Shading of windows influences building cooling and heating loads through control of solar heat gains, and lighting load through access to available daylight. Shading shape thus presents an important factor both in building energy analysis and building aesthetics. Curvilinearity of solar paths suggests that the optimal shading shape may be curvilinear as well, and our aim here is to test this expectation. To accommodate curvilinearity of shading shape, outer edges of shading, which consists of overhang, western and eastern fins, are modeled as non-uniform rational basis spline (NURBS) curves, a widely accepted representation standard for curves in design industry. As a case study, a cellular office is considered in the Pacific Northwest National Laboratory (PNNL) office building model, with its overhang lined up by seven control points, and the fins lined up by five control points each, with two ending control points joint for the overhang and the fins. With control points allowed to take on nine different alternative depths, genetic optimisation is employed for 16 representative USA climates with respect to total equivalent source energy for heating, cooling and lighting loads. The main finding is that in a very close proximity to optimal shadings found by genetic optimisation there exist shadings with much simpler control point structure, obtained by identifying depths of successive control points, that have nearly rectangular overhangs. Since the difference between these simpler shadings and the optimal ones is less than 0.24%, this partially rejects the expectation that the optimal shading shape should be curvilinear. Structure of these near-optimal shadings also suggests a new way to partition shadings into independent regions: the lower and the upper parts of the western fin, joints of the overhang with the western and the eastern fin, the interior part of the overhang and the rest of the eastern fin.
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