Flame merging in multiple fires

A simple model of a multiple fire is considered in which the separate, free burning fires form a square matrix. A theoretical scaling law is deduced for the conditions under which the individual flames will merge, which is independent of the number of fires involved, and in which the height of the flames and the size and separation of the individual fuel beds scale geometrically. By this means data covering a wide range of scales and configurations are correlated, and within the limitations of the data, the separation at the onser of merging is proportional to the height of the flames. On the basis of this scaling law it is suggested that in large fires in cities the flames from individual buildings will only merge when the building area density is very high, greater than about 65 per cent.