Is there a maximum possible size for an airplane?

Question

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

Answer 1

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):

to this (source):

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.

Answer 2

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.

Answer 3

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?

Let's 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 let's 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 too 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 let's 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.

Answer 4

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.

Answer 5

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'

Answer 6

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.

Answer 7

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.

Answer 8

There is no theoretical limit, given a large enough planet with a large enough population. But there are several practical limits.

Weight scaling

Most significant, and badly misunderstood by several answers here, is the issue of weight. Where a bird is a solid object and scales with the cube of its span, an aircraft is a hollow shell, a surface, and so it actually scales with (nominally) the square of its span. This has important implications.

• Ignoring Reynolds number, a wing profile can only support the same loading (weight per unit area) at any scale. Double the dimensions mean four times the area so four times the lifting capacity.
• With the same wing loading, the stressed skin need be no thicker. So it only weighs four times more.
• An I-spar doubles in depth. Strength of a given amount of material increases with the square of its depth, so it can carry four times the stress, which accounts for the aircraft weight, for the same amount of material. Except, the spar is now twice as long. The stress is also proportional to that, so it doubles. So you need twice the cross-section, twice as long, making the spar four times the weight in all.

So theoretically the size can be increased indefinitely, with the number of passengers increasing with the square of the wingspan. But eventually, practical limitations kick in.

One problem is that the skin needs more stiffeners (ribs and subsidiary spars) to stop it wrinkling. These must themselves be braced by more cross-pieces. These cross-pieces must be stiffer to cope with being twice as long. The web of an I-spar (the vertical bit) is an example. Designers cope by keeping the various members spindly and adding more subsidiary stiffeners to hold the main ones in position, a technique known as increasing cellularity - everything inside is a skeletal fabrication, there are few solid sheets any more.

But the practicalities of manufacturing and materials limits how far you can go with all this, and it is expensive. Unless you are very crafty, you soon reach a point where adding another level of stiffeners also adds another level of weight. So at some point the design can go no bigger, and weight starts to creep up as corners are cut (or, rather, filled in!) to ease manufacture and costs.

Control surfaces

There is also a problem with the control authority and responsiveness of large aircraft. An aileron four times the area will exert four times the control force. The wing has four times the weight, so it accelerates at the same rate. But it also has twice as far to move in order to reach the same bank angle, so it takes longer to get there. If no control system changes are made, the plane will respond sluggishly and pilots must make decisions early. This can be dangerous if an instant flight correction is required.

So large aircraft have extra flight control surfaces added, such as wing spoilers, inner flaperons, larger tail surfaces and the like. Clearly, there is a limit to how far one can go in chunking out ever more, ever bigger pieces of an ever wider-span wing, while keeping it structurally stiff. Moreover the bigger control surfaces suffer the same problem with sluggish response times.

Systems creep

All this brings further issues over the amount of control, monitoring and related equipment carried in order to fly the plane. Landing wheels tend to become more numerous rather than just larger. Complex and massive control surfaces and landing gear need complex and massive control systems, bigger payload space tempts the designer to a more complex interior fit, cubing the air can cube the provision of fire suppression, ventilation and conditioning, and so on. In practice, large aircraft scale rather more than the square of the span, though far less than the cube.

Operations

Next, there is the problem of where to take off and land. The chief designer of the Airbus A380 has explained that it has winglets mainly because longer wing tips would not have fitted modern airports. The Stratolaunch Roc has the largest span of any plane to have flown, and only a handful of US air bases are large enough to take it. Howard Hughes' Spruce Goose was a seaplane so all it needed was open water - but that's an awful lot of water to check for floating logs and other debris. So you have to find somewhere that other people will still help you do stuff on such a grand scale.

And finally there is the marketplace. Even before Covid the 747 had ceased production and the A380 was winding down. Airlines were buying smaller planes because customers wanted more frequent services on more routes. Stratolaunch have resorted to building their own payload, a spaceplane. You would have to know where your payload was coming from too.

Answer 9

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.