Mutual shading computation of spacecraft solar antennas
The goal of the study is geometric modeling of solar batteries illumination process onboard a spacecraft or while their location on the surface (on Earth, or, for ex-ample, in lunar settlements). With a specified geometry of their location, the issues of their effective area are studied herewith with account for their mutual shading by each other, as well as by other foreign objects. Solution of these issues should form the basis of software and mathematical sup-port development for solar batteries and concentrators placement and orientation automation on both the ground surface and onboard a spacecraft. The goal of the study consists in effectiveness evaluation of solar batteries layout both among themselves and with other objects, such as a space station hull. This article describes both physical and mathematical statement of the optimization problem on solar batteries placement either in space, or on Earth. It demonstrates that in mathematical statement this problem is considered as an optimization problem of mathematical programming aimed at maximally effective utilization of these high-tech energy sources for both space orbital stations and space settlements. The solution method of this problem is geometric modeling of space station and solar batteries with a certain orientation. The receptor geometric models, discretizing both batteries location area and a space station itself were used as a modeling method. Using C# the software complex allowing solar concentrators’ effective area modeling was developed based on the developed receptor geometric model. The graphic shell was developed herewith, allowing display numerical values of the obtained results. When the software complex is operating after the station and batteries geometry loading in parametric form, geometric model is converted to matrix form, and layer by layer sections' scanning starts. In each layer of the 3D matrix a 2D matrix is formed, presenting a kind of a 3D matrix slice through a specified distance. Current solar batteries slices' areas and effective (accumulated) area of a space station's hull sections are calculated in each section (slice) of receptor matrix. This accumulated area is the spacecraft solar batteries’ effective working area of a specified geometry and sun orientation with account for all kinds of solar batteries' geometry. The authors developed also a method allowing converting geometry models of the studied objects, developed with any geometry modeling system, such as Solid Works, into receptor models, used for computation operations. The developed mathematical support and software allow evaluating the solar batteries’ effective area at spacecraft specified design parameters and its solar energy flow direction orientation. Simulation procedure allowing optimize the spacecraft solar batteries' design and geometry parameters among permissible constructive solutions based on the described above receptor model is outlined either. The application area of the obtained results is the design automation of spacecraft and geo-electric power stations located on Earth, or in space colonies.