Optimal staging of serially staged rockets with velocity losses and fairing separation

Abstract

Currently, algorithms exist for the optimal staging of serially staged rockets under loss-free conditions. These algorithms are based on the Tsiolkovsky rocket equation. Here, one variant is extended to include velocity losses and/or fairing separation. Instead of simply adding the velocity losses to the required loss-free Δv and freely distributing the total amount among all stages, a two-step process is implemented. First, the loss-free solution is obtained to determine the optimal velocity gain for each stage. Then, the rocket's stages are iteratively scaled up, starting with the uppermost stage and continuing downwards. The size of each stage is enlarged so that it generates Δv equal to the optimal velocity gain plus the losses occurring during its flight. Also, each stage accounts for the increased mass of the stages on top of it. Adding the velocity losses after the optimization step ensures that they are allocated to the correct stages. Ariane 40 is used as an example for a three-stage rocket. In this case, the proposed method produced realistic payload ratios, in contrast to the old idea of adding the velocity losses directly to the required loss-free Δv. As the method requires inputs that stem from a trajectory analysis, it works best when iteratively coupled to a trajectory optimizer. In doing so, Ariane 40's total payload ratio was increased, while taking both velocity losses and fairing separation into account.