Modeling Passive Solar Buildings with Hand Calculations

Passive solar design can be encouraged by a better theoretical understanding of the performance of passive solar buildings and the ability to predict the thermal response of various designs. But existing public-domain computer programs do not yet handle solar gains precisely and are inaccurate in modeling buildings with large solar gains. Even when they are revised to properly describe solar effects, they may still fail to provide insight into the thermally important features of the building.

To address these problems, we derive an analytic model of passive solar building performance. We use heat balances on the surfaces of materials that absorb sunlight (e.g., the inside surface of a mass wall or concrete floor), along with solutions to the diffusion equation, to derive response functions for surface temperature as a function of solar flux and ambient temperature. These expressions are combined to form building response functions. These explicit building response functions allow one to write relatively simple, analytic expressions for room temperature as a function of time over the course of a design day in terms of ambient temperature, sunlight, and heater output (if any).

Parallels between our analytic model and computer codes can be exploited to provide a better intuitive understanding of the programs and to assist in the incorporation of accurate passive solar simulation into these codes.