28 



(1) 



(2) 



H = Const 



--4-..- 



Const 



Afflne dietortlon in the direction Affine distortion in the direction 

 of the y-£ixls of the z-axis 



(3) (4) 



-^^ 



B/H = Const 



I BH = Const 



Similarity distortion 



Figure 8 - Variations of Proportions 



Affine distortion along y and z 



b. Another limiting condition may be derived from Hogner's resistance 

 formula [l8] for a pressure system. Using, for simplicity, a constant pres- 

 sure over a rectangular region of the free surface, it was found that n(P) in 

 the formula 



R 



[16] 



is always smaller than 2, For example, n(P) =1-5 for P = 0.25; in principle 

 n(F) depends upon BA.. Although this application is rather tentative, we may 

 iixfer that for surface ships n is smaller than 2. 



c. Finally, some information may be obtained from more advanced theo- 

 ries mentioned later, but no numerical computations have so far been performed. 



Thus, the results of all the endeavors made to date is rather meager. 

 However, from the known form of the solutions, we can infer that within the 

 range of normal ship forms the wave resistance is a smooth function of B, and 

 that small proportional changes in the beam cause correspondingly small 

 changes in the wave resistance. When model experiments sometimes yield an 

 abnormal result (as for Instance in the case of the "NORMANDIE" ) , it is possi- 

 ble to assert that such a pathological behavior is not significant as to the 

 wave resistance of the ship, whatever the reasons may be. 



