Thermal Efficiency
The "thermal efficiency" of any engine is defined as the amount of useful energy output divided by the amount of energy input . It is not a fixed quantum but varies according to the engine's load and conditions of operation.
In the case of steam locomotives, the term thermal efficiency may refer to "Cylinder or Indicated Efficiency", "Drawbar Thermal Efficiency" or even "Boiler Efficiency". These are described on separate pages, however their definitions are importantly different as outlined below: Three types of efficiency are described on separate pages as follows:
Cylinder efficiency is defined as the the amount of energy delivered by the cylinder to the piston divided by the amount of energy delivered to the cylinder in the form of steam delivered to the steamchest;
Drawbar efficiency is defined as the the amount of energy delivered at the locomotive's drawbar (the hook at the back of its tender) divided by the amount of energy available in the fuel placed into its firebox.
Boiler efficiency can be defined as the amount of energy delivered from the boiler in the form of steam divided by the amount of energy delivered to the firebox in the form of fuel/chemical energy.
Both the cylinder and drawbar efficiencies vary with speed and power output, maximum cylinder efficiency being achieved at much higher speed than maximum drawbar efficiency. This is because, as speed rises, a locomotive's rolling resistance also rises and the tractive force avalable at its drawbar falls until, at a certain speed, the drawbar force becomes zero and thus the drawbar efficiency also becomes zero.