TABLE OF CONTENTS Derived in this chapter are two direct consequences of the Mechanical Efficiency Limit Theorem proven in the preceding chapter. One consequence is a surprising intrinsic limitation on the geometry of certain engines. The other consequence is the determination of the maximum shaft work that can be obtained from engines under common restrictions. This yields a theoretical standard to which particular engines can be conveniently compared.
That there are restrictions on the compression ratio one can use in an engine is an unexpected implication of the Mechanical Efficiency Limit Theorem. This limitation can be seen by considering the behavior of ? ms (E, ?, r) as a function of r for fixed E, and ?. Maximal mechanical efficiency ? ms is simply equal to E as long as r ? 1 / ?. For r > 1 / ?, it is easily determined by elementary calculus that ? ms (E, ?, r) is monotone decreasing with increasing r. It is also readily found that lim r ?? S( ?, r) = ?/(1 ? ?), which gives
Thus, if E 2 > ?, ? ms will asymptotically approach a positive lower bound. However, when E 2 < ?, then limit (4.1) is negative. This means ? ms decreases and becomes zero at a finite value of r. When its mechanical efficiency...
