Dynamic similarity and the peculiar allometry of maximum running speed Maximum running speed in animals varies non-monotonously with body size, with the fastest animals being of intermediate size. This pattern is an exception to typical scaling relationships, which are usually monotonous. The study shows that this peculiar allometry arises from the competition between two musculoskeletal constraints: kinetic energy capacity (dominant in small animals) and work capacity (dominant in large animals). The physiological similarity index Γ, a dimensionless number similar to the Reynolds number, defines the transition between these constraints. Γ quantifies the competition between kinetic energy and work capacity, and its magnitude defines conditions of dynamic similarity that enable comparison of locomotor performance across animals. Γ challenges the Froude number as the prevailing dynamic similarity condition and reveals that the differential growth of muscle and weight forces is of secondary importance for most terrestrial animals. The study suggests avenues for comparative analyses of locomotor systems. The variation of locomotor performance with animal size is of substantial ecological and evolutionary importance. Empirical data show that maximum running speed increases up to a critical body mass and then decreases. This pattern is a noteworthy outlier among scaling relationships. The study argues that this peculiar allometry arises from the competition between kinetic energy capacity and work capacity. The physiological similarity index Γ, a dimensionless number, captures this competition and defines conditions of dynamic similarity. Γ challenges the Froude number as the prevailing dynamic similarity condition and reveals that the differential growth of muscle and weight forces is of secondary importance for most terrestrial animals. The study suggests avenues for comparative analyses of locomotor systems. The study shows that the peculiar allometry of maximum running speed is due to the competition between kinetic energy capacity and work capacity. The physiological similarity index Γ, a dimensionless number, captures this competition and defines conditions of dynamic similarity. Γ challenges the Froude number as the prevailing dynamic similarity condition and reveals that the differential growth of muscle and weight forces is of secondary importance for most terrestrial animals. The study suggests avenues for comparative analyses of locomotor systems. The study also shows that the transition mass between the Hill- and Borelli-limit is approximately 54 kg, and the critical mass is approximately 15 t. The study provides empirical data on maximum running speed and physical parameters of musculoskeletal systems. The study concludes that the physiological similarity index Γ is a fundamental dimensionless number for musculoskeletal dynamics, which may be used and interpreted akin to the Reynolds number. The study also discusses the functional significance of the gear ratio G and the effective coefficient of restitution η. The study concludes that the largest extinct animals will have moved with larger gear ratios. The study highlights the importance of empirical data and the need for further research to understand the allometry of musculoskeletal systems.Dynamic similarity and the peculiar allometry of maximum running speed Maximum running speed in animals varies non-monotonously with body size, with the fastest animals being of intermediate size. This pattern is an exception to typical scaling relationships, which are usually monotonous. The study shows that this peculiar allometry arises from the competition between two musculoskeletal constraints: kinetic energy capacity (dominant in small animals) and work capacity (dominant in large animals). The physiological similarity index Γ, a dimensionless number similar to the Reynolds number, defines the transition between these constraints. Γ quantifies the competition between kinetic energy and work capacity, and its magnitude defines conditions of dynamic similarity that enable comparison of locomotor performance across animals. Γ challenges the Froude number as the prevailing dynamic similarity condition and reveals that the differential growth of muscle and weight forces is of secondary importance for most terrestrial animals. The study suggests avenues for comparative analyses of locomotor systems. The variation of locomotor performance with animal size is of substantial ecological and evolutionary importance. Empirical data show that maximum running speed increases up to a critical body mass and then decreases. This pattern is a noteworthy outlier among scaling relationships. The study argues that this peculiar allometry arises from the competition between kinetic energy capacity and work capacity. The physiological similarity index Γ, a dimensionless number, captures this competition and defines conditions of dynamic similarity. Γ challenges the Froude number as the prevailing dynamic similarity condition and reveals that the differential growth of muscle and weight forces is of secondary importance for most terrestrial animals. The study suggests avenues for comparative analyses of locomotor systems. The study shows that the peculiar allometry of maximum running speed is due to the competition between kinetic energy capacity and work capacity. The physiological similarity index Γ, a dimensionless number, captures this competition and defines conditions of dynamic similarity. Γ challenges the Froude number as the prevailing dynamic similarity condition and reveals that the differential growth of muscle and weight forces is of secondary importance for most terrestrial animals. The study suggests avenues for comparative analyses of locomotor systems. The study also shows that the transition mass between the Hill- and Borelli-limit is approximately 54 kg, and the critical mass is approximately 15 t. The study provides empirical data on maximum running speed and physical parameters of musculoskeletal systems. The study concludes that the physiological similarity index Γ is a fundamental dimensionless number for musculoskeletal dynamics, which may be used and interpreted akin to the Reynolds number. The study also discusses the functional significance of the gear ratio G and the effective coefficient of restitution η. The study concludes that the largest extinct animals will have moved with larger gear ratios. The study highlights the importance of empirical data and the need for further research to understand the allometry of musculoskeletal systems.