Wavemaking Resistance of Ships with Transom Stem 



and the wave profile 



C(x) = U4>x(x,0)/g, (DIO) 



now becomes 



TTf/v/o sgn (x) r e ° {cos{wkof)+wsin(wkof)} 

 U;(x)/2Tnn = - ^ J" \ — - — g dw 



- {1 - Sgn (x)} e ° cos (kof). (Dll) 



It is obvious that for f = the wave profile of the line source be- 

 comes discontinuous at x = 0, For any nonzero value of f the 

 profile remains theoretically continuous at x = 0, However, for all 

 practical purposes it is discontinuous in the limit f — ^ as shown in 

 the accompanying figure (see Curve 2) for kgf = 0,00001. 



If we assume Po/pg = - Zirm/U, then the potentials of the 

 pressure step (D6) and the line source (D9) become identical in the 

 limit f -* 0. But the wave profiles differ by the first term of (D8). 

 Incidentally, the author's Eq. (1) differs from our (Dll) by a factor 

 of 2. But his relation (6) seems to have a compensating error of 

 factor 1/2 so that his wave profile (7) does agree with our (D8). 

 We have not investigated what effect this discrepancy has on the 

 author's further calculations of wave resistance. But we did notice 

 an obvious slip in Eq, (18) for the strength of the line sink repre- 

 senting the transom stern. If (r, is regarded as a line density, 

 apparently a factor L is missing on the R.H.S, On the other hand, 

 if (Tj is interpreted as a surface density, then the R,H, S. should 

 contain the Delta function 6(0) as a factor. 



We also find the idea of using a line sink to represent the 

 transom stern rather unconvincing. The line sink would tend to 

 force the flow around the corner of the transom, which in practice 

 occurs only at low speeds, but in a highly viscous manner not 

 tractable by ideal fluid theory. The case of real interest is the 

 one at high speeds where the flow separates smoothly from the 

 transoin. In this regime, we feel that the line sink should not be 

 used so that the excess sources in the hull can produce a semi- 

 infinite half-body. We would appreciate the author's comments on 

 this point. 



Notwithstanding minor differences of opinion, we wish to 

 congratulate the author on his imaginative approach to a very inter- 

 esting problem. 



603 



