The methods of finite-time thermodynamics are used to find the optimal time path of an Otto cycle with friction and heat leakage. Optimality is defined by maximization of the work per cycle; the system is constrained to operate at a fixed frequency, so the maximum power is obtained. The result is an improvement of about 10% in the effectiveness (second-law efficiency) of a conventional near-sinusoidal engine.
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Mozurkewich et al. (1981) studied this question.
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