16100lectre18_cg

16100lectre18_cg - Force Calculations for Lifting Line Recall N y = = 2bV An sin n n =1 b y = cos 2 The local two-dimensional lift distribution is

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Force Calculations for Lifting Line Recall: θ cos 2 sin 2 ) ( ) ( 1 b y n A bV y N n n = = Γ = Γ = The local two-dimensional lift distribution is given by Kutta-Joukowsky: ) ( ) ( y V y L Γ = ρ = = N n n n A V b L 1 2 sin 2 ) ( To calculate the total wing lift, we integrate L : 2 2 2 1 () s i n 2 2s i n s i n 2 b b N n n o b LL y d y d y d b bV A n d π θθ = ==   =     But: 0, sin sin , 2 o mk d = = In this case, n m = and 1 = k . So, the only non-zero term is for 1 = n . 2 (2 ) 22 n b Lb V A = 1 2 2 2 A V b L = 2 1 1 2 1 2 L A CA S VS = Α

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Force Calculations for Lifting Line 16.100 2002 2 The induced drag is similar. In this case: ) ( ) ( y y V D i i Γ = α ρ From previous lecture, = = N n n i n nA 1 sin sin ) ( θ 11 sin 2s i n sin NN in n nm n D V nA bV A m ∞∞ ==  ′ =   ∑∑ Integrating along the wing: () 2 2 22 0 0 only 0 for sin sin sin sin sin sin b ii
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This note was uploaded on 11/06/2011 for the course AERO 100 taught by Professor Willcox during the Fall '03 term at MIT.

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16100lectre18_cg - Force Calculations for Lifting Line Recall N y = = 2bV An sin n n =1 b y = cos 2 The local two-dimensional lift distribution is

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