The square law Flame detector
square law
if distance between flame , flame detector large compared dimension of fire square law applies: if flame detector can detect fire area on distance, 4 times bigger flame area necessary if distance between flame detector , fire doubled. in short:
double distance = 4 times bigger flame area (fire).
this law equally valid optical flame detectors, including video based ones. maximum sensitivity can estimated dividing maximum flame area square of distance between fire , flame detector: c = a/d. constant c can, same flame detector , same type of fire, maximum distance or minimum fire area calculated: a=cd , d=√a/c
it must emphasized, however, square root in reality not valid anymore @ high distances. @ long distances other parameters playing significant part; occurrence of water vapour , of cold co2 in air. in case of small flame, on other hand, decreasing flickering of flame play increasing part.
a more exact relation - valid when distance between flame , flame detector small - between radiation density, e, @ detector , distance, d, between detector , flame of effective radius, r, emitting energy density, m, given by
e = 2πmr/(r+d)
when r<<d relation reduces (inverse) square law
e = 2πmr/d
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