by this amount could have a significant influence on any subsequent engineer- 

 ing study. Second, energy levels and directional locations are very different 

 as asymmetry increases. Energy density is more than twice as high at the 

 peaks of the most asymmetric classes (lower-right subplots) than it is at the 

 peak of the symmetric class (upper-left subplot) at the same spread. Though 

 the two groups represented by Figures 40 and 41 include only about 3.3 percent 

 of the data (based on case count) , the same types of behavior are evident in 

 the most common groups shown in Figures 36, 37, 38, and 39. 



240. The groups with the greatest spread (Figures 42, 43, and 44) show 

 a continuation of the trends just described. They are relatively uncommon, 

 representing only about 1.2 percent of all cases, but they do suggest the 

 large -spread asymptotes of directional shapes. Here, the extreme shift in 

 peak direction is about 30 deg relative to center-of -energy direction (Fig- 

 gure 44) . The symmetric members of this group are characterized by broad, 

 relatively flat peaks in the directional distributions; that is, the energy 

 density is nearly uniform over a span ranging from about 60 deg in Figure 42 

 to about 80 deg in Figure 44. 



241. This property illustrates a problem in trying to characterize 

 distributions with a parameter denoting peak direction. Compared with the 

 narrow distributions (Figures 32, 33, and 34, for example) which have well- 

 defined peak directions, the broad, symmetric distributions of Figures 42, 43, 

 and 44 have rather diffuse peaks. In two of these cases (Figures 42 and 43), 

 peak directions deduced from the solid lines occur on distibution shoulders. 

 This shifts the angle which might be called peak direction by 30 to 40 deg 

 from the center of the energy distributions (0 deg on the ^-axis). Such 

 curves are much less ambiguously characterized by integral measures of energy 

 distribution such as the derived parameters A^ , A , and 6 used in this 

 report. 



242. There is natural concern that the distributions classified here as 

 asymmetric are not common, but occur so rarely that they may be ignored in 

 practical application. If this was true, only the symmetric curves would need 

 to be considered, and the bulk of data could be characterized with directional 

 spread alone. Based on the case counts, this does not appear to be true. 

 Symmetric distributions (as defined here) occur in only about 24 percent of 

 all cases and in about 26 percent of the most common cases (Figures 36, 37, 

 38, and 39). If the first nonsymmetric classes are added to the symmetric 



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