A Wind-Driven Fire Grows as an Ellipse with a Length-to-Breadth Ratio
A point ignition burning in uniform fuel under a steady wind does not grow as a circle. It grows, to good approximation, as an ellipse with the ignition point at one focus: a fast head in the wind direction, slower flanks, and a very slow backing edge. The shape is summarised by the length-to-breadth ratio, which is close to 1 in calm air and grows with wind speed through fitted relations such as \( LB = 0.936 e^{0.2566 U} + 0.461 e^{-0.1548 U} - 0.397 \) for wind speed \( U \) in the units the relation was fitted in. Given the head spread rate and \( LB \), the flank and backing rates follow from the ellipse geometry, so one spread number plus one wind number gives you the whole shape. The confusion this resolves: the ellipse is a description of a fire growing freely in uniform conditions, not a law. Real fires depart from it wherever the fuel, slope or wind change, which is exactly why the propagation methods in the next nodes apply the ellipse locally rather than to the fire as a whole. After this Concept you can sketch the shape and flank speeds of a fire from its head spread rate and the wind.
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A point ignition burning in uniform fuel under a steady wind does not grow as a circle. It grows, to good approximation, as an ellipse with the ignition point at one focus: a fast head in the wind direction, slower flanks, and a very slow backing edge. The shape is summarised by the length-to-breadth ratio, which is close to 1 in calm air and grows with wind speed through fitted relations such as \( LB = 0.936 e^{0.2566 U} + 0.461 e^{-0.1548 U} - 0.397 \) for wind speed \( U \) in the units the relation was fitted in. Given the head spread rate and \( LB \), the flank and backing rates follow from the ellipse geometry, so one spread number plus one wind number gives you the whole shape. The confusion this resolves: the ellipse is a description of a fire growing freely in uniform conditions, not a law. Real fires depart from it wherever the fuel, slope or wind change, which is exactly why the propagation methods in the next nodes apply the ellipse locally rather than to the fire as a whole. After this Concept you can sketch the shape and flank speeds of a fire from its head spread rate and the wind.
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