flyboyseven
Topic Author
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### Is There A Theoretical Max/min Wing Size?

This was a random wondering I had while laying in bed at 1:30am last night. I would, with my limited knowledge as a newbie pilot figure that there would be a min size for sure, and probably a max size too.

For the minimum size, I would figure that one would reach a size where the relative size of the wing to the air molecules would be too small. You would reach a point where a molecule of air would simply smack into the wing, and just sorta bounce off. That is kinda just a random pondering, and not really useful to anything, but the max size is.

For that, would you reach a size where the wing is so large that the airflow cannot remain laminar long enough to create the required lift? or would it be exactly the same as a more common sized wing, just bigger? I can argue both sides, but as I said, I don't really have too much knowledge into this area.

Any thoughts, or facts for that matter?

Cheers,
Graham
As long as the number of take-offs equals the number of landings...you're doing fine.

vikkyvik
Posts: 12112
Joined: Thu Jul 31, 2003 1:58 pm

### RE: Is There A Theoretical Max/min Wing Size?

 Quoting flyboyseven (Thread starter):For that, would you reach a size where the wing is so large that the airflow cannot remain laminar long enough to create the required lift?

Airflow over a wing doesn't tend to be laminar all the way to the trailing edge. In fact, having a turbulent boundary layer helps keep the airflow attached to the wing.

If you're talking about a theoretical wing that isn't mounted on an airplane, I'm not sure there would be a maximum size. Obviously, for a practical wing attached to an airplane, there are considerations of weight, structure, etc.
I'm watching Jeopardy. The category is worst Madonna songs. "This one from 1987 is terrible".

flyboyseven
Topic Author
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### RE: Is There A Theoretical Max/min Wing Size?

I know that the airflow is not laminar even nearly all the way, depending on the wing, but i was thinking that you might reach a size where the wing would become just too big for the air to wrap around it in a way that creates lift. I thought it might become like a big blunt edge that just pushes the air out of the way.

And again, this is a poorly formed idea i had while lying in bed in the middle of the night.

[Edited 2010-03-22 09:40:00]
As long as the number of take-offs equals the number of landings...you're doing fine.

ANITIX87
Posts: 2983
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### RE: Is There A Theoretical Max/min Wing Size?

I think there are two questions at work here.

1) For a given airfoil section, is there a maximum size at which is becomes too inefficient or even ineffective?

2) For ANY airfoil, is there a maximum size allowed?

Question 1: No, I'm not sure there is, though I imagine it would take come actual testing to be sure. An airfoil's coefficient of lift is NOT dependent on size and, therefore, would allow the airfoil to generate lift at any scale (theoretically, and assuming dimensional similarity). Whether, in the same medium, at the same speed (and therefore Reynolds Number), an exponentially larger wing (let's be ridiculous and assume a thickness of 100 meters) will provide the same lift characteristics as a wing with a thickness of 0.5m, I can't answer. Someone who does this for a living would be able to answer more effectively. It could be that I'm completely wrong.

Question 2: In short, no. If the above answer does have a limitation, then you would have to change your airfoil shape (increase the curvature of the leading edge, for example) to ensure good flow characteristics. If the above answer has no limitation, then we've already addressed this question.

Don't take my post as gospel. Wait for someone like tdscanuck (or the other industry guys on here) to correct me, first!

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

### RE: Is There A Theoretical Max/min Wing Size?

 Quoting ANITIX87 (Reply 3):Whether, in the same medium, at the same speed (and therefore Reynolds Number)

That's not quite correct as you have stated it. Reynolds Number, as applied to wings, has the chord of the wing as one of its factors. The equation (if I remember correctly) is:

Re = (ρVL) / μ

where ρ = density, V = velocity, L = characteristic length (in this case, the chord of the airfoil), and μ = coefficient of viscosity

So to maintain similar flow conditions, for a wing that has twice the chord, you need flow that is half as fast.

With that in mind, there actually will be a difference in the flow as the wing gets larger and larger, if you keep the flow velocity the same. Eventually, as the adverse pressure gradient got larger, the flow might separate.
I'm watching Jeopardy. The category is worst Madonna songs. "This one from 1987 is terrible".

tdscanuck
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Joined: Wed Jan 11, 2006 7:25 am

### RE: Is There A Theoretical Max/min Wing Size?

 Quoting flyboyseven (Thread starter):For the minimum size, I would figure that one would reach a size where the relative size of the wing to the air molecules would be too small. You would reach a point where a molecule of air would simply smack into the wing, and just sorta bounce off.

This was actually Newton's original explanation for how lift worked...it's completely wrong in all but a rarified gas, but for very very tiny wings (or very large ones in very sparse gases) it still works, and you do get lift. Just not nearly as much.

Once you're smaller than a few mean free molecular paths, you'll have almost no control over the direction of the lift though (Brownian motion will overtake your lift unless you're going supersonic).

 Quoting flyboyseven (Thread starter):would you reach a size where the wing is so large that the airflow cannot remain laminar long enough to create the required lift?

You can reach a size where the airflow cannot remain laminar; you can't reach a size where you can't create lift (assuming infinite amounts of space, air, materials, etc.).

 Quoting flyboyseven (Thread starter):or would it be exactly the same as a more common sized wing, just bigger?

Pretty much.

 Quoting flyboyseven (Reply 2):I know that the airflow is not laminar even nearly all the way, depending on the wing, but i was thinking that you might reach a size where the wing would become just too big for the air to wrap around it in a way that creates lift.

As you get larger, viscous effects (including laminar flow) become less important. For extremely large wings, they disappear to zero and you end up with flow that very nicely approximates the inviscid assumptions that your aero prof told you never happen in real life.

 Quoting ANITIX87 (Reply 3):1) For a given airfoil section, is there a maximum size at which is becomes too inefficient or even ineffective?

No.

 Quoting ANITIX87 (Reply 3):2) For ANY airfoil, is there a maximum size allowed?

No.

 Quoting vikkyvik (Reply 4):That's not quite correct as you have stated it. Reynolds Number, as applied to wings, has the chord of the wing as one of its factors.

It doesn't have to be the chord, it just has to be be some charachteristic length. Chord is logical one to use for wings, but it's not required. However, whatever length you use, the Reynolds number will go up with size. Since Reynolds numbers are basically the ratio of intertial to viscous forces, high Reynolds number equates to flows where viscosity is mostly irrelevant, which causes them to become size-insensitive.

 Quoting vikkyvik (Reply 4):So to maintain similar flow conditions, for a wing that has twice the chord, you need flow that is half as fast.

Yes (or change viscosity or density, but that's annoying).

 Quoting vikkyvik (Reply 4):With that in mind, there actually will be a difference in the flow as the wing gets larger and larger, if you keep the flow velocity the same. Eventually, as the adverse pressure gradient got larger, the flow might separate.

The adverse pressure *gradient* gets smaller as the wing gets larger. The total pressure differential is size insensitive (as long as we're talking real-world sizes and speeds), and the distance is getting larger as your wing gets bigger, so the gradient gets shallower.

Aerodynamics, except at very small sizes, assumes continuous fluid. The larger you get, the faster you go, and the thinner your fluid, the closer you get to approximating perfectly continuous inviscid flow. As a result, there's no upper size bound, since all the size effects drop away as you get bigger.

At the small end (low Reynolds numbers) the physics change a lot, viscosity and laminar flow start becoming very important, and things get weird. This is part of the explanation for why insect wings don't look like they should work.

Tom.

vikkyvik
Posts: 12112
Joined: Thu Jul 31, 2003 1:58 pm

### RE: Is There A Theoretical Max/min Wing Size?

 Quoting tdscanuck (Reply 5):The adverse pressure *gradient* gets smaller as the wing gets larger. The total pressure differential is size insensitive (as long as we're talking real-world sizes and speeds), and the distance is getting larger as your wing gets bigger, so the gradient gets shallower.

Ah, I didn't think that one through! Thanks.

 Quoting tdscanuck (Reply 5):It doesn't have to be the chord, it just has to be be some charachteristic length.

I know - that's why I said:

 Quoting vikkyvik (Reply 4):L = characteristic length (in this case, the chord of the airfoil)

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sovietjet
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Joined: Sat Mar 15, 2003 12:32 am

### RE: Is There A Theoretical Max/min Wing Size?

 Quoting tdscanuck (Reply 5):At the small end (low Reynolds numbers) the physics change a lot, viscosity and laminar flow start becoming very important, and things get weird. This is part of the explanation for why insect wings don't look like they should work.

Very true. When we got to this part of study last semester it was quite interesting(and hard)

ajd1992
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### RE: Is There A Theoretical Max/min Wing Size?

Does wing size affect your theoretical top speed as well, no matter the power? What I mean is, even though the frontal surface of the wing is still minimal, does the wing area change it? I understand the more towards your Vne speed you are, the aircraft wants to pitch over.

I mean the F-104 had tiny little wings that meant it landed at 170kts+, but it flew like a bullet as well. A commercial aircraft has comparatively big wings and flies far slower (ignoring the fuselage size).

tdscanuck
Posts: 8572
Joined: Wed Jan 11, 2006 7:25 am

### RE: Is There A Theoretical Max/min Wing Size?

 Quoting ajd1992 (Reply 8):Does wing size affect your theoretical top speed as well, no matter the power?

Not really. For any particular wing, there's an angle of attack to give you just as much lift as you need for arbitrarily large speeds.

When you start going supersonic there are certain shapes (planforms) that will cause you problems, but that's a shape thing, not a size thing.

 Quoting ajd1992 (Reply 8):What I mean is, even though the frontal surface of the wing is still minimal, does the wing area change it?

No. For a given wing area (and weight and configuration) your minimum speed is constrained but, aerodynamically, your maximum speed is not. Maximum speed usually comes from structural issues, or stability & control issues.

 Quoting ajd1992 (Reply 8):I understand the more towards your Vne speed you are, the aircraft wants to pitch over.

This because you get a rearward shift in center-of-pressure as you go trans- and then supersonic. Provided you've got the right controls, you can manage it.

 Quoting ajd1992 (Reply 8):I mean the F-104 had tiny little wings that meant it landed at 170kts+, but it flew like a bullet as well. A commercial aircraft has comparatively big wings and flies far slower (ignoring the fuselage size).

A commercial jet could have F-104-style wings...it would just have to land ridiculously fast too. What you're seeing there is a product of design trades for different missions more than it's an inherent speed limit.

Tom.

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