114 Samuel Karp, Jack Kotik, and Jerome Lurye 
7 (26680) 
Fig. D1(c). Optimum longitudinal distribution 
they differ. Occasional erratic behavior has been disregarded for present purposes. We are 
primarily interested in the variation of the shape with the three assumptions listed. Figure 
D1(a) (n(+1) = 0, ap = 0) shows the well-known swan-neck form; the curve for 2f/L = 0.25 in 
Fig. D1(b) may be doubtful. 
In the range of low Froude numbers y, = 15, F = 0.183 we find in Fig. D1(d) the orthodox 
hollow distribution (y(+1) = 0, a, = 0); in Figs. D1(e) and D1(f) we see the relatively small 
end ordinates and doublets respectively. 
Figure D1(g) finally shows the optimum forms for ahigh prismatic 9=0.80 and y, =1/2F7=15. 
In general the results do not present great surprises except for the appearance of a concen- 
trated doublet at small F and the large reduction in resistance due to the former as compared 
with the assumption @p =.0. An explanation can be found by comparing the generated body 
shapes which display marked differences. The resulting forms and data for other Froude 
numbers will be the subject of a more elaborate report. 
The numbers R* stand for dimensionless wave resistance values. Obviously, they indi- 
cate that the latter is negligible for 2f{/L = 1 and in some cases for 2f/L = 0.5 at the Froude 
numbers considered. Thus the investigations presented by the authors have contributed to 
clarify a basic problem of ship theory. For purpose of practice we shall be forced to inves- 
tigate more general forms than the Michell ship. E.g., in the range of higher Froude numbers 
conclusive experiments have shown that by using a flat stern a definite improvement can be 
reached. A further step in this direction may be the investigation of the so-called Hogner 
interpolation formula although some essential difficulties must be overcome. 
