Energy state revisited

Kaiser (1944) has introduced the concept of "resultant height' in connection with aircraft minimum-time climbs. Its use as a state variable in trajectory work is attractive because it is a "slower' variable than either altitude or velocity. Kelley (1972, 1973) has made an attempt to synthesize "slow' state variables in connection with singular-perturbation procedures. In the present investigation, attempts are made to synthesize both "fast' and "slow' variables for the minimum-time-climb problem along lines explored by Kelley. Attention is given to climb equations, energy-modeling simplifications, "slow'-variable choice, "fast'-variable-choice considerations, a singular-perturbation analysis, the choise of a "fast' variable, and the climb-dash problem.