Nowaekt and Sharma 
APPENDIX D 
DOUBLE BODY CALCULATIONS 
D.1. Motivation 
All calculations described in Appendix B are based on the 
first-order thin ship theory in which the hull is represented by a li- 
nearized (with respect to the beam) source distribution on the center 
plane, see Equation (B6). This has the great advantage that "potential" 
(i.e. zero Froude number) effects and wave (i. e. finite Froude number) 
effects can be calculated consistently using the same source distri- 
bution. However, the accuracy of the results depends in an uncontroll- 
ed manner on the ''thinness'' of the ship. In order to obtain a quanti- 
tative estimate of the error involved in the application of thin ship 
theory to our hull, a few wake calculations were also performed by 
the method of Hess and Smith (1962), which does not impose any res- 
trictions on hull geometry. As is well known, the Hess and Smith al- 
gorithm provides a general solution of the Neumann problem of non- 
lifting potential flow about arbitrary bodies by means ofa surface dis- 
tribution of sources, Due to the enormous amount of numerical com- 
putation involved, however, the application of this method to the cal- 
culation of flow about ships is still limited to the so-called zero 
Froude number approximation, in which the ship (including the pro- 
peller) is conceptually replaced by a deeply submerged double body 
generated by reflecting the under water form about the static water 
plane. In our terminology, therefore, only the pure potential effects 
(as distinguished from the viscous and wave effects) can be evaluated 
by this method, An improved version of the original Hess and Smith 
computer program was made available to us by the Naval Ship Re- 
search and Development Center. 
D.2. Results 
Without going into the intricate details of the Hess and Smith 
method we report here only a few relevant results obtained by this 
program, First, a series of nominal wake calculations was perform- 
ed with the propeller disk assumed in its proper transverse and ver- 
tical position (¥p= 0 , z4= -0.5 T) but at five different longitudinal 
positions as shown in the following table. Since the accuracy and com- 
puting effort in this method depend critically on the number and size 
of the body surface elements, we tried four different arrangements 
involving N = 100, 125, 145 and 150 elements. As our double body 
had three planes of symmetry, the elements are understood to cover 
only one eighth of the total body surface. To ensure finer detail near 
the stern the element size was not uniform over the entire length of 
the hull but made increasingly smaller toward the ends. 
1912 
