Meeting Abstract
When humans push off against the ground during locomotion, the foot transmits the ground reaction force from the forefoot to the heel joint. Such loading causes the foot to bend in the longitudinal direction, severely so for other primates and people with flat feet. We find that the transverse arch is the key structural element of the foot that stiffens it to such deformation and thereby facilitates propulsion. Our primary means to determine the contribution of the foot arches to the stiffness is to model it as a curved elastic shell. Structural analysis of a shell reveals an amplification of its stiffness above that of a flat plate depending on a dimensionless morphological parameter ψ = κ L2/t, where κ is the transverse curvature, L the length of the shell, and t its thickness. For small ψ, the shell approaches a flat plate and the amplification factor approaches unity, but as ψ increases beyond 10, the amplification factor increases steeply as ψ3/2. Application of this relation to human feet implies an approximately 6-fold increase in stiffness compared to flat feet purely because of its transverse curvature. On one hand, this contribution explains the difference between the experimentally observed foot stiffness and the contributions from the longitudinally oriented arch, ligaments, and aponeurosis. On the other hand, the dimensionless morphological parameter provides a quantitative functional interpretation of the transverse arch, and allows us to compare ts role across hominin fossil feet without access to the soft tissue. In particular, the ψ for the foot of an unknown hominin species found in Burtele is estimated to lie in the range from 10 to 16, which is suitable for bipedal terrestrial locomotion.
