Force-velocity profile in uphill running 

Ana Vanessa Bataller Cervero, Pablo Jesús Bascuas, Hector Gutiérrez, Hector Gutiérrez, Eduardo Piedrafita, Cristina Comeras Chueca, César Berzosa. 

Introduction 

In trail running, and more specifically in vertical running, athletes apply a net force to overcome the slope, which is related to their movement speed. The objectives were: to estimate the force-velocity (F-V) profile of mountain runners during a simulated maximal vertical race; and to identify whether different F-V profiles exist depending on the runners’ performance. 

Methods 

Eleven mountain runners with at least one year of competitive experience were recruited. Participants performed a maximal vertical running test over a 4.64 km course with an 835 m ascent. Each runner wore an Apex Stats Sport GPS device on their back, recording data at 1 Hz frequency. The variables recorded were distance, altitude, and time. GPS data were collected every 20 seconds, calculating the average gradient and average speed for each segment. Assuming constant average speed over each 20-second interval, the net force (F) applied to raise the centre of mass uphill was calculated as: From this, a scatter plot of force and velocity was generated, and an F-V profile was modelled using the formula proposed in (1): 

 Where F₁ is the force due to the gradient that allows movement at 1 m/s, V₀ is the maximum velocity in the absence of a slope, and C is the curvature of the profile. The approximation was performed using a trust-region nonlinear least squares minimization algorithm in Matlab2024. After an initial approximation, outliers were identified through residual plots and removed, followed by a second optimization. To divide participants into two performance groups, the estimated parameters (F₁, V₀, and C) were compared using a cutoff time of 49 minutes, resulting in 5 runners below this time (Group A) and 6 above (Group B). Curve parameters were compared using an independent samples t-test (SPSS, version 29.0). 

Results 

The analysis showed that athletes in Group A had a significantly lower curve than those in Group B, with higher values of F₁ and V₀ (Table 1). Therefore, it can be stated that the best runners (Group A) are characterized by higher velocity in the absence of slope (V₀) and greater force when moving at 1 m/s (F₁). 

Table 1. F-V Profile Parameters in Elite and Amateur Runners 

Group A Group B p d (Cohen) 

Mean V0 (m/s) 4.30 3.26 0.005 0.80 

Mean F1 (N) 3.32 2.45 0.032 0.45 

Mean C 3.58 2.43 0.147 1.70 

Figure 1. Estimated Average F-V Profile of Group A (blue) and Group B (red) 

Conclusion 

An F-V profile in maximal vertical running was identified, with differences observed between groups. For coaches, understanding the F-V profile during ascent is highly valuable to improve athletes’ weaker points and/or assess training effectiveness. 

References 

Delhaye C, Rozier-Delgado P, Vonderscher M, Di Domenico H, Bowen M, Millet G, Morin JB, Samozino P, Morel B. Submaximal force-velocity relationships during mountain ultramarathon: Data from the field. J Sports Sci. 2024; 42(20): 1881-1890. DOI: 10.1080/02640414.2024.2413715 

GRANTS AND FUNDING SOURCES 

This study was funded by the Government of Aragón (ValorA, S08_23R) and the Ministry of Education and Vocational Training (FPU2020-06437).