Introduction

Jumping is an important athletic task in several sports. However, high-impact loading when landing from a jump often causes sports injuries [1,2,3]. Impact loading is measured by the peak ground reaction force (GRF) or the loading rate, which is calculated by dividing the peak GRF by the time to peak GRF [4,5,6]. Recently, the loading rate has received more attention than peak GRF as an indicator of impact loading [7, 8]. To reduce sports injuries, it is necessary to identify the physical functions related to the loading rate. However, these functions have not been clarified.

Since the loading rate is defined by force and time, we assume that the ability to produce explosive force and adjust the timing are important determinants of the loading rate. However, explosive force is considered to be more critical than the maximal force for landing [9]. This is because the time to peak GRF at landing (< 200 ms) [10, 11] is far shorter than the time to peak force in maximal isometric contraction (> 400 ms) [12, 13]. Explosive force production ability is evaluated by the rate of force development (RFD) [13, 14]. RFD is often obtained by the slope of the isometric contraction torque–time curve across the time from the onset of contraction to 50 ms (RFD50) or to a longer time (e.g., 100 ms, 200 ms, peak time) [14]. Of these, RFD50 plays an important role in determining jump performance [15].

The ability to adjust timing is very important for motor performance, which requires adaptation of body segment movements to environmental events [16]. This ability has been extensively studied in areas such as sports skills [17], child development [18], and the motor aspects of cerebral palsy [19].

It is important to predict the right timing of foot contact to begin lower limb movement upon landing. The ability to adjust the timing is evaluated by the time difference between the arrival of the stimulus and the response. Sports experts have better ability to adjust the timing, such as the coincident timing, than novices [20].

Based on these ideas, the ability to produce an explosive force at the right time is necessary for a soft landing. In addition, the countdown is a very common evaluation method for adjusting the timing [21]. Therefore, we proposed a new test to measure the RFD in accordance with the countdown signal, which we coined as the countdown RFD. Using this method, we believe it would be possible to determine if individuals capable of producing a timely explosive force have less loading rate at landing. The aim of this study was to test whether individuals with a higher countdown RFD have a lower landing impact and whether individuals with a lower countdown RFD have a higher landing impact.

Methods

Participants

Twenty-nine healthy young men volunteered to participate in this study. All participants had no current injuries or illnesses that limited their ability to perform physical activities; no lower extremity or back injuries within 6 months before testing; and no history of hip, knee, or ankle surgery [22]. As described in a previous study, the dominant limb was defined as the limb used to kick a ball the farthest [23]. The experimental procedures, study design, and possible risks were explained, and the participants signed an informed consent form. This study was approved by the ethics committee of our university and conformed to the tenets of the Declaration of Helsinki.

Procedures

Timing effect of knee extension RFD

The knee extension RFD and peak torque (PT) of the dominant leg were measured during maximal isometric contractions using a Biodex System 3 dynamometer (Biodex Medical System, Shery, NY, USA) interfaced with MyoResearch Master Edition 1.08 XP software (Noraxon, Scottsdale, Arizona, USA). The reason for this is that in the case of isometric contraction, force is applied to a fixed device; thus, it is easy to apply force and has high reproducibility [14, 24]. Before testing commenced, the participants performed approximately 10 min of warm-up exercises consisting of dynamic stretching and light jumping. Then, each participant was seated on the dynamometer chair, and their knees were positioned at 90° of flexion. A thigh strap, waist strap, and two chest straps were secured to stabilize the participant. Before the measurements were taken, participants were initially given a series of practice trials to familiarize themselves with the testing procedure. Knee extension RFD and PT were measured in two tasks: the standard and countdown task. The standard task is a normal RFD measurement method that has been reported previously [12]. The participants were instructed to contract the quadriceps “as hard and fast as possible” for 2–3 s against the dynamometer after the presentation of the start signal. The start signal was a beeping sound produced by the MyoResearch system. The countdown RFD, which is our newly proposed terminology, requires participants to synchronize the timing-predictable signal and muscle contraction. The beeping sound signal occurs three times at 1-s intervals. The participants were instructed to predict the third beeping sound and to contract the quadriceps synchronously “as hard and fast as possible.” In both tasks, the participants were instructed to avoid countermovement or pretension.

RFD50 was calculated by dividing the force at 50 ms after onset contraction by the corresponding time (e.g., force at 50 ms/50 ms). Because the time to peak GRF during landing occurs at approximately 50 ms [25, 26], we used RFD50 in this study. The onset of contraction was defined as the time point at which the knee extensor torque exceeded the baseline < 7.5 Nm [27]. The RFD for each task was collected at five acceptable trials, and the average RFD of the three best trials was used for analysis.

The timing effect was defined by the change ratio of RFD50 between the standard and countdown tasks and was calculated using the following formula by referring to previous studies [28, 29] on change ratio in other tasks:

$${\text{Timing}}\,{\text{effect index}}\,\left( \% \right)\, = \,\frac{{{\text{countdown}}\,{\text{RFD50}}\, - \,{\text{standard}}\,{\text{RFD50}}}}{{{\text{standard}}\,{\text{RFD50}}}}\, \times \,100$$

A decrement in the countdown RFD50 was represented by a negative value, and an improvement in the countdown RFD50 was represented by a positive value. We divided the participants into two groups based on the results of the timing effect index: the negative group (in which the timing effect was a negative value) and the positive group (in which the timing effect was a positive value).

Impact loading at landing

The participants were then asked to perform a single-leg drop landing on a force plate (AMTI, Watertown, MA, USA) from a 20-cm high box located 3 cm behind the force plate [30] (Fig. 1). They were barefoot, and their arms were crossed over their chests during landing. They were instructed to stand at the edge of a box with their dominant leg, step off the box without jumping up or stepping down, and land as softly as possible onto a force plate using the same leg. After the participants practiced three times, three drop landings were collected.

Fig. 1
figure 1

Single leg drop landing from a 20-cm high box

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Force data were collected using a force plate at a sampling frequency of 1000 Hz and low-pass filtered at 50 Hz with a fourth-order zero-lag Butterworth filter [31]. The outcome variables of interest were defined and calculated as follows: the peak GRF, the highest recorded vertical GRF during landing, was calculated using the force plate; the magnitude of the landing force was divided by the individual’s body weight (BW) in Newtons to allow for the expression of the landing force as BW. This normalization allowed for comparisons between the individuals. The time to peak GRF (i.e., the time taken to achieve the highest vertical GRF) was calculated by subtracting the time at maximal vertical force by the time of initial foot contact (where the vertical force exceeded 10 N) [32]. The loading rate, which is the speed at which forces impact the body, was calculated by dividing the peak GRF by the time to peak GRF.

Statistical analysis

We determined the sample size by estimating the magnitude of the effect size for the two groups to be analyzed. We assumed that the effect size for this study was large (0.8) and desired an 80% confidence level for rejecting the null hypothesis when comparing the two groups. Therefore, we set the power to 0.8.

Results are expressed as the mean ± standard deviation. All parameters were normally distributed in the two groups, as confirmed by the Kolmogorov–Smirnov test. We used the Student’s t test to compare the two groups. We analyzed the data using SPSS version 25.0 (SPSS Corp., Chicago, Illinois, USA) and considered P-values < 0.05 to be statistically significant.

Results

We divided the patients into two groups according to the results of the timing effect index: the positive (n = 11) and the negative (n = 18) groups. The participants’ characteristics are presented in Table 1. No significant differences in characteristics were identified between the groups. The results of the PT and RFD50 are presented in Table 2. The PT in each task and the RFD50 in the standard task were not significantly different between the groups. However, the RFD50 in the timing task was greater in the positive group than in the negative group.

Table 1 Characteristics of participants in each group
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Table 2 Peak torque and RFD characteristics of standard and countdown tasks in each group
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The comparison of peak GRF and time to peak GRF during single-leg drop jump landing between the groups is shown in Table 3. There was no significant difference between the two groups in peak GRF. However, the time to peak GRF was significantly longer (P < 0.01) in the positive group than in the negative group. A comparison of the loading rate during single-leg drop jump landing between the two groups is shown in Fig. 2. The loading rate was significantly lower (P < 0.01) in the positive group (34.7 ± 7.1 BW/s) than in the negative group (47.4 ± 11.2 BW/s).

Table 3 Comparison of variable results for single-leg drop landing between the negative and positive groups
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Fig. 2
figure 2

Comparison of the loading rate during single-leg drop jump landing between the negative and positive groups. *Significant difference between the groups (P < 0.01)

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Discussion

This study aimed to examine whether the ability to produce explosive force at the right timing is related to the ability to land from a jump. Participants with increased RFD in the countdown task had a lower loading rate at landing, and those with decreased RFD had a higher loading rate at landing.

The softness of the landing is determined by the magnitude of the loading rate, which consists of the peak GRF and the time to peak GRF. Soft landing requires at least one of the following: a smaller peak GRF and a long time to peak GRF. In this study, compared to the participants with decreased RFD, the participants with increased RFD experienced a longer time to peak GRF. These results indicate that the time to peak GRF was the primary determinant of the loading rate in this study.

A low loading rate at landing was reportedly produced by the high angular velocity of the lower limb [33] and a large range of movement [34] immediately after landing from a jump. To move the lower limb joints quickly and over a large range of motion after landing, it is necessary to start moving the lower limbs according to the timing of the foot making contact with the floor. The ability to adjust the timing is essential for absorbing impact loading during landing. On the other hand, the participants with increased RFD in the countdown task, as compared to that in the standard task, also exhibited a high ability to adjust the timing. The “loading rate at landing” and the “RFD in the countdown task” measured in this study are similar in that they both evaluated the ability to adjust the timing. Participants with increased force production ability in the countdown task might have also been able to land softly.

The factors affecting landing can be roughly divided into environmental and human factors. In terms of environmental factors, impact loading changed by approximately 15% depending on the condition of the floor or the type of shoe worn [35, 36]. In terms of human factors, the difference in impact loading between athletes and non-athletes was 15–20% [37, 38], and the intervention of injury prevention training reduced impact loading by approximately 25% [39]. The difference in the impact loading at landing between the two groups in this study was 26.8%, which is much larger than that of environmental factors and similar to that of human factors. The ability to adjust the timing is considered an important human factor that determines landing ability.

The present results demonstrated that participants with increased RFD in the countdown task had a lower loading rate at landing. In other words, the ability to produce explosive force at the right time was related to the ability to absorb the impact loading at landing from a jump. Considering that sports injuries are strongly associated with the magnitude of the loading rate during landing, the ability to produce explosive force at the right time is crucial to preventing sports injuries. Based on our findings, an increased focus on the ability to produce explosive force at the right time may help reduce the incidence of sports injuries. These results may be helpful when developing an injury prevention program.

Our study had some limitations. First, only healthy male individuals were included. Because the impact loading and movement patterns during landing differ between males and females, we cannot generalize our results to females [40, 41]. Second, the force plate was used to assess landing performance. It is unknown whether the participants with increased RFD in the countdown task quickly move the lower limb joints according to when the foot makes contact with floor. Thus, obtaining kinematics and kinetics data is important to understand the detailed differences between the two groups divided by the ability to adjust the timing.

Conclusions

This study investigated the relationship between the ability to produce explosive force at the right timing and the ability to land from the box. The participants with increased RFD in the countdown task had a lower loading rate at landing. These results suggest that the ability to produce an explosive force at the right time was related to the ability to absorb the impact loading when landing from a jump.