Efficiency
Not every joule of energy released by burning fuel makes it to an engine's output shaft. Some is lost inside the cylinders themselves, and more is lost to friction on the way out — tracking exactly where each joule goes is what the three standard efficiency definitions are built to do.
Completing the power chain
The previous lesson introduced input power (the chemical energy supplied by the fuel each second) and indicated power (the power actually developed inside the cylinders, measured from the area of the p-V loop). Two more quantities complete the chain from fuel to usable output.
Output power, also called brake power, is the actual usable power delivered at the engine's output shaft — the power available to turn the wheels, or whatever the engine is driving. It's found from the torque $T$ delivered at the shaft and the shaft's angular velocity $\omega$:
The name "brake power" comes from how it's measured in practice: a dynamometer (a calibrated brake) is used to load the output shaft and measure the torque it can deliver at a given rotational speed, giving a direct, independent measurement of usable output power.
Not all of the power developed inside the cylinders reaches the output shaft — some is lost overcoming internal friction between moving engine parts. This lost power is the friction power:
Friction power is simply the gap between what the gas manages to do inside the cylinders and what actually survives to be delivered usefully at the output.
Three efficiencies, one connected chain
With input power, indicated power, and brake power all defined, three efficiency ratios describe how energy is lost at each stage of the chain from fuel to useful output.
| Efficiency | Definition | What it measures |
|---|---|---|
| Overall | $\dfrac{\text{brake power}}{\text{input power}}$ | Fuel's chemical energy that ends up as useful output |
| Thermal | $\dfrac{\text{indicated power}}{\text{input power}}$ | Fuel's chemical energy converted to work inside the cylinders, before friction |
| Mechanical | $\dfrac{\text{brake power}}{\text{indicated power}}$ | Power developed inside the cylinders that survives friction losses to reach the output shaft |
These three efficiencies aren't independent of each other — overall efficiency is exactly the product of thermal and mechanical efficiency, since the input-power and indicated-power terms cancel:
This relationship is a genuinely useful check: if you calculate all three efficiencies independently in a multi-part question, the overall efficiency should always come out equal to the product of the other two — a mismatch is a sure sign of an arithmetic slip somewhere upstream.
Notice how small the mechanical efficiency is compared with the thermal efficiency in the worked example above — this is realistic. Most of the energy loss in a real engine happens not in the combustion process itself (thermal efficiency can be high) but in mechanical friction between moving parts on the way to the output shaft (mechanical efficiency is often much lower). This is exactly why overall efficiency, the number that actually matters for how much useful work you get out of your fuel, is so much lower than either of the two efficiencies that multiply together to produce it.
Key takeaways
- Brake (output) power $P = T\omega$ is the usable power delivered at the output shaft, typically measured with a dynamometer.
- Friction power = indicated power − brake power: the power lost to internal friction before reaching the output shaft.
- Overall efficiency = brake power / input power: how much of the fuel's energy ends up as useful output.
- Thermal efficiency = indicated power / input power: how much of the fuel's energy is converted to work inside the cylinders.
- Mechanical efficiency = brake power / indicated power: what fraction of the power developed in the cylinders survives friction losses.
- Overall efficiency = thermal efficiency × mechanical efficiency — a useful check across a multi-step calculation.
- Multi-step questions typically require working through input power, indicated power, brake power, friction power, and all three efficiencies in sequence.