Approximate determination of losses in characteristic velocity and increments in flight altitude of the multistage launch vehicle upper stages

An important role is assigned to design-ballistic calculations at the initial stage of developing a new type of the launch vehicle. Results of such calculations are a necessary condition in solving a more general multidimensional boundary value problem of the ballistic design. It should be noted that ballistic conditions determine the design-ballistic parameters ratio to solve the boundary value problem, and its algorithms could be used as components of the higher-level optimization problems. In order to save computer time, development of the so-called fast algorithms implemented using the analytical approaches to solving a ballistic problem becomes expedient. In the logical chain of calculation dependencies making part of the ballistic calculation algorithms, the main are those relations that connect losses in the characteristic velocity with the design and ballistic parameters. They are understood as the minimum set of parameters that uniquely determine the rocket trajectory. Analytical calculated dependences of the characteristic velocity losses and of the flight altitude increments on the design-ballistic parameters of the second and third stages of three-stage launch vehicles were derived.