Do the ballooning lifeforms ('ballonts') of Avatar 3 make sense?

By Gert van Dijk and Abbydon 

If you like speculative biology, you cannot escape the Avatar films: they are spectacular. Regular readers will know that this blog likes its science 'well done' rather than 'medium' or 'rare'. But with television and film 'medium' is usually the best you can hope for. If the story is good enough, we are willing to suspend disbelief. The Avatar films are spectacular but have their share of biomechanical problems: the illogical anatomy and gaits of Avatar's six-legged animals were something best ignored in the first film, and the skimwing's size and mode of swimming in the second film did not withstand close inspection either. This post is aimed at the third film ('Fire and Ash'); as that is not even out yet, isn't it too early to start dissecting its biology? 

Based on the trailer, we thought we could have a first close look. 'We' here means Abbydon, who is a physicist, and me (Gert van Dijk/ Sigmund Nastrazzurro). Abbydon has his own blog and has written guest posts here before, on the subject of aerographene and foam as a way to make viable 'ballonts'. 'Ballonts', by the way, is a term one of us (Gert) came up with to describe life forms that move through the air using a lighter-than-air principle. At one point, I imagined a large array of floating lifeforms on Furaha, ranging from tiny aeroplankton to immense 'zeppeloons'. That bubble burst when I did the mathematics that proved that small ballonts simply could not work on an Earth-like planet, so all those lifeforms underwent a sad but sudden mass extinction. If you wish to follow the mathematics (just Archimedes' Principle, really), there is a list of posts at the end of this post. 

Click to enlarge; source: Avatar 3 trailer

The trailer for Avatar 3 is out, and it's got ballonts in it. Seeing that nature seems to conspire against ballonts, we looked at it critically. Let's start with a description. 

Click to enlarge; from Avatar trailer

There seem to be two ballont species: a large one, a 'barge', towed by a smaller one, the 'tug'. Apparently, these are known as 'medusa' and 'manta kite', respectively. A Na'avi-made ship is suspended from the barge animal so the Na'avi can use it for aerial transport. The medusa/barge animal largely consists of a large sac, elongated from front to back. It has two lateral vertical surfaces that we will call sails. Tendrils hang down and move about a bit; these are probably there to feed with and to anchor the animal. The tug is much smaller and has undulating fins, rather like Earth's rays, cuttlefish and Furahan cloakfish. Those fins propel it. 

What does this tell us? 

Ballonts need to be very large on an Earth-like planet to work (read the posts on ballonts to understand why). Gravity on the moon Pandora, where all of this takes place, is said to be low, which sounds good for balloons. But, and this may surprise you, low gravity doesn't make a balloon more practical! 'Practical', as far as a balloon goes, means a small bladder and a large liftable mass. On Earth, physical circumstances makes balloons impractical by dictating that they must have a very, very large bladder to lift even a small mass. Gravity does NOT influence the balance between the size of the bladder and the mass to be lifted, and so does not help to make a balloon more practical. Two things that do help are a high density of the atmosphere, which can be achieved by adding heavy gases to it, and a high pressure. Pandora's atmosphere is said to have a density that is 20% more than that of Earth, while the surface pressure is a bit lower at 0.9 atmosphere. Those changes are not impressive from a ballooning point of view. 

The Pandoran barge looks very large, which it has to be; so far so good. But why does it have those two large sails at its sides? To catch the wind for propulsion? We hope not, as that cannot work! Balloons are, by their nature, as light as the air around them, so they will, after a short while, move at exactly the same speed as the air around them. That leaves no wind to power anything! You can only harness the power of the wind if the air moves relative to you, for instance because you are held back by the ground or by water. 

Or do the 'sails' serve some other purpose? Are they themselves a source of propulsion? They could perhaps function like oars, folded up when moving forwards and spread out when going backwards. Or do they undulate? As they are vertical, undulation would allow vertical but not horizontal mobility. But the sails look completely immobile in the trailer. The barges do not seem to have any kind of propulsion mechanism, and if they did, they probably wouldn't have to be towed. Do the sails serve another purpose, such as heating? This is unlikely, as they are transparent; the sac should offer enough surface area anyway. Do they then help to orientate the animal with help of the wind, for instance when the animal is tethered (if it can do that)? For orientation you would want them at one end of the animal, not the middle. In short, we cannot make any sense of the barge's sails. 

Is the tug, the manta kite, large enough to float? Without a better estimate of its size, there is no way to check. The undulating fins can provide some propulsion force in air, but probably not much. If this were an animal swimming in water, fins of this relative size would work because they would displace a substantial volume of water, which is heavy. But swimming through air differs from swimming through water in various ways: there is about a thousandfold difference in density that affects thrust and drag, as well as a fiftyfold difference in viscosity. No air animal use undulation to achieve true flight on Earth, making it difficult to predict how well undulating flight would work out. Based on the low density of air, we suspect that you would need either very large or very fast-moving fins to effectively swim through air. So, whether an animal like the manta kite would swim well in air is as yet uncertain, but its proportions suggest that the animal might feel more at home under water than in the air. 

The tug does not only have to move itself but also has to drag the barge along. And 'drag' is a key word here, as in movement studies 'drag' also indicates resistance to movement. We can be certain about one thing: those immense barge sails will function as pretty efficient air brakes, making the tug's job that much harder... 

Mind you, there are some interesting loose ends about balloons and their steering that may deserve another post. Meanwhile, we hope that the film will solve the riddles. Our biggest surprise was that the trailer seems to show sails to catch the wind on a free-floating balloon; but surely the designers wouldn't have done that? 

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Posts on ballonts that help understand the physics

Ballonts III: basic physics
Ballonts IV: effects of density and pressure
Ballonts V: ballonts in gas giants
Ballonts VI: effects of the envelope 
Ballonts VIII: foam 
Ballonts IX: aerographene  

 

 

Ballonts IX: Blue Sky Thinking (Part 2)

By Abbydon

The previous article discussed the possibility of using soap bubbles to create small lighter than air organisms. A second possibility is more sophisticated and relies on the wonder material, graphene. It was discovered in 2004 by two scientists at the University of Manchester who were subsequently awarded a Nobel prize for their work.

Graphene is made of a flat sheet of carbon atoms, so it is a little bit like 2D diamond. It has many interesting properties but is most well-known for its high strength (100 times stronger than steel) and low density (less than 0.001 grams per square metre). An amusing illustration of this was provided in the Nobel prize paper. Imagine a one square metre graphene hammock tied between two trees. This could hold a 4 kg cat before breaking yet would only weigh as much as one of the cat’s whiskers.

As impressive as this is, recent work suggests that graphene has another property that is extremely relevant to ballonts. Graphene is also impermeable to gases. With such an amazingly low density it effectively produces a matte-black massless membrane even when a few thousand layers are used.

It would however be extremely challenging for life to produce a graphene balloon with absolutely no defects. A more robust approach is to copy the bubble foam concept and use a mass of small graphene “bubbles” instead. Conveniently, a material extremely similar to this called aerographene has been invented by scientists. It consists of a complex 3D network of graphene and carbon nanotubes where most of the volume is air. For this reason, when measured in a vacuum it has a density slightly lower than helium at 0.16 kg/m3.

Click to enlarge; copyright unknown; source here

While aerographene itself is not airtight it is not inconceivable that a material like it could be produced that contains many small airtight compartments in a similar way to a bubble foam. If these compartments contained a lifting gas, then the entire structure would float. When I mention aerographene below I am actually referring to this possibility and not the real material. The chart below shows that both a 1000-layer graphene membrane and a “solid” aerographene balloon would easily enable small (or large) ballonts.

Click to enlarge; copyright Abbydon

This strongly suggests that an “magic” aerographene like material could be used to enable small ballonts to exist. Since they cannot have a membrane then any aerographene produced would be an external structure grown from the bottom up, like hair, and could not be repaired only replaced. Additional graphene would be produced on the lower surface where the organism was hanging while the top surface would slowly degrade.

It is unfortunately unknown whether life could produce graphene in the first place as it does not appear to be produced naturally by life on Earth. Industrial processes for producing graphene based products typically require temperatures beyond the reach of even the most extreme of extremophiles. However, Shewanella oneidensis bacteria can be used to produce graphene from graphene oxide which is at least a start.

I am not a chemist and this is not the blog to delve deeply into the exact chemical process that life could use to produce graphene at ambient temperatures. There is some justification that it would not be implausible though. Inspired by photosynthesis the direct conversion of carbon dioxide into graphene at high temperatures has been demonstrated. A slightly different approach has even been shown to work at room temperature.

As an example of what is possible, an approximately spherical lump of dark grey aerographene with a 9 cm radius can lift about 3 g. This could support something like a praying mantis that is about 7 cm long though could perhaps be longer and thinner. A cup-like abdomen could contain the graphene and hydrogen producing organs while the four long rear legs partially surround the sphere to maintain a grip. Four independent wings could provide mobility. The long forearms would then provide good reach to gather food. Due to the benefits of aerographene this hanging mantis would be able to float even when small and could grow to a size only limited by other factors. 

Click to enlarge; copyright Gert van Dijk. Note that the graphene 'floating body' is narrower at the tope than the bottom, because the animal grew in-between forming the early top and the more recent bottom graphene.  

The soap bubble and aerographene concepts don’t mean that the small ballont problem is solved as they are really just meant to inspire others to come up with their own ballont concepts. In the absence of any lighter-than-air organisms for comparison on Earth there are still many unanswered questions to be considered and that is all part of the fun of speculative evolution.

For example, why would an organism evolve to be lighter-than-air? Is it always lighter-than-air or is it only temporary? How does it control its movement when floating? How does it protect itself from predators? How does it feed? Can it repair or replace its balloon if punctured? How is the lifting gas generated? How fast does the lifting gas leak from the balloon?

If we were only interested in creature design then this would all be sufficient to inspire a range of organisms based on shimmering soap bubbles or black graphene. Speculative evolution requires more than that though. Demonstrating that physics supports the idea and that there is a plausible way for the organism to implement the idea are both important. To be thorough, it is also important to consider whether the proposed organism could have evolved through a series of plausible steps, rather than just spring into being fully formed.

There are various ways that life on Earth already generates hydrogen, such as through fermentation, so that part is not unusual. The formation of chemical laced water to form longer lived bubbles is also fairly common as fish, frogs, snails and insects are already known to do this. A soap bubble based ballont as shown in the previous article therefore seems reasonably plausible.

On the other hand, the formation of graphene is more challenging to justify in a series of steps and I cannot give a solution to this. Graphene does have the ability to absorb light efficiently at all wavelengths, which is why it is black after all. A plausible evolutionary path could involve algae or plants in low light environments developing graphene for photosynthesis related reasons. Since hydrogen can be produced by algae as part of the nitrogen fixing process perhaps forests of lighter-than-air pitch black plants could feasibly evolve. That is however an idea for another time but perhaps it will eventually appear on my recently created blog. It describes the tidally locked world Khthonia, which orbits twin red dwarfs.

Finally, I am very grateful for the opportunity to share my thoughts on this matter in this blog and I hope that they inspire people to develop their own ideas in this area. Please comment to let everyone know what you think about graphene and its possibilities.

Ballonts VIII: Blue Sky Thinking (Part 1)

By Abbydon

Over the past few years, I have discovered an interest in astrobiology as it combines my childhood fascination with both astrophysics and biology. Linked to this I also enjoy speculative biology though sadly my artistic talents are embarrassingly poor (For reference, I did not produce any of the pictures shown below). For this reason, I have followed the various articles on lighter-than-air organisms (also known as ballonts) with interest.

Like many other people, I have found it disheartening that designing a plausible small ballont has proven challenging. Large ballonts appear to be viable as they can generate sufficient lift to allow both the balloon and a body to float but smaller ballonts cannot get off the ground.

This is unfortunate as it means infant “large” ballonts would be unable to float until they had grown sufficiently large. Small ballonts are also interesting as they can form only part of an organism’s lifecycle which may allow the body to have reduced functionality. This could be a mechanism for spore dispersal from an otherwise sessile organism as a more sophisticated version of a dandelion clock. Alternatively, it could be for reproduction only like an adult mayfly which can have a life measured in minutes.

As previously discussed on this blog, the problem for small ballonts is the membrane needed to contain the lighter than air lifting gas. A small volume of lifting gas without a membrane would of course float but it wouldn’t take anything with it. Therefore, clearly a membrane of some form is needed to separate the lifting gas from the rest of the atmosphere. Unfortunately, the mass of the membrane is proportional to the surface area of the ballont whereas lift is proportional to the volume. Since all membranes have mass this means that for small ballonts the mass of membrane is typically greater than the lift produced by the lifting gas.

Solving this problem requires reconsidering what could be used as a membrane in an attempt to get closer to the “magic massless membrane” than Mylar. Mylar is used for long lived helium party balloons and has a thickness of 0.1 mm with a density 1.2 times water, which is perfectly adequate for large ballonts but insufficient for small ones.

Two possible ideas sprang to mind which might achieve this, the first of which will be discussed in this article, with the second reserved for a following article. The first possibility to be considered is whether soap bubbles could be used. There are many videos online showing lighter-than-air hydrogen filled bubbles being produced, though they do normally come to fiery end which is not what we want to happen to our poor ballonts.

Soap bubbles may not seem the ideal form for a ballont but a bubble film is typically around a thousandth of a millimetre thick and has a density of approximately water. This is much closer to a massless membrane than Mylar so perhaps it will enable smaller ballonts. A ballont would not literally use soap to produce bubbles but would instead use some alternative organic chemical.

In previous articles a hypothetical Mylar based ballont was shown to float only once its radius was above 30 cm but the chart below shows that a hydrogen filled soap bubble could provide lift at much smaller sizes. For reference,

LIFT = AIR MASS - BUBBLE FILM MASS - HYDROGEN MASS.

Click to enlarge; copyright Abbydon

However, while the Guinness world record for bubble size is just under 100 cubic metres we don’t expect plausible ballonts to use single bubbles that large. The next chart shows smaller hydrogen filled bubbles can still lift a few milligrams if they have a radius larger than 3 mm.

Click to enlarge; copyright Abbydon

Scientists are known to do strange things in the name of Science but perhaps one of the weirdest papers I have read involves weighing 90 leaf cutter ants to determine their load carrying performance. Apparently they ranged from 1.2 to 36.8 mg with an average of 9.3 mg. The extreme low end of this is light enough that it could be lifted by a single bubble with about a 7 mm radius. Perhaps an alien leafcutter ant could generate a bubble to get to the top of a tree, harvest a leaf and use the ballast to descend once again. Such an “antballont” might look like a honeypot ant with a bubble for an abdomen as shown in the sketch below.

Click to enlarge; copyright Gert van Dijk. The squares are 1 mm in size. The panel on the left shows a circle with a 7 mm radius and a small leafcutter ant. the panel on the right shows an evolved ant holding a bubble between its hind legs.  

A single bubble could be viable for tiny ballonts such as the ant but it would be too fragile for large ones. A better solution for larger ballonts would be to produce a foam of many small bubbles. Each of these bubbles would produce lift on its own and a foam mass would produce more. This approach has been used to generate floating helium filled foam letters for advertising purposes!

The chart below shows that such a foam mass produces less lift than a single bubble of the same volume but a 5 cm radius spherical foam mass of individual 0.5 cm radius bubbles could still carry just over a quarter of a gram. This again sounds light but it could certainly carry a bundle of seeds or an insect several times larger than an ant. It is probably even enough to carry a vertebrate such as the 7.7 mm long frog, Paedophryne amanuensis with its legs spread out to stay in contact with the bubbles.

Click to enlarge; copyright Abbydon

This all suggests that the soap bubble idea is valid for producing a somewhat plausible small ballont without too much hand waving. This is possible because of the thin water-based membrane but there is one important disadvantage, a short lifespan. The bubble will pop eventually unlike a solid membrane. This can be managed if the ballont does not need to remain aloft indefinitely, perhaps because it is only part of a lifecycle (e.g. a seed or a mayfly) or perhaps because it only creates the foam to float at night. Alternatively, the organism could regenerate the bubbles constantly while in flight to maintain and even adjust lift.

How long can a bubble last though? About a hundred years ago, in a sealed container it is claimed that Scottish scientist James Dewar managed to get a 19 cm diameter bubble to last for over three years and a 32 cm diameter bubble to last for 108 days. This is not likely under realistic conditions but it shows what is possible.

Bubbles burst when the membrane becomes too thin as the water in the membrane flows to the bottom of the bubble or it simply evaporates. While low temperature and high humidity conditions may enable bubbles based ballonts to last longer, a more feasible approach is to add chemicals to the bubble mixture to make the membrane more resilient. For fun at home the Soap Bubble Wiki has several recipes for this.

It remains an open question as to how long a bubble foam could last but several minutes is possible with these home-made bubble mixes. Some species of frogs and fish make bubble nests that last for days, however, these require maintenance and might be too heavy to float. It is therefore conceivable that a biologically possible option in between these two extremes could produce a bubble foam that would be light enough to float but had a longer duration than normal. This would be ideal for seed, spore or larva distribution where a 5 cm radius foam containing a few hundred bubbles could be generated by the parent before being sent on its way to pastures new. This is shown below with the small Furahan “brochos” larvae suspended in a floating foam to enable longer range travel than would otherwise be possible.

Click to enlarge; copyright Gert van Dijk. This is a sketch for a painting that has already been finished and will appear in The Book.

Click to enlarge; copyright Gert van Dijk. The Book will contain many secondary illustrations; this one will accompany the one above.

This article will be concluded with a discussion of the alternative option to soap bubbles for small ballonts. Please let us know what you think of soap bubble ballonts by commenting below.

Since people seem interested in my thoughts on these topics I thought I should perhaps produce my own blog. Since I am a physicist and no artist this will be quite different to the Planet Furaha blog. I have therefore started Exocosm which will discuss the possibilities of planets around other stars (i.e. exoplanets). Time will time whether I can manage to continually produce worthwhile articles though…

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This was the first ever guest post on this blog, and I hope you liked it. Abbydon and I decided to split it into two parts; the second one has already been written, but I need to produce an additional illustration before it can be posted. 

If anyone else is interested in writing a guest post, write to me about the idea and do not send a complete text yet!

Sigmund Nastrazzurro 
(nastrazzurro  AT gmail DOT com)
 

Tabulae Mortuae IV (Archives XIV, Ballonts VII)

I thought I might present another post combining old paintings, well, sketches, with ballonts as their main theme. The reason to do so was because of the comments on earlier posts on ballonts. If you read the last one, you will have noted that the troublesome part of ballont physics, the part that conspires against having small balloons, is the membrane enveloping the lifting gas. For small balloons the membrane is simply too heavy for the lifting power of the little bit of gas it envelops. The best solution to deal with that was to think of vary large ballonts, but they would probably be completely at the mercy of the winds as a result. Sadly, small ones could not make it even of the ground. Still, here are some old sketches.

Click to enlarge; copyright Gert van Dijk

The ballonts as I first envisaged them and have presented them here were 'complete' animals, meaning they carried every organ they needed to live, including digestive organs, membranes, nervous systems, etc. But I had also played with another way of using ballonts, and that was a more limited version: they might only serve to disperse seeds or larvae. In this view, the gas and membrane would be produced by a much large parent organism, itself definitely heavier than air. The sketch above shows one expression of that idea: we are looking at something like a water lily, with most of the organism hidden from view below the water's surface. But there are 'ballontogenetic' organs in there; you can see one larva that has just been released, while another is in the process of getting its balloon filled. The idea was that the parent inflates the sac, and that, once released, the larva passively plugs the vents through which the parent injected gas.
 

Click to enlarge; copyright Gert van Dijk

 The image above shown a very similar idea. Here, most of the parent is hidden under the sand of this marsh, or beach, or wherever this takes place. Although it has a Dali-like character, I thought this design visually less pleasing than the previous one.

Click to enlarge; copyright Gert van Dijk

Now this apparently similar scheme rested on another mechanism to form the membrane. Here, a kind of microbial mat under and on a water surface has the ability to produce a lighter-than-air gas, perhaps methane. The gas would push the surface layer of the mat upwards, forming a bulge. As the volume of gas increased, the bubble lifts the membrane up some more. It might dry out to become lighter, while also shrinking at the bottom, forming a kind of tether. I admit that it was not quite clear to me what kind of membrane there would be to keep the bubble intact. If you look closely, you will see that there is a definite round structure within the outer slime mat. What that was, and how it would work, wasn't exactly thought through: while sketching, shapes just coalesce, and the process is only partly a conscious one. With hindsight, I can now add one word that might perhaps solve this problem: foam. But more about that in a later post.

I really liked the concept of some witches' microbial brew forming slimy mats that would in the end produce a nice ballont, carrying the whole microbe culture to wherever the winds would take it.
  

Click to enlarge; copyright Gert van Dijk

This one is very similar, just a bit more worked out, and more pleasing as far as its potential for a painting was concerned. ( I do not know why I wrote 'Colonia volitans' underneath; that should be 'Colonia volans', the 'flying settlement'.)

Click to enlarge; copyright Gert van Dijk

Actually, I could not resist spending an additional 15 minutes on it, quickly adding some colour to see whether life could be injected into this old sketch. It's not too bad, I think; something like this may work artistically. 

Something new for this blog
While 'artistically pleasing' is certainly important when designing speculative lifeforms, it is not the only thing requiring artistry. There has to biological and physical feasibility too, and those are not  easy either. Please keep in mind that the sketches above unfortunately rested on a complete lack of physical feasibility, and that is why they were banned. The previous posts and comments made it clear that small ballonts really need a 'magical massless membrane'. But 'massless' is already 'magical', at odds with 'physics'.

Still, one commenter, Abby, short for Abbydon, came up with an ingenious idea. He wrote that graphene membranes might allow for very small and nearly massless membranes. Whether creating graphene biologically is plausible or feasible remains to be seen. But I liked the idea that this might make ballonts at least physically feasible, so I invited Abbydon to do something I have never done before, and that is to write a post for this blog. Mind you, this doesn't mean that previous commenters were less smart; it's just that I never thought to ask anyone to contribute directly to the blog. Abbydon accepted, so you may expect the upcoming post 'Ballonts VIII' to carry his signature.

Ballonts VI; back from the brink, or still lead balloons?

Over the years, many readers expressed how sorry they were to learn that ballonts, i.e. lighter-than air lifeforms, were almost impossible to achieve on an Earth-like planet. The only way you can have a ballont on such a world is to shape it similarly to actual balloons on Earth: they have to be very, very large. What I had badly wanted was ballonts as aerial plankton floating through forests, or small ballont 'seedlings' released by their parent organisms, or something tiptoeing over the plains, as in the previous post. Such ballonts were an integral part of the Furahan menagerie, until I sat down to do the math. The sobering results are to be found here, here and here.

With that knowledge in mind, I was quite surprised to see a video showing a very small balloon on YouTube. I copied two stills from it to show you, but advise you to see it on youTube.

The video shows a very small balloon, of a size that would lend itself very well to a ballont! Was I wrong to think that small ballonts, or small balloons for that matter, are impossible? The video's narrator says that the balloon weighs 0.3 grams and needs only "naught point five eight litres of helium to float". The video shows a hand releasing a string, or so we assume, as I do not see the string in question, and the image of the balloon then rises. That sounds like a strong assertion that the balloon actually goes up into the air when released. But the video was made for advertising purposes, and advertising and truth are not the best of friends. Beware: the part where the balloon rises after being released looks like an animation rather than live action, and in the rest of the clip there is no actual video of the balloon floating. 

Luckily, they showed numbers: the video specifies a volume of helium, of 0.058 L. Volumes do not depend on weight or mass, so I suppose they meant the volume of the inside of the inflated balloon, as that seems the only thing that would make sense. We can easily find out how large a sphere should be to take up 0.058 L. Turn that into cubic meters, apply the equation for the volume of a sphere (4/3 x pi x R^3 with R as the radius of the balloon), and you get a radius of 0.024 m, or a diameter of 4.8 cm for the balloon. That looks like the size they showed in the clip. Very well, but how much mass can that volume of helium actually lift?

Well, under 'standard' circumstances, meaning 20 degrees centigrade and one atmosphere, the density of helium is 0.179 kg per cubic meter, and of air 1.2019. From that it is easy to calculate the mass of 0.058 L of helium and of 0.058 L of air. Subtract the two, and that is the mass you can lift. You get 0.059 gram. That is almost nothing! Mind you, for a balloon to work it must first lift the mass of its own envelope. In this case, the envelope has to have a mass LESS than 0.059 gram, or else it cannot float. Good luck with that. I am beginning to think that the balloons in the clip were not kept aloft by a bit of string, but that they were held up by a length of stiff wire.     

Still, I wondered if there was anything to be done about the physics. In my previous models, I had used the characteristics of PET for the membrane of the balloon, because that is a strong material that will not let even gases escape. Unfortunately, PET has a density of some 900 kg per cubic meter, so it is only a bit less dense than water.    

Click to enlarge; copyright Gert van Dijk

Here is my old model again. The x-axis shows the radius of spherical balloon in cm and the y-axis shows mass in grams. A balloons works if there is a mass difference between the displaced air and the gas inside the balloon. If that difference is larger than the mass of the membrane, you get lift. In the graph, the red line shows lift: if the values are negative, the balloon sinks, and if they are positive, it floats. This PET-balloon will not float if the radius is smaller than 25 cm; that is a big balloon. Actually, that is MUCH bigger than the balloons you can buy for parties. The membrane of latex balloons must weigh a lot less than the one in my model.

Click to enlarge; copyright Gert van Dijk

Here is the same model, but now the membrane is magically completely massless. That helps a lot! Mind you, that third power is still being difficult: a balloon with a radius of 10 cm can still only lift 5 g. To lift just one gram, you need a radius of 6 cm. Even without such a weightless membrane you cannot have truly small balloons. This raises the question what the mass of a typical children's balloon is, and how small manufacturers can make them?

I asked balloon manufacturers, and they were friendly enough to reply. It turns out that helium balloons of 9 inches can float, and that 5 inch balloons are the smallest ones to float. But they do so weakly and only for a short while, because the helium leaks out though the latex. Now, I refuse to use illogical mediaeval units of measurement, so I will substitute 12.5 cm for the width of five working men's thumbs held next to another. That is a radius of 6.25 cm.  The manufacturer told me that the weight of such a balloon is roughly 0.7 g, if made out of white latex. The colour affects the weight.         

Well, that makes sense if you compare it to the magical massless membrane: the magical one could lift one gram with a 6 cm radius, and now we find that the actual weight of the membrane of a balloon of that size is 0.7 g. That leaves 0.3 g for lift. That is just enough.

Today's lesson is that physics still conspires against ballonts. A secondary lesson may be that advertisers can waste your time. I knew that already. Sigh.


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PS this is an additional figure I had prepared but not posted. However, it ties in so well with Abby's comment below that I decided to add it.

Click to enlarge; copyright Gert van Dijk

 

Tabulae Mortuae III (Archives XIII)

Clich to increase; copyright Gert van Dijk

 It is with some trepidation that I show you this particular dead painting. (If you wish to see more, just use the search function to find 'Archives'.) It is one of the oldest in the series of paintings that later became the Furaha universe. The subject is neither thought out well nor painted well. The sky used to be ochre, but I secondarily, after a year or so, decided to paint it over with bluish tints to improve the demarcation of foreground and background. That helped a bit, but not enough. I admit that I have now decreased the contrast of the background digitally to improve the sense of depth in the painting.

At the time of painting I was still enamoured of ballonts (there are many posts on this blog about 'ballonts'). I was exploring what you could do with them. So here is a ballont species with the ability to hover a bit above the ground, tiptoeing from stem to stem if it chose to do so. If endangered, it was supposed to be able to release its hold and shoot upwards like a cork in water. I did not stop to think how such animals would be able to regulate the upwards force of their balloon. Perhaps it could contract its bladder forcefully, decreasing its volume and compressing the gas inside.

Anyway, I remember that the tree (?) in the background started out as a gigantic slug-like creature moving across the landscape with interesting mushroom-shaped organisms on top. When the painting was redone, I transformed it into a sessile lifeform, but the mushrooms stayed. These can obviously tilt or bend in such a way that they deflect the wind. Although I have no idea what these mushroom organs are actually for, I still like the idea of them forming a buffer against the wind.

You will not be surprised to learn that the tomatl did not make it into the modern, more sensible, Furaha universe. Now they do, and the quality of the paintings have improved too, or so I like to think. It was fun to simply paint whichever shapes suggested themselves, without wondering whether they made any sense or not. Progress...         

Ballonts in Gas Giants ('Ballonts V')

More ballonts? Well, yes: I had previously explored whether it is possible to produce a fairly small life form floating around using the lighter-than-air mechanism, but there were some loose ends left. As the last one was posted in 2011, it may be wise to recapitulate a bit (or work your way up from here, through here, to this one).

Click to enlarge; copyright Gert van Dijk

The image above show a scene on Earth on sea level at about 20 degrees Centigrade. A default local sophont (let's call him 'Julius') holds a stick indicating two meters. There is also a balloon with a radius of 62.03 cm. Why 62 cm? Because that yields a sphere with a volume of exactly one cubic meter (m^3). The skin is made of a 0.1 mm thick mylar-like material with a mass of 0.5802 kg. The balloon is filled with the lightest possible gas, hydrogen. Hydrogen has a density of about 0.0899 kg/m^3 at 20 degrees, while the air has a density of 1.2019 kg/m^3. So, the 1 m^3 balloon has 0.0899 kg of hydrogen in it, while the corresponding volume of air has a mass of 1.2019 kg. The balloon can therefore lift 1.2019-0.0899 = 1.1120 kg (that is the part needed to understand how balloons work). As the skin masses 0.5802 kg, that leaves 1.1120-0.5802 = 0.5318 kg to build a nice body out of. That is not a nice big body at all; given a body density of 1.1 kg/m^3, which is like our bodies a bit heavier than water, we can hang a spherical body with a radius of just 4.9 cm under our balloon, and the ensemble will then just float. Of course, a real animal would have tentacles and limbs and mouthpieces etc.

As said, I wanted ballonts with a body mass of, say, 10 kg but with only a moderately sized sac. As the example above shows that does not work on Earth. The hydrogen inside the balloon cannot be made lighter, but we can alter the atmosphere outside it; this is speculative biology after all. There are two ways of doing so: the first is to stuff the atmosphere with very heavy gases such as argon, but such elements are quite rare in the universe. The other is to add mass by increasing pressure, as that will squeeze more mass in the same volume. So, let's explore gas giants, where high pressures are easily found.

Click to enlarge; Source: Brian Vanderwende University Colorado

The pictures above show information about 'our' gas giants: the composition of the atmosphere, the temperature and the pressure. Not surprisingly, atmospheric pressure increases the deeper you descend into the atmosphere. For our first try, we should perhaps be a bit conservative and stay with biology in fluid water. A temperature of 20 degree centigrade should not upset Julius; it is the same as 293 degrees Kelvin. For Jupiter, the 293 Kelvin zone results in an atmospheric pressure of some 9-10 times that of Earth, which sounds like a decent start. Instead of jumping in directly, it may be easier to take it in stages, building on the Earth model shown above.

Click to enlarge; copyright Gert van Dijk

The image above shows the first step: Earth's atmosphere is changed to a Jovian one at one atmosphere and 20 degrees centigrade. Internet sources show that the Jovian atmosphere consists of about 86% hydrogen, 14% helium and a smattering of other compounds. Based on the densities of hydrogen (0.0899 kg/m^3) and helium (0.1664 kg/m^3) the density of a 86:14 hydrogen/helium mixture should be 0.1006 kg/m^3. Oops! That is only very slightly denser than pure hydrogen, which we need to fill the ballont with! If you thought Earth air was a bad medium for ballonts, think again. So what are the effects? Well, the liftable mass is 0.1006-0.0899= 0.0107 kg. Remember that the skin had a mass of 0.5802 kg? There's nothing left for a body, so this balloon is not getting off the ground at all.

Click to enlarge; copyright Gert van Dijk

We were aiming for high pressures, so let's increase the pressure to 10 atmospheres. The mass in the balloon will be 10 times higher, and so will the mass of the equivalent volume of air. So the liftable mass also becomes 10 times larger: 10 x 0.0107= 0.107 g. That's still nowhere near the mass of the skin, so this balloon isn't going up either.

Click to enlarge; copyright Gert van Dijk

Let's leave Jupiter and find a ballont-friendlier place. Uranus and Neptune have atmospheric pressures about 50 times Earth's at the 293 Kelvin range. That's better, and apparently the Uranian atmosphere is heavier, with 2.3% methane thrown in. I make the density of its mixture to be 0.1148 kg/m^3 at 1 atmosphere and at 20 degrees C. So, the 1 m^3 balloon can lift 0.1148-0.0899 =0.0249 kg. That is not good enough, but at 50 atmospheres the liftable mass is 50 times that, or 1.2450 kg. Subtracting the skin leaves 0.6648 kg. Finally, a floating balloon! Hurrah!

Or perhaps not 'hurrah', as that is only a tiny bit more than what we had on Earth to start with... Let's go up to 200 atmospheres in Uranus: the liftable mass, skin already subtracted, would be 4.4 kg, and at 500 atmospheres it would be 11.9 kg. Finally we have what we wanted!

Well, not really; these values are not yet adapted for the lower temperature. Julius is left behind, as we need a wholly new biochemistry. The atmosphere is now also so soupy that you would not want to think about the wind or moving in it. Adding even more problems, there is another potential disaster lurking in these gas giants: gravity. The gravity constant for Uranus is nice at 8.85 m.s^-2, a bit less than Earth's at 9.8 m.s^-2. But Jupiter has a value of over 25, so if you thought you could get away with a nice fragile ballont there, waving its slight tendrils through the air and looping in prey with slender tentacles, think again: the animal would need the sturdy limbs befitting a 2.5G environment.

It really does seem as if the universe is trying to sabotage ballonts, doesn't it? Gas giants do have high atmospheric pressures, but their beneficial effects are counteracted by the fact that the atmospheres consist of very light elements. It seems that the only way to get a viable (pun intended) ballont on a Jovian planet is to make the ballont extremely large. But that is where we started... I am beginning to think that there may not be any appreciable advantage in locating ballonts in gas giants, even though science fiction is full of them. They do about as poorly there as they do on terrestrial planets, meaning they can in fact work, but they have to be big, very big. Perhaps gas giants have other advantages for ballonts: there's certainly a lot of atmosphere to play with in them.

Ca I still claim that ballonts are so common in gas giants that they are boring? Yes, but they will be big, as usual; perhaps that's what makes them boring. The best way out for small ballonts seems to be offered by terrrestrial planets with heavy gases and high pressures: Venusian analogues? Perhaps there will be a 'Ballonts VI', one day.   

Salsa invertebraxa

Some books cannot be classified into a category with any ease; 'Salsa invertebraxa' is definitely such a book. It deals with fictional animals, which criterion by itself reduces the number of books in the putative category enormously. It is not told in a pseudoscientific manner as if the life forms in it actually exist. Dougal Dixon's books are pseudodocumentary in nature, and so is Barlowe's 'Expedition'. If Snaiad, Nereus or Furaha ever make it into book form, they will also fit in the same pseudofactual category. 'Salsa' does none of that; its focus is to tell a story of life through images. It deals with fictional insects functioning as characters with heart and wit, and does this admittedly surprising job brilliantly, I think. I first learned about it through the magazine ImagineFX, and then soon found it on the Behance site. I was intrigued but puzzled by the wonderful but complex images. I found reviews, but the reviewers seemed at a loss to describe what to make of the book. The author, Mozchops, has a page on DeviantArt as well as his own site. If you are interested you should visit all these sites, as they show a fairly large number of the digital paintings Mozchops produced for the book (there is a still larger number of unpublished paintings in the book though. When I found the site of the publisher, Pecksniff Press, I needed but a day or so to decide that I just had to have the book. It was promptly delivered a few days later, but meanwhile I had already contacted Mozchops (Paul Phippen), who was kind enough to explain one or two things about his work. So what is 'Salsa invertebraxa'? You could describe it as a 'graphic novel' telling the story of two insects, comrades from different species travelling through a forest. They are pranksters, stealing eggs from spiders and centipedes. They adorn themselves with the moulted exoskeleton from a cicada-like insect. Decked out in such fashion, they capture colourful caterpillars, suspend them from threads and ride them through the air as if they themselves are knights in armour sitting on war horses. While true, this description might cause the book to come across as silly or even childish. It is neither. It is in fact an extremely complex work that does not give away its secrets lightly. Working out the story needs attention to detail, and there is more to the story than just the above synopsis. The images themselves need careful analysis, because they are full of details and because the artist makes no concessions nor steps down to clarify what it is about. The reader has to rise to the challenge, one I personally enjoyed. There are bits of sparse text, but the words are there to evoke an atmosphere, certainly not as a legend to explain the images. I found myself studying the book several times, and only then did the story start to become clear in my mind. If you like your fantasy biology straight, with little arrows pointing to biological details, you may not like this book. But you would risk missing the incredibly capable artwork. There are certainly enough odd insect shapes in there to satisfy those who like alien animals. Or perhaps their shapes are the result of an alternate evolution on Earth; who knows? I do not think everything in this biology can work. For one thing, I very much doubt that there is space in an insect's head for the neural machinery needed to produce an intelligent prankster, but this is one of those instances where such criticisms are completely beside the point. Ignore it. On rereading the above text, I still doubt that it gives you a full idea what the book is about; you will probably have to read it yourself. I will show a number of images I chose that Mozchops was kind enough to send me in a high-resolution form.

Click to enlarge; copyright Mozchops 2011

Here is an early scene of the two protagonists flying about; the one on the left has clublike extremities while the other is mosquito-like. Just note the shimmer of the wings of the 'mosquito'; it takes skill and belief in your skills to dare paint motion-blurred wings like that, with so little indication of what you see.

Click to enlarge; copyright Mozchops 2011

This image is out on the web already, I think. The two heroes encounter an army of termites, armed to the teeth. I include it so you will get a feeling for how the text adds to the image.

Click to enlarge; copyright Mozchops 2011

Obviously, I could not resist including this one. Regular readers may remember that I did some calculations regarding 'ballonts' some time ago. I had to conclude, to my considerable irritation and disappointment, that my idea of filling Furahan skies with ballooning plankton was not going to work: small ballonts do not work. Luckily, Mozchops had not read that and had designed animals like that. He provided a twist to the idea that I like very much: you are probably all aware of the peculiar mating flight of some dragonflies: the male clasps the female by the neck using claspers on his abdomen. Together the two then fly around to deposit eggs in suitable places. Well, in Mozchops' view the male has a balloon instead of wings, and so the two can float around serenely. Aren't they wonderful? It makes me wish to ignore my own reasoning that small ballonts cannot work...

Click to enlarge; copyright Mozchops 2011

This is one you may have to look at for a while. One of the protagonists, the one with the clubby legs, is riding a caterpillar, as colourful as the saddle cloth of any mediaeval war horse with pennants trailing behind it.

Click to enlarge; copyright Mozchops 2011

At the end of the book the two are met by a host of insects working together as a troupe, the purpose of which is our guess. I wish to show it to you so you can see the inventiveness of the insect shapes. Note the one flying on the right, with its near-mechanical shape and its protruding tongs. The multi-species insect armada contains some of the most wonderful insect shapes in the book.

Click to enlarge; copyright Mozchops 2011

Click to enlarge; copyright Mozchops 2011

Here, a host of insects, from small to majestic, takes to the skies in an exodus the reasons of which we are not told. Mozchops was kind enough to send me an early sketch of this painting, which is an exclusive for this blog. I would like to draw your attention to one insect at the left, the one with twin booms sticking out backwards. I love its shape, with its twin booms evoking the shape of aircraft such as the P38-Lightning. Note that the entire painting is filled with many such inventions. Other people would probably be content to paint just one such design on one painting; here, we are spoilt for choice. All in all, this may be one of the oddest books I have, but it certainly is also among the ones I like best. It certainly deserves more attention, and I hope that this post helps bring that about.

Ballonts under pressure (Ballonts IV)

The previous post dealt with the physics of balloons, with an eye on what it would take to design a viable animal using a lighter than air approach. The main thing that emerged, not very surprisingly, was what makes a balloon work is the difference in density between the gas inside it and the air outside it. It was also clear that balloons below a certain size do not even get off the ground; bigger is better for balloons. And that could raise difficulties, for how do big ballonts breed if not by producing little ones?

Click to enlarge; copyright Gert van Dijk

Seeing how small ballonts cause trouble, here's one painting in the Furaha collection with small ballonts. It was destined for oblivion regardless of whether the ballonts it showed could work. It was an early painting; the hexapod (Caeruleacornu rubrum) is much too insectile and I don't like the colours or the composition anymore. The 'balloon tree' (Mollum trisiphonitum) is a mixomorph making use of sunlight to create little hot spots in which interesting thermal reactions take place. That gave me a nice excuse to paint half-transparent bubbles, always a nice thing to do. Molla (that would be the plural of 'mollum') launch their young into the air in the form of a larvae suspended from a balloon sac. The adult mollum blows gases into the sac, forcing it upwards through one of its siphons. Once the sac pops free, a valve between the sac and the larva closes, and the larva drifts off into the wild blue yonder (or hither, as the case may be). The larva is supposed to crawl around a bit before becoming sessile for the rest of its life.

As you can see, the mollum contains some of the ideas mentioned in the comments on the previous post, such as using a ballont for just one stage on a being's life cycle, or having it produced by an adult. What it also shows is the kind of ballonts I would have liked to have, i.e. fairly small ones... Oh well; what remains to do now is to play around with all the factors in the ballont equation to see how we can get as big as body mass as possible with as little a sac as possible.

A thinner membrane
In the calculations the membrane consisted of a Mylar-like substance. The Mylar party balloons you see everywhere use metal to resist gases diffusing through the Mylar. Whether animals can do that as well is uncertain, but, as fishes face a similar problem with swim bladders, and their sealing method works. I looked at spider silk to see if that would be better, but its density is about the same as that of Mylar. I did not dare to make the membrane thinner than 0.1 mm, which I thought was stretching it already (sorry about that one...).

Change the gas in the balloon
The lighter a gas is inside a balloon, the better, and hydrogen is as light as it gets. About the only way to get less mass would be to heat the hydrogen: after all, hot air balloons float because one cubic meter of hot air weighs less that one cubic meter of colder air. Does heating hydrogen make a difference? The 'ideal gas law' nicely describes the relation between pressure, volume and temperature of a gas. After expanding the ballont model a little bit the model allowed a calculation how much mass of hydrogen could be saved to fill a balloon with a 1 meter radius for a range of temperatures. This is what came out: this hypothetical balloon could lift 4.8519 kg with the inside and outside both at 15 degrees centigrade. With hydrogen heated to 25 degrees less hydrogen was needed to get the same pressure and so the balloon could lift more: an additional 12.4 grams, to be precise.

What!? A bit more reflection clarified why this was so. A hot gas requires fewer molecules to exert the same pressure as a colder gas, and the differences in the amount of molecules needed determines the difference in mass, i.e. how much it lifts. But hydrogen weighs so little that the reduction doesn't amount to anything. It does if you are dealing with a heavier gas such as air. In air, there's not much point in using a hot hydrogen balloon. By the way, those designing their own ballonts should make certain that the bladder is filled with hydrogen only. Water vapour is much heavier than hydrogen, so the bladder should not be 'contaminated' with it!

Change the composition of the atmosphere
Adding heavy gases to your atmosphere will increase how much mass a ballont can lift. Earth air largely contains nitrogen and oxygen, but there are heavier gases. The real heavyweights are noble gases such as krypton (3.7 kg per cubic meter) and xenon (5.86 kg per cubic meter). Radon is even heavier but radioactive. You can dream about replacing half of the nitrogen in the Earths air by xenon: the density of the air would increase 2.4 times, and so would the lifting power of a hydrogen-filled ballont. The snag is of course that heavy elements are very rare in the universe, so such an atmosphere would make little sense. Some other gases might help, such as chlorine, sulfur dioxide or benzene. Large amounts of those would create a nice atmosphere for ballonts. Do not ask me to design a biochemistry to make such an atmosphere probable; I would not know.

Change atmospheric pressure
Another way is to increase atmospheric pressure. Gases can be squeezed, and the physics aren't complicated. Say a given volume of air on a planet X would have a mass of 1 kg; the same volume of hydrogen might have a mass of 0.1 kg. That leaves 0.9 kg to lift something with. Now we increase the pressure twofold. The same volume of air now masses 2 x 1 = 2 kg, and that volume of hydrogen masses 2 x 0.1 = 0.2 kg. The difference now is 1.8 kg, also doubled. So atmospheric density has a linear effect on liftable mass.

Click to enlarge; copyright Gert van Dijk

The graph above shows liftable mass; see the previous post for how that was arrived at. Start at the line for 1 atmosphere (that is Earth itself). If you increase the radius of your balloon, the liftable mass rises, and more so for as the radius increases. We knew that. Go to the next line, one for two atmospheres of pressure, and you get a similar curve. It is just higher.

Click to enlarge; copyright Gert van Dijk

The image above does something similar. It builds on the balloons in the previous post. Under '1 atm.' (that would be Earth) there are two balloons, one with a 0.5 meter radius and one with a 1 meter radius. Underneath are slung the bodies they can just lift. Now let's see what happens if we decide that we want balloons to lift these same bodies, but under a higher atmospheric pressure. The balloons get smaller, but not as much as you might think or wish. For instance, the balloon that had a one meter radius under one atmosphere of pressure can have a radius of 79 cm under two atmospheres of pressure (that radius defines a sphere with half the volume of the with a one meter radius - with twice the density, the mass is the same; see?).

No matter what you do, that third power effect of radius conspires against having small ballonts. I think that I will delve into the possibilities of atmospheres with hundreds of times the pressure of Earth in a later post. That should do justice to 'Jovian floaters'; in the New Hades bookshop you will find that they were supposed to be so common in every gas giant as to be boring. We'll see.

You can of course keep on increasing atmospheric pressures even on a terrestrial planet, but there will be consequences; there always are. Think of wind forces, think of hothouse effects; there are probably lots of other effects. One is 'drag', or the force that resists moving through fluids or gases. If you want a ballont to move against the wind, you will want as small a bladder as possible to reduce drag. With an enormous bladder all a ballont can do is float with the wind, against which resistance would be futile. In a dense atmosphere the bladder would be smaller, making a self-propelled ballont more feasible. But drag also increases with density; as I said, there are always complications, even in a simple Newtonian universe.

In the past I had worked on the physics of ballonts a bit but not in detail. Those earlier efforts had made me settle on a pressure of about two earth atmospheres for Furaha. Two atmospheres is about what you get with a depth of 10 meters of water on Earth. Human bodies can adapt to that, as evidenced by underwater habitats. I did not dare, then or now, to go higher for fear of the consequences. What the current more detailed analysis yields is that smaller ballonts are, how to put it, exempt from existence.

But large ballonts will stay, at least for now. How Furahan ballonts breed and what their evolutionary history is are things that need quite a bit of reflection. I would not be surprised if regular commenters solve these issues long before I ever get round to them...

Ballooning animals and Newtonian fitness (Ballonts III)

Click to enlarge; copyright Gert van Dijk

I have always had a weakness for balloon animals. Not the toy balloons that squeak when you twist them into shape, but lighter-than-air living beings. I would like to see such 'ballonts' float silently and majestically over the plains. One such is shown above (well, two of them). Nice, isn't it? I could do screensavers if anyone wants them.

Click to enlarge; copyright Gert van Dijk

Smaller ballonts, less than a meter, are even more to my taste. These might descend from a rain forest canopy to siphon fluids from carcasses, or something equally mysterious. No wind there, so it might be a good environment for them. They could flap around a bit as well.

Click to enlarge; copyright Gert van Dijk

Less dramatic but much more common would be tiny ballooning seeds drifting with the wind across the world, forming a sort of aerial plankton. Books on biomechanics never mention lighter-than-air flight, but do not discuss radial flight either, as neither exists on Earth. The usual question is whether the absence of lighter-than-air animals on Earth signifies that evolution so far forgot to take off in this direction or that the idea won't fly.

I have written about ballonts before (mostly here and here), but this time the focus will lie on 'hard science', so there will be some formulae and a few calculations. Sorry about that, but it is not really difficult. The goal is to see what is needed to achieve a ballont that can lift a nice hefty body with as small a gas bladder as possible. Because there is a bit of explaining to do we will not get further than Earth in this post.

The first step is to realise that floating in air works exactly the same as floating in water. As 'buoyancy' you will find that in biomechanics textbooks (for instance here and here). It all starts with Archimedes' principle, who stated that 'the upwards force of an object in water equals the weight of the displaced volume of water'. That works in air too, but let's start with water, because that is a bit more intuitive.

• Archimedes started with 'the displaced volume of water'. OK; let's make a box of 20 by 20 by 20 cm and hold it under water. It is not difficult to find the volume of the water it displaces: that is the volume of the box itself, which is 0.2 x 0.2 x 0.2 = 0.008 cubic meters.
• To get weight we first need to know what the mass of that amount of water is. The density of fresh water is 1000 kg per cubic meter (sea water is a bit denser). For 0.008 cubic meter, we get a mass of 0.008x1000= 8 kg.
• Weight is not mass! It is the product of mass with the gravity constant g, and on Earth that is 9.8 m/(s^2). So the upwards force acting on our box is 9.8x8= 78.4 Newton.

Upward force = g x Density of water x Volume of object

Nice, but so what? Well, the presence of g in the formula means that the upward force increases directly with gravity. On a world with twice the gravity of Earth the upwards force will be twice as large as on Earth. One consequence of this is that a floating object rises faster than on Earth. But will it also lift a larger body mass, which is what we want? As we will see, the answer is no, but first we have to calculate how much mass a balloon can lift. The first step to get there is to calculate the object's own weight. We know how to calculate weight: upwards force was weight of water, after all:

object weight = g x Density of object x Volume of object

The net force is obtained by subtracting them, which can be written as follows:

net force= g x (Density of water - Density of object) x Volume of object

The gravity constant g is still in there, but focus on the rest of the formula. If the object is denser than water the net force is downwards -it sinks- and if the object is less dense, it will float. No matter what you do to g, that balance will not change. Without g, the formula describes a mass (density times volume). For a net upwards force, that resulting mass is what the object can lift:

liftable mass= (Density of water - Density of object) x Volume of object

Here is an example: Suppose the object is made of cork with a density of 250 kg/cubic meter. Fill in the numbers for cork and fresh water and you get (1000-250) x 0.0008 = 6 kg. If you tie a mass of 6 kg from the cork cube, the ensemble would just stay in place under water, as its combined density now is the same as that of water. (1) All we need to do to turn this into a formula for the bladder of a ballont in air is to supplant 'water' with 'air', and 'object' with 'bladder':

liftable mass= (Density of air - Density of bladder) x Volume of bladder

The gravity constant g is still not in the equation; although true, the full picture is a bit more complex: the density of the atmosphere is in fact strongly influenced by the strength of gravity, among other factors, so its effects are there still, but hidden. Let's focus on atmospheric density, as it will turn out to be very important for ballonts.   

The density of air on earth at sea level is only about 1.2 kg per cubic meter, so we need very light materials to make a ballont work. The choices are limited. Helium would be great, but it is probably difficult to find on a terrestrial planet, and concocting a biochemistry to produce helium may be taking things too far. Hydrogen is easy to find, can be fabricated, and only weighs 0.0899 kg per cubic meter. We are now almost ready for the real stuff.

Click to enlarge; copyright Gert van Dijk

The image above shows a simple ballont scheme. It builds on the scheme above. Here are the ingredients, supposed to work at one Earth atmosphere and 20 degrees centigrade:

• A spherical bladder. It consists of a membrane, which will weigh something. I have great faith in the ability of Darwinian evolution to come up with amazing substances, so I chose something like Mylar. The membrane will be just 0.1 mm thick, and its density is 1.2 times that of water, based on PET and similar substances. The radius of the sphere allows its area to be calculated, and with that its mass. That is a downwards force.
• The bladder contains hydrogen gas. Its radius gives us its volume, and together with the density of hydrogen (0.084 kg/(m^3) at about 20 degrees) we get the mass of the hydrogen. This is another downwards force. Note that the balloon is not pressurised to have it hold its shape; we will assume that it stays spherical anyway.
• The volume of the displaced air is found from the radius of the bladder and the density of air (1.2 kg/(m^3)). This is an upwards effect.

Subtract the two downwards effects from the one upwards one. What we have left is how much mass the bladder can lift. We will tie a body underneath with a density of 1.1 times that of water. (2)

Click to enlarge; Copyright Gert van Dijk

Click to enlarge; copyright Gert van Dijk

The graph above shows results for bladders of 0.1 to 1 meter radius. The blue line (displaced air) is what determines the upwards force, and the membrane (black) and the hydrogen (green) pull downward. The red line is the difference, and that determines the mass of a body you can suspend from the bladder. Hm; a balloon with a radius of one meter still only lifts about 3 kg, as shown in the image below the graph (the man is a 3D object I found on the internet). While 3 kg is enough to build an interesting animal -think of a cat!- the relative sizes of the bladder and the body mass are not pleasing. Even if we clap on some wings to the body, the animal will still be extremely vulnerable to the slightest wind. It does not even get close to the kind of animal we want. I think we need to do better. Even a protoballont should have some advantage of its bladder, or else Darwinian evolution will not take off.

Click to enlarge; copyright Gert van Dijk

Perhaps the ballont seedlings work better, so let's do the job for a radius of up to 40 cm. Hang on: the red line goes below zero, so the smaller ones cannot lift anything at all! The reason is that their membrane is too heavy at small sizes. On further reflection that is understandable: the mass of the membrane increases with the square of the radius, and lifting ability (volume) with the third power. For very small ballonts, the membrane can outweigh the lifting power! Alas, there go the balloon seedlings. Struck down, not by a lack of Darwinian fitness, but because they are unfit in a Newtonian universe.

Click to enlarge; copyright Gert van Dijk

Let's try again for balloons with a radius of 1 to 5 meter. That's better: we can lift hundreds of kg now, enough for an impressive animal, with limbs, a digestive system, a hydrogen-producing organ (however that works), tentacles for tethering and grasping food, etc.. You may protest that the membrane is too flimsy for an animal of this size. I agree, but even with a thicker membrane, compartments etc., the effect of the third power of volume will easily priduce a net lifting force. Unfortunately, a balloon with a 5 meter radius is still very large indeed, nowhere near the shape we were looking for....

So it is the density difference of the lifting gas compared to the surrounding air that makes a balloon work. Perhaps surprisingly, gravity does not determine the liftable mass, or only indirectly as it affects atmospheric density. Some elements scale with the square of the radius and others with the third power. We saw earlier that this limits the size of land animals (start here for that subject). For ballonts it is just the opposite: bigger is better, at least as far as liftable mass is concerned. Whether the animal is viable in the Darwinian sense is something else entirely. Earth is a poor place for ballonts: blame Newton. To get them to work we need to manipulate not the ballont, but the planet! More on that in the future.

(1) In reality, the object you tie underneath the object also has both weight and an upwards force. The figure of 6 kg holds for the mass difference between the two.(2) The body also displaces a bit of air, but that has so little mass we will ignore its upwards force.