A predictive model for vertical ground reaction force during incline push-ups

Push-ups enhance upper body strength without special equipment, yet the impact of different inclinations on intensity is not well-understood. Although the load-velocity relationship is established in resistance training, its relevance to push-ups needs further exploration. Previous studies have suggested that inclination affects muscle activation, but accurate models for predicting exercise intensity remain underdeveloped. To address this gap, this study aims to develop a reliable predictive model based on ground reaction forces measured during push-ups performed at different inclinations and speeds. Twenty-seven male university students participated, performing push-ups at 10°, 20°, and 30° inclinations with feet elevated, at three metronome-enforced tempos (7 reps/10 s, 5/10 s, and 4/10 s). Body measurements, vertical ground reaction forces, and average speeds were recorded for each angle. This study developed a predictive model for vertical ground reaction force during push-up exercises that incorporates body mass, incline angle, and movement tempo. Force data were collected with a Kistler force platform (Model 9281EA, Switzerland) and modeled via multiple linear regression. Agreement between predicted and measured forces was summarized using Bland-Altman analyses: mean biases were small (|bias| ≤ 16.66 N) and the 95% limits of agreement were approximately ± 104-206 N across conditions. Significant angle-specific associations were observed between tempo and force. At 10°, maximum force correlated with fast (r = 0.58, p = 0.005) and medium tempos (r = 0.69, p < 0.001). At 20°, all tempos correlated with maximum force, most strongly at slow tempo (r = 0.74, p < 0.001), and minimum force correlated with medium (r = 0.61, p < 0.001) and slow tempos (r = 0.75, p < 0.001). At 30°, both fast (r = 0.55, p = 0.009) and slow tempos (r = 0.54, p = 0.010) were associated with maximum force. These findings support the use of the model to inform individualized load prescription across common incline angles and tempos. Within the tested conditions (10°, 20°, 30° and three tempos), the regression model showed moderate predictive performance with acceptable agreement between predicted and measured forces. The 20° models for minimum force performed best at medium and slow tempos. Because body mass was a positive predictor of force across angles, individual body mass should be considered when prescribing push-up intensity.