Optimum thrust programming for a sounding rocket

The problem of optimal thrust programming for a sounding rocket of minimum starting weight to reach specified height with given final weight and propellant characteristics is first formulated as a problem in variational calculus. The general solution for arbitrary drag function is given. The solution is then applied to two special cases, one with quadratic drag dependence on velocity and the other with linear drag dependence on velocity. Complete numerical data are given. The results are then compared with the results of constant thrust to show the advantages of thrust programming. Thrust programming is shown to be able to increase appreciably the pay load of a high altitude sounding rocket.