QantasA332
Topic Author
Posts: 1473
Joined: Sat Dec 13, 2003 5:47 pm

### Zero Induced Drag Wing Design

Okay, we all know about wingtip vortices and how exactly they cause induced drag (see my post [reply number 6] in http://www.airliners.net/discussions/tech_ops/read.main/77356/).

Theoretically, if an airplane's wing could have infinite span (i.e infinite aspect ratio), or if there were somehow no wingtips, the wing would generate no induced drag.

The other day I was wondering: Couldn't you design an aircraft with an elliptical wing and eliminate induced drag altogether? That is, imagine bending the wing up and around until the two tips met, forming a horizontally situated ellipse as you look from the front of the plane. The top and bottom of the ellipse would both be "active" airfoils.
This configuration would simulate infinite span and eliminate wingtips, thus reducing induced drag close to, if not exactly, zero.

Theoretically, would that work? I know that for various weight reasons and operational feasibility this design would be unwieldy, but disregarding that, am I correct?

Thanks,
qantasA332

MITaero
Posts: 485
Joined: Mon Jul 28, 2003 8:00 am

### RE: Zero Induced Drag Wing Design

Good to think outside the box..

I'm pretty sure tip vortices would still form. Aside from being aerodynamically poor and heavy, such a wing design would not eliminate vortex generation - just because there is no "tip" doesn't mean the wing behaves as an infinite wing.

The proposed design would be like a biplane with a wingtip fence connecting the two tips, if you can imagine that. However, there is no reason that this would eliminate vortex formation. Another argument: "fill in" the inside of the ellipse (pay attention only to the very top of the wing and the very bottom), and there is just a very thick wing with two tips.

Some of you guys with time can give more technical explanations

flyf15
Posts: 6633
Joined: Tue May 18, 1999 11:10 am

### RE: Zero Induced Drag Wing Design

Something a little like that?

Don't really know much about it, aside from the fact that it is a Lockheed tanker/transport concept. Its called the "Advanced Mobility Aircraft." Apparently one of the reasons for designing the wing like that was to eliminate vorticies (or at least greatly reduce them) so that the aircraft being refueled are less affected.

http://www.nationaldefensemagazine.org/article.cfm?Id=423

Guest

### RE: Zero Induced Drag Wing Design

About 15 years ago someone designed and installed a set of winglets on a G-II that were tubular shaped. Besides being very "un" esthetics, they apparently didn't work very well - they just faded away into obscurity.

Back in the '60s there was an experimental light twin that had a wing design along the lines of what Quantas332A described - it was unsuccessful as well.

Jetguy

BlatantEcho
Posts: 1893
Joined: Wed Sep 27, 2000 10:11 am

### RE: Zero Induced Drag Wing Design

As jetguy said, it's been done on a Gulfstream-II.

Near the wingtip, the wing bent back up, over itself, and reattached a few feet inboard from where the winglet would be.

Looked cool, but wasn't pretty. Never heard if it worked out cost wise, sounds like a no.

George

L-188
Posts: 29881
Joined: Wed Jul 07, 1999 11:27 am

### RE: Zero Induced Drag Wing Design

There have been some suggestions that the E-2 and S-3 replacement have a wing simular to that photo that flyf15 put up.
OBAMA-WORST PRESIDENT EVER....Even SKOORB would be better.

Ralgha
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Joined: Tue Nov 09, 1999 6:20 pm

### RE: Zero Induced Drag Wing Design

Induced drag isn't only from the vortices. It also comes from angle of attack, so even if you did somehow eliminate the vortices, you'd still need AoA and would still have induced drag.
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QantasA332
Topic Author
Posts: 1473
Joined: Sat Dec 13, 2003 5:47 pm

### RE: Zero Induced Drag Wing Design

Thanks for the replies everyone.

qantasA332

MITaero
Posts: 485
Joined: Mon Jul 28, 2003 8:00 am

### RE: Zero Induced Drag Wing Design

>Induced drag isn't only from the vortices.

I think it is, I could be forgetting. (Higher angle of attack increases lift, which is the cause of vortices)

QantasA332
Topic Author
Posts: 1473
Joined: Sat Dec 13, 2003 5:47 pm

### RE: Zero Induced Drag Wing Design

Induced drag isn't only from the vortices. It also comes from angle of attack...

Again, check out reply number 6 in the thread I gave a link to above (sorry to keep refering back to this, I don't really have time to go through it all again...). In it I detail exactly what causes induced drag. Wingtip vortices are the sole source.

However, AoA certainly does affect induced drag:

Cdi = k X (Cl^2 % AR) ... where Cdi is induced drag coefficient, k is a proportionality constant, Cl is, of course, lift coefficient, and AR is aspect ratio.

Looking at that equation, you can easily see that because an increase in AoA means an increase in Cl and an increase in Cl increases Cdi (and hence induced drag itself), AoA obviously affects induced drag.

BUT:

The change in induced drag due to AoA is still because of vortices. As MITaero said, increased AoA just increases lift, which in turn amplifies vortices. That is, the vorticies are still the sole cause of induced drag.

Hope that's clear enough,
qantasA332

buckfifty
Posts: 1278
Joined: Tue Oct 16, 2001 4:05 pm

### RE: Zero Induced Drag Wing Design

Drag is also increased at higher AoA when the boundary layer at the trailing edge separates with increased downwash, inducing turbulent flow. The lift of the wing decreases with the same mass airflow, and thus the resultant is considered to be increased drag (i.e. in a stall situation).

SkyGuy11
Posts: 532
Joined: Fri Oct 26, 2001 7:09 am

### RE: Zero Induced Drag Wing Design

In it I detail exactly what causes induced drag

Quantas, no offense meant, but just because you detail what causes induced drag does not mean it's correct...

If you could actually elimate wingtip vorticies you would still have induced drag. Reason? As you said in your other post, lift acts perpindicular to the realtive wind. As the air flows over the wing, it changes direction and is forced down, and the lift arrow points backwards.

Anyway, an eleptical wing has been made before; take a look at the Spitfire... sure it's efficient but it's also expensive and the wing tends to stall all at once if not built with signifigant washout.

[Edited 2004-02-01 09:06:04]
.

vikkyvik
Posts: 12115
Joined: Thu Jul 31, 2003 1:58 pm

### RE: Zero Induced Drag Wing Design

There would definitely still be induced drag on an elliptical shaped wing (this having been said, I'm assuming that what I picture in my head is what QantasA332 was describing). I think MITAero might have said something similar to this, but the pressure around the outside edges of the ellipse (what used to be wingtips) will be lower as you move from the bottom wing to the top wing. Therefore, the air will still have the tendency to move from bottom to top, same as around a wingtip. Also, though I am just speculating here, if you had two lift-producing airfoils, such as in a biplane, wouldn't the higher pressure air immediately under the top airfoil move down to the lower pressure region above the lower airfoil? Just something I hadn't thought about before, that could affect both lift and drag.
SkyGuy11,
While I don't dispute that the turned airflow may generate some drag, my learning is that induced drag is due exclusively to vortices. But I may be wrong...
~Vik
I'm watching Jeopardy. The category is worst Madonna songs. "This one from 1987 is terrible".

MITaero
Posts: 485
Joined: Mon Jul 28, 2003 8:00 am

### RE: Zero Induced Drag Wing Design

>As the air flows over the wing, it changes direction and is forced down, and the lift arrow points backwards.

This argument (lift vector tilt) is good for quickly explaining induced drag, but the true reason behind induced drag is energy put into vortices.

There isn't any way to turn flow downward with a finite wing and have no vortex generation. It's in the math

FredT
Posts: 2166
Joined: Thu Feb 07, 2002 9:51 pm

### RE: Zero Induced Drag Wing Design

Gotta second in with the other engineers (and engineers in spe) here. Induced drag is caused by lift caused by AoA, not by AoA on it's own.

An wing such as the proposed design (which is not at all what we normally call an elliptical wing, as we are talking about the planform and spanwise lift distribution in that case) has been built, I think it was in Italy. Didn't work too well. There has also been a contraption alongt those lines flying into Oshkosh in recent years if I remember correctly.

But picture the pressure distribution along the outside of the circle. You'll have a wing top surface along the upper segment, with the associated low pressure, and a wing bottom surface along the lower segment along the bottom segment with the associated less low ( ) pressure... and nothing to stop the air from moving from one to the other.

And then the same, but in reverse, on the inside of the circle. You'll have air streaming downards inside the circle, and air streaming up on the outside... put together, whoa! Vortices!

Cheers,
Fred

[Edited 2004-02-01 14:37:31]
I thought I was doing good trying to avoid those airport hotels... and look at me now.

SkyGuy11
Posts: 532
Joined: Fri Oct 26, 2001 7:09 am

### RE: Zero Induced Drag Wing Design

There isn't any way to turn flow downward with a finite wing and have no vortex generation. It's in the math

I'm not dispuiting the fact that wingtip vorticies exist... just also saying that if you could somehow eliminate all vorticies you would still have induced drag.
.

MITaero
Posts: 485
Joined: Mon Jul 28, 2003 8:00 am

### RE: Zero Induced Drag Wing Design

>if you could somehow eliminate all vorticies you would still have induced drag.

How?

MITaero
Posts: 485
Joined: Mon Jul 28, 2003 8:00 am

### RE: Zero Induced Drag Wing Design

>The lift of the wing decreases with the same mass airflow, and thus the resultant is considered to be increased drag (i.e. in a stall situation).

This is pressure (not induced) drag.

Also note that turbulent flow helps flow stay attached (less separation), so it actually is beneficial in some cases (except right after transition, where skin friction drag is increased).

FredT
Posts: 2166
Joined: Thu Feb 07, 2002 9:51 pm

### RE: Zero Induced Drag Wing Design

Oh yeah, fergot.

Boundary layer separation typically reduces downwash rather than increase it.

Compare it with the infamous P-38 tuckunder problem. The separation causing the loss of downwash on the horisontal stab was caused by shockwaves in that case, but the same holds true for more normal separation such as in a high AoA situation.

Cheers,
Fred
I thought I was doing good trying to avoid those airport hotels... and look at me now.

QantasA332
Topic Author
Posts: 1473
Joined: Sat Dec 13, 2003 5:47 pm

### RE: Zero Induced Drag Wing Design

Sorry for my late reply to this -- I was asleep here in Oz...

Seconding Fred on that one, boundary layer separation does reduce downwash, because it's adding overall kinetic energy to the airflow making it seperate from the wing further back. This is why a golf ball has dimples: to make the flow slightly turbid to keep it from separating too soon and causing a lot of pressure drag.

Also, now I clearly see that there would still be vortices with an elliptical (not planform) design, if on a different scale, sort of...thanks again for the explanations...

qantasA332

PS: vikkyvik and Fred, you're now on my R.R. list! thanks for the help! (MITaero, you're already on it).

lehpron
Posts: 6846
Joined: Tue Jul 10, 2001 3:42 am

### RE: Zero Induced Drag Wing Design

" Couldn't you design an aircraft with an elliptical wing and eliminate induced drag altogether"

This is me thinking outloud: If one wanted to get rid of induced drag, one must deal with the induced flow properly. This flow is created by the drop of pressure on top of the wing and the bottom trys to get on top over the tip. Swept back leading and trailing edged wings have their flow going back which also happens with straight wings. This flow will never go against the flow of the incoming airstream, hence the vortices.

But forward-swept wings have flow moving in the opposite direction, this accounts for the 29% reduction in drag due to the cancelling of reverse induces flow underneth the plane proven in the X-29 program. (see Janes all the World's aircraft 1994-95 for details, or atleast an in-depth book on the plane) Forward swept concepts are complex and costly, that is one of many other reasons why we don't see them that often. On the other hand, I have faith in the future.

There has to be an average forward swept angle where the inboard wing produces normal induced flow and the outboad wing produced inward induced flow. Maybe a curved leading edge that started out straight inboard and gradually sweeps forward at the tip or a zero-degree straight edge with varing trailing edge dimensions. My guess since elliptical wing have the least induced coeff, then it would be a good place to start.

My Conclusion: take an elliptical wing and slice it spanwise so it has a flat sharp front edge (sharp for jet speeds). This would be a zero-induced flow wing (drag may be a different story), but this would only work at a constant speed. Go any faster or any slower and you will vary the induced flows direction because speed changes the wing's pressure patterns. I figure it would make sense to design this type of wing for a landing sequence as that is where vortices bother people the most.

Or if you don't like ellipses or agree they are just as costly and complex as FSW's, build a silly "W" shaped wing (planform wise) with inboard half swept-back and the outboard half swept-forward. It would still only work at one speed -- make your pick.

Again this is just me thinking outloud, I've thought of this for a number of years and think it is worth trying. How bout y'all?
The meaning of life is curiosity; we were put on this planet to explore opportunities.

lehpron
Posts: 6846
Joined: Tue Jul 10, 2001 3:42 am

### RE: Zero Induced Drag Wing Design

Forgot to include something else. If you have ever looked at the way a bird's wings are shaped during landing, it should give a good idea of how a wing could be. For one, I can bet that birds land without having to deal with induced vortices, their landing drag must be real low and may have double the coeff of lift. Their wings are not only forward swept at the tip but their wingtips are curved downwards. My guess is that they act either like a scoop or a parachute during their landing sequence. If one considered that the high AoA renders a greater profile are on landing, then the parachute example I gave was intended to cushoin rather than act as even greater drag.

If anyone needs clairification, just ask; I am starting to watch seagulls more closely thesedays...

BTW: I focus on landing more because, like I said b4, vortices affect more than just the aircraft in question.
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