How many legs should animals in speculative biology projects have?

By Sigmund Nastrarruzzo and Biblaridion

We recently published the first of two posts in response to comments on Biblaridion’s YouTube review of Sigmund/Gert’s book ‘Wildlife on the planet Furaha’. The number of legs of Furahan creatures evoked many comments, in particular Furahan scalates. Scalates are animals with some similarities to Earth vertebrates, such as a comparable size range and bilateral symmetry. But the six legs of Scalates urged some people to argue that larger animals should always have at most four legs. The previous post dealt with limits posed by a Bauplan: the genetic building plan that defines an animal’s main anatomical features. In this post, we start with discussing Bauplan effects some more and then try to work out what effects the number of legs may have on animals. 

Bauplan limitations 

The odd thing about a Bauplan is that its contents are largely locked and cannot be modified through evolution, and yet that same Bauplan can only have come into being because its contents were at one point highly malleable! If the number of legs is locked in a Bauplan, that number stays fixed. The four limbs of Earth vertebrates are locked, so vertebrates will not have offspring in which the basic pattern jumps to two, six, or eight legs. There are three major lessons here. 

1. The fact that ‘four legs’ is part of the vertebrate Bauplan does not mean that this number works significantly better or worse than another number; all we can conclude from the long history of vertebrates is that four legs work well enough. 
2. The number of legs does not have to be locked in a Bauplan in each and every animal clade! The number is in fact variable in Earth millipedes, and speculative biology creators can use that fact to decide whether the number of legs in their creations is fixed or malleable (it is variable in Furahan rusps). 
3. The basic instruction ‘make four limbs’ still allows anatomical modification of those four limbs. Evolution can find other purposes than walking for front legs, a principle baptised ‘centaurism’ in this blog; examples are the front legs of mantises, wings in birds, the hands of primates and theropods, and mouth parts in just about any arthropod. The result is that the animal gains new functionality at the cost of a pair of walking legs. Such centauric evolutionary changes probably starts with animals using their front legs both for walking and for a new purpose, and over time the new function takes over completely, so the walking role is lost. Some commenters on Biblaridion’s video felt that many-legged animals would lose legs until they arrived at four legs, without a new function. But in an evolutionary process each step has to bring an advantage. To make their scenario work, animals would have to start using only four of their six legs even though all six were fully functional; we see no clear advantage in that, and evolution is not driven by future goals, but by advantages here and now. 

Building costs 

If a leg is only a weight-bearing cylinder, then each leg can be more slender the more legs there are. But what is the total mass of many slender legs, compared to that of a few stout ones? The calculations on that question (here and here) showed less total weight with fewer legs, with the least mass for just one leg! But you only have to think about how fatiguing it is to hop on one leg to realise that building costs cannot be the only consideration. In evolution, many factors usually play a role, and the best solution then is a compromise between conflicting demands. For example, factors such as stability and surviving harm may outweigh saving weight. 

Surviving harm

If a one-legged or two-legged animal breaks a leg, it will be unable to eat or drink, and will quickly become someone’s dinner. Four-legged animals are probably also doomed (dogs and cats can adapt in amazing ways, probably because humans help them through the critical phase). A six-legged animal can probably limp away after the loss of one leg, and the consequences of injury become less severe with a larger number of legs. Do millipedes even walk slower after losing a leg? In short, multiple legs allow better chances of surviving injury than four or fewer legs. 

Speed 

Animals that walk fast use four principles to speed up. The first three are simple: steps become longer, step frequency increases, and the fraction of time a leg is in the air increases, while time on the ground decreases. The fourth factor is gait, meaning phase differences between legs. During a slow walk, the body has to be supported at all times, which is best done by having all legs move at different times, so no two legs move in synchrony. For slow walks, this works best with four or more legs. However, fast running works best if the gait contains jumps, meaning periods in which all legs are off the ground at the same time. To achieve that, leg movements have to be synchronised to a degree, which can -in principle- be done regardless of the number of legs. For instance, take a Furahan rusp with 24 legs. When such animals run, all right-sided legs move in unison, and so do the left-sided legs, but exactly 50% out of phase. 

Bipedal running cockroach; click to enlarge. From Full and Tu 1991

 

However, that is not how many-legged animals run on Earth. Cockroaches, crabs and lizards may use just two legs when running fast. Why do they not use all their legs and run like rusps? Well, rusps have their feet close to the midline, which makes it easier to support the body with legs on one side only; cockroaches, crabs and lizards have splayed legs, which makes one-sided support difficult. Another part of the answer appears to be that the preferred legs for bipedal running in cockroaches and lizards are longer than other legs, so the other legs are less useful for speed. Note that, even though crabs may need only two legs for maximum speed, this hasn’t resulted in crabs with only two legs! The other legs are useful at other speeds. For instance, crabs need good stability when walking slowly, helped by having more legs, and their life may depend on their ability to cling to a rock using all legs in heavy surf. 

For large animals, it is less likely that one pair of legs provides enough power for maximum speed, so they need more legs to achieve that. Perhaps another factor weighs in too, such as the animal not achieving stability with only two legs while running. 

Stability and size 

We will use ‘stability’ essentially as the likelihood of not falling, while standing or walking. Animal size is extremely important here, because the effects of gravity are relatively much more important for large than for small animals. In contrast, sideways forces such as wind and water currents are more important for small animals.  

Gravity always presses large animals firmly to the ground, so their feet do not have to cling to the ground or grasp it. Stability primarily means keeping the centre of gravity over the area defined by where the feet touch the ground (a support diagram), and secondarily being able to keep the body orientation the same. 

Small animals, say insect size, do need to cling to or grasp whichever surface they reach, regardless of whether that is vertical (as in the illustrations below), horizontal or even upside-down. For them, stability is keeping the body position and orientation stable regardless of where the footholds are. 

What happens to stability and position for large and small animals when the number or legs increases?

Click to enlarge; copyright Gert van Dijk

• One leg allows a large animal to stand and to hop, with gravity ensuring it always returns to the ground. One-legged standing and hopping amounts to a continuous balancing act, which in turn needs very sophisticated nervous and muscular systems. Animals that are just learning to walk on dry land will not yet have evolved such sophisticated systems, so it is doubtful that one-legged animals could even begin to evolve the skill of walking. For a one-legged small animal, hanging from its one leg, life is simple: if it relinquishes its grip, it falls away from its support surface; not a good idea. 

Click to enlarge; copyright Gert van Dijk

• Two legs means fewer directions to fall in, which helps. Birds, some other dinosaurs and people all walk well with two legs. It is not easy though: faster walking requires dynamic stability, meaning the centre of gravity needs to kept over a continuously changing support diagram. To do that, you will again need exquisite control, so we advise bipedal animals that aim to become terrestrial walkers, but cannot do so yet, to not bother. Very small two-legged animals could theoretically hang from one leg while moving the other, but it would be very difficult to prevent the body from just hanging down from one leg: not a good idea. 

 

Click to enlarge; copyright Gert van Dijk

• Three legs, for larger animals, allow a neat support triangle; that is all you need to stand still, and you do not need complex control for that either. But walking with three legs will require excellent control. Very small animals can hang from two legs, but it will still be difficult to control body position. 

 

Click to enlarge; copyright Gert van Dijk

• Four legs, in larger animals, do not make standing easier than with three legs, except when there are strong sideways forces such as water currents or strong winds. If there are, it helps to have a leg sticking out in the direction of that force. Walking with four legs offers a fundamental advantage over walking with three legs: you can lift one leg and still remain stably supported by the other three. This is still not exactly easy: tortoises, moving slowly, have stability problems, as they tend to fall in the direction of the lifted leg. It takes a specific order of moving the legs to prevent that, so here’s that neural control again. Small animals with four legs can maintain their body position using three legs, while one limb moves to a new foothold. 

 

Click to enlarge; copyright Gert van Dijk

Click to enlarge; copyright Gert van Dijk

• Five and more legs will not improve stability much, for large standing or walking animals. This probably holds for small animals too: with many legs, they can choose which ones grab a surface and which ones move to the next foothold, all while nicely keeping the body in position. However, many legs may help to grasp objects better: the eight legs of crabs may act as fingers, making a crab a sort of hand to grab rocks with; insects walking uphill may keep more feet on the ground than they do on a horizontal surface; the many legs of millipedes may help them bulldoze through dead leaves or soil. 

Stability becomes easier with more legs, at least up to a point; we guess that stability will not increase much beyond, say, six or eight legs. We suspect that ‘beginner walkers’, animals that are just learning the art of moving on dry land, will find the task easier if they have more legs, say six or more. If you are just learning to walk and have only four legs, don’t expect to be able to lift the body at all times at first! Start by crawling on your belly, and only try to lift the body when your control system can guarantee stability. However, if you start with six or more legs, you’ll learn to walk in no time! 

Planetary effects 

Many of these effects will depend on local gravity. On a planet with low gravity all legs can be spindly, and falling won’t hurt as easily. With a very strong gravity, legs have to be very strong and as many legs should be on the ground for as long as possible, which is easier the more legs there are. With a high gravity a lifestyle clinging to branches and twigs is asking for trouble, unless there are always lots of legs keeping a secure grip. 

Conclusion 

The number of legs plays a role in stability, building costs, surviving harm, locomotor efficacy and probably factors we didn’t consider. The number is restrained by evolutionary aspects and may be locked genetically. Whenever there are many factors determining an outcome in biology, it is usually impossible to identify one factor as the sole determinant of success or failure. We think that this holds for the number of legs too. The optimum number of legs is like most biological optima: a summation of many functions with lots of compromises. 

However, this can only be true if the number of legs can in fact vary freely, in which case evolution can modify the number as the outcome of such a summation. But if the number is locked, which seems more likely, then evolution has to work with what it was given. The number may then constrain evolution: for instance, an animal with just two legs would find it difficult to combine flying with walking. 

With all these factors weighing in, we do not think it likely that all large animals in the universe must have four legs (or six, for that matter). There are too many variables at play, so we expect the usual evolutionary mixture of Bauplan constraints and many factors weighing in. That seems to be how biology works, and for that reason speculative biology should work that way too. Are we certain of that? No, we aren't; it’s all speculation, remember? 

 

Short reading list

• Büschges, Ache. Motor control on the move: from insights in insects to general mechanisms. Physiol Rev 2025; 105: 975–1031
• Full RJ, Tu MS. Mechanics of a rapid running insect: two-, four-and six-legged locomotion. Journal of Experimental Biology. 1991; 156: 215-231
  
• R McNeill Alexander. Optima for animals, Revised edition. Princeton 1996 
• R McNeill Alexander. Principles of animal locomotion, Princeton, 2003
• Riiska CA, Harrison JS, Thompson RD, Nina JQ, Gallice GR, Rieser JM, Bhamla S. Katydids shift to higher-stability gaits when climbing inclined substrates. Integrative and Comparative Biology. 2025 Dec;65(6):1667-77. 
• Weihmann T. The smooth transition from many-legged to bipedal locomotion—Gradual leg force reduction and its impact on total ground reaction forces, body dynamics and gait transitions. Frontiers in Bioengineering and Biotechnology. 2022; 9: 769684  

From erect dinosaurs to pivoting fly feet (Frustrating feet 2)

This post is long, fairly complicated and rambles along a bit, so do not say I did not warn you. We are so used to seeing big mammals that most ‘alien’ legs in drawings and films are just mammal legs. One thing you will find in many books is that a key feature of mammal locomotion is that the legs are 'erect'. 

 

Click to enlarge. From Box 4.3 in: Fastovsky & Weishampel. Dinosurs A concise natural history. Fourth Edition Cambridge University Press 2021

 

The image above shows such a scheme, making the point that dinosaurs legs are as erect as mammal legs, using a human as an example. I have always felt that the legs of the dinosaur in the picture are not really 'erect', while the human's leg both are less erect than they usually are in a standing human. 

Click to enlarge; copyright Gert van Dijk

Let's explore this further. Above, you see the species Disniformis inexpectus and on the left its cousin, D. expectus. The elbows and knees of D. inexpectus stick out sideways, while those of D. expectus do not. Which animal stands in the most energy-efficient way, and which is the most 'erect'?

 <pause to think>

Many readers may feel that D. expectus wins on both accounts. But have a closer look: in both animals the feet are placed precisely underneath the hips, and the leg segments are tilted in opposite directions as you move down. Because the joints are angled, energy has to be spent to keep these joints from bending further under the influence of gravity. How much energy depends on the angle of the joints and how far these joints are situated from the vertical line connecting hips and feet. Guess what: the legs and joints angles are exactly the same. The legs were just rotated, except for the feet, so exactly the same amount of energy is needed to keep the joints stable.

Personally, I would call a leg fully 'erect' only if the segments are all vertical, as they largely are in standing elephants (and standing people!). If all segments are fully erect, the feet must end up directly underneath the hips. In the dinosaurs and both species of Disniformis, the feet are also placed directly underneath the hips, and it seems some authors use the word 'erect' to mean only that aspect. The opposite of 'feet underneath hips' (FUH) must be 'feet away from hips' (FAFH). If the feet are placed well to the side of the animal, you get a sprawling stance, like salamanders and insects use.         

Perhaps you feel that all this changes when the species start to walk, and then we will see that D. inexpectus can only plod along while D. expectus trots elegantly out of sight. Not so! The legs of both species can extend to the same length and the joints move through the same arcs. This means that  elbows and knees can be kept close to the centre of the animal regardless of whether they deviate to the inside, outside, back or front.

 

Click to enlarge; copyright Gert van Dijk

Still, D. expectus will have a gait advantage in that its joints can be designed much simpler than in D. inexpectus. The dinosaur drawing and the reworked D. expectus above show simple hinge joints that allow the legs to move only in a fore-and-aft direction. That save energy; nice, right?

It would be nice if animals were like trains, only moving along predefined linear tracks. But they also need to turn and to step sideways and do other things beside walking in a straight line. An animal must be able to move its feet fore and aft, but also to the side, and must also be able to turn toes in or out. This requires rotation along all three axes. You can be creative and appoint different movements to different joints, but iff you wish to obtain the largest reach for the foot, you should give the hip joint the most freedom. That is probably the reason mammal hips have ball joints (and dinosaur hips too, as far as I know). My guess is that the most proximal joints (hips/shoulders) in alien animals will also have three axes of rotation. Mind you, the three axes do not have to be used to the same degree in daily life (fore-aft movements will see more use than toe in/out movement).

The ankle joint should allow the foot to adapt to uneven ground, so the joint must allow a toe up/down rotation and also a thumb up/down rotation. That is two axes already; we will get back to the third axis. This leaves joints in between, and these need only have one direction of rotation, like mammal knees (that need not be universal though and is probably something for another post).

 

Click to enlarge; copyright Gert van Dijk

We are now getting to something that has vexed me for years. Above is an image from a post from 2010, showing D. salamandris. This is what I wrote at the time: "To get a movement suitable for walking, its foot should move in a straight line from front to aft … But ensuring that the foot always points forwards also requires that there is a way to rotate some of the bones around a longitudinal axis."

It is the need for that third rotational movement in animals with FAFH ('sprawling') legs that vexes me. Humans are very good at this movement, called pronation and supination (if you hold your arm in front of you, turning the palm down is pronation and turning it up is supination). But I couldn’t find good discussions on this type of movement in the prototypical sprawlers: arthropods. If readers know about such studies, please let me know.

I looked at some internet videos of walking insects to see whether their feet remained fixed to the surface while the leg rotated; if so, these insects had pro- and supination. I would expect the tarsus to allow that movement, even though the text I found previously said that the tarsus only allowed flexion and extension. If the foot would rotate along with the leg, it would pivot over the ground, something hardly compatible with a firm grip.

There weren't that many videos that allowed such close scrutiny, but here is one, showing a fly walking across glass. The foot stays in largely the same position and does not rotate along with the leg. To allow it to that while the hip is moving forward, something has to 'bend'. The tarsus indeed seems to bend a bit, but not much. In fact, the tarsus keeps on pointing in the same direction all the time. 

 

Click to enlarge; copyright Gert van Dijk

I thought of a possible explanation, and it involves a different kind of hip movement. Above are two spidrids. The first has a typical vertical axis of rotation through the hip; that's a normal spidrid. The rest of the leg lies in a plane, and the movement is shown by two 'ghost legs' (this is typically how crabs move). The second image has another hip, with the axis horizontal. The animal can still reach fore and aft, but the results looks different.

 

Here is what the differences amount in an animated view: first a typical spidrid movement with a vertical axis. The gray structures indicate the planes in which the legs move.

 

And now a Neospidrid with a horizontal axis (the model caters for intermediate angles too).

An thay means we can get back to flies; in a textbook of arthropod anatomy (Manton 1977) I found indications that insects hips have an added 'rocking' movement that would indeed allow some rotation around a horizontal axis. But there's a rub. With such an axis, you still need pro- and supination to keep the insect's 'palm' against the surface. I still do not know how insects solve the need for this longitudinal foot movements. Crabs are probably easier, as they have no feet in the common sense, so they can just pivot on the tips of their legs. 

I confess that designing alien animals is sometimes easier than studying Earth animals. In particular when it comes to feet!                    

 

 

How do tetropters walk? (Tetropters IX)

In a recent post I showed my latest animation of tetropter flight, using a brightly coloured farfalloid species as an example. As I wrote then, the reason to get down to the nuts and bolts of tetropter anatomy and movement was that I am painting a few tetropters paintings.

Click to enlarge; copyright Gert van Dijk

Here is a small fragment of the latest one. I had given most attention to tetropter wing movement, but naturalistic paintings also require details about the rest of their anatomy, such as eyes, mouth and legs. The radial nature of tetropters is very reminiscent of that of spidrids; tetropters obviously share a common ancestor with spidrids. On the whole, tetropters are much smaller than spidrids. Whereas spidrids are in the crab range, tetropters are more like insects in size. The Furahan atmosphere is denser than Earth's, which makes flying easier. The tetropter respiratory system does not wholly depend on passive diffusion, so it does not form a crucial limiting factor. Some tetropters, such as the Red Baron shown earlier, are quite a bit larger than current earth insects. There may well be tetropter species in remote areas that are as large as the giant dragonflies from Earth's Carboniferous era. These areas have not been explored in detail yet: they are far away and travel is expensive.

Tetropters have eight legs, just as spidrids do, and their gaits are in many cases exactly like those of spidrids. There are exceptions though. Tetropter legs differ in some aspects from spidrid legs. The most obvious difference is that the legs of a tetropter need not be all alike. In contrast,  all eight legs of any spidrid are virtually identical. Again, this is a bit like insects' legs, that usually differ markedly in size and shape between front, middle and hind legs. This probably makes sense because these legs have different mechanical roles, whereas tetropters do not even have a front or a back. The asymmetry of tetropter legs takes a shape that is peculiar to their radial nature, and quite fitting: there are four large legs and four smaller ones, and they alternate: big, small, big, small, etc. Over evolutionary time, the differences have become quite marked in some clades. In predators such as the 'Red Baron' the outer ring of legs has gained a grasping function. In most species both the outer and inner rings are used for walking. Some say that the differences came about in response to a need to stop the legs becoming entangled; that sounds good, but spidrids do not seem to suffer from tripping over their own legs! Others say that the small size of tetropters means they needed legs that are splayed very wide to stop them being blown over by the wind. But why should that hold for just four legs? Sometimes we just do not know... (meaning I will shelve the question for later, or perhaps I will leave it unsold. There are many things unclear in Earth biology, so perhaps I do not have to explain everything).

Anyway, here is a schematic tetropter using the 'double table' gait. Its wings are neatly held in their vertical resting position. At any time there are four legs of either the outer or the inner ring on the ground. For a brief moment there are eight. This system is just as stable as the 'double tripod' of insects. There is little or no chance of falling. Note that the body wobbles a bit. I did that just so you could see that there is a joint between the 'corpus' holding the legs and mouth on the one hand, and the cephalothorax holding eyes and wings on the other hand.

   
This specimen proves that the gait can be a bit more fanciful than the 'double table' without destroying overall stability. You may also note that the joints of the legs are arranged in a different way. In the previous species, and in all spidrids, the angles between the three big leg segments always bend in the same direction, so the leg gets curved more inwards and downwards as you progress from the proximal portions near the body to the distal parts at the tip. In this particular species, the first joint bends in the other way. In earth arthropods you can easily find these patterns too.

Finally, here is a walking tetropter in which the joints of the legs of the outer ring all curve inwards, while the inner legs have yet another pattern, starting with a downwards followed by an upwards bend. The gait is somewhat complex as well, which I like, as it gives the animal a more biological feel.

So there we are; now I can safely paint an explanatory diagram explaining how tetropters walk. After that, it's back to 'toe studies' again. I must say I am distracted because I watched season 4 of Game of Thrones again. There is a scene in a giant rides a mammoth. Hang on; as I calculated earlier, such a giant should weigh about 1440 kg! Mammoths are big and probably strong, but that is some weight! How much weight can a mammoth actually carry? That is obviously a very silly question, but also one quite worthy of this blog. I may need to find out...

Run, rusp, run!

I keep coming back to rusps because their basic centipede shape allows me to play with gaits and movements more than I thought at the start. So far, I have only shown very large rusps, 'megarusps', having a mass equalling or surpassing that of sauropods. If you need to brush up on your crambology (yes, I invented a word to describe the knowledge of rusps), start with some earlier posts: one, two, three and four (there are more, but these will do). Of course, you can also learn about rusp gaits on the main Furaha page.  

Now, megarusps are immense, and you should not expect them to hop and jump around a place like a rabbit on speed. Instead, expect them to move ponderously and solemnly. Still, megarusps must have evolved from smaller ancestors, and that by itself suggests there could be lots of medium and small rusp species, and indeed there are. And then I wondered whether their multilegged nature might keep them from running fast?

Click to enlarge; copyright Gert van Dijk

Here is my earliest sketch of small rusps again. I have not done any full paintings of such minirusps yet, but I do envision a fruitful adaptive radiation, including arboreal and burrowing species.  I have finished two paintings showing metriorusps ('metrio-' indicates medium-sized), and to do so I had to think about their gaits and in which way these would differ from those of megarusps.

    

Digging rusp. Click to enlarge; copyright Gert van Dijk

Varkrusp. Click to enlarge; copyright Gert van Dijk

 Here are some sketches of metriorusps, that did not make it to 'evolved' status. I played with the idea of differential leg development, so I could have digging species. That design has not made it to a painting, but running and armoured rusps did make the 'evolved' status, though.     

Millipedes and centipedes on Earth can move pretty fast, but they do not really run. Can rusps run?  The answer lies in what exactly is meant by 'running'. On the one hand you can simply interpret the word as 'walking quickly', but there are more complex biological connotations too.
  Walking consists of cyclical strides, and each stride consists of two phases. In the stance phase, a leg is pushed down onto the ground and backwards, providing upwards and forwards force. In the swing phase, the leg is lifted and moves forwards so it will be ready for the next stance phase. During the lift phase the animal should not fall, and preventing that is usually accomplished by having other legs on the ground at that time. To walk more quickly there are few options: increase stride frequency and increase stride length. The latter can be done by having long legs and by swinging it over the largest distance possible, and to get that working, the time a leg is on the ground will have to be shortened.

copyright Gert van Dijk

 This is precisely what happens on Earth. Here is an old animations of mine showing a horse walking. When walking, each leg is on the ground for more than half the time, so there are likely to be multiple legs on the ground at any one time. The slower an animal moves, the more the situation resembles standing still, and for an animal standing still its centre of gravity must fall within the area described by the feet: that is static stability. The stars in the animations represent the corners of that area. The order in which the leg moves ensures that the area has the shape of a triangle under the body.

copyright Gert van Dijk

For a galloping horse, each leg only touches the ground for a short fraction of its movement cycle. The result is that the chances are low that many legs will touch the ground at any time. In fact, there may well be no legs on the ground at all at some times, so the animal is in fact making a series of jumps. At high speeds static stability gives way to dynamic stability, meaning the animal is kept from falling through inertia and a footfall at the correct time and place.

Running is regularly defined as walking with each leg touching the ground for less than half a walking cycle. On earth, all really fast animals use these principles. Having said that, it is time to go back to centipedes and rusps. Centipedes do not run: their stance phase typically lasts much longer than their swing phases. This increases the chance that there are many legs on the ground at any one time, and, seeing how many legs rusps have, this is almost a certainty. This adds up to there being no jump phases, which seems a bad idea if we want a fast rusp.

   

The answer, I thought, would lie in the gait. The animation above shows a rusp with a slow gait: each foot is on the ground more than half the time. In real life, the animation may have to be sped up for a more realistic effect, but at least the movements are well visible. To support the body well, no region of the long rusp body should be unsupported for a long time, and that is achieved by choosing specific phase differences between the legs. In this case, these seem to work reasonably well. Mind you, rusps have typical 'zigzagzig' legs (see here, here and here for what that means).

The next step, above, is to equip the rusp with a different movement cycle for its legs; the legs now swing further and touch the ground less than half the time. I kept the phase differences the same for comparison. Fortunately for this rusp, its legs do not kick one another with this setting, so the result is not at all bad. There are always legs on the ground though, and that may limit a further increase in speed.

So the gait is the next parameter to tweak. Here, the phase difference between successive legs is much less than before, so the legs on one side move almost in unison. Still, at the moment the last leg on one side leaves the ground, there is already a leg just touching the ground on the other side.            

That can easily be amended. Now the phase differences are almost gone, and there are two periods in the movement cycle when there is no foot on the ground at all. Again, you will have to imagine a proper film speed. This rusp is going so fast, its feet hardly touch the ground!  

So yes, I think there are ways to have rusps run. Actually, they might be able to change phase differences very subtly and continuously, giving them a 'continuously variable transmission', unlike Earth's large mammals, that typically have up to three gaits to choose from (walk, trot and gallop), each with a specific preferred speed.  But that will also depend on energy requirements, something I haven't studied in any detail. 

Click to enlarge; copyright Gert van Dijk

So here is the scale diagram of the runrusp, one of the metriorusps that has already been painted. To close with, it may be interesting to know that I leave hexpods for last, because I am not fully satisfied with the animation of their middle legs yet. But I must say that exploring all the nonhexapod lineages on Furaha is perhaps not a bad idea: it gives more attention to designs that are least Earth-like.  

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?.