dR 



(3) 



-T 2] S,(2-cos2^J^ 



Ship Waves and Wave Resistance 

 K 



A^^ cos (W^7o^) - R^'^ sin (W^7o<f) 



But from Eq. (28) we may derive that 



KyM^ = Ky ( 2K, - 1 ) = 1/(2- cos ^ ^^ ) 

 Thus 



d^. (45) 



(46) 



dR 



(3) 



- 2T 



CD 



kl'^ cos(W^7o^) + B^'^ sin (Vl^y,^) 



-r 



( 1 ) free 



(3) 



(47) 



This is not yet the whole contribution of the strip to Rj , however; from Eq 

 (27) we have to add 



dR 



(3 





^\^<V) 4^x\^'V,0) d77d^. 



(48) 



This leads to the simple result 



.(3) 



J - 00 J- T 



with 



-y (1) ( l)free 



(49) 



(50) 



The potential ^ would correspond to the solution of the first-order boundary 

 value problem if we had postulated waves traveling ahead of the ship instead of 

 behind the ship. For a ship symmetrical to the midship section we may insert 



0(X) = ^(i)(-X). 



The above integral, Eq. (49), will have significant contributions to resist- 

 ance only from the vicinity of the ship, as & has strong decay ahead and the 

 factor 0x shows a decay aft. The overwhelming contribution should therefore 

 come from the rhombe-shaped region bounded by a Kelvin angle drawn from the 

 bow and an opposite angle from the stern. 



The expression for Rj^^ could have been derived directly as the Lagally 

 force of the wave field due to the surface disturbance 8(^,^) acting on the sin- 

 gularities creating the first-order flow field of the ship. It would, therefore, 

 have been found by Sisov under use of the proper radiation condition. For the 

 case of a nonsubmerged body, we felt that formal application of Lagally 's law 

 even for higher order contributions deserved caution. Inserting Eq. (13) we have 



663 



