Analytic method for performance modelling of passive solar systems

Analytic approximations are obtained for the performance of passive solar systems using frequency domain methods, and are numerically evaluated and discussed for simple examples. The basic ideas are the use of a transmission line analogy for massive building elements, combined with a lumped-circuit analogy, and the systematic use of impedance methods and analytic properties in the frequency domain. Detailed results are obtained for a direct-gain system with mass; the effects of varying the system parameters are examined. Analytic expressions are obtained for the temperature gain and temperature swing, and numerical results evaluated and discussed. As a second example, the effects of earth-sheltering are modelled in a simplified way, and illustrated by quantitative results in a simple example. Finally some analytic results are discussed qualitatively, including the storage effectiveness of massive building elements.