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There are some agreeably large planes out there, like the C-5 Super Galaxy. But how big can these planes' wings really get?

The heavier the plane, it is usually larger, and with size of the fuselage comes size in the wings (most of the time). But is there a limit to how big you can make your wings?

If you make your wings so big that they're 6 feet thick and an absurd length long, say, for a colossal plane, will those wings provide enough lift? I mean, if the wing gets that big, It not only has to lift the plane, but its own weight then becomes a concern. But, with that weight comes the size. Another issue, is how the aerodynamics work on such a crazy big plane.

The thicker the wing, the more air is contacting the wing. This causes more resistance on the wing at a given chunk than a smaller wing. The question comes from seeing several shows that depict planes so large they're like flying cities, and it just doesn't look realistic to me, the sheer size of those planes.

Pondlife
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Ginger
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    Closely related, perhaps even a dupe? – Pondlife May 20 '21 at 17:49
  • No, my question is actually concerning the wing size, if the wings will work the same at such a size in comparison to the general smaller wings. But thanks for trying to help clear things up! – Ginger May 20 '21 at 17:50
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    The big flying boats had wings a guy could walk through. Assuming that wasn't the tallest guy, the wing would still need to be about 5-6 feet thick at the thickest part. And they flew and flew well. – jwenting May 20 '21 at 18:11
  • If the wing grows large enough relative to the other parts, you end up with a flying wing airplane. At the latest, then your question becomes a dupe. – Peter Kämpf May 21 '21 at 02:25

1 Answers1

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No, there is no theoretical limit to the size of a wing. You could make a wing big enough to lift the entire Earth (assuming, of course, you somehow had an atmosphere to fly it in).

There are, of course, many practical limitations to wing size. The lift a wing develops is proportional to the square of the scale of the wing, all else being equal. However, the weight of the wing (and the rest of the airplane it's attached to, for that matter) is proportional to the cube of the scale. So, if you double a plane's size, the lift developed by the wings goes up four times, but the weight goes up eight times. So, in that case, the wings would need to be even larger compared to the plane in order to lift the added weight. This is referred to as The Square-Cube Law (Wikipedia, Aerospace Research Central, TVTropes). You eventually reach a point where there are no materials strong enough to withstand the stresses imposed on such a massive wing.

HiddenWindshield
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    This is wrong in part. The weight is in fact proportional to the square of the scale, not the cube. A plane is mostly surface and stiffening members. The wing loading, and hence the stiffening stresses throughout, are the same regardless of scale. Only the volume of empty space genuinely cubes up. The ARC guy seems to know more about airships (whose lift does depend on that empty space), but he is partly right about aeroplanes because the stiffening gets increasingly difficult to manage and weight creep does set in. – Guy Inchbald May 20 '21 at 19:05
  • The TVTropes link is bang on. – Camille Goudeseune May 20 '21 at 19:41
  • @GuyInchbald I'm curious about this. The scale, by you mean the size? Isn't there several other factors such as the aerodynamic efficiency of the wing, that make it impossible to simply relate the weight as being proportional to the square of the scale? I may be wrong on this. – Ginger May 20 '21 at 20:13
  • hi @Wasabi It's straightforward, and explained (at incredible length) on the three familiar links given. – Fattie May 20 '21 at 21:26
  • @GuyInchbald No, the weight of anything is in fact proportional to the cube of the scale. If you double the size of the wing, the structural members double in width, length, and height. That's eight times the volume, so if density doesn't change, that's eight times the weight. – HiddenWindshield May 21 '21 at 00:00
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    @HiddenWindshield, not everything has a weight proportional to the cube of scale. For example, over a reasonably large size range, the optimal wall thickness of a cylindrical tank is effectively constant, giving a weight proportional to the surface area (ie. the square of scale). – Mark May 21 '21 at 00:48
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    @GuyInchbald Statistical analysis shows that the exponent of scale for airplane weight is between 2.3 and 2.4. So both of you are only partially right and there is indeed a higher mass increase with scale than the increase in wing area. – Peter Kämpf May 21 '21 at 01:58
  • @Mark Generally, at least in my experience, when you're talking about a hypothetical (such as wings the size of the Earth), then "scale" simply refers to blindly making things bigger (or smaller), as in a "scale model". That's the sense I was using in my answer. If you're going to design something at a different size, then, yeah, the weight isn't going to be exactly the cube of the size. – HiddenWindshield May 21 '21 at 03:45
  • @Wasabi, you are right, it is not quite that simple. The basic scale effect is a structural one which becomes increasingly difficult to engineer at larger scales, hence the intermediate figures noted by Peter Kämpf. Also, the Reynolds number affects the aerodynamics, so an exact scaling of the external profile is probably not what one would do in practice. Then there is the handling responsiveness, which also gets harder as it scales. You might like to ask a more general design question about scale effects, than this one. – Guy Inchbald May 21 '21 at 08:16
  • @HiddenWindshield Your intuitive assumption of scaled-up cross-sections is in fact quite wrong. For example wing loading remains nominally constant, so skin thickness remains constant and large aircraft therefore have proportionately thinner skins. Similar issues mean that the total spar weight scales with the square law too. The difficulty lies in keeping the wing rigid, with the internal structure becoming more complex and spider-webby (sometimes referred to as increasing cellularity); this is the structural aspect that gets harder to engineer at scale. – Guy Inchbald May 21 '21 at 08:33
  • Now that this question has been marked a duplicate, I have posted a fuller answer over there, i.e. https://aviation.stackexchange.com/questions/27401/is-there-a-maximum-possible-size-for-an-airplane – Guy Inchbald May 21 '21 at 12:27
  • @GuyInchbald Well, I think we're just going to have to agree to disagree on this one. – HiddenWindshield May 21 '21 at 13:28