Malmo wrote:
Why does that bother you? Force and work are directly proportional. The fact that a force is applied and the subject moved an unknowable distance is moot. Delta d becomes a constant.
my reply:
First off, I agree the Lieberman paper has many flaws, let's not propagate them with loose and incorrect use of physics terms, since they are so elegantly defined.
In running, the foot, arch, achilles, whole leg etc. all act in a spring-like manner.
A spring is defined by its stiffness, k = F/delta d
Your assertion that "force and work are proportional" is only true if stiffness is constant. See study abstract below showing that to be a bad assumption. "A significantly higher leg stiffness during the stance phase was found for the barefoot condition."
The distance that the foot/arch/leg springs etc. deform is not unknowable, Lieberman didn't measure them but others have and do.
J Biomech. 2000 Mar;33(3):269-78.
Biomechanical analysis of the stance phase during barefoot and shod running.
De Wit B, De Clercq D, Aerts P.
Department of Movement and Sport Sciences, University of Ghent, Belgium.
Abstract
This study investigated spatio-temporal variables, ground reaction forces and sagittal and frontal plane kinematics during the stance phase of nine trained subjects running barefoot and shod at three different velocities (3.5, 4.5, 5.5 m s(-1)). Differences between conditions were detected with the general linear method (factorial model). Barefoot running is characterized by a significantly larger external loading rate than the shod condition. The flatter foot placement at touchdown is prepared in free flight, implying an actively induced adaptation strategy. In the barefoot condition, plantar pressure measurements reveal a flatter foot placement to correlate with lower peak heel pressures. Therefore, it is assumed that runners adopt this different touchdown geometry in barefoot running in an attempt to limit the local pressure underneath the heel. A significantly higher leg stiffness during the stance phase was found for the barefoot condition. The sagittal kinematic adaptations between conditions were found in the same way for all subjects and at the three running velocities. However, large individual variations were observed between the runners for the rearfoot kinematics.