# Induced drag

Discussion in 'Hydrodynamics and Aerodynamics' started by Konstanty, Aug 15, 2018.

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### Doug HalseySenior Member

That result is derived from lifting-line theory, so another limitation is large aspect ratio.

At aspect ratios that are common in sailing, the classical results don't apply very closely and lifting-surface theories must be used instead. Lift-curve slopes and spanwise loadings for elliptic planforms will be different from the familiar formulas; and it is no longer true that camber & other chordwise considerations are unimportant.

I can give you references to exact lifting-surface theories in the published literature, and results of my own vortex-lattice code to illustrate what I'm claiming, in case you would like to see them.

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### sandhammaren05Senior Member

You don't want a sharp angle at the leading edge, only at the trailing edge. The mast approximates the rounded leading edge of a wing.
The angle of attack is the angle from center of boom to trailing edge, as on a wing (the mean camber surface determines the angle of attack).

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### KonstantyJunior Member

How do you calculate the induced drag of these?

Last edited: Aug 20, 2018
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### sandhammaren05Senior Member

Sorry, but you are completely wrong. Max. L/D for a flat elliptic-shaped wing at small attack angle is an exact result that has nothing to do with lifting line or lifting surface approximations. It is based upon no approximation.

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### sandhammaren05Senior Member

The induced drag is calculated from integrals over the spanwise circulation density and its derivative. The wake leaves the trailing edge as a free vortex sheet. That sheet is unstable and rotates/rolls up into a single tip vortex. There is no mystery in that: the sheet is mathematically equivalent to a system of parallel vortices, paralel are unstable against any small perturbation and rotate about each other. That's the twisting into a single tip vortex. There is no misconception in any of this, you have to understand basic vortex dynamics in order to follow it.

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### sandhammaren05Senior Member

How do you calculate the induced drag on a feather? The point is that thinking like a physicist, which is most useful, means ignoring
irrelevant details and going straight to the heart of the matter.

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### Doug HalseySenior Member

My post didn't say anything about L/D.

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### KonstantyJunior Member

Direct of apparent wind above gaff or under boom for litle sails placed there is less sharp. The angle of attack can be the same.

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### tspeerSenior Member

That's not quite right. Minimum induced drag for a given span is obtained when the "downwash" velocity is uniform along the span. That is not the same as the trailing vorticity. For an isolated planar wing, an elliptical spanwise lift distribution produces a uniform downwash velocity and has minimum induced drag. But for other configurations, such as a vertical lifting surface in the presence of a ground plane, or a nonuniform freestream velocity, the induced drag will still be minimized with a uniform wash velocity distribution but the lift distribution will not be elliptical.

For minimum induced drag for a given heeling moment, it is the wash velocity that is linear along the span, not the vorticity distribution. Note that the uniform wash distribution is just a special case of the linear wash distribution.

If you want the math, check out NACA TR-121 and NACA TN 2249.

And it doesn't matter if the wing is cambered or not, provided the wake velocities are the same.

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### KonstantyJunior Member

One more drawing.

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### DCockeySenior Member

@Konstanty What does this drawing have to do with the topic?

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### KonstantyJunior Member

Here, the edge flow would be used for a forward force.

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### ErwanSenior Member

I don't know what you are smoking, but for sure that's a good one

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### KonstantyJunior Member

What did they have to smoke?

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### philSweetSenior Member

Konstanty, you can't do anything constructive with this approach. You can't locally exploit the tip vortex directly and do anything useful. You have to look at this from a global perspective. All you can do is change the pressure distribution over the entire hull and rig in such a way that the downwash-caused induced drag decreases by more than the additional friction losses increase. There are no local exploits in this game. If you suck some power out of the wind, put it to the best possible use - propulsion. It will be anywhere from 3 to 10 times as effective there than in down drafting. The way to get down-deflected air is by canting the entire rig to windwards. If you do this by 5 degrees, the effective span of the rig changes by only 0.4%, but the up force is now about 8.7% of the total force on the sail. And this is about where you want to call it quits for most boats. The tip vortex is your friend, not your enemy. A smaller tip vortex does not translate into less induced drag via direct intervention. It translates into more induced drag.

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