Building Shape - Surface Area to Volume Ratio

The surface area to volume (S/V) ratio (the three dimensional extrapolation of the perimeter to area ratio) is an important factor determining heat loss and gain. The greater the surface area the more the heat gain/ loss through it. So small S/V ratios imply minimum heat gain and minimum heat loss.

To minimize the losses and gains through the fabric of a building a compact shape is desirable. The most compact orthogonal building would then be a cube. This configuration, however, may place a large portion of the floor area far from perimeter daylighting. Contrary to this, a building massing that optimizes daylighting and ventilation would be elongated so that more of the building area is closer to the perimeter. While this may appear to compromise the thermal performance of the building, the electrical load and cooling load savings achieved by a well-designed daylighting system will more than compensate for the increased fabric losses.

In hot dry climates S/V ratio should be as low as possible as this would minimize heat gain. In cold-dry climates also S/V ratios should be as low as possible to minimize heat losses. In warm-humid climates the prime concern is creating airy spaces. This might not necessarily minimize the S/V ratio. Further, the materials of construction should be such that they do not store heat.

The factors of the external environment that influence heat transfer through the building envelope are:

In principle, to minimise heat transfer through the building envelope the building shape should be as compact as possible,tending toward a cube. However, to optimize the building shape while considering the three factors above is a more complex matter.

A cube may not be optimum if, for instance, you need to minimize the exposure of walls to hot winds from the West as well as solar radiation from the western side. Here the orientation of the building as well as the relative dimensions of surfaces facing different directions would have to be considered.

Basam Behsh, who researched this problem, found that the S/V ratio is not a correct indicator of thermal behaviour of buildings with complex plans.

In order to compare different options of building shape, especially for buildings with complex plans, one would have to resort to simulation by an advanced computer software.

References:
  1. Basam Behsh, Building Form as an Option for Enhancing the Indoor Thermal Conditions
  2. Heating, Cooling, and Lighting as Form-Givers in Architecture