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Airships are cool, and I would love to use them and see them used outside of steampunk a lot more. One key aspect of Airships is that they seem to have the square cube law reversed. For other things in the world they'll be able to carry less weight the bigger they are while Airships will have more gas volume and more lifting capacity because of it.

At first glance that might mean that Airships can be almost unlimited in size. But there are (potential) limiting factors. For example the Hindenburg needed to vent large quantities of its lifting gas as it crossed the atlantic to prevent gliding off too high as it burned fuel and became lighter during the trip. There's also the structural stength of the frame to consider, as forces from the engines, wind and steering will need to be supported by the Airships envelope or risk breaking apart.

The question I'm asking is: what is the (approximate) maximum size an airship could be?

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Lockheed Martin is currently releasing a prototype for a new range of airships that are designed from scratch to be the biggest in the world. The LMH1 is an airship capable of lifting 20 tonnes of cargo, but they also state that the design can scale up to a carrying capacity of 500 tonnes.

Why 500 tonnes? Why not 5,000? I don't know the answer to that although I suspect that it's a matter of practicability - despite the inverse square cube law applying as you rightly point out, there reaches a point where even the most powerful engines can't compete with the sail area such a volume represents. Also, helium is a valuable and non-replenishible resource; there are already many doctors out there arguing that helium should be restricted for use as a medicine so that we don't run out of it. Getting that much helium together for an airship in the future may well be the limiting factor because of the cost of the gas. That said, you wouldn't vent it to manage ballast weights, you'd just pump it back into high pressure containers for reuse, but I digress.

Of course, one of the other limiting factors is size. Once you go beyond 800m in length, the practicality of storing or hangaring such a machine can become problematic. Not to mention getting cargo to it while it's inflating its air bladder with helium, and how long it might take to in/deflate that same bladder. There is also the fact that going beyond that size actually makes mountains a hazard if it can't maneuver through ranges and the like, and while I have no hard data on this topic I suspect that the bigger it becomes, the larger the engines need to be to counter wind resistance. In other words, while the square cube law works in its advantage in terms of weight, it doesn't in terms of friction with the wind. To move such a craft through normal atmospheric pressures might take more engine power than you think.

So, if Lockheed Martin are to be believed at least, then you're looking at around 800 feet in length being the maximum scale of an airship, although the precise reasons why they say that is the upper bound is something you'd have to ask them directly.

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  • $\begingroup$ Many answers I was looking for, wonderful! On the topic of wind resistance: wouldnt a larger ship again benefit from the square cube law? Its surface area where wind can push it compared to its volume become smaller as it increases in size. If the engines can push this mass (not weight) to similar speeds as a smaller airship, then wouldnt a larger airship have less problems with wind? $\endgroup$
    – Demigan
    Mar 26, 2019 at 13:22
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    $\begingroup$ @Demigan well, not really. You can't have it both ways; if the lower density benefits the airship in terms of lift, it also hinders it in terms of thrust. You have more air needing to be displaced, but less mass (and therefore less momentum) with which to do it. Ultimately, you end up with engines actually increasing in size at a higher proportional rate to the volume of the ship to deal with the atmospheric displacement issue, which also causes problems with things like wind shear. Ironically it's the ability to stay still in a breeze that may well be your limiting factor. $\endgroup$
    – Tim B II
    Mar 26, 2019 at 13:35
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    $\begingroup$ @TimBII You have O(n^2) more air that needs displacing, and O(n^2) ship surface area (where much of the mass is), plus a smaller O(n^3) factor of "internal baffels and structure" -- I don't see how the effort to displace air is getting harder, it just isn't getting much easier? $\endgroup$
    – Yakk
    Mar 26, 2019 at 14:54
  • $\begingroup$ Correct me if I'm wrong but square cube law means 2x the size is 8X the volume. Imagine some Airships going the same speed in the same winds at the same heights. Since they are at the same height they'll be of the same density. If you have one airship and compare it to 8 of the same Airships, you have 8X the volume, 8X the carrying Capacity&mass, 8X the engine power to push it and 8X the surface area for air resistance and wind. A ship twice as large as a single airship would have 8X the volume, 8X the carrying capacity and mass, require 8X the engine power and have ONLY 2X! The surface area. $\endgroup$
    – Demigan
    Mar 26, 2019 at 16:01
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    $\begingroup$ @Demigan No, its surface area would scale with n², in your example that 4 times the surface area. $\endgroup$
    – Jonas
    Mar 26, 2019 at 19:39
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TBH I think the question is best answered by focusing on what your airship is meant to DO. For example: The size of modern ships aren't limited by what CAN be built, but rather by the size of the port facilities they want to visit, and by the Panama Canal. The latter wouldn't be relevant for an airship, but the former would. For example, you might be ABLE to build an airship five miles long, but it wouldn't be very practical either as a civilian or military vessel unless you had port facilities five miles long everywhere you wanted to go.

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    $\begingroup$ To add to that - at some point it becomes large enough that you need some mode of transportation to get from one end to the other as walking becomes impractical. At this point I'd say it's impractical to make a single larger airship given you'd need smaller ones just to get around. $\endgroup$
    – Skyler
    Mar 26, 2019 at 15:21
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    $\begingroup$ Well put. If OP has the market for airships capable of lifting a whole refinery there is no technical reason in the way. Height of the atmosphere might be a natural barrier to the z-dimension, though, come to think of it. An airship 100km long going 1 km/h would have about the same Reynolds Number as a 747 btw... $\endgroup$
    – bukwyrm
    Mar 26, 2019 at 15:43
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    $\begingroup$ Another point related to "What does it DO" - After you blow past port sizes for a super large vessel you may find that the vessel Becomes the port. It itself becomes the destination and smaller craft go to it. [Also a few of the old airships already had mini cart systems to make getting from one end to the other easier and safer] $\endgroup$
    – TheLuckless
    Mar 26, 2019 at 15:54
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    $\begingroup$ @bukwyrm Oh, yeah... being able to move the entire refinery to wherever your raw materials are is a pretty useful economic niche. $\endgroup$
    – Morris The Cat
    Mar 26, 2019 at 16:11
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Other posts highlight issues with having to vent the lifting gas. One solution is a hybrid balloon, known as a Rozière, which has a non-heated lifting gas (e.g. helium) and a heated lifting gas (hot air).

This design allows partial control of buoyancy via heating, whilst the bulk of buoyancy is provided by the lighter-than-air lifting gas, so fuel usage isn’t excessive. This might be relevant as you’re presumably looking to lift cargo with your huge airship.

The design is apparently popular for extreme long duration flights (e.g. the Breitling Orbiter 3, and Fossett’s Spirit of Freedom, which circumnavigated the world).

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I believe cluster ballooning can make an airship to get size. With redundancy comes stability in ballooning and size unlimited. Using a centered ballast to control altitude I believe a massive air ship could be used in so many ways from launching interplanetary rockets to living. I had asked a few questions in Space, Physics, Earth science and other SE sites about the limits of an airship. Also, the square inverse law to build an air ship this way using with balloons would be similar to building an upside down pyramid.

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    $\begingroup$ With all due respect, I don't believe any of those questions are relevant to this question. You should edit this to focus on answering the question properly, because right now it just looks like you're trying to promote your own questions instead. $\endgroup$
    – F1Krazy
    Aug 10, 2019 at 18:52
  • $\begingroup$ @F1Krazy I am because I would like the op to look at them and I gave my answer.. Thank you I will make them comments. $\endgroup$
    – Muze
    Aug 10, 2019 at 18:55

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