft-lb/second

Now, one horsepower is equivalent to 550 ft-lb/second, so ...

    Horsepower = 370 / 550 = 0.7 HP (rounded off a little)

That's less than one horsepower! A human is not all that powerful when it comes to muscular exertion -- not as strong as a horse, at least -- and it is unlikely that the person could maintain that pace for very long at all.

4. Torque

Torque is a twisting force. A familiar tool is the torque wrench. What does a torque wrench measure? The twisting force, that is, the torque applied to a nut or a bolt. And that's all that torque is; a twisting force. It is not energy; it is not power. It's related to energy and power in many applications, but it is not the same.

Now, suppose we have a wrench whose handle is 2 feet long. It is applied to a nut, and we push at right angles on the end of the wrench handle with a force of 5 pounds. What amount of torque is applied to the nut?

It is 10 foot-pounds. Multiply the length of the handle (called the “moment arm”) by the force to get the torque. That is,

    Torque = Force x Moment arm

Coincidentally, the unit of measure of torque (ft - lb) is the same as the unit of work, but this is only a coincidence. The two are not the same.

Now, we can measure distance in inches, feet, or meters. And force can be measured in ounces, pounds, or newtons. It follows that there are several possible units for measuring torque in addition to the foot-pound. The most common is the inch-pound:

    1 foot-pound = 12 inch-pounds

To convert from foot-pounds to inch-pounds, multiply by 12.

To convert from inch-pounds to foot-pounds, divide by 12.

To illustrate, a sparkplug may need to be seated with a torque of 8 ft-lbs. This is 96 inch-pounds.

5. Rotational Work

Suppose we have a torque wrench whose handle just happens to be 19.1 inches long (1.5915 ft). We push on the end of the handle with a force of 8 lbs and turn it through 1 complete revolution in the process of tightening a fairly large bolt. How much work is done?

Work = Force x Distance. The distance the end of the handle moves in making one revolution is 10 ft (which is why we took the handle to be 19.1 inches long). So, the work done is 8 lbs x 10 ft = 80 ft-lbs.

Now let's look at it from a different point of view.

    The torque applied to the bolt: 8 lbs x 1.5915 ft = 12.732 ft-lbs.

Multiply this by 2 pi (pi = 3.14159), which is 6.28318, and we get ...

    Work done = 6.28318 x 12.732 ft-lbs = 79.997 ft-lbs

Except for round-off error, this is the same as the 80 ft-lbs obtained above. So what do we conclude?

    Rotational work for one revolution = 2 pi x Torque

If we turn the wrench for more than one revolution, the total work done will be

    Total rotational work = 2 pi x Torque x Number of Revolutions.

Incidentally, the 2 pi comes in above because the circumference of a circle of radius R is 2 pi R.

6. Rotational Power

Suppose we're using a torque wrench to rotate a nut on a bolt through several turns. To make this more meaningful, suppose further that the bolt is rusty and the nut is hard to turn, but the torque required remains the same.

We do a certain amount of work each time we turn the wrench through one revolution. If the nut is hard to turn, a large torque will be required and we will do more work per revolution than if the nut turns real easy.

The faster we turn the wrench, the faster we do the work. This is reasonable enough. Turning the wrench really slow doesn't require nearly the physical exertion on our part as when we turn it really fast.

Because the power output is how fast the work is done, it follows that ...

    Rotational power is proportional to the product of the torque and RPM.

Now, to do calculations and get numbers for the power output, we must use units for the torque and rotational speed that are compatible. In most cases relating to engines, torque is measured in foot-pounds and rotational speed in RPM.

When you combine units and conversion factors, here's the final result:

    Horsepower = Torque x RPM / 5252
    where the torque is measured in foot-pounds.


At 6,000 RPM, the Rotax 503 produces a torque of 40 ft-lb. (Obtained from charts published by Rotax.) What horsepower is it producing when it operates in this manner?

Using the formula above:

    Horsepower = Torque x RPM / 5252
        = 40 ft-lb x 6,000 RPM / 5252

        = 240,000 / 5252 = 45.7 HP

To put this in perspective, imagine that a certain bolt is to be torqued down to 40 ft-lb. What is your impression of a torque of 40 ft-lb? It's a lot! You will need a wrench with a long handle, and considerable force will be required.

Now think of this in terms of an engine driving a prop on a plane. Is the prop hard to turn? Darned right it is! Are we saying that it takes a torque of 40 ft-lbs to turn a prop? Yes, at least. In fact, the torque applied to the prop is more than this. Read on.

7. Torque Reduction and Multiplication by a Transmission

You know that a transmission, gearbox, or belt drive changes the RPM. Further, the transmission doesn't change the horsepower (except for a small loss due to friction, which we neglect here).

In the previous section, we see that the power is proportional to both the RPM and the torque, the two being multiplied together to get the power.

Here's the point: if the power transmitted is the same on both sides of the transmission, and if the RPM changes because of the gear ratio, the torque must also change:

    If the RPM is reduced, the torque goes up.

    If the RPM is increased, the torque goes down.

This is just saying that we can trade RPM for more torque, or vice versa.

An example is the drive train on a log truck in the lowest gear for a hard pull up hill with a heavy load. The RPM of the engine is stepped down dramatically so that the wheels turn very slowly but exert tremendous torque. Later, on top of the hill and driving down a level road with a tailwind, not so much torque is required. So what do we do? Shift gears. Trade torque for a higher RPM, so we get there quicker.

The change in torque is just the reciprocal of the change in RPM. That is, if you reduce the RPM to one-half of what it was, the torque will be doubled.

On a Challenger, the belt drive system (tall redrive) reduces the RPM from engine to prop by a factor of 2.6 : 1. This means that the torque delivered to the prop is

    2.6 x 40 ft-lbs = 104 ft-lbs.

This is an amazing thing. It is hard to imagine that a prop spinning only in air could be so hard to turn! But then, the prop is moving a lot of air, and air is heavy. A refrigerator full of air weighs almost 2 lbs and it would take a strong individual to carry the air contained in an average-sized room, even if you could get a handle on it.

Author:   Doc Green