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What is the formula for jumping?

The mechanical work performed to accomplish a vertical jump can be determined by using the jump height distance that was measured (using Work = Force x Distance where Force = Mass x Acceleration). However, Power can not be calculated (Power = Work / time) since the time that force is acted on the body is unknown.

topendsports.com - Vertical Jump Power Calculation - Topend Sports
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Vertical Jump Power Calculators

Vertical Jump tests are usually just reported as the distance jumped in centimeters or inches. This does not always tell the full story. A heavier person jumping the same height as a lighter one has to do much more work to move a larger mass. Therefore it is sometimes useful to convert the score to units of power or work. The mechanical work performed to accomplish a vertical jump can be determined by using the jump height distance that was measured (using Work = Force x Distance where Force = Mass x Acceleration). However, Power can not be calculated (Power = Work / time) since the time that force is acted on the body is unknown. Power can be directly measured using a force plate, though these are not readily available. Over time a few different formula have been developed that estimate power from vertical jump measurements. A few of these are presented below, with examples. The examples below all use a hypothetical vertical jump of 60 cm (0.6 meters or 23.5 inches) by a person 75 kg and 180 cm. As you can see, there are widely different results achieved. This is partly due to it not always being clear if peak power or average power is being estimated.

Lewis Formula

The Lewis formula or nomogram (Fox & Mathews, 1974) is a commonly used formula (found in many high school text books). This formula only estimates average power, and is based on a modified falling body equation. The original formula used the units of kg·m·sec.-1. To convert it to Watts, the standard unit for Power, the factor of 9.81 has been added. Average Power (Watts) = √ 4.9 x body mass (kg) x √ jump-reach score (m) x 9.81

Example

Average Power = (square root of 4.9) x body mass(kg) x (square root of jump distance(m)) x 9.81

Average Power = 2.2136 x 75 x 0.7746 x 9.81

Average Power = 1261.6 Watts

Harman Formula

To improve on the limitations of the Lewis formula, Harman et al. (1991) established equations for both peak and average power through multiple regression procedures. The two equations are listed below. In the first equation, it may actually be -1,822 instead of + 1,822, see comments below. Peak power (W) = 61.9 · jump height (cm) + 36.0 · body mass (kg) + 1,822 Average power (W) = 21.2 · jump height (cm) + 23.0 · body mass (kg) – 1,393

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Examples

Peak power (W) = (61.9 x jump height (cm)) + (36 x body mass (kg)) + 1822 Peak power (W) = (61.9 x 60) + (36 x 75) + 1822

Peak power (W) = 3714 + 2700 + 1822

Peak power (W) = 8236 Watts

Average power (W) = (21.2 x jump height (cm)) + (23.0 x body mass (kg)) – 1393 Average power (W) = (21.2 x 60) + (23 x 75) - 1393

Average power (W) = 1272 + 1725 - 1393

Average power (W) = 1604 Watts

Johnson & Bahamonde Formula

Johnson and Bahamonde (1996) also developed a formula for the calculation of peak and average power from the vertical jump test, using the countermovement jump. These equation use the additional factor of body height. Power-peak (W) = 78.6 · VJ (cm) + 60.3 · mass (kg) - 15.3 · height (cm) - 1,308 Power-avg (W) = 43.8 · VJ (cm) + 32.7 · mass (kg) - 16.8 · height (cm) + 431

Examples

Peak power (W) = (78.6 x VJ (cm)) + (60.3 x mass (kg)) - (15.3 x height (cm)) -1308 Peak power (W) = (78.6 x 60) + (60.3 x 75) - (15.3 x 180) - 1308

Peak power (W) = 4716 + 4522.5 - 2754 - 1308

Peak power (W) = 5176.5 Watts

Average power (W) = (43.8 x VJ (cm)) + (32.7 x mass (kg)) - (16.8 x height (cm)) + 431 Average power (W) = (43.8 x 60) + (32.7 x 75) - (16.8 x 180) + 431

Average power (W) = 2628 + 2452.5 - 3024 + 431

Average power (W) = 2487.5

Sayers Formula

The Sayers Equation (Sayers et al. 1999) also estimates peak power output (Peak Anaerobic Power output or PAPw) from the vertical jump. PAPw (Watts) = 60.7 · jump height(cm) + 45.3 · body mass(kg) - 2055

Example

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PAPw = (60.7 x jump height(cm)) + (45.3 x body mass(kg)) - 2055

PAPw = (60.7 x 60) + (45.3 x 75) - 2055

PAPw = 3642 + 3397.5 - 2055

PAPw = 4984.5 Watts

Bosco Formula

A formula for average power measurement from the Bosco Repeated Vertical Jump Test has been determined. The average power generated (W) is calculated from the test duration (Ts from 15 to 60 s), the number of jumps (n) total flight time (Ft ), and where g is the acceleration due to gravity, so that;

W = (Ft Ts g2) / 4n (Ts - Ft)

Other

I have also come across this formula for calculating power from vertical jump height. This formula was used until recently at the NHL Combine.

Power (ft-lb/sec) = 4 x weight (lb) x √ jump height (ft)

References

Bosco C, Luhtanen P, Komi PV (1983) A simple method for measurement of mechanical power in jumping. European Journal of Applied Physiology 50:273-282.

50:273-282. Harman, E.A., Rosenstein, M.T., Frykman, P.N., Rosenstein, R.M., and Kraemer, W.J.

(1991). Estimation of Human Power Output From Vertical Jump. Journal of Applied Sport Science Research, 5(3), 116-120. (1991). Estimation of Human Power Output From Vertical Jump. 5(3), 116-120. Johnson, D.L., and Bahamonde, R. (1996). Power Output Estimate in University Athletes. Journal of strength and Conditioning Research, 10(3), 161-166. 10(3), 161-166. Keir, P.J., V.K. Jamnik, and N. Gledhill. (2003) Technical-methodological report: A nomogram for peak leg power output in the vertical jump, The Journal of Strength and Conditioning Research Volume: 17 Issue: 4 Pages: 701-703. Volume: 17 Issue: 4 Pages: 701-703. Sayers, S., et al. (1999) Cross-validation of three jump power equations. Med Sci Sports Exerc. 31: 572.

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topendsports.com - Vertical Jump Power Calculation - Topend Sports
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