mapping and detection (Hirsch and others 1%8). The Sundance 

 Fire (Anderson 1968), with documented weather and fire spread 

 history, was mapped by infrared imagery (Hirsch 1968). The 

 long elliptical shape was evident, although some of the nar- 

 rowness was due to nonlinear features of the scanning portions 

 of the infrared mapping equipment. 



Aerial photography points out such characteristics as shown 

 in the examples given by Wade and Ward (1973). The Air 

 Force Bomb Range Fire and the Exotic Dancer Fire show ellip- 

 tical patterns in the vegetation bands that outline the fire's 

 perimeter at progressive stages of development. Controlled 

 burning in the Everglades has generated the same pattern of 

 burning in sawgrass stands (Klukas 1972). The initial circular, 

 then oval, shape of the fire's perimeter is usually lost in the 

 subsequent burnout of the area. 



McArthur (1966) showed that the length to width ratio is a 

 function of windspeed, so only an estimate of the forward 

 spread rate is needed to calculate fire size. Van Wagner (1969) 

 used an ellipse to estimate fire size and perimeter. Although it 

 is a simple and flexible mathematical method, it is necessary to 

 know or estimate three rates of spread at the head, flanks, and 

 rear of the fire. A similar but expanded approach is provided 

 by Simard and Young (1978) who define the spread rate at the 

 head, two flanks, and the rear of the fire. This approach pro- 

 vides a means to evaluate aerial and ground suppression op- 

 tions against fire growth. A fire potential assessment model 

 developed by Van Gelder (1976) determines the length to width 

 ratio by slope, windspeed, and fuel characteristics. Fire size is 

 estimated by use of available fire weather reports and a fuel 

 model to apply Rothermel's (1972) fire spread model. Examples 

 show that the elliptical model is useful for rapid evaluation of 

 the fire potential of given situations. Earlier application of the 

 concept presented by Storey (1972) uses input parameters of 

 size at discovery, the length to width ratio, and the forward 

 rate of spread. An expansion by Bratten (1978) considers the 

 size at attack and size at containment. Length to width ratios 

 and forward spread rates were used as defining parameters. 

 Other work on the containment problem by Albini and others 

 (1978) — involving a complex analysis incorporating forward, 

 flank, and backing rates of spread — show that the general 

 shape follows an elliptical profile. 



Experimental Results of 1939 



Fons reported on a series of 198 test fires conducted in a low 

 velocity wind tunnel. The objective was to establish the effect 

 of compactness in pine litter on the spread of surface fires with 

 varying wind velocity and moisture content (table 1). Wind 

 velocity that was measured 1 ft (0.3 m) above the fuel surface 

 was varied from 2 to 12 mi/h (3.2 to 19.3 km/h). This meas- 

 urement is comparable to midflame height. Fires were started 

 from a point source and allowed to grow until they were ap- 

 proximately 18 inches (45.7 cm) in width. At that point, wind 

 generation was stopped and the fire was quenched with water 

 to preserve the fire's shape (fig. 1). 



The notation used in the development of the mathematical 

 description of fire size and shape is in figure 1. The focus, f,, 

 represents — the origin of the fire and the point from which all 

 measurements to the perimeter were made by Fons. The for- 

 ward distance traveled with a given rate of spread for a given 

 interval of time is defined by d. The other dimensions are 

 defined as: 



Table 1.— Forward spread of firs in ponderosa pine needles 

 under various conditions (fronn Fons'') 



Fuel Fuel bed compactness (inches) 



Wind moisture 

 velocity content 0.06 0.08 0.10 0.12 0.14 0.16 



^'1^^ Forward spread - feet per minute 



per tiour Percent 







4 



0.38 



0.54 



0.67 



0.76 



0.84 



0.97 







8 



0.30 



0.42 



0.49 



0.55 



0.60 



0.67 







12 



0.19 



0.27 



0.32 



0.36 



0.38 



0.42 







16 



0.10 



0.15 



0.18 



0.18 



0.19 



0.20 



2.0 



4 



0.93 



1.32 



1.62 



1.78 



1.85 



2.15 



2.0 



8 



0.72 



0.98 



1.17 



1.28 



1.30 



1.58 



2.0 



12 



0.51 



0.68 



0.82 



0.89 



0.90 



1.00 



2.0 



16 



0.30 



0.42 



0.45 



0.51 



0.45 



0.58 



4.0 



4 



1.80 



2.53 



3.12 



3.34 



3.50 



3.90 



4.0 



8 



1.40 



1.93 



2.29 



2.42 



2.53 



2.85 



4.0 



12 



1.02 



1.39 



1.62 



1.70 



1.80 



2.00 



4.0 



16 



0.60 



0.85 



1.00 



1.03 



1.03 



1.22 



6.0 



4 



2.89 



4.09 



4.98 



5.38 



5.75 



6.60 



6.0 



8 



2.26 



3.18 



3.74 



4.01 



4.20 



4.75 



6.0 



12 



1.68 



2.30 



2.68 



2.85 



3.00 



3.40 



6.0 



16 



1.00 



1.45 



1.72 



1.78 



1.80 



2.20 



8.0 



4 



4.16 



6.02 



7.40 



8.10 



8.70 



10.35 



8.0 



8 



3.34 



4.74 



5.56 



6.15 



6.60 



7.35 



8.0 



12 



2.50 



3.45 



4.09 



4.37 



4.63 



5.35 



8.0 



16 



1.58 



2.25 



2.66 



2.83 



2.95 



3.50 



10.0 



4 



5.69 



8.40 



10.52 



11.75 



12.90 



15.30 



10.0 



8 



4.70 



6.68 



8.00 



8.97 



9.70 



10.75 



10.0 



12 



3.57 



4.95 



5.95 



6.46 



6.83 



7.75 



10.0 



16 



2.34 



3.32 



4.00 



4.24 



4.58 



5.25 



12.0 



4 



7.59 



11.32 



1^40 



16.70 



18.70 



21.65 



12.0 



8 



6.36 



9.13 



11.16 



12.52 



13.40 



14.95 



12.0 



12 



4.93 



6.88 



8.30 



9.15 



9.60 



10.85 



12.0 



16 



3.40 



4.84 



5.84 



6.36 



6.70 



7.60 



See footnote 1 in text. 





c 























t 



p 



1 



1 focus__^- — - 





I ' ° 















a, " 



- 



Figure 1.— Definitions of dimensions used for a 

 two semiellipse model of fire shape. 



2 



