Page 264 - Aerodynamics for Engineering Students
P. 264
--- Finite wing theory 247
V
nA, sin ne
~v=l"P 4sVCA, sin n8 s sin 8 de
I r dz
= pV22 L" nA, sin 8 A, sin ne de
The integral becomes
This can be demonstrated by multiplying out the first three (say) odd harmoni thu
rr
(A1sin8+3A3sin38+5Assin58)(A1 sin8+A3sin38+ Assin8)d8
= L"{A; sin2 8 + 3A: sin2 8 + 5A: sin2 8 + sin8sin38and
other like terms which are products of different multiples of 81) df3
On carrying out the integration from 0 to 7r all terms other than the squared terms
vanish leaving
I = L"(Af sin2 8 + 3Az sin2 38 + 5A: sin2 58 + .)dB
7T
7r
=-[A;+3A:+5A:+..-] =2cnAi
2
This gives
1
DV = 4pV2?ZcnAi = C,-pV2S
2 2
whence
CDv = .rr(AR) (5.49)
From Eqn (5.47)
(5.50)
