Panel Discussion 



large-scale ships. Webster and Huang [1] have therefore proposed the following 

 relationship, which is a proposed extension of the Schoenherr curve to flow with 

 a pressure gradient: 



0. 46 C n(R0) 

 0. 678 1' 



\0.46 ^nCRg- I) ,, . ., 



a(H) = 0. 019 X 10 , , . W) 



n = -0.256 + 0.004 i n^^Rg) . 



This result is based on the assumption that at a given Rg, the ratio of c.^ without 

 and with a given pressure gradient by Ludwieg and Tillman and by Schoenherr 

 are the same. 



The initial condition for the differential equations (l)-(3) is: At station 1/2 

 (that is, 5% aft from the bow), /3 = 0, ^ and h are chosen to be identical to that 

 which would exist on a flat plate of the same length between stations and 1/2. 

 These approximations may be sufficient for computing the boundary- layer char- 

 acteristics at the stern section of the ship but not for that near the bow. 



POTENTIAL FLOW ABOUT THE SHIP 



The potential flow about the ship will be determined under the assumption 

 that thin- ship theory of Michell [5] is valid. With this assumption, it is possible 

 to write down formulas for the streamlines, free- surface elevation, and pres- 

 sures on the hull of the ship (for instance, see Wehausen, [6]). The formulas 

 for these quantities would be exceedingly tedious to evaluate. The improper 

 integrals involved in these expressions converge so slowly that, even with to- 

 day's high-speed computers, their computation is not an insignificant task. For 

 the purposes of this study, the method of Guilloton [7], as presented by Korvin- 

 Kroukovsky in [8], was adopted. This technique is ideally suited for digital- 

 computer application, since the difficulties with the improper integrals are 

 concentrated into universal functions, which have been tabulated in this 

 reference. 



In the Guilloton method, the hull is represented as a summation of simple 

 geometric wedge shapes. Thin- ship theory is used to compute the flow about an 

 elemental wedge; the functions which describe the constant-pressure lines and 

 the streamlines of this flow comprise the aforementioned Guilloton functions. 

 The flow about the given ship is then found by the summation of the flows about 

 the wedges which make up the ship. This operation is valid because the velocity 

 potential and the first-order thin-ship boundary conditions are all linear. The 

 errors incurred by approximating the exact hull shape by the Guilloton wedge 

 system appear to be quite small [7, 9, and lOj. 



A recapitulation of the details of the derivation of the Guilloton method will 

 not be given here, but the reader is referred to the detailed exposition given in 

 [8]. For the purposes of this boundary- layer study, none of the somewhat ques- 

 tionable second-order corrections to the theory, introduced in this reference 

 have been adopted. The tables given in the reference have been punched on 



1631 



