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Airships are interesting vehicles, in that they are, as far as I know, the only ones to turn the square-cube law to their advantage. For a proportional increase X in length, width, or height of the gas bag, the lifting power of the airship increases by a factor of X^3.

Therefore, it would seem that, if you're making an airship, it's better to make one really big one rather than several smaller ones.

As of yet, I can only identify one problem with this, which is that more surface area = more space for wind to push on the ship. However, the effects of this on the ship's structure can likely be solved with aerodynamic design and modern materials, as well as using engines/propellers to counteract the force of the wind.

So - aside from potentially-solvable issues with high wind, what are the structural problems of an airship, whose lifting element is say, a cylinder a kilometer long and 175 meters in diameter?

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  • $\begingroup$ I just want to make absolutely clear what you mean by cylinder. Is it shaped aerodynamically or flat on it's edges? Maybe keep that option open for people to create the airship without that constraint? $\endgroup$
    – Trioxidane
    Nov 14, 2021 at 10:46
  • $\begingroup$ Square cubes maintains density, and the lift will scale with area, so the gains are proportional to X^2 I think. $\endgroup$
    – The Square-Cube Law
    Nov 14, 2021 at 10:50
  • $\begingroup$ @TheSquare-CubeLaw Sure, The lift doesn't scale with area. The area increases, yes, but the amount of force on each unit of area also increases. $\endgroup$
    – KEY_ABRADE
    Nov 14, 2021 at 11:12
  • $\begingroup$ @Trioxidane That can be kept open, yes. The entire airship is shaped aerodynamically; just assume a cylindrical volume for the lifting element. $\endgroup$
    – KEY_ABRADE
    Nov 14, 2021 at 11:13
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    $\begingroup$ If you're filling it with hydrogen rather than helium, then Anton Chekhov will insist it has to explode. $\endgroup$
    – kaya3
    Nov 15, 2021 at 14:10

4 Answers 4

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Zeppelins were "rigid" airships with an internal frame for a very good reason.

Besides all the points mentioned by "the Square-Cube Law" there is the matter of structural integrity of your huge air-ship.
A structure that long is subject to external pressures (of weather) that can vary greatly from one end to the other.
Consider rain/snow: The nose of the airship may be inside the rain/snow already while the stern is still outside the rain. This causes very uneven strain on the whole airship (vertically).
Add wind as well, especially when you are changing course, and you have a (horizontal) wind-shear to deal with that is also uneven.
And a kilometer long is long enough to have local air-turbulence cells act differently on several places of the ship.
This all gets far worse when you get into a storm. And an airship isn't fast enough to outrun a storm-front. You have to be able to ride it out.

So it needs to be able to withstand all that without excessive flexing, torsion, bending or breaking.
That is going to take a lot of internal structure for strength that will add a lot of weight to your airship, reducing your carrying capacity.

We have better materials science today, but your ships are 3x longer than a Zeppelin. It is going to be a real challenge to make one that big and still keep it safe enough for use in anything but the very calmest of weather.

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    $\begingroup$ Gave you a +1, but how about flying higher than storms and such? You have a kilometer long airship, so you could use it for more buoyancy. The wind might be stronger, but I'm guessing generally more even. No rain or snow. Lower air pressure, although you need less gas in the bag again for the lower weight if the air higher up. I still agree the structure would likely fail, but those can help it fail less quickly could it not? $\endgroup$
    – Trioxidane
    Nov 14, 2021 at 12:13
  • $\begingroup$ @Trioxidane: You still have to be able to get through cloud cover on take-off and landing, and there's the problem that the higher you go, the less buoyant the airship is since the atmosphere density decreases. I like the idea off-hand, but I think it's worth doing the maths. $\endgroup$
    – Matthieu M.
    Nov 14, 2021 at 19:11
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    $\begingroup$ @Trioxidane The loss of buoyancy is major at the altitudes you really need (6 kilometers up and higher). And at those altitudes there are very strong winds to deal with (jet-stream). And as Matthieu also mentioned.: You still need to traverse the lower layers of atmosphere to get up to those altitudes or get back down to land. And air-ships are not quick to gain and loose altitude, so you would be stuck in the lower atmosphere for some quite time. So you still need to engineer for low altitude and then you want to add high altitude engineering (like pressure cabins) on top of that. $\endgroup$
    – Tonny
    Nov 14, 2021 at 22:37
  • $\begingroup$ "without excessive flexing, torsion, bending or breaking." Of course breaking is bad, but could we make a floppy airship that happily flexes, torses (?) and bends? It might be difficult to control and probably makes its passengers uncomfortable, but could it work? $\endgroup$
    – Thomas
    Nov 15, 2021 at 12:43
  • $\begingroup$ I'm not an engineer, but could some of the problems you mentioned get solved by splitting one large body into multiple smaller bodies? Like having multiple air balloons instead of one? Perhaps connected in a way where they don't crash into each other but are still mostly independent? $\endgroup$
    – Katai
    Nov 15, 2021 at 14:22
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Speed of sound in metal is very different than in gas. For example the speed of sound in air at room temperature is 330 m/s, while in aluminum is about 6000 m/s.

Speed of sound is also the velocity at which mechanical solicitations propagate into a medium.

This means that a mechanical solicitation, for example a strong wind gust in the nose of the ship, will take only 1/6 of a second to reach the tail in the aluminum frame, but 3 seconds in the hydrogen.

This means you have an internal source of vibrations, on top of the engines. It would be an interesting source of beats and cross talks when the ship is crossing a storm, with all the wind shear involved.

Probably not something dramatically fatal, but surely something of "shot, we didn't think about it when we designed it!".

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  • $\begingroup$ Can this be overcome by dampening vibrations with a clever switch of material in key junction points? (I do believe I've heard about that on bridges, for example) $\endgroup$
    – Matthieu M.
    Nov 14, 2021 at 19:16
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    $\begingroup$ Speed of sound in a metal bar is much lower than in bulk metal, depending on geometry. And speed of sound in hydrogen is about three times of that in air. (Also I think there would be more serious problems in a superbig airship than mechanical resonances.) $\endgroup$
    – dominecf
    Nov 15, 2021 at 9:36
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You only leverage the square/cube law in certain areas, in others, it will bite you.

  • Plus:

    • Have a bubble of lifting gas with a membrane around, double the size. The gas now has eight times the lift, and the membrane now only weighs four times as much (given that it has the same thickness. in reality, you might choose to scale the thickness even by more than 2, which would give you 8+ times the weight...)
    • Wind will only pummel you on your quadrupled surface, while your vessel has eight times the mass, making it less jittery ( but see the minus re: propulsion below)

  • Minus:

    • Have a steel cable, now make it double the size. It is now eight times as heavy, while only having increased its cross sectional area (and thus breaking point) by 4... same with girders and any other structural elements. It is mostly cross sectional area that counts for strength, and that only increases with the square. So you need to design disproportionally thicker, eating into your lift-gains.
    • The possible attachments for propulsion and control machines, and the control surfaces themselves, go with the square, whilst the mass of the controlled thing goes with the cube, making it hard to accelerate and steer.

  • Non-square/cube problems:

    • Ducking out of the wind becomes ever harder. There will be no hangars
    • i doubt this will be allowed within 100km of cities with any higher buildings (let alone skyscrapers) - if this is blown rudderless onto a tall building, that building will give way, without much fight

So the ideal use would be a high-altidude platform that does not need to evade any structures, does not need to land, and does not need to retain location or shape (Zeppelin only needed to retain shape because it was supposed to move through the air - if that requirement falls, and you just move with the air, your structure can wobble)

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Flamability

Any hydrogen container in an O2 rich atmosphere is a ticking bomb. To counter this, a zeppelin should not contain hydrogen as a single blob, but rather hold many smaller containers inside. This reduces the chances of an explosion, and makes explosions more survivable.

Unfortunately for you this reduces your gains from scaling.

Serviceability

The larger the craft, the more hull you have to service. There is more surface that can be eroded, bent or pierced through. It gets more and more expensive to keep it all in working condition as you scale up.

Heat

The lift you get depends on the temperature of the lifting gas. The more gas you need to heat, the more fuel you need to reach a certain temperature, and therefore the moreextra weight you need as you scale. Again, this leads to extra operational costs and diminishing gains.

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    $\begingroup$ @Lemming It seems to me that if solar provided the needed energy, you could just paint the surface black and skip all the electronics and burners altogether. That real hot-air balloons don't do that implies to me that it wouldn't be enough energy. $\endgroup$
    – Cadence
    Nov 14, 2021 at 11:30
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    $\begingroup$ Heat can certainly improve the flight capability, but is not necessary. Especially in rigid airships it only matters if by heating the gas you also let some escape. The envelope doesn't get any bigger, so you rely on the weight reduction from needing less gas. In a hydrogen airship I would certainly hold off on adding heating elements. Many airships simply rely on having a gas packed lighter than air inside a big container. Rigid airships would fly with (near) vacuums if the structure strength would allow it, like proposed on planets with thinner atmosphere. $\endgroup$
    – Trioxidane
    Nov 14, 2021 at 11:33
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    $\begingroup$ @Lemming Oh, I assumed you meant solar panels over the surface of the zeppelin! If you intend to have larger panels extending off the sides, that might be feasible... though it presents its own engineering challenges at larger scales. $\endgroup$
    – Cadence
    Nov 14, 2021 at 12:06
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    $\begingroup$ @Lserni Yes, but unless you can carry out repairs while aloft, the cost of berths, hangars, cranes, etc. goes up rather aggressively with size. $\endgroup$
    – Cadence
    Nov 14, 2021 at 13:46
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    $\begingroup$ Flammability: The Hindenburg was based on a 80+ years old technology. $\endgroup$
    – FluidCode
    Nov 14, 2021 at 14:30

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