Biomechanics

Objectives: This study compares linear sprint force–velocity (F–v) mechanical variables between elite Under-19 (U19) academy players and senior professional players. Methods: Thirty-eight senior players (SP; mean age 24.5 ± 4.3 y) and 214 U19 academy players (YP; mean age 17.4 ± 0.5 y) from 14 first-division club academies were tested during October 2023 using a motorized resistance device (1080 Motion). The following F–v variables were assessed: maximal theoretical force (F₀, N·kg⁻¹), maximal theoretical velocity (v₀, m·s⁻¹), maximal ratio of horizontal-to-resultant force (RF_max, %), and decrease in the ratio of forces (DRF, %). Between-group comparisons were performed using the t-test, and Cohen’s d effect sizes were reported. Results: Senior players outperformed U19 players across all F–v variables. F₀ exhibited a mean difference = 0.220 N·kg⁻¹, with a 95% confidence interval (CI) [0.056, 0.384], p = 0.0166, and d = 0.46. v₀ exhibited a mean difference = 0.560 m·s⁻¹, with a 95% CI [0.410, 0.710], p < 0.0001, and d = 1.07. RF_max exhibited a mean difference = 1.470%, with 95% CI [0.830, 2.110], p = 0.0003, and d = 0.69. DRF exhibited a mean difference = 0.260%, with a 95% CI [0.103, 0.417], p = 0.0013, and d = 0.53. Conclusions: U19 players demonstrated lower F₀, lower v₀, and reduced mechanical effectiveness compared with senior players. Regular monitoring of F–v profiles and individualized training interventions (force- or velocity-targeted) may be useful for training and monitoring strategies aimed at supporting physical preparation during the transition to senior soccer.

Background/Objectives: Quasi-static inverse dynamics is widely used in biomechanical analyses due to its computational simplicity; however, neglecting inertial effects may introduce joint-specific torque estimation errors during dynamic movements. The purpose of this study was to quantify torque estimation errors introduced by quasi-static assumptions during bodyweight squats performed at different movement frequencies. Methods: A planar MATLAB-based (version R2022a) musculoskeletal model incorporating standard anthropometric parameters was developed to simulate squat motions at 1.00, 0.75, 0.50, and 0.25 Hz. Joint torques calculated using quasi-static inverse dynamics were compared with fully dynamic inverse dynamics at the ankle, knee, and hip. Model agreement was evaluated using Root Mean Square Error (RMSE), normalized percentage error relative to peak dynamic torque, and bootstrapped 95% confidence intervals (CI). Results: Quasi-static modeling produced negligible torque estimation errors at the ankle and knee across all movement frequencies, with percentage errors consistently below 0.1% and narrow confidence intervals. In contrast, the hip joint demonstrated a clear frequency-dependent underestimation of torque when inertial effects were neglected. At 1.00 Hz, the hip RMSE reached 14.4 Nm, corresponding to 14.01% of peak dynamic torque (95% CI: 13.97–14.06%). Error magnitude increased systematically with movement speed. Conclusions: The validity of quasi-static inverse dynamics strongly depends on joint location and movement frequency. While quasi-static models are appropriate for ankle and knee torque estimation during moderate-speed squats, accurate hip torque assessment during faster squats requires full dynamic modeling. These findings provide quantitative benchmarks to inform model selection in biomechanical research, rehabilitation engineering, and assistive device design.

Background/Objectives: In pole vaulting, the capacity to store elastic energy within the pole (E_pole) significantly influences performance. This study investigated the characteristics of E_pole storage by analyzing the box reaction force and vector angle. Methods: Eight male pole vaulters, including World Championships participants, were examined. A motion capture system (VICON) and force plates (Kistler) were used to measure the vector angle (angle between the compression force (CF) and box reaction force vectors) and horizontal velocity of the center of gravity (COG) (Vcogh). E_pole was calculated as the integral of the CF (estimated from the box reaction forces), and pole bending displacement. The relationships between each variable and the peak height of COG (HP) were assessed using Pearson’s product–moment correlation coefficients. Results: HP correlated with Vcogh in the pole plant (PP) (r = 0.82) and E_pole (r = 0.94). Vaulters with a higher HP maintained a vector angle < 2° between 20% and 80% of the pole bending phase, indicating closer directional alignment between the box reaction force vector and pole chord direction, whereas vaulters with lower HP exhibited larger vector angles (4–8°), associated with a relative reduction in the axial component of force transmitted to the pole. Conclusions: A smaller vector angle effectively enhanced the CF, thereby increasing pole bending and promoting greater accumulation of E_pole. Therefore, maintaining a small vector angle may enable more effective force transmission along the pole chord, and vector angle characteristics and PP horizontal velocity may assist appropriate pole selection and training strategies to enhance elastic energy storage and performance.