Countermovement strategy changes with vertical jump height to accommodate feasible force constraints

In this study, we developed a curve-fit model of countermovement dynamics and examined whether the characteristics of a countermovement jump can be quantified using the model parameter and its scaling; we expected that the model-based analysis would facilitate an understanding of the basic mechanisms of force reduction and propulsion with a simplified framework of the center of mass (CoM) mechanics. Ten healthy young subjects jumped straight up to five different levels ranging from approximately 10% to 35% of their body heights. The kinematic and kinetic data on the CoM were measured using a force plate system synchronized with motion capture cameras. All subjects generated larger vertical forces compared with their body weights from the countermovement and sufficiently lowered their CoM position to support the work performed by push-off as the vertical elevations became more challenging. The model simulation reasonably reproduced the trajectories of vertical force during the countermovement, and the model parameters were replaced by linear and polynomial regression functions in terms of the vertical jump height. Gradual scaling trends of the individual model parameters were observed as a function of the vertical jump height with different degrees of scaling, depending on the subject. The results imply that the subjects may be aware of the jumping dynamics when subjected to various vertical jump heights and may select their countermovement strategies to effectively accommodate biomechanical constraints, i.e., limited force generation for the standing vertical jump.     

Evaluation of a torque-driven model of jumping for height

This study used an optimization procedure to evaluate an 8-segment torque-driven subject-specific computer simulation model of the takeoff phase in running jumps for height. Kinetic and kinematic data were obtained on a running jump performed by an elite male high jumper. Torque generator activation timings were varied to minimize the difference between simulation and performance in terms of kinematic and kinetic variables subject to constraints on the joint angles at takeoff to ensure that joints remained within their anatomical ranges of motion. A percentage difference of 6.6% between simulation and recorded performance was obtained. Maximizing the height reached by the mass center during the flight phase by varying torque generator activation timings resulted in a credible height increase of 90 mm compared with the matching simulation. These two results imply that the model is sufficiently complex and has appropriate strength parameters to give realistic simulations of running jumps for height.     

The relationship between vertical jump power estimates and weightlifting ability: a field-test approach

The purpose of this study was to assess the usefulness of the vertical jump and estimated vertical-jump power as a field test for weightlifting. Estimated PP output from the vertical jump was correlated with lifting ability among 64 USA national-level weightlifters (junior and senior men and women). Vertical jump was measured using the Kinematic Measurement System, consisting of a switch mat interfaced with a laptop computer. Vertical jumps were measured using a hands-on-hips method. A counter-movement vertical jump (CMJ) and a static vertical jump (SJ, 90 degrees knee angle) were measured. Two trials were given for each condition. Test-retest reliability for jump height was intra-class correlation (ICC) = 0.98 (CMJ) and ICC = 0.96 (SJ). Athletes warmed up on their own for 2-3 minutes, followed by 2 practice jumps at each condition. Peak power (PP) was estimated using the equations developed by Sayers et al. (24). The athletes' current lifting capabilities were assessed by a questionnaire, and USA national coaches checked the listed values. Differences between groups (i.e., men versus women, juniors versus resident lifters) were determined using t-tests (p < or = 0.05). Correlations were determined using Pearson's r. Results indicate that vertical jumping PP is strongly associated with weightlifting ability. Thus, these results indicate that PP derived from the vertical jump (CMJ or SJ) can be a valuable tool in assessing weightlifting performance.     

Relative net vertical impulse determines jumping performance

The purpose of this investigation was to determine the relationship between relative net vertical impulse and jump height in a countermovement jump and static jump performed to varying squat depths. Ten college-aged males with 2 years of jumping experience participated in this investigation (age: 23.3 ± 1.5 years; height: 176.7 ± 4.5 cm; body mass: 84.4 ± 10.1 kg). Subjects performed a series of static jumps and countermovement jumps in a randomized fashion to a depth of 0.15, 0.30, 0.45, 0.60, and 0.75 m and a self-selected depth (static jump depth = 0.38 ± 0.08 m, countermovement jump depth = 0.49 ± 0.06 m). During the concentric phase of each jump, peak force, peak velocity, peak power, jump height, and net vertical impulse were recorded and analyzed. Net vertical impulse was divided by body mass to produce relative net vertical impulse. Increasing squat depth corresponded to a decrease in peak force and an increase in jump height and relative net vertical impulse for both static jump and countermovement jump. Across all depths, relative net vertical impulse was statistically significantly correlated to jump height in the static jump (r = .9337, p < .0001, power = 1.000) and countermovement jump (r = .925, p < .0001, power = 1.000). Across all depths, peak force was negatively correlated to jump height in the static jump (r = -0.3947, p = .0018, power = 0.8831) and countermovement jump (r = -0.4080, p = .0012, power = 0.9050). These results indicate that relative net vertical impulse can be used to assess vertical jump performance, regardless of initial squat depth, and that peak force may not be the best measure to assess vertical jump performance.     

Determination of subject-specific model parameters for visco-elastic elements

The determination of subject-specific model parameter values is necessary in order for a computer simulation model of human motion to be evaluated quantitatively. This study used an optimisation procedure along with a kinematically driven simulation model of the contact phase in running jumps to determine the elastic parameters of segmental wobbling masses and the foot-ground interface. Kinetic and kinematic data were obtained on running jumps for height and distance performed by an elite male high jumper. Stiffness and damping coefficients of the visco-elastic elements in the model were varied until the difference between simulation and performance was minimised. Percentage differences of 6% and 9% between the simulated and recorded performances were obtained in the jumps for height and distance, respectively. When the parameters obtained from the jump for height were used in a simulation of the jump for distance (and vice versa), there was poor agreement with the recorded jump. On the other hand, a common set of visco-elastic parameters were obtained using the data from both recorded jumps resulting in a mean difference of only 8% (made up of 7% and 10%) between simulation and performance that was almost as good as the individual matches. Simulations were not overly sensitive to perturbations of the common set of visco-elastic parameters. It is concluded that subject-specific elastic parameters should be calculated from more than a single jump in order to provide a robust set of values that can be used in different simulations.     

The effect of dropping height on jumping performance in trained and untrained prepubertal boys and girls

Plyometric training in children, including different types of jumps, has become common practice during the last few years in different sports, although there is limited information about the adaptability of children with respect to different loads and the differences in performance between various jump types. The purpose of this study was to examine the effect of gender and training background on the optimal drop jump height of 9- to 11-year-old children. Sixty prepubertal (untrained and track and field athletes, boys and girls, equally distributed in each group [n = 15]), performed the following in random order: 3 squat jumps, 3 countermovement jumps (CMJs) and 3 drop jumps from heights of 10, 20, 30, 40, and 50 cm. The trial with the best performance in jump height of each test was used for further analysis. The jump type significantly affected the jump height. The jump height during the CMJ was the highest among all other jump types, resulting in advanced performance for both trained and untrained prepubertal boys and girls. However, increasing the dropping height did not change the jumping height or contact time during the drop jump. This possibly indicates an inability of prepubertal children to use their stored elastic energy to increase jumping height during drop jumps, irrespective of their gender or training status. This indicates that children, independent of gender and training status, have no performance gain during drop jumps from heights up to 50 cm, and therefore, it is recommended that only low drop jump heights be included in plyometric training to limit the probability of sustaining injuries.     

Sensitivity of vertical jumping performance to changes in muscle stimulation onset times: a simulation study

The effect of muscle stimulation dynamics on the sensitivity of jumping achievement to variations in timing of muscle stimulation onsets was investigated. Vertical squat jumps were simulated using a forward dynamic model of the human musculoskeletal system. The model calculates the motion of body segments corresponding to STIM(t) of six major muscle groups of the lower extremity, where STIM is muscle stimulation level. For each muscle, STIM was allowed to switch “on” only once. The subsequent rise of STIM to its maximum was described using a sigmoidal curve, the dynamics of which was expressed as rise time (RT). For different values of stimulation RT, the optimal set of onset times was determined using dynamic optimization with height reached by the center of mass as performance criterion. Subsequently, 200 jumps were simulated in which the optimal muscle stimulation onset times were perturbed by adding to each a small number taken from a Gaussian-distributed set of pseudo-random numbers. The distribution of heights achieved in these perturbed jumps was used to quantify the sensitivity of jump height to variations in timing of muscle stimulation onsets. It was found that with increasing RT, the sensitivity of jump height to timing of stimulation onset times decreased. To try and understand this finding, a post-hoc analysis was performed on the perturbed jumps. Jump height was most sensitive to errors in the delay between stimulation onset times of proximal muscles and stimulation onset times of plantar flexors. It is explained how errors in this delay cause aberrations in the configuration of the system, which are regenerative and lead to relatively large jump height deficits. With increasing RT, the initial aberrations due to erroneous timing of muscle stimulation are smaller, and the regeneration is less pronounced. Finally, it is speculated that human subjects decrease or increase RT depending on the relative importance of different performance criteria. Received: 16 February 1998 / Accepted in revised form: 1 March 1999     

Pelvic kinematic method for determining vertical jump height

Sacral marker and pelvis reconstruction methods have been proposed to approximate total body center of mass during relatively low intensity gait and hopping tasks, but not during a maximum effort vertical jumping task. In this study, center of mass displacement was calculated using the pelvic kinematic method and compared with center of mass displacement using the ground-reaction force-impulse method, in experienced athletes (n = 13) performing restricted countermovement vertical jumps. Maximal vertical jumps were performed in a biomechanics laboratory, with data collected using an 8-camera motion analysis system and two force platforms. The pelvis center of mass was reconstructed from retro-reflective markers placed on the pelvis. Jump height was determined from the peak height of the pelvis center of mass minus the standing height. Strong linear relationships were observed between the pelvic kinematic and impulse methods (R2 = .86; p < .01). The pelvic kinematic method underestimated jump height versus the impulse method, however, the difference was small (CV = 4.34%). This investigation demonstrates concurrent validity for the pelvic kinematic method to determine vertical jump height.     

The effects of 6 weeks of preseason skill-based conditioning on physical performance in male volleyball players

The purpose of this study was to determine the changes in physical performance after a 6-week skill-based conditioning training program in male competitive volleyball players. Sixteen male volleyball players (mean ± SD: age 22.3 ± 3.7 years, body height 190.7 ± 4.2 cm, and body mass 78.4 ± 4.5 kg) participated in this study. The players were tested for sprinting (5- and 10-m sprint), agility, and jumping performance (the vertical-jump test, the spike-jump test, and the standing broad jump [SBJ]). Compared with pretraining, there was a significant improvement in the 5- and 10-m speed. There were no significant differences between pretraining and posttraining for lower-body muscular power (vertical-jump height, spike-jump height, and SBJ) and agility. Based on our results, it could be concluded that a preseason skill-based conditioning program does not offer a sufficient stimulus for volleyball players. Therefore, a general conditioning and hypertrophy training along with specific volleyball conditioning is necessary in the preseason period for the development of the lower-body strength, agility and speed performance in volleyball players.     

Dependence of jumping performance on muscle properties when humans use only calf muscles for propulsion

Using optimal control techniques, maximum height jumps were simulated for humans who held their body rigid except for the ankle. Three dynamic models of ankle torque generation based on known calf muscle properties were used. Force and kinematics obtained from the simulations using nominal and perturbed parameters were compared with data obtained from humans who had performed this type of jump. One torque model incorporated the series elastic, force-length and force-velocity properties of muscle. Our results suggest that higher jumps would be achieved by those who have the most compliant and fastest contracting muscles. It was also found that height attained depended much more on the ability of muscles to generate isometric force at long lengths than at short lengths. Studies of forward and strictly vertical jumps using similar computer methods suggest that for any maximal jump the optimal strategy is first to achieve a unique state (position, velocity and acceleration) with the feet flat on the ground, and then to maximally activate one's calf muscles until lift-off.     

The effect of drop jump starting height and contact time on power, work performed, and moment of force

The purposes of this study are (a) to examine the effects of contact time manipulation on jump parameters and (b) to examine the interaction between starting height changes and contact time changes on important jump parameters. Fifteen male athletes performed a series of drop jumps from heights of 20, 40, and 60 cm. The instructions given to the subjects were (a) "jump as high as you can" and (b) "jump high a little faster than your previous jump." Jumps were performed at each height until the athlete could not achieve a shorter ground contact time. The data were divided into 5 groups where group 1 was made up of the longest ground contact times of each athlete and groups 2-4 were composed of progressively shorter contact times, with group 5 having the shortest contact times. The jumps of group 3 produced the highest maximum and mean mechanical power (p <0.05) during the positive phase of the drop jumps regardless of starting jump height. The vertical takeoff velocities for the first 3 groups did not show significant (p < 0.05) differences. These results indicate that the manipulation of jump technique plays larger role than jump height in the manipulation of important jump parameters.     

Gender and bilateral differences in single-leg countermovement jump performance with comparison to a double-leg jump

Expectations may be for both legs to function identically during single- and double-leg vertical jumps. However, several reasons might prevent this from occurring. The goals of this investigation were twofold: assess the presence of side-to-side jump height differences during single-leg jumps in a homogenous group of healthy subjects and determine if those with a jump height asymmetry possessed consistent biomechanical differences during single-and double-leg jumps. Thirteen men and 12 women with competitive volleyball experience volunteered for the study. Significance was assessed at p < 0.05. The men jumped significantly higher than the women in all conditions and possessed differences in several anthropometric, kinematic, and kinetic parameters. Based on a three-jump average, all subjects had one leg that they could jump higher with (the dominant leg, DL). The men generated significantly greater maximum ground reaction forces and ankle joint powers on their DL whereas the women had no differences during the single-leg jumps. The only side-to-side differences that existed during the double-leg jumps were in the average ground reaction forces during propulsion. These findings suggest that equality of single-leg jump performance is the exception rather than the norm, with identification of consistent biomechanical attributes difficult within a group.     

A deterministic model of the vertical jump: implications for training

Increasing vertical jump height is a critical component for performance enhancement in many sports. It takes on a number of different forms and conditions, including double and single legged jumps and stationary and run-up jumps. In an attempt to understand the factors that influence vertical jump performance, an extensive analysis was undertaken using the deterministic model. Once identified, practical training strategies enabling improvement in these factors were elucidated. Our analysis showed that a successful vertical jump performance was the result of a complex interplay of run-up speed, reactive strength, concentric action power of the take-off leg(s), hip flexors, shoulders, body position, body mass, and take-off time. Of special interest, our analysis showed that the concentric action power of the legs was the critical factor affecting stationary double leg vertical jumps, whereas reactive strength was the critical component for a single leg jump from a run-up.     

Optimal compliant-surface jumping: a multi-segment model of springboard standing jumps

A multi-segment model is used to investigate optimal compliant-surface jumping strategies and is applied to springboard standing jumps. The human model has four segments representing the feet, shanks, thighs, and trunk-head-arms. A rigid bar with a rotational spring on one end and a point mass on the other end (the tip) models the springboard. Board tip mass, length, and stiffness are functions of the fulcrum setting. Body segments and board tip are connected by frictionless hinge joints and are driven by joint torque actuators at the ankle, knee, and hip. One constant (maximum isometric torque) and three variable functions (of instantaneous joint angle, angular velocity, and activation level) determine each joint torque. Movement from a nearly straight motionless initial posture to jump takeoff is simulated. The objective is to find joint torque activation patterns during board contact so that jump height can be maximized. Minimum and maximum joint angles, rates of change of normalized activation levels, and contact duration are constrained. Optimal springboard jumping simulations can reasonably predict jumper vertical velocity and jump height. Qualitatively similar joint torque activation patterns are found over different fulcrum settings. Different from rigid-surface jumping where maximal activation is maintained until takeoff, joint activation decreases near takeoff in compliant-surface jumping. The fulcrum-height relations in experimental data were predicted by the models. However, lack of practice at non-preferred fulcrum settings might have caused less jump height than the models' prediction. Larger fulcrum numbers are beneficial for taller/heavier jumpers because they need more time to extend joints.     

Effects of Different Types of Jump Impact on Trabecular Bone Mass and Microarchitecture in Growing Rats

Substantial evidence from animal studies indicates that jumping increases bone mass and strength. However, most studies have focused on the take-off, rather than the landing phase of jumps. Thus, we compared the effects of landing and upward jump impact on trabecular bone mass and microarchitecture. Male Wistar rats aged 10 weeks were randomly assigned to the following groups: sedentary control (CON), 40-cm upward jumps (40UJ); 40-cm drop jumps (40DJ); and 60-cm drop jumps (60DJ) (n = 10 each). The upward jump protocol comprised 10 upward jumps/day, 5 days/week for 8 weeks to a height of 40 cm. The drop jump protocol comprised dropping rats from a height of 40 or 60 cm at the same frequency and time period as the 40UJ group. Trabecular bone mass, architecture, and mineralization at the distal femoral metaphysis were evaluated using microcomputed tomography. Ground reaction force (GRF) was measured using a force platform. Bone mass was significantly higher in the 40UJ group compared with the DJ groups (+49.1% and +28.3%, respectively), although peak GRF (−57.8% and −122.7%, respectively) and unit time force (−21.6% and −36.2%, respectively) were significantly lower in the 40UJ group. These results showed that trabecular bone mass in growing rats is increased more effectively by the take-off than by the landing phases of jumps and suggest that mechanical stress accompanied by muscle contraction would be more important than GRF as an osteogenic stimulus. However, the relevance of these findings to human bone physiology is unclear and requires further study.     

Training specificity of hurdle vs. countermovement jump training

The objective of this study was to compare bilateral and unilateral hurdle jumps with traditional countermovement jumps (CMJs). Thirteen athletes were tested during continuous forward bilateral and unilateral hurdle jumps and single CMJ. Countermovement jump height was used to establish the hurdle height. Subjects jumped forward over 4 hurdles with the force plate positioned after the second hurdle to measure vertical ground reaction force (VGRF), contact time (CT), and rate of force development (RFD). For bilateral jumps, hurdle height was established at maximal (100%) CMJ height and at 120, 140, and 160% of the CMJ height. The athletes were instructed to jump as fast as possible to mimic a training session drill. For unilateral jumps, hurdle height was set at 70, 80, and 90% of the CMJ height. Bilateral 160% jumps showed a significantly longer CT than bilateral 100, 120, and 140% jumps. The bilateral 100, 120, and 140% jumps had significantly shorter CT than the unilateral jumps and CMJ. The VGRF during bilateral jumps was higher than unilateral jumps and CMJ. Bilateral 160% jump RFD was significantly higher than CMJ and unilateral jumps but significantly lower than the other bilateral jumps. In conclusion, the characteristics of the bilateral jumps were substantially different from those of the CMJ and unilateral hurdle jumps. As bilateral hurdle jumps with a height between 100 and 140% of the CMJ provide similar CTs and VGRF as many reported sprint or jump actions, they may be considered a more training-specific power training drill than the CMJ.     

The relationship between kinematic determinants of jump and sprint performance in division I women soccer players

The purpose of this study was to determine the relationship between measures of unilateral and bilateral jumping performance and 10- and 25-m sprint performance. Fifteen division I women soccer players (height 165 ± 2.44 cm, mass 61.65 ± 7.7 kg, age 20.19 ± 0.91 years) volunteered to participate in this study. The subjects completed a 10- and 25-m sprint test. The following jump kinematic variables were measured using accelerometry: sprint time, step length, step frequency, jump height and distance, contact time, concentric contact time, and flight time (Inform Sport Training Systems, Victoria, BC, Canada). The following jumps were completed in random order: bilateral countermovement vertical jump, bilateral countermovement horizontal jump, bilateral 40-cm drop vertical jump, bilateral 40-cm drop horizontal jump, unilateral countermovement vertical jump (UCV), unilateral countermovement horizontal jump, unilateral 20-cm drop vertical jump (UDV), and unilateral 20-cm drop horizontal jump (UDH). The trial with the best jump height or distance, reactive strength (jump height or distance/total contact time), and flight time to concentric contact time ratio (FT/CCT) was recorded to analyze the relationship between jump kinematics and sprint performance. None of the bilateral jump kinematics significantly correlated with 10- and 25-m sprint time, step length, or step frequency. Right-leg jump height (r = -0.71, p = 0.006, SEE = 0.152 seconds), FT/CCT (r = -0.58, p = 0.04, SEE = 0.176 seconds), and combined right and left-leg jump height (r = -0.61) were significantly correlated with the 25-m sprint time during the UCV. Right-leg FT/CCT was also significantly related to 25-m step length (r = 0.68, p = 0.03, SEE = 0.06 m) during the UDV. The combined right and left leg jump distance to standing height ratio during the UDH significantly correlated (r = -0.58) with 10-m sprint time. In comparison to bilateral jumps, unilateral jumps produced a stronger relationship with sprint performance.     

A simple method for measuring force, velocity and power output during squat jump

Our aim was to clarify the relationship between power output and the different mechanical parameters influencing it during squat jumps, and to further use this relationship in a new computation method to evaluate power output in field conditions. Based on fundamental laws of mechanics, computations were developed to express force, velocity and power generated during one squat jump. This computation method was validated on eleven physically active men performing two maximal squat jumps. During each trial, mean force, velocity and power were calculated during push-off from both force plate measurements and the proposed computations. Differences between the two methods were not significant and lower than 3% for force, velocity and power. The validity of the computation method was also highlighted by Bland and Altman analyses and linear regressions close to the identity line (P<0.001). The low coefficients of variation between two trials demonstrated the acceptable reliability of the proposed method. The proposed computations confirmed, from a biomechanical analysis, the positive relationship between power output, body mass and jump height, hitherto only shown by means of regression-based equations. Further, these computations pointed out that power also depends on push-off vertical distance. The accuracy and reliability of the proposed theoretical computations were in line with those observed when using laboratory ergometers such as force plates. Consequently, the proposed method, solely based on three simple parameters (body mass, jump height and push-off distance), allows to accurately evaluate force, velocity and power developed by lower limbs extensor muscles during squat jumps in field conditions.     

Critical jump sizes in DNA-protein interactions

Interaction of a protein molecule with a specific-site on the DNA lattice can be modeled as an unbiased random jump process. Here we show that there exists a critical jump size (kc) beyond which site-specific association of a protein molecule with a DNA lattice cannot be facilitated. The maximum achievable association rate is predicted to be approximately 10(10) mol-1 s-1. This critical jump size scales with the total length of DNA lattice (N) as kc proportional, variantN2/3. Beyond kc the mean first passage time MFPT (denoted as T) required for the protein molecule to target the specific-site follows a linear scaling law as T proportional, variantN rather than the usual T proportional, variantN2 scaling law. On the basis of these results we argue that the evolution of the super coiled structures of the genomic DNA must be a consequence of the existence of this critical jump sizes. We finally show that the random jump method of searching for the specific-site by the protein molecule on the DNA lattice itself introduce an abstract linear type potential favoring the site-specific association rate.     

Acute effects of heavy-load squats on consecutive squat jump performance

Postactivation potentiation (PAP) and complex training have generated interest within the strength and conditioning community in recent years, but much of the research to date has produced confounding results. The purpose of this study was to observe the acute effects of a heavy-load back squat [85% 1 repetition maximum (1RM)] condition on consecutive squat jump performance. Twelve in-season Division I male track-and-field athletes participated in two randomized testing conditions: a five-repetition back squat at 85% 1RM (BS) and a five-repetition squat jump (SJ). The BS condition consisted of seven consecutive squat jumps (BS-PRE), followed by five repetitions of the BS at 85% 1RM, followed by another set of seven consecutive squat jumps (BS-POST). The SJ condition was exactly the same as the BS condition except that five consecutive SJs replaced the five BSs, with 3 minutes' rest between each set. BS-PRE, BS-POST, SJ-PRE, and SJ-POST were analyzed and compared for mean and peak jump height, as well as mean and peak ground reaction force (GRF). The BS condition's mean and peak jump height and peak GRF increased 5.8% +/- 4.8%, 4.7% +/- 4.8%, and 4.6% +/- 7.4%, respectively, whereas the SJ condition's mean and peak jump height and peak GRF decreased 2.7% +/- 5.0%, 4.0% +/- 4.9%, and 1.3% +/- 7.5%, respectively. The results indicate that performing a heavy-load back squat before a set of consecutive SJs may enhance acute performance in average and peak jump height, as well as peak GRF.