Monopods: getting off on the wrong foot?

How many legs can animals have? That is a subject that has been discussed more than once in this blog and its comments. A first gross division of 'leggedness' could be whether the number of legs is even or odd (for odd numbers see here and here), and a second one whether the overall pattern is one of radial or bilateral symmetry. Last week Petr commented on the Xenohox Gazelle, an animal on the doubly odd side of this classification, in that in combines a radial design with an odd number of legs. For those of you who are well-versed in such things, the difference between the radial design of animals such as my tetropters and the Xenohox gazelle is that the axis of symmetry is vertical in the former and horizontal in the latter.

 Fragment from The Future is Wild

Getting back to the topic at hand, Petr asked what I thought of animals with just one leg. I realised that I had omitted walking with one leg or with no legs at all (whether the latter is possible may be a matter of semantics, but there are aspects of moving without legs that resemble those of true walking). Are there many such beasts in speculative fiction? The first one to come to mind is the 'desert hopper', an animal evolved from snails in 'The future is wild'. The DVD is easily available. There is also the Eponan springcroc; there are undoubtedly more.

What should be the proper term for this mode of locomotion? There is a choice between  Greek and Latin equivalents. Examples are the Greek 'tetrapod' and the Latin 'quadruped'. For one-leggers, the words could be 'uniped' (Latin) or 'monopod' (Greek). I prefer the rhythm of the Greek one, so let's stick to that one.      

Monopods have biomechanical problems. The first can be demonstrated easily by hopping on one leg. You will it fatiguing. One reason, but not a major one, is that one set of muscles does the work normally done by two. Fair enough, but the bigger problem has gravity as its cause. Any walk cycle has a stance phase in which the leg pushes against the ground and a swing phase in which thee leg swings forwards, free from the ground. During that swing phase the body will of course fall down, unless another leg supports it. Monopod animals, not having another leg, must deal with the tendency of the body to fall. Do not underestimate this: a normal human biped walk cycle lasts about 1 second, and each leg is off the ground for about 40% of the cycle, meaning about 0.4 seconds. In that time the other leg s supports the body, but what if there wasn't one? Under Earth gravity a time of 0.4 seconds is long enough time to fall 78 cm, much too far to catch up easily with the next step. That unsupported phase should therefore be as short as possible: for 03 second the fall will be 44 cm, for 0.2 seconds it will be 20 cm, and for 0.1 second it will be a mere 5 cm.

During running there are periods in which no leg touches the ground, resembling the monopod problem. Still, our bodies do not move down a long way during the unsupported phase: the unsupported phase does not last long because we do have two legs and because the rate of cycling is much higher than during walking; also we actually jump up enough to combat the falling tendency.
 
Let's turn the biped human into a monopod human. If you keep the leg moving at the same rate as if you were walking with two legs, the unsupported phase will be about 0.4 seconds as shown above. The only way not to fall 80 cm during that time would be to jump up in each step. This is a sizable jump, costing lots of energy. Of course, speeding up the rate of movement helps, but that calls for high acceleration and deceleration, also costing lots of energy. There is probably an optimal balance in there, minimizing the energy for forward movement. The balance would, as holds for any gait with any number of legs, depend on speed. Monopod animals might not be good at low speeds, because gravity does not allow for a slow jump.

A monopod animal is like a human on a pogo stick. 'Pogoing' (we need a verb) would cost less on a low-gravity world, so perhaps they should be sought there. There is probably an optimal mass for pogoing animals. Jumping is not a good idea for animals with a large mass, because they then need disproportionately heavy skeletons. There would be lower limits too: you might think that falling is irrelevant for animals as small as insects, as they would not hurt themselves much by doing so. Then again, the short distance means that there is no time to break the fall, and whatever your size, during a fall control of the body is lost, never a good idea.

Click to enlarge; copyright Gert van Dijk

Another big problem for a monopod would be stability, as shown above. Standing on three legs or more is easy, because there is little skill involved in holding the centre of gravity over the support area on the ground, defined by the points where the feet touch the ground. Bipeds can only stand upright with a sophisticated neural control system. For a monopod such as 'Unipes disneyi', on the left,  the support area is small, requiring an even more sophisticated control system. Sideways forces would pose a very large problem for monopods. Wind is more likely to blow very small animals over than larger ones, and for insects and the like it pays to splay their legs: it produces a large support area. So, alien monopods perhaps should probably not live on planets with very dense atmospheres. The obvious way to solve that problem would be to have long toes sticking out in all directions: the middle monopod in the illustration. They would have to be very strong to counter a tendency of the body to move. In this respect the toes would probably be inferior to legs that stick out towards the same points on the ground but starting from the body, shown on the right. But if the starting point is one leg, the toes would probably be the answer. I do wonder about the body scheme of an animal with just one leg; would that preclude the presence of other paired limbs or organs?        

Finally, having one leg results in no redundancy whatsoever: a monopod with a leg injury is probably doomed, whereas a biped might limp away, and a millipede would simply continue on its way.

Click to enlarge; copyright Gert van Dijk

Are there workarounds? I am tempted to think so. Take the large-toed animal at the left above and make it stand on the tips of its toes. Evolve it a bit to get the animal at the right: the toes get bigger and the upper part of the leg shrinks. Now that animal could just swing one toe forwards while keeping the other ones on the ground. By repeating this movement for the other toes it would no longer need to jump up. But what that does, obviously, is upgrading the status of the toes to that of legs, and then the animal is no longer a monopod but a secondary tetrapod. And a very silly one at that.