Calculation of the shadow-penumbra relation and its application on efficient architectural design

Abstract

Shadow Dispersion is the effect by which any opaque object’s shadow progressively becomes penumbra. This effect originates from a partial obstruction of the visibility of the solar disk. It allows diminishing solar gain in places where there is high radiation intensity, facilitating visual ergonomics and energy efficiency. Although architecture in the tropics offers a wide array of strategies for creating penumbras, i.e., meshes, lattices, architectural fabrics, openwork walls and pergolas, there is no method for its design. Solar architecture literature simplifies the shadow projection phenomenon and always assumes sunrays as being parallel, but penumbra calculation does not allow for this simplification. In order to bridge this gap, calculating equations are deduced here and the tables needed to appraise suitable architectural areas not to block but soften sunlight are included. This paper defines the penumbra rate and shows its application on a building built in Medellin in 2006, designed for housing exhibitions of orchids, which depend on penumbra to survive. The work concludes by outlining the future possibilities of incorporating penumbra zones into the architectural design process. Other applications of the method are also mentioned.