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Original Research

Relationships Between Explosive and Maximal Triple Extensor Muscle Performance and Vertical Jump Height

Chang, Eunwook1; Norcross, Marc F.1; Johnson, Sam T.1; Kitagawa, Taichi2; Hoffman, Mark1

Author Information
The Journal of Strength & Conditioning Research: February 2015 - Volume 29 - Issue 2 - p 545-551
doi: 10.1519/JSC.0000000000000652
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Improving performance is an essential and fundamental goal among elite athletes and recreationally active populations. Various performance variables, such as muscular strength, sprinting times, and vertical jump, have been used to quantify an individual's athletic performance (22,25). Previous researchers reported the critical time period for muscle contraction during daily and sports activity is between 50 and 250 milliseconds after onset of contraction, (6,19,20) whereas the time required to reach peak torque (PT) is between 300 and 500 milliseconds (1,17). Therefore, increasing the magnitude of force that can be produced quickly, rather than just increasing maximal strength production capacity, seems to be important for improving performance in sport-related activities.

Power is the ability to produce explosive muscular forces rapidly. Because power is important to athletic performances such as vertical jumping and sprinting (27,29), monitoring and training individuals' ability to generate power may be crucial with respect to improving performance. Rate of torque (or force) development (RTD) is a commonly used method to quantify the amount of torque produced per unit time (slope of the torque-time curve) (1,36). Therefore, greater RTD is indicative of an individual's ability to generate greater torque over a given period of time. Although RTD has been considered as an important factor with respect to the performance of explosive muscle contraction (7,8), the relationships between lower extremity joint (i.e., hip, knee, and ankle) RTDs and functional measures of athletic performance that require the overall actions of these multiple joints have not been thoroughly investigated.

Among sports performance professionals, maximal vertical jump testing is frequently used to assess maximal muscle power and functional performance because it is a simple and reliable test (14,22,23). McLellan et al. (21) reported that greater peak and average rates of vertical ground reaction force development were associated with greater vertical jump height performance during a countermovement jump. Vertical ground reaction force represents the combined actions of primarily the lower extremity triple extensors (hip, knee, and ankle extensors) during vertical jumping. This suggests that increasing the capability of these muscles to develop joint torque quickly is likely serve as a key factor for improving jump performance. As a way to seek the importance of an individual joint force generation capability related to vertical jump, previous researchers have reported the relationship between knee extension RTD and vertical jump performance (7,8,30,34). However, we are unaware of any studies that have examined the relationships between hip or ankle extensor RTD and vertical jump performance. Understanding the underlying relationships between individual joint RTD and jump height could be crucial for developing training programs to optimize vertical jump performance.

There is also evidence suggesting that it is also important to evaluate RTD during both the early and later phases of torque development due to potentially different neuromechanical factors underpinning the magnitude of RTD during these times. The level of neural drive excitation is reported to be the primary determinant of force production in the early phase of explosive muscle contraction (<50 milliseconds), whereas muscle intrinsic contractile properties likely influence force production during the later phase of muscle contraction (>150 milliseconds) (1,2,10,31). Furthermore, De Ruiter et al. (7,8) reported a correlation between the torque-time integral of the first 40 milliseconds of an isometric knee extension contraction and vertical jump height. This result relative to the phase of contraction, coupled with the fact that the time period for executing many explosive athletic performance tasks is often between 50 and 200 milliseconds (6,17,18), suggest that the time interval during which greater torque can be generated (e.g., 0–50 vs. 0–200 milliseconds vs. PT) may also be an important factor relative to vertical jump performance.

Therefore, the purpose of this study was to examine the relationships between maximum vertical jump height and (a) RTD calculated during 2 time intervals, 0–50 milliseconds (RTD50), and 0–200 milliseconds (RTD200) after torque onset and (b) PT for each of the triple extensor muscle groups. We hypothesized that greater vertical jump height would be highly correlated with hip and knee extension but show a weaker correlation with ankle extension. Furthermore, we hypothesized that greater vertical jump height would be most closely associated with triple extensor RTD at all 3 lower extremity joints when calculated during the early time period (RTD50) after the onset of muscle contraction.


Experimental Approach to the Problem

This study was performed using a cross-sectional study design. The purpose of the study was to examine the relationships between maximum vertical jump and RTD50, RTD200, and PT of the triple extensor muscle groups. RTD50, RTD200, and PT were assessed during maximum isometric voluntary hip, knee, and ankle extension contractions. Then, subjects were asked to perform countermovement vertical jumps to evaluate maximal jump height. The relationships between vertical jump height and triple extensor muscle RTD over both time periods and PT were then assessed using bivariate correlation coefficients.


Thirty recreationally active individuals (15 men and 15 women) aged between 18 and 30 years (mean ± SD: age = 23 ± 2.5 years; height = 172.76 ± 9.48 cm; and mass = 72.18 ± 14.03 kg) were recruited and volunteered to participate in the study. Recreationally active was defined as engaging in moderate intensity exercise for at least 150 minutes per week (12). All subjects had no current injuries or illnesses that limited their ability to perform physical activity, no lower extremity or back injuries in the 6 months before testing, and no history of hip, knee, or ankle surgery. Subjects were asked to refrain from any strenuous, fatigue-inducing physical activity before testing on the day of testing. Informed written consent approved by the University's Institutional Review Board was obtained from all subjects before participation.


Before testing, subjects warmed up on a stationary bicycle for 5 minutes at a submaximal intensity. After the warm-up, leg dominance was assessed by: (a) observing subjects which leg they would use to kick a ball for distance, (b) observing which leg subjects used to step up onto a step, and (c) observing which leg subjects used to recover from a small perturbation from behind (15). Subjects were then asked to remove their shoes, and height and mass were measured.

Rate of Torque Development

Hip extension, knee extension, and ankle extension (plantarflexion) RTD and PT of the dominant leg were measured during maximal isometric contractions using a Biodex System 3 dynamometer (Biodex Medical Systems, Inc., Shirley, NY, USA) interfaced with a BIOPAC MP100 Data Collection System (BIOPAC systems, Inc., Goleta, CA, USA). The subjects were instructed to contract “as hard and fast as possible” for 3–5 seconds against the dynamometer after presentation of a light stimulus. Subjects performed up to 5 trials for each condition with 60 seconds of rest between trials. After each trial, the recorded torque-time curve was visually inspected and any trial with an initial countermovement or trial where the torque-time curve did not reach a plateau (signifying maximal torque) was disregarded and repeated. Three successful trials for each condition were captured with the order of testing counterbalanced to eliminate any effects of learning and fatigue on the RTD and PT measures. To evaluate hip RTD and PT, subjects were positioned prone with the anterior superior iliac crest placed at the edge of the dynamometer table. The greater trochanter of the femur of the test leg was aligned with the axis of rotation of the dynamometer. The resistance pad was positioned on the distal aspect of the hamstrings just above the popliteal fossa. The testing positions of the hip and knee were then standardized for all participants using 30 and 85° of hip and knee flexion, respectively (26). Subjects' arms were wrapped around the dynamometer chair and the trunk stabilized with a resistance strap over the lower back, so that extending the trunk or flexing the knee during the hip extension trials was restricted. For knee extension trials, subjects were secured to the dynamometer chair with the trunk reclined 70° and the knee flexed to 70° (1). The axis of rotation of the dynamometer was aligned to the lateral femoral epicondyle of the test leg. The resistance pad was strapped over the musculotendinous junction of the gastrocnemius. To prevent hip motion, the thigh of the test leg and the pelvis was firmly strapped to the dynamometer. The arms were crossed over the chest during the testing. To evaluate ankle extension RTD and PT, subjects were secured to the dynamometer chair with the trunk reclined 70° and arms crossed over the chest and the knee in XX. The foot of the test leg was placed on a foot plate connected to the dynamometer. The axis of the rotation of the dynamometer was aligned with the lateral malleolus. The foot was firmly strapped with the ankle positioned in an anatomically in neutral joint position. Subjects were instructed to push the foot plate by plantar flexing ankle as if pushing on gas pedal (Figure 1).

Figure 1
Figure 1:
Testing posture for (A) hip extension, (B) knee extension, and (C) ankle extension maximal voluntary isometric contractions.

Vertical Jump

To assess maximal vertical jump height, subjects performed countermovement jump using a shoulder width stance with the dominant and nondominant feet, respectively, positioned in the center of 2 force plates (Bertec, Corp., Columbus, OH, USA). Subjects were instructed to stand in a comfortable and upright position with the feet parallel to each other, subjects then performed a countermovement by flexing the hips and knees as they swung their arms backwards. Once subjects reached a preferred countermovement depth, they explosively extended their hip, knee, and ankle joints while simultaneously bringing up their arms to perform a maximal vertical jump. To provide a target during the jump trials, a Vertec (Questek, Corp., Northridge, CA, USA) was placed next to the force plates and subjects were instructed to touch the highest vane possible on the Vertec during the jump. Trials in which either the dominant or nondominant foot was not centered on the force plate or touched on the opposite side of force plate were discarded and repeated. Subjects performed 5 total good countermovement jumps with 1 minute of rest between trials.

Data Sampling and Reduction

The raw voltage signal from the Biodex System 3 dynamometer was sampled at 1000 Hz using the BIOPAC MP100 during the isometric contraction trials. The recorded voltage signal for each trial was digitally low-pass filtered at 10 Hz using a fourth-order Butterworth filter and converted to torque (N·m) through a calibration equation function using custom written computer software (LabVIEW; National Instruments, Corp., Austin, TX, USA). This same custom software was also used to calculate RTD during each isometric muscle contraction during the initial 50 (RTD50) and 200 (RTD200) milliseconds after the onset of muscle contraction (i.e., time point when torque exceeded 2.5% of PT) and to identify the PT during each trial (i.e., maximal torque value during the trial). Rate of torque development was calculated as the slope of the line that best fit the torque-time curve over the 2 time intervals of interest (Figure 2). All RTD and PT outcome measures were normalized to body mass × [kg]−1 (30) and the maximum value obtained across trials was used for statistical analyses (2).

Figure 2
Figure 2:
An example of a torque-time curve during an isometric maximum voluntary contraction. The RTD was determined at 50 milliseconds (dotted line) and 200 milliseconds (dashed line) from onset of the torque-time curve. The peak torque was determined at the maximum value of the torque-time curve.

Force plate signals during vertical jump trials were sampled at 200 Hz using The MotionMonitor motion-analysis software (Innovative Sports Training, Inc., Chicago, IL, USA) (9). Custom computer software was used to determine flight time, which was defined as the time during vertical jump trials when the vertical ground reaction force was equal to zero. Maximal vertical jump height was calculated as a function of flight time using previously described methods (9). As with the RTD and PT measures, the maximal vertical jump height across trials was used for statistical analyses.

Statistical Analyses

Simple Pearson's product-moment correlations were used to assess the relationships between maximal vertical jump height and hip extension, knee extension, and ankle extension RTD50, RTD200, and PT. All statistical analyses were performed using RStudio version v0.97 (RStudio, Inc., Boston, MA, USA) with statistical significance established a priori (α ≤ 0.05).


Mean and SD of vertical jump height was 37.6 ± 12.3 cm. Mean and SD of triple extensors RTD and correlations between vertical jump height and triple extensors RTD in each time windows are presented in Table 1 and Table 2, respectively. Greater vertical jump height was associated with greater knee and ankle extension RTD50, RTD200, and PT (p ≤ 0.05). However, hip extension RTD50, RTD200, and PT were not significantly related to maximal vertical jump height (p > 0.05).

Table 1
Table 1:
Mean values andSDs for hip, knee, and ankle extensors RTD50, RTD200, and PT.*
Table 2
Table 2:
Pearson's correlation (r) coefficients between vertical jump height and hip, knee, and ankle extensors RTD50, RTD200, and PT.*


In this study, we investigated the relationships between vertical jump height and individual lower extremity triple extensor PT and RTD during critical time periods. The primary finding of this study was that greater vertical jump height was associated with greater knee and ankle extension RTD and PT, but not hip extension RTD and PT.

Although previous work relative to these measures and vertical jump performance is equivocal, our results are consistent with previous investigations that have reported significant correlations between vertical jump height and knee extension RTD calculated over various time intervals (30,32,34). Our results indicate that 47.6% of the variability in vertical jump height was explained by knee extensor RTD50, compared with just 28.1 and 31.4% explained variances for knee extensor RTD200 and PT, respectively. These findings suggest that knee extensor RTD50 likely plays a major role in inducing the greater vertical jump performance compared with RTD200 and PT. This relationship between vertical jump performance and knee extension RTD is likely due to the fact that the knee extensors are type II muscle fiber dominant (18). Previous studies have reported that maximal jump performance was related to the proportion of type II fibers in muscle (5,13). Furthermore, Andersen et al. (3) found that increased knee extension RTD after training was associated with greater extent of type II a fiber from muscle biopsies.

The finding from this study that greater ankle extension RTD is related to greater vertical jump height is unique. Previous studies (11,16) reported that the net ankle joint moment and power measured during a vertical jump influences vertical jump performance the least among lower extremity joints measured. However, our results show that there are correlations between vertical jump performance and ankle extension RTD and PT. The current results indicate that ankle extensor RTD50 explained 32.5% of the variability in vertical jump height compared with 28.1 and 13.7% explained variances for ankle RTD 200 and PT. From this result, we suggest that early phase RTD is more closely related to vertical jump performance. The different approaches used for measuring lower extremity muscle performance RTD and PT during isometric contractions vs. net joint moments during vertical jumping may partially contribute to the different relationships between ankle extensor muscle force generation property and vertical jump height. However, there is 1 previous study that agrees with the current finding related to the role of the ankle extensors during vertical jumping. Vanezis and Lees (33) reported that athletes assigned to a high vertical jump performance group showed greater net ankle extensor peak power and positive joint work during a countermovement jump than a low performance group. It could be speculated that an increased ability to generate greater ankle extension RTD during isometric contraction would result in greater potential to produce peak power during functional activities. Stone et al. (28) reported greater RTD is associated with greater peak power generation. According to given relationships between RTD and peak power generation, it could be suggested that a subject who could generate better ankle extension RTD might perform greater vertical jump.

A previous investigation reported strong relationship between vertical jump height and mean hip extension torque during a high speed isokinetic measure (32). Therefore, we expected that hip extension RTD and PT would be related to vertical jump performance. However, unlike the relationships noted between knee and ankle extension RTD, respectively, and jump height; neither hip extension RTD during the early (RTD50) nor later period time (RTD200) or hip extension PT were significantly associated with maximal jump height. Isometric muscle torque testing may result in a discrepancy from a previous result using isokinetic testing (32); however, this report could be meaningful because it is the first to investigate the relationship between maximum hip extension RTD and vertical jump. Furthermore, previous studies have reported that the hip extensors tend to have greater influence on the performance of horizontal movements such as sprint starting (24) and the horizontal deceleration of the center of mass during jump landings (35). Therefore, it could be speculated that in a vertical jump task, which is primarily dependent on vertical acceleration of the body, hip extensor muscle action influences performance to a lesser extent than knee and ankle extensor actions.

Finally, the results of this study suggest that vertical jump performance may be more closely related to the capacity to generate greater torque in the early phases of muscle contraction (RTD50) than the later phase of muscle contraction (RTD200) or PT. We propose that deliberately focusing on improving an athlete's ability of the knee and ankle extensor to generate force quickly (i.e., during the initial 50 milliseconds of contraction) is likely essential for individual participating in sports requiring vertical explosive actions. However, future research is necessary to investigate this hypothesis whether improved vertical jump performance might be attained by focusing on fast movement training of the knee and ankle to increase the early phase RTD of these muscle groups. Finally, given that only 47.6 and 32.5% of the variability in maximal jump height was explained by knee extensor and ankle extensor RTD50, it is also apparent that other factors, such as technique and lower extremity movement coordination, also influence maximal vertical jump performance. In addition to improving the ability to rapidly generate torque during the early phase of contraction, technique and movement coordination training are also likely warranted to truly maximize vertical jump performance.

One potential limitation of this study is that triple extensor RTD and PT were measured during a single joint isometric contraction. It has been suggested that isometric muscle contraction and open kinetic chain muscle strength measures may not be associated with performance on complex, multijoint functional movements (4). However, De Ruiter et al. proposed that greater explosive muscle force is related to the ability to rapidly activate the motor unit pool, and this capability is likely more dependent on subjects' ability than the task as long as all subjects perform the same task (i.e., countermovement vertical jump) (7). Therefore, it is likely, and our results support, that subjects who were capable of performing more explosive contractions did so during both the isometric contraction and the vertical jump task.

The other limitation of this study was the fact that we used simple bivariate correlations, rather than a multiple linear regression model for statistical analyses. Although a multiple regression model would have allowed us to evaluate the collective influence of the hip, knee, and ankle muscle performance measures (RTD50, RTD 200, and PT) on vertical jump height, these measures were highly correlated among the 3 lower extremity extensor muscle groups. As a result of this multicollinearity issue, it was not appropriate to use multiple linear regression. However, despite of this limitation, the results obtained using bivariate correlations clearly offer some interesting and novel insights into the relationships between vertical jump height and triple extensor RTD during different time critical periods.

Practical Applications

In this study, significant correlations existed between knee and ankle extension RTD and vertical jump performance. Our findings may provide the mechanical insight regarding how vertical jump performance is related to lower extremity triple extensors. Therefore, these results suggest that training specifically targeted to improve knee and ankle extension RTD, especially during the early phases of muscle contraction, may be effective for increasing maximal vertical jump performance. From a training perspective, the results indicate that it is useful to not just focus on improving and measuring PT production capacity, but to also, and perhaps more importantly, focus on the RTD.


The results of this study do not constitute endorsement of the product by the authors or the National Strength and Conditioning Association.


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rate of torque development; countermovement jump; explosive strength

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