The **West number** is an empirical parameter used to characterize the performance of **Stirling engines** and other Stirling systems. It is very similar to the Beale number where a larger number indicates higher performance; however, the West number includes temperature compensation. The West number is often used to approximate of the power output of a Stirling engine. The average value is (0.25) for a wide variety of engines, although it may range up to (0.35) [1], particularly for engines operating with a high temperature differential.

The West number may be defined as:

- $W_{n}={\frac {Wo}{PVf}}{\frac {(T_{H}+T_{K})}{(T_{H}-T_{K})}}=B_{n}{\frac {(T_{H}+T_{K})}{(T_{H}-T_{K})}}$

where:

**W**_{n} is the West number
**W**_{o} is the power output of the engine (watts)
**P** is the mean average gas pressure (Pa) or (MPa, if volume is in cm^{3})
**V** is swept volume of the expansion space (m^{3}) or (cm³, if pressure is in MPa)
**f** is the engine cycle frequency (Hz)
**T**_{H} is the absolute temperature of the expansion space or heater (kelvins)
**T**_{K} is the absolute temperature of the compression space or cooler (kelvins)
**B**_{n} is the Beale number for an engine operating between temperatures *T*_{H} and *T*_{K}

When the Beale number is known, but the West number is not known, it is possible to calculate it. First calculate the West number at the temperatures *T*_{H} and *T*_{K} for which the Beale number is known, and then use the resulting West number to calculate output power for other temperatures.

To estimate the power output of a new engine design, nominal values are assumed for the West number, pressure, swept volume and frequency, and the power is calculated as follows:

- $W_{o}=W_{n}PVf{\frac {(T_{H}-T_{K})}{(T_{H}+T_{K})}}$
^{[1]}

For example, with an absolute temperature ratio of 2, the portion of the equation representing temperature correction equals 1/3. With a temperature ratio of 3, the temperature term is 1/2. This factor accounts for the difference between the West equation, and the Beale equation in which this temperature term is taken as a constant. Thus, the Beale number is typically in the range of 0.10 to 0.15, which is about 1/3 to 1/2 the value of the West number.

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