16100lectre14_cg

16100lectre14_cg - Solution 2 y V = 100 mph 8 3 =10 miles 1...

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Solution 0 = n u K K at control pt #1: The velocity at control pt #1 is the sum of the freestream + 3 point vortices’ velocities at that point: 123 1 222 uV i i i j πππ ΓΓΓ =+ +    KKKK K AAA The normal at control pt #1 is: 1 12 11 0 22 ni un V ππ =− ΓΓ ⇒⋅= −− + = K K KK AA Rearranging: V −= (1) 0 = n u K K at control pt #2: Now, following the same procedure for control pt #2: ± =10 miles V = 100 mph 8 Γ 1 Γ 2 Γ 3 x y
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Solution 16.100 2002 2 2 23 22 13 0 2 ni j V un ππ =+ ΓΓ ⋅= − + = KK K AA 2 V −= (2) 0 = n u K K at control pt #3: 3 33 0 2 j V =− ⋅= + − = K 2 V ⇒− + = (3) Final System of Equations Combine the numbered equations: N 1 2 3 vortex strengths (unknowns) Influence matrix 11 0 0 2 0 2 i Vn V V V   Γ −Γ = Γ     K i ±²³ ±´´´²´´´³ The problem with these equations is that they have infinitely many solutions.
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16100lectre14_cg - Solution 2 y V = 100 mph 8 3 =10 miles 1...

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