The Aerodynamics of Sails 

 Table 1 (Continued) 



The problem of determining the conditions needed for minimum induced drag, 

 with fixed lift, of a lifting line in an unbounded fluid with the free stream speed 

 being dependent on the position in the plane perpendicular to the stream direction, 

 was solved by Von Karman and Tsien (1945). The result is that minimum induced 

 drag occurs when the induced angle is constant over the span, which reduces to 

 the well-known case of constant downwash when the stream speed is independent 

 of position. When the method of Von Karman and Tsien is applied to a lifting line 

 over and normal to an infinite plane, the condition for minimum induced drag is 

 the same as before — constant induced angle. However, the circulation distribu- 

 tion needed to cause a constant induced angle over the span depends on the dis- 

 tance from the base of the lifting line to the infinite plane. Table 2 shows the 

 values of the first ten a 's divided by Ai needed to result in a constant induced 

 angle for various values"of h/b. The values in this table were determined by 

 inversion of Eq. (22), subject to the condition of constant induced angle. 



The total lift l is given by 



r 



(y) dy 



(30) 



1405 



