Friday, 15 July 2011

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.

23 comments:

trex841 said...

*sigh* well, it seems that my floating fish could never be. oh well, i still love ballonts, i'm shere i'll find some place for them.

Luciano N. Ribeiro said...

Excellent post (and images)!

I've always imagined that, on worlds with an atmosphere density at least equal to, but preferably greater than Earth's; there could be an entire food chain starting with hydrogen-producing free floating microbes that get eaten by jellyfish-like animals which store the gas of their prey in a disproportionally-huge bladder

Despite your disproving of balloon-seeds, I have a feeling that balloon-microbes are still in because there are regular microorganisms that spend their whole lives afloat here on Earth. Perhaps there is a point where the mass of the body because so small that it will float anyway, carried by the weakest winds!

Anyway, I think I know where you're going with part II. Waiting to hear your thoughts on that subject as well :- )

Luke said...

Thanks for this informative and long-awaited post. Interesting that ballonts are almost the mirror image of regular, compressional organisms; bigger is better. That's an important rule that we'll all be keeping in mind from now on.

Can't wait for further installments of the series!

Sigmund Nastrazzurro said...

Trex841: I know it is little consolation, but if your fish have swim baldders, they are in a sense ballonts. Just in water, not in air.

Luciano: Quite a few very small organisms use drag on hairs and plumes and the like to travel upwards in with the air. Lots of 1-2 mm spiders do so. it is even called 'spider ballooning'. I wished to see what true ballooning could do.

Luke: that might be a while. Posts like this one take a lot of time.

Zerraspace said...

While you've convinced me that ballonts are possible from a mechanical perspective, I still feel that the explanation is as yet incomplete. How could such creatures evolve? I can't see the balloon as anything more than a vulnerability till it grows large enough to carry future ballonts upwards, and even then it may be their downfall (more on this below). Did they originate in an isolated environment where there were no animal threats to their ascent? If weight that can be carried rapidly decreases as the balloon grows smaller, how do infant ballonts thrive (or, for that matter, the millimeter length balloonlings)? As far as I've seen most of your illustrated ballonts don't seem to have any obvious wings or means of guidance aside from vestigial fins - how do they control their flight? The zeppeloon's method of changing its body color and with it gas temperature would help it to rise and sink, but it wouldn't help it steer, and the process would be agonizingly slow. I can't help but feel that they would be at the mercy of wind, or more dangerously, having their membranes punctured. All it would take is a bump into a large thorn, sharp branch, or even a hungry predator. How do they defend themselves from predators? Slow ballonts would make easy prey for Furaha's heavier-than-air fliers, which would only have to fly up and puncture them then wait till they run out of hydrogen and die. For that matter, how much energy would it cost to produce the hydrogen required to fill those huge balloons?

I admit it's silly of me to argue this point seeing as I have suggested lighter-than-air flight for other exobiology projects; I just feel the sloth of a purely lighter-than-air flier and its inability to direct itself would be its downfall, just as hot air balloons give way to other aircraft (in both cases when I suggested ballonts, there were no threats to directionless flight and no real need to direct it). Originally I intended to have lighter-than-air insectoids on Zainter which simply used surrounding air and heated it within their bodies to achieve lift, but I've long since scrapped the idea - chances are the gas would have to be heated to a temperature unbearable for the rest of the organism just to rise off the ground, and the heating process would be too energy intensive for the insectoid to handle. Hearing that smaller balloons carry progressively smaller payloads further dissuades me from including them.

Knowing your thoroughness I'm sure you've already solved these problems, but I would like to know how on Earth (or Furaha) you've managed it. ;)

Sigmund Nastrazzurro said...

Zerraspace,

I think I have caused a misunderstanding of large proportions. When I first painted ballonts I had not taken the trouble of working out their basic physical nature (odd, as my knowledge of physics was fresher than it is now). I just assumed, as do many people in speculative biology, that a nice idea would be enough. Later I became more and more convinced that ballonts might not be viable. However, without a proper quantification I felt there was room for doubt. That explains why you may find statements in earlier posts that microballonts might be feasible and large ones might not. In today's post, I argue the exact opposite, but this time I actually did the maths!

I should have done it sooner though, as I had my doubts for a long time, evidenced by this post: http://planetfuraha.blogspot.com/2009/08/lighter-than-air-mechanical.html. In it, I wrote "The more I think about it, the more I am convinced that I cannot really get away with ballonts on Furaha." There is a similar remark in my recent newspaper interview (in Dutch), and that finally prompted me to sit down and do the job properly.

Without that background you might think that today's post was about defending the zeppeloon, seeing that it is still on my site. Well, the next instalment will probably be the end of ballonts on Furaha. Let me get to that post in my own time. Afterwards ballonts on Furaha are likely destined for oblivion, not so much for Darwinian as for Newtonian reasons.

Evan Black said...

Though there are no animal ballonts on Nereus, I do plan on several plants having lighter-than-air qualities. Thanks to this post I'll keep in mind that any floating seeds I have in mind can't be too small.

Once again, your work is insightful and helpful!

j. w. bjerk said...

Thank you very much! This covers some topics i've tried to calculate for myself in the past, and wasn't confident of the results.


Re: Floating seeds vs giant blimps.

If i follow you correctly, you've calculations assume that the membrane is the same thickness/density for the 5mm seedlings, and the 5m giants. While i have no idea what a realistic density for the membrane would be, i'm reasonably sure that a 5mm object could get away with a much thinner, weaker, and less dense membrane than a larger balllont would require.


Re: Removing Ballonts from Furaha

Is your planet so well established that you can't increase the air density? That could give you enough wiggle room to make the Ballonts more viable.


Zerraspace:
For ways that ballonts could survive (once you get them to float) consider earth's jellyfish or salps. Many of the questions you raise are answered by them. Such passive, slow, fragile creatures are probably better models for ballonts than sharks or whales-- at least in atmosphere than is not many times denser than ours.

For sustenance total or partial reliance on photosynthesis, or photosynthetic algea/bacteria, seems probable to me.

Zerraspace said...

Lift for lighter-than-air seeds might be a different story. They would want to caught by the wind and blown around, unlike potential animal ballonts, so perhaps increasing surface area to catch wind with minimum weight gain would be beneficial to them. Lighter-than-air plants were also planned for Epona, although I'm not sure the idea ever came to fruition. Do you think we'll have to break the news to it? For that matter, does this invalidate ballonts living on gas giants where the air pressure is enormously higher?

Well, that definitely wasn't the answer I was expecting, Sigmund Nastrazzurro, particularly since the physics seemed to support the idea of large ballonts - at a glance at least. While I was never quite a believer in them I will mourn the ballonts' passing; they seem to me symbolic of the wonder of Furaha's wildlife, just like the tetropters so often discussed here. If you remove the zeppeloon, will you replace it with another flier, or just a "flying with..." page (and for that matter, will you include lighter-than-air flight in this explanation?)

rodlox said...

no Ballonts from here on? :(

I forget how author Robert Silverberg devised them, but he created ballont-like plants: they are shrub- and tree-sized succulents(?) that, as the plant ages, the spot connecting a branch to the rest of the plant weakens and eventually breaks off -- but as the attachment point is weakening, the branch is growing larger and larger (and lighter)...and the branch eventually floats away to take root somewhere far away.


Zerraspace - how do they avoid predators? well, maybe they live above where the predators live.

Luke said...

I desperately want the ballonts to be saved :( .

Let me try and address Zerraspace's points as best I can.

Evolution:

Perhaps the ballonts started as pelagic creatures who stayed afloat with gas bags that, by a quirk of their biochemistry, happened to be full of hydrogen. They were basically giant portuguese man o' wars, catching prey with their tentacles and using their bladders to catch the wind. Larger bladders had a greater surface area and caught the wind more easily; over time, some of these creatures developed gas bags that flew well above the surface of the water, practically lifting the whole animal into the air.

At some point, some ballonts became adapted to rise completely out of the water when they entered a stretch of barren ocean; hopefully the wind would carry them to more productive waters. The ballonts would drift in a comatose state until some cue, maybe a chemical signal from a tentacle trailing in the water, prompted them to come down again.

The development of greater flying ability allowed some ballonts to evolve a longer lifecycle; rather than dying when the winter came around, the ballonts could rise above the weather and wait for plankton to bloom again in the spring.

From there, the rest was a fairly straightforward increase in flying ability; stronger balloons, color changing ability, acute sensitivity to winds and temperatures etc. The ability of some ballonts to come down to land was a later development, perhaps with a transitional stage of visiting freshwater lakes.

Navigation:

Ballonts like the Zeppeloon don't need to worry about turning quickly to avoid an obstacle; even when they descend to feed, it is only their tentacles that get close to the ground. What they do need to worry about is staying within the right range of latitudes, and presumably they accomplish this by taking careful note of things like air pressure, wind speed and direction, the angle of the sun, and other things. They use this information to instinctively determine at what altitude to hover in order to catch the right wind or stay above unpleasant weather. Tiny creatures like bees and butterflies manage similar navigational feats on a different timescale.

Defense:

The zeppeloon is obviously beyond the reach of most creatures, both by virtue of its size and the altitude at which it flies. For smaller ballonts closer to Earth, poison seems like an option, especially since they will already be equipped with (presumably) stinging tentacles. They won't make very appetizing prey in any case, being hard to reach for land animals, and containing little to no muscle.

The balloon wouldn't be easy to puncture if it was made of a mylar-like substance as Sigmund assumes. I'm with him in thinking that a mylar-like cuticle isn't a stretch to evolve.

Energy:

Unfortunately, I have no idea how much energy it would cost to generate the hydrogen to fill a balloon. It does suggest an interesting lifestyle of "gas parasites", ballonts that obtain a large portion of their hydrogen by puncturing the gasbags of others with a proboscis. They wouldn't be able to track their prey, but perhaps could rely on chance encounters like the pelagic sea slug Glaucus atlanticus http://en.wikipedia.org/wiki/Glaucus_atlanticus (scientists apparently aren't sure if it can control its movement through the water, but even if it can it must rely mostly on chance to bring siphonophores close by).

That addresses all the side issues, although the evolution of ballonts could be improved still. I'm with J.W. Berk in wondering if the atmosphere of Furaha could be tweaked to solve the physical problems; presumably it's already thicker than Earth's, since Furaha has higher gravity. But I guess Sigmund will have an answer in the next blog post :) .

Sigmund Nastrazzurro said...

My friends, I think I have never had so many nor such long and detailed immediate replies to any post before. Thank you.

"Keep ballonts aloft"; well, I have thought about atmospheric density, temperature, membrane composition and bladder-to-body ratio, and am still very doubtful about ballonts.

However, I have not studied all these aspects in the detail they deserve yet. But after this first quantitative exercise I am inclined to think that passive large ballonts are feasible from a physical point of view. Biologically the story may be different, and small ones are difficult in any sense.

The comparison with jellyfish and the like is very apt. Passively floating organisms with little control over their whereabouts are feasible. The main problem may be that jellyfish can be small and extremely numerous, while we are used to large animals being rare. Are exceptions possible?

It is quite possible that large ballonts are feasible if a jellyfish-like environment is available, as may be the case for Jovian planets: high pressure, possibly abundant resources, etc. In the New Hades store you will find a cover blurb stating that Jovian Floaters being common enough to be boring. The real challenge is designing ballonts for terrestrial planets.

I'll be back.

rodlox said...

large jellyfish exist - Lion's Mane and Man'o'War, as two examples.

dP said...

Very interesting!

Based on your issues with small balloons not having enough lift to overcome their own weight, I'd say you'd definitely have to start looking at a butterfly-type lifecycle, with a terrestial phase to grow before going airborne.
Is there any possible way to have your lift gases also function in digestion?
It seems ithat the most outlandish physical adaptations in nature, the ones of questionable survival usefulness, all wind up going back to sex. So a balloon phase most likely wouldn't be eating, it would be all about finding a mate and distributing eggs all over wherever the wind took you before you used up all your stored energy.....

Sigmund Nastrazzurro said...

Rodlox:

I did not know about the Lion's mane (how could it have escaped me?) Thank you.

dP:
A very logical conclusion. I have once painted a sessile mixomorph whose ballont larvae spread through the air, but there weren't any who used it to disperse many seeds at a time. The idea makes good sense.

Evan Black said...

That balloon phase to distribute eggs (seeds, in my case) like dP mentioned is exactly how I plan to use it with my own project.

I just think that ballonts are too interesting to abandon in my own work. It's a shame they will be leaving Furaha, but while I do think they are plausible, they would also be very rare and shouldn't show up everywhere.

rodlox said...

had a thought in the car: what if the balloon part of the ballont only grows when the herbivores and carnivores are all elsewhere (ie a Serengeti-type mass migration)

Sigmund Nastrazzurro said...

Evan, Rodlox,

With all the comments I am starting to struggle to keep ballonts in some way or another. As Evan said, they are too interesting...

I cannot keep them as they were. Small ones have to go. Even with a '2 atmosphere' atmosphere they have too be big and passive (I guessed as much earlier).

Dispersal in any shape or form is a good idea, including seasonal patterns, but the riddle remains how to get the system started...

rodlox said...

hm...maybe a system like the Drakensberg (South Africa), herbivores and carnivores going up and down the mountains.

meanwhile, warmth-generating plants (they exist on Earth, I assume other worlds have them too) develop bubbles or other structures for storing heat at night/dispersing seeds (or both).

and go from there?

dP said...

Well, didn't feathers start for warming purposes, before being used for flight? So could balloon-like organs start for some other reason (I'm thinking, once again, sexual display like an elephant seal's nose taken to extremes) and evolve from there (it's such a delicate system it'd have to evolve in a relatively isolated ecology I suspect, like an island).

Regarding minimum size, I was just reading on Wikipedia that Sea Spider muscles consist of one cell each. I don't know if that's true, but if so it suggests that you can get away with very little in the way of body....I'm wondering if you could strip a small balloon with a few muscle cells and still get it to wiggle like the blimps in your previous ballonts post...

What was the 2 atmosphere idea? Was that like those saline lakes located under the ocean (http://www.geekologie.com/2008/09/wait_what_an_underwater_lake.php)? That would be interesting. I'd love to see a post about making athmosphere more dense but still somewhere humans could visit, what you would have to change chemically to make that happen.

Sigmund Nastrazzurro said...

Hi dP,

That is creative thinking. I am still struggling with how to get the evolution of ballonts rolling.

As for minimal mass, perhaps. I guess I wanted something to look at and that would be complex enough to look back at me.

As for the '2 atmospheres', I did not put that very well. What I meant was an atmosphere under a pressure of twice that of our atmosphere.

Evan Black said...

The best Darwinian scenario I can imagine to bring about ballonts is a man o' war-like creature that floats at the surface of the water that suddenly faces an influx of predators. Though stinging cells may curb many attacks, perhaps there is too much damage due to attrition (the predator is stung but the victim is damaged as well). Those who float higher, and can even leave the water based on buoyancy, will survive. Predators leap from the water to try and catch them and the evolutionary arms race is off! There may be better scenarios, but that's one that seems pretty clear in my mind.

A ballont complex enough to "look back" will have to be very large to lift the weight of the heavy brain and supportive organs. The size of the balloon could be diminished by a denser atmosphere.

Dan said...

Really interesting and informative - I'll take all of that into account with balloon worms.