Submerged Two-Dimensional Bodies 



DISCUSSION 



J. p. Giesing 



Douglas Aircraft Company, Inc. 



Long Beach, California 



This very good paper compares wave-resistance theory with an excellent 

 set of experimental data obtained by the author. The comparison is designed to 

 illustrate the importance of the higher order terms in the wave -resistance 

 theory. There are two types of higher order terms (higher than first order), as 

 pointed out by the author. One type is due to nonlinear free-surface effects, and 

 one type is due to the satisfaction of the boundary condition on the body surface 

 to higher than zeroth order. The author has included the second-order, non- 

 linear free-surface term but has omitted the second-order term related to the 

 body-surface boundary condition. This was done with the hope that the one 

 omitted would be small compared to the one retained. His experiment indicates 

 that, for the specific conditions considered, this is not the true case for speeds 

 greater than 5 ft/sec. As an aid in explaining a possible cause of this failure of 

 the theory, it may be helpful to inspect the terms in the wave-resistance expan- 

 sion, especially those that were omitted. 



In the author's notation, wg , q = 0, 1, 2, , . . , are the 0th, 1st, 2nd, . . . 

 order contributions to the complex potential due to the singularities on or within 

 the body, and wp , q = l, 2, . . . , are the 1st, 2nd, . . . order contributions to the 

 potential due to the free -surface disturbance, A multipole expansion plus a 

 vortex may be used to represent Wg as 



J_ 



277 



ir^^Un z + E D^, 



q) 



q= 0, 1, 2, 



where r(^) are all real but D^^^ are complex. In the vicinity of the body sur- 

 face the effects of the free surface may be expanded as a Taylor series as 

 follows: 



wp = ^ E C^^^-". q=l, 2, ... , 



^ n- 1 



where the C^''^ are complex. With these definitions and the aid of the Blasius 

 theorem, it can be shown that the wave resistance of a symmetrical body at 

 zero incidence is 



629 



