Author(s): MUÑOZ DE LA CRUZ, V., MUÑOZ-GARRIDO, M.J., VALERO, F., ALDA-BLANCO, A., RODRÍGUEZ-BARBERO, S., GONZÁLEZ-MOHÍNO, F., Institution: UNIVERSITY OF CASTILLA-LA MANCHA - TOLEDO CAMPUS: UNIVERSIDAD DE CASTILLA-LA MAN, Country: SPAIN, Abstract-ID: 1690

INTRODUCTION:
The Force-velocity (F-V) profile has become a key tool to assess athletes’ performance and to orientate training. Traditionally, the F-V relationship has been described using linear models [1]. However, several studies suggests that this relationship may exhibit a hybrid behavior, combining quasi-linear characteristics at high force levels with curvilinear (hyperbolic) behavior at low force levels [2]. The aim study was to compare the effectiveness of three different equations—linear 0–100% F0, linear 45–100% F0, and a hybrid equation—in describing the F–V profile in trained individuals, and to determine which model provides a more accurate and practical representation for training prescription.
METHODS:
Twenty-six trained adults (21 men and 5 women) performed incremental loading tests in back squat, bench press, and pull-up exercises. Movement velocity was measured using a linear encoder. F–V profiles were constructed for each exercise using the three equations. Key variables analyzed included theoretical maximal force (F0), theoretical maximal velocity (V0), maximal power output (Pmax), optimal force (Fopt), optimal velocity (Vopt), and coefficient of determination (R²). Statistical analyses included repeated-measures ANOVA.
RESULTS:
Significant differences between equations were found in most variables, particularly in bench press, where F0, V0, Pmax, Fopt and Vopt differed significantly. In pull-ups and back squat, significant differences were mainly observed in Pmax. The hybrid equation generally provided intermediate F0 and V0 values compared to linear models and showed higher Pmax estimations. These findings support the notion that the F–V relationship cannot be fully described as linear across the entire force spectrum, especially at lower loads.
CONCLUSION:
The hybrid model appears more suitable for comprehensive neuromuscular assessment, particularly when light loads are included (<45% F0), as it better captures the curvilinear region of the profile. Linear models may still be useful in field-based assessments or when evaluating moderate-to-high load ranges (45–100% F0), where the relationship behaves more linearly. These findings highlight the importance of equation selection when constructing F–V profiles, as inaccuracies in estimating Pmax or optimal variables may lead to suboptimal training prescriptions.
This study provides preliminary evidence supporting the use of a hybrid equation to more accurately represent the F–V relationship in different multiarticular exercises. Future research should include larger samples including women
1 Hill. The heat of shortening and the dynamic constants of muscle. Proc R Soc Lond B Biol Sci 1938;126:136–95.
2 Alcazar J, Pareja-Blanco F, Rodriguez-Lopez C, Gutierrez-Reguero H, Sanchez-Valdepeñas J, Cornejo-Daza PJ. A novel equation that incorporates the linear and hyperbolic nature of the force–velocity relationship in lower and upper limb exercises. Eur J Appl Physiology 2022; 122:2305-13