In this paper, the effects of different grain shapes of a hybrid rocket motor (HRM) and different payload mass/orbit heights on the design of small launch vehicles (SLVs) are systematically discussed. An integrated overall design model for the hybrid rocket motor-powered small launch vehicle (HPSLV) is established, and two groups of three-stage SLVs capable of sending small payloads to the low earth orbit (LEO) are designed and optimized. In the first group, the SLVs with different grain shapes and different numbers of chambers in HRMs at the 1st and the 2nd stages are optimized and analyzed. In the second group, the SLVs capable of sending different payload mass to different orbit heights are optimized and analyzed. Pareto graphs of the design results show that the design of HRM at the 1st stage has the greatest impact on the take-off mass, total velocity increment, and maximum axial overload of the SLV. Self-organizing maps show that the take-off mass, maximum diameter, overall length, and velocity increment of the SLVs have the same variation tendency. For the 1-chamber HRM at the 1st stage, the wheel-shaped grain is better than circle-shaped and star-shaped grains in terms of reducing the total mass and length of the SLV, and the 4-chamber parallel HRM has more advantages over all 1-chamber designs for the same reason. The theoretical velocity increments are calculated by the Tsiolkovsky formula, and the actual velocity increments are obtained based on the trajectory simulation data. The results indicate that the HPSLV has a regular distribution in terms of the ratio of theoretical (actual) velocity increments at three different stages, and the estimated distribution ratio is around 1 : 1.55 : 1.69 (1 : 1.9 : 2.39), which can provide some reference for future development of HPSLV.

中文翻译：

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混合火箭发动机动力小型LEO运载火箭的设计优化和参数分析

在本文中，系统地讨论了混合动力火箭发动机（HRM）的不同颗粒形状和不同的有效载荷质量/轨道高度对小型运载火箭（SLV）设计的影响。建立了混合动力火箭发动机小型运载火箭（HPSLV）的集成总体设计模型，并设计和优化了两组能够将少量有效载荷发送到低地球轨道（LEO）的三级SLV。在第一组中，对第一阶段和第二阶段HRM中具有不同晶粒形状和不同室数的SLV进行了优化和分析。在第二组中，对能够将不同有效载荷质量发送到不同轨道高度的SLV进行了优化和分析。设计结果的Pareto图表明，第一阶段的HRM设计对起飞质量的影响最大，总速度增量和SLV的最大轴向过载。自组织图显示，SLV的起飞质量，最大直径，总长度和速度增量具有相同的变化趋势。对于第一阶段的1室HRM，在减小SLV的总质量和长度方面，轮状晶粒优于圆形和星形晶粒，而4室平行HRM具有更多优势出于相同的原因在所有1腔室设计中使用。通过Tsiolkovsky公式计算理论速度增量，并基于轨迹模拟数据获得实际速度增量。结果表明，HPSLV在三个不同阶段的理论（实际）速度增量之比具有正态分布，