Friday, 8 August 2014

King Kong, Dragons, and the Tyranny of Size

     If there is one biological mistake which science fiction writers make more than any other it is ignoring the consequences of size. Size affects every aspect of an animal's biology, not just its strength. It affects it food requirements, its temperature control, its senses, every its very shape. Yet nearly all of these ramifications are the results of a simple paradox: an animal has three dimensions, but its surfaces and cross-sections have only two.
    If, for example, King Kong is five times as tall as a normal gorilla, then it follows he must be five times as wide and five times as deep. Therefore, he must weigh 5 x 5 x 5 = 125 times as much, or about 20 tonnes - three times as much as the tyrannosaur he fought, and probably enough to cave in the roof of the Empire State Building. More relevant would be what it would do to his legs. The cross-section of leg bones would be only 25 times normal because a cross-section, by definition, has width and depth, but no height. It follows that, whenever the huge ape walked, every part of his legs would be carrying five times as much as that of a normal gorilla. The odds are he would break a leg as soon as he stood up.
     Even if that were not the case, the acrobatics of the ape in the second King Kong remake would be totally impossible (like just about everything else in that film). When it comes to size, the bigger they are, literally the harder they fall. A mouse can emerged unscathed from a fall which would injure a man, and kill an elephant.
     Obviously, King Kong would need a radical reshaping in order to cope. The first thing would be to reduce weight in areas which do not count - such as the non-weightbearing bones. An elephant's skull, for instance, must be huge to house the muscles used in chewing, and to support its tusks, but it is as full of air cavities as a honeycomb.
     But the most obvious requirement would be to make his limbs far more massive. Compare a gazelle's legs with those of an elephant's. The limbs of very heavy animals always resemble tree trunks or pillars: very thick, with very broad, flat soles. At the same time, they move in such a fashion as to avoid placing too much weight on any one point for any length of time. Something as small as a gazelle walks on the tips of its toes i.e. its hooves. When it gallops, it launches all four feet off the ground, then lands abruptly on just one. On the other hand, an elephant endeavours, both in walking and running, to keep at least three feet on the ground at any one time.
     Admittedly, this is not so easy if one has only two legs, but the bipedal dinosaurs seem to have managed. Nevertheless, their pace would be smoother and more even. Whereas a human being can take all his weight on a single heel, a tyrannosaur, or King Kong, would need to keep much of its weight over the whole foot while the heel of the second touched the ground, then swiftly transfer all the weight to the entire sole in one smooth motion. Even then, there is room for variety. The flesh-eating dinosaurs probably strode pigeon-toed, placing one foot directly in front of the other. A giant ape would be more likely to lurch from side to side.
     Viewers of the Jurassic Park franchise may have noticed that the giant dinosaurs seemed to walk in an unnatural fashion: with a slow-motion, rolling sort of gait. Technical limitations may have been partly responsible, but I suspect it was actually a deliberate attempt by the producer to accurately depict the method the giant beasts would have used to transfer their weight. If this sounds cumbersome, remember that the only predator such a giant need fear is one suffering the same size restrictions. Also, animals as big as elephants are capable of surprising bursts of speed - if only because of the length of their stride.
     Just the same, even the largest bipedal dinosaur was only a third the weight of King Kong. The fact that nothing so enormous has ever existed should raise doubts about whether one ever could.
     Even at more mundane levels, size can have unexpected repercussions. In 1871 two giants got married. Martin Bates was 7 foot 2½ inches [220 cm], his bride, Anna Swan 7 foot 5½ inches [227 cm]. Anna was thus 1.4 times as tall as the average woman, and as the cube of 1.4 is 2.7, you should not be surprised to learn that she weighed 400 lb [182 kg]. Equally, it should be no cause for surprise that her first baby was 27 inches [68½ cm] long and weighted 18 lb [8.2 kg], her second 30 inches [76 cm] and nearly 24 lb [10.9 kg]. The reasons were probably not genetic, but mechanical. Giants typically suffer from excess growth hormone. The grow faster than normal people, but they are not normally born bigger. Anna's children were outsized probably because her womb was large, allowing for more space and more nourishment to grow. However, her birth canal still had only two dimensions to the womb's three. The results was a very protracted labour in both cases, and the death of both babies.
     In a race of giants, of course, anatomy would be more closely adjusted to the requirements of reproduction. It would just happen to be different to human anatomy.
     Also, although this blog is about zoology rather than botany, a few words need to be said about the absolutely gigantic trees which occasionally turn up in science fiction. If trees were made of stone, they could grow as high as the Washington Monument. If they were made of steel, they could reach the height of the Eiffel Tower. But they are made of wood, whose weight bearing strength is considerably lower. Also, they need to move sap without the use of any active pump. The maximum height on earth is not likely to be greatly excelled on other planets.

     Have you ever wondered why the largest birds, such as the ostrich and emu, are all flightless? Nowhere is the tyranny of size so evident as in flight. A 2-D wingspan is required to lift a 3-D body off the ground, a body whose greatest bulk lies in the very muscles which operate the wings. And the only thing holding up the wings is air, which is not a notoriously heavy medium. Increase in size means a rapid increase in the weight/lift ratio, which soon reaches a critical limit.For this reason, large birds such as swans are cumbersome at take off, getting airborne being rather more difficult than staying aloft. Even the 20 lb [9 kg] albatross is adapted for long-distance soaring rather than flapping flight. Indeed, all large birds operate close to their weight/lift limit; their prey must be much smaller than themselves if they have any hope of flying off with it.
     So, just what is the maximum size for a flying animal? Everyone knows that the extinct flying reptiles, the pterosaurs were outstanding in this regard: giant flying dinosaurs able to swoop down on any luckless human time traveller and carry him off to their eyries. Well, not exactly. For a variety of reasons, pterosaurs tended to possess longer wings than birds of a comparable body size. Also, the real giants appeared only at the end of the age of reptiles. For the whole of the Jurassic, which lasted 56 millions years, only the occasional pterosaur was larger than a chicken.
     For a long time the largest pterosaur was thought to be Pteranodon ingens, with a wingspan of 20 feet [6 metres]. Hence, a great deal of study has been done of its probable flying abilities. It is believed to have been a reptilian albatross, soaring on thermals above the sea, and eating fish. Wind tunnel tests suggest that its stalling speed would have been about 10 mph [16 kph], which implies that a headwind greater than that speed would enable it to take off by simply stretching its wings. In lighter breezes it would rise into the air by flapping its wings once a second. After that it would need to flap only on rare occasions. Its low stalling and low sinking speeds allowed it to soar on even the smallest thermals. A difference in temperature between sea and air of a mere 1° would have been sufficient.
     All this, however, is somewhat different from how they are portrayed in fiction. For a start, Pteranodon itself weighed no more than a human being, and probably less. In 1971, however, came the discovery of the largest flying animal ever: one of the very last of the pterosaurs, Quetzalcoatlus northropi. Almost everything about the lifestyle of this monster is a matter of controversy, particularly its weight and its flight ability. With a wingspan of 36 feet [11 metres], it had a weight of probably twice that of a human being. It is hard to imagine that such a gigantic creature would be able to fly at all, but its huge wings indicate that it could. It probably stalked over the landscape with its head as high off the ground as a giraffe's, preying on (relatively) smaller reptiles and mammals like some monstrous stork, then flapping its wings to gain altitude before soaring on the hot Cretaceous thermals.
     Irrespective of the nature of its aerodynamics, the bottom line is this: the all time monarch of the sky was only twice the size of a man,  and at at the maximum size for sustained flight. So where does this leave all those stories of giant birds or reptiles carrying off hapless humans or, on a more positive note, being tamed by man and letting him ride them through the sky? Up in the air, that's where. The only way this could be even marginally possible would be in an environment of very much weaker gravity and/or denser air than we know on earth. Unfortunately, these two conditions tend to be mutually exclusive. If gravity is too weak, a planet is likely to lose its atmosphere. Mars is a good example. Dense atmospheres, on the other hand, will be limited mostly to high gravity planets. There are exceptions, of course, but they come with their own problems. Venus, for instance, is earth sized, but its heavy atmosphere has resulted in a hothouse inimical to life.
     As for dragons, you may as well dispense with wings and allow them to fly like Superman. It can be stated with absolute confidence that nothing that size could ever hope to fly except by magic.

Giant Arthropods
     Giant insects and spiders (no, spiders are not insects!) have long being a mainstay of science fiction. The tremendous strength and voracity of these tiny monsters, their utter, insensate "otherness" in their normal size, makes the thought of expanding them to our own size frame send a shiver up the average person's spine. Seldom does it occur to anyone to ask why they have never reached such a size on our own world.
     Part of the problem should be obvious from the previous discussion. Their spindly legs would collapse under their weight. Their stubby wings would beat uselessly against the weight of their massive bodies. It would be totally impossible to grow to mammalian size without adopting the body proportions of mammals. Nevertheless, one might might ask why a modified version of a giant insect is not possible.
     Arthropods, which are what these creepy-crawlies are called, comprise 80% of all animal species in the world, and are by far the most successful of all animal types. Nevertheless, they are all small because they have a number of common features which are only compatible with smallness.
     For a start, they have no bones. Their skeletons are completely external. Of course, this is more easily seen in a crustacean such as a lobster or prawn, but anyone who feels, or merely looks at, an insect can see that its "skin" is rigid. This exoskeleton, as it is called, must not only support its weight, but also serve as an attachment for its muscles. Every time it moves its leg, the exoskeleton of that leg will be warped by the pull of the muscles. Again, a ten-fold increase in size would result in a 1000-fold increase in weight and a mere 100-fold increase in the surface of its exoskeleton, leading to a ten-fold increase in the original strain. A 100-fold increase in dimensions means a 100-fold increase in strain. The only solution would be to greatly thicken the integument, then strengthen it with mineral deposits - all adding to its weight and rigidity. The outcome should be obvious. Imagine a knight whose armour must support his body as well as protect him. Imagine a giant tortoise. A spider or praying mantis the size of a lion would be a fearful sight, but you would have no trouble outrunning it.
     Although such a cumbersome giant would lose much of its menace, it is nevertheless theoretically possible. But there are other factors. For reasons going back to the evolutionary origin of the group, arthropods do not have a blood circulation system such as ours. Our own bodies are designed so that the internal organs fit into a special body cavity. The corresponding cavity in an arthropod is filled with blood, bathing the innards. A primitive heart is present, along with some major blood vessels, but basically the function of the heart is to keep the blood sloshing around in the body cavity. Such a system works quite well for tiny creatures, but in a large animal it would be totally inefficient. Nevertheless, over vast periods of time evolution could find a solution. It would involve constricting the haemocoele, as the body cavity is called, until it was converted into a complex of genuine blood vessels. However, there is one more, insurmountable problem.
     They have no lungs. Instead, respiration is performed by passive diffusion, using tracheae, or fine tubes through the integument, or book lungs, which are actually dry gills, designed to allow diffusion across their folded surface. But diffusion, by its very nature, is a slow process, suitable only for small organisms. Large animals require some sort of pump. And since diffusion is faster at high temperature, it is no mystery why the largest insects and spiders exist in the tropics, and the largest of all occurred in the Carboniferous Era, when the concentration of oxygen in the air was much greater than today.
     A giant lobster might be more feasible. At least it had gills, which could probably adapt to large size, and water could support the heavy body.
     The reason for these defects, if they can be so called, go back to the very origin of the arthropods. The way in which an animal group can evolve is determined by the direction it took at the very beginning. As an animal becomes larger and more complicated, all it can do is elaborate on the features it already possesses. It may elaborate them to the nth degree, to the point where they are hardly recognizable, but evolving a new organ from scratch is just too difficult. The first fish which crawled ashore were of moderate dimensions, and already possessed an air pocket would could develop into a lung. The first arthropods, however, evolved from very small, segmented worm-like creatures. When they came onto land it was a simple matter to breathe through their skin, then develop pores as the skin hardened. But it meant they could never change. Some creatures are destined to stay small.
     It need not, of course, be exactly the same on another planet.

Allometry, or Why One Part is Longer Than Another
     In everyday life we take it for granted that the proportions of the body change with growth. A baby comes into the world with short, stubby limbs. In order to reach adult proportions, they have to grow faster than the body as a whole - a phenomenon known as positive allometry. A side effect of that this process is that a tall person's limbs are also longer in proportion to his body than those of a short person. "Long and lanky" is a phrase that rolls off the tongue as readily as "short and stocky". Not everyone fits these stereotypes, of course. People grow sideways as well as upwards, so one can be tall and solid, or short and slight, but never, never tall and stocky.
     What is not often realised is that the same process applies in evolution. It is simpler for natural selection to alter the basic growth rate, or prolong it for a longer period, than alter the proportions of the parts. For that reason, short races have stumpier legs than tall races. If ever there evolved a race, or even a separate species, of human beings twice as tall as present, we may rest assured that they would be notable for their long, gangling arms and legs - unless, of course, long limbs had for some reason become a disadvantage.
    "Unless" is the operative word. For example, the hunting style of cats dictates that their jaws are relatively short. The growth rate of their jaws has been slowed compared to (say) a dog species of the same size. But even then, big cats such as lions have longer jaws than their smaller counterparts.
     Often the growth rate changes at certain stages of life e.g. at puberty or at birth. For example, most of the higher animals find it useful to come into the world with a fully functional brain. Thus, brain growth shows positive allometry before birth and negative allometry afterwards. Inevitably, this means that the larger the individual or species, the smaller the brain in relative terms, despite being bigger in absolute terms. The combination of positive allometry for jaws and negative allometry for brains results in an interesting phenomenon: once a certain size is reached there will not be enough space on the skull to anchor the muscles which work the jaws or hold the head upright. In each case, the solution is to produce bony crests along the top of the skull and in a semicircle around the rear. Indeed, it is largely the pull of the muscles against the bone during growth which cause the crests to develop, and you can see them on the skulls of any medium to large size mammal. It is only small animals and those, like us, with large brains who possess smooth skulls.
     The rule of allometry applies to almost every external feature - tail, combs, crests, tufts of hair or feathers - wherever it is not actually ruled out by more important size restraints, or by special environmental considerations. Perhaps the most visible application is with elongated animals. An anaconda is not simply a common grass snake built large. If it were, it would have difficulty supporting its bulk. Elongated animals always become more elongated and thinner as they grow larger. Marine animals are a particular case in point, because the buoyancy of water often permits sizes not possible on land. If a scientist finds a shark tooth twice as long as the largest known specimen, he may rest assured that the owner was a lot more than twice as long. In fact, a really huge marine creature will have more than a passing resemblance to a sea serpent.

Here is a much more detailed academic discussion.
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