How is the efficiency of a mechanical power transfer in a gear train defined?

• A. η = P_in / P_out
• B. η = P_out / P_in
• C. η = ΔP / P_in
• D. η = (P_out - P_in) / P_in

Answer: (B)

Efficiency in a mechanical power transfer is the fraction of the input power that actually appears as useful output power after losses. It is defined as the output power divided by the input power: η = P_out / P_in. This makes sense because if all the input power were delivered to the load, efficiency would be 1 (100%). In a real gear train, some power is lost to friction, heat, and other losses, so P_out is less than P_in and η is less than 1. For example, if 1000 W goes in and 900 W comes out, η = 0.9 (90%).

The reciprocal, P_in / P_out, would give a value greater than 1 whenever there are losses, which doesn’t represent efficiency. Using a difference, ΔP / P_in, mixes a power change with a ratio and isn’t the correct definition. And (P_out - P_in) / P_in equals η − 1, not η.