In an outstanding piece of mathematical analysis, Gustav Schmidt developed a basic model of the Stirling engine and obtained a closed-form expression for its indicated cyclic work (Schmidt, 1871). It is an idealized model, but one which superbly captures essential features of the engine, especially the basic interplay between the mechanically constrained motion of it parts and the resulting thermodynamic cycle. It provides a best-case analysis that at the very least helps identify general Stirling engine characteristics and behavior. Schmidt used it to quantify and interpret the performance potential of contemporary engines.

The form of the Schmidt indicated work formula is far too complex to reveal analytically the optimum geometry of a Stirling engine. In addition, the calculations required to obtain numerical approximations of the optima were too many and too long to do before the advent of the electronic computer. It was about 90 years after Schmidt s pioneering mathematical work that the optimization problem was first taken up (Finkelstein, 1960; Kirkley, 1962; Walker, 1962). The work focused on finding the maximum indicated cyclic work relative to a characteristic cycle pressure and relative to the total mass of the working fluid or to the total swept volume.

As already pointed out in Chapter 7, in light of the Fundamental Efficiency Theorem, it is quite clear that obtaining the maximum indicated output does not ensure getting the maximum shaft or brake output. As has been shown throughout this book, shaft work is not a simple multiple...