Why is muscle force more dependent on cross-sectional area than on fiber length?

Question

I was looking up why smaller animals are proportionally stronger than larger animals. The answer that comes back everytime is that muscle force depends on the number of muscle fibers, which is proportional to the cross-sectional area of the muscle. However, I don't understand why muscle force wouldn't depend on fiber length. I'm not a native english speaker, so I'll try my best to articulate my reasoning in the most concise way possible.

• Force is exerted by the myosin motors. Force is therefore proportional to the number of myosin motors.
• The number of myosin motors is proportional to the fiber length.
• The number of myosin filaments is proportional to the cross-sectional area.
• Then, muscle force is proportional to muscle volume, and therefore to muscle mass.

What am I missing ? Why is muscle fiber length not that important to muscle force ?

Thank you in advance for your help.

Answer 1

Here is a thought experiment that might help. Consider a single muscle fiber as being like a rope. Granted, a rope won't shorten on its own, but if you think of an isometric muscle contraction, then it's closer to what is happening when a single fiber contracts.

Now think about two situations:

1. You double the length of the rope. Does the total force that the rope can hold get larger, smaller, or stay basically the same?
2. You halve the length of the rope by doubling it up (so two ropes instead of one). Does the force that the rope can hold get larger, smaller, or stay basically the same.

So lining up more fibers in series is like making a longer and longer rope. It's still basically as strong (or weak) as a single rope. But when you bundle more ropes, increasing the cross-sectional area, the overall force that they can hold increases.

I'm not sure why a thought experiment needs citations, but here you go:

• The canonical source for discussion of muscle fiber architecture is Gans C. 1982. Fiber architecture and muscle function. Exerc Sport Sci Rev 10:160–207.

Answer 2

There is a distinction to be made between the tensile strength of the muscle, that is, how much force can be applied to it before it breaks, and the strength the muscle is capable of applying to move something. In an actual game of tug-of-war, the rope is very strong, and what is being contested is the motive strength of the two teams. But the motive strength of a muscle is obviously no greater than its tensile strength, which as a matter of materials science is measured on a per-area basis. There may be more to it than this, but I think this is at least part of the answer.

To extend the tug-of-war example, if you had unlimited staffing to pull stones up the ramp to the pyramid, you would add pullers to each rope until you were afraid to add any more because the rope might break. So the pulling strength would ultimately depend on the number of ropes.