Generalized Theory of the Optimum Thrust Programming for the Level Flight of a Rocket-Powered Aircraft

Abstract

Two theories are presented for the analysis of the opti m u m burning program for horizontal flight. The first theory is based on Green's theorem which leads to a s imple straightforward proof of the necessary and sufficient conditions for the existence of a m a x i m u m . A linear relat ionship between thrust and engine mass flow is assumed. Hibbs' results are generalized by lifting any restriction concerning the shape of the drag polar and by considering a finite m a x i m u m burning rate for the engine. Two regions of best range are detected, one subsonic-transonic, the other one supersonic. The influence of the boundary conditions on the o p t i m u m technique of flight is discussed. A simple similarity rule for stratospheric solutions is pointed out . The second theory, based on the variational method of Lagrange multipl iers, considers the general case of an arbitrary oneto-one correspondence between thrust and propellant mass flow. Particular a t tent ion is devoted to the case of a polygonal thrust characteristic. An example of application is worked out . The concept of index value presented in a previous note is here emphasized. Such an index value appears to be a very effective device in controll ing the composit ion of the o p t i m u m path for discont inuous Eulerian solutions.