APPENDIX C 

 METHODS OF ANALYSIS AND FAIRING OF RESULTS 



D 



For each — value, 15 models were built and tested, the three models at each block 

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 coefficient covering a range of — values. It is desirable to have sets of contours to facili- 



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tate the interpolation of the results given in this paper. The contours also will give ship 

 designers a visual picture to guide them in choosing the principal proportions and coeffi- 

 cients of the ship. 



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Consider the contours of — . A two-way interpolation is involved-first between — 

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values at each block coefficient and then across the block coefficient at each — value 



B 

 Such interpolation could be done by drawing curves through the test points as shown in 



Figures CI and C2. Then Figure C2 would be replotted by using constant — values as 

 parameter, C g as abscissa and -— as ordinate to obtain the final contours. However, it is 

 not easy to follow this procedure. In general, the points taken along any horizontal line in 

 Figure C2 will be quite scattered in the final plot. A tedious cross fairing is then necessary 

 among these three plots. This process has to be done for many values of —:=. , At the end, 



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a plot of against— =: as lifted from the contours for fixed values of Cg and — may not 



A v^ B 



be a fair curve. Further refairing among the four plots is necessary. With the experience of 



fairing a set of ship lines between two plots, body plan and waterlines, it is quite evident 



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that it would be extremely tedious and frustrating to obtain a set of consistent contours 



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A 



by manual fairing. Accordingly, it was decided to interpolate between — and across the 



B 



block coefficients mathematically and to program the computation work into^ UNIVAC 



computer, by the method devised by Dr. P.C. Pien. 



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For interpolating between — values, three values of corresponding to three — 



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values at each block coefficient and a fixed value of — , are known from the model tests. 



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It was rather difficult to decide how the interpolation should be done since an infinite number 

 of curves can be drawn to pass through three given points. Without any definite knowledge 

 as to how such a curve should look, a simple curve expressed as follows was chosen 



X ='^"Ki)''(^) 



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With this equation, - — values for — values between 5.5 and 8.5 at intervals of 0.25 were 

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computed for each block coefficient at constant values of ~p^ . 



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