MUSCLE MECHANICS - Biomechanics and Motor Control of Human Movement - page 237

Figure 9.12 Force -velocity characteristics of skeletal muscle for different levels of
muscle activation; shown are 25%, 50%, 75%, and 100% levels of activation. All such
measures must be taken as the muscle shortens or lengthens at a given length, and
the length must be reported. During shortening, the curves follow the hyperbolic Hill
model, but during lengthening, the curves depend on the experimental protocol; the
solid lines are for isotonic activity, while the dashed lines are for isovelocity activity.

the total effect is similar to that of viscous friction in a mechanical system
and can, therefore, be modeled as some form of fluid damper. The loss of
tension related to a combination of the number of cross-bridges breaking and
reforming and passive viscosity makes the force-velocity curve somewhat
complicated to describe. If all the viscosity were passive, the slope of the
force-velocity curve would be independent of activation. Conversely, if all
the viscosity were related to the number of active cross-bridges, the slope
would be proportional to the activation. Green (1969) has analyzed families
of force-velocity curves to determine the relative contribution of each of these
mechanisms.
A curve fit of the force-velocity curve was demonstrated by Fenn and
Marsh (1935), who used the equation:

= V 0 e P /B − KP

V (9.2)

where: V = shortening velocity at any force

V 0 = shortening velocity of unloaded muscle

P = force

B, K = constants