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Induced Drag.... what the

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Induced Drag.... what the

Old 25th Feb 2010, 08:07
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QJB
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Induced Drag.... what the

Hello all,

I have been studying up on aerodynamics recently and something has been bothering me. I just can't get my head around the drag curve. I might just be getting caught up with definitions...

I understand the normal explanation that induced drag varies inversely with the square of TAS and Parasite drag varies directly with the square of parasite drag. I also read that the formula for parasite drag is Dp = Cd A q and the formula for induced drag is
k L^2/ 1/2 p V^2 S pi AR

Thus a wing with infinite aspect ratio also has no induced drag. Since the back side of the power curve is attributed to induced drag I wonder what does the power curve look like for a theoretical aircraft with an infinite aspect ratio wing look like. If the back side of the power curve is due to induced drag then theoretically there would be no back side. It seems more intuitive that drag would still increase as angle of attack is increased due to pressure drag and an effective increase in parasite area. Hope that I'm making sense. Can someone please clarify this for me.

J
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Old 25th Feb 2010, 09:56
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Don't tie yourself up in knots worrying about infinite sized objects is my advice!

It really is pretty meaningless, but since you ask if the span is infinite the wing area is also infinite so CL can be 1/infinity, so your alpha is just 1/infinity more than the zero lift alpha, however much lift you need. If the increase in alpha is 1/infinity then the incremements in zero lift drag are also infinitessimal.

Intuition is not a handy tool for analysing infinity.
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Old 25th Feb 2010, 17:20
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It seems more intuitive that drag would still increase as angle of attack is increased due to pressure drag and an effective increase in parasite area.
Yes. If you have a look at the drag polars of aerofoils (rather than finite wings), you still see a roughly quadratic dependence on lift coefficient (i.e. on AoA). For cambered wings, the minimum drag is not at zero lift coefficient. But that's not induced drag.

but since you ask if the span is infinite the wing area is also infinite so CL can be 1/infinity
I started off thinking along the same lines, but actually you can imagine reducing the chord as you increase the span such that the wing area remains constant. You're flying a very long, narrow plank. In that case the AoA does indeed have to increase at low speed.
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Old 25th Feb 2010, 21:26
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I started off thinking along the same lines, but actually you can imagine reducing the chord as you increase the span such that the wing area remains constant.
Eh?

Are we still talking about a wing of infinite span here?

If so, then surely an infinite span would have to have an infinite area.
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Old 25th Feb 2010, 22:48
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Not if it has zero chord.
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Old 25th Feb 2010, 23:05
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QJB
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Thanks for the replies, I see what you are saying about the perils of thinking about infinite span aerofoils. Maybe I should re phrase the question:

Is the entire back end of the power curve completely a function of induced drag, ie, backwards tilting of the lift vector due to downwash, or is it also due to the increase of pressure and parasite drag with increasing angle of attack?

as bookworm said:

If you have a look at the drag polars of aerofoils (rather than finite wings), you still see a roughly quadratic dependence on lift coefficient (i.e. on AoA). For cambered wings, the minimum drag is not at zero lift coefficient. But that's not induced drag.
J
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