Brard 



^A'p;(m,,t') = (J)^^R(--t')+J -A(^)^^R(,, t'-.')dr' 



(17) 



We note that the first term in R(m,0) comes from the fact that the circula- 

 tion around the body is null at t ' = 0+. It leads to a deficiency of the pressure. 

 But the second term acts in the opposite direction. 



In the quasi-steady motion, the resultant force and the resultant moment 

 referred about the origin of the moving axis are respectively 



^0 1 (5)^, = - (S),, If PoiC-e) n(m,) dS(m,) , ^gj 



loi (u),, -- - (jj],, If Poi(-e) Om.AnCm,) dS(m,) . ^^g^ 



In the real motion, the resultant force and the resultant moment are, re- 

 spectively, 



^l(t') = ?oi (g)^, + 3^1^'Vt') - A'f;(t'), (20) 



Il(t') = loi (u)^, + Il^'Vt') - A'Il(t'), (21) 



with, for instance: 



^'i^'^(^') = ^r^(u),, If ri(n^.O+) n(m^) dS(m^) , 

 A'y;(t') . -p Jl dS(m)n(m) [g) R(m,0) . ^^2) 



c L 





The force ?i''^\t') and the moment ij (t') act in order to increase the ap- 

 parent inertia of the body and will be included in the final formulae in the set of 

 forces y. (see par. 5.4). They do not exist in the theory of the thin airfoil of 

 infinite aspect ratio. On the contrary, the force A'?j(t ') and the moment 

 A'ij(t ') are quite analogous with those found in this theory. 



Similar formulae can be obtained when (u/U)^, ^ 0, (w/U)^, - 0, (Lq/U)^/ =0 

 for t'>o (case "bg") or when u/U(t') =0, (w/U)^/ = 0, (Lq/U) ^ , :!= (case "bj")- 

 The total set of forces due to the wake in the most general case is the sum of 

 those found in the three cases "bg," "b/' and "bj." 



850 



