58 J. A. Sparenberg 
where 
att 
pte) = | Tyo¢Co,) ds. (5.9) 
We consider the asymptotical representation of I" 
After some analysis we find from (5.8) 
tot/?25) in the neighbourhood of s = a. 
att 
£9) 2 { 
1 It a 
SMG tie se pemeth reeroeee | Vo) [a(o) + F'(o)] 
~ [63(9) + wa"(o)]o + wo) In (2) 
" ory }VAt2=* do + 7? wo) VE ys- a |. (5.10) 
We have to satisfy the condition that the velocity of the fluid remains finite at the trail- 
ing edge. This is equivalent to the demand that the total vorticity I, ,,(?,s) for s = a equals 
the free vorticity in the wake. Hence we find from (5.10) 
att 
B(9) = 2 | { vo) [a(p) + f'(c)] - @O;(9) + oa'(9)] 
ee fei upie 
+ w(9) In ae + ocr} vette? ae, (5.11) 
and 
- 27 Wo) = ¥(9,)- (5.12) 
Equation (5.11) determines 8() in terms of the still unknown angle of incidence 9), while 
(5.12) is satisfied automatically (Eqs. (2.12) and (5.4)). 
The last condition we have to satisfy states that the integral over the bound vorticity 
of the profile has to have the known value I'(9?). Hence first we have to calculate the bound 
vorticity I'(9,s). We start from the definition of ’,,,(9,s) 
Peot( S) = ¥(9,'8) + PQ, s) (5.13) 
where y(Q,s) is the free vorticity passing along the profile. Using (2.6) we obtain 
att 
Poel S) Ss | (9,0) do 
2 RV1 + pw? + 2ucos 6 
+ T(o,s) + Q(ry 6.14) 
