Ogilvie 



0.3 0.5 07 0.9 I.I 



FROUDE NUMBER, U/Vtgb) 



firjt-order theory; 

 inconsistent second-order theory 

 (neglecting body correction effects); 

 consistent second order theory 



(From Solvesen (19691) 



Fig. (5-6). Theoretical Wave- Resistance 

 Curves for € = t/b = 0.30. 



The figure is a very interesting one. The difference between 

 the linear-theory curve and either of the other two curves is pre- 

 sumably a second- order quantity, and yet that difference is -- in 

 one case --of the same order of magnitude numerically as the 

 linear-theory curve itself. The problem is worth further discussion, 



Salvesen defines his small parameter as follows: 



e= t/b, 



where t is the thickness (or some other characteristic dimension) 

 of the body, and b is the submergence of the body below the undis- 

 turbed free-surface level. It is not assumed that the body is "thin" 

 in any sense; it could be a circular cylinder (Tuck's problem), for 

 example. Salvesen's calculations and experiments were carried out 

 for a rather fat, wing-shaped body with a sharp trailing edge. The 

 body was symmetrical about the horizontal plane at depth b. If the 

 free surface had not been present, there would have been no lift on 

 the body. 



A complex velocity potential, F(z) = <^(x,y) + i4j(x,y), can be 

 defined for the problem, with z = x + iy measured from an origin 

 located in the body at a depth b below the undisturbed free surface. 



788 



