The question is this: Is there a point where adding more muscle bulk on will not lead to greater contractile strength in a muscle? Assuming, of course, idealized nervous response. I know Bompa states directly that contractile strength is directly proportional to muscular cross section, but I have been questioning that from a physical standpoint.

My basis for skepticism here is geometric: The first muscle fiber which runs essentially straight from the insertion point to the insertion point, and meets the insertion point at a 90 degree angle. The next muscle fiber will have the belly deflected by the thickness of a fiber (t), and will thus meet the insertion point at a small angle (a).

If we assume all fibers are capable of similar contractile force F, and all fibers have the same diameter, and that those fibers are incompressible we see:

(Total Force) = Sum (F*cos(a))

For a round muscle of length L, with fibers of thickness t, we can approximate

(Total Force) = Sum ( (F*L/2) / ((n*t)^2+(L/2)^2)^0.5 )

Where n is the number of fibres between the fiber of interest and the center of the muscle.

The first thing we can see in this formula is that the further away from the center of the muscle the fiber is, the less contractile force it is contributing. Is this decrease significant? To determine this properly I would need to know the thickness, length, contractile force and compressibility of the underlying muscle. This leads us to the problem where a muscle fiber could, theoretically, contract and pull itself lower into the underlying fibers, reducing its arc-length, leaving it?s contractile force dependant on the solidity of the underlying muscle. The more solid (and friction free!) the surface, the more force it will transfer. The softer the underlying muscle, the less force will be transferred, and the more of the peak of the muscle will flatten out.

Another interesting corollary that a longer muscle should be slightly stronger than a shorter muscle of the same cross section. Essentially it would transfer the tension to the tendon more efficiently.

If you want to play with this sort of geometry grab the rope-attachment on the cable-row, and play around with narrower and wider grips. You can easily see how much more tension you need in the rope in order to pull the same weight with your hands further apart.

To the original point: Is it possible to build a muscle fiber which is so arched that it does not contribute appreciably to the strength of a contraction? Bompa could certainly be correct given certain characteristics of muscle, which I have to go off and look up now.

Dammit Jim, I’m a physicist not a biologist!