UNIVERSAL GRAVITY TURN CURVES,
THOMPSON RAMO WOOLDRIDGE INC LOS ANGELES CALIF
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The powered flight trajectories of long range missiles, satellites, etc., may involve an atmospheric portion, in which aerodynamic forces and moments are of importance, and a post-atmospheric section, in which these effects are negligible. During this latter part of the flight, the trajectory to be followed is quite simple. A trajectory which can be used for this part is the gravity turn sometimes referred to as a zero angle of attack or no-lift trajectory. It consists in keeping the thrust always parallel to velocity, starting from some non-zero, non-vertical, initial velocity, v sub 0. This report describes a method which has been used to obtain such universal solutions for gravity turns which begin very shortly after the launching time. The physical problem is presented, and an analytical solution for the case of constant thrust-weight ratio is given. A method of numerical solution for the case of constant thrust and mass flow rate is discussed and universal curves for this problem are presented.