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I'm currently writing a military science fiction story set in a post cyberpunk world I've been building. The story focuses on a tank crew, but it also prominently features an enormous airship that functions as a flying airfield or aircraft carrier. I'm trying to get a sense of scale such a ship would have. The nice thing about the square cube law is that it means that doubling the size of an airship octuples its volume.

  • The airship needs to be large enough to carry at least 40 strike fighters with a maximum takeoff weight of roughly 20 tonnes each, and at least two helicopters with a maximum takeoff weight of 10 tonnes each. Plus extra fuel, munitions, and other expendables.
  • The airship uses hydrogen as a lifting gas. I realize this is very flammable, but I think it can be made safe enough through the use of compartmentalization, blow off panels, and lightweight graphene armor to protect against stray shell fragments. I'm also considering helium, it would an even bigger airship, but the reduction in required safety features may make up for this.
  • The airship is propelled using ducted electric fans powered by an onboard anuetronic fusion reactor (less than 1% of the reactor's output is in the form of high energy neutrons.)
  • The airship needs to have 360 degree turret coverage for its point defense weapons systems. It's a big ship, so it will need at least a dozen of these turrets (let's use the Phalanx CIWS as a reference at 6.2 tonnes each)
  • The airship's flight deck should ideally be long enough to land the above mentioned fighters without arresting cables. If they overshoot, they can just fall until they regain enough airspeed to try again. Likewise, there is no need for catapult launches. I'm thinking the flight deck will be suspended below the airship's envelope, with the hangers within the envelope.
  • This airship is not designed to land on the ground. Instead it can be docked to a tower like traditional airships were and resupplied using its own cargo winches.

So, my question is: What would the length, width, and height of airship like this be for it to contain enough hydrogen (or helium) to lift its fully loaded weight of approximately 50,000 tonnes? Assume a prolate spheroid (typical cigar shape) for any volume calculations.

Edit: My sleep deprived brain took the name "square-cube law" too literally. Someone pointed out that burying the reactor and the ammunition magazines deep within the ship would provide adequate protection since if anything penetrates that far, the ship is doomed anyways. My initial reason for using hydrogen was that it is a better lifting gas and is currently far more abundant on Earth than helium. However, given the prevalence of fusion power in my world, helium may be readily available in large quantities. At this point, I'm preferring helium.

I am aware that 50,000 tonnes is half the displacement of a modern super carrier, but those are predominantly made from steel. My airship is made predominantly from woven graphene fiber which is a couple hundred times stronger than steel by weight. The lack of steam catapults, arresting cables, and dramatic reduction in the need for radiation shielding compared to a fission reactor also translates into significant weight savings.

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    $\begingroup$ IMHO this is in-topic here, but you'd have a higher chance of getting an answer somewhere else. $\endgroup$
    – o0'.
    Sep 3, 2015 at 10:55
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    $\begingroup$ You might want to reconsider a lot of things. The USS Macon was a huge Zeppelin which could carry only six very small biplane fighters and had no armour or on board weapons at all. Instead of an air wing, you might carry a squadron, and instead of fighters, drones or UAV's which are much smaller and lighter in size. $\endgroup$
    – Thucydides
    Sep 3, 2015 at 11:31
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    $\begingroup$ I want to know why you want to be lifted by hydrogen when you have a far more powerful lifting power in the form of anuetronic fusion power plants? That's like building a Tesla Model S then insisting it be pulled by horses. $\endgroup$
    – Green
    Sep 3, 2015 at 11:55
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    $\begingroup$ You need (50,000 tons * 1,000,000 g/T) of air displacement. If we approximate 1/22g=L of hydrogen, and air at 1.19g/L each liter of displacement gives you (1.19 - 1/22) grams of air. So you need: 50,000*1,000,000*(1.19-1/22) = 57227272727.3 liters of hydrogen displacement of air to get your lift. This results in a sphere with a radius of 250 meters. However, I expect that your 50,000 ton estimate is VERY low for a functional airship like this, a Nimitz class carrier displaces 100k tons and this is nearly guaranteed to be more. $\endgroup$
    – enderland
    Sep 3, 2015 at 13:06
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    $\begingroup$ Jet fighters and a gasbag of Hydrogen leaking out all around are a very ...volatile....combination. $\endgroup$
    – Oldcat
    Sep 3, 2015 at 16:52

3 Answers 3

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You need (50,000 tons * 1,000,000 g/T) of air displacement. If we approximate 1/22g=L of hydrogen, and air at 1.19g/L each liter of displacement gives you (1.19 - 1/22) grams of air. So you need: 50,000*1,000,000 grams / (1.19-1/22 liter/gram) = 43,685,464,654 liters of hydrogen displacement of air to get your lift.

This results in a sphere with a radius of about 250 meters, give or take a few. Or a diameter of 500 meters (about 1500 feet).


The story is not over though.

This is all assuming a few key things:

  • Changes in air densities don't matter as you climb
  • 50k tons is the right amount

I expect that your 50,000 ton estimate is VERY low (perhaps by multiple orders of magnitude) for a functional airship with what you are describing. A Nimitz class carrier displaces 100k tons and this is nearly guaranteed to be more. Your airship is basically an entire aircraft carrier plus a ton more equipment.

Since you are going to be flying an insanely huge floating bomb, combined with all sorts of things that can go wrong, you are going to need large amounts of protection equipment/etc.

Some additional insights as to why it's going to be heavy:

The airship needs to be large enough to carry at least 40 strike fighters with a maximum takeoff weight of roughly 20 tonnes each, and at least two helicopters with a maximum takeoff weight of 10 tonnes each.

So these strike fighters are slightly heavier than F-18's, so you can guesstimate that the flight deck characteristics of this airship will be similar to a carrier's.

Keep in mind that you will need lots of supporting... personnel and living quarters and other amenities for life for this ship. It's probably ever harder to refuel/rearm than a carrier.

An aircraft carrier services less than 100 planes and yet has a crew of many thousand. This airship will be no different.

The airship uses hydrogen as a lift gas with an inert gas (possibly helium) surrounding each hydrogen gas bladder.

How does it land? Does it land? If so, you need a hugely complex internal support structure to land. It's not trivial to just drop a 50k ton object that is about the size of most skyscrapers (or larger) onto ground somewhere to land/rearm/refuel. The internal structure is going to have to support this, which means more weight and more volume.

A carrier gains benefit because water also provides support. Ships need much less structural integrity as a result, because the water is a very firm foundation/base. Air is not the same, so you again are going to need to take more care to ensure the structure is self supporting.

You are also going to need an incredibly complex altitude regulating system. Carriers just displace enough water that a bunch of stuff sticks out, so as they gain/lose 10,000 tons of weight all that happens is the ship sits lower/higher. An airship... with not have this advantage, at all. So your airship will need some way to regulate its altitude, by either compressing hydrogen (and pumping oxygen in/out) or otherwise having insane fans/lift.

The airship's envelope is made from graphene able to withstand hits from shell fragments and 30mm autocannon fire.

Lets just use that 25mm steel as a frame of reference. The volume for 2.5cm around a 250M radius structure is:

  • 3.14*(250^3 -(250-0.025)^3) = 14700 cubic meters

Steel weighs about 7850 kg/meter^3. Or about 4 tons/meter cubed. So just in your protective shell you have about 50,000 metric tons of steel.

Add more if you are doing a non-sphere shape as a sphere is the most efficient volume for a shape.

The airship is heavily compartmentalized to prevent the spread of fire and uses automated gaseous fire suppression equipment throughout.

Fire isn't your primary problem, explosions are your problem. Electrical shortages, battle damage (one missile => boom?), sabotage, etc. Fire onboard your ship is death through explosion.

The airship's reactor and ammunition magazines are encased in at least 25mm of face hardened ballistic steel on top of any required radiation shielding.

This is probably less needed since you have a ship the diameter of 5 football fields, so you can just put all the explosive stuff in the middle and figure if something gets there you're already screwed.

The airship needs to have 360 degree turret coverage for its point defense weapons systems.

This is going to be super weight intensive since your ship is... huge. Keep in mind the more weight you add, the more volume you need, and the more volume you need, the more coverage/etc you need.

The airship's flight deck should ideally be long enough to land the above mentioned fighters without arresting cables. If they overshoot, they can just fall until they regain enough airspeed to try again. Likewise, there is no need for catapult launches.

This might work, but if you are high enough for this to happen that also means your air density is very low. This means your ship is... going to be even larger.

Notice that in this picture from here:

enter image description here

air density decreases pretty significantly even only going up 1000 meters. All those calculations above are considered at sea level, as you go up, you need even more displacement for your ship to float.

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I realize that I'm not only answering your question (enderland posted some numbers in his comment, and see my first bullet point), but here are my two cent, anyway ...

  • Square cube means that area scales with $length^2$ and volume scales with $length^3$. Scaling this one up, you would get 0.75 miles length.
  • Those strike fighters will need fuel and ordnance. Say 20 tons takeoff weight are actually 10 tons of fighter and 10 tons of consumables. Call it five missions where all fuel and ordnance are consumed and ten missions where five tons of fuel are expended. Each strike fighter gives you 110 tons. Most of that is fuel and missiles, which require damage-proof storage.
  • Is this hydrogen/helium combo really worth the complication? Hydrogen doesn't burn if there is no oxygen, so it will only burn if the gas cells are ruptured. If the internal partitions are splinter-proof, the airship gets too heavy.
  • Armor against 30mm autocannon is about the level of a Bradley IFV. Getting that airborne is a tall order. Attack helicopters are sometimes billed as being able to come home after a few autocannon hits, but that's not the same.
  • Face-hardening 25mm of armor won't make much of a difference.

Summarized, for a this gets downchecked.

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I know I'm late for the party, but here's my two cents:

  1. You can keep quite some of the lifting benefit by only using helium in a "shell" around the hydrogen. You'll compartmentalize anyway so just keep your bags sorted.

  2. You shouldn't care about armoring. Standard bullet holes don't do much loss for a giant air-ship, not even at 30mm. Make the outer envelope triple-walled and fill it with a two-components self-sealing foam.That should allow partially sealing the outer structure, reducing the losses.

  3. To enhance safety, you can add external layers, which helps against direct incendiary ammunition or surface-explosives.

  4. Have your flight-deck below your main body. This design will require tensile strength rather than compressive strengt and therefore make structures lighter.

  5. Zylon is a polyaramid (just like Kevlar). It got an impressive specific tensile strength of 3766 kNm/kg which is 13 times that of tough steel, and still double that of monocristaline "iron-wisker"-fibers, which have the higher total strength. It doesn't burn (except if put in oxygen concentated above 68%) and melts at 650°C. Without a doubt, 22 century tech can get beond that, but at the very least, they could build composite panels and sheets where there's a net of iron-wiskers suspended in a weave of Zylon and sealed in other aramids. This should give you specific tensile strengths of roughly 3.5 MNm/kg, at a density of 2100 kg/m3 and total tensile strengths of 6620 MPa. If built correctly, the iron-wiskers net could double as sensor: a snapped wire, broken by a bullet, will no longer conduct, signaling where to patch, much faster than any pressure sensor ever could. All while being just about fireproof and with no really exotic materials.

  6. Sub-presurized cells: The lower the pressure, the less dense the lifting gas. Usually you'd want pressures slightly, or well above sourrounding airpressure. However, at that size you might get away with a bunch of lifting-bags with less than airpressure. If you get high-pressure bags in a certain shape, you could have them build a hollow bubble with really low pressure. Even better: from the envelope towards the center, in each layer of bags, drop the pressure slightly. Near the exterior or the coridors you got helium slightly above atmosphere, while towards the inner you got less and less pressure until you finally hit hydrogen at .1 of the outside airpressure. Even if something peirces through, the helium would flush out the air and flush inward the hydrogen, so a combustion is really unlikely. Don't go nuts with it though, as you still have to keep the pressure-differential somewhere. Having the over-all pressure just slightly above outside should make it the most light on the materials. The real benefit comes from making it rather safe to use hydrogen in the maiority of cells.

  7. Another place where it really makes sense to use low-pressure bags is in the boancy-correction-chambers. If you compress air in, the bags collapse, making room for more air. Otherwhise they inflate, providing more lift.

  8. Aerogels are extremly lightweight solid foams. They are very good insulators, as well as usually being quite fireproof and okay-ish concerning their stability compared with their weight. As they can be filled with a liftgas, they might be used in junktion with the liftgas cells. Aerogels go from 160g/m3 (aerographene) to 500kg/m3 (heavy silica-aerogel) and average at 100kg/m3. They leak their cellgas, but rather slowly, so that a balloon with helium-filled aerographene would be rather resistant against bulletholes, allthough it might provide only 85 to 86 percent of the original lift. Since they need far less pressure-guarding, many compartment-walls could be replaced by very thin foil or even be removed, raising the effective lift back up. Their real use is in insulation and as support below the paneling though.

Let's say you use cube cells, 50 m, filled with helium at 1.1 times the sourrounding pressure, the walls being of the aforementioned Zylon at 1 mm. Each provides a lift of ((50 * * 3) * (1.19-0.179 * 1.1) - 6 * (50 * * 2) * 0.001 * (1540))=101'037 kg (with 2 mm walls of the compound it would be 61'137 kg). That leaves you at 50'000'000 kg/61'137kg/cell = 818 cells. Or in other words: 102.25 million cubic meters. A cube 468 meters each direction. Go for half a kilometer and you got 25% savety. Enough to make most of it consist of aerographite, making it basically bullet-ignoring. And since such a cube is really large you could have sections with hydrogen (as long as nobody shoots it with oxygen-tanks).

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  • $\begingroup$ Good answer, but you should probably add some reference links to your source material. Welcome to worldbuilding! $\endgroup$
    – DWKraus
    Sep 10, 2020 at 1:02
  • $\begingroup$ @DWKraus Thank you. :-) True. Well, it's mostly wikipedia, but still, I'll look it up again and then edit them in. And thanks, as soon as I find some time, I might be here more often. $\endgroup$
    – Teck-freak
    Sep 10, 2020 at 22:51

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