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I am studying for my ATPL and was curious if and how induced drag varies based on wing anhedral and geometric washout.

I have a basic understanding that spanwise flow affects induced drag since there's a tendency for pressure to equalise at the wing tips (at least that's what they teach in ATPL training programs...) and was curious what happens to induced drag if it was restricted by geometric washout (where the wing root has a higher angle of incidence compared to the wing tip) and wing anhedral on low-wing aircraft. Do these wing characteristics make a difference?

Would appreciate any input, thank you very much!

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    $\begingroup$ This very good answer should answer your question $\endgroup$
    – sophit
    Oct 14, 2023 at 17:47
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    $\begingroup$ @sophit that is indeed a phenomenal answer, but I don't know I'd agree it's appropriate for this question. P. Kämpf's deep dive into the efficiency of wing tips is not targeted at discussing anhedral nor washout. Perhaps those experienced in the mathematics of fluids could extend his answer to this question. However, I don't think we can assume that that level of expertise is widespread, esp. as the OP admits to no more than "a basic understanding" gleaned from the ATPL coursework. $\endgroup$ Oct 15, 2023 at 11:20
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    $\begingroup$ @KennSebesta: agreed. Maybe I should have written: the part regarding induced drag should answer your question 😉 $\endgroup$
    – sophit
    Oct 15, 2023 at 11:27
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    $\begingroup$ Thank you gents. Looks like I have a lot more to learn! $\endgroup$
    – Nick M
    Oct 15, 2023 at 13:27

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Induced drag is not really about spanwise flow. It is about the spanwise load distribution. The closer your spanwise load distribution is to elliptical, the lower your induced drag.

Washout will un-load the tips. So, if your load distribution is super-elliptical at the tips, then washout will reduce induced drag. However, if your load distribution is sub-elliptical at the tips, then washout will increase induced drag.

We also use washout to prevent tip stall. If a wingtip is highly loaded, it is more likely to stall at the tips first -- which is bad.

The difference in these is that when we're talking about induced drag, we're looking at the load distribution $l=q\,c\,c_l$ in terms of lbs/ft.

However, when we're thinking about local stall, we're just thinking about the local lift coefficient $c_l$ and how it compares to the local $c_{l,\mathrm{max}}$.

Since $q$ (dynamic pressure) is the same across the wing, the difference between the two is the local chord $c$. For induced drag, we care about the distribution of $c\,c_l$ being elliptical. For stall, we care about local $c_l$ staying away from stall.

The sweep of the wing has a significant effect on the spanwise load distribution. Sweep tends to load up the tips.

In addition, the amount of taper in the wing has a significant role to play.

Consequently, straight wings tend to have taper ratios of about 0.5 to 0.6 -- and swept wings tend to have taper ratios of 0.4 or less.

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  • $\begingroup$ Thanks Rob! So if I understand correctly, by reducing load towards the wing tip we can reduce induced drag? $\endgroup$
    – Nick M
    Oct 15, 2023 at 8:29
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    $\begingroup$ @NickM: "by reducing load towards the wing tip we can reduce induced drag?" That's not the whole picture. Induced drag is at a minimum when the spanwise lift distribution is elliptical. So the big picture is having an elliptical distribution and reducing lift at the tip is a part of this big picture. As a side note: obviously reducing induced drag doesn't imply that the total drag gets also reduced $\endgroup$
    – sophit
    Oct 15, 2023 at 10:11
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    $\begingroup$ @NickM When I said super-elliptical and sub-elliptical at the tip, I meant was the distribution locally higher or lower than an elliptical distribution. If you want to minimize induced drag, you want to get as close to elliptical as possible. Sometimes that requires increasing the tip load, other times it requires decreasing the tip load. I.e. It depends on the situation. $\endgroup$ Oct 15, 2023 at 15:45

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