Force, Work, Power, and Torque (Part Four)

in Physics


Torque is a very interesting concept and occurrence, and it is definitely something that needs to be discussed in conjunction with work and power. Whereas work is described as a force acting through a distance, torque is described as a force acting along a distance. Torque is something that creates twisting and tries to make something rotate.

If we push on an object with a force of 10 lb and it moves 10 inches in a straight line, we have done 100 in‑lb of work. By comparison, if we have a wrench 10 inches long that is on a bolt, and we push down on it with a force of 10 lb, a torque of 100 lb-in is applied to the bolt. If the bolt was already tight and did not move as we pushed down on the wrench, the torque of 100 lb‑in would still exist. The formula for torque is:

Torque = Force × distance

Even though the formula looks the same as the one for calculating work, recognize that the distance value in this formula is not the linear distance an object moves, but rather the distance along which the force is applied.

Notice that with torque nothing had to move, because the force is being applied along a distance and not through a distance. Notice also that although the units of work and torque appear to be the same, they are not. The units of work were inch-pounds and the units of torque were pound-inches, and that is what differentiates the two.

Torque is very important when thinking about how engines work, both piston engines and gas turbine engines. Both types of engines create torque in advance of being able to create work or power. With a piston engine, a force in pounds pushes down on the top of the piston and tries to make it move. The piston is attached to the connecting rod, which is attached to the crankshaft at an offset. That offset would be like the length of the wrench discussed earlier, and the force acting along that length is what creates torque. [Figure 3-6]

Figure 3-6. Piston engine and torque.

Figure 3-6. Piston engine and torque.

For the cylinder in Figure 3-6, there is a force of 500 lb pushing down on the top of the piston. The connecting rod attaches to the crankshaft at an offset distance of 4 in. The product of the force and the offset distance is the torque, in this case 2,000 lb-in.

In a turbine engine, the turbine blades at the back of the engine extract energy from the high velocity exhaust gases. The energy extracted becomes a force in pounds pushing on the turbine blades, which happen to be a certain number of inches from the center of the shaft they are trying to make rotate. The number of inches from the turbine blades to the center of the shaft would be like the length of the wrench discussed earlier.

Mathematically, there is a relationship between the horsepower of an engine and the torque of an engine. The formula that shows this relationship is as follows:

Torque = Horsepower × 5,252 ÷ rpm

Example: A Cessna 172R has a Lycoming IO-360 engine that creates 180 horsepower at 2,700 rpm. How many pound-feet of torque is the engine producing?

Torque = 180 × 5,252 ÷ 2,700 = 350 lb-ft