f/L ratio has been added. Special investigations are made on the influence 

 of asymmetry, and some examples of resistance curves refer to forms selected 

 from the TMB Series. 



Following an earlier attempt distributions of least wave resistance 

 are investigated. 5 Former results 5 are checked and refined. Particularly, 

 the distributions obtained lead to rather peculiar "swan-neck" forms, for 

 higher Froude numbers. Finally it is shown how systematic sets of resis- 

 tance curves can be obtained for families of sectional-area curves (doublet 

 distributions) . 



2. THE REPRESENTATION OF SINGULARITY DISTRIBUTIONS 

 AND SECTIONAL-AREA CURVES BY POLYNOMIALS 



2.1 . CONNECTION BETWEEN BODY FORM AND GENERATING HYDRODYNAMIC SINGULARITIES 



In establishing a relationship between body form and generating 

 hydrodynamic singularities two well-known problems can be formulated: 



a. Given a distribution, find the shape of the body (sectional-area 

 curve A(x) ) . 



b. Given a body form (sectional -area curve A(x)), establish the appro- 

 priate distribution. 



In the present report we disregard the complications connected 

 with problem b and treat it in a very approximate way. The contemporary 

 rudimentary state of knowledge on problems of wave resistance justifies this 

 procedure to some extent; our investigation deals essentially with resistance 

 properties of hydrodynamic distributions and merely some assumptions are made 

 as to the probable shape of the bodies generated by these distributions. 



Thus two essential sources of error are involved when investigating 

 the wave resistance of bodies of revolution: 



a. The approximate character of the wave-resistance theory, and 



b. The generally admitted approximation that for a given body the 

 deep-immersion distribution of singularities can be used instead of the 

 actual distribution valid for near-surface conditions. 



The second assumption (b) appears to be a serious one when the 

 body is close to the surface. It has been proved by Havelock 9 that it leads 

 to inconsistent results with respect to added masses; however, by following 

 numerous comparisons between theoretical and experimental results referring 

 to surface ships it works reasonably well when applied to the resistance 

 problem. 



In the present report the assumption will be made that the shape 

 of the body generated by singularities moving close to the surface is 



