## Introduction

Assessment of neuromuscular function (^{2,4,7,9,10,12,14,18,20,23,25}) and the prescription of resistance training loads (^{3,5,8,13,14,15,27}) often rely on the calculation of power applied during resistance exercise (^{1}). According to mechanical principles, the accurate calculation of power relies on the ability to record accurate measures of the force applied to the resistance of interest and its resultant velocity (^{17}), where the resistance of interest tends to be the barbell or barbell-and-body system center of mass. It is generally accepted that force applied to the barbell can be obtained by multiplying the acceleration of the barbell by its mass, whereas force applied to the barbell-and-body system center of mass can be recorded using a force platform (ground reaction force [GRF]) (^{10,17}).

Recently it has been suggested that accurate measures of power applied during resistance exercise can only be obtained if barbell and body center of mass parameters are combined (referred to as CM for clarity), multiplying the velocity of the barbell by the force applied to the CM (GRF) (^{3,5,11,19,28}). This approach is based on the assumption that the velocity of the barbell represents the velocity of the CM (^{5}), but ignores the contributions made by large body segments to CM motion. However, evidence to suggest that failure to consider these contributions can lead to a significant overestimation of the velocity of the CM and the power applied to it remains largely ignored (^{17}).

Analysis of the CM using whole-body three-dimensional (3D) motion analysis and force platform analysis enables comparison of power applied during resistance exercise that is calculated by multiplying GRF by the velocity of the barbell, and the velocity of the CM (derived from 3D motion analysis and GRF data) independently. Further, it enables study of the effect that differences between the displacement and velocity of the barbell, the CM, and its composite body segments has on differences on power applied to the CM. Thus, it is critical that research using this type of analysis is undertaken so that methodological concerns about the misapplication of the combined method can be investigated and insight about the differences in measures of power applied to the CM obtained using the different methods gained (^{5,10,17}).

Therefore, the aim of this study was to compare measures of power obtained by multiplying GRF by the velocity of the barbell, GRF by velocity of the CM derived from 3D motion analysis, and GRF by velocity of the CM derived from GRF data. It was hypothesized that multiplying GRF by the velocity of the barbell would lead to a significant overestimation of the velocity of and the power applied to the CM.

## Methods

### Experimental Approach to the Problem

To compare measures of power obtained from different methods during lower-body resistance exercise, 10 resistance-trained men performed 3 sets of single maximal-effort back squats with 60% 1 repetition maximum (1RM) on 2 force platforms while 3 synchronized high-speed digital cameras recorded whole-body motion. Measures of power applied to the CM were obtained by multiplying GRF by the velocity of the barbell, GRF by the velocity of the CM derived from 3D motion analysis, and GRF by the velocity of the CM derived from GRF data; these were time normalized and compared using repeated measures analysis of variance (ANOVA). Further, the velocity of the barbell was compared with the velocity of the CM and the velocity of individual body segment centers of mass using 1-way ANOVA to gain insight about the factors underpinning differences.

### Subjects

Ten physically active men with between 4 and 9 years of resistance exercise experience participated in this study. Their mean (Â±*SD*) physical characteristics were as follows: mass, 82.3 (7.3) kg; stature, 1.77 (0.03) m; back squat 1RM, 140.5 (46) kg; and 1RM normalized to body mass: 1.69 (0.45) kg per kg of body mass. All volunteers had been free of lower-body pathology for at least 6 months before data collection. Ethical clearance was granted before data collection, and after a thorough explanation of the study aims and protocols, subjects provided written informed consent.

### Procedures

Subjects attended 2 laboratory-based testing sessions. During the first session, maximal back squat strength (1RM) was established using a protocol similar to the one described and used by Wallace et al. (^{26}). Seven days later, subjects returned to the laboratory to perform power testing, where after warming up they performed 3 sets of maximal-effort single back squats with 60% 1RM, with 2 minutes rest between each lift. This load was selected because it is the load with which power tends to be maximized during back squat performance (^{5,12,23}). The descent phase of squat performance continued until the tops of the thighs were parallel to the ground, after which subjects were instructed to perform the ascent phase as quickly as possible.

### Instrumentation

Before data collection spherical, retroreflective markers illuminated by spotlights positioned behind each camera were affixed to the left and right barbell end and anatomical landmarks (see Figure 1).

Three high-speed digital cameras (Basler A602fc-2; Basler, Ahrensburg, Germany) positioned around the front of and approximately 5 m from the subject recorded back squat performance after first recording a 17-point calibration frame (Peak Performance Technologies Inc., Englewood, CO, USA) (^{19}). Simultaneously, vertical GRF of both feet were recorded from two 0.4 Ă— 0.6-m force platforms (Kistler, Alton, United Kingdom) (^{16}). Motion and GRF data collection was synchronized using a Vicon MX control unit. Motion was captured at a sampling frequency of 100 Hz, and GRF at 500 Hz. Motion data were interpolated to 500 Hz using Vicon Motus 9.2 software.

All performance footage was cropped to include 10 frames before the start and after the end of the propulsion phase (^{22}). Vicon Motus 9.2 software was used to digitize the top of the head, sternal notch, left and right shoulders, elbow, wrist, hip, knee, and ankle joint centers, mid-toes, and barbell ends, from which an 18-point, 13-segment digital model of the barbell, head, trunk, upper and lower arms, upper and lower legs, and feet was created. Hand mass was combined with barbell mass (Figure 1). Markers affixed to the barbell ends were digitized automatically using Vicon Motus 9.2 software. However, the anatomical markers were not used to identify the remainder of the points of interest because back squat performance led to significant hip and shoulder marker dropout and shoulder marker skin artifact. Therefore, remaining points of interest were digitized manually.

After the digitization of all barbell and anatomical landmarks, data were reconstructed using Vicon Motus 9.2 software and raw data smoothed using a low-pass Butterworth filter with a cutoff frequency of 6 Hz that was selected using residual analysis described by Winter (^{29}). Body segment parameters (considering barbell mass in relation to body mass) proposed by de Leva (^{7}) were inputted into Vicon Motus 9.2 software to enable the calculation of CM kinematics. The propulsion phase of each trial was then identified using the methods described by Sanchez-Medina et al. (^{22}), and time normalized using the methods described by Frost et al. (^{9}).

Data of interest were displacement of the barbell and displacement of the CM derived from 3D motion analysis; velocity of the barbell and velocity of the CM derived from 3D motion analysis and velocity of the CM derived from GRF data; GRF and force applied to the CM derived by multiplying the acceleration of the CM obtained from 3D motion analysis by barbell and body mass; and power applied to the CM obtained by multiplying GRF by the velocity of the barbell, GRF by velocity of the CM derived from 3D motion analysis, and GRF by velocity of the CM derived from GRF data (see Figure 2). Only vertical displacement, velocity, acceleration, and force were considered.

Test-retest reliability of the 3D motion analysis and GRF data was found to match previously reported reliability data from our laboratory (^{16}), with the following coefficients of variation: displacement of the barbell: 3.2%; displacement of the CM derived from 3D motion analysis: 5.9%; velocity of the barbell: 3.4%; velocity of the CM derived from 3D motion analysis: 6.2%; velocity of the CM derived from GRF data: 3.1%; GRF: 0.9%; force applied to the CM obtained from 3D motion analysis: 3.3%; power applied to the CM obtained by multiplying GRF by the velocity of the barbell: 6.5%; power applied to the CM obtained by multiplying GRF by the velocity of the CM derived from 3D motion analysis: 6.3%; and power applied to the CM obtained by multiplying GRF by the velocity of the CM derived from GRF data: 3.2%.

### Statistical Analyses

All results were presented as mean (Â±*SD*) unless otherwise stated. Two-way repeated measures ANOVA was used to determine differences between measures of displacement, velocity, force, and power (dependent variables) obtained from the different methods (independent variablesâ€”Figure 2) across the time-normalized propulsion phase. Further, velocity of the different body segment centres of mass was compared with the velocity of the barbell using a 1-way ANOVA. An alpha of *p* â‰¤ 0.05 was used to indicate statistical significance, and post hoc analysis was performed where appropriate applying the Holm-Sidak correction. All statistical analyses were performed using SPSS (version 17.0 for Windows; SPSS Inc., Chicago, IL, USA). Effect sizes (*d*) between the dependent variables obtained from the different methods were calculated using the methods described by Rhea (^{21}).

## Results

Key results are presented in Figures 3â€“5, which illustrate the significant differences found between the displacements and velocities of the barbell and CM derived from 3D motion analysis and their effect on power applied to the CM. There were no significant differences between the force applied to the CM derived from 3D motion analysis and GRF (*p* = 0.125), and velocity of the CM derived from 3D motion analysis and GRF data (*p* = 0.961), but multiplying GRF by the velocity of the barbell resulted in a significant overestimation of power applied to the CM when compared with measures of power obtained by multiplying GRF by the velocity of CM derived from either 3D motion analysis (18.7%; *d* = 1.06; *p* < 0.001) or GRF data (23%; *p* < 0.001; *d* = 1.21). Figure 6 illustrates the velocity of the barbell-and-body segment CM time normalized across the propulsion phase. The peak and mean propulsion phase velocities of the barbell were significantly greater than velocities of the foot (peak: 98.2%; *d* = 9.87, mean: 99.2%, *d* = 16.96), lower leg (peak: 91.9%; *d* = 8.18, mean: 94.3, *d* = 14.07), upper leg (peak: 56.9%; *d* = 4.74, mean: 56.7%, *d* = 7.15), and trunk (peak: 18.8%; *d* = 1.16, mean: 14.4%, *d* = 1.55) segment CM equivalents. However, differences between the velocity of the barbell and head, lower arm, and upper arm segment centres of mass did not exceed 5% (*d* = âˆ’0.25 to 0.30).

## Discussion

It is critical that the selection of methods used to obtain measures of power applied to the mass of interest during lower-body resistance exercise is based on an understanding of the theory that underpins the method and its limitations. Theoretically, investigators should obtain measures of power by multiplying the force applied to the mass of interest by its velocity (^{17}). However, review of the literature indicated promotion of a method that obtains power by multiplying the force applied to the CM (GRF) by the velocity of the barbell, relying on the assumption that the velocity of the barbell provides an accurate representation of the velocity of the CM, despite research findings to the contrary (^{5,10,17}).

The results of this study supported the hypothesis that multiplication of GRF by the velocity of the barbell would lead to a significant overestimation of the velocity of and the power applied to the CM. This finding is of critical importance to strength and conditioning practitioners and investigators because it shows that the combined method is not valid. Calculations of power and the product of the force applied to a resistance and its resultant velocity must be based on force and velocity components that are recorded from the resistance of interest. Therefore, the velocity of the barbell should only be considered when the power applied to the barbell is of interest, and GRF should only be considered when the velocity of the CM, derived from 3D motion analysis or GRF, is available, and the power applied to the CM is of interest.

The lack of a significant difference between measures of force applied to the CM derived from 3D motion analysis and GRF and velocity of the CM derived from 3D motion analysis and GRF data indicated that the velocity of the CM can be accurately derived from GRF, countering suggestions made in recent research to the contrary (^{5}).

Significant differences found between the velocity of the barbell-and-body segment centres of mass provide insight regarding the factors that underpin what has been referred to as an underrepresentation of the velocity of the CM when derived from GRF (^{5}), further questioning the validity of the combined GRF multiplied by the velocity of the barbell method. Peak and mean propulsion phase velocities of the trunk, which represented 21.5% (Â±3.1%) of mean CM, were 18.8% (Â±4.3%) and 14.4% (Â±2.4%) less, respectively, than the velocity of the barbell; peak and mean propulsion phase velocities of the upper leg, which represented 14% (Â±2%) of mean CM, were 56.9% (Â±7.8%) and 56.7% (Â±3%) less, respectively, than the velocity of the barbell.

This suggests that strength and conditioning practitioners and investigators must be cognizant that a considerable portion of the CM is displaced at a rate that is significantly slower than the barbell during back squat performance and that this will affect the method that should be used to obtain measures of resistance exercise power.

To summarize, the velocity of the barbell significantly overestimates the velocity of the CM and, therefore, the power applied to the CM. This can and should be avoided by using methods that consider the force applied to and the velocity of specific masses of interest.

## Practical Applications

The results of this study clearly demonstrated that strength and conditioning coaches and investigators should not obtain measures of power applied to the CM by using the increasingly popular method of combining the velocity of the barbell and the force applied to the CM. During back squat performance, the barbell undergoes significantly greater displacement at a significantly greater velocity compared with the CM. Therefore, strength and conditioning practitioners and investigators are urged to obtain measures of power by using the force applied to and the velocity of either the barbell or CM (^{10}). Continued use of the combined approach will result in overestimations of velocity and power, which may compromise the methodological integrity of neuromuscular assessments and the prescription of resistance training loads.

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**Keywords:**

back squat; methodology; velocity; displacement