53 



Thus, comparatively simple types of surface equations appear applicable (see 

 Appendix 1, Equation [4l]). 



As a starting point, the fact is used that parts of the displacement 

 near the surface offer more resistance than those near the bottom of the ship. 

 Hence, U-shaped sections appear to be superior to V-shaped sections as far as 

 wave resistance Is concerned. Since for moderate Proude numbers the forebody 

 produces more waves than the afterbody, R.E. Proude 's rule* for design can be 

 deduced: U-shaped sections for the forebody, V-shaped sections for the after- 

 body (the latter with the purpose of reducing "eddy resistance"). 



Actual calculations prove the superiority of U-forms in almost all 

 cases; however, under exceptional conditions a V-shaped forebody may be super- 

 ior. Experimental results of this kind were found by Lindblad^^ for a fast 

 cargo ship form. 



A physical explanation can be given, which will be applied later to 

 bulb forms: Although the wave resistance generally decreases by increasing 

 the depth of immersion of displacement, favorable interference effects may be 

 reduced by shifting some parts of the volume vertically downwards. 



In general, agreement has been found between theory and facts, al- 

 though Important examples are known where V-shaped forms were superior to U- 

 shaped forms, contrary to theoretical deductions.^'*'"'' The following effect 

 has been stated experimentally for Proude numbers P > 0.53: V-shaped models 

 with low or moderate t-values prove to be better than U-shaped models with 

 high t-values although both features (U-shape and large t) are advantageous in 

 the light of theory. In such cases the resistance qualities cannot be pre- 

 dicted from the sectional-area curve alone; Taylor's well known diagrams rep- 

 resenting R/a as functions of t and v/vl7 are no longer applicable. No theo- 

 retical explanation of these anomalies has so far been found, so presumably 

 the attitude of the model has an important bearing on the subject. When hull 

 shapes depart appreciably from the double wedge form, as for instance in the 

 afterbodies of destroyers, we can no longer rely on the results of resistance 

 calculations, especially in the range of high speeds, without introducing more 

 consistent physical concepts of the phenomena. Consequently, one must be 

 cautious in applying the simple rule of thumb given for the Influence of verti- 

 cal displacement distribution in complicated cases. 



♦Obviously, considerations of propulsion can change this rule! 



