On feasibility of launch vehicle designs

We Study various launch vehicle designs for a spacecraft to be launched vertically and ascending to all Earth orbit located at Space Station altitude (h = 463 km). We optimize the trajectory front the maximum payload viewpoint with respect to the angle of attack time history and thrust setting time history. We consider single-stage, double-stage, and triple-stage configurations. To perform the study, we employ a newly developed member of the family of sequential gradient-restoration algorithms for optimal control problems, the multiple-subarc sequential gradient-restoration algorithm. Assuming that the engine specific impulse has the best value available today (I-sp = 450s), we Study the effect of the structural factor P. (ratio of the structural mass to sum of structural mass and propellant mass) oil the payload and then develop simple relations connecting the structural factor to the payload. With these relations, we are able to predict the limiting value of the structural factor for which the payload vanishes. To two significant digits, the limiting value is approximately epsilon congruent to 0. 11 for a single-stage configuration, epsilon congruent to 0.27 for a double-stage configuration, and epsilon congruent to 0.33 for a triple-stage configuration. Based oil these results, we Conclude that, given the current values of the engine specific impulse and spacecraft structural factor, a single-stage configuration is not feasible at this particular time, while double-stage and triple-stage configurations are feasible. The above limiting values refer to multistage configurations designed with uniform structural factor. Higher payloads and higher limiting values for the last stage structural factor are possible for configurations designed with nonuniform structural factor, that is, with a last-stage structural factor much higher than the structural factors of the previous stages. For example, a double-stage configuration with epsilon(1) = 0-10, epsilon(2) = 0.25 can deliver to orbit a payload mass equal to 4.7% at the takeoff mass; a triple-stage configuration with epsilon(1) = epsilon(1) = 0.10, epsilon(3) = 0.25 can deliver to orbit a payload mass equal to 6.8% of the takeoff mass. (c) 2004 Elsevier Inc. All rights reserved.