25 



APPENDIX B 



EFFECT OF ERRORS IN BODY SHAPE ON RESULTING VELOCITY 

 AND PRESSURE DISTRIBUTIONS 



Errors in body shape may arise from misalignment of the body in the tank or from 

 errors in machining. If the model may be approximated by a prolate ellipsoid, the errors in 

 machining may produce a change in the eccentricity of the equivalent ellipsoid. On the other 

 hand, a small mound or depression on a section where the transverse curvature is small may 

 be treated as two-dimensional flow over a mound or depression. The error in pressure distri- 

 bution produced by changes in eccentricity has been reported by Eisenberg, ^^ and the flow 

 past a mound or depression is treated in standard texts on hydrodynamics, such as that by 

 Milne- Thompson. ^ The results of these investigations will be outlined here. 



The pressure coefficient for a prolate spheriod at an angle of attack a can be shown to 

 be^l 



h^'o 



l'(rflV^) ^°^' " " r^^ \/i^-e'Hl-,^) sin 2a 



cos CO 

 [24] 



where 



1 - 



1 - e 



2e 



2 1 + e 

 - In 



1 - e J 



[25] 



The eccentricity 



/3 = 2e- 



, 1-^2 1 + e 



1 - 2e2 In 



2e 1- e 



e= l/l 



lA 



[26] 



[27] 



where a and b are the semimajor and semiminor axes of the ellipsoid. Also, fi equals-^ where 

 X is measured from the minor axis, and co is the angle between a meridian plane and the xy 

 plane. At zero angle of attack, the minimum pressure coefficient at ^ = is 



