a, = major axis of semiellipse at the rear of the fire, 

 a2 = major axis of semiellipse at the front of the fire, 

 b = the common minor axis, the maximum flanking fire 



spread distance, 

 c = the portion of axis, aj, that is the backing fire spread 



distance, 



p = semilatus rectum of the rear semiellipse and represents 

 the flanking fire at the origin. 



Fons made measurements of the downwind distance from the 

 origin to the perimeter at various angles from the direction of 

 maximum spread (table 2). He used data from the experiments 

 to generate a series of cross plots involving windspeed, com- 

 pactness, and moisture content. With these cross plots, dif- 

 ferences between the observed data and the fitted data provided 

 residuals that were used for obtaining the final set of curves. 

 Table 1 shows the values of forward spread from the final 

 curves and table 2 presents the statistical measures Fons com- 

 puted for forward spread at each windspeed. 



Table 2.— Statistical measures of ratios of forward spread to 

 spread at other angular distances^ 



Wind 



Direction from maximum spread^ 



Fons assumed that the shape of the burned area in any one 

 fuel type is independent of compactness and moisture content. 

 He confirmed this by comparing the means of the ratio of 

 angular spread distance to maximum spread distance obtained 

 within each wind class for the upper and lower ranges of com- 

 pactness and moisture content (see examples in table 3). The 

 analysis found that the shape of the burned area was dependent 

 only upon the wind velocity. The ratio of maximum length to 

 width for mat beds of ponderosa pine needles was found to be 

 a function of wind velocity by: 



(d + c) 



where: 

 c -I- d 

 b 

 U 



1.0 + 0.50 U 



(1) 



total spread distance, according to figure 1, 



minor axis, according to figure 1, 



wind velocity in miles per hour, at midflame height. 



Cases velocity 10° 20° 30° 40° 60° 90° 130° 180° 



For field tests in ponderosa pine needles, the constant was 

 found to be 0.44 rather than 0.50. 



Table 3.— Samples of Fons'^ data illustrating that compact- 

 ness and moisture content do not influence fire 

 shape 



Miles per 

 Number hour 



Mean spread ratio (actual) 



32 



2.2 



0.943 0.843 0.739 0.649 0.525 0.431 0.362 



0.328 



34 



4.3 



.882 



.724 



.600 



.510 



.399 



.312 .246 



.218 



40 



6.4 



.815 



.607 



.468 



.377 



.276 



.205 .157 



.142 



35 



8.4 



.753 



.522 



.391 



.311 



.223 



.163 .119 



.105 



33 



10.5 



.689 



.443 



.314 



.243 



.169 



.115 .079 



.066 



24 



12.5 



.664 



.413 



.293 



.226 



.154 



.103 .066 



.057 







Standard deviation of spread ratio 





32 



2.2 



0.025 0.041 0.050 0.060 0.054 0.049 0.073 0.084 



34 



4.3 



.040 



.063 



.073 



.073 



.069 



.063 .058 



.057 



40 



6.4 



.045 



.062 



.062 



.056 



.045 



.034 .035 



.043 



35 



8.4 



.041 



.052 



.049 



.043 



.033 



.028 .030 



.032 



33 



10.5 



.041 



.046 



.039 



.033 



.027 



.021 .023 



.025 



24 



12.5 



.054 



.053 



.044 



.037 



.028 



.021 .020 



.020 





Standard deviation of spread ratio - 



percent 





32 



2.2 



2.7 



4.9 



6.8 



9.2 



10.3 



11.4 20.2 



25.6 



34 



4.3 



4.5 



8.7 



12.2 



14.3 



17.3 



20.2 23.6 



26.1 



40 



6.4 



5.5 



10.2 



13.2 



14.9 



16.3 



16.6 22.3 



30.3 



35 



8.4 



5.4 



10.0 



12.5 



13.8 



14.8 



17.2 25.2 



30.5 



33 



10.5 



6.0 



10.4 



12.4 



13.6 



16.0 



18.3 29.1 



37.9 



24 



12.5 



8.1 



12.8 



15.0 



16.4 



18.2 



20.4 30.3 



35.1 



Fractional spread in different 

 directions from origin 



Moisture Compactness Wind- 



content 





speed 



10° 



20° 



30° 



40° 



60° 



90° 









Ratio of angular distance to 



Percent 



Inches 



Mi/h 



distance of maximum spread 



6.8 



0.067 



2.2 



1.00 



0.83 



0.75 



0.58 



0.50 



0.42 



6.9 



.160 





.93 



.87 



.73 



.67 



.53 



.47 



11.9 



.067 





1.00 



.80 



.80 



.80 



.60 



.40 



11.6 



.160 



2.2 



1.00 



.90 



.80 



.70 



.60 



.50 



5.3 



.067 



6.4 



.90 



.71 



.52 



.43 



.33 



.29 



4.8 



.160 





.81 



.61 



.49 



.40 



.28 



.19 



11.2 



.067 





.84 



.63 



.47 



.42 



.31 



.26 



12.1 



.160 



6.4 



.87 



.65 



.52 



.39 



.32 



.26 



4.7 



.067 



12.5 



.76 



.53 



.39 



.30 



.21 



.14 



6.2 



.140 





.64 



.33 



.22 



.16 



.10 



.06 



11.1 



.067 





.64 



.39 



.27 



.21 



.14 



.11 



13.7 



.160 



12.5 



.62 



.42 



.30 



.24 



.16 



.11 



^See footnote 1 in text. 



^See footnote 1 in text. 



^Directions expressed as angular distances in degrees fronn direction of 

 maximurT\ spread. 



3 



