Attachment 4 - Optimal Trajectories of Air and Space Vehicles

Abstract

This chapter discusses a theory developed on optimal trajectories for air vehicles with variable wing areas and with conventional wings. This chapter applies a new theory of singular optimal solutions, and obtains in many cases the optimal flight. The wing drag of a variable area wing does not depend on air speed and air density. At first glance the results may seem strange, however, this is the case, and this chapter shows how the new theory may be used. The equations that follow enable computations of the optimal control and optimal trajectories of subsonic aircraft with pistons, jets, rocket engines, supersonic aircraft, winged bombs with and without engines, hypersonic warheads, and missiles with wings. The main idea of the research is to use the vehicle's kinetic energy to increase the range of missiles and projectiles. This chapter shows that the range of a ballistic warhead can be increased 3–4 times if an optimal wing is added to it, especially a wing with variable area. If increased range is not needed, the warhead mass can be increased. The range of large gun shells can also be increased 3–9 times. The range of an aircraft may be improved by 3–15 % or more. The results can be used for the design of aircraft, missiles, flying bombs, and shells for large guns.