Monday, 24 March 2014

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?.


Jan said...

Hello. One of the solutions for a giant animal or an animal living on high gravity world could also be having more than two rows of legs, for example like this
What do you think about it?

Andrew Broeker said...

This is totally off-topic Gert, but I wanted to make sure you would see this:

It's a machine that generates power using clapping wings!

Sigmund Nastrazzurro said...

Jan: You are right in that there is no definite reason why legs should be confined to two rows. You cold say that rusps have four ows, with the legs in a staggered fashion, so they do not kick one another. In an earlier blog post I also once considered four rows for another reason: on a very heavy planet you need vertical legs to bear weight, but if that planet also has very strong winds, legs sticking sideways would provide a way for the animal not to be blown over by the wind. Come to think of it, three legs might work for such an animal: a middle row to bear weight and two sideways rows to stay upright.

Andrew Broeker: nice! Every now and then I check what the people of Festo are up to, and very often they come up with something amazing.

Spugpow said...

Great post. Can't say I'm blown away by the creature design, although the vertebrate-type mouth that opens horizontally on the aquatic predator is somewhat appealing. Incidentally, my hypothesis regarding jaw orientation is that mouths that open on a horizontal plane will be more common in animals with many paired limbs to convert into mouthparts, as seen in the case of arthropods and many annelids (though apparently not this one: ), as well as centipedes, which have converted the pair of legs behind the head into fangs.

I have a question regarding leg "zig zagging"; is there any reason to think that a large spidrid-type animal would have issues moving with radially arranged legs bent back on themselves?

Christmas Snow said...

I'm surprised the computer simulation did not show the example of a millipede: Each pair of legs moves in a phase slightly behind its front neighboring pair. This causes the distinctive wave-like pattern of moving legs to become very apparent.

Sigmund Nastrazzurro said...

Spugpow: that is a very interesting idea. Let's see if I understand your meaning correctly: with 'mouths that open on horizontal plane' you mean mouths like the one in the video, right, so the jaws move left/right in rather than the vertebrate up/down pattern? And you suppose that the left-right movement is more likely when mouth parts are derived from legs. I suppose you are right: legs changes will be symmetrical and mirror-sided on the two sides of the body. If you recruit one pair of legs to function as jaws, they can move outwards/inwards already. To get upper and lower jaws on tne right and left side, two pairs of legs would have to change together. Very shrewd.

About the zigzagging: you will have to be more clear about what you mean with leg 'bending back on themselves', as I am not feeling very shrewd today ;-)

Christmas Snow: true. I have been thinking about such simulations, and am confident that are various solutions. The program will no doubt find a solution that fits with whatever parameter is given the most weight; play with relative importance, and there are likely to be changes.

Spugpow said...

You got my meaning correctly regarding the jaws. Maybe it's obvious, but I suppose the same principle applies to the jaws of radial organisms; they'll conform to the symmetry of the animal (as evidenced by the jaws of sea urchins). This could have some interesting results down the line if the animal in question becomes secondarily bilaterally symmetrical. For one thing, such an animal would have many jaws at its disposal to specialize into a complex masticatory toolkit, as insects have done with their many mouthparts derived from legs. Many of Alex Ries's creatures seem to have this evolutionary history, though their jaws are generally not specialized in the way I'm imagining.

What I meant by legs folded in on themselves is simply legs with joints that alternately bend in opposite directions, of the kind you described in a previous blog post. Sorry for being unclear.

Petr said...

I enjoy any new space discoveries, especially when "an earth's distant twin" is considered :) the documentaries seem to be very interesting as well, the aquatic predator had quite inventive anatomy for something out of a space documentary of this sort, especially in comparison with creatures in the stephen hawking space documentary series, the name of which escapes me at the moment, I recall you have made a blog showing how the cliff-crawling/climbing herbivores would fall down, had they not been cgi, because their anatomy was absolutely unfit for that lifestyle.

Titanlizard said...

Hi, Sigmund! Great post and I love the whole Furaha blog/project :)

I have a question for you.

We have a planet which has 4 times bigger gravity than on Earth and the atmosphere is extremely thick with full of Oxigene. Creatures which are extremely big (for example...3 times bigger than Amphicoelias) should be possible if their bones are stronger than titanium and have 6 or 10 limbs?

Unknown said...

En 2011 les chercheurs et ingénieurs de la NASA ont découvert un Système Planétaire situé à 620 al (distance D) de notre Système Solaire grâce au Télescope Spatial KEPLER lancé en 2009 depuis les USA par la NASA, ainsi le système planétaire a été surnommé KEPLER pour faire hommage au Télescope Spatial et surtout à l’Astrophysicien Johannes Kepler né en 1571 et décédé en 1630, les 620 al sont la distance du Centre d’Inertie de notre Soleil au Centre d’Inertie de l’Etoile du Système Planétaire Kepler. Dans la zone habitable de Kepler se trouve une exoplanète tellurique très semblable à notre Terre baptisée Kepler 22b par les scientifiques, son rayon est 2,38 fois plus grand que le rayon de la Terre, ce qui veut dire que son volume est 13,48 fois plus important. (V = 4PI.R^3/3) avec PI = 3,141592654. Kepler 22b est une exoplanète où la couleur bleue prédomine de petites tâches blanches, elle se situe dans la zone habitable de son étoile, elle est suffisamment éloignée pour éviter que l’eau soit vaporisée et éjectée vers l’espace et suffisamment proche pour que l’eau ne s’y trouve pas à l’état solide sur toute la planète. Pour atteindre Kepler 22b il faudrait 620 années à un vaisseau spatial se déplaçant à la vitesse de la lumière, ce qui est hors de notre portée scientifiquement et techniquement parlant.
D = 620 al
D = 620 X 365 X 24 X 3600 X 300.000.000 mètres soient 5,87 E15 km
Kepler-22b est donc une exoplanète en orbite autour de Kepler-22, une étoile de la séquence principale et de type spectral G5, semblable au Soleil mais de métallicité moitié moindre elle se situe dans la constellation du Cygne. Il s'agit de la première planète découverte par le télescope spatial Kepler dans la zone habitable d'une naine jaune, La composition de l'atmosphère joue aussi sur la distance D: une atmosphère chargée en gaz à effet de serre et donc réchauffée peut maintenir l'eau à l'état liquide, même si la planète est plus éloignée de son étoile. La probabilité de trouver sur Kepler 22b de la vie organique est élevée, dommage qu’elle soit tant éloignée de la Terre. Dans le pavé de texte à caractère scientifique THEORIE DE L’INFINI VERSION ALAIN MOCCHETTI, il est écrit qu’il y a eu dans le passé une infinité de Big Bang suffisamment espacés pour éviter toute interférence entre 2 galaxies issues de Big Bang différents et dans le futur, il y aura une infinité de Big Bang avec les mêmes caractéristiques que le passé. Ainsi, l’Univers est infini dans les sens du terme, infinité de Big Bang, infinité de Galaxies, infinité d’Etoiles, infinité d’Exoplanètes du type tellurique, infinité de Géantes Gazeuses, mais aussi infinité de Trous Noirs………

Alain Mocchetti
Ingénieur en Construction Mécanique & en Automatismes
Diplômé Bac + 5 Universitaire (1985)
UFR Sciences de Metz