Analytical optimization of simple roof shading devices

Parametric and algorithmic design tools have developed significantly in the last few years with the advent of several commercial and open-source applications and simulation software. These tools have been used extensively in the design and analysis of various building elements such as glazing, screens, massing and shading devices. Typically, ether iterative, parametric or optimization techniques are coupled with simulation software to reach an optimum design for the considered element. Setting up these problems usually requires time and effort, but sometime the designers need a simple tool to design particular elements. This paper presents an analytic approach for designing simple roof shading devices. The proposed approach is based on a ground-up analysis of the shading device geometry to reach global optimum designs for the elements. The approach is applied to a simple roof shading element and it is shown how different objectives and situations can be modelled using this approach. The results are compared to ENERGY PLUS simulations to verify the results. It is shown that comparable results can be achieved with the proposed approach without the need for the numerical simulation and in less time.