Search for the optimal shape of fixed exterior shading in a cooling-dominated climate

A well known heuristic sets the length of an overhang as the intersection of lines joining window's top and bottom edges with the respective positions of the sun during the solstices, thus providing complete shade during the summer solstice and full insolation during the winter solstice. The solstices, however, are just two isolated moments, while the solar energy influences building's heat balance throughout the year. The optimal shape of fixed external shading must thus depend in a more complex way on the building latitude and climate. As the solar trajectory is curvilinear, it is natural to expect that the optimal shading shape will also be curvilinear. It is assumed here that the outer end of the eastern fin, the overhang and the western fin may be representable as a NURBS curve. Since such curves cannot be directly entered into EnergyPlus, they are approximated by dividing the shading into trapezoidal segments whose outer ends jointly approximate a NURBS curve. Optimization of segment depths is performed using jEPlus+EA for the desert climate of Phoenix, Arizona, with objectives being the cooling, heating and lighting loads of a single office. The Pareto front is clustered after optimization in order to identify the set of optimal shading shapes.