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Aerospace Derivation of Aerodynamic Forces

  1. Mar 8, 2016 #1
    Good day all:

    I'm having trouble deriving the forces for Lift and Drag in the attached diagram.

    The text I have (Fundamentals of Aerodynamics - John Anderson) states the solution to be:
    L = N cosα - A sinα
    D = N sinα + A cosα

    Can anyone guide me through this? I think the cofunction identity is used somewhere:
    sin(90 - x) = cos x
    cos(90 - x) = sin x

    But that's as far as I've gotten.

    Help is appreciated, thanks!
     

    Attached Files:

  2. jcsd
  3. Mar 8, 2016 #2

    Samy_A

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    angles.jpg

    For ##L##:
    ##\cos (\alpha + x)=\frac{L}{R}##
    So ##L=R\cos(\alpha + x)=R\cos x \cos \alpha -R\sin x \sin \alpha \ \ \ \ (1)##
    Now ##\cos x=\frac{N}{R}## and ##\sin x=\frac{A}{R}\ \ \ \ (2)##.
    Then (1) becomes: ##L=N \cos \alpha -A\sin \alpha##.

    Similarly for ##D##:
    ##D=R \cos y= R \cos(\frac{\pi}{2}-\alpha -x)=R\sin(\alpha + x)=R\cos x \sin \alpha + R\sin x \cos \alpha##.
    Using (2) again, you get ##D=N\sin \alpha + A\cos \alpha##.
     
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