Share this article on:

A Proposed Method for Determining Peak Power in the Jump Squat Exercise

Li, Li; Olson, Michael W; Winchester, Jason B

The Journal of Strength & Conditioning Research: March 2008 - Volume 22 - Issue 2 - p 326-331
doi: 10.1519/JSC.0b013e3181635606
Original Research

In recent years a great deal of research has been published using peak power (PP) in the jump squat (JS) exercise as a measure of athletic performance. However, no standardized method for the determination of PP exists at this time to accurately evaluate this variable. Our proposed method (PM) for determining PP (PPPM) in the JS uses the product of vertical ground reaction forces and velocity of the center of mass of both the subject and the external resistance of a loaded Olympic bar. Fifteen male subjects with a mean age of 27 ± 3 years, weight of 78 ± 17 kg, and height of 175 ± 10 cm participated in this study. PP was measured in the JS at five different testing loads (30%, 35%, 40%, 45%, and 50% body weight) based on methods commonly discussed in the literature to compare PP results of previous methods to those obtained using the PM. Paired t-tests at different load levels were used for statistical analysis with an overall α = 0.05. The average PP among five testing loads, measured by the PM, was 3782 ± 906 W. PP derived from the product of force and velocity of the bar alone was 72% lower than PPPM at 1057 ± 243 W (P < 0.0001). The PP estimated by the product of bar velocity and vertical ground reaction forces of the bar plus the subject was 8% higher than PPPM at 4100 ± 844 W (P = 0.0001). Our results indicate that using the methods traditionally reported in the literature may cause an overestimation of PP during athletic performance. Using the PM in future research will facilitate test validity and enable the generalization of results outside the scope of specific research projects.

Department of Kinesiology, Louisiana State University, Baton Rouge, Louisiana

Address correspondence to Dr. Li Li,

Back to Top | Article Outline


An athlete's power production capability is a great concern in many sports. There are a variety of ways that power can be defined and measured (4), but no standardized method exists for determining power in strength training movements. The jump squat exercise (JS) is a popular form of ballistic resistance exercise commonly used for improving power production among athletic populations (10-12). Besides its use as a training tool, the JS is also used by researchers for testing power production among various populations (3,4,8,15). The JS assists in assessing power performance measurements in sports for which peak power (PP) is a vital component, such as gymnastics (6), and is positively correlated with 5-m sprint start performance (14). In addition, the importance of vertical power production and its relationship to other sports is widely noted (1).

Among physical attributes that relate to athletic performance, JS power has been used particularly to compare the relationship between power and strength. For example, Stone and colleagues (15) observed that 10% of 1 repetition maximum (1RM) obtained in the back squat exercise seemed related to optimal power output during JS. However, they reported that people with greater isometric strength tended to achieve their optimal power with greater loads up to 40% 1RM.

In recent years, JS power has also been used as one of the criterion measures for investigating the effect of different training methods (5,8,10,16). Baker et al. (2) used JS power to evaluate the resistant training effect of Australian Rugby League players. Their observations indicated that training with higher load levels for resistance training might be beneficial for maximal power output. The amount of research published in recent years regarding optimal loading for maximal power and the assessment of training interventions raises concerns as to whether methods used in determining power performance in the JS are valid (4).

In recent years, several investigations have attempted to address power loading and measurement in the JS (4). The researchers in these studies used a variety of techniques to determine power. The four most popular methods for power measurement are briefly summarized in the following paragraph. A more detailed description of methods addressed may be found by referring to Dugan et al. (4). In their article, Dugan et al. (4) pointed out the different methods of JS power estimation in the literature and highlighted the need for identifying the advantages and disadvantages of these methods.

The first such method used the displacement of the bar and its derivatives to estimate power production. For example, V-scope 120 has been used to measure and track the displacement of the bar by means of ultrasound (15). The first derivative of the bar displacement is the velocity of the bar. The second derivative of the bar displacement is the acceleration of the bar. Acceleration multiplied by the mass of the body and the bar, minus the weight of the body and the bar, are used to derive the force applied to the bar (Fbar = Abar*Mbar+body-Wbar+body). These variables are used to calculate power (P = F*V). In this first method, velocity (Vbar) = dx/dt, acceleration (Abar) = d2x/dt2, force (F) = Mbody+bar*Abar-Wbody+bar, and power (P) = F*Vbar. According to Newton's second law, the calculation of force should use compatible mass and acceleration. The acceleration used here is the acceleration of the bar, but the mass used is the sum of the body and the bar. The power calculated in this method, by the mismatched force and the bar velocity, does not represent the power the athlete used to move the bar, nor does it represent the power that moved the body and bar system.

A second method of determining power employs an accelerometer attached to the bar (18), in which force can be calculated by the measured acceleration and bar mass product minus bar weight; and bar velocity is calculated by the integration of the measured acceleration. Again, the product of force and velocity are used to provide the desired power values. When examined mathematically, this method will yield the same results as the above-mentioned method. Bar acceleration and velocity (after integrated from bar acceleration) are used in the calculation of power in this method.

In a third method, JS power is calculated by the product of the vertical ground reaction force (VGRF) measured by force platform and velocity derived from bar displacement measures (13). Use of this method could cause an overestimation of power production as the bar displacement and, hence, bar velocity, may be greater than that of the body bar system.

A fourth method of JS power estimation uses the VGRF (7). The velocity change of the body and bar system center of mass is calculated by using the impulse-momentum relationship, VGRF*time/Mass(body+bar). The JS power is calculated as the product of the VGRF and the velocity. To correctly use this relationship, the impulse should be calculated by the sum of the all external forces. Specifically, the literature uses only the VGRF, but all vertical forces (VGRF and gravitational) acting on both the body and the bar should be calculated. Using this method, velocity can be overestimated, thus overestimating power values, as gravitational forces are acting in the opposite direction of VGRF.

The common mistake in the above-mentioned methods is the mismatch between the mechanical systems during the analysis. The system that we are studying consists of the athlete and the bar as one unit. Power is defined as the product of all the external forces applied to the system and the velocity of the center of the mass of the system. All forces involved in the calculation should be external to the system. For example, all vertical forces (VGRF and gravitational) are applied to the bar and the athlete acting as one system. Masses of both the athlete and the bar should be included if mass is involved in the calculation. Finally, velocity used in power calculation should be the velocity of the center of mass of the system (athlete and the bar), rather than velocity of the bar alone.

It is our contention that the four methods we discussed above are theoretically unsound methods of power measurement and misrepresent the principles of Newtonian mechanics. To ensure the validity and generalizability of research utilizing JS power performance, a standardized method of estimating JS power needs to be identified. The solution to these problems may be the implementation of a mechanically correct method for measurement of PP.

The purpose of this study was threefold. First, PP in the JS was analyzed mechanically, and the theoretically correct composition was identified to establish our proposed method (PM). Second, PP was measured experimentally along with the peaks of the different components that contribute to power production. Lastly, the PPs calculated with other methods used in the literature were determined and compared with PP values obtained using the PM (PPPM ).

Back to Top | Article Outline


Experimental Approach to the Problem

Three different types of power should be defined. Power in the JS calculated by the PM (PPM) is the power that the neuromuscular system produces to move the body-bar system during the JS. The bar power (Pbar) is the power directly applied to the bar by the subject, which causes subsequent movement the barbell itself. The body power (Pbody) is the power that the subject generated and used to move the body independent of the bar load. Thus, Pbody would equal the product of the body's center of mass velocity (Vcom) and the VGRF applied to the body alone.

In Newtonian mechanics, power is defined as the product of force applied to an object and the velocity of the same object. To be consistent with the literature, mechanical parameters focus on the vertical direction only. Movements in the medial-lateral and anterior-posterior directions are ignored because their effects are relatively small compared with the effects of the vertical direction. Although it is likely that the nonvertical components of the movement would not significantly affect our results with respect to power in this situation, detailed study regarding the mechanisms that elicit maximal power production should include all three components of all the mechanical parameters.

The powers can be theoretically computed as the following:

where PPM is the power production related to the motion of the system (person and barbell) and calculated with our proposed method, FT is the total of the external forces applied on the system, and VT is the velocity of the center of the mass (COM) of the bar-body system;

where Pbar, Fbar, and Vbar, are the power production, the sum of the external forces, and the COM velocity of the barbell, respectively;

where “body” indicates the person performing the JS.

During an experiment that measures JS power, there are two quantities usually measured: the VGRF at the foot-floor interface and the vertical displacement of the barbell (DB). There are several measures in equations 1-3 that can be directly or indirectly related to these two measures.

The external force applied to the system can be calculated:

The total external force applied to the body-bar system is the combination of the vertical ground reaction applied at the foot of the person (upward), the weight of the person (downward), and the weight of the barbell (downward). There is no other external force applied on the system in the vertical direction.

The velocity of the system's COM is

aT is acceleration of the COM of the two-object system, and Mbody, Mbar are the masses of the person and the barbell, respectively.

VTO is the initial velocity of the system.

VT0 is 0 if the measurement starts when the system is not moving.

The practical format of equation (5)" is:

Δt is the time interval during which two consecutive force data are sampled; n indicates the nth data points at which the velocity measure is desired.

Therefore, the PPM (PPM = FT*VT) can be measured by only using the VGRF and its integrations, through equations 4 and 5''', respectively.

The velocity of the barbell and external forces applied to the barbell can be estimated using DB.

The velocity of the barbell can be calculated as,

The force applied to the barbell can be calculated through the following process:

then the power applied to the barbell (Pbar = FB * VB) can be calculated using equation 2 and the results of equations 6 and 7' combined.

Finally, the power that is associated with only the motion of the person is calculated:

Back to Top | Article Outline

Implementation of Equations 1'-3' in Data Collection and Analysis

The mass of the barbell (Mbar) and the mass of the performer (Mbody) can be measured before the experiment. If the VGRF and DB were collect at sampling rate Rs, then the duration between two consecutive data points is Δt = 1/Rs. The data can be expressed as in Table 1 at any given moment (n) of the data collected.

Table 1

Table 1


where n indicates the nth data point within the sampled data.

Back to Top | Article Outline


Fifteen men with a mean age of 27 ± 3 years, weight of 78 ± 17 kg, and height of 175 ± 10 cm participated in this study. Subjects were familiarized with the JS before testing. All subjects had been training regularly in resistance exercise for a minimum of 2 years and were familiar with a variety of forms of ballistic resistance exercise as defined by Baechle and Earle (1). Informed consent was obtained from the participants before any testing was performed, and all procedures were approved by the university institutional review board. Participants were free of neuromuscular injuries that would preclude participation in ballistic resistance exercise. The procedures of the experiment were carefully explained, and all questions were answered before the onset of testing.

Back to Top | Article Outline


An Olympic barbell and assorted weight plates were used to apply different loading intensities during the experiment. For the purposes of this study, JS were defined as a loaded countermovement jump with an Olympic bar placed on the back as if performing a traditional back squat exercise. For a description of bar placement for the back squat, see Baechle and Earle (1). Kinematic data were collected at 60 Hz using a CDC high-speed digital camera system (COHU, San Diego, CA) and Eva 6.0 software (MotionAnalysis Corp., Santa Rosa, CA) to monitor the motion of a 2.5-cm reflective marker attached to the middle of the barbell. The vertical motion of this marker was used to calculate bar velocity. VGRF were collected at 960 Hz using an oversized (400 × 800 mm) OR6 force platform (Advanced Mechanical Technologies, Inc, Newton, MA). Force data were then resampled at 60 Hz. Velocity of the bar-lifter system's center of mass was calculated as the integration of the VGRF. The time series of kinematic and force data were synchronized with Eva 6.0 software. Data were then smoothed using a low-pass Butterworth digital filter at 5 Hz.

Before testing, subjects were asked to warm up with a 5-min walk on a treadmill at a self-selected pace. There were five testing conditions differentiated by five masses of the bar: 30%, 35%, 40%, 45%, and 50% of the subject's body mass. During testing, a combination of weight plates was used to get to the nearest 2.3 kg of the targeted mass percentage. Three trials of each condition were performed, and the highest peak power per condition was chosen for analysis. The condition order was randomized to eliminate any potential for order effect.

The following procedures were followed for each trial: 1) the camera was positioned behind the subject and the force platform was zeroed; 2) the investigators positioned the barbell onto the participant's shoulders and affirmed that the reflective marker was not obstructed; 3) the participant stood next to the force platform and waited for an electronic auditory signal that determined the beginning of data collection; 4) after the auditory signal, the subject stepped onto the force platform and was instructed to remain motionless for 2 seconds before performing the JS; 5) upon conclusion of one JS repetition, the subject was instructed to stand motionless for 2 seconds before stepping off the force platform. Data collection for the trial was then terminated. Trials were repeated if individuals did not land on the force platform from the JS. Three minutes of rest time was allowed between each trial throughout the testing session.

PP values in the PPM, Pbar, Pbody, and a combined power (Pc = VGRF*Vbar) were then calculated using custom software with MS Excel Macro according to equations 1"-3". Overestimation of power production from the use of VGRF without the consideration of gravitational forces (6) can be easily identified according to equation 1"; therefore, this method was not used to compare with the results of PPM. Peaks of these powers during the push-off phase were then identified from the power time histories and recorded.

Back to Top | Article Outline

Statistical Analyses

The differences among PPPM, PPbar, and PPc at different load levels were then tested using paired t-tests. The overall level of statistical significance was set as α = 0.05 among the 15 tests; therefore, the α level after Bonferroni's correction for each individual test was set at 0.05/15 = 0.0034.

Back to Top | Article Outline


The criterion measures were averaged among the three trials of each condition for all subjects. PP output was estimated based on the PM (PPPM), bar velocity (PPbar), and the bar and ground reaction force combined method (PPC). The mean (±SD) peak values for PPPM, PPbar and PPc were 3782 ± 906, 1057 ± 243, and 4100 ± 844 W, respectively. PPbar underestimated predicted PPPM by 72% (P < 0.0001) among all testing loads (Figure 1). PPc overestimated PP by 8% (P = 0.0001). When comparing PPc and PPPM (Figure 2), the overestimation of PPc was consistent among all tested loads.

Figure 1

Figure 1

Figure 2

Figure 2

The peak values of PPPM, PPbar, and PPbody at different load levels are illustrated in Figure 3. PPbody was approximately two-thirds of PPPM among all the testing loads.

Figure 3

Figure 3

Back to Top | Article Outline


The purpose of the study was to identify and demonstrate a PM of estimating PP in JS. We analyzed the methods of PP estimation in the JS according to Newtonian mechanics and identified what we believe to be a correct process for estimating PP. To meet the conditions of Newtonian mechanics, it was important to define the body-bar as one system to correctly calculate PP. The results of this experiment indicate that the combination of bar force and bar velocity underestimates PP significantly compared with results of PPPM, which was calculated by using the PM. In addition, the product of the bar velocity and the VGRF overestimates PP in JS when compared with PPPM. Finally, PPPM was decomposed and the contributing factors, bar (PPbar) and body (PPbody) power, were measured.

The ratios of PPbar to PPbody were 26%, 31%, 32%, 36%, and 43%, corresponding to the loads of 30%, 35%, 40%, 45%, and 50% body weight, respectively (see Figure 3). This disproportional PP development was caused by the different acceleration time histories of the bar and the body. The bar velocity is greater than the velocity of the center of mass of the body (VCOM) during the initial push-off phase. The bar velocity was similar to the velocity of the shoulder, but the feet maintained contact with the ground; hence, the shoulder velocity is greater than VCOM. PP was achieved at the final phase of the pushoff where VCOM has to increase to compensate for the already high velocity of the bar at takeoff. The acceleration of the body should be greater than the acceleration of the bar at the final push-off phase. PP values were calculated by F*V and F = M*A. The velocity is similar between the body and the bar, but the body accelerates at a greater rate; therefore, the peak Pbody out-proportioned peak Pbar at the final push-off phase.

The selection of different load levels was used to illustrate the relationship of different power derivatives at these different loads. Selection of an optimal load is an important consideration in practice, but it is not the focus of this article, and any discussion of optimal loading is outside its scope. To determine the optimal loading to elicit PP, power must be measured according to the correct theoretical framework. For example, PPPM might react differently to variations in loading intensity than PPbar (see Figure 3 for reference). Use of mechanically unsound methods (identifying single portions of the system rather than the system as a whole in analysis) to calculate JS power can possibly lead to an erroneously identified optimal load for maximal power production.

In the process of analyzing the existing power analysis methods in the literature, we realized the most common mistake was mismatching mechanical parameters. PP in the JS should be defined as the power that moves the bar and body together and should be calculated by the corresponding force and velocity. VGRF at the feet-floor interface is the mechanically correct force to use as it includes the forces that move the body and the bar together. VGRF can be measured directly using a force platform. Of course, this force can also be estimated by the second derivative of the displacement of the center of mass of the bar-body system (d2xbar-body/dt2). The force cannot be estimated by the displacement of the bar alone regardless of how the bar displacement is measured. From our calculations, the velocity of the center mass of the bar-body system is the correct velocity to use in the power calculation for the JS. For the purposes of this study, we chose to calculate bar-body system velocity by the integration of acceleration of the system center of mass, where a = (VGRF - Wbar-body)/Mbar-body, but this is not the only method that can correctly identify velocity of the bar-body center of mass. This velocity could also be calculated by using the kinematics collected via a whole body marker set combined with marker(s) on the bar itself. Velocity of the bar, or velocity derived from the bar displacement alone for that matter, is not a correct representation of this velocity.

Back to Top | Article Outline

Practical Applications

Power output of JS, especially its PP output during the push-off phase, has been used to identify optimal training load, to measure training effects, and to evaluate power capabilities of different groups of athletes (9). It is important to measure JS PP correctly. We have identified a standardized method of determining JS PP (PPPM) by recognizing the analysis has to focus on a system that includes both the bar and the body on both sides of the power equation. Therefore, the force in the power calculation is the force applied to the body-bar system, and the velocity is the velocity of the center of the mass of the bar-body system. Taken together, the PP of individuals who perform high-power movements can be better understood, leading to more productive training protocols. The use of our PM requires no additional equipment compared with the other methods commonly used, which we cited earlier. In the future, use of a standardized method for power measurement will allow greater generalizability of data among laboratories, improve our understanding of how power is produced, and allow for clear and concise communication of the applicability of power-related research to practitioners. Further research should be conducted to establish the reliability of our procedures and their validity in the measurement of JS power.

Back to Top | Article Outline


1. Baechle, TR and Earle, RW. Essentials of Strength Training and Conditioning (2nd ed.). Champlain: Human Kinetics Publishing, 2000.
2. Baker, D, Nance, S, and Moore, M. The load that maximizes the average mechanical power output during jump squats in power-trained athletes. J Strength Cond Res 5: 92-97, 2001.
3. Driss, T, Vandewalle, H, Quievre, J, Miller, C, and Monod, H. Effects of external loading on power output in a squat jump on a force platform: a comparison between strength and power athletes and sedentary individuals. J Sports Sci 19: 99-105, 2001.
4. Dugan, EL, Doyle, TLA, Humphries, B, Hasson, CJ, and Newton, RU. Determining the optimal load for jump squat: a review of methods and calculation. J Strength Cond Res 18: 668-674, 2004.
5. Duthie, GM, Young, WB, and Aitken, DA. The acute effects of heavy loads on jump squat performance: an evaluation of the complex and contrast methods of power development. J Strength Cond Res 16: 530-538, 2002.
6. French, DN, Gomez, AL, Volek, JS, Rubin, MR, Ratamess, NA, Sharman, MJ, Gotshalk, LA, Sebastianelli, WJ, Putukian, M, Newton, RU, Häkkinen, K, Fleck, SJ, and Kraemer, WJ. Longitudinal tracking of muscular power changes of NCAA Division I collegiate women gymnasts. J Strength Cond Res 18: 101-107, 2004.
7. Hoffman, JR, Liebermann, D, and Gusis, A. Relationship of leg strength and power to ground reaction forces in both experienced and novice jump trained personnel. Aviat Space Environ Med 68: 710-714, 1997.
8. Jones, K, Bishop, P, Hunter, G, and Fleisig, G. The effects of varying resistance-training loads on intermediate- and high-velocity-specific adaptations. J Strength Cond Res 15: 349-356, 2001.
9. Kawamori, N and Haff, GG. The optimal training load for the development of muscular power. J Strength Cond Res 18: 675-684, 2004
10. McBride, JM, Triplett-McBride, T, Davie, A, and Newton, RU. The effect of heavy- vs. light-load jump squats on the development of strength, power, and speed. J Strength Cond Res 16: 75-82, 2002.
11. McGuigan, MR, Sharman, MJ, Newton, RU, Davie, AJ, Murphy, AJ, and McBride, JM. Effect of explosive resistance training on titin and myosin heavy chain isoforms in trained subjects. J Strength Cond Res 17: 645-651, 2003.
12. Newton, RU, Häkkinen, K, Häkkinen, A, McCormick, M, Volek, J, and Kraemer, WJ. Mixed-methods resistance training increases power and strength of young and older men. Med Sci Sports Exerc 34: 1367-1375, 2002.
13. Newton, RU, Kraemer, WJ, and Häkkinen, K. Effects of ballistic training on preseason preparation of elite volleyball players. Med Sci Sports Exerc 31: 323-330, 1999.
14. Sleivert, G and Taingahue, M. The relationship between maximal jump-squat power and sprint acceleration in athletes. Eur J Appl Physiol 91: 46-52, 2004.
15. Stone, MH, O'Bryant, HS, McCoy, L, Coglianese, R, Lehmkuhl, M, and Schilling, B. Power and maximum strength relationships during performance of dynamic and static weighted jumps. J Strength Cond Res 17: 140-147, 2003.
16. Toumi, H, Thiery, C, Maitre, S, Martin, A, Vanneuville, G, and Poumarat, G. Training effects of amortization phase with eccentric/concentric variations: the vertical jump. Int J Sports Med 22: 605-610, 2001.
17. Wilson, GJ, Newton, RU, Murphy, AJ, and Humphries, BJ. The optimal training load for the development of dynamic athletic performance. Med Sci Sports Exerc 25: 1279-1286. 1993.

    ballistic; training; validity; measurement; strength training

    © 2008 National Strength and Conditioning Association