Alexander Bolonkin. Optimal Trajectories of Air and Space Vehicles

Natural Sciences / Mathematics / Differential equations

Submitted on: Apr 01, 2015, 19:37:41

Description: The author has developed a theory on optimal trajectories for air vehicles with variable wing areas and with conventional wings. He applied a new theory of singular optimal solutions and obtained 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 will show 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, and 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 vehicleEs kinetic energy to increase the range of missiles and projectiles. The author shows that the range of a ballistic warhead can be increased 3E"4 times if an optimal wing is added to it, especially a wing with variable area. If we do not need increased range, the head mass of rockets can be increased. The range of large gun shells can also be increased 3E"9 times. The range of an aircraft may be improved by 3E"15% or more. The results can be used for the design of aircraft, space ship, head of rockets, missiles, flying apparatus and shells for large guns.

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