Walking on Kepler-22b, or: How many legs are best for megamonsters? II

The documentaries 'Alien planets revealed' and 'Aliens: are we alone?' are nearly identical productions about the Kepler satellite, looking for planets around other stars. Planet hunting has been very successful: in a few years knowledge expanded from not knowing whether our own solar systems was the only one in existence  to the realisation that planets are a dime a dozen. The free app 'exoplanet' regularly updates what is known about such planets. At the time of writing it has data on 1768 confirmed exoplanets. Most are 'hot Jupiters', massive planets very close to their stars. They, and any moons orbiting them, are too hot for Earth-like life, so what everyone is really looking for are planets of an Earth-like mass circling their star in its habitable zone. This 'Goldilocks zone' is not too hot, nor too cold, but just right to have water in fluid form and therefore life as we know it.

From Exoplanet app; click to enlarge

The various techniques of detecting exoplanets all have in common that the planets most easily detected are the most massive ones close in to their star. Even so, techniques gradually get better and smaller and smaller planets can be detected. The graph above was produced by the exoplanet app, and shows the mass of planets compared to the year of discovery: if techniques keep on getting better, many planets with a mass around that of Earth will be discovered in the near future, and we may even expect much smaller planets to be discivered. I suppose that for a while each new Earth analogue will be announced everywhere, and perhaps that will generate interest in speculative exobiology as well ('Hey! We thought so all the time. Come and have a look at Furaha, Nereus, Snaiad and the others!').

'Alien planets revealed' is in part about the planet Kepler-22b, while 'Aliens: are we alone?' is about Kepler is about '701.04', or Kepler-62f, discovered later. The radius of Kepler-22b is 2.38 times that of Earth, and its mass is estimated to be 6.4 times that of Earth; for Kepler-62f the values are 1.41 times Earth for its radius and a mass of 2.8 times Earth. Both documentaries use the same image material to illustrate the consequences of a high gravity for legged locomotion, which is perhaps more apt for Kepler-22b than for Kepler-62f. Oh well, never mind...

Both might be 'ocean worlds'. Both contain a discussion of life in the seas, of which a short clip is shown above. While the text mentions the need for streamlining as something of universal value for a swimming animal, the animals are less streamlined that I would have thought. Perhaps, but I am guessing here, that is due to an unwillingness of the animator to give the animals a completely fish-like of dolphin-like shape. Even though that would make sense, the result might not look sufficiently alien anymore.

My attention was caught more by a discussion of life on land. A high surface gravity has been discussed in the blog more than once, which is not surprising as it affects so many design features of animals and plants (for instance here and here). The documentary is about walking, and high gravity can be expected to have at least four effects on the design of a walking animal.

Firstly, to minimise muscle energy expenditure you may expect pillar-like vertical legs. Any position with angled bones requires energy to keep the joints from bending. You can expect legs to become more vertical on a planet as animal mass increases, which is very visible on Earth. You would also expect animals with the same mass to have more columnar legs on a high-gravity than on a low-gravity planet; I may do the calculations one day to investigate how animal mass and gravity together should affect bone and muscle size. 

A second effect not directly found in textbooks, but which seems to make sense to me, is the 'zigzagging' of a series of leg bones: they will tend to angle forwards and backwards in alternating fashion (the principle is discussed here and here). The idea behind that is to keep all joints fairly close to a vertical line from the hip down to the foot: this decreases the leverage of the joints and again saves on muscle effort. 

A third effect is found in the number of legs. In a post entitled 'How many legs are best for megamonsters? For megamonster syou may read 'high mass animals on an Earth-sized world', but also 'medium maas animal on a high-gravity world'; the effects are very similar. I calculated the relation between the mass of an animal and the mass of all leg bones, assuming that each leg would support its fair share of the animal's mass. I was surprised to find that the least bone mass was needed if the animal had fewer legs, so theoretically one legs would be most efficient. However, that high 'efficiency' only holds true if less bone mass is the only factor to be considered. But there are other factors, and an optimal solution is biology usually represents a careful weighing of many factors. A larger number of legs would protect against falls and allows better survival chances in case of injury of a leg. In the documentaries, someone must have decided that this risk avoidance would be best served by equipping the animal with eight legs. I do not think that we know what the optimal number is, but meanwhile I have nothing against eight legs.
  

Finally, there are gaits to consider: there is an infinite number of ways to describe the order in which you can move eight legs in a walking cycle, but which is best? The safest solution is to move just one leg at a time, leaving the other seven on the ground. At the other side of the spectrum there are very fast gaits using just two legs: even crabs and cockroaches can run bipedally! But running can cause falling, and a fall on a high-gravity world may kill you. A safe solution is to always support the body by at least three legs, forming a tripod. So, based on safety and a guarantee that there must be three legs on the ground at any time, how many legs are needed?  It the animal has four and uses a lift-one-leg-at-a-time strategy, the puzzle can be solved. With six legs you can form the basic insect gait with two alternating tripods. That is shown above: note that the left and right legs of each pair move alternately, and each pair is exactly out of phase with the pair in front of it. The results are, going front to back, the left-right-left pairs move in unison, as do the right-left-right legs; but exactly out of phase, of course.

Are eight legs better? Well, it allows the animal to lift more legs at a time while still having three on the ground, and that can be done in various ways. Another solution is simply to expand the principle of the hexapod, and have the new pair of legs move exactly out of phase with the one in front of it. Each tripod becomes a tetrapod; a 'table' if you like. In the 'double table' scheme shown above you can lift and move each table and keep the animal perfectly stable and safe.

And here is the result of the documentary. The person doing the introduction is Lewis Dartnell, who once introduced Furaha at the Cheltenham science fair. Hi Lewis! The documentaries develop the same 'double table' gait through a genetic algorithm. That is fascinating, as it is based on a model taking many forces into consideration. The person who did those simulations, dr. Bill Sellers, has a very interesting home page on animal movement simulation. I had hoped that the genetic algorithm would have resulted in something a little more surprising than the double table that the old-fashioned logical approach predicted, but the double table does make good sense. I am playing with the idea of writing a genetic algorithm myself to see whether this is just one optimal solution, or whether there are several that are nearly just as good. Perhaps it will help to begin to answer the question 'what is the optimal number of legs for large animals taking lots of variables into consideration?.

Avatar's 'Walking with hexapods' or 'Don't walk this way'

I guess everyone will have seen Avatar by now. If you haven't, and if you like speculative biology, go out and see it now. You can read this post before you go, as it will not spoil the storyline. The film is an amazing spectacle. I loved it, and was fascinated by the computer generated graphics. There is a short 'featurette' in the form of a short documentary on the internet that you should all watch, because it explains some of the basic tenets of the film. Here it is, but remember that there is a much better version on YouTube.

Before Avatar appeared in cinemas, there was this rumour going around that it would be solidly grounded in biology. For a film with floating mountains in it, coherent biology may not be the first thing you would expect. Still, let's look a bit closer at that claim, and start with the natives. As narrated in the 'featurette', the Na'vi (the natives) look very human and have four limbs while all large animals have six. The reason for this apparently has nothing to do with biology and everything with economics. The director, James Cameron, made that quite clear in an interview with Playboy magazine:

Playboy: How much did you get into calibrating your movie heroine’s hotness?
Cameron: Right from the beginning I said, “She’s got to have tits,” even though that makes no sense because her race, the Na’vi, aren’t placental mammals.

So biology did not have to make sense, and in Hollywood facts and fiction do not seem to be regarded as fundamentally different, as they are in science. Oh well, perhaps we should just embrace the natives (the hero does) because there would otherwise not have been any film at all. So let's hope the rest of the Pandoran biosphere is more plausible. The first job at hand has to be how to squeeze four-limbed humanoids into a evolutionary tree in which every big terrestrial animal has six limbs; hm.

Prolemuris from 'featurette'; click to enlarge

The book 'Avatar, an activist survival guide' presents some notes on the Na'vi's presumed evolutionary background. There is an animal, the Prolemuris, that 'has two arms that bifurcate into four forearms; the upper bones of the arms have fused... Biologists believe that this may be an evolutionary precursor to the two-armed Na'vi'. There are two difficulties with this: I suspect that this arrangement would not function at all well, but, more importantly, 'limb fusion' as an evolutionary process seems utterly incredible. If you want to lose limbs, have them gradually decrease in size (the insectoid aliens in 'District 9' did have such minuscule middle legs, if I remember correctly). You might expect the resulting 'fused limbs' to look different from our own, but the natives' arms are so human that you might as well assume that human arms are the result of limb fusion. As a joke you could argue that the presence of two bones in our forearms suggests this to be true... But I really wonder how the film's biological advisors reacted to 'limb fusion'. I doubt they invented it, and surely they raised similar objections?

Thanator from book; click to enlarge

On towards the hexapods. I was not the first to design large alien animals with six legs and won't be the last. But I did think hard about how such animals might walk, and wrote computer programs to explore gaits in a six dimensional phase space to prove it. I know this sounds a bit pedantic, but the Furaha page shows I did. Just go to the land page, or directly here. One of Avatar's stars is the thanator, a large predator, as sleek and supple as a panther. Its middle and front pairs of legs are very close together, as can be seen on the image above, from the book mentioned above. The anatomy and the movement pattern of the first two pairs of legs are virtually identical, which is very odd. Other Pandoran hexapods have this same peculiar arrangement, as can be seen on the following images from the same book (the white triangles here and there are due to the fact that the images on the book were printed at an angle to the page, and I tried to rectify that).

Hammerhead from book; click to enlarge

Sturmbeest from book; click to enlarge

Viperwolf from book; click to enlarge

One result of having the front and middle legs so close together is that there is no good way to connect the shoulder girdle to the torso. The images above show that the animals have typical mammalian shoulder blades; the thanator image even shows typical mammal muscles. One such, the latissimus dorsi, can be seen running from the shoulder blade of the middle leg backwards to the torso. There are typically other large muscles running in all directions from the shoulder blade. How do you solve having two such sets in the same space?

Fragment from 'featurette'

Another result is that such legs almost certainly have to move in unison or they will collide. You typically do not get a long view of anything in Avatar, so here is a small video in which a fragment of direhorses is repeated a few times. The front and middle legs on one side indeed move in tandem. Not always, but generally they do. Mind you, there are two other solutions to avoid clashing legs that I will not go into here, but neither seems to be in use on Pandora. Anatomically these animals have six legs, but functionally they are tetrapods. I do not think that leg clashes can be prevented completely with this anatomy. With that in mind, the scene of the thanator chasing the hero could have ended quite differently: just when the thanator is about to grab the hero, the poor beasts trips over its own legs and crashes to the floor...

Again, you wonder why this design was chosen. According to one internet site one of the advisors, Wayne Barlowe, had this to say: "There was some concern as to the biomechanics of the six legs but my guess was that if they were grouped four towards the front and two in the rear locomotion issues would be solved. Those worries were pretty much put to rest after some informative motion tests were run."

But why should there be any concern about the biomechanics of six legs to start with? Six legs are part of the standard insect design, so six-legged locomotion isn't exactly a novel concept. I am not aware of any insects moving like Avatar's hexapod animals. The insect standard gait is a double tripod, a perfectly sensible solution for slow movement. Insects of course make good use of the fact that they have six legs, and, unlike Pandoran hexapods, do not pretend to have four only. The given explanation has an odd ring to it coming from someone with biological acumen, almost as if there was another, nonbiological reason for this clumsy and implausible arrangement. Perhaps the producers felt that the animals would look too alien if the animals moved in too unfamiliar a manner. I have no idea.

Go see Avatar; I loved most of it. But not for the biomechanics. Surely it would not have been that difficult to make better use of easily accessible knowledge; facts are not expensive. Not many people may notice or care, but the ones that do notice are probably the ones who care a lot.

Locomotion in the game 'Spore'

'Spore', for those few who do not yet know, is a long-awaited computer game in which the player must design and guide a creature from life in some warm pond to a space-faring civilization. While there may not be that much overlap between those who play computer games and those who are interested in exobiology, 'Spore' should hold some interest for either party.

A few weeks ago a part of the game was introduced on its own: the 'Creature Creator'. If you type that into Google with 'spore' along, you will find it in no time. There is a free trial version as well as an inexpensive complete version. The 'creator' allows the user to stick various bits and pieces together to design interesting animals. The parts can be rotated, scaled, etc., and the animal can be coloured to great effect. The program works very smoothly. The resulting animals have a characteristic cartoonish shape and mode of movement to them, so I recommend playing with the trial version.

There are many things you cannot control, however. For instance, you can control the thickness of a body segment, but this works fro all dimensions of that segment. It would be hard to depict a very flat animal with this program, at least so it seems to me now. Another thing that had me puzzled was how the programmers dealt with movement: you can stick on predefined limbs, and then the animal will walk all by itself. I was interested in how the programmers had solved the problem of gait. The Furaha site contains a page on various gaits, and those who have read that will know that there are many different gaits, that all depend on the number of limbs. To see what would happen, I designed a simple animal with a sausage-shaped body, and stuck on up to five pairs of limbs.

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Let's start with the simplest design, a biped, with just one pair of limbs:

By the way, the video catch mode is built into the program; very neat! As you can see, the phase difference between the legs is exactly 50%, or indeed what you would want a walking bipedsuch as ourselves to do. I haven't sen anythingresembling gait controls, and if there aren't, there will be no way to get a kangaroo-like gait. That's a pity in a way, but I guess the complexity of gait control might confuse many players. To keep the number of videos down, I will not show you a tetrapod gait. It turns out there is only one, and it is a trot: the left fore and the right hind leg move in unison, and opposite to the other pair. Again, only a trot, so no walk, pace or gallop! Perhaps a walk could be added in the future: having a slow and a fast gait might make the species involved more interesting to look at, and it can't be very difficult to put in.

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Now, let's increase the number of legs to three; what gait will that give us?

It's a tripod walk! Nice one. The right front, left middle and right hind legs move together, in phase opposite the remaining pair. You can also view this as the phase changing by 50% as you go from to first to the second pair of legs, and from the second to the third pair.

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And now, of course, four or five pairs of legs. The result follows:

Well, well, the programmers decided to stop following that pattern, and now all legs on one side simply move together (except during turns, and designing a neat way of turning must have taken some thought). Using five pairs had exactly the same effect. Again, there is no way to control the gait, so there is no way to obtain the nice rippling effect successive small phase differences have on the general feel of how a centipede moves.

While I would like to see more control over body shapes and gait, let me stress how much fun it is to play around with this program. It really does what it sets out to do extremely well. In fact, the programmers even foresaw that some players would develop animals without any legs at all: even then you get movement of a sort. And oh yes, stride freqency seems to go down as body size goes up. I'm impressed.