A number of empirical relationships between fire shape and wind speed have been developed (Alexander 1985). Some of the relationships use midflame wind speed and others an open wind speed at 20ft or 10m above the vegetation. At present, FARSITE employs Anderson's (1983) model for length to width ratio of the ellipse because it uses mid-flame wind speed and because of its stated applicability to any fuel type. A simple ellipse is used, however, rather than the double ellipse. The midflame wind speed is a simpler value to obtain in the simulation because the wind-slope vector (above) is a midflame value. The appropriate open wind vector would have to be inferred from this midflame value.
Anderson's model does not yield a circular fire with zero wind and slope. Thus, as implemented in FARSITE, the length to breadth ratio from Anderson's model is adjusted by subtracting 0.397 from the predicted length to width ratio. This is not seen as a serious problem. Variation in wind direction at higher frequencies than represented in the wind stream will decrease the eccentricity of an elliptical fire. Simard and Young (1978) developed a model of fire shapes that accounted for Gaussian variation in wind direction. They recommended using a standard deviation of 10 degrees for all wind speeds (Alexander 1985). Their model has recently been found to agree reasonably well with a theoretical analysis of effects of wind variation on elliptical fire shape (Richards 1993). All other models assume wind speed and direction to be constant. However, the empirical nature of some of these relationships suggests that wind variation must have affected the original field data to some degree.
Most of the work using elliptical fire shapes assumes the origin of a fire is at the rear focus of an ellipse (Anderson 1983, Alexander 1985, Andrews 1986). This provides an implicit means to calculate the backing fire spread rate.
Catchpole et al. (1982), Alexander (1985), and Bilgili and Methven (1990) suggest however, that this assumption has not been adequately examined; using the focus as the ignition point may under predict backing fire spread. It also appears to produce a temporary decrease in fire area for small length to breadth ratios as wind speed increases (Bilgili and Methven 1990). On the other hand, using the no wind-no slope spread rate as the backing rate may over predict spread with increasing slope or winds (Byram 1959). Van Wagner (1988) and Cheney (1981) show that backing spread decreases as slope inclines to about 20+ degrees. In effect, spread may be faster down steeper slopes because of ignition by rolling or sliding debris.