1: spherical cow/fermi estimate
You can probably produce more power approximated by the volume of the muscle though.
This never made any sense to me. Muscles are made up of groups of fibers, which are made up of chains of sarcomeres. How could strength be proportional to cross sectional area rather than volume of the muscle?
The same reason that's true of strength of passive members; the limiting factor is the force that will cause shearing, which is basically the strength of one bond in the lengthwise direction times the number of them supporting in parallel in the cross section. So, given the same material, cross sectional area determines strength.
The entire line of reasoning seems to rest on the idea that the smallest unit we consider runs from one end all the way to the other.
It doesn't really matter, except the not being homogenous end-to-end means it's the weakest point that matters. But, irrespective of the structural details, there is some force in the direction of contraction that will cause failure, and that force is proportional to, basically, the number of linkages it is distributed across in parallel (not connections in series, such as along the chain) which is proportional to cross-sectional area.
> The entire line of reasoning seems to rest on the idea that the smallest unit we consider runs from one end all the way to the other.
It is not (in fact, the entire reason it is true of any material is because even structures which seem to be end to end are composed of smaller structures with fallible linkages; if there were indivisible end-to-end structures, this would cease to be a concern.)
Although I was basing that on force exerted by gravity (which is proportional to mass), whereas deceleration might be spread out proportional to length, so it might work out to L² anyway. It's too late to edit though.
Or is this a myth?