From Horners book, some quotes without comment. (excuse typing mistakes) From here to bottom all quotes, not by me:-)

At the location of lifting line or wing, the flow is deflected by an average angle which is half the final theoretical downwash angle. that angle is the induced angle of attack ..............the force "F" originating in a direction normal to the average direction of the flow in the vicinity of the wing, is therefore tilted backward by the incuded angle

alphai - CL / pi A

In this manner, the force exhibits a component in the direction of flow, which is the induced-drag, represented by the minimum coefficient

CDi = CL tan alphai = CL CL / pi A..........

Any deviation from the elliptical distribution results in a certain increase of the average or effective induced angle of attack. There are other effects of wing shape (sweep, dihedral) that make the induced drag larger.........

In low aspect-ratio wings, the lateral edges have an important influence upon lift and drag...... A similar but smaller effect of wing tip shape is also found in other aspect ratios. .........

A series of shapes has, therefore, been investigated on a basically rectangular wing............ Shapes with sharp lateral edges are seen to give the widest effective spans, while rounded edges result in a loss of effective span or aspect ratio. ......

It is seen that the shapes having the widest vortex spans, are generally the ones exhibiting the least drag due to lift.............

In conclusion, the shape of the tips can be more important for the performance of an airplane than the plan form of the wing.......

I read on the swept forward wings thread that forward swept wing reduce tip voticies. is this true.

Ben,

Thanks for bringing some authoritative information to the discussion.

One thing I find surprising from Hoerner is the conclusion that the wing tip can be more important than planform for performance. What makes this less surprising is that this analysis seems to be limited to the case of low aspect ratio, which is actually a primary characteristic of planform. So Hoerner's statement seems to be that, once you have decided you need a low aspect ratio, the tip shape can become more important. To the extent that the tip shape can increase the vortex span, this is not too surprising, since a small increase in vortex span would be a bigger improvement for a short span wing than for a long span wing. It's not clear from the context, but I am curious which flight regimes are being considered in his conclusion. Since induced drag goes up in proportion to the square of CL, but goes down proportionally with AR, it would seem that even a low AR wing would be concerned with induced drag mainly at high CL. High CL conditions are things like takeoff, landing, and pylon-like turns. We don't much care about a little induced drag for landing, but it would be nice to reduce it for takeoff, if power is limited. For 'sport flying', induced drag is not a concern.

From Hoerner's first paragraph above, I see that my preferred round tip is indeed the worst choice for induced drag, which surprises me a little. For a wing of typical AR, I still tend to think that it would outperform a square tip in terms of overall drag. It would seem that a sharp tip might be best of both worlds. This is pretty much what a Hoerner tip is. No coincidence, I suppose. I did do some more looking around on the web, and I can't find any source that shows test results regarding wing tip shapes, apart from winglets. If Hoerner's book, which is a little expensive for me, has results from wind tunnel tests, I'd be interested to see a summary.

Thanks,

banktoturn

To a certain extent, yes. It's a bit more complex than that. Just about anything that you can find on NASA's X-29 program will cover this phenomena.

See this post:

http://www.rcuniverse.com/forum/m_88...tm.htm#1130513

No, a 2D wing does not generate downwash, which is why it produces no induced drag. In no sense is induced drag a differential between upwash and downwash. I have no idea what you are saying here.

Again, I have no idea what you are trying to say. This does not explain how spanwise flow is required for induced drag.

banktoturn

Don't believe me... here's a quote from a NASA webpage:

Here's the page it is from:

http://history.nasa.gov/SP-367/chapt4.htm

The only difference between a 2D wing and a 3D wing is vortex shedding. A 2D wing has a bound vortex that cannot be shed (there is nowhere to shed it to). Therefore, any upwash on the 2D wing MUST be matched by downwash. You may be confused by the term downwash... downwash is simply any downward component of velocity of a wing-deflected flow.

A 3D wing sheds it's vortex in the form of a wake. This vortex causes a differential downwash. Why? Because the lift across the span of a wing is not constant. The finite nature of a 3D wing causes high pressure air on the bottom of a wing to "spill over" to the top. This "spilling over" is the tip vortex.

OK, fine.... what does that mean... it means that you CANNOT shed a vortex without spanwise flow... in other words, 2D wings have no "net" downwash. 3D wings DO have a net downwash that is caused by that vortex... that is caused by that spanwise flow. No spanwise flow, no vortex shedding, no wake, no downwash.

I don't know how else to explain it. Here's a pretty picture:

banktoturn,

It was a low aspect ratio wing of about 3 that Horner was using. The square tips gave more effective span and lower induced drag. With a really high aspect ratio wing (or even a moderately high one I guess) the shape of the wing tip starts to be a non player with respect to induced drag. There may be some other drag components of the wing tips that change with shape though.

The figures are not totally clear in the book, the figure that shows the tip shape and center of the vortex is just showing the difference in spanwise location of the center of the vortex. There are some other figures with wing shape and you put the together and allegedly come up with Horners conclusions. The figures in the Horner book are hand drawn and don't reproduce well, it is difficult to see some of them in the book! There isn't any kind of wind tunnel data that I would like to see on the subject.

I am sure other sources have better data but I don't have any at hand.

I know when wing tips were a subject at work we would talk about all the neat good stuff and pull out some old reports and end up with the same old shape for the fighters. Of course the high aspect ratio heavy lifters pulled out reports for their airplanes and got different answers.

It comes down to a matter of aspect ratio... a high aspect ratio wing is an approximation of a 2D wing, and will have the least induced drag for the total amount of lift that it produces. In that case, parasite drag dominates.

All that we have been saying thus far is that a higher effective aspect ratio will give you lower drag for the amount of lift that you are getting. Extending the wing out does this, as does adding an engineered tip.

The opposite of this is a low AR wing like a sharp delta wing. In this case, there is quite a bit of induced drag from very powerful tip vortices.

Ken,

You asked me before to tell you if you had written anything stupid. Now you have. I don't think that continuing this discussion will be fruitful.

banktoturn‹s

Ben,

Thanks for the update. I guess I'll have to save my pennies and get myself a copy of Hoerner's drag book.

banktoturn~

I don't understand. What part of what I have written is wrong? Do you still disagree that spanwise flow is not necessary for downwash (net downwash, that is)? Do you disagree that the difference between 2D and 3D wings is vortex shedding?

I don't mind ending this discussion, but it seems like you just don't want to believe what I wrote. If it's wrong, at least tell me why.

Ken,

An infinite span wing can indeed shed vortices. Just stall it and watch. What it cannot do is trail vortices, as the Helmholtz theorem requires a finite wing to do. Having said that, I read through the NASA page you linked to, and I see how the notion of balancing downwash is being used. This is a reasonable explanation, and I should have read the text before making my comments. Sorry about that.

Spanwise flow is simply not required for induced drag, although it is almost certain to occur for a lifting finite wing. To prove this to yourself, just ask whether a wing with no spanwise flow could generate lift, and consequently generate induced drag. The answer is yes. You may not be able to build such a wing, any more than you could build one with infinite span. As I suggested in a previous post, one could run a computer simulation of a lifting, finite span wing, enforcing the condition that flow on the surface of the wing be chordwise. This wing would generate trailing vortices, as any lifting, finite span wing must, and consequently would suffer induced drag. My original point on this topic was that it is invalid to think that the tip vortex can be weakened or eliminated by preventing spanwise flow, or by making it harder for air to 'spill' from the bottom to the top of the wing. The tip vortex is simply the trailing vortex, which has the same strength as the bound vortex. To weaken the tip vortex, you must reduce lift. Methods which successfully reduce induced drag do so by reducing the effect that the tip vortex has on the wing, generally by pushing it's center out.

banktoturn

Good call on the trailing vortices... vortex shedding is indeed a different phenomena. Trailing vortices are what I meant, just not what I wrote. (Oh surrrrrre, he says. Sure they were!)

We gonna have to agree to disagree! LOL

Don't forget that spanwise flow is not limited to being on the wing planform. Most of it can be aft of the wing. Case in point... engineered tips (that is, engineered to control spanwise flow) don't make too big of a deal on a supersonic wing -> e.g. just about any supersonic modern jet fighter. This is because there is little to no induced drag in supersonic flight (at least not this type of induced drag, supersonic flight also has what is called "wave drag due to lift", but it's not the same thing).

When low speeds are important (and induced drag is at it's highest) this spanwise flow becomes important... e.g. the drooped tips of the A-10. Or Hoerner tips on some GA aircraft. It's really just a judgement call on the part of the designer... you'd have to do some tests to prove that an engineered tip is helpful for a particular configuration, depending on the aircraft's purpose/mission.

The faulty assumption here is that a lifting wing always produces induced drag. An infinite wing does produce lift, yet no induced drag. This is really a chicken and the egg question. The tip vortex, the downwash, and the induced drag are all part of one and the same phenomena - and of course a tip vortex cannot flow without spanwise flow, so throw that in there too. The downwash is simply the vortex flow considered along a vertical longitudinal plane. Yes, reducing the vortex is reducing induced drag.

Johng,

Of course an infinite span wing has no induced drag. I'd say we've pretty well covered that. No faulty assumption was being made, since I referred to a lifting, finite span wing. I am not too concerned about a type of wing that cannot be built. When I refer to spanwise flow, I mean at or very near the surface of the wing. I think this is the most common usage of the term. Spanwise flow at the surface of the wing is not required for induced drag to occur. If you can make a compelling case to the contrary, I would like to hear it. Obviously, if a tip vortex exists, there will be spanwise flow somewhere far from the wing. Yes, reducing the tip vortex strength will reduce induced drag. The only problem with that is that you can't reduce the tip vortex strength without reducing lift. Methods that reduce induced drag without reducing lift (significantly) do so by modifying the effect of the tip vortex on the wing, usually by shifting the tip vortices out, or increasing the vortex span. This is why it pains me to hear people attribute induced drag to the tip vortex, rather than the downwash. It leads to this fallacy that tip vortices can be somehow impeded or reduced, which can really only happen by reducing lift.

banktoturn

Is has to start somewhere, and that somewhere is at or near the leading edge of the wing. It just happens to be most "visible" after it has left the wing surface (the pretty picture I posted). As the aircraft goes faster, it "leaves behind" this spanwise flow and becomes more efficient... as is evidenced by reduced induced drag at higher speeds.

Not really... induced drag is basically an inefficiency of a finite span wing compared to an infinite span wing. So, by having a tip vortex, you are not going to get increased lift/drag by having a more powerful vortex. Conversely, you will not lose lift/drag by reducing the strength of the tip vortex. This strength though, must be viewed in terms of the overall lift that the wing is producing at the same time. Increasing the AR is one way of doing this, so is modifying the tip geometry.

The thing that I don't think you understand is that the downwash itself is a result of the tip vortex, and the tip vortex is a result of spanwise flow. Remember, spanwise flow is any component of the flow coming off the wing, in the span direction. Downwash is a result of the inefficiency of the wing and is not necessary for lift.

You mentioned before that induced drag is a short name for lift induced drag. However, some sources I've recently consulted (as a result of this discussion) also call it "vortex drag".

OK, I went back and read thru the posts, and have figured out that I disagree with both Ken and banktoturn. [sm=eek.gif] The physical cause of induced drag is the pressure differential at the wing tip. This causes the vortex flow, with both spanwise flow and downwash being the result. Niether is the physical driver or cause of the phenomena.

Now on to the quotes:

I can't see the relevance of this distinction at all. OK, so say the surface layer of the air has "a boundary condition on the wing which precludes spanwise flow". So what? A molecues' distance above this you have spanewise flow, and all your condition might have done is increased the thickness of the boundary layer. That has no real effect on the spanwise flow of the mass of air being influenced by the wing.

Hmm, better let the wind tunnels know. I've seen plenty of real 2d wings built for wind tunnels - that experience real aerodynamic forces. Plenty of lift, no tip vortex circulation, no induced drag.

That's just silly. Obviously you can reduce vortex strength to zero and maintain lift - as in the 2-d wind tunnel wing ( or airfoil to be techinically correct). Wingtip shapes are just an attempt to emulate this on aircraft. That wingtip shape will not necessarily reduce lift, in fact it will increase it if designed well. I have a design report somewhere on my bookshelf including the design of winglets onto a wing. The winglets were designed to both reduce induced drag and improve lift distribution - and thus overall lift of the wing at the same angle of attack. -Computed with CFD and proven in flight. Your statement would have me believe that the downwash and vortex strength are preserved in this case. I do not.

I've had enough. I'll leave further replies to others.

That's what I'm saying. Not just at the tip, but the pressure differential between the bottom and the top of the wing, which causes fluid it to flow around the tip. High pressure on the bottom moves fluid outboard, low pressure on the top moves fluid inboard... which is spanwise flow. This spanwise flow "rolls up" into the tip vortex.

Johng,

Fine, you can build a 2D wing in a wind tunnel. You can't build a plane with one.

You can't reduce the tip vortex strength without reducing lift. You can modify the effect of the vortex's downwash on the wing, consequently affecting induced drag. Believe it or not.

A wing must exert a net force down on the air to provide lift to the plane. This, not a local pressure difference at the tip of the wing, is the cause of tip vortices. The only way that air, as a fluid, can provide the reaction force to the wing's downward push is to flow. Part of the resulting flow is the tip vortices, and their overall strength depends on the amount of force (lift). How the 'downwash' part of the vortices affects the wing depends on other factors ( aspect ratio, spanwise lift distribution, tip treatment, etc. ), in addition to the amount of force. Those other factors are the reason that induced drag can be reduced somewhat without reducing lift.

banktoturn

Ken,

Spanwise flow is simply not the cause of tip vortices. It is a largely incidental local flow phenomenon. If you don't like the earlier thought experiments, imagine a lifting, finite span wing with a huge tip plate. Huge enough to push spanwise flow as far from the surface of the wing as you want. Will there be a tip vortex? If there isn't, tell me how the air provides the reaction force to the wing.

banktoturn

The air is able to provide the reaction force in the form of a pressure differential between the top and bottom of the wing. Any -additional force- provided by deflecting flow downward is an inefficiency of a wing.

An inefficiency you say? YES! Because the other side of the vortex pushes air UP. It takes energy to do this. That energy is taken away from the pure pressure differential of the idealized 2D wing. This is why a 3D wing always has less lift than a 2D wing (at least within linear theory).

This is the exact opposite of how a jet propulsion system works. In a jet propulsion system, force is created by momentum transfer. Any additional force provided by a pressure differential between the exit plane and the atmosphere is an inefficiency.

Ken,

The reason that your statement is false is a consequence of the definition of a fluid. A solid can support a force by deforming. If I push on the end of cantilever beam, it bends a certain amount, just enough to balance the force, and stops. A fluid can not do that. Apart from the special case of a confined fluid, like the hydraulic fluid in a cylinder, a fluid must continue deforming to support a load. An unconfined fluid, like the atmosphere, simply cannot support a force, like the weight of a plane, without flowing. This is absolutely fundamental to the nature of a fluid, and is absolutely not a matter of inefficiency of the wing.

banktoturn

But that is exactly why it works, the fluid is flowing... over the surface of the wing, constantly deforming. If your airplane stops, there is no pressure differential created and bye bye birdie!

There MUST be a force pushing the plane forward to create this differential. This is how airfoils work.

Ken,

You are incorrect. I need to back up to your previous post. You said:

Any -additional force- provided by deflecting flow downward is an inefficiency of a wing.

This is wrong. The net force exerted by the wing, which is the integral of the pressure difference between the top and bottom surfaces, must cause the downward deflection you mention, no matter how efficient the wing is. It is this downward deflection that causes tip vortices to be created as long as the wing is lifting. Remember the Helmholtz theorem. You mentioned the bound vortex which must persist as long as lift is being created. You can't have that without the tip vortices, as required by the Helmholtz theorem, and they can't have different strength either.

banktoturn

Yes, but as discussed before, this is balanced by upwash in front of the wing... providing NO net momentum.