D{e) = G(s) cos''(0/2) 



s = 



G(s) = (2^7360°) r'(s + 1)/r(2s+1) 



140.0 ■ 



^,^ 



-^ 60.0 



^^^.^-"^^ 



// ^'^-^ - 



A / 



'^ / 20.0 



1 / 



// 12.0 



1 1 / / 



// 9.0 ■ 



/ // 



/// ^-^ 



y /// 



// 6.0 - 



f\\ / /// 



/X 4.5 



Waw, 



// 3.0 



^w" 



- 



■ _^^^ 



^^_ 



120 60 -60 -120 



Q (deg) 



Figure 45. Examples of model directional distribution function 



proposed by Longuet-Higgins , Cartwright, and Smith (1963) 



for several values of parameter s 



lines. Directional spread classification and value of fitted parameter s 

 are listed in each subplot. 



246 . Examination of Figure 46 reveals that the model characterizes the 

 data quite well for spread parameter in the range 22 deg < A^ < 34 deg . At 

 all spreads narrower than this, 10 deg < A6 < 22 deg , the fitted curves 

 might be considered reasonable. They underestimate the distribution peaks, by 

 as much as about 10 percent for the narrowest class, and fall off faster than 

 the distribution tails. Fitted curves could resolve the peaks better by 

 restricting the set of fitted data to peak regions of the direction axis (near 

 deg). This would make the model distributions narrower still, which would 

 degrade the fit on the tails of the observed distributions. Since these tails 

 are regions of low energy, this approach would allow the model to characterize 

 data at these spreads with reasonable verity. 



119 



