Panel Discussion 



Finally, we wish to obtain the coefficients aj, a^, • • • of the mapping 

 functions 



^1 33 ^5 



Aw + + ^ + — T + ■ • • 



w^ w^ 



Express the original profile in polar coordinates (Fig. 1), 



z = r ( tp ) e 



iCP 



(30) 



z = x + i y 



Figure 1 



and since w = e'^P, (30) becomes 



i(P k iO , ~ id j_ „ - 3 i^ , 



re * = Ae + aje + a ^e + 



Then 



and 



* = ^/"'<"-'" 



^ J r(Cp) cos (cp- 9) dt 



= J_ r(q)) COS [cp+ (2n - 1)^] dd . n = 1.2, • • 



n-l 277 J 







1625 



(31) 



(32) 



