77 



2 . Prom the form of the wave integral It follows immediately that for 

 research the appropriate independent speed variable is Proude number referred 

 to the length of the ship. This rule holds for all slender bodies. 



3- When investigating the wave resistance as a function of the ship 

 form, two working hypotheses are widely used: 



a. A more basic division, in which the resistance is con- 

 sidered as being a separate function of the principal dimensions 

 (or their ratios) and of the dlmensionless shape and, 



b. A splitting up of the resistance due to the dlmensionless 

 shape into functions dependent upon the longitudinal and vertical 

 distribution of displacement. More general and more rigorous in- 

 vestigations are required to consider the mutual interdependence 

 of most of the factors concerned. 



4. The wave resistance R depends upon the square of the beam R ~ B^ 

 and in a more complicated manner upon H. Relations R = R(H) can be estab- 

 lished by somewhat cumbersome but not difficult computations. However, the 

 limits of validity of R(B) and R(H) derived from Michell's integral are 

 restricted. 



5. The concept of the sectional-area curve, which embodies the longi- 

 tudinal distribution of displacement , proves to be fruitful both from a the- 

 oretical as well as from a practical viewpoint. It has been shown that the 

 basic parameters ^ and t are indispensable for any research work on the sub- 

 ject; in addition it has been demonstrated that Taylor's curvature parameter 

 K Is valuable when dealing with fine lines. However, even the three param- 

 eters ^, t and K may not be sufficient to fix the wave resistance properties 

 of a ship line. Por fuller shapes the length of paralleled middle body re- 

 places the curvature k as the third parameter. 



6. Prom this fact it follows that any systematic research on ship forms 

 should be based on analytically defined lines and surface equations. The most 

 suitable expressions are polynomials. 



7- By evaluating the resistance integral for a sufficient number of 

 "longitudinal" poljmomlals, the resistance properties of the whole field of 

 normally shaped sectional-area curves can be derived. This may lead to the 

 use of further parameters as enumerated in the present report. Besides, import- 

 ant results for such peculiarities as bulbs and cruiser sterns already have 

 been obtained. 



