APPENDIX n 



Notes 



The five example fires cited previously (pages 8 through 

 19) and the four here (examples 6 through 9) have their 

 critical values tabulated and compared to values computed for 

 a simple ellipse using the quadratic equation approach, and for 

 the double ellipse model using equations 2 through 9. The docu- 

 mented values of column 1 are obtained from reports and tables 

 or transcribed from maps of fire growth. The perimeter, if not 

 available, is estimated as 2.5 times the spread distance. 



The simple ellipse column uses the area and perimeter values 

 of column one in the quadratic equation (equation 13) to deter- 

 mine the major and minor semiaxes, a and b, of the ellipse. 

 The total major axis dimension, 2a, is entered as the spread 

 distance. The ration, a/b, is entered as the i/w ratio. 



The third column, for the double ellipse model, uses the 

 spread distance of column 1 and applies the wind reduction 

 factors (Albini and Baughman 1979) to the wind at 20 ft 

 (6. 1 m) to compute the average wind on the fire. These values 

 are used with equations 2 through 9 to calculate the area, 

 perimeter, and //w ratio values that are listed. The wind reduc- 

 tion factors are derived using descriptions of the fire behavior 

 to estimate where the fire is burning into the fuel complex — 

 surface, understory, or overstory, and from descriptions of 

 vegetation types to determine the resistance to air movement. 



The adjusted double ellipse of column 4 shows the best fit 

 the model can make to the documented data. The //w ratio 

 that is documented is used with figure 7 to estimate the average 

 wind over the fire. This, along with the spread distance, is used 

 to compute the area and perimeter of the fire. Minor adjust- 

 ments to windspeed and/or spread distance may be made to 

 improve the match to column one. This is an iterative process 

 to try to provide insights to where the greatest uncertainties 

 exist. 



The dimensions used in the table are for spread distance in 

 miles, windspeed in miles per hour, perimeter in miles, and area 

 in acres. If figure 6 is used, area has to be expressed as the 

 square of the unit used to measure the spread distance — for in- 

 stance, if miles for distance, then square miles for area. 

 Perimeter and spread distance must be measured in the same 

 units. 



24 



