Development of Fire Shape Model 



Analysis of the above data show that the elliptical shape 

 describes results closely. The best fit of the experimental data 

 was found to be with two semiellipses. 



The original development^ considered the spread distance at 

 various angles as fractions of the forward spread distance, d, as 

 presented in Pons' data tables 1 and 2. The dimensions of the 

 double ellipse were analyzed as functions of windspeed using 

 data in Pons' tables and from the curves of fire shape at 

 various windspeeds (fig. 2). Relationships between dimensions 

 of an ellipse besides log regressions were used to express each 

 dimension as a function of windspeed. The minor semiaxis, b, 

 was defined in terms of p and a, using the semilatus rectum ex- 

 pression for an ellipse. Further study showed that b could be 

 better described as a log function of windspeed. The dimen- 

 sions of Pons' curves were reevaluated as fractions of the 

 spread distance, d (table 4). 



A least-square fit of log regressions for the following dimen- 

 sions provided equations as functions of windspeed and frac- 

 tions of the forward spread distance: 



2 



(Ml/H) 



Figure 2.— Diagrams showing influence of wind 

 velocity on shape of bums. 



Table 4.— Summary of data measured from Pons'— curves 

 (fig. 2) for fire shape and used for equations 2, 

 3, 4, and 6 



Windspeed 



ai 

 fraction 



b 



fraction 



c 



fraction 



P 



fraction 



Mi/h 

















0.500 



0.500 



0.500 



2 



0.560 



.465 



.348 



.432 



4 



.416 



.348 



.230 



.315 



6 



.346 



.260 



.160 



.226 



8 



.358 



.210 



.112 



.160 



10 



.346 



.163 



.072 



.119 



12 



.315 



.140 



.058 



.093 



^See footnote 1 in text. 



c = 0.492 EXP [-0.1845 U], r^ = 0.9% 

 Sy • x = 0.162 



p = 0.542 EXP [-0.1483 U], r^ = 0.993 

 Sy • X = 0.140 



a, = 2.502 [SSUJ-'^-^o, r^ = 0.918 

 Sy • X = 0.046 



= 1 + c - a, 



= 0.534 EXP [-0.1147 U], r^ = 0.988 

 Sy • X = 0.143 



(2) 



(3) 



(4) 



(5) 

 (6) 



These equations provide a means of quantifying important 

 dimensions of the double ellipse representation of fire shape. 

 When these values along with the spread distance are used in 

 equations for area and perimeter, we can estimate fire growth. 

 In addition, the length to width ratio and the envelope of the 

 bum area can be estimated. 



Calculations of area and perimeter require multiplying the 

 fractional expressions of ellipse dimensions by the forward 

 spread distance. The following equations have been used or 

 adapted to make estimates of the fire dimensions (Albini 1976a, 

 1976b; Albini and Chase 1980): 



Area = A =- 



TTbd^ 



(aj + Oj); ft^, m^, etc. 



(7) 



Perimeter = P = 



Trkjd 



(a, 



b) + 



Trk,d 



(SL2 + b); ft, m. 



(8) 



M„ 



(a„ - b)/(a„ + b) 



. < . . . . (9) 



64 256 



(Bauneister 1958) 



(10) 



(Bauneister 1958) 



See footnote 2, page 1. 



4 



