Force-Velocity Profile in Middle- and Long-Distance Athletes: Sex Effect and Impact on Endurance Performance Determinants

Abstract

Background: Muscle strength plays a critical role in the performance of middle- and long-distance athletes. However, the vertical force–velocity (F–V) profile has not been studied in this population. The objectives of this study were twofold: (i) to characterize the F–V profile in middle- and long-distance athletes and (ii) to explore its relationship with physiological and biomechanical performance variables. Methods: Thirty-nine highly trained athletes (13 middle-distance and 26 long-distance athletes), comprising men (18) and women (21), participated in this study. Each athlete performed a squat-jump to determine their F–V profile, followed by two 5 min bouts of low-intensity running and a graded exercise test to assess physiological and kinematic parameters. Results: Significant differences (p ≤ 0.05) were observed in maximal estimated power (P_max) and jump height between middle- and long-distance female athletes (21.20 ± 4.78 W·kg⁻¹ vs. 15.80 ± 2.83 W·kg⁻¹; 26.00 ± 0.05 cm vs. 19.50 ± 0.03 cm), and between male and female long-distance athletes (19.70 ± 2.87 W·kg⁻¹; 24.10 ± 0.02 cm). Stride length during low intensity running showed significant correlations with P_max (r = 0.340) and jump height (r = 0.374). P_max was positively associated with running economy (RE) (r = 0.396) and VO_2max (r = 0.346), and negatively correlated with F–V imbalance (FV_imb) (r = −0.531). Conclusions: Middle- and long-distance athletes demonstrate similar F–V profiles; however, middle-distance athletes exhibit a rightward shift, resulting in higher P_max and jump height, particularly among women. Nevertheless, F–V profile characteristics display only weak associations with physiological and kinematic variables which directly influence performance.

1. Introduction

Strength training is related to improvements in endurance performance determinants [1]. Strength training typically includes heavy loads to increase or maintain muscle maximum force at slow velocities, and low loads, such as explosive or plyometric exercises at fast velocities [2]. Previous studies have found that running economy (RE) improved following strength training, whether with heavy loads or through plyometrics [3]. In addition, different modalities of strength training aiming to improve power properties have shown improvements in RE [3,4,5] and endurance performance [6]. This improvement could be due to an enhancement in the stiffness of the Achilles tendon, which minimizes muscle shortening, using elastic energy, and reducing energy cost during running [7]. RE is also associated with running biomechanics. It is possible that an increase in strength may favorably modify running technique by reducing undesirable frontal and transverse plane motion in the lower limb during running [8] or by altering ground contact time [9].

The ability to produce high mechanical power output during jumps is one of the main physical performance determinants in several sports [10,11]. For example, a significant correlation has been observed between jump capacity and middle- and long-distance events (800, 3000, and 5000 m) in highly trained athletes [12], although ballistics movements (e.g., jumps, and therefore, the jumps executed in running strides) are predominantly influenced by the maximal power output of the lower limbs [13]. During locomotion, the limb skeletal muscles are required to perform concentric (shortening) and eccentric (lengthening) contractions against a load of varying magnitude, governed by the force–velocity relationship for skeletal muscles. Since the early work of Hill [14], it has been known that this relationship for both fast- and slow-twitch skeletal muscles is hyperbolic, with the maximal velocity of shortening occurring at near-zero load. In general, when performing an exercise and measuring velocity and load, the results follow a linear pattern, particularly in the central part of the curve, with different individuals displaying distinct F–V profiles [15].

Differences have been found in the F–V profiles between elite and lower-level athletes, sexes, and sports, indicating that this factor could influence overall performance [13,16,17,18]. Delving further, Samozino et al. [19] developed the theory that there exists an individual optimal F–V profile, and if it could be achieved, ballistic performance would improve even if maximal power output did not. This theory has been confirmed in various studies when performance has improved after individualizing training to address a deficit in velocity or force [20,21,22].

As already stated, maximal power plays an important role in long-distance athletes, possibly even more so in middle-distance athletes due to the shorter and faster nature of their events, although this population is not as extensively studied [9]. However, it remains unknown what balance of force and velocity distinguishes high-level athletes from those with lower-level performance. Additionally, it is unclear whether a specific F–V profile may have a strong correlation with performance in middle- and long-distance athletes, as is the case with sprint sports [23,24]. Therefore, the aims of our study were two-fold: (i) to characterize the F–V profile in middle- and long-distance athletes, and (ii) to investigate the relationship between the F–V profile and physiological and biomechanical performance variables.

2. Materials and Methods

2.1. Participants

Thirty-nine national and international track and field athletes participated in this study. All of them usually participated in middle- and long-distance events. To determine sample size for our study, statistical power was calculated employing G*Power [25]. For a large effect size of 0.6 for ANOVA (alpha = 0.05, 1-β = 0.95, and df = 1), a total sample size of 39 participants is required.

Participants trained between 5 and 6 times per week (i.e., 5–6 running sessions and 1–2 strength sessions). All runners were classified as Tier 3 (Tier 3: Highly Trained/National Level) according to the classification framework of Mckay et al. [26]. Participants’ characteristics are presented in

Table 1. Participant’s anthropometric and performance data.

		Age (y)	Height (m)	Body Mass (kg)	WA Points	VO2max (mL/kg/min)
Men n = 18	Middle-distance athletes. n = 6	25.7 ± 8.6	1.76 ± 0.06	63.6 ± 5.0	821 ± 156	64.3 ± 6.7
	Long-distance athletes. n = 12	27.7 ± 5.7	1.74 ± 0.06	60.5 ± 4.7	889 ± 61.8	64.4 ± 6.2
Women n = 21	Middle-distance athletes. n = 7	23.4 ± 5.4	1.64 ± 0.05	52.6 ± 6.7	824 ±164	56.4 ± 5.4
	Long-distance athletes. n = 14	24.9 ± 4.6	1.67 ± 0.07	52.8 ± 4.4	848 ± 220	52.6 ± 6.2

WA, World Athletics.

. To standardize the intensity to assess RE, the exclusion criteria included the ability to run at 11 km·h⁻¹ and 13 km·h⁻¹ (women and men, respectively) with a respiratory exchange ratio below 1.0 to ensure a similar relative intensity for all participants. Participants were recruited from different training groups during the months of October and November in the pre-season phase of training. In addition, they were informed about the testing protocol and possible risks during the test and an informed consent was provided, and their coach provided written approval for retrospective analysis. The investigation was conducted in compliance with the principles of the Seoul Declaration (October 2008) and the experimental procedures received approval from the local ethical committee. No significant differences in height or body mass were found between middle-distance and long-distance female athletes (p = 0.30 and p = 0.89, respectively) or male athletes (p = 0.68 and p = 0.21, respectively).

2.2. Experimental Design

This study employed a cross-sectional design. The procedure included a familiarization session for those participants with no previous experience in the F–V profile test. All tests were performed on the same day. Participants refrained from caffeine intake or any ergogenic aid before the testing session and did not perform intense exercise 24 h prior. First, anthropometric data was collected. Height was measured to the nearest 0.1 cm with a portable stadiometer and body mass was measured to the nearest 0.1 kg with a portable balance (Seca^®, Bonn, Germany).

2.3. Procedure

Squat-Jump F–V Profile Evaluation

Before the evaluation of the F–V profile, leg length (from the hip to the toes in plantar flexion) and distance from hip to the floor in 90° squat was measured following the instructions in [27]. Then, participants started with an easy 5 min warm-up on a cycling ergometer (Wattbike Pro, Nottingham, UK), followed by mobility exercises and five countermovement jumps (CMJ) with no additional loads before starting the F–V incremental test. The test consisted of at least six loads and two attempts for each one. All participants started with no weight and were adding 5 to 10 kg depending on the strength level of the athlete. The recovery time between loads was 3 min. The supports of the rack were positioned so that the bar would touch when the legs formed a 90° angle. Once they touched the supports, they had to wait for the sound signal and jump as high and fast as possible against the load, with their legs fully extended in the air. Jump height was measured using a force platform and MARS software (v3.07.999.4, Kistler, Winterthur, Switzerland). The test ended when participants jumped 10 cm or less and at least 5 loads were completed [15].

2.4. F–V Profile Analyses

Further F–V profile analyses were conducted by calculations used in previous studies [15,27]. The variables we obtained were maximum estimated force (F₀), maximum estimated velocity (V₀) and maximum estimated power (P_max). F₀ is defined as the value of the force when V₀ = 0 and vice versa in the case of V_0. P_max is estimated using the formula: P_max$= {\displaystyle \frac{\mathrm{F}0·\mathrm{V}0}{4}}$ [19]. All F–V profiles reported R² scores above 0.95. The mean R² in this study was 0.971 ± 0.017.

2.5. RE and Maximal Incremental Running Tests

After completing the F–V test, participants were allowed to rest for 20 min before the RE evaluation. Subsequently, they completed a 5 min warm-up running on the treadmill at 8 km·h⁻¹ for women and 10 km·h⁻¹ for men. Then, 2 × 5 min bouts at 11 km·h⁻¹ and 13 km·h⁻¹ (for women and men, respectively) with 5 min rest were performed to measure RE. Then, participants started a graded exercise test (GXT) on the treadmill (HP Cosmos Pulsar, HP Cosmos Sports & Medical GMBH, Nussdorf-Traunstein, Germany). The test commenced at a speed of 8 km·h⁻¹ and 10 km·h⁻¹ (for women and men, respectively) and the speed was then increased by 1 km·h⁻¹ every minute until volitional exhaustion. The treadmill slope was 1% to imitate external wind conditions [28]. Both during the RE trials and during the incremental test, respiratory variables were continuously measured using a gas analysis system (CPX Ultima Series MedGraphics, St. Paul, MN, USA), with gas calibration before each test session performed automatically by the system using both ambient and reference gases (CO₂ 4.10%; O₂ 15.92%). For the RE assessment, VO₂ values from the last 120 s of each bout were used to determine RE as the oxygen cost of running. The VO_2max was determined as the average of oxygen uptake values recorded during the final 30 s of the incremental test. This approach was chosen due to the significant breath-by-breath variability in pulmonary gas exchange (PGE), making the use of 30 s averaged PGE values highly effective for incremental exercise tests [29].

In both tests, the spatiotemporal parameters of the gait cycle (contact time [CT], stride frequency [SF], stride length [SL], and flight time [FT]) were recorded using the Stryd^® Power Meter device (Stryd Power Meter, Stryd Inc. Boulder, CO, USA) with a sampling frequency of 1000 Hz. Then, the information was analyzed through the Stryd Power Center program available on the website. The 120 s period used for the RE assessment and 20 central seconds from each stage of the incremental test provided the 32 steps recommended for running biomechanics measurements to identify technique differences between participants [30]. To analyze relations between the F–V profile and kinematic variables at higher intensities, we used the stage of 16 km·h⁻¹ for women and 18 km·h⁻¹ for men. These intensities were those below the value 1 in the respiratory exchange ratio.

2.6. Statistical Analysis

All data are presented as mean ± standard deviation. The significance level for the analyses was set at α = 0.05. The normality was checked before any analyses using the Shapiro–Wilk test and data followed a normal distribution. A two-factor ANOVA (sex × distance) was performed. In addition, squared correlation coefficients (r²) were calculated for all correlations. Following Hopkins et al. [31], the magnitude for r² was considered as trivial (r² < 0.01), small (0.01 < r² < 0.09), moderate (0.09 < r² < 0.25), large (0.25 < r² < 0.49), very large (0.49 < r² < 0.81), nearly perfect (r² > 0.81), and perfect (r² = 1.0). Statistical analyses were carried out using the software Jamovi 2.3.18 for Mac.

3. Results

The results of F–V profiles are displayed in

Table 2. Squat-jump force–velocity profile results.

		F0 (N·kg−1)	V0 (m·s−1)	Pmax (W·kg−1)	Jump Height (cm)	FVimb
Men n = 18	Middle-distance athletes. n = 6	29.80 ± 5.02	2.80 ± 0.65	20.50 ± 4.26	28.10 ± 5.43	79.3%
	Long-distance athletes. n = 12	30.80 ± 5.66	2.64 ± 0.59	19.70 ± 2.87	24.10 ± 2.23	81.3%
Women n = 21	Middle-distance athletes. n = 7	30.40 ± 6.35	2.97 ± 1.20	21.20 ± 4.78	26.00 ± 4.59	84.3%
	Long-distance athletes. n = 14	29.60 ± 5.18	2.39 ± 1.02	15.70 ± 2.78	20.10 ± 3.39	79.3%

F₀, maximum estimated force. V₀, maximum estimated velocity. P_max, maximum estimated power. FV_imb, force–velocity imbalance.

. ANOVA and effect size results are presented in

Table 3. ANOVA results and effect size.

		F0	V0	Pmax	Jump height	FVimb
Middle-distance men × long-distance men	Md (CI)	0.983 (−4.640, 6.606)	−0.156 (−1.064,0.752)	−0.733 (−4.270, 2.804)	−0.040 −0.077, −0.002)	2.000 (−36.344, 40.344)
	p	0.984	0.985	0.974	0.163	1.000
	d	0.177	−0.174	−0.211	−1.067	0.053
Middle-distance women × long-distance women	Md (CI)	−0.832 (−6.104, 4.440)	−0.581 (−1.432,0.271)	−5.488 (−8.804, 2.172)	−0.059 (−0.094, −0.024)	9.176 (−26.776, 45.128)
	p	0.988	0.516	0.010 **	0.009 **	0.954
	d	−0.150	−0.650	−1.577	−1.597	0.243
Middle-distance men × middle-distance women	Md (CI)	−0.619 (−6.876, 5.638)	−0.170 (−1.181, 0.840)	−0.690 (−4.626, 3.245)	0.021 (−0.021, 0.063)	−4.952 (−47.617, 37.713)
	p	0.997	0.986	0.984	0.744	0.995
	d	−0.112	−0.190	−0.198	0.563	−0.131
Long-distance men × long-distance women	Md (CI)	1.196 (−3.306, 5.698)	0.255 (−0.472, 0.982)	4.064 (1.232, 6.896)	0.040 (0.010, 0.071)	−12.128 (−42.828, 18.571)
	p	0.949	0.892	0.030 *	0.047 *	0.853
	d	0.216	0.285	1.168	1.093	−0.321

F₀, maximum estimated force. V₀, maximum estimated velocity. P_max, maximum estimated power. FV_imb, force–velocity imbalance. *, p ≤ 0.05. **, p ≤ 0.01. d, effect size. Md, mean difference. CI, confidence interval.

. Significantly higher P_max (Figure 1) (p = 0.01) and jump height (p = 0.009) were found in middle-distance women athletes compared to long-distance women athletes (21.20 ± 4.78 W·kg⁻¹ vs. 15.80 ± 2.83 W·kg⁻¹ and 26.00 ± 0.05 cm vs. 19.50 ± 0.03 cm). Long-distance men also presented significantly higher P_max (p = 0.03) and jump height (p = 0.047) than long-distance women (19.70 ± 2.87 W·kg⁻¹ and 24.10 ± 0.02 cm vs. 15.70 ± 2.78 W·kg⁻¹ and 20.10 ± 3.39 cm). However, the rest of the F–V profile variables were similar between groups. In addition, no significant differences were found between groups regarding F–V profile imbalance.

Regarding the correlations between F–V profile variables and performance, biomechanics, and physiological variables, no significant correlations were found for most variables. However, both P_max and jump height show a significant correlation with SL at low intensity during RE assessment (r = 0.374, p ≤ 0.05; r = 0.374, p ≤ 0.05, respectively) and high intensity during the GXT (r = 0.361, p ≤ 0.05; r = 0.400, p ≤ 0.05, respectively). In addition, P_max was positively related to RE (r = 0.396, p ≤ 0.05) and VO_2max (r = 0.346, p ≤ 0.05) and negatively related to FV_imb (r = −0.531, p ≤ 0.001).

4. Discussion

To our knowledge, the vertical F–V profile of middle-distance and long-distance runners has not been reported previously in other studies. Most studies explain the characteristics of F–V profiles in sports involving rapid actions, such as sprinting, taekwondo, weightlifting, and speed climbing, among others [15,16,32]. Therefore, the aims of this study were (i) to characterize the F–V profile in middle- and long-distance athletes and (ii) to investigate the relationship between the F–V profile and physiological, biomechanical, and performance variables.

The main finding of our study was that there are no differences in F₀ and V₀ between middle-distance and long-distance runners. However, P_max and maximum jump height were significantly higher in middle-distance women compared to long-distance women and significantly higher in long-distance men compared to long-distance women. P_max values are relative to body weight, which may differentiate men and women; however, significant sex-based differences remain. These differences could be attributed to testosterone levels and the higher proportion of type II, IIa, and IIx muscle fibers in men, compared to the greater prevalence of type I fibers in women [33]. The same applies to middle-distance runners, who incorporate more type II fiber work (sprints, plyometrics, and resistance training) into their periodization compared to long-distance runners [34,35].

Although there were no differences in the F–V relationship, the trend suggests that middle-distance athletes have a F–V profile that is more shifted to the right (higher F₀ and V₀ values), resulting in a higher power output and therefore, a significantly greater jump height in middle-distance athletes. This phenomenon occurs in both sexes and may be due to the higher percentage of type II fibers present in the musculature of middle-distance athletes, who perform training at higher speeds and with longer recoveries that recruit these types of fibers [36].

The findings from previous studies suggest that neuromuscular characteristics may play a relevant role in RE [4,37]. None of the physiological determinants of the endurance performance variables analyzed showed any relationship with the F₀ and V₀. Only P_max was negatively correlated with RE and positively correlated with VO_2max, meaning that more efficient runners achieved lower P_max values during the F–V profile test. In addition, due to the inverse relationship between energy cost and VO_2max found in the literature [38], a higher value of VO_2max has been found in those runners with higher Pmax values during the F–V profile. In that sense, [38] found that less power is associated with greater RE, similar to our results. However, maximum jump height was not correlated with RE or VO_2max. It is likely that the force–velocity profile in the squat jump does not show a significant correlation with physiological variables such as RE or VO_2max but may correlate with anaerobic physiological variables or tests, which are also highly important in middle- and long-distance events, as has been seen in other studies [39]_. Therefore, future research could explore the relationship between the force–velocity profile in the squat jump or squat exercise and tests such as the vMART or 20–30 m sprints.

All studies that relate the F–V profile to performance evaluate more explosive actions such as jumps or sprints [40], and as far as we are concerned, there are no results that physiologically analyze the possible influence of the vertical F–V profile on middle- and long-distance performance. Nevertheless, the correlation between the F–V profile variables and the athletes’ level (WA points) was also not significant. This indicates that in middle-distance and long-distance events lasting 2 min or more, jump height and the combination of force and velocity are not as determinant as other measurements like the rate of force development or reactive strength index. These measurements, which provide different information about force and power characteristics, have been found to be correlated to RE and time trial running tests [41,42].

Regarding the data obtained on the optimal F–V profile, we did not find that the profile of one group is more optimized than the other, nor that the degree of imbalance from the optimal profile is related to performance. Although there are various studies showing that having an optimized F–V profile is strongly related to performance in jumping or sprinting [14], the value of this tool is also questioned [20]. One of the criticisms of Samozino’s model [43] is that it assumes the average velocity of the jump to be a constant derived from the take-off velocity divided by two. The amount of effective work produced during a lower limb extension depends less on the average velocity and more on the time-history of the velocity throughout the jump [44]. In any case, 69.23% of middle-distance athletes and 72% of long-distance athletes showed a strength deficit. The same is observed when looking at the proportion by sex; 65% of women and 72.2% of men, respectively, showed a force deficit. This would indicate that the population of athletes exhibits a force deficit and should undergo more strength training through high-load exercises. However, in our study, FV_imb was not related to physiological determinants in endurance running performance such as RE or VO_2max. Therefore, the use of the F–V profile in long-distance runners does not seem to be very useful in improving the orientation of strength training in this population.

It has been demonstrated that changes in biomechanical factors such as step frequency and step length affect RE, and therefore, overall running performance [45]. These biomechanical alterations are influenced by lower limb strength training. Stride length is highly individual, with each subject adapting their stride to achieve a more economical running style, often by reducing it [44]. However, in our study, we found a significant and moderate positive correlation between step length and P_max and a large positive correlation with jump height (Table 3). Contrary to what might be expected, this correlation was stronger at lower speeds than at higher speeds, even though step length increases with speed.

Understanding the F–V profile of an athlete is crucial to determining whether their sport demands more high-speed exercises, such as plyometric training, or heavy-load exercises that target maximal strength. Coaches should assess this profile in their athletes to identify whether they exhibit a strength deficit or a velocity deficit, allowing them to tailor the training plan accordingly. Similarly, knowing which types of exercises are associated with physiological factors that directly impact performance helps coaches select the most effective exercises for strength training.

However, there are some limitations in the present study that should be taken into consideration. Some of the participants were familiar with the squat-jump exercise, as they regularly included it in their strength training sessions. Nevertheless, this was not the case for all participants, as some, despite undergoing the familiarization session, did not exhibit the same ease in performing the exercise, which could influence the results. The sample size could be considered small, but it represents a very specific population of well-trained middle- and long-distance athletes (mean over 800 WA points and a VO_2max greater than 52 mL/kg/min in women and 64 mL/kg/min in men), in addition to including a similar number of men and women.

In conclusion, middle-distance and long-distance athletes exhibit a similar F–V profile, although the profile of middle-distance athletes is shifted further to the right, resulting in a significant difference in P_max and consequently in jump height. This difference is even more pronounced between female middle-distance and long-distance athletes. However, the characteristics of the F–V profile are only weakly related to physiological and kinematic variables that show a close relationship with the athletes’ final performance. Moreover, any force–velocity imbalance was associated with running performance, and therefore, strength training oriented to obtain an optimal profile may play a less important role for middle- and long-distance athletes. Some potential future research directions could include longitudinal strength training studies to analyze whether changes in the F–V profile influence physiological factors in running. In addition to those studied in this article, other physiological factors related to anaerobic mechanisms could also be explored.