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

机译：具有速度损失和整流罩分离的级联火箭的最优分级

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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 Av 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 Av 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 Av. 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. (C) 2019 Elsevier Masson SAS. All rights reserved.
机译：当前，存在在无损条件下优化级联火箭分级的算法。这些算法基于Tsiolkovsky火箭方程。在此，一种变型扩展为包括速度损失和/或整流罩分离。代替简单地将速度损失添加到所需的无损失Av并在所有阶段之间自由分配总量，实现了两步过程。首先，获得无损解以确定每个阶段的最佳速度增益。然后，从最上层阶段开始一直向下不断地迭代放大火箭的各个阶段。每个阶段的大小都会扩大，因此它会产生等于最佳速度增益加上飞行过程中发生的损耗的Av。同样，每个阶段都说明了其上阶段的质量增加。在优化步骤之后添加速度损失，以确保将其分配给正确的阶段。阿丽亚娜（Ariane）40被用作三级火箭的示例。在这种情况下，与将速度损耗直接添加到所需的无损耗Av上的旧想法相反，所提出的方法产生了实际的有效负载比。由于该方法需要来自轨迹分析的输入，因此在迭代地耦合到轨迹优化器时，它的效果最佳。这样一来，阿丽亚娜40的总有效载荷比率得以提高，同时兼顾了速度损失和整流罩分离。 （C）2019 Elsevier Masson SAS。版权所有。

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