spread as a function of the polar angle. We establish the reference direction (9 = o) 

 to be in the direction of the maximum rate of spread, and express the radial rate of 

 spread as: 



r(e) 



+ (v^ - v^) cos e, < e < tt/2 



t Ft 



Vn + (V^ - V^) sin"e, tt/2 $ 9 <■ tt 



D ID 



(9) 



where: V = the forward or frontal rate of spread 



r 



= the rate of spread at the flank 

 = the backing rate of spread 



D 



n = a shape parameter to be determined empirically for various fuel types. 



This functional form is quite flexible, and can be used to generate a wide variety 



of shapes. Figure 2 displays some of the shapes generated by this formula; in the 



figure all shapes are normalized by the maximum dimension (that is, r(9)/V is plotted). 



r 



/Vp = 1.0 



Figure 2. — Shapes of fires 

 generated by equation 9. 

 In all cases J the fire pe- 

 rimeter is drawn to a scale 

 such that the distance from 

 the point of ignition ( tic 

 mark on horizontal line) to 

 the head of the fire (right- 

 hand edge of each outline) 

 is the same. In the upper 

 figure ^ -q/^ ^ = ^-0; in the 



lower figure ^ -^^ j ^ 0- ^> 



for both figures n = 4. 



