Vacuum airships

Question

Airships fly thanks to their weight. The m3 you occupy should be lighter than the m3 of whatever you want to float around in (bit of a simplification). To achieve this they make a big balloon and fill it with a light gas, making it overall lighter than air.

Theoretically a vacuum airship is thus the best method to fly. Without mass in the bag it gets a whole lot lighter. However, the creation of a vacuum chamber requires such sturdy materials that it automatically becomes heavier than air. The problem is the atmospheric pressure that puts too much force on the shell of the vacuum chambers.

Using modern materials, at what kind of atmospheric pressures could we make a vacuum airship that can function? For more details: Imagine an airship that can carry about a hundred people including crew, sleeping quarters, dining and such. I think about 200.000kg not including the balloon, but using modern materials you might get that down a few pegs. The atmosphere is most preferably akin to ours in composition and assume earthlike gravity.

Any pressure, high or low, is acceptable if you can support it with facts. Venus has a tremendous pressure, allowing even a shipping container to float. However, could it support a vacuum airship under such pressures? Lower pressures have a different problem, because the lower the pressure, most often also the lower the mass per m3. That means the balloon needs to get much bigger. In the end it also needs to support the dirigible, which requires to withstand the outside pressure as well.

For extra creativity I'll not add the hard science tag, but sources are very welcome.

This question is not the same as vacuum instead of gas, as I'm interested to make it work by altering the atmosphere it floats around in.

Answer 1

Use mars

A mars like atmosphere is a good bet. Also use a lower gravity. this would allow you to build thin walled, and therefor lighter vacuum. This is not a problem because the pressure of a planet's atmosphere is dependent on its mass anyway and the simplest way to change it is to change the mass.

There is some documented evidence of this being viable on mars in real life.

Sources: https://www.nasa.gov/directorates/spacetech/niac/2017_Phase_I_Phase_II/Evacuated_Airship_for_Mars_Missions/

https://space.stackexchange.com/questions/23709/mars-vacuum-blimp-feasability

https://curious-droid.com/302/zeppelins-mars-havoc-venus-nasas-new-planetary-airships/

Answer 2

Using modern materials, at what kind of atmospheric pressures could we make an airship that can function?

Aerographene is porous but less dense than helium, and while different sources report different structural properties, it seems that it can withstand compressive forces almost as well as steel.

So, it would be possible to have a sphere with a diameter of two meters, 10 cm thickness, covered in airtight aluminum foil, withstand pressures up to 100 atmospheres (a depth of 3,000 feet of water) like bathyspheres do. The outer volume would be about 4.18 cubic meters, the weight about 1200 grams (182 grams of graphene and about one kilogram aluminum). The net lift in ordinary air would be about three kilograms.

Put together one thousand such spheres - a cube twenty meters each side - and you've got yourself three tonnes of lift. Actually, since the packing factor of spheres is about three fourths, one thousand 4.18 m^3 spheres would occupy an average volume of 5.6 cubic meters each; 5600 cubic meters would be a cube only about 18 meters each side.

Fill with those a volume equivalent to the Hindenburg (200,000 cubic meters), closely packed, and you can fit 35714 spheres, with a lift of 107,14 tonnes on Earth. Not bad considering that the Hindenburg (filled with explosive hydrogen) could lift 232 tonnes.

I have padded my calculations; it's likely that these results might be improved.

For example, having more spheres together might allow using a less sturdy sealant than aluminum for the outside of each sphere, leaving the job to the external bag. Or maybe a less sturdy sealant or less thick aluminum foil is enough anyway; or the sphere can be made less thick, even if that wouldn't change things very much - of the 1200 g of each sphere, only 180 or so are the graphene. Or smaller spheres or "caltrop" shapes might be packed between the 2m spheres, increasing the packing ratio from its 0.75 baseline (with perfect packing, a 33% increase in lift might be possible).

Making the sphere twice as large, the surface increases fourfold (so 1kg aluminum becomes four), the volume eightfold (so 180g graphene becomes 1.44 kg), and a 5.44 kg sphere has now eight times the lift - about 33 kg net, giving about 27 kg net lift versus the 24 kg of eight separate spheres.

Spheres three times as large would need 9 kg aluminum, 4.86 kg graphene, weighing about 14 kg with 27 times the lift - 110 kg net, giving 96 kg lift versus the 81 of 27 separate spheres. And so on. Note: the pressure on each sphere grows with the same ratio. Past a certain point, either we increase the thickness again, or the sphere will be crushed by atmospheric pressure.

Answer 3

Frame challenge: Why bother with the vacuum balloon if we can vary the atmosphere?

So we need a engines for thrust, a way to climb and descend as needed, a way to steer and pivot and roll and pitch, a passenger compartment, a baggage compartment, toilets, a kitchen, enough to keep the passengers comfortable on their long journey. If only there was some ready made object with all these things we could use as a base....

This is Us Airways Flight 1549, with everything we need to make a long voyage comfortable, floating in a fluid of density 997kg/cubic meter:

I've been struggling to calculate the actual density of a modern aircraft (no-one publishes volume information for the entire airframe), I've been calculating around 100 - 300 kg/cubic meter but I'm unsure. However from the photo we can tell it's floating quite high in the water. The underside of the nose is above water, as well as the rear decals that's midway up the fuselage, It looks like its about 80% out of the water. From this I'm estimating it's density at ~150kg/cubic meter.

This suggests the plane will be neutrally buoyant at 125atm of air pressure. This is 12MPA of air pressure with our current atmosphere. This is a lot (and we don't need to push back the whole lot, just the difference between the passengers and the outside), but not beyond our engineering. Lightweight carbon fibre 3d printing that even my cheap 3d printer works with can handle 50-300MPA, so surely professionals could come up with something, although it may be a bit excessive to literally retrofit an airliner, this should give a guide as to what we can be building if we can tweak the atmosphere to accomplish it. Humans can actually breathe an atmosphere of oxygen and helium at these pressures (up to 19 mpa actually), with acclimatization, so you walk outside without a respirator.

However since we can tweak the atmosphere, and it's not actually a requirement that it be breathable, lets make the atmosphere Radon, a noble gas. At 9kg/cubic meter at STP, we only need ~15atm of pressure before our plane floats up like a balloon. That's only ~1.5MPA. That's much easier to work with!

Your "airships" launches by pumping air out the fuselage until its down to minimum comfortable levels, and then by releasing the docking clamps and it slowly floats up. A little bit of thrust from the engines and forces applied on the rudder and flight controls and it's able to steer. The engines can power it in the horizontal direction at speed, and when it arrives, the flight controls can bring it back down to ground, where it can let air in / pump oxygen in from the terminal, (depending on which atmosphere we went with) , where it will get heavy and sink to the ground, where it can be roped and held onto the ground.

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To make it directly answer the question in a tongue in cheek way, you can duct tape a small, rigid, Thermos to the inside ceiling of the plane - they have chambers of pure vacuum. Now we have a vacuum chamber at the top of a large comfortable pressure vessel carrying passengers, which floats in the custom atmosphere.

Answer 4

A pressure cooker clearly can withstand vacuum and float in water, which also is gas in liquid form. Soo then floating vessel with a difference of pressures of inside and outside is possible, in some conditions, then what about the generalization of that.

problem isn't simple if we approach the problem more seriously. Constructions working against compressive forces are a bit more complex subject and is as an example the serious field of research in NASA - as it is directly connected to the mass of a rocket and all that - they have a lab of experimental researches how exactly basically a thin-walled cylinder crumbles under a load.

The necessity of that lays in a difference of theoretical ideal construction and how much influence on a result imperfection of construction and materials have on the situation. The same applies to bridges and house building - finite element analysis goes hand to hand with experimental testing, and the safety factor is quite high, not only because it has to last long, but also for that negation of imperfection influences.

one of the places to start with theoretical parts is Euler's critical load and material science in general. I won't, not competent enough, I'ma doomer and it easier for me to look at Hydraulic press channel and they's not so long ago established dive 3km deep setup v.onemillion Shrinking Styrofoam Cups with Deep Sea Chamber and alike.

in general attempt to google how much a sphere will hold of outside pressure leads to strange places u never been and does not bring clear answers, even if it is a typical modeling task for the mechanics of materials field of science, and not much luck for those who aren't familiar with all that.

All that said, all below is not perfect, and no guarantees.

a little bit of trivia and water again

A submarine is a relatively big underwater vessel, which is capable to dive at significant pressures like 60 bar down, or ones of WWII like 20 bar typical.

And steering in direction of venus - density of liquid carbon dioxide is

1101 kg/m3 (liquid at saturation −37 °C (−35 °F))

Critical point (T, P) - 31.1 °C (304.2 K), 7.38 MPa (72.8 atm)

So a modern submarine potentially can float in liquid CO2, in all 1-74 bar pressure, in conditions when CO2 is liquid. The density of CO2 will change with the rising of temperature, but no so essential for us, a change of 10-20 percent or something - a difference in a range of ballast tanks.

let's start our speculations

The compressive strength of ductile materials such as mild steel used for most structural purposes is around 250 MPa.

that is the stuff nails made of - not the best, bends easily and all that, but we take that number as a measuring stick.

unfortunately lost my gnuplot skills so, let's jump straight to how it looks like for 100 bar.

Sphere 1m radius, crushing force will be 31MN, so crossection has to be 0.1256m2, hence wall thickness 0.02m, and resulting mass of our sphere around 1885kg

The volume of that sphere is 4.2 m3.

So the thing will float in something of a density of 450 kg per cubic meter.

• However, if we apply safety factor for all imperfections and all that, it may sink easily, but to not mess with it we took not the best material, even among the steels - one negates another and we can assume to have enough of safety factor here.

So half of the density of water, not bad, and considering real constructions which did dive at Mariana Trench, we are not that far off with all that.

how all that scales up/down?

pretty much linearly - crushing force scales proportionately to the square of linear sizes, so as resistance is proportional to the surface of cross-section, the strength of materials, mass proportional to cross-section aka wall thickness multiplied by surface area aka volume as the result, lifting capacity proportional to volume.

so no cheat codes like square-cube law. A variety of sizes is big enough before there will be some nonlinear effects, and they are, and 10m radius and we probably have to account for them, 10-20 percent range with steel, less for titanium.

let's plunge into Venus. Venus, my love, I come ...

what is the density of those 93 bars of pressure, near-surface of it?

wiki>>The density of the air at the surface is 67 kg/m3, which is 6.5% that of liquid water on Earth.

Soo, it seems we miss our target by 6.7 times. Density isn't high because of the high(relatively, 740K) temperature there, so we have the additional challenge of the steel to lose structural strength at the temperatures, but not a huge deal, the second order of magnitude effect, as there are steels which work well enough with higher temperatures.

unfortunately, there is no positive, for us in the case, square cube laws, so we can't outnumber the situation by changing the size. (maybe wrong, but do not see any, but can be mistaken)

So the variables to change are mostly density and strength of material with that density, composites, more sophisticated ways to squeeze their all from available materials.

But perspectives do not look that promising if we do not bring the new game in town like carbon something. it much easier to have carbon monoxide as lifting gas for those purposes. And if we cross the threshold with conventional materials then just barely - so imperfection of our original assumptions may be detrimental for the answer, as so the importance of experimental data can't be underestimated here.