The use of vector calculus in calculating areas of geometrical shapes in shade or in direct sunlight

Abstract

Many building services consultancies use commercial software to predict which surfaces of a building are in direct sunlight and which are in shade at any given time in the year. Such an approach can yield very satisfuctory results and a large number of 'pretty pictures'. However, it does not lend itself to an understanding of what the basic physical principles are behind such a calculation. Such an analysis is particularly useful in calculating the solar gain for the large glazed geometrical shapes particularly beloved of architects. This paper is an attempt to explain these principles and to enable simple spreadsheet calculations to be carried out. The work described was carried out as part of the environmental analysis and design of the Great Glasshouse at the National Botanic Garden of Wales, Llanarthne, Carmarthenshirew.