Crossley cycles are described by two isometric processes and two polytropic processes of the same kind. The ideal Stirling cycle and the twostroke Otto, or so-called adiabatic Stirling, are special cases. These two cases in fact bracket the spectrum of the four-step cycles that appear to be reasonable idealizations of the actual cycle of real Stirling engines.

Although the ideal Stirling cycle yields the best case analysis, it is a grand idealization of the actual state of affairs in real engines. The isothermal processes present the chief difficulty because of limited heat transfer rates in a real engine. A more realistic model is one in which the isothermal expansion and compression occur at temperatures somewhat displaced from the maximum and minimum engine hardware temperatures; this would model the temperature differential that is necessary to drive the heat transfer to and from the engine gas. This is treated in detail in Chapter 11. In many real engines the expansion and compression processes for the most part occur in engine spaces that have relatively little heat transfer area. Thus, it seems that the expansion and compression processes might be closer to adiabatic than to isothermal. Therefore, using the two-stroke Otto cycle has been advocated as a more faithful, but still idealized, cycle for representing real Stirling engines.