46 



and A*(£). In extreme cases the shape of the body can be calculated by- 

 methods due to Landweber and Amtsberg; no corrections, however, are given for 

 the influence of the free surface on the shape. 



Within the first-order theory the resistance can be split up into 

 a main part due to a symmetric distribution with respect to the midship sec- 

 tion and a part due to asymmetry, which can be investigated independently. 

 Large amounts of asymmetry can influence the resistance detrimentally in 

 some ranges of the Proude number. 



The investigation of the resistance as a function of the body form 

 leads to conclusions which sometimes are contrary to those derived for sur- 

 face ships. The choice of appropriate prismatic coefficients varies deci- 

 sively with the range of the Froude number, as is clearly Illustrated by 

 the numerous graphs. The same applies to the influence of- the tangent value 

 t. Ceteris paribus the resistance is approximately proportional to the 

 square of the midship section. 



The dependence of the resistance upon the depth of immersion is in- 



2_TT 2 



vestigated; this dependence is best explained by the ratio f/X, where k= g u 

 is the length of the free wave. Thus for common prismatic coefficients the 

 wave resistance decreases rapidly with increasing f except in the range of 

 high Proude numbers (large X values) . In the range of high F the calculation 

 of forms (distributions) of least resistance leads sometimes to results bare 

 of practical applicability; by introducing suitable restrictions such diffi- 

 culties are avoided. These investigations show important peculiarities of 

 the distributions. 



A set of resistance diagrams calculated for the family (2,4,6;0;t ) 

 gives a survey of the resistance properties of a class of normal bodies. 



Acknowledgment is made of the valuable help provided by Messrs. 

 Samuel Lum and David Rego and Miss Janet Kendrick of the Taylor Model Basin. 

 The author further wishes to express his gratitude to Dr. Alt, Dr. Levin and 

 Mr. Blum of the National Bureau of Standards. Finally, it is a pleasure for 

 the author to thank his colleagues, Mr. Cummins and Mr. Landweber, for re- 

 viewing the present report. 



