SUPPLEMENTARY EXPLANATORY DETAIL FOR EXAMPLE 2 



Lsig 



The left segment of figure 4 has a constant cross-section over F for 1240 <_ S <_ 

 5000, approximated in the descriptor by a sigmoid oriented at F = LO and extending 

 leftward a distance of 20 units in F. Twenty is about the minimum operational span 

 for the sigmoids here. At the upper extreme of S, (S = 5000), the left-segment sigmoid 

 is expected to be completely specified in the range 27 >_ F >_ LO, as in figure 5. Set- 

 ting 28 as the upper level of F within which all left-segment sigmoids must be completely 

 specified, we turn to the limiting case at S = 0. Here L0 = 8.888 and the sigmoidal 

 range must then be at least (28 - 8.888) = 19.112; so, 20 was adopted as the operational 

 span. Note that a larger span could have been adopted. 



The F-scale is reversed to LO+20-F, as shown in figure 11, to associate the largest 

 value of the sigmoidal span, 20, with the peak of the sigmoid at L0. Scaling control 

 points from the left cross-section at S = 1240 (fig. 11) to 1.0 in X, (L0+20-F) , and Y, 

 (score, t) , and making an overlay curve (see Matchacurve- 1) , an appropriate sigmoid was 

 identified from the Standards. 



SEGMENTS 



LU 



o 



O 

 CO 



•LEFT- 



CENTER 



■RIGHT- 



FLOW (F) 

 (LO + 20) - F 

 |RO - 11| + F 



Figure 11. — t-oross-seotion over F at S = 5000. Note: The cross- sectional shape 

 of the left segment is constant in the range 1240 <_ S < 5000; the right segment, 

 although different in cross-sectional shape, is also constant in shape over the 

 range 1240 < S < 5000. 



14 



