Milgram 



Fig. 1 - Model sails with tufts in a wind tunnel 



velocity gradient and that it has a solid boundary beneath it formed by the hull 

 and the sea surface. The effects due to these differences can be determined 

 from the lifting line theory. The actual design of sail shapes must be carried 

 out by the lifting surface theory (see, e.g., Milgram, 1968). However, for the 

 linearized problem the lifting line theory and the lifting surface theory yield 

 identical flows in the Trefftz plane. Hence gross quantities such as lift, in- 

 duced drag, and heeling moment can be calculated by the lifting line theory. 



Consider a steady, incompressible, inviscid flow in the presence of a 

 heeled lifting line. The flow is taken to be irrotational except on the lifting line 

 and its trailing vortex sheet. The boundary conditions beneath the lifting line 

 are approximated by a plane parallel to the sea surface lying somewhere be- 

 tween the deck of the hull and the sea surface. To satisfy the boundary condi- 

 tion of no-flow through this plane, henceforth called the image plane, the method 

 of images is used as shown in Fig. 2. The free stream velocity is approximated 

 by a linearly varying function of height having the value Uq at mid span and a 

 slope of K. The direction of the free stream is taken to be constant in this de- 

 velopment, whereas on an actual sailing vessel the incident stream direction is 

 not constant. This occurs because the incident wind is the vector sum of the 



1398 



