What is the most important measure of an engine’s output? Is it the power or the torque? The best way to answer this question is to look at the basic definitions.
The words force, work, energy and power, which are used very loosely in ordinary speech, have to be defined precisely for engineering use
The concept of force is difficult to pin down, but we see the result of forces in action all around us. Any movement is initiated and stopped by forces.
The metric, or more correctly, the SI (Systeme Internationale) unit of force is the newton (N).
Torque, measured in Nm, is the rotational equivalent of a force. It is the force in newtons causing rotation multiplied by the perpendicular distance in metres from the line of action of the force to the centre of rotation. A torque wrench is a good example. The force you apply gets multiplied by the arm of the wrench to give the reading on the dial.
When you push a car over a distance to get it to start, you’re doing work. The amount of work is defined as the force applied times the distance over which the force is applied.
For example, if you apply a force of 200 N over a distance of 50 metres before the car starts, then the work done is 200 x 50 = 10 000 Nm or 10 kNm. However, work is measured in joules (J) to avoid confusion with the torque unit, so in this case the answer should be 10 kJ (One Nm = one J).
Work requires a modified definition when rotation is involved. It is now the torque (rotational force) times radians (rotational distance) that the engine has turned through.
Engineers don’t use degrees but prefer radians because this simplifies the mathematics. One revolution (360 degrees) is defined as being equal to 2π radians.
You have expended energy to push the car, and energy is defined as the potential to do work, so that energy is also measured in joules. In this case you have used up 10 000 joules (10 kJ) of the energy your body creates from food. A soft drink contains more than this amount, so you can put the energy back by drinking one!
The amount of power that your muscles applied to the car depends on how fast you were pushing it. Power, measured in watts, is the work done in joules divided by the time taken in seconds, so that work done at the rate of one joule per second is equal to one watt (W).
If the car started after 100 seconds of pushing, then 10 000/100 gives you an output of 100 watts, which most people can manage for a short time. Kilowatts (kW), which are 1000 times bigger, are used in the motor industry because a watt is a very small unit.
For rotation, the power is equal to torque times radians divided by the time in seconds. When this formula is applied to an engine revving at N r/min we get watts = 2πNT/60 where 2πN is the revs in radians per minute and T is the torque in Nm.
We divide by 60 to change revs per minute to revs per second because the definition requires it and finally, we divide by 1000 to get kW = 2πNT/60 000. This very important relationship is the link between power and torque. It means that when the revs and the torque are known the kW can be calculated, or if the revs and kW are known the torque can be calculated.
A dynamometer cannot measure kilowatts. It measures the torque and revs and the computer calculates the kilowatts.
Kilowatt or Newton.metre?
We are now at last in a position to answer the question asked in the beginning. The definition of torque (force times perpendicular distance) does not include a time component, so that aspects of a car’s performance that does not involve the time taken depends entirely on the torque. Examples would include which gear you need to pull up a steep hill, and what mass of trailer you can tow comfortably in top gear.
A gearbox is a torque multiplier, but leaves the kilowatts unchanged, apart from some small frictional losses. Whenever you change gear you’re changing the torque that goes to the rear wheels.
Your car could not pull away on the maximum torque the engine supplies. It gets multiplied by the gear ratio in use as well as the final drive ratio. For example, the transmission on a car with a 3:1 first gear and a 4:1 final drive will multiply the engine torque by 3 x 4 = 12 on its way to the wheels.
The definition of kilowatt involves the revs per minute, so that the time taken is a part of the definition. This means that aspects like speed and acceleration, which can be measured with a stop watch, are dependent on the kilowatts developed by the engine. However, a good torque delivery is needed to develop power, so that the torque is in some ways the dominant component of an engine’s output.