Flame Detection - The Square Law

The Square Law

The square law applies to flame detection and relates the flame area and the distance from the flame to the flame detector: If a flame detector can detect a fire with an area A on a certain distance, then a 4 times bigger flame area is necessary if the distance between the flame detector and the fire is doubled. In short:

Double distance = four times bigger flame area (fire).

This law is valid for all flame detectors, also for the ones, which are based on camera technique. It is a law, which is valid for all optical detectors. The maximum sensitivity can be determined by dividing the maximum flame area A by the square of the distance between the fire and the flame detector: c = A/d2. With this constant c can, for the same flame detector and the same type of fire, the maximum distance or the minimum fire area be calculated: A = cd2 and d = √(A/c). It must be emphasized, however, that the square root in reality is not valid anymore at very high distances. At long distances other parameters are playing a significant part; like the occurrence of water vapour and of cold CO₂ in the air. In the case of a very small flame, on the other hand, the decreasing flickering of the flame will play an increasing part.