1.    Introduction
Humans have long sought to enhance physical capabilities, striving to improve jump height, speed, strength, and technical skill (1). Gymnastics, as a multifaceted sport, promotes the development of balance, strength, flexibility, agility, and coordination (2). Achieving proficiency in gymnastics typically requires rigorous training that often begins in early childhood (3). The back salto is a fundamental acrobatic skill in gymnastics involving coordinated jumping, flight, rotation, and landing (1). Successful execution demands not only proper technique but also adequate jump height, joint angular velocity, and flight time (2). These biomechanical elements are essential for both performance effectiveness and injury prevention. Talent identification and athlete development programs play a pivotal role in gymnastics success, enabling the early recognition of potential and alignment of athletes’ physical attributes with the specific demands of the sport (4). Such programs help guide children toward sports suited to their developmental stage and physical readiness (5).
Kinematic studies have shown that jump height significantly influences back salto performance (1), while appropriate angular velocities at the hip and knee joints support controlled rotation and safe landings (6). Achieving sufficient jump height depends on vertical take-off velocity, which results from effective ground force application (7), and extended flight time facilitates optimal rotation and landing control (2). Research in sports science underscores the importance of morphological and anthropometric characteristics in determining athletic performance (8). These traits are often sport-specific and are frequently used as indicators in talent identification programs. Anthropometric variables commonly associated with jumping performance include the sitting height-to-height ratio, lower limb length, thigh and calf circumference, foot length, height, and body mass (3,9). Prior studies suggest that a lower sitting height-to-height ratio and longer lower limbs are advantageous for jumping tasks (7), while increased thigh and calf muscle girth contributes to enhanced vertical jump capacity (10). Although the relationship between anthropometric factors and jump performance has been explored in various sports, limited research has examined their influence on the unique biomechanical demands of the gymnastics back salto—a movement characterized by its complex rotational component. Therefore, the aim of this study is to predict jump height, vertical take-off speed, flight time, and angular velocity of the hip and knee joints during the back salto based on selected anthropometric variables, using two-dimensional kinematic analysis.
2.    Methods
Sixty-eight elite male gymnasts aged 17 to 26 years, each with more than three years of national-level experience, participated in this study. Individuals with skeletal abnormalities or those experiencing pain during testing were excluded. Written informed consent was obtained from all participants before data collection commenced. Anthropometric measurements were conducted using a standard anthropometer. Standing height was measured using a wall-mounted tape measure, while sitting height was recorded from the seated base to the top of the head. Lower limb length was measured in the supine position from the greater trochanter to the lateral malleolus. Thigh and calf circumferences were taken while participants stood upright with weight evenly distributed. To ensure accuracy, each circumference was compared with measurements taken slightly above and below the initial location, following standard procedures (13). Participants were asked to perform a back salto on a marked take-off area following a start signal. This movement involved a vertical jump, backward rotation around the frontal axis, and a controlled landing. A qualified gymnastics coach supervised all performances. Each participant completed three trials with adequate rest between attempts. The best attempt, determined based on performance quality and jump height, was selected for analysis. For consistency, gymnasts were instructed to land as close as possible to a calibration tape placed on the ground. The movement was captured from the sagittal plane using a Redmi Note 8T camera with a resolution of 720p and a frame rate of 240 frames per second. The camera was placed 3 meters from the take-off point at a height of 1.40 meters. Four reflective markers (3×3 cm²) were attached to the lateral malleolus, greater trochanter, lateral epicondyle of the knee, and greater tuberosity of the shoulder (13). A one-meter calibration tape was also visible in the camera frame to facilitate scaling. Two-dimensional kinematic analysis was conducted using Kinovea software. Jump height was calculated as the vertical displacement of the greater trochanter marker from take-off to the peak of the jump. Flight time was determined from take-off to landing of the same marker. Initial vertical velocity was estimated based on vertical displacement, assuming zero velocity at the jump’s apex. Angular velocities of the hip and knee joints were computed from the trajectories of their respective markers during the movement (Fig. 1). Statistical analysis was conducted using SPSS version 27. The normality of the data was assessed using the Shapiro–Wilk test. Stepwise linear regression was used to evaluate the ability of anthropometric variables to predict biomechanical outcomes. Statistical significance was set at an alpha level of 0.05.

3.    Results
To establish valid regression models, key statistical assumptions were examined. The normality of data distribution was confirmed using the Shapiro–Wilk test. Multicollinearity among predictor variables was assessed via the Variance Inflation Factor (VIF), and low VIF values indicated minimal multicollinearity. Predictor variables were entered into the regression model based on their Pearson correlation coefficients (14). The Durbin–Watson test confirmed the absence of autocorrelation among residuals. To improve the accuracy of the jump height model, one outlier (standardized residual = 3.020), exceeding ±3 standard deviations, was identified and excluded from the analysis. Pearson correlation analysis revealed significant relationships between jump height, vertical take-off speed, and flight time with at least one anthropometric predictor. However, no significant correlations were observed between any anthropometric variable and hip or knee angular velocities. Therefore, regression modeling was conducted only for jump height, vertical speed, and flight time.
For jump height prediction, thigh circumference was the first variable to enter the model, explaining 9.8% of the variance. The subsequent inclusion of lower limb length and foot length increased the explained variance to 16.3% and 29.8%, respectively. A fourth variable was excluded from the final model due to loss of significance (p = 0.057). Ultimately, lower limb length and foot length remained in the final model, jointly explaining 25.6% of the variance in jump height (R = 0.506; R² = 0.256; p = 0.001). The regression equation indicated that each 1 cm increase in lower limb length was associated with a 2.065 cm decrease in jump height, whereas each 1 cm increase in foot length corresponded to a 5.861 cm increase in jump height (Table 1).

Regarding vertical take-off speed, foot length emerged as the sole significant predictor, accounting for 14.7% of the variance (R = 0.384; R² = 0.147; p = 0.001). The model suggested that each 1 cm increase in foot length led to a 0.116 m/s increase in vertical speed. For flight time, lower limb length entered the model first, explaining 12.6% of the variance. Adding foot length improved the model, raising the total explained variance to 31.7% (R = 0.563; R² = 0.317; p = 0.001). According to the regression equation, each 1 cm increase in lower limb length reduced flight time by 0.007553 seconds, while each 1 cm increase in foot length increased flight time by 0.017996 seconds.
4.    Conclusion
This study investigated the relationship between selected anthropometric characteristics and biomechanical performance during the execution of the gymnastics back salto. The key findings revealed that both lower limb length and foot length significantly predicted jump height and flight time, while foot length alone was also a significant predictor of vertical take-off speed. The negative correlation observed between lower limb length and both jump height and flight time suggests that gymnasts with shorter legs may achieve greater elevation and remain airborne for longer durations. This could be attributed to more favorable leverage, greater force production over a shorter range of motion, or a more advantageous strength-to-weight ratio. These results contrast with findings from other sports, where longer lower limbs are often associated with improved jumping ability—likely because such movements typically lack the rotational complexity inherent in skills like the back salto (15–19). In contrast, foot length exhibited a positive correlation with jump height, vertical speed, and flight time. This indicates that a longer foot may contribute to more effective force application during takeoff, potentially due to a larger contact area with the ground. This finding aligns with previous research emphasizing the mechanical role of foot structure in generating propulsive force (20, 21).
No significant relationships were found between anthropometric variables and angular velocities at the hip and knee joints. This suggests that joint rotational velocity during the back salto may be more strongly influenced by other factors, such as muscular strength, neuromuscular coordination, or technical proficiency—none of which were directly assessed in this study. The practical implications of these findings are relevant to both talent identification and training program development in gymnastics. Coaches may consider foot and lower limb lengths as potential indicators of jumping ability when evaluating young athletes. However, it is essential to interpret anthropometric characteristics as just one component of a gymnast’s overall performance profile. Other critical factors—including strength, coordination, flexibility, and technical skill—must also be considered for a comprehensive assessment and optimal athlete development.

Ethical Considerations
Compliance with ethical guidelines
All ethical principles were considered in this article (ETHIC-202401-1149).
Funding
This research was extracted from the MSc. Thesis of the first author and did not receive any financial support from government, private, or non-profit organizations.
Authors' contributions
All authors contributed equally to preparing the article.
Conflicts of interest
The authors declare that there are no conflicts of interest associated with this article.