The results of unloading and loading in simulated SJ were very similar to those in simulated CMJ. However, in SJ, peak
were smaller by approximately 5% and 30%, respectively (Table 1). The smaller mean
was ultimately due to the relatively slow dynamics of active state. In SJ, there is by definition no countermovement, so the active state is quite low in the initial posture. After all, only gravitational forces have to be counteracted, and this requires only small MTC forces and low active state (note the differences in ground reaction force between stick diagrams labeled “initial” in SJ and “bottom” in CMJ in Fig. 2). Thus, the active state must increase during the push-off, and, in fact, a large part of the range of motion is travelled at submaximal force so that submaximal work is produced in SJ (2). As a consequence, the push-off takes more time, and the mean
is less in SJ than that in the CMJ at the same extra force (Fig. 2 and Table 1). When peak
occurs, the active state of the muscles is still not as high in SJ as it is in CMJ at the same extra force, and this causes the P CE of VAS, P CE,tot, and
to be lower in SJ (Tables 1 and 2).
In the literature, substantial drops in “power” have been reported with both unloading and loading in jumping. It is tempting to try and explain these drops with the help of the intrinsic force–velocity–power relationship of muscle (15): if the reference condition provides the load that allows for maximal power production, then both unloading and loading will cause power production to drop (Fig. 1). However, there might also be an effect of load-dependent changes in
during CMJ in some studies (e.g., ). Moreover, it is not certain that subjects were able to quickly tune their control to changed loading conditions, which is required for maximal performance (5). The purpose of the present study was to gain a solid understanding of how and why negative and positive loading affect muscle power output during jumping, and for this purpose, a model of the musculoskeletal system was used. The STIM(t) input of the model could be optimized to ensure maximal performance, and by setting a penalty on the deviations of the minimum height of the CM from a predefined value,
in CMJ could be kept constant. This way, the pure effects of unloading and loading on maximal output in jumping could be studied. It was found that unloading did not cause a decrease in peak
as observed in experiments with subjects (e.g., ) but instead caused a small increase (Table 1). Loading did cause a decrease in peak
, as observed in many experiments with subjects (e.g., ), but the magnitude of the decrease was very small. It was shown that the variations in peak
in the simulated jumps were due only in part to the intrinsic force–velocity–power relationship of muscle. Figure 1 was in fact based on the intrinsic force–velocity–power relationship of VAS; at the instant that peak
occurred, v CE was below optimum in all loading conditions, and as the extra force was changed from +60% BW to −60% BW, v CE increased by the amount indicated by the dotted section in Figure 1. Thus, it got closer to the optimal v CE, but the corresponding increase in P CE was small (dotted section in Fig. 1, see also Table 2). In addition to the small effect of variations in v CE, there were small effects of variations in CE length and active state among loading conditions (Table 2 and Fig. 4). It seems, therefore, that the intrinsic force–velocity–power relationship explains at most a small part of the effects of unloading and loading reported in the literature. Below, it will first be argued that the simulation model represents the salient properties of the real system. Subsequently, other possible explanations for the difference in the effects of unloading and loading between the simulation model and the human subjects will be presented and supported by ad hoc simulation experiments. Finally, on the basis of the simulation results, current interpretations of the results of unloading and loading described in the literature will be called into question.
When it comes to simulation results, the first question is always whether the model used is a valid representation of the real system. The model used here included the force–length and force–velocity relationships of CE (25), the excitation dynamics (2,3), and the interaction between CE and SEE (1). After the optimization of STIM(t), it has successfully reproduced various types of jumps in terms of jump height, kinematics, kinetics, and even muscle activation patterns (e.g., [3,4,27]). The values that were obtained in the present study for peak
in the reference condition, 46.1 and 28.6 W·kg−1 in CMJ and 44.0 and 19.4 W·kg−1 for SJ, respectively, were reasonably close to the values reported by Pazin et al. (22) for a group of “active subjects”; the peak
and the mean
in the reference condition for that group were 61 and 30 W·kg−1 in CMJ and 47 and 20 W·kg−1 in SJ, respectively (values derived from Fig. 3 and Table 1 of Pazin et al. ). Note that Pazin et al. (22) had their subjects perform CMJ with arm swing, which may explain why
reached higher values in their study than in the CMJ without arm swing simulated in the present study. Considering the results obtained for CMJ with this in mind, and considering the results obtained in SJ, it seems safe to say that the model successfully reproduced the jumping performance of subjects participating in one of the key studies on the effects of unloading and loading on
in jumping. Thus, although the model is by definition a simplification of the real system, it still satisfactorily represented the properties of the musculoskeletal system that are important for jumping.
In the literature, an extra force equal to 30% BW pulling upward on the trunk could cause a decrease in peak
during jumping of more than 10% of reference (22), whereas in the simulation model, the same amount of unloading caused a small increase in peak
. In the literature, an extra downward force of 30% BW could cause a decrease in peak
of approximately 30% of reference (17), but in the simulation model, the same amount of loading caused a decrease of less than 3% in peak
(Table 1). What is the explanation for the differences between the results obtained in the experiments on subjects and those obtained in the simulation study? If the simulation model is a valid representation of the real system, then the simulation results establish unambiguously how different loading conditions affect
in maximal jumps with a predefined minimal height of the CM, obtained by the optimization of STIM(t). Over the whole range of loading conditions studied, that is, from EF−60%BW to EF+60%BW, the peak
and the mean
varied by less than 10% (Table 1). Performing simulations with lower values for Hill’s parameter b (thus with reduced speed of the muscle fibers) caused an overall reduction in performance and even smaller variations in peak
(results not shown). If larger effects of unloading and loading occur in the subjects than in the simulation model, the subjects must be doing something different than the simulation model. One important difference could lie in variations of
in CMJ, and hence in the height of the CM at the start of the push-off in CMJ; it has been shown in the literature that variations in the latter affect jump performance (2,3). The group of Marcovic and Jaric (17,22) left
free, to allow subjects to optimize their movement pattern and to produce maximal output. In one study by this group (17), the subjects lowered their CM by approximately 31 cm in the reference condition (Fig. 3B of Marcovic and Jaric ), similar to the 34 cm in the present simulation study), and only by approximately 17 cm when the extra force was +30% BW. In the latter condition, peak
was approximately 30% smaller than reference. In a later study by this group (22), subjects chose about the same
in the condition where the extra force was +30% BW as they did in the reference condition (Fig. 4d of Pazin et al. ), and their peak
was only approximately 6% smaller than reference. This suggests that the variations in height of the CM at the start of the push-off have a large effect on the outcome of load manipulations. To test this in the simulation model, a new optimization was performed for a CMJ in EF+30%BW, this time setting a penalty on the deviations of
from 20 cm rather than from the standard 34 cm. This caused peak
to drop from 44.9 to 39.5 W·kg−1, that is, from 97% to 86% of the reference value. It seems that the load-dependent variation in
in CMJ has more effect on peak
) than the variation in loading itself. Could this also explain the discrepancy between the results of unloading obtained in the simulation study and those obtained in experiments on subjects? First of all, the latter results are not consistent in themselves: the group of Marcovic and Jaric (17) observed a nonsignificant increase in peak
with unloading by −30% BW in their first study, but a decrease in peak
by 11%–18% with the same amount of unloading in a later study (22). Second, in both studies,
increased by approximately 12 cm compared with reference. To test the effect in the simulation model, a new optimization was performed for a CMJ in EF–30%BW, this time setting a penalty on the deviations of
from 46 cm rather than from the standard 34 cm. Opposite to the experimental results, this caused an even further increase in peak
from 47.4 to 50.1 W·kg−1, that is, from 103% to 109% of the reference value. In the simulation study, no scenario could be found that caused peak
in maximal jumps to decrease with unloading. This then prompts the question of whether subjects were producing a truly maximal performance in all conditions. Marcovic and Jaric (17) seem convinced that subjects were able to quickly tune their control to new loading conditions and perform maximally, but the authors did not base their conviction on measurement results. With the simulation model, the importance of a lack of tuning could easily be tested: if a CMJ was simulated after application of an extra upward force of −30% BW without reoptimizing control, a drop of more than 25% occurred in peak
In the literature, the force–velocity relationship has been implicated to explain the effects of unloading and loading on peak
in jumping (e.g., [15,17,22]). In the present study, it has been shown with the simulation model that the load-dependent variations in
and a potential lack of tuning of control have larger effects on peak
than the intrinsic force–velocity–power relationship. This then calls into question the current interpretations of the results of unloading and loading described in the literature. It has been claimed that physically active people who regularly overcome their own BW and limb inertia produce their highest power output when jumping without additional masses or extra forces, whereas strength/power-trained athletes produce their highest power output when loaded with additional mass or downward extra forces (for references, see ). These findings have been explained by theorizing that (a) the optimal load that maximizes the dynamic output in rapid movements is related to the particular design of the muscular system, which includes the force–velocity–power relationship of muscle (15,17), and (b) the design of the muscular system is considerably influenced by the actual load that humans regularly overcome during their daily activities (15). According to the present simulation results, however, variations in peak
across loading conditions are minimal, the variations that do occur are explained only in part by the intrinsic force–velocity–power relationship of muscle, and there is no particular reason why the highest peak
would occur at the condition where no additional load or extra force is applied (Tables 1 and 2, Fig. 4). A more straightforward theory would be that subjects produce the highest peak
in the loading conditions to which they are most accustomed in their training because they will have optimized their control by painstaking practice for these conditions and not for other loading conditions. Thus, when other loading conditions are applied, the subjects produce submaximal peak
The simulation results presented in this study establish that in maximal jumps with a predefined minimal height of the CM, obtained by the optimization of STIM(t), unloading and loading have only a small effect on peak
. However, the model used in this study is not a model of how the musculoskeletal system and the central nervous system adapt to training exercises, and the simulation results should not be taken to imply that loading conditions are unimportant when it comes to designing training programs for long-term development of power in jumping. Typically, such programs start with high loads to build general muscle strength (10,16). This makes sense from a theoretical point of view because if the force generated by a muscle is greater for any given velocity, peak power will be greater as well; this explains why maximal jumping performance of a simulation model is very sensitive to the strength-to-weight ratio of the body (21). Results of training studies, especially in weak subjects, support this: after strength training, the subjects are able to produce a higher ground reaction force at each velocity of the CM during the push-off phase in jumping and to reach higher velocities and vertical displacement of the CM (8,9). Subsequently, according to experts (e.g., 10), power training programs ideally combine traditional resistance training with high loads, ballistic training with low loads, plyometric training, and sport-specific technique training. This also makes sense from a theoretical point of view: strength training should be combined with painstaking sport-specific practice so that the athletes are able to tune their control and perform maximally with their strengthened musculoskeletal system (5). Another important consideration is that training only at the optimal load might not constitute a sufficient trigger to maintain strength and thus could lead to a decrease in performance. To date, however, the complicated mechanisms explaining how physical exercise leads to adaptations in the musculoskeletal and central nervous systems remain elusive (10), and more research is needed before we can construct musculoskeletal simulation models that are useful for designing power training programs.
The author does not have professional relationships with companies or manufacturers who will benefit from the results of the present study. The author did not receive funding for this work from any of the following organizations: National Institutes of Health, Wellcome Trust, Howard Hughes Medical Institute, and others.
The author declares no actual or potential conflict of interest, including any financial, personal, or other relationships with other people or organizations that could inappropriately influence this study.
The results of the present study do not constitute endorsement by the American College of Sports Medicine.
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Keywords:© 2014 American College of Sports Medicine
BIOMECHANICS; MUSCULOSKELETAL MODEL; OPTIMIZATION; CONTROL; FORCE–VELOCITY RELATIONSHIP