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 gar 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...