Design and construction of petal solar reflectors: paraboloid and catenoid

Abstract A detailed geometric study is presented of different designs of solar reflectors based on the methodology of petal diagrams. The paraboloid model is analyzed and a new model is introduced, the catenoid, discussing its advantages and disadvantages on a comparative basis. Conventional and optimized designs are presented for both kinds of surfaces, analyzing quantitatively several critical aspects such as focal distance, effective area and number of petals. Criterions and suggestions are offered to select materials and to plan the size of the system according to its purpose. Some constructed models are presented which evince a good convergence of reflected rays.

摘要 本文基于花瓣图方法，对各类太阳能反射器的不同设计开展了详尽的几何特性研究。文中先对抛物面（paraboloid）模型进行分析，随后引入一种新型悬链面（catenoid）模型，并通过对比分析探讨了该模型的优劣特性。针对上述两类曲面，本文分别给出了传统设计与优化设计方案，并从焦距、有效面积、花瓣数量等多个关键维度开展了定量分析。此外，本文还提出了材料选型准则及适配不同应用场景的系统尺寸规划建议。最后展示了若干已搭建的实验模型，其反射光线汇聚效果表现优异。