.{o 



Salve sen 



+ Re 





) ( 1 ) 



Cn.in(n+1) 



0(1) 

 0(e) 



+ Fe 



E(0 ) (2) 

 Dn C,,,n(n+1) 



0(62) 



The terms enclosed within the rectangle are the second-order terms arising 

 from the boundary condition on the body surface. These terms are neglected by 

 the author. 



A conclusion reached by Tuck* was that the second-order free -surface 

 correction term is more important than the second-order body-surface correc- 

 tion term. This conclusion was arrived at by assuming, in part, that the body 

 could not maintain circulation; i.e., r (^^ = o. With this assumption, Tuck's con- 

 clusion may be expressed as 



Re 



E(0 ) ( 2) V" 



Dn C^+in(n+ 1) > Re 2^ 



(1) ( 1 ) 

 Dn C„.in(n+1). 



The body considered here by Salvesen cannot remain circulation-free, since it 

 has the shape of a hydrofoil. Therefore, in this case. Tuck's conclusion may 

 not be used. If the inequality given above is still valid, there may be justifica- 

 tion for neglecting the term on the right-hand side; however, the term 

 Re [ir^i) C^j^^] must still be considered. It may be that the omission of this 

 term causes the major part of the difference between the theory and the ex- 

 perimental data presented. 



The term Re [ir^ ^^Cj^^] is just the wave resistance of the first-order cir- 

 culation. The zeroth-order circulation is zero, since the body is symmetrical 

 and at zero incidence. The first-order wave system causes a nonuniform flow 

 field that, in general, produces a first-order circulation, this circulation being 

 required to maintain the Kutta condition at the trailing edge. 



A method developed by Giesing and Smitht is based on a theory that is 

 complementary, in terms of wave resistance, to the theory used by Salvesen. 

 Specifically, it retains the terms in the rectangle in the expression for the 



*E. O. Tuck, "The Effect of Non-Linearity at the Free Surface of Flow Past a 

 Submerged Cylinder," J. Fluid Mech. 22:401-414 (1965). 



ij. P. Giesing and A. M. O. Smith, "Potential Flow about Two-Dimensional Hy- 

 drofoils," Douglas Aircraft Company Engineering Paper 3541, 1965. 



630 



