Walking dynamic similarity induced by a combination of Froude and Strouhal dimensionless numbers: Modela-w

- Similar experimental conditions are necessary to compare normalized parameters.
- Nfr and Str allow to determine similar experimental conditions.
- Modela-w (combination of Nfr and Str) induces dynamic similarity in human walking.
- Modela-w allows to remove the anthropometric effects on normalized parameters.

The aim of this study was to assess the accuracy of a new dimensionless number associating Froude (Nfr) and Strouhal (Str) called Modela-w to induce walking dynamic similarity among humans of different sizes. Nineteen subjects walked in three experimental conditions: (i) constant speed, (ii) similar speed (Nfr) and (iii) similar speed and similar step frequency (Modela-w). The dynamic similarity was evaluated from scale factors computed with anthropometric, temporal, kinematic and kinetic data and from the decrease of the variability of the parameters expressed in their dimensionless form. Over a total of 36 dynamic parameters, dynamic similarity from scale factors was met for 11 (mean r = 0.51), 22 (mean r = 0.52) and 30 (mean r = 0.69) parameters in the first, the second and the third experimental conditions, respectively. Modela-w also reduced the variability of the dimensionless preceding parameters compared to the other experimental conditions. This study shows that the combination of Nfr and Str called Modela-w ensures dynamic similarity between different-sized subjects and allows scientists to impose similar experimental conditions removing all anthropometric effects.