Ship Waves and Wave Resistance 



R</>- P<^>., .W...3..- 



as 



/*C0 00 03 



•'-00 u = -oo X = -oo L 



fij 7o4L/(/°B-'cO 



%(X) ap^(X) - /3 (X) /3^(X) + 7 (X) 7^(X) 



dX 



n.M^-^) 



a^(X) a^(X) + ^^(X) /3^(X) + 7^(X) y^(X) 7,^.x,(-X) 



(56) 



due to the Fourier orthogonality relations for y integration, where the X inte- 

 gral may be truncated soon after x exceeds 1 in absolute value. 



The above formula can easily be extended to the case of infinite tank width 

 as T->oo; however, for practical evaluation it is recommended to consider T as 

 inverse of spacing in integration by trapezoidal rule and let T be just large 

 enough, dependent on X, that for <f = ±X the actual wave pattern is well within 

 |y| < t, i.e., that no tank effect can be felt. 



For actual calculations we have to reintroduce dimensions; we have 



and 



y^R'-^^ = (B/L)Vc^(L/2)2 R(3) = pc^B^/(4L)R<' ^' 



y^R^^^ = (B/L)Vc^(L/2)2 R(2) = pc2bV4R(2) 



(57a) 



(57b) 



(compare Eqs. (18), (25), (26), and (27)), where fl^^^ and fl^^^ are the actual 

 third-order and second-order resistance components. 



NUMERICAL RESULTS 



For most of the computations done so far, at the present stage the author's 

 caution predominates over the temptation to have them presented prematurely. 

 From the field of wave pattern analysis, however, two typical examples shall be 

 shown. 



For a ship with parabolic waterlines and a draft/length ratio equal to 1/20, 

 in Fig. 2 we have plotted our calculations for 



Rxy(X,Y) 

 R(2) 



J_ X J- " J-as 



R(2) 7„(B/L)2 



It has been shown by Ward (14) that this quantity, measured by him as an inte- 

 gral over the product of X force and Y force experienced by a vertical cylinder 

 placed at distance y from the ship's path, is representative for the portion of 

 the total wave resistance R^ ^^ which is manifested in the energy transport of 



665 



