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Ignoring the plausibility of their evolution and sources of food, could a whale-like creature which internally consists largely of hydrogen bladders/gasbags realistically stay aloft?

If these creatures are plausible, would larger creatures be able to float more easily, given that their volume (and hence space for available gasbags) increases with the cube of their size, while the surface area (and hence, weight of the parts that keep the hydrogen inside) increases with the square of their size. (e.g., the square-cube law). If larger creatures do float more easily, what is the minimum size required for such a creature to be plausible?

Note: I am aware of this question, which talks about the evolution of such a creature, and this question, which talks about the uses of a biologically engineered flying whale, but as neither of these directly address the feasibility of the concept, I believe that this is distinct enough not to be a duplicate.

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    $\begingroup$ You may also like to look at this question on purely biological dragons, it may be enlightening. $\endgroup$ – Ash Nov 1 '17 at 10:59
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    $\begingroup$ As a side note you can make the atmosphere also really dense. $\endgroup$ – GaboSampaio Jan 29 at 17:54
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    $\begingroup$ Prior art by Douglas Adams $\endgroup$ – Gary Walker Mar 6 at 15:59
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Sadly, no. Tl;dr: the minimum size of such a creature is on the scale of kilometers and thus pretty infeasible. Instead, try making the creature some kind of colonial organism and boosting your planet.

First, let's consider the simple hypothetical: how much hydrogen would it take to simply lift a whale? Well, a blue whale weighs 200 tons- that's 200,000 kg. Each cubic meter of hydrogen can lift approximately 1.1 kg, so to lift a whale we're talking about 181,000 cubic meters of air. This is about the same size as the Hindenburg or your classic zeppelin- which you probably think is a lot smaller than it actually is:

Hindenburg size comparison, from http://www.airships.net/hindenburg/size-speed/

It also brings to mind some really fun mental images of a whale soaring through the sky while strapped to the bottom of a zeppelin. Unfortunately, that comparison is unhelpful because the skin of the zeppelin is assumed to have a negligible weight- something that we can't do with biology.

So, let's assume a spherical whale.

What we're trying to figure out here is the minimum size of a biological gasbag. We model that as a sphere of $H_2$ gas surrounded by a thin shell of skin.

Beware, physics below

Our initial equation starts out pretty simply:

$V_{hyd}*F_{buoy} = M_{skin\ shell} = V_{shell}*\rho_{shell}$

where $\rho$ is the density of our shell.

This is then expanded to give us some actual formulas. We're trying to solve for the radius of this biological gasbag, so we're hoping to end up with $r$ alone on one side set equal to a bunch of numbers.

$\frac{4}{3}\pi r^3*F_{buoy} = 4\pi r^2t*\rho_{shell}$

Where $t$ is the thickness of the shell- I'm going to assume it's 1 meter thick. Sounds approximately right to me. We can simplify a bit with that information and some quick algebra:

$r^3 * F_{buoy} = 3r^2*\rho_{shell}$

Which immediately simplifies to exactly what we were hoping for!

$r * F_{buoy} = 3*\rho_{shell}$

Let's deal with those other two variables. The $F_{buoy}$ is the force of buoyancy due to our lifting gas, in this case, hydrogen. There's a lot to it, but Wikipedia has a shortcut: $1\ m^3$ of hydrogen can lift $\approx 1.1kg$. Cool! We can also deal with the other variable, $\rho_{shell}$. Here, a quick google search tells us that the density of skin is about $800\frac{kg}{m^3}$. Let's plug those numbers in.

$r*1.1 = 800*3 = 2400$

Note: I fudge my units for simplicity's sake here. The $F_{buoy}$ term is a good bit more complex.

So our minimal radius for our idealized gasbag is $\approx 2200m$, or 2 kilometers.

spherical cow, from http://abstrusegoose.com/406

Biological assessment:

Totally infeasible. A whale 4 kilometers long is nowhere near plausible, and that's the absolute minimum. You'd have to add things besides skin, and that all adds weight, and every time you add something you increase the radius that much further. With some back of the envelope calculations, I get a minimum size of 8 kilometers; including water and muscle mass as well as a tubular body. What really sunk this, however, was the circulation system. Even though the volume scales as the cube of the radius, the amount of liquid needed to provide circulation throughout the body scales even faster. Sad.

Fictional solutions

There are two main ways I see to combat the problems above.

Modify the organism

If the mammalian whale-like characteristics aren't a hard necessity, I humbly submit the siphonophore for your consideration. It's a marine creature that's actually colonial- made up of individual cells working in unison. There are two big perks to this. One, they're clearly capable of it- the Portugese man o' war is a siphonophore, and it already has a large float that could be modified to hold hydrogen (in a fictional universe). Plus, many siphonophores are bioluminescent, which would be awesome to see as a large creature floating overhead. I estimate the minimum size of these to be 5 kilometers in diameter (water weighs more than skin, but they're fine being spherical), so they'd be like glowing clouds. If that isn't epic sci-fi, I don't know what is.

Modify the environment

I fudged the buoyancy term in my derivation above, but it's based on essentially two things- the force of gravity and the density of the atmosphere. Here in Worldbuilding, we're free to modify both of those! What we want is a small planet (low gravity) with a dense atmosphere. If we have an atmosphere like Venus, which is some 60 times denser than Earth's, and a planet about the size of Titan, which has a gravity about 1/8th of ours, we can get a much larger buoyancy force. On this planet, every cubic meter of hydrogen is going to be able to lift around 250 kg- a massive increase from the 1.1 we used on Earth. This cuts our minimum radius down to just 10 meters! That's much more reasonable for an organism, especially one that's supposed to be a whale, and quite manageable in any fiction novel.

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    $\begingroup$ Additional note- a floating creature full of hydrogen would be incredibly vulnerable to lightning. Just saying. $\endgroup$ – Dubukay Nov 1 '17 at 9:42
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    $\begingroup$ It could do photosynthesis: flying is a protection against herbivores... $\endgroup$ – peufeu Nov 1 '17 at 10:14
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    $\begingroup$ I remember once trying to work out how to make a Lego zeppelin using the same kind of maths. Lots and lots of bricks was the answer. $\endgroup$ – Joe Bloggs Nov 1 '17 at 12:42
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    $\begingroup$ Great answer, my only complaint would be with the 1M thick skin. Interestingly the equation simplfies to a constant ratio between skin thickness and radius. This means that 2.4km floater with 1m skin, would be as buoyant as a 2.4m floater with 1mm skin. $\endgroup$ – MongoTheGeek Mar 5 at 14:57
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    $\begingroup$ no self respecting physicist would assume a spherical cow when a pointlike cow will do $\endgroup$ – jk. Apr 4 at 16:23
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Full Disclaimer: I am the OP of this question, so this answer may be biased towards this being possible.

TL;DR: If we make some optimistic assumptions, this may be possible without even having to mess around with atmospheric density and/or gravity!

I've decided to work out an example creature with a total body mass (without the mass of the hydrogen) of $500kg$. According to Dubukay's excellent answer, Hydrogen has a lifting capacity of about $1.1 kg/m^3$. This means that to lift our $500kg$ beast, we need about $455 m^3$ of H2. Assuming this hydrogen is kept in a spherical container (which isn't quite accurate but is a good enough approximation for now) and that my math is right, this container will need about $286 m^2$ of whatever surface is used to contain the hydrogen for the outside of its gasbag.

According to this paper, the wing loading for a bat can get as low as $0.14 g/cm^2$. Wing loading is mass per cm^2 of wing loading, so actual bat wings will be much thinner because a substantial portion of their body mass is their actual body. Therefore, we can assume this as an upper limit for wing mass. We need $286 m^2$ of surface area, which means that if we use the same skin bats do for their wings (probably several layers of it due to this being an upper bound, which will make the gasbag even stronger), so if my math is correct, the outer skin of the gasbag will weigh a touch over $400 kg$. This means we are able to retain almost $100kg$ of weight for any necessary vital organs, steering and locomotion devices such as flippers and flaps, and hydrogen generation apparatus.

Of course, this makes some optimistic assumptions, such as assuming a perfectly spherical shape for the hydrogen containment organ, but we can cut quite far into that remaining 100kg before we begin to run into issues with the requisite mass of vital organs, so this concept seems to be at least somewhat feasible, and the gasbag will be several times stronger than the wing of a bat, which should be sufficient for most purposes.

Amusingly, this also demonstrates that if you could find a way of connecting bats together in a way that prevented the leakage of hydrogen, a $400kg$ sphere of bats filled with hydrogen could easily lift an adult.

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    $\begingroup$ I like this answer. How fast would hydrogen escape through a bat wing though? $\endgroup$ – Tim B Mar 8 at 9:13
  • $\begingroup$ @Tim B I unfortunately don't have numbers for that. Remember that it'll be several layers of wing, as most of a bat's mass is in their body and these numbers are for the entire wing loading. So hydrogen escape would be far slower than through ordinary bat wing. $\endgroup$ – Gryphon - Reinstate Monica Mar 8 at 13:35
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    $\begingroup$ Additionally, as long as the rate of escape is reasonable (and I don't see why it wouldn't be), it's not difficult to slowly replace hydrogen via the electrolysis of water. $\endgroup$ – Gryphon - Reinstate Monica Mar 8 at 13:46
  • $\begingroup$ If you downvote, a comment with reasons would be appreciated so that I can improve the answer or fix issues. ;) $\endgroup$ – Gryphon - Reinstate Monica Mar 22 at 12:25
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Depends on the wind.

The maximum size of these things will be dictated by whether or not they can still eat sufficient amounts to stay alive, and whether they can breed in order to continue the line of sky whales. Both of those things require being able to move under your own power.

If the sky is very calm (no wind at all) then this isn’t an issue, so your creatures can get very big. If there is wind then your creatures have issues.

For starters: these whales will have to have huge flight surfaces (tail and fins) in order to get any power even on a calm day. On a windy day, these will turn your whale into a kite.

Secondly: the whales will not be dense (by their nature), so the wind will throw them across the sky like.. well, a balloon.

This leads to a balancing act between size, control, and wind. In theory, the whales could gain more control with more powerful muscles to flap their tails more often, but more powerful muscles are larger and denser, requiring more lifting volume and creating a larger area for the wind to hit.

It’s possible you could have the whales use the wind to their advantage, using it to power their flight towards migrating swarms of skykrill, but that will only work if the winds are predictable and steady.

For example: take a look at the Festo Air Penguin and ask yourself how well it would handle in a gentle breeze. It uses helium, but it gets the idea across.

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  • $\begingroup$ Interesting. I hadn't thought about problems with wind, but that makes a lot of sense. I'm planning on asking another question about how large their tail/flippers will have to be to make movement at any reasonable speed work. I'll definitely take the wind into consideration for that. $\endgroup$ – Gryphon - Reinstate Monica Nov 1 '17 at 8:08
  • $\begingroup$ 1) Can the wind not be considered a aerial current? We might consider them to be rather random, but certain weather patterns are quite predictable (like the Pacific trade wind system). 2) Give your whale the ability to flatten/streamline it's body area to minimize wind impact, or to or expand its surface area to use it to better effect (sort of but not really like a sail). Oh, and Joe Bloggs: +1 for the skyrill! $\endgroup$ – Rissiepit Nov 1 '17 at 11:01
  • $\begingroup$ @Rissiepit: 1: yes, but because of the small difference in densities it’s like a current vs a jellyfish rather than a current vs a fish. 2: the volume has to remain the same, so the whale would have to be an amazingly amorphous blob rather than a whale. $\endgroup$ – Joe Bloggs Nov 1 '17 at 12:38
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Happily, Yes.

Dubukay correctly identified the relation

r = (3 * Skin Density * Skin Thickness) / Specific Uplift

for floating spherical creatures. To use this relation with a Skin Thickness of 1m was the problem, though - Early hot air balloons were made from silk and latex, both biological materials, and nature has found several ways to create and uphold membranes of impressive strength. Bat wings are built from two layers of epidermis 10um thick.

Thus, a bat-wing sphere of radius ~25mm filled with hydrogen would be self-lifting.

It is quite easy to imagine a creature built from 100mm-diameter (i added some volume to give the creature lift for some brains etc.) gas-cells (good redundancy, too), able to move via pneumatic 'muscles' driven by gas exchange and the resulting pressure differentials. The movement of such a creature would be very majestic indeed.

The cells would give it good damage resistance, as well as the (story-telling-wise important) ability to not look like a blimp, (i.e. completely convex) but like a sky whale, warts and all. Having the outer skin rich in some other gas, not reactive with neither hydrogen or oxygen, would also alleviate the dangers of skin-puncturing in the presence of ignition sources (though the smart hydrogen-lifted creature would have learned to avoid those anyways). Nitrogen would be very easy to come by, though perhaps a lighter gas would not put such a burden on the creature.

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  • $\begingroup$ Majestic? Definitely. But also hilarious, in the Looney Tunes way. The gas will be straining against its literally paper-thin container constantly, so the slightest nick will likely create a hole, causing this creature to shoot around like an untied balloon... before crashing to the Earth below. $\endgroup$ – Dayton Williams Mar 23 at 21:01
  • $\begingroup$ Those are baglets, as cells, each about as big as a small grapefruit, that make up the creature. There will be no shooting around. But yes, it is an object naturally buoyant in air, it will be dainty. Less so than the Hindenburg, though. $\endgroup$ – bukwyrm Mar 25 at 6:13
  • $\begingroup$ Paper-thin skin does seem likely to be at risk from lightning, unlike the meter-thick skin proposed earlier. Thin skin would be harder to contract and reliably seal to starve fire of oxygen. $\endgroup$ – SRM - Reinstate Monica Mar 25 at 10:32
  • $\begingroup$ @SRM living creatures getting hit by lightning would mayhaps not have fire-control as their sole headache.... But an outer 'skin' of nitrogen-rich cells would greatly alleviate the danger, at no great cost in weight. Additionally, a foamy structure has quite a high specific resistance, so the lightning would not be that interested, imho. $\endgroup$ – bukwyrm Mar 25 at 12:56
  • $\begingroup$ @bukwyrm Once punctured, the outgassing of hydrogen is going to happen unless there's a counterpressure -- and it'll happen at a speed commensurate with the surrounding air pressure (the whole point is that the whale is lighter than air because of the contained hydrogen). It'll push the heavier gasses out of the way. The skin being rich in other gasses may keep the skin from burning, but the whale still has to be able to be able to seal the gap, and contracting to seal the hole requires musculature throughout. $\endgroup$ – SRM - Reinstate Monica Mar 25 at 17:22
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You can get flying whale-like creatures, but they wouldn't be whales anymore, and they probably wouldn't exist on planet Earth.

The most obvious solution is to have a planet with a super dense atmosphere, and a whale like organism with a body that is less dense than the air. For example hollow bones, air-sac in its body filled with some low density gas. You could then get a creature that looks like a flying whale, and floats around, but it would not be like today's whale's on earth. It would be (1) lighter, (2) may not need to hold its breath, (3) may prefer a different body shape, (4) would need to eat something other than sea creatures, (5) may not be related to actual whale species since it would be a case of convergent evolution, etc. It would also need to have a coherent ecosystem in the air, that could support it.

Is it feasible? Well what are your constraints? If you are free to theory craft any world you want, with any combination of elements and properties, then yes you could create a world where flying "whales" could exist/evolve/survive. However such a planet might not be habitable for humans.

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Evolution would seem to rule out the possibility. Anything large and buoyant enough to stay afloat would be slow (if self-mobile at all) and hence vulnerable to predators.

At the start of the First World War, Zeppelins had a height advantage over airplanes and were initially able to bomb London from a safe height. That height advantage disappeared by 1916, at which point fighter planes were able to literally fly in circles around the Zeppelins, riddling them with bullets until they burst into flames. Even when they didn't burst into flames from incendiary bullets, battle damage would all to easily cause them to lose buoyancy and fall to the ground (or into the sea). Very few Zeppelins survived the war. By 1917 a combat Zeppelin mission was virtually a suicide mission. No nation seriously considered using airships in a direct combat role in the Second World War (although they were used in antisubmarine patrols by the US Navy). Both war and evolution are about survival of the fittest, and airships proved to be phenomenally unfit.

It is hard to imagine a world in which birds of prey wouldn't drive floating whales to extinction.

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  • $\begingroup$ While you make some valid points, there are some advantages that biological gasbags have that Zeppelins didn't. Firstly, they probably aren't going to be fighting numbers of coordinated, highly motivated opponents in large battles, they're going to be occasionally attacked by single birds or small groups. Secondly, a bird of prey has a fundamentally different method of flight than a fighter plane does, and I fail to see how a bird of prey could have anything close to the flight ceiling of one of the proposed gasbags. Finally, birds of prey don't have machine guns or incendiary bullets. $\endgroup$ – Gryphon - Reinstate Monica Mar 23 at 17:13
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William Kumler was correct. Modify the environment to one with as little gravity and as dense atmosphere as is consistent with other elements of the story justifying it as well as you can. As a general rule, planets with lower surface gravity have lower escape velocities and lower ability to retain their atmospheres but there are examples of planetary bodies having much denser atmospheres than planetary bodies with greater gravity.

But Kumler did make one major mistake in his calculations. The size of the many species of whales is highly variable. I once saw a video of a man and a woman carrying a sea creature they found stranded on a beach, which they thought was a dolphin but actually was a whale, a dwarf (Kogia sima) (c. 550 pounds) or pigmy (Kogia breviceps) (c. 880 pounds) sperm whale. And probably a baby since adults would be a few hundred pounds too heavy for two people to carry.

Kumler sort of overstated the weight of blue whales at 200 tons. Typical adult weights seem to range from about 50 to 150 tons, and so many adults are no more than 100 tons. The heaviest weight recorded was 173 metric tons or 190 short tons. There have probably have been a few blue whales weighing over 181 metric tons or 200 short tons.

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  • $\begingroup$ Yeah, thanks for catching that, M.A.! All I did for that number was a quick Google search which popped up the "sensationalist" number of 200 tons for a blue whale. No doubt most people want to know how big they can be, not how small. However, the spherical shell calculation should still be correct- I'm solving with respect to the weight of the shell, not the weight of a whale. $\endgroup$ – Dubukay Nov 1 '17 at 21:34
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Making the critter hydrogen proof would be a problem. But methane has half the lift of hydrogen.

How large a critter do you need? If they just need to be whale-sized, but not whale massed, then your model is a lot closer to the Goodyear blimp, than the Hindenburg.

Most of this critter is in effect a large lung: Lots of fairly small bladders a few inches across with a somewhat heavier outer skin.

Perhaps it's a commensal creature: Multiple different organisms making a life together. Algae in the skin act to to photosynthesis. Some parts much like jellyfish to move slowly about by pumping air. Give it chromatophores like an octopus so that it can change colour. In this way, it can change colour to warm up and cool off to give altitude control.

If it can shed tiny brainless copies of itself, it can use them as probes to find more favourable winds.

With intelligence, it needs to communicate. Think of philosophic discourse via billboards. If they can emit light, as well as modulate it, they can talk at night too.

In addition, emitted light, and probe cells that had internal corner reflectors make it easy to track probes at much longer distances.

Add handwavium: Figure out a way for the emmitted radiation to be phased. So the critter acts like a giant phased array radar. This allows communication at vast distances, and the potential of a hive mind with all beasts talking to all the neighbours that are in line of sight.

Give them a primitive critter -- similar to their probes -- that also float. These are the bottom of the food chain.

Put them on a planet with a thicker atmosphere than earth. Takes less gas to float. Don't make it too thick, however, as then very little light makes it to the surface.

Aside from burning, a lot of the early dirigibles fell victim to weather. See the accounts of the U.S. Navy Shanandoah. Some of this was control issues,but a large object in wind sheer is subject to large forces.

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