Finite Wings

  1. If I take an infinitely long, thin wing and measure its lift curve slope I should get 2pi.

    Now if I take a 1/2-wing and fit 1 end to a plate and test it in a wind tunnel, it should simulate the flow around a full span wing, am I wrong? Therefore measuring lift and working out the CL values using the area of the half wing, air density, and flow speed I should get approximately the same results for CL as for a full wing (same section) twice the area and twice the aspect ratio (with no plates fitted to the ends).

    I've done that experiment for a NACA 0015 aerofoil section and my results are confusing me. I understand the theory and the limitations of Prandtl's lifting line theory but this doesn't seem to be helping me here.

    I was expecting the theoretical and experimental results to match up fairly well (looking at Prandtl's graphs they are pretty much identical).

    The 1/2-wing I used was AR 3. Therefore it simulated the full wing AR 6. If I use AR 3 for the theoretical calculations the graphs match perfectly, but I can't do this, because the 1/2-wing AR 3 was simulating a wing AR 6 with that attachment plate on 1 end. So... experimentally the lift curve slope is 3.5rad-1 and theoretically it's 4.5rad-1.

    Can anyone just point me in the direction of the reason for this massive difference? I'm guessing it's something to do with the 1/2-wing with a centre-line plate mount not properly simulating the flow around a full span wing, but this to me would suggest a steeper lift curve slope than theoretically predicted because there's 1 less wing tip vortex to cause more downwash over the rest of the wing.

    I hope someone can make sense of that - I'm sure the only reason I can understand what I've written is because I know what I'm trying to say!
     
  2. jcsd
  3. As is usually the case I answer my own question: the main (obvious reason) is that the theory I was using (Prandtl's lifting line theory) assumes invsicid flow and of course there are viscous effects (even if small).
     
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