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Positive and Negative Loading and Mechanical Output in Maximum Vertical Jumping


Medicine & Science in Sports & Exercise: October 2007 - Volume 39 - Issue 10 - p 1757-1764
doi: 10.1249/mss.0b013e31811ece35

Purpose: The aim of this study was to evaluate the effect of external loading on mechanics of vertical jumping. We hypothesized that the muscular mechanical output could be higher under no-load conditions than in the presence of either positive or negative external loads.

Methods: Fifteen physically active men performed maximal countermovement jumps (CMJ) on a force plate while a pulley system provided approximately constant vertical force acting in a way to either reduce or increase the body weight. As a result, the weight of the body approximately corresponded to the gravity acceleration from 0.70 to 1.30g (g = 9.81 m·s−2).

Results: Regarding the jumping kinematics, we observed a significant (P < 0.001) load-associated decrease in both the peak velocity and lowering of the center of mass during the eccentric jump phase, but not in the duration of the subsequent concentric jump phase. Regarding the muscular mechanical output, both the mean power () and peak momentum (M) revealed significant (P < 0.001) changes associated with loading, and further post hoc analyses revealed significantly higher values (P < 0.05-0.001) of both and M for 1.00g compared with most of the other loading conditions applied.

Conclusion: The results suggest that subject's own body provides the optimal load for producing maximum mechanical output in vertical jumping. If corroborated by the results of future studies performed on other rapid movement, our findings could support the hypothesis that the muscular system is designed for producing maximum mechanical output in rapid movements when loaded only with the weight and inertia of its own body.

1Faculty of Kinesiology, University of Zagreb, Zagreb, CROATIA; and 2Department of Health, Nutrition, and Exercise Sciences, University of Delaware, Newark, DE

Address for correspondence: Slobodan Jaric, Ph.D., Human Performance Lab, Rust Ice Arena, 547 South College Avenue, Newark, DE 19716; E-mail:

Submitted for publication January 2007.

Accepted for publication May 2007.

Skeletal muscles actively produce force that leads to a functional output. This output is usually evaluated by mechanical variables assessing the associated movement performance. Regarding individual muscles, it is well known that changes in muscle architecture (specifically, changes in fiber length and the angle of pennation) affect the force-velocity relationship in a way to produce a trade-off between the abilities to contract at high speed and to exert high force (12). One of the consequences is that due to changes in muscle architecture, the maximum muscle power (i.e., the product of muscle force and velocity of muscle shortening) can be shifted either towards lower external loads (and, consequently, higher movement velocities), or in the opposite direction (11,12).

When analyzing movements of the entire body with respect to the environment, a number of researchers are more interested in externally measured mechanical variables than in the mechanical contribution of particular elements, such as individual muscles and muscle groups. The main reason for this interest is not the fact that internal forces and power are hard, if not impossible, to measure in vivo, but that the human body is moved by external forces (although exerted by internal ones), the most important of which is the ground-reaction force. As a consequence, most of the physiological assessments of human movements are based on the externally recorded mechanical variables often referred to as output. For example, whereas the movement velocity is assessed by velocity of the body's center of mass, maximum muscle strength tests are based on directly measured force applied against an external object (i.e., force output), and muscle power is either assessed from the external resisting force and speed (e.g., cycle ergometer tests (25)), or from the change of body's potential energy and time (e.g., Margaria test (18)), or from the ground-reaction force and the velocity of the center of mass (e.g., vertical jumping test (6)), which corresponds to the power output.

Effects of external loading on human mechanical output have been extensively studied for purposes such as assessing optimum training regimens (4), designing human powered devices (21), assessing the effects of body size on physical performance (5), or understanding basic principles of the design of human locomotor apparatus and its mechanical properties (22). However, an accurate and valid interpretation of the results of loading experiments is inevitably affected by a number of methodological problems. For example, when performing rapid movements the muscular system is "loaded" by forces originating from both the weight and inertia of the limbs, and the contribution of each of them is movement specific. Vertical jumping seems to be predominantly affected by body weight (BW), whereas running is mainly loaded with limb inertia (i.e., resistance to acceleration and deceleration of the limbs (22)). As a result, loading of different body segments, such as arms and legs in running, can produce very distinctive effects (24). It should be also pointed out that external loading alters movement kinematic patterns not only because of a change in resistance to active forces (23), but also through changes of the central neural command that adapt the pattern of muscle activation to produce the optimal mechanical output (14,28). The later point will be of particular importance in further text for selection of the tested movement task, as well as when interpreting the obtained results.

A particular methodological problem in the loading experiments is providing adequate mechanical conditions to study the effects of negative load (i.e., unloading). Although in some movements BW can be partly compensated by using external pulling systems, the limb inertia cannot be adequately reduced. As a result, we are deprived from knowledge that could be gained from studying the effects of loading over the full range from negative to positive loads. The attempts, such as studying the general effects of unloading on running mechanics by just partly supporting subjects' center of mass should be disregarded because only the less important component of load (i.e., gravitational) was accounted for (3).

In the present study, we selected the countermovement jump (CMJ; the natural vertical jump performed with a preparatory lowering the body) to test the effects of both positive and negative load that simulates changes in BW. This selection was based on several important factors. First, CMJ highly corresponds to natural vertical jumps where the maximum performance is based on a high muscle mechanical output exerted during natural stretch-shortening cycle. The consequence of the mechanical output is assessed through the effects of the ground-reaction force. Second, when compared with sprint running, the inertial forces of the limbs are relatively low with respect to the load originating from BW. As a result, the above discussed problem of the role of limbs' inertia (see previous paragraph) could play a minor role. Third, contrary to many previous studies that applied positive loads at the subject's shoulders and reported conflicting findings while studying power-load relationship during jumping (for review, see Cronin and Sleivert (4); see also Discussion), we applied both positive and negative loads near the subject's center of gravity. Fourth, because we were interested in the maximum mechanical output of the neuromuscular system, we selected a movement that allows for optimization of the kinematic pattern to different loading conditions (e.g., adjustment of the preparatory lowering of the body).

We hypothesized that the mechanical output for the no-load conditions would be higher than for either positive or negative load applied. The hypothesis was based on several indirect sources of evidence. First, similar to the force-power curve of a single muscle (22), different cycling tests performed on lab ergometers or squat jumps also provide maximum muscle power output for certain external load applied (8,10,21,25). For instance, a number of studies have demonstrated that humans exert maximum power (i.e., optimal combination of the resisting torque and cranking velocity) in cycling exercise at a crank velocity of 110-120 rpm (21,25). Therefore, natural human movements, such as running or jumping could also provide maximum output under particular loading conditions. Furthermore, it is plausible to assume that the optimal load could be the one for which the muscular system is designed for: the load of one's own body. Some experiments performed on animals (17) and humans (7,26) speak in favor of this assumption. For example, Davies and Young (7) found that an increase in external loading was associated with reduced generation of the power output in maximal vertical jumping and speculated that body size and speed of movement could be optimally matched for the production of lifting work during vertical jump. However, the authors did not apply negative loading that could provide direct evidence supporting the speculated effect. Similar finding in sedentary individuals was also observed by Driss et al. (9). Finally, our recent study suggests that the physical performance tests based on performance of rapid movements could measure the same physical ability as the tests of muscle power under the condition that the latter ones are properly normalized for the effect of body size (19). A possible interpretation could be that the maximum power could be exerted in movements resisted by load of the subject's own body.

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Fifteen physically active physical education students (age: 23.5 ± 3.4 yr, body mass: 79.7 ± 7.0 kg, height: 1.80 ± 0.07 m; mean ± SD) volunteered in the study. Although not trained athletes, the subjects had an extensive experience in vertical jumping through participation in the courses of physical activities within their standard academic curriculum, as well as through participation in various sporting activities that include vertical jumping (i.e., basketball, handball, track and field, volleyball, etc.). Moreover, all the subjects had at least 1 yr of experience in resistance training and, at the time of testing, trained recreationally at least three times a week. The study was approved by the ethics committee of the Faculty of Kinesiology, University of Zagreb, and all subjects signed an informed consent document according to Helsinki Declaration. None of the subjects reported any medical problems or recent injuries that would compromise jumping performance.

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The pulley system.

For the purpose of this study, we designed a low-friction pulley system that allowed us to mimic either an increase (Fig. 1A) or a decrease (Fig. 1B) in the subject's BW. Initially, we used external weights acting via specially designed harness and a modified weightlifting belt to provide the pulling force. However, temporary lagging of the weights attributable to their inertia produced a very irregular loading pattern that disrupted the movement coordination. Therefore, we replaced the weights with long rubber bands (resting length = 2.8 m). This loading system allowed the subjects to perform CMJ without any movement constraints when applied to pull subjects either vertically upward (negative load) or vertically downward (positive load). When three or six bands were used in parallel, they revealed the elasticity constants of 28.3 and 56.6 N·m−1, respectively. On the basis of pilot data, we selected the loads of 123 N (corresponds to 12.5 kg of mass) and 245 N (corresponds to 25.0 kg of mass) that required stretching the rubber bands about 4.3 m. Loads higher than 245 N acting in either direction seemed to disrupt coordination in a way that some subjects complained that they "do not jump any more." A fine tuning of the selected loads was done by weighting each subject with each external load a force plate. During performance of CMJ, the subjects lower their center of mass for approximately 0.3 m (20), which corresponds to about 4% of the total elastic bands' stretch. For the highest lowering of the center of mass observed in our study (i.e., 0.5 m), the total elastic bands' stretch was about 7%. Thus, the change in length of the elastic bands during lowering the subject's center of mass resulted in the same relative changes of the load (corresponding to the maximum changes in loading force of 8.5 and 17 N for the selected loads of 123 and 245 N, respectively). As a result, one could consider that the applied load forces were approximately constant during the take-off phase. That was of a particular importance because the external load was supposed to alter subjects' BW, which also remains constant through the jump.



When expressed in terms of the subjects' average BW, the above-mentioned loading forces of 123 and 245 N approximately corresponded to 15 and 30% of BW, respectively. Because only BW was altered, but not the body mass and the mass-related inertia, the mechanical conditions closely resembled those accomplished in parabolic flights aimed to alter the effect of gravity acceleration (g) (2). As a result, in the text below we will refer to the five loading conditions tested as 0.70g (unloading body by 30% of BW), 0.85g (unloading by 15% of BW), 1.00g (no load applied), 1.15g (loading BW by additional 15%), and 1.30g (loading BW by additional 30%).

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Experimental protocol.

To adjust the jumping kinematic pattern to different loading conditions and produce the maximum mechanical output, the subjects performed a total of 50 practice trials during two familiarization sessions performed within the week preceding the experiment. The subjects were instructed to avoid any strenuous exercise 48 h before the experiment. The experimental session was preceded by a standard warm-up and stretching procedure. Thereafter, each subject performed three consecutive experimental CMJ trials under each of the five loading conditions (0.70, 0.85, 1.00, 1.15, and 1.30g; see above for details). The order of the loading conditions was randomized for each subject. Subjects were instructed to perform each CMJ with maximum effort and jump as high as possible using the preferred countermovement squat depth. One minute of rest was allowed between two consecutive jumping trials, and 2-3 min between the consecutive loading conditions. Fatigue was never an issue.

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Data analysis.

The jumps were performed on a force plate (Kistler type 9290AD; sampling frequency 500 Hz) mounted according to the manufacturer's specifications. On the basis of each subject's "effective" BW (i.e., BW adjusted for the load condition), the following variables were calculated from the recorded vertical component of the ground-reaction force using inverse dynamics: peak velocity of the center of mass during the concentric jump phase (v peak), relative lowering of the center of mass during the eccentric jump phase (Δh ecc), duration of the concentric jump phase (t con), peak ( peak) and mean power output () during the concentric jump phase, and peak momentum during the concentric jump phase (M). The velocity of the center of mass was obtained from the integral of the acceleration provided by the vertical force signal. Power output was calculated as a product of the vertical component of the ground-reaction force and the velocity of the center of mass. corresponded to the power output averaged over the duration of the concentric phase (i.e., the time interval from the instant of the velocity became positive to the end of the contact with platform). Finally, M was calculated as a product of the v peak and the effective body mass (i.e., body mass corrected for the mass corresponding to the applied external load). For each loading condition, the trial with the highest was used for further analyses.

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Statistical analyses.

Descriptive statistics were calculated for all experimental data as means (SEM). To assess the reliability of the measured v peak, Δh ecc, t con, , peak, and M, intraclass correlation coefficients (ICC) were calculated by means of repeated-measures ANOVA (27). Bonferroni post hoc multiple-comparison test was used for detecting the possible systematic bias between three consecutively measured trials for each mechanical variable under each load. Effects of positive (1.15 and 1.30g) and negative loading (0.70 and 0.85g) on all mechanical variables with respect to the no-load condition (i.e., 1.00g) were tested using repeated-measures ANOVA and Tukey post hoc multiple-comparison test. The level of statistical significance was set to alpha = 0.05.

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Regarding the reliability of the selected dependent variables, there were no significant differences in any of the six mechanical variables among the three consecutive trials under each of the evaluated loading conditions (P > 0.05). Intraclass correlation coefficients (ICC) and their corresponding 95% confidence intervals for all dependent variables are depicted in Table 1. Note that the results suggest high reliability because all ICC were above 0.90.



Figure 2 illustrates the effect of external loading on the selected kinematic variables obtained from a representative subject. As anticipated, an increase in external load (i.e., increase in g) was associated with both an increase in ground-reaction force (Fig. 2A) and a decrease in v peak (Fig. 2B). The subject also demonstrated a marked load-associated decrease in the lowering of the center of mass during the eccentric jump phase (Δh ecc; Fig. 2C). Finally, note that although the peak of power tends to decrease with load (Fig. 2D), the peak of momentum (M) is highest for the no-load condition (i.e., 1.00g; see Fig. 2E).



When averaged across the subjects, the movement kinematics were in line with the effects of loading obtained from the representative one (Fig. 3). One-way ANOVA revealed a significant effect of loading on both v peak (F 4,56 = 589.7; P < 0.001) and Δh ecc (F 4,56 = 216.6; P < 0.001), whereas t con seems to be unaffected (F 4,56 = 1.20; P = 0.15). The post hoc analyses revealed significant differences (P < 0.01) in both v peak and Δh ecc between the 1.00g and all remaining loading conditions.



The main findings of our study are the loading-associated changes in the mechanical output (Fig. 4). Both the mean power (; F 4,54 = 26.3; P < 0.001) and maximum momentum (M; F 4,54 = 85.0; P < 0.001) revealed significant changes associated with loading. Further post hoc analyses revealed significantly higher (P < 0.05 to 0.01) values of both and M in 1.00g condition compared with most of the positive and negative loads applied. Even the only exception (i.e., the difference in between the 0.85 and 1.00g conditions; see Fig. 4A) showed the differences close to the level of significance (P = 0.06). Although the peak power also showed the effect of load ( peak; F 4,56 = 47.5; P < 0.001), the post hoc analysis revealed a significant difference (P < 0.01) between the 1.00g and positive loading conditions only (i.e., 1.15 and 1.30g; Fig. 4B).



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Before discussing the main findings of our study, several important methodological aspects need to be stressed. First, our subjects were not only young and physically highly active, but their average jumping height of 0.51 m observed under the no-load condition was comparable with the one observed in elite soccer players (30), suggesting a high level of physical performance. However, the main methodological point for discussing could be the movement selected for testing the effects of external loading. Because we were interested in the maximum mechanical output of the muscular system, we had to allow for adjustments of the movement kinematic pattern for different loading conditions. Therefore, instead of the squat jump performed from a fixed starting position that was tested in the most of previous studies (4), we selected CMJ that would allow for optimization of the movement kinematic pattern (e.g., speed and distance of the preparatory body lowering, duration of the eccentric and concentric jumping phase) for producing the tested maximum output. The recorded load-associated decrease in the lowering of the center of mass (Δh ecc) is in line with both the phenomenon well known in strength training and a general finding that larger animals use smaller joint excursions when jumping (22). Of particular importance could be a vast body of motor-control literature suggesting that the "central neural controller" needs only few, if not only one, trial to adjust the movement kinematic pattern to both expected and unexpected changes in external loading (14,28). These findings, taken together with both the applied familiarization procedure and the high reliability obtained from all dependent variables, generally suggest that our subjects were able to adjust the jumping pattern to exert the maximum mechanical output under the tested loading conditions. Finally, CMJ provides conditions for the stretch-shortening cycle, which characterizes most rapid human movements, and the jump performance also highly correlates with sprinting performance (16,29). Therefore, one could conclude that the present study provided both a reliable and valid set of data, and also that the observed findings could be partly generalized to other types of rapid human movements.

The main finding of our study represents the effect of external load on the muscle mechanical output. Whereas a decrease in both v peak and Δh ecc could be considered an expected effect of an increase in external loading, the same trend could not be expected from the load-associated changes in power and momentum. Nevertheless, on the basis of some indirect evidence, we hypothesized that the maximum output could be the highest for the no-load condition. Most of the data obtained seem to be in line with the hypothesis. Specifically, both and M suggest maxima for 1.00g, although, strictly speaking, the differences in observed between the 1.00 and 0.85g loading conditions were slightly below the level of significance. Some earlier studies based only on positive loading (i.e., loading ≥ 1.00g) also have revealed a load-associated decrease in (7) and peak (7,9) in vertical jumping. However, both the lack of negative loading and the selected jumping technique (9) prevented the authors from assessing the external load that provides the maximum mechanical output in vertical jumping. In contrast, several other research groups reported that the maximum and peak output during squat jumps and/or CMJ was attained with additional loading ranging from 0% (i.e., BW only) to 70% of their maximal squat strength (4). However, none of these studies have evaluated the effect of negative loading, and some of them also have failed to include the output of nonloaded body in the analysis. Some of these studies also have failed to include the subjects' BW in the calculation of muscle power (6). However, note that the above-mentioned studies placed weight on subjects' shoulders (usually through a Smith machine) instead of in the vicinity of the center of gravity. This loading approach inevitably prevented subjects from performing unconstrained jumps and likely increased forward trunk inclination during jumping (13,15), thereby increasing the relative mechanical contribution of hip extensors (13). Finally, the fixed starting position of the squat jumps testedin most of the other studies did not allow for adjustment of the kinematic pattern that could lead to maximum performance. As a consequence, the validity of the discussed results for jumping performance should be questioned.

From the mechanical aspect, our finding suggests that the load of one's own body (i.e., 1.00g loading condition) provides conditions for muscles to exert the maximum net impulse (i.e., the ground-reaction force reduced for body weight and integrated over the duration of the concentric phase) that corresponds to the maximum momentum M of the body (maximum velocity multiplied by body mass). In addition, the same load also provides the maximum of the averaged product of the ground-reaction force and velocity of the center of mass (which equals mean power ). Note that the muscle power output represents the most commonly used variable to assess maximum performance (6,18,25), whereas the momentum have been suggested to be the most valid variable to assess the performance of rapid movements, including, in particular, jumping (1).

Because peak has been often used in previous literature to assess the effects of external loading on muscular mechanical output (7,9,10), we also included peak among the selected dependent variables. We found that peak failed to provide the maximum for the 1.00g loading condition as and M. However, it should be kept in mind that the duration of the concentric phase used to calculate remained unaffected by external loading. Therefore, it seems that the loading only altered the temporal pattern of power by providing the maximum (i.e., peak) that remained approximately constant under the negative loads and the no-load conditions. Regarding the relative importance of these two measures of power, it should be kept in mind that the maximum performance (e.g., jump height, peak movement velocity, etc.) in movements performed over the same interval of time should be associated with the highest , but not the highest peak. As a result, could be a more valid variable for assessing the muscular mechanical output under various loading conditions than peak.

Taking into account the complexity of both the muscular system involved in the tested movement and the neural control mechanisms affecting the movement kinematic pattern that can heavily affect the recorded performance, we could only speculate on the interpretation of the observed findings. The starting point could be the design of the muscular system already briefly discussed above in our introduction. Specifically, changes in architecture (e.g., pennation angle and fiber length) of an individual muscle can affect the muscle-shortening velocity that allows for producing the maximum mechanical output. Generalized to complex movement, there should be also an optimum movement velocity that provides conditions for maximum mechanical output (e.g., or M) of the entire muscular system. Because external loading inevitably affects the movement velocity, our findings suggest that the load originating from one's own body weight and inertia provides the aforementioned optimal conditions. If one could generalize the present findings from jumping to other rapid movements of obvious importance from evolutionary perspective (e.g., running, throwing, kicking), one could generalize our research hypothesis to the concept that the muscular system is designed to produce maximum mechanical output in rapid movements performed against the load that originates from the weight and inertia of its own body. High correlations between jumping and sprinting performance seem to support this hypothesis (16,29). This hypothesis also seems plausible from an adaptive point of view. Namely, it suggests that the muscular system is adapted to provide maximum mechanical output under the loads that we usually overcome in our daily living (i.e., moving our body or body parts under the 1g loading condition). A long-term exposure to higher or lower loads (e.g., simulating higher- or lower-gravity conditions) would then result in shifting the optimal loading for maximum mechanical output under either higher or lower loads. Although this generalization could require further research, it is indirectly supported by a vast strength training literature.

Several problems remain to be dealt with in future testing of the discussed hypothesis. The problem of reducing the inertial load that dominates resistance in movements such as running or kicking has been already mentioned in Introduction. Regarding our methodological approach, we accounted only for the gravitational load by providing constant external force, and the inertial load remained not accounted for. The neural control aspects could also deserve attention. Although the ability of the central nervous system to quickly adapt the control pattern to changed loading conditions in well practiced movements seems well documented (see Discussion above), one could question the same ability in less familiar tasks. From a more general perspective, one could also argue that the muscular system is not only designed for maximizing mechanical output, but also for endurance, elaborate control of precision movements, flexibility, etc. Finally, the subject-specific effects of external loading that could be observed in future studies could also prevent us from generalizing our findings. For example, the optimal load for exerting maximum power is considerably higher for strength- and power-trained athletes than for sedentary individuals (26).

To conclude, we found that CMJ performed under no-load conditions provided higher mechanical output regarding M and P than when either a positive or negative load (mimicking either increase or decrease in BW, respectively) was applied. Although a number of methodological problems remain to be solved, similar evidence obtained from other rapid body movements could support the hypothesis that the muscular system is designed for producing maximum mechanical output when loaded only with the subject's own body weight and inertia. That evidence would not only provide a new insight in the principles of design of the muscular system, but also provide a basis for new approaches in assessment of muscular function.

The study was supported in part by grants from Croatian Ministry of Science, Education, and Sport (034-0342607-2623), from Serbian Research Council (#145082), and from Croatian National Science Foundation postdoctoral fellowship to G. Markovic.

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