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?.