For interpolation between block coefficients, there are five points, one for each 



L V 



block coefficient for given values — and -7= ■ The polynomial 



R 



could be used for this interpolation. However, it was felt that the interpolation near one end 

 of the curve might be influenced unduly by the values near the other end. It was decided to 

 use two equations of the following type, one for each end of the curve: 



R D 



— = A + B ■ Cb + C ■ Cb^ + D ■ Cb^ 



The coefficients of the equations were so determined that each equation would pass through 

 three points and have equal ordinates and first and second derivatives where they joined at 



R^ 

 the midpoint. Values of — at intervals of 0.01 in Cg values were computed by using these 



^ L 



two equations. Figures CI and C2 show the interpolating curves between the — values and 



B 



across block coefficient, respectively, as obtained by using the foregoing equations. 



L ^R 



If we consider a three-dimensional surface plot with Cg as x, as y, and 



B A 



as 3, then Figure CI indicates the cuts of this surface by a series of planes with constant 



a>values, and Figure C2 indicates the cuts of this surface by a series of planes with constant 



y-values. The cuts of this surface by a series of planes with constant 2-values are the 



^/? 

 required contours of — ~ — . 



^R V B 



Figure C3 shows the contours of — obtained in this way for a -7= of 0.60 and a — 



^R 

 value of 3.0. Also shown are the actual values of — for the 15 models (having three values 

 L 



A 



of — at each of five block coefficients) from which the contours were derived. It will be 



D 



agreed that the contours show an excellent interpolation among these 15 points and give 

 confidence in their use for power estimates. 



The three-dimensional surface mentioned is determined by 15 points from model test- 

 ing. Each of the points follows a faired curve as ~rr changes. Any spot at fixed values of 



X and y, therefore^will follow a faired curve of its own as —= changes. That is to say, the 



f^R ^^ V 



-^ values of any particular model lifted from the contours at various ~7^ values will give 



. y V^ 

 a faired curve when they are plotted against ""zr . 



C-2 



