Would linear increase of a muscle's dimension increase the power as well?

Question

The square-cube law applies to bodies with the same shape, and require them to be increased/decreased in all three dimensions. If you were to take a cube, with every edge being a long, and expand it to be 3a in length on the y axis, it would be three times the weight and area. And with that, you just defeated the only hurdle standing between you and your giant woman fetish.

Okay, maybe not that, but it sounds reasonable for muscles. The magnitude of force, exerted by the muscle, is the function of the muscle's cross-section, after all, though it gets wonky with certain arrangements. It does bring up the question of attachment sites, but we'll deal with that later.

Would scaling muscles in one axis only be able to avoid the square-cube law and linearly increase the force-generating ability?

Answer 1

To clarify, the square-cube law is a structural integrity issue, not a force issue. It is actually easy to make a muscle stronger, but the problem of scale is that it's integrity increases in proportion to the the weakest point of its cross-section whereas the weight increases in proportion to the volume.

So, if by Y-axis, you mean the muscles length, then then answer is no. Because you did not increase the cross-section, the muscle can sustain exactly as much tension as the shorter muscle, but it is 3 times as long and therefore 3 times as heavy.

If you mean keeping the muscle the same length, but making it 3 times as wide, then this does make you 3 times stronger, but not any taller; so, this does not help you make a giant. In this case, the muscle is exactly as strong for its mass as the thinner muscle of same length, but it results in greater total strength.

Making an animal bigger generally includes fundamental reconfigurations of the whole body that go beyond the simple X,Y,Z issue. A muscle designed for a larger animal will have less metabolic and motility organelles and more/better constructed structural membranes. The bones also need to be more hallowed out relying on the relative strength of lattices instead of the absolute strength of more solid structures. Joints need to be better designed for weight distribution and more stability, this means joints that could have before been more radially configured for better mobility must now be more vertically aligned to stay in line with gravity, and looser more flexible ligaments need to tighten up to prevent the more extreme torsion stresses that happen at greater angles of flex. The cardiovascular system needs to be redesigned to circulate enough blood efficiently enough to make sure oxygen is making it to all of your extremities without overworking the heart. This could involve the addition of more artierties that bypass proximal tissues, secondary pumping organs, arterial valves designed to relieve stress on the heart as it may take several pumps to elevate blood to your top most extremities, etc.

That said, bigger is still in some ways better. In some cases, a longer, proportionally weaker limb can do things that a short and stocky limb can not, due to certain mechanical advantages. A really strong short arm for example, will often throw a light projectile slower than a weaker long arm. This is because the hand at the end of a 1 unit long arm turning at N radians/time moves much slower than for a 2 unit long arm turning at N radians/time.

Answer 2

Trivially yes, and [see edit!] even along any axis/direction.

There are three axes along which a muscle could be "extended". Let's say the muscle is aligned with the z-axis (so, by contracting, it would pull something along the z-axis). Then we could extend the muscle along the z-axis (making it longer), the x-axis (making it wider), or the y-axis (making it...taller, I suppose.)

I'm not certain what would happen if you extend the muscle along the z-axis. I expect a better answer than mine will come along and delve into that.

But if you were to extend the muscle along the x or y axis, you would certainly increase its power, linearly with the amount it has been extended. Consider a detached bicep muscle, floating in space. If it contracts, it would exert some power P. Now imagine an identical bicep muscle beside it. If both were to contract, they would exert a power of 2P. Now squish them together, so that they're effectively one muscle that's twice as wide (ie. extended along whichever single axis corresponds to "width"). You now have a single muscle, which has been scaled by a factor of 2 along one axis, that would contract with power 2P.

Edit: It's time to deal with that question of attachment sites!

(Inspired partly by reading Demigan's excellent comment on my answer)

So you can totally increase power along the z-axis, if you're willing to play with attachment sites. Let's take our two floating biceps and arrange them end-to-end along the z-axis. If we connected them to each other, in series, then we increase the range-of-motion but not the power. If, however, each bicep runs a tendon past the other, bypassing it and connecting directly to the target attachment site, then we have two muscles arranged as if in series but actually connected in parallel. This arrangement would increase the power but not the range-of-motion--the double-muscle could only move its load up to the same distance as a single muscle.

(As described, though, this is a hack. For starters, we'd probably want the muscles to be running tendons through each other, so that they're not awkwardly pushing each other to the side when contracting. And I'm sure there would be even better ergonomic arrangements than just having the two muscles stacked end-to-end.)