Power Output Estimate in University Athletes - CiteSeerX

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Journal of Strength and Conditioning Research, 1996,10(3),161-166 © 1996 National Strength & Conditioning Association

Power Output Estimate in University Athletes Doug L. Johnson and Rafael Bahamonde Biomechanics Laboratory, Ball State University, Muncie, Indiana 47306 . not use standard units of power ; (b) it does not take gravity into consideration ; and (c) it does not state whether it measures peak or average power. Harman et al . found that the Lewis formula only predicts the average power of a jumper as he or she falls back to the ground . Harman et al . (10) and Garhammer (8) have stated that the Lewis formula is inaccurate . Harman et al . (10) developed prediction equations for peak and average power but performed two separate jump tests, one on a force platform and the other off the force platform . Also, Harman et al . (9, 10) used very few subjects to develop the equations . Garhammer (7) modified the Lewis formula for each gender but did not state the accuracy of their method and only tested 13 subjects . There has not been a simple formula developed using the results from a countermovement jump and reach test from a force platform . Also, though there are gender differences in power output, gender has never been used as a variable to predict power (12,15) . The purpose of this study was to devise a simple mechanical power formula for both peak and average power using the countermovement jump and reach test in college male and female athletes .

Reference Data Johnson, D .L ., and R. Bahamonde . Power output estimate in university athletes . j. Strength and Cond . Res . 10(3) :161-166 . 1996 .

ABSTRACT A simple mechanical power formula was devised for both peak and average power using a countermovement jump and reach test from a force platform . College athletes (49 F, 69 M) were measured for height, weight, thigh circumference, thigh skinfold, thigh length, and foreleg length . A Vertec was used to measure vertical jump height, and the force platform was used to help determine power output . Eight anthropometric measurements, vertical jump height, and gender were used in a stepwise multiple regression to develop the prediction equations . Gender was not significant (p > 0 .05) and therefore was not loaded into either equation . Estimated and actual peak power values were 4,707 ± 1,511 and 4,687 ± 1,612 watts, respectively Estimated average and actual average power values were 2,547 ± 760 and 2,463 ± 753 watts, respectively. Vertical jump height, mass, and body height were the significant variables selected by the stepwise multiple regression to predict both peak and average mechanical power, accounting for 91 and 82% of the variance in peak and average power output, respectively . This indicates they are good predictors of peak and average power output in college athletes .

Methods Subjects Subjects were 69 male college athletes (13 baseball, 23 football, 12 tennis, 8 track & field, and 13 volleyball players) and 49 female college athletes (10 basketball, 13 softball, 7 tennis, 12 track & field, and 7 volleyball players) . Anthropometric measurements taken were height, body mass, thigh skinfold, thigh circumference, thigh length, and foreleg length, all leg measurements taken from the right leg .

Key Words : power prediction, vertical jump height, peak power, college athletes

Introduction The vertical jump test is one of the most popular ways to assess power output . But an accurate determination of power output requires force platforms and/or high speed film analysis . Most high schools and colleges do not have such sophisticated pieces of equipment . One of the most popular power prediction equations used with the vertical jump is the Lewis formula (11) : I

where BM is the body mass in kg and hj is the vertical jump height in meters . The Lewis formula was developed to obtain a true measure of power output, where body weight and jump speed were taken into consideration . It is relatively simple to administer and requires little equipment . However, Harman et al . (10) discovered that the Lewis formula has several flaws : (a) it does

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Procedures The vertical jump test employed a Kistler force platform (sampling rate 500 Hz) interfaced with a Zenith microcomputer that used the Fadap (Fadap, Inc ., Indianapolis) computer program to collect force platform data . Jump height was measured with a Vertec jump training apparatus . Once reach height was determined with the dominant arm, the subject performed a vertical countermovement jump with an arm swing and touched the highest lever possible with the dominant arm . Arm movements and depth of knee flexion (countermovement) were self-determined . No jab step or preparatory 161



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run was permitted . Vertical jump height was the difference between the reach height and the highest point touched during the jump . Subjects were allowed 10 min to warm up and stretch prior to testing . They performed 3 practice jumps followed by 3 test jumps . The jumps were measured to the nearest 1/2 inch on the Vertec and were converted to centimeters . The height of the best vertical jump test was used for the power regression equation . Vertical

oped, a full-model multiple regression using all the varioped, ables tested and the best model . The latter was a stepwise regression procedure that obtained the best prediction results with a minimum amount of variables . Also, if gender turned out to be a significant variable, separate regression equations would be developed and compared .

Results

velocity (Vz) and vertical jump power (VJP) output were determined from the parameters obtained from the Kistler force platform . The change in vertical velocity (AVz) was calculated using Equation 2 :

Figures 1, 2, and 3 show the plots of the power vs . force, power vs . velocity, and force vs . velocity representative of one subject's performance . Descriptive statistics for the subjects are presented in Tables I and 2 . No signifidifferences were found between the cross-valida2) ( At/m - 1z cant AVz=F tion and the validation group for any of the variables where Fnz was equal to the force Fz obtained from the (see Table 1) . In contrast, significant differences were force platform minus the subject's body weight, t was found between genders for all variables except thigh the time interval and was equal to 0 .002 sec, and m was length (Table 2) . . This equation gave the net vertical force the body mass There were no significant differences (p > 0 .05) in . Net Vz was determined that created the change in Vz the cross-validation group between actual and preby adding AVz to Vz at the start of each time interval . Vertical velocity was calculated from the first positive force value equal to body weight following the countermovement jump to takeoff . A FORTRAN computer program was used to calcu late mechanical power from the force platform data . VJP was the product of vertical force Fz times vertical velocity Vz, VJP = F, - Vz . Peak and average VJP were calculated over a period from the beginning of the jump to the takeoff. Peak VJP was the highest positive instantaneous power output value achieved ; average VJP was calculated by computing the area under the positive instantaneous power output curve achieved during the jump .

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body mass, thigh girth, thigh skinfold, thigh girth/ skinfold ratio, thigh length, foreleg length, and thigh/ foreleg length ratio as independent variables . Thirty subjects were picked at random and withheld from the development of the regression equation to be used as a cross-validation group to determine prediction accuracy . The remaining 88 subjects were used in the development of a stepwise multiple regression equation with no forced variables for both peak and average mechanical power . T tests for dependent means were used to examine the differences between predicted and actual mechanical power in the cross-validation group . If no significant differences were found between predicted and actual power values, the validation and cross-validation group's results were combined to develop a more accurate stepwise regression equation for both peak and average mechanical power . Two models were devel-

POWER FORCE

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Peak and average mechanical power prediction equations were calculated using the force platform results as the dependent variable . Multiple regression analysis employed gender, subject height, vertical jump height,

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Figure 1 . Power vs . force in the VJ using a countermovement jump .

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Figure 2. Power vs . velocity in the VJ using a countermovement jump .

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dicted values for mean scores for either peak mechanical power : 4,687 ± 1,612 vs . 4,707 ± 1,511 W, or average mechanical power, 2,463 ± 753 vs . 2,547 ± 760 W. Pearson correlation coefficients between actual and predicted values for peak and average power were r = 0 .97 and 0 .92, respectively. Based on these results, the regression equations derived using the cross-validation sample were considered valid . Equations 3 and 4 were the validated equations for peak and average power output .

Figure 3 . Force and velocity in the VJ using a countermovement jump . Table 1 Descriptive Statistics of Subjects in Each Group

Test variables Age (yrs) Height (cm) Mass (kg) Thigh girth (cm) Thigh skinfold (mm) Thigh girth/skfd. Thigh length (cm) Foreleg length (cm) Thigh/foreleg ratio Vertical jump (cm) Peak power (W) Avg . power (W) Note. No

Validation

Cross-valid.

(n = 88)

(n = 30)

M ± SD

M ± SD

19.66 179 .64 73 .12 54 .77 15 .91 3 .98 41 .82 42 .40 1 .02 55 .95 4,765 2 ,559

. 130 11 .02 12 .14 4 .44

19 .33 176 .90 72 .76 54 .97 17 .93

6 .10 1 .60 2 .67 3 .53 0 .08 12 .86 1,532 822

3 .49 41 .05 41 .85 1 .02 54 .95 4,687 2,463

Combined (N= 118) M

1 .03 12 .18 13 .28 4 .44 6 .66 1 .42 2 .82 3 .15 0 .09 13 .86 1,612 753

± SD

19 .58 178 .94 73 .03 54 .82 16 .42 3 .85 41 .63 42 .26 1 .02 55 .70 4,745 2,535

1 .24 11 .34 12 .38 4 .42 6 .28 1 .56 2 .71 3 .43 0 .08 13.07 1,546 804

significant differences (p < 0.05) between groups . Table 2 Gender Descriptive Characteristics Men

Women

(n = 69)

(n = 49)

Variables

M

Height (cm) Mass (kg) Thigh girth (cm) Thigh skinfold (mm) Thigh girth/skfd . ratio Thigh length (cm) Foreleg length

±

±

Ppeak (W) = 78.6 . VJ (cm) + 60.3 . mass (kg) - 15 .3 • height (cm) - 1,245

(3)

Pavg (W) = 43.8 . VJ (cm) + 32.7. mass (kg) - 16 .8 . height (cm) + 721

(4)

These equations accounted for 91 and 82% of the variance for peak and average power output . As suggested by Pedhazur (16), once the regression equations were validated, the cross-validation and validation groups were combined and the equations reported afterward were derived from the entire sample (N = 118) . Prediction of Peak Mechanical Power

The results of the analysis for predicting peak mechanical power are listed in Table 3 . In the stepwise procedure, vertical jump, F(1, 116) = 313 .5; mass, F(1, 116) = 126.2; and height, F(1, 116) = 6 .6, were the only significant variables (F = 4.0, p < 0 .05) . When gender was used as the only variable to predict peak mechanical power, it produced an R2 value of 0 .64 . However, in the stepwise procedure, gender, F(1, 116) = 0 .02, was not a significant predictor variable (p < 0 .05) . The model that used vertical jump height, body mass, and body height had an adjusted R2 value of 0 .91 with a standard error of ±462 watts. Equation 5 was the best for predicting power with the least number of significant variables . Ppeak (W) = 78 .5 . VJ (cm) + 60 .6 - mass (kg) - 15 .3 . height (cm) - 1,308

(5)

Prediction o f Average Mechanical Power

SD

M/F X 100 ratio t-ratios

SD

M

185 .54 80 .11 56 .38 12 .74

8 .27 9 .26 3 .92 3 .48

169 .65 63 .06 52 .61 21 .61

8 .12 8 .87 4 .18 5 .66

10 .4* 10 .0* 5 .02* 10.5*

109 .4 127 .0 107 .0 59 .0

4 .77

1 .39

2 .56

0 .55

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186 .3

41 .46 43 .58

2 .74 2.99

41 .87 40 .39

2 .79 3 .15

0.82 5.59*

99 .0 107 .9

0 .08 8 .34 1,123 638

0.97 43 .02 3,285 1,828

0 .07 6 .11 563 351

6 .49* 15 .5* 14 .3* 12 .0*

108.2 150 .4 176 .0 166 .1

(cm)

Thigh/foreleg ratio 1 .05 Vertical jump (cm) 64 .70 Peak power (W) 5,782 Avg . power (W) 3,037

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*Significant differences between men and women (p

< 0 .05) .

The results of the analysis for predicting average mechanical power are listed in Table 4 . Vertical jump height, F(1,116) = 155 .9; body mass, F(1,116) = 59 .7; and height, F(1,116) = 9 .6, were the only significant variables (F = 4 .0 , p < 0 .05) selected to predict average mechanical power . When gender was forced as the only predictor variable, it produced an R2 value of 0 .55 . However, when no variables were forced, gender, F(1, 116) = 0 .0, was not a significant predictor variable (p < 0 .05) in the multiple regression equation . The stepwise regression equation with the vertical jump height, body mass, and height variables entered produced an adjusted R 2 value of 0 .82 with a standard error of ±346 watts . The average mechanical power prediction Equation 6 developed was as follows : P

(W) = 41 .4 . VJ (cm) + 31 .2 - mass (kg) - 13 .9 . height (cm) + 431

(6)

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Johnson and Bahamonde Table 3 Regression Coefficients for Selected Model for Peak Mechanical Power Zero order correlation

Parameter Gender Height (cm) Mass (kg) Thigh girth (cm) Thigh skinfold (mm) Thigh length (cm) Foreleg length (cm) Thigh/skinfold ratio VJ heght (cm) Intercept

0.671 0.815 0 .608 -0 .558 0 .120 0 .527 0 .619 0 .894

Best model

Full model 88 .0 -20.53 71 .15* -14 .33 -15 .24 263 .71 -255 .99 3 .18 75 .15* -10,715

-15 .31 60 .57

78 .46 -1,308

Note. R2 = 0.916 and 0 .913 for full and best models, respectively. *Variable significant in full model at 0.05 level . Table 4 Regression Coefficients for Selected Model for Average Mechanical Power

Parameter Gender Height (cm) Mass (kg) Thigh girth (cm) Thigh skinfold (mm) Thigh length (cm) Foreleg length (cm) Thigh/skinfold ratio VJ heght (cm) Intercept

Zero order correlation

0 .591 0.755 0.569 -0.547 0 .059 0 .466 0 .601 0 .849

Full model 189 .53 -19 .28* 45 .38* -15 .03 -22 .04 194 .55 -198 .87 -8 .34 37 .15* -6,487

Best model

-15 .31 60 .57

41 .41 431

Note . R 2 = 0 .831 and 0 .819 for full and best models, respectively. *Variable significant in full model at 0 .05 level .

Discussion Power prediction equations were developed to estimate peak and average mechanical power output in athletes . Both equations had strong correlations with actual peak and average power . However, the hypothesis that gender would be a significant predictor of both peak and average mechanical power after adjusting for other predictor variables in a multiple regression model was not supported in this study. Many athletic and work activities involve jumping or movements that simulate jumping, such as lifting objects dynamically. Jump tests are relevant because of the commonality of the jumping motion in various activities . Previous studies (1, 14, 15) have found that correlations between VJ height and VJP using the Lewis formula were significant but low . Despite the low correlations, Dowling and Vamos (5) found that maximum positive power had a correlation coefficient of r = 0 .93

with VJ height . Instead of using a prediction equation, maximum power was determined by the subject doing a VJ from a force platform . In the present . study VJ height was the first variable selected by the stepwise multiple regression procedure for both peak and average mechanical power . It accounted for 80 and 72% of the variance at Step 1 for peak and average mechanical power, respectively . Vertical jump height had a correlation of r = 0 .88 with peak power and r = 0 .82 with average power. The strong correlation is due to the components needed to achieve the height in a vertical jump . VJ height depends on the vertical ground reaction force and takeoff velocity generated . The product of these two variables is mechanical power. In this study, vertical jump height and actual peak and average mechanical power were determined from the same jump on a force platform . When Harman et al . (10) developed their power prediction equation, two squat jumps were performed, one using a force platform and the other to determine VJ height . In this study we employed the countermovement jump (CMJ) instead of the squat jump because it produces greater power (2, 9) and we felt it was a more natural movement for the subjects to perform (10) . Vertical jump height can be improved by using an arm swing and a countermovement before the jump . Harman et al . (9) found that the arm swing increased velocity, vertical center of mass displacement, and power output in the vertical jump . Previous studies (2, 3, 6, 9) have shown improved utilization of elastic energy, increased takeoff velocity, increased. vertical center of mass displacement, and increased power output using a CMJ over a squat jump . Thus it is understandable why the VJ height from the CMJ is a good indicator of VJP . Body mass was loaded at Step 2 in the stepwise multiple regression equations for both peak and average mechanical power . It accounted for 11 and 9% of the variance for peak and average mechanical power, respectively . Various studies (1, 4, 13-15) found strong correlations between body mass and VJP. Mayhew (13) classified the VJP test as a mass-power test, which emphasizes the ability to move the body mass with power . One of the two variables that determine VJ height is the vertical ground reaction force . The amount of force needed in a VJ depends on the subject's mass . The greater the force-output-to-body-mass ratio, the greater the VJ height, and therefore the greater the resulting power output . The heavier person must produce more power to achieve a VJ height equal to that of a lighter person . Body mass in conjunction with VJ height are good indicators of the vertical ground reaction force being exerted to lift the individual . Thus it is not surprising that body mass was the second variable selected by the multiple regression procedure . Body height was the third and final significant variable chosen by the stepwise multiple regression procedure

Power Output Estimate to be used in both mechanical power equations . It accounted for less than 2% of the variance for both peak and average mechanical power . Height was found to be statistically significant for peak mechanical power (F = 6 .58, p < 0 .05), but not in the full-model Multiple regression procedure (F = 1 .67, p < 0 .05). It was statistically significant for average mechanical power for both the stepwise multiple regression (F = 9 .62, p < 0 .05) and the full-model multiple regression (F = 2 .19, p < 0 .05) procedures . Height had zero-order correlations of r = 0 .67 and 0 .59 with peak and average mechanical power, respectively. Other studies (1, 14, 15) have also found significant but weak zero-order correlations between body height and VJP . Beckenholdt and Mayhew (1) and Mayhew and Salm (15) found correlations of r = 0 .32 and 0 .13, respectively, for males . Mayhew et al . (14) and Beckenholdt and Mayhew (1) reported correlations of r = 0 .61 and 0 .32, respectively, for females . The zeroorder correlations of height to power output would indicate that taller persons produce greater power . However, in the regression equation the coefficients were negative, indicating that when VJ height and mass were partialed out, the effect of height became negative . Thus the taller subjects would be expected to generate less power than the shorter subjects . One possible explanation may be that during a vertical jump taller persons tend to go through a greater range of motion at a slower velocity, which takes more time . This would tend to decrease the takeoff velocity, in turn decreasing the power output. Although height was a significant variable loaded in both equations, it did not produce significant changes in the percentage of variance accounted nor to the standard error of estimate (SEE) of both equations . With height loaded after VJ height and body mass, the percentage of the variance accounted for increased by 0 .4% for peak mechanical power and 1 .72% for average mechanical power. Also, the SEE was only reduced by ±11 and ±12 watts, respectively, in peak and average mechanical power stepwise regression equations . There were significant differences (p < 0 .05) for both peak and average mechanical power, respectively, be tween men (5,782 ± 1,123 and 3,037 ± 638) and women (3,285 ± 563 and 1,828 ± 351) (Table 2) . When the gender variable was forced first in the stepwise multiple regression equation, it produced an adjusted RI value of 0 .64 for peak power and 0 .55 for average power. But after holding VJ height, body mass, and height constant by partial correlations, the effect of gender on peak and average mechanical power was nonsignificant (r = 0 .014 and -0 .001, respectively) . The results cannot be interpreted to mean there are no differences between men and women in mechanical power production, but rather that gender was not a significant variable in helping to improve the accuracy of predicting mechanical power output using our regression equation. Perhaps the difference between genders

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in power production is more a function of size and strength rather than a male/female difference . Other studies have found significant differences in power output between genders (12, 15) but have not been able to explain why. Maud and Shultz (12) found a significant difference of 55 .9% between men and women in vertical jump power using the Lewis formula, but when the values were expressed relative to lean body mass, no significant differences were found for VJP. In contrast, Mayhew and Salm (15) found significant gender differences in VJP after controlling for body composition, anthropometric measurements, and strength and neuromuscular performances . Both Maud and Shultz (12) and Mayhew and Salm (15) used the Lewis formula to measure VJP . However, since the Lewis formula has been proven inaccurate (10), incorrect power values were recorded and differences between gender in power output may have been distorted . Further testing would help improve the accuracy of our prediction equations . This study did not determine or use body fat percentage and lean body mass values as variables, all of which may play an important role in refining the accuracy of a mechanical power equation . The subjects in this study were college athletes ; this renders the equation population-specific . More research is needed on subjects of all ages and activity levels in order to develop a generalized prediction equation for estimating mechanical power output from jumping.

Practical Application Because VJ, body mass, and body height are relatively simple to measure and require little equipment, these prediction equations can be useful to physical educators, coaches, athletic trainers, athletes, and other fitness specialists . They can be used to monitor athletic performance, analyze injury rehabilitation, and aid in team selection .

References 1 . Beckenholdt, S., and J. Mayhew. Specificity among anaerobic power tests in male athletes . J . Sports Med . Phys . Fitn . 23 :326-332. 1983 . 2 . Bosco, C., and P. Komi. Potentiation of the mechanical behavior of the human skeletal muscle through prestretching . Acta Physiol . Scand .106:467-472 .1979 . 3 . Bosco, C ., and P. Komi . Influence of countermovement amplitude in potentiation of muscular performance . In: Biomechanics VII-A . A. Morecki, K . Fidelus, K . Kedzior, and A . Wit, eds . Baltimore: University Park Press, 1980 . pp . 129-135 . 4 . Davies, C. Human power output in exercise of short duration in relation to body size and composition . Ergonomics 2:245-256 . 1971 . 5 . Dowling, J ., and L . Vamos . Identification of kinetic and temporal factors related to vertical jump performance . J . App! . Bianec,h . 9:95-110.1993 . 6 . Fukashiro, S ., and P. Komi. Joint moment and mechanical power flow of the lower limb during vertical jump . Int . J. Sports Med . 8:15-21 .1987 . 7 . Garhammer, J . Maximal human power output capacity and its determination for male and female athletes . In : Proceedings of



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Johnson and Bahamonde University of Western Australia, 1991 . pp . 67-68 . Garhammer, J . A review of power output studies of Olympic and powerlifting : Methodology, performance prediction, and evaluation tests.] . Strength Cond . Res . 7 :76-89 . 1993 . Harman, E ., M . Rosenstein, P Frykman, and R . Rosenstein. The effects of arms and countermovement on vertical jumping . Med . Sci . Sports Exerc . 6 :825-833. 1990 . Harman, E ., M . Rosenstein, P Frykman, R . Rosenstein, and W. Kraemer. Estimation of human power output from vertical jump. J . Appl . Sport Sci . Res . 3 :116-120.1991 . Mathews, D., and E. Fox . The Physiological Basis of Physical Education and Athletics (2nd ed .) . Philadelphia : Saunders, 1979 . Maud, P., and B. Shultz. Gender comparisons in anaerobic power and anaerobic capacity tests. Br . J . Sport Med. 2(20)51-54 .1986 . Mayhew, J . Specificity among anaerobic power tests in untrained males and females. Annali dell Instituto Superiore di Educazione Fisica L'Aquila 2:399-405 . 1986. the XIII International Congress on Biomechanics .

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14 . Mayhew, J ., M . Bemben, D . Rohrs, and D . Bemben . Specificity among anaerobic power tests in college female athletes . J . Strength Cond . Res. 8 :43-47. 1994. 15 . Mayhew, J ., and P. Salm . Gender differences in anaerobic power tests . Eur. J . App! . Physiol . 60 :133-138 . 1990 . 16 . Pedhazur, E . Multiple Regression in Behavioral Research (2nd ed .) . New York : Holt, Rinehart & Winston, 1982 .

Acknowledgments We would like to thank Dr. Mitchell Whaley, Dr . Gale Gehlsen, and Tim Demchak from Ball State University, and Dr. Jerry Mayhew from Northeast Missouri State University, for their assistance with this project .