title: Modela-r as a Froude and Strouhal dimensionless numbers combination for dynamic similarity in running.
abstract: 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.
authors.affiliation: Université de Toulouse, UPS, PRISSMH, 118 route de Narbonne, F-31062 Toulouse Cedex 9, France. Electronic address: david.villeger@univ-tlse3.fr.
authors.forename: David
authors.initials: D
authors.lastname: Villeger
authors.affiliation: Université de Toulouse, UPS, PRISSMH, 118 route de Narbonne, F-31062 Toulouse Cedex 9, France.
authors.forename: Antony
authors.initials: A
authors.lastname: Costes
authors.affiliation: Université de Toulouse, UPS, PRISSMH, 118 route de Narbonne, F-31062 Toulouse Cedex 9, France; CNRS, LAAS, 7 avenue du colonelRoche, F-31077 Toulouse, France.
authors.forename: Bruno
authors.initials: B
authors.lastname: Watier
authors.affiliation: Université de Toulouse, UPS, PRISSMH, 118 route de Narbonne, F-31062 Toulouse Cedex 9, France; Université de Toulouse, UPS, Centre de Recherche sur la Cognition Animale, 118 route de Narbonne, F-31062 Toulouse Cedex 9, France; CNRS, Centre de Recherche sur la Cognition Animale, 118 route de Narbonne, F-31062 Toulouse Cedex 9, France.
authors.forename: Pierre
authors.initials: P
authors.lastname: Moretto
mesh_terms: D000293:Adolescent; D000328:Adult; D001696:Biomechanical Phenomena; D049628:Body Size; D006112:Gravitation; D006801:Humans; D007700:Kinetics; D008124:Locomotion; D008962:Models, Theoretical; D012420:Running; D055815:Young Adult
keywords: Center of mass; Dimensionless parameters; Similar frequency; Similar speed; Spring Mass Model