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Is there any theoretical or practical limit to the maximum number of passengers - and therefore size - one can build an airplane for?

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    $\begingroup$ hmm, approx 7Bn, as any more than that would be wasteful and unusable. $\endgroup$ – Jamiec May 6 '16 at 15:21
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    $\begingroup$ With all due respect, I don't understand the down votes or the votes to delete. It seems to me to be a perfectly legitimate question borne of curiosity from one who is not in the aviation field. $\endgroup$ – Terry May 6 '16 at 16:17
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    $\begingroup$ @Terry Definitely! And the first time I saw an A380 up close, my first thought was "that's crazy, how much bigger can they make these things?" $\endgroup$ – Pondlife May 6 '16 at 16:39
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    $\begingroup$ There have to be structural limits beyond which material just won't hold up, or will be too heavy to fly. There is also a limited amount of atmosphere to fly in. Seems kind of like a Worldbuilding question but I think the subject fits well here. $\endgroup$ – fooot May 6 '16 at 18:13
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    $\begingroup$ @FreeMan: Regardless of the materials, I think you reach a practical limit when you have to start giving your wings a downwards curve so the tips don't stick out of the atmosphere :-) $\endgroup$ – jamesqf May 6 '16 at 18:47
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Yes, there is an upper limit, but that upper limit might change with technological innovation.

An airplane flies because of the lift coefficient $L=\frac12\rho v^2 A C_L$, with $v$ the airspeed, which is a combination of the speed of the plane and the wind speed, $\rho \approx 1 \, \text{kg m}^{-3}$ at a theoretical mimimum of 5 km height (remember that most planes reach 10 km, but I took this a little more extreme to show an upper limit), $A$ the area, and $C_L$ an coefficent with a typical value less than 2, that might change with technological innovation.

So the only factors we can influence are $v$ and $A$. However, if we increase $A$, the mass $m$ increases faster than the area $A$ because there is more material needed to avoid the plane form breaking under the huge forces. Increasing $A$ quadratically gives more than a quadratically in $m$, and hence in the needed $L$.

If we increase $v$, we need more fuel. The amount of fuel per distance unit increases linearily in $v$, because it increases quadratically per unit of time in $v$. Hence $L$ increases quadratically where $m$ only increases linearily. This means that we might do something with increasing $v$. That means that airplanes have to go faster before liftoff, which will need drastically longer takeoff lanes. Note that we can't keep increasing $v$ because we can't lose control.

In summary, things we can improve are $v$, the speed, $C_L$, with technological innovations and $\rho$ by lowering flying height. However, it is not practical.

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    $\begingroup$ You can't naively apply scaling rules like this. Scaling rules assume that certain things stay constant, e.g., the shape of the object. There is no reason to make such an assumption. $\endgroup$ – Ben Crowell May 7 '16 at 22:00
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    $\begingroup$ I won't pretend to understand the equation, but I do recognise the square-cube law when I see it, and I think it should be explicitly named and a relevant resource linked to. $\endgroup$ – Pharap May 8 '16 at 14:45
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    $\begingroup$ @Pharap It is not really the square-cube law. It can also be less than cubic (that was a bad assumption on my point, so I edited my answer), but it is certainly more than quadratic, because there is really extra material needed to increase strength. As Ben Crowell points out, the shape can change, as in Peter Kämpf's answer. However, we can't to that with, say, four planes, because it is likely to break in the middle, unless we add more materials and hence more mass to make it stronger. $\endgroup$ – wythagoras May 8 '16 at 14:50
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    $\begingroup$ @wythagoras I think the square-cube law is still worth a mention at least. The actual values might not be completely cubic due to shape change, but the relation to the square-cube law might make the explanation easier to understand for those less well-versed in mathematics. $\endgroup$ – Pharap May 8 '16 at 15:00
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    $\begingroup$ The size and shape of aircraft often are decided by other things besides efficiency. For instance, the Super Guppy, which was designed to carry ungainly loads like rocket boosters. Someone I once knew flew on an empty Super Guppy and played touch football while the plane was in flight. d2rormqr1qwzpz.cloudfront.net/photos/2015/07/08/… $\endgroup$ – Howard Miller May 10 '16 at 21:48
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It is no accident that the biggest birds are flightless. The ability to fly goes down with increasing size, so there is also an upper limit for aircraft. The main reason is that as size increases, masses go up with the cube of the size increase while the load-carrying structures like wing spar cross sections only grow with the square of the size increase. This power law is the simplest of the scaling laws.

Since the loads on an aircraft's wing depend not only on its size, but also on many more parameters (angle of attack, speed, aspect ratio …), there is no clear boundary, and advances in materials help to shift the size limit up. If one would try to build the biggest airplane in the world, the wingspan could easily be double of what todays biggest airplanes measure, but the utility of this airplane would be very limited.

Using this airplane for passenger travel would add more restrictions like the number of emergency exits and the maximum distance to the nearest exit, but this could be overcome by using several smaller fuselages. A double-hull airplane would also spread out the payload weight, so the wing would experience a reduced root bending moment. Going from this (source):

He-111H in flight

to this (source):

He-111Z in flight

would immediately raise the size limit substantially. However, it would require new, wider runways to take off from. And adding more fuselages to the same wing will run into flutter problems soon.

The next indication could be designs which have been studied and deemed feasible but were eventually not built for economical reasons. Here the biggest are ground effect vehicles: Flying slowly in dense air pushes the size limit up. The Boeing Pelican was planned with 152 m wingspan, and Beriev proposed one with 2500 t take-off mass and 125.5 m wing span.

I would guess that a wingspan of 200 m is still feasible, and when spreading the weight even 500 m should be realistic, but totally unpractical. Taking a lesson from history, this would be a multi-hulled flying boat which flies in ground effect, similar to the (mono-hulled) biggest aircraft record holders in the 1920s.

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    $\begingroup$ As your second picture shows, there's theoretically no limit: you can keep tacking wings, engines, and fuselages on forever. However, as the crashes of experimental high-aspect-ratio aircraft have shown, keeping everything coordinated is a bit tricky, as your airplane no longer acts like a rigid structure. $\endgroup$ – Mark May 7 '16 at 1:21
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    $\begingroup$ @Mark When your plane is so big you have to take into account the curvature of the earth from wing tip to wing tip, you're in a whole new realm of engineering. $\endgroup$ – corsiKa May 7 '16 at 2:51
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    $\begingroup$ @corsiKa True, but it is still a realm of engineering, rather than physics. From a physics standpoint, it's possible. From an engineering standpoint, it's completely impractical. Also, I think curvature of the Earth is the least of your problems if you're trying to build the aircraft described in Dave's answer. $\endgroup$ – reirab May 7 '16 at 16:01
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    $\begingroup$ @reirab But then you have the limit impressed by going full circle around the earth Maybe you could go around a few times, like a corkscrew -- but at some point, you'll fill all the gaps and can't go around any more. So I guess the theoretical limit of an airplane is a Dyson Sphere? :) $\endgroup$ – yshavit May 7 '16 at 16:16
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    $\begingroup$ @yshavit Once you go all the way around Earth, it's not really an airplane anymore. Even that isn't the theoretical limit to the size of an airplane, though, as there are planets much larger than Earth which have atmospheres. $\endgroup$ – reirab May 7 '16 at 16:25
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Theoretically, unlimited (well bigger than is practically necessary)...

TL;DR

Airplanes scale fairly well and it would be physically possible to build and airplane of just about any size. Granted there are some things that come into play from a structure standpoint but there are surely ways around that. You may have to stray away from the traditional single fuselage, two wing and empennage design but none the less.

There are lots of realistic factors that will stand in your way before you even need to design such a plane.

  1. You don't have enough money to build such a plane
  2. Boeing does not have enough money to build such a plane
  3. Juan Trippe has no interest in such a plane so there is probably no reason to build it.
  4. There are no runways that could handle such an aircraft. Planes like the A380 and 747 are already route limited by runway length/weight capacity. You would need to modify runways to handle anything significantly bigger. That is of course assuming that it lands in a similar fashion to most airliners (i.e. not VTOL)
  5. What route is it going to fly? Planes are not the size they are because we cant build them bigger, they are the size they are because the routes dictate them being such a size. Do you really need to move 1,000 people on a given route at once? How many routes have this much travel density?

Lets look at this hypothetically, Jamiec makes an excellent point that a plane that has the capacity in excess of 7Bn would be kind of useless so lets take that as a maximum. XKCD what if covers this in a similar question and estimates that shoulder to shoulder all the people on earth take up roughly the size of Rhode Island. For the sake of argument lets say that you would need seats and toilets and what not for this many people so to fit everyone on earth in a plane you would need maybe twice the size of Rhode island or a bit more. Unlike that question we can build up so a 4-8 story (or any amount) of plane would be plausible. The average FAA person weighs about 180 lb (81.65 kg) so you would need to lift

1,260,000,000,000 lb Or 630,000,000 tons (572,000,000,000 kg or 572,000,000 metric ton )

To provide a frame of reference the A380 has a maximum structural payload of 330,300 lb (149,822 kg). Keep in mind this is only payload, you also need to lift the weight of the airframe, engines, and fuel (if you actually want to go anywhere). So basically you would need a multi level plane close to the size of Rhode Island that had most of the combined thrust available on the planet and enough liquor to keep everyone calm for the flight.

The structural issue in some regards boils down to wing loading. One commonly self imposed limit these days is that most planes are typical low wing cantilever monoplanes so we view things in relation to that. In other words the fuselage may stress about the wing mounting points and the wings are generally long and low but there is nothing preventing us from using an alternate design with multiple wings or a full lifting body design to accomplish the structure we need. As such the idea of big wings can be overcome and historically this is how the problem was solved in early aviation (tri-planes etc...) The weight issue (from a practical standpoint) is something we concern ourselves with for efficiency reasons. If we are just building a giant plane we can use jets, rockets and all manners of high thrust devices for the purpose of science. You could fly a cement plane if it was shaped right and you had enough thrust.

Remember if Thrust > Drag and Lift > Weight you will fly (I learned this the first day in flight school). Doing so in a controlled and organized manner took significantly more time to learn....

-- Edit --

Since the question has been edited to involve the passenger count there are other issue that crop up.

  1. You need to realistically load and unload the plane which takes time. A plane that takes to long to load and unload will not be economical to operate.
  2. Weight (Americans are getting fat) (see above)
  3. You need a reason to move that many people that far all at once.
  4. Depending on flight length you need to consider food, water, and restrooms to accommodate everyone (waste tanks are not infinitely large).
  5. Are there even enough people in one place. Planes move people (and often stuff) from one place to another but lets take NYC for example which has a population of about 8.5 million people the chances that all of them are going to the same place at once is near 0%. So you don't need an 8.5 million passenger plane, but you can start a bit smaller.

From an airline standpoint (The people actually buying) planes like the 747 are already big enough and expensive enough. The 747 nearly bankrupt Boeing at the time but has had a fairly successful run since. The A380 is fairly new but it will be interesting to see how it changes the game.

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    $\begingroup$ We could always go back to really big flying boats :-) $\endgroup$ – Dan Pichelman May 6 '16 at 16:30
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    $\begingroup$ To save time Googling for those unaware of Juan Trippe, he was the founder and CEO of Pan American World Airways, and he wanted something bigger than the 707. He famously told Bill Allen of Boeing concerning the proposal to build the 747, "If you build it, I'll buy it". Allen replied, "If you buy it, I'll build it." $\endgroup$ – Terry May 6 '16 at 16:39
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    $\begingroup$ The XKCD What If answer that you cite addresses your point 3. We need a plane that size to get everyone out of Rhode Island after they all find themselves standing there shoulder-to-shoulder. $\endgroup$ – Mike Scott May 7 '16 at 8:50
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    $\begingroup$ Concerning waste tanks: I guess as your plane size approaches the Rhode Island size, its total waste tank size may approach zero, since the contents could just be vented out without the problem of affecting non-passengers... 3:-) $\endgroup$ – fr13d May 7 '16 at 14:42
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    $\begingroup$ The first bottleneck is a SECURITY check time, we already experience it, and it needs to be solved first. Key observation -> "A plane that takes to long to load and unload will not be economical" $\endgroup$ – kubanczyk Dec 6 '16 at 9:51
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Certainly a plane can't be bigger than Earth. I would even say 10 miles long aircraft is quite useless, because you need to have some transportation inside of it to deliver all passengers on theirs seats. An airport for keeping such places should be also a big. Therefore limitations are coming not from weight/lifting power, they are coming from practical uses of such big planes.

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    $\begingroup$ It sounds crazy, but what about an airplane that has the form of a circle and circumvents the Earth? $\endgroup$ – descheleschilder May 6 '16 at 23:54
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    $\begingroup$ @descheleschilder That's called a Dyson Ring. You'll want Space Exploration Stack Exchange or World Building Stack Exchange for more information on those. $\endgroup$ – corsiKa May 7 '16 at 2:50
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    $\begingroup$ There is nothing in the question which limits the plane to flying over an Earth-sized planet. A plane could designed and intended for flight over a much larger planet (e.g. Jupiter). $\endgroup$ – Makyen May 7 '16 at 9:48
  • $\begingroup$ @Makyen, I doubt Jupiter's atmosphere could be described as "air", so airplane might then not be the exactly correct term :-) Oh boy, now we are getting into astronomy: what size planets could sustain an air-like atmosphere.... $\endgroup$ – fr13d May 7 '16 at 14:47
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    $\begingroup$ @descheleschilder At that point, can it really be called an aeroplane? Circumventing the earth would make it impossible to land, thus it would either need constant fuel or it would have to orbit the earth (outside the atmosphere). It would also have to be very carefully planned as the Earth isn't spherical. As corsiKa said, that's a question best asked at World Building, since this is getting into the realms of speculation and fantasy. $\endgroup$ – Pharap May 8 '16 at 14:49
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A flying city, such as those proposed by Georgii Krutikov.

As most of the problems seem related to taking off and landing, best probably would be to keep such a giant plane constantly airborne, very high where the air is more stable and compose of multiple modules that could take off self-dependently and then join that bigger "flying castle" - like a space station. Docking seems tricky but should be possible as areal refueling is possible.

This castle could be solar-powered or nuclear-powered, for instance.

It is more difficult to think what would be the use of it.

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The Convair XC-99, cargo and passenger version of B-36 bomber, was rejected by airlines, they say, because airports were not prepared to handle over 200 passengers and their luggage disembarking at the same time, one of the main problems in the giant Airbus may be that it's close in undercarriage width to some airstrips, you remind an aircraft carrier ship deck take off and landing when watching an Airbus 380.

The type of take-off and landing of Saab Viggen, designed to eventually operate from Swedish highways, is not acceptable for commercial flights, and the marginal vortex in the tips of Airbus 380 is so powerful, that the airport must be closed for some minutes after one of these giants used it, in order to avoid an smaller airplane being send down when entering the turbulence, thus limiting the whale airplane advantage in passengers per day in this airport.

Regarding huge size flying machines, you may have to look at Sci-Fi and UFO writers, eg., 'Rendezvous with Rama', or the case of a commercial flight pilot, if I remember well, going from Barcelona to Pamplona, in Spain, who watched an stationary round cloud hovering high over a dam lake, that draw his attention, and reported requesting permit from air traffic control tower to turn 360º around the cloud. He concluded the cloud wasn't a cloud, but a metallic object one and a half kilometers in size (sorry, I don't know if it was diameter or circumference), this is really much bigger than the Kalinin K-7, a heavy bomber built in 1933, that crashed for an structural failure of because a mid-air collision with a smaller airplane.

Who knows what the future may be in airplane size?

In the end, as in the movie: 'The yellow Rolls-Royce', 'Tomorrow never comes'

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(source: h-cdn.co)

This is about as big as you can build a conventional airplane. The weight of the wing requires a downward wing slope, which cannot be sustained for larger sizes.

Assuming away that constraint, we run into other problems. With perfectly laminar airflow, a wing can be extended infinitely. In reality, though, there will be minor irregularities which will strain the wing.

This is a YB-49. It later broke apart in flight due to materials strain from a dive.


(source: check-six.com)

The exact math would be difficult, because of the complexity of fluid dynamics. But I don't think you could build a mile wide airplane without it tearing apart in the first flight.

A helicopter or rocket is a different matter, because it does not require a wing.

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  • $\begingroup$ This is about as big as you can build a conventional airplane the other answers here suggest otherwise... could you provide more detail on your reasoning? $\endgroup$ – fooot Sep 22 '16 at 14:32
  • $\begingroup$ I see phrases like the wingspan could easily be double of what todays biggest airplanes measure albeit realistic, but totally unpractical. So while not a mile long, its still significantly larger than we have today. $\endgroup$ – fooot Sep 22 '16 at 15:16
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    $\begingroup$ The anhederal nature of the AN225 wings has nothing to do with their weight. $\endgroup$ – Jamiec Sep 22 '16 at 16:01
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    $\begingroup$ The strain means that the wing material is in the plastic region and ready to collapse. I wouldn't build a bigger plane than that. $\endgroup$ – Bob b Sep 22 '16 at 16:17
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    $\begingroup$ A helicopter without a wing would fall very quickly... $\endgroup$ – DaG Dec 26 '17 at 14:16
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The limits you are asking about have been pushed by the antonov. Anything bigger than that is certainly possible but not very much economical and may not be safe. While the global economy is in melting ice and a few solid patches here and there it would be a very unsuitable experiment to justify. Rather diverting the funds to improving the current airplanes may have a better result compared to an increase in size.

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    $\begingroup$ Welcome to aviation.se. While your considerations are correct, I feel that your answer lacks in detail. I encourage you in editing it and expanding it. $\endgroup$ – Federico May 8 '16 at 8:22
  • $\begingroup$ The first two sentences discuss the question, the other sentences are less relevant. $\endgroup$ – Pharap May 8 '16 at 14:55
  • $\begingroup$ Amazing how a potential development can be discussed without highlighting the economic impact. It remains relevant even when some do not want to accept it. $\endgroup$ – Stanley Nyadzayo May 8 '16 at 15:06
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    $\begingroup$ Economic reasons are undoubtedly important but the question didn't ask about economic limits, it asked "Is there any theoretical or practical limit" which suggests the question is about engineering limits more than political, social, legislative, economic or other types of limit. $\endgroup$ – RedGrittyBrick May 9 '16 at 11:14
  • $\begingroup$ Just for clarity, my question is purely out of curiosity, but I surely don´t want airplanes actually getting bigger and bigger or that there will be more and more built. But that´s another topic. $\endgroup$ – descheleschilder May 10 '16 at 6:24
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A larger aircraft could exist as basically 2 aircraft glued loosely together side by side with flexible joint and computers to carefully manage engines and controls to keep all the pieces from breaking apart... you could extend it by making entire aircraft a flexible wing that follows curve of earth.

A larger aircraft could be mostly a "lighter than air" airship that is a little heavier than air and using "lifting body" forward motion to get the extra little bit of lift needed to rise.

"Limits" can be overcome but end result becomes less and less practical beyond a certain size.

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  • $\begingroup$ In conventional world the practical size is dictated by typical airport runways. $\endgroup$ – David Kay Sep 12 '17 at 9:33

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