Wall area, volume and plan depth in the building stock

The relationship between the volume of a building and its wall area follows an allometric rule that implies that building shape distorts to capture as much surface area, hence natural light, as possible as it increases in size. For a sample of house plans, Bon in 1973 established that the relationship between wall area W and volume V scaled as W∼ V0.77, and Steadman in 2006 demonstrated a similar relationship for his archetypal building. Empirical work in Cambridge and Swindon, UK, also revealed a similar allometry as measured by the depth ratio based on V/W, which provides a direct measure of the way building shapes become distorted with increasing size. This paper demonstrates positive allometry for building blocks taken from a large urban database (approximately 3.2million blocks) for Greater London which is constructed from Ordnance Survey building footprint data augmented by remote sensing light detection and ranging (LIDAR) height data. For the domestic and then non-domestic stock, the blocks are categorized into eight bands and the depth ratios in six inner-London boroughs including the City, which is the financial quarter, are then examined. This is demonstrated in two ways - first, from the depth ratio; and second, from fitting allometric relationships to the band data. The allometric coefficients converge to values of around 0.77,thus confirming the magnitude of Bon's relationship, implying that positive allometry not only is a feature of small samples of houses and archetypal buildings, but also is more generally the case for real building databases at the very largest urban scales.