I am interested in why many small animals such as ants can lift many times their own weight, yet we don't see any large animals capable of such a feat.
It has been suggested to me that this is due to physics, but I am not even sure what to search for. Could someone explain why indeed it is easy for smaller objects/lifeforms to support several times their own weight, but this is harder as objects/animals become larger?
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:
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!
To answer this question you just need to know that the force scale like the transection surface of a muscle. In other words the bigger the muscles the stronger. Therefore you have
$F ∝ σ_s S$,
where $σ_s$ is the maximum developed muscle stress. It so happens that on earth the muscles work pretty much the same in all the animals (from the ants all the way up to the elephant) so it is pretty universal (it can still vary from one species to another but not by one order of magnitude). For mammals it is around 10 N/cm$^2$.
Then the general allometric law (or spherical cow argument) gives :
$l∝ M^{1/3}$,
$S ∝ l^2 ∝ M^{2/3}$,
where M is the animal weight.
Ok now let's consider the problem of lifting up a weight of mass $M_0$. To do so you have to lift up your own weight plus this mass using your muscles :
$F \sim (M+M_0)g $
$\dfrac{σ_s}{ρ^{2/3}}M^{2/3} \sim (M+M_0)g$
$\dfrac{M_0}{M} \sim a M^{-1/3} -1$
You thus see that the mass that an animal can lift up compare to its weight scale like $M^{-1/3}$. This leads to the impressive strength of ants.
Interestingly enough, you can also use this in a single species to compare the stronger and the heaviest :
$M_0 \sim a_h M^{2/3}(1-\dfrac{M{1/3}}{a_h})$
This function as a maximum ($\dfrac{dM_0}{dM}(M_{strongest}) = 0$) and 2 values for which M_0 = 0 (M=0, boring ; and $M_{heaviest} = a_h^3$. You will easily check that :
$M_{strongest} =\dfrac{8}{27}M_{heaviest}$.
Ok so what? well if you use it for human, we can estimate the value of $a_h$ using the weight of the heaviest man ($M_{heaviest} = 635 kg, Jon Brower Minnoch). Therefore the strongest man should be around 190kg. Well this is exactly the weight of the "strongest man" the Iranian Hossein Reza Zadeh...
Best,
Rémi
To lift anything, a life form on this planet needs muscles. If you want to lift heavier things you need
Stronger muscles and bones need to be supplied with more oxygen, nutrion and so on which leads to needing a stronger heart, a better digestive system and so on. Or simpler: if you want to be stronger, you will get heavier and you need to support your own weight too. And the additional weight increases faster then the additional force you can get out of that.
