Modela-r as a Froude and Strouhal dimensionless numbers combination for dynamic similarity in running.

The aim of this study was to test the hypothesis that running at fixed fractions of Froude (Nfr) and Strouhal (Str) dimensionless numbers combinations induce dynamic similarity between humans of different sizes. Nineteen subjects ran in three experimental conditions, (i) constant speed, (ii) similar speed (Nfr) and (iii) similar speed and similar step frequency (Nfr and Str combination). In addition to anthropometric data, temporal, kinematic and kinetic parameters were assessed at each stage to measure dynamic similarity informed by dimensional scale factors and by the decrease of dimensionless mechanical parameter variability. Over a total of 54 dynamic parameters, dynamic similarity from scale factors was met for 16 (mean r=0.51), 32 (mean r=0.49) and 52 (mean r=0.60) parameters in the first, the second and the third experimental conditions, respectively. The variability of the dimensionless preceding parameters was lower in the third condition than in the others. This study shows that the combination of Nfr and Str, computed from the dimensionless energy ratio at the center of gravity (Modela-r) ensures dynamic similarity between different-sized subjects. The relevance of using similar experimental conditions to compare mechanical dimensionless parameters is also proved and will highlight the study of running techniques, or equipment, and will allow the identification of abnormal and pathogenic running patterns. Modela-r may be adapted to study other abilities requiring bounces in human or animal locomotion or to conduct investigations in comparative biomechanics.