Testing the Shoulder Point Compression Framework on 13 Pairs of Used Athletic Shoes
Publication Date : Jul-10-2026
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Abstract :
Athletic-shoe cushioning is commonly characterized by pressing on the heel with a materials-testing machine and extracting descriptors from the resulting force–compression curve. These values are peak compression (PC), foam stiffness over low, mid, and high force ranges, energy absorbed (Eabs), and energy return efficiency (η). A recent paper proposed four additional “shoulder point” parameters describing the point of maximum energy absorbed per unit force: the efficiency (E/F)max, the force (Fopt), the compression (xopt), and the energy absorbed (Eopt). The original authors treated all four as independent, but whether they add information beyond the conventional descriptors has not been tested. We tested 13 used pairs of athletic shoes from high-school students on a materials-testing machine and examined the relationships among descriptors using correlation and principal component analysis. Two shoulder point parameters, (E/F)max and xopt, tracked peak compression almost exactly, adding little new information. A third, Fopt, was unrelated to every conventional descriptor but closely tracked the foam-stiffening ratio Kmid/Klow. The fourth, Eopt, was well predicted by Eabs and Fopt together. In this sample the shoulder point framework therefore added one new dimension to the description of cushioning, not four, with Fopt the most informative parameter and a possible marker for how cushioning changes as a shoe wears. These findings come from a small convenience sample of 13 pairs of used shoes and should be regarded as preliminary; confirmation in larger and more varied samples is warranted.
