Why is there a size limitation on human/animal growth? Assuming the technology exists for man to grow to 200 feet high, it's pretty much a given that the stress on the skeletal structure and joints wouldn't be possible to support the mass or move…but WHY is this? if our current skeletal structures and joints can support our weight as is, wouldn't a much larger skeletal structure do the same assuming it's growing in proportion with the rest of the body? And why wouldn't a giant person be able to move like normal sized humans do? (I'm honestly thinking Ant Man, or even the non-biological sense of mechs/gundams/jaegers)…I'm just having a hard time grasping why if it were possible to grow to gigantic sizes or create giant robots, why it then wouldn't be possible for them to move.
Popular Science – Why is There a Size Limitation on Animals?
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Zasso pointed it already out:
Scaling up a ant to human size means volume (weight) increasing by length proportional $l^{3}$, but the force of muscles is determined by cross section (not muscle weight), so muscle force goes proportioal to $l^{2}$.
Smaller factors are likely:
- stiffness (or strentgh of the skeleton)
- balance point (center of mass)
- leverage (human skeleton is "sub-optimal" for this, we are afaik best optimized by evolution for long runs, more than any other animal)
i did some quick further search on "robot insects" on this interesting topic. This article is quite worth reading and relating biological to technological limits as well as current state of the art in nanobionics:
Interestingly, the force generated from a wide variety of actuator materials and devices has been found to be surprisingly invariant when compared with the actuator mass. A few years back, a comparison of the force-to-weight ratio of various organisms and machines found a striking similarity, with the force scaling linearly with mass over 20 orders of magnitude – from individual protein molecules to rocket engines ("Molecules, muscles, and machines: Universal performance characteristics of motors"). Remarkably, this finding indicates that most of the motors used by humans and animals for transportation have a common upper limit of mass-specific net force output that is independent of materials and mechanisms. Therefore any actuating device produces the same force per mass regardless of the material from which it is constructed and the mechanism by which it operates. This study also makes clear that biological systems dominate at the small mass, small force, range. In contrast, human-made machines dominate at the large mass range.
short example as Sonny asked for in comment:
ant with 10 mm length & 10 mg mass
$\Rightarrow$ lets scale up to human size (2m) $\Rightarrow$ means a factor of 200. So the mass scales with 200x200x200=8000000 (Volume $\propto$ $l^{3}$ ) $\Rightarrow$ human sized ant=80 kg. But muscle forces scales only by factor 200x200=40000. The small ant can carry 100x10mg of her own mass=1g, the human sized ant should be able to carry 1g x 40000=40 kg.
Conclusion: pretty comparable to a avg. 80 kg human man able to carry 40 kg!
I can't claim to know the full answer, but it's amusing to note that this question has a fairly long history in biology. Way back in 1928, J.B.S. Haldane (my great-great uncle) wrote a popular-science article called "On being the right size", about the importance of scaling laws for biological anatomy. The following passage is relevant for the question at hand:
You can drop a mouse down a thousand-yard mine shaft; and, on arriving at the bottom, it gets a slight shock and walks away, provided that the ground is fairly soft. A rat is killed, a man is broken, a horse splashes. For the resistance presented to movement by the air is proportional to the surface of the moving object. Divide an animal’s length, breadth, and height each by ten; its weight is reduced to a thousandth, but its surface only to a hundredth. So the resistance to falling in the case of the small animal is relatively ten times greater than the driving force.
Haldane claimed (without offering direct evidence) that the difference could be explained because of air resistance. The force of air resistance scales as $f_r \propto L^2$, where $L$ is a characteristic linear dimension of the animal. However, the force due to gravity scales as $f_g\propto L^3$ (assuming fixed density). The ratio of these quantities scales as $$\frac{f_r}{f_g} \propto L^{-1}, $$ meaning that smaller animals are buoyed up more effectively by air resistance as they fall.
I expect that there is probably more to the story than this, however, as noted in the comments, these sorts of experiments are tricky to get funding for...
Best Answer
The following fact lies at the heart of this and many similar issues with sizes of things: Not all physical quantities scale with the same power of linear size.
Some quantities, like mass, go as the cube of your scaling - double every dimension of an animal, and it will weigh eight times as much. Other quantities only go as the square of the scaling. Examples of this latter category include
at least to a first approximation. You could also come up with other quantities that scale differently with size.
As a result, simply scaling up an organism will undo the balance that has been achieved for that particular size. Its muscles will likely be too weak, its bones will likely break, and it will generate so much internal heat (if it is warm blooded) that the only equilibrium achievable given its comparatively small surface area would be at a high enough temperature to denature many proteins.
For a completely non-biological example, consider the fact that airplanes cannot be made arbitrarily large, and in fact different sizes of planes have very different shapes and engineering requirements. The surface area of the wings does not scale the same way as the total mass, and the stresses and pressures the material needs to withstand will not stay constant as you enlarge the plane.