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INTRODUCTIONStrength and power are the measures of the output ofthe motor system. One useful way to distinguishbetween these two parameters is to considerer theforce-velocity relation of muscle (Hill, 1938; Boscoand Komi, 1979). The force-velocity relation ischaracterized as compromising four distinct regions:velocity = 0, force = 0, velocity > 0, and velocity < 0. Strength is usually defined as the point on the force-velocity curve where velocity is close to zerowhereas the power produced by the motor systemcorrespond to the region in which velocity is ≠ 0.The power that a muscle can produce under normalmovement conditions in which several joints areinvolved, depends on the product of muscle force andthe velocity of shortening. Power production ismaximal when the muscle acts against a load that’sabout 40% of maximum isometric force (MIF), orwhen the speed of shortening of the extensor legmuscles reach 35% of the maximal angular kneeextension velocity (Bosco and Komi, 1979). Inmethodology of training, the maximal powerproduced during a ballistic movement or against thegravity, in which the body represents thegravitational load, the term explosive strength is

preferred. Vertical jumps are a typical expression ofhuman maximal muscle power. Observing differentbasic movements in sports or general physicalactivity as well as the features peculiar of movementin the infancy and puberty we can immediatelyrealize that explosive strength is the most commonand natural expression of force. Explosive strengthcan be defined as the ability of the neuromuscularsystem to develop high gradient of force in a shorttime as possible (Bosco, 1985). The explosivestrength of a muscle depends upon numerous factorswhich include: fiber type, number of cross-bridges inparallel, force per cross-bridge, force-velocityrelationship, fiber Vmax, force-pCa2+ relationship, andforce-frequency (action potential, Hz) relationship.Additionally, neural factors, such as cortical drive,afferent inputs to the central nervous system, andalpha motor neuron recruitment patterns, all affectthe force and power of a muscle or muscle group(Fitts et al.,1991).The power produced by the motor system can bedetermined by a task performance (e.g. vertical jump,weightlifting, standing long jump), with the use of anergometer, or by an isolated-muscle experiment. Theevaluation of a task performance provides an index

Center of gravity height calculationand average mechanical power during jump performance

Riccardo Di Giminiani1, Renato Scrimaglio2

1 Faculty of Sport Sciences-University of L’Aquila, Via Cardinale Mazzarino - 67100 L’Aquila, Italy2 Department of Physics-Faculty of Sport Sciences-University of L’Aquila, Coppito 67100 L’Aquila, Italy

digi.e@tiscalinet.it

ABSTRACTDi Giminiani R, Scrimaglio RCenter of gravity height calculation and average mechanical power during jump performanceItal J Sport Sci 2006: 13: 78-84

The use of flight time to calculate the height or power during vertical jumping strongly has influenced the development of an instrumentable to measure flight time without using the expensive and sophisticate force plates. The platform on which the subjects can performsingle (SJ; CMJ) or continuos vertical jumps (HT) is called “Ergojump” (Bosco, 1983). This electronic apparatus is made up of aresistive (or capacitative) platform connected by a cable to a digital timer (±0,001 s) which is able to record the flight time as it istriggered, during a jump, by the feet of the subject at the moment of release from the platform, and will be stopped at the moment of touchdown. In addition, the average mechanical power produced in watts/kg is calculated.

KEYWORDS: center of gravity, jump performance

(vf) at touch down. The time spent moving upward ordownward will be the same and equal to:

1/2 tf [s] (1)

As the acceleration of gravity is 9,81 m/s2 thevelocity (vf) is equal to:

vf = 1/2tf·9,81 [m/s] (2)

and the average velocity (vm), upward or downward,is:

vm = 1/4tf·9,81 [m/s] (3)

Consequently, the height of jump (h), is calculatedusing the average velocity (vm) and the time flight(1/4tf) as follows:

hf = vm·1/2tf [m] (4)

Replacing vm by its formula given in equation 3 wecan rewrite:

hf = 1/4 tf·9,81·1/2tf

hf = 1/8(tf)2 or 1,226·(tf)2 (5)

AVERAGE MECHANICAL POWER DURINGJUMP SERIES AS HTTo calculate the average mechanical power duringe.g. 10s the following basis of calculation is used(Bosco et al.,1983):

Power = W/tc [watts] (1)

Where W = the total average work performed during10 s and tc = the average total contact time of verticaljumps.The total work (W) performed during a vertical jumpcan be calculated using the following formula:

W = m·g·h [J] (2)

Where m = the mass of the subject; g = theacceleration of gravity; and h = the totaldisplacement of the center of gravity (CG)The total displacement of the center of gravity (h) iscalculated summing the displacement during theflight (hf) and contact period (hc) as follows:

h = hf + hc [m] (3)

The displacement of CG during flight (hf) is

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of the whole body power. The vertical jump iscommonly used for this purpose. Asmussen andBonde-Petersen (1974) had a brilliant idea andintroduced a system to measure the height during avertical jump based on flight time. Flight time ismeasured as the space between force at takeoff andforce at landing. Jumping techniques varyconsiderably according to such factor, as whether thetakeoff is performed from a standing position or froman approach run, and the movement can beperformed with (SI) or without a countermovement(CMJ). Additionally, during human hopping in place (HT)the average mechanical power can be calculated fromthe contact time with the ground and from the flighttime (Bosco et al. 1983) and used to estimate theexplosive strength during this ballistic movementthat involves a stretch-shorten cycle of the legs.During this bouncing gait, the action of the body’smany musculoskeletal elements, including muscles,tendons, and ligaments, are integrated together sothat the overall musculoskeletal system behaves likea single spring.The use of flight time to calculate the height orpower during vertical jumping strongly hasinfluenced the development of an instrument able tomeasure flight time without using the expensive andsophisticate force plates. The platform on which thesubjects can perform single (SJ; CMJ) or continuosvertical jumps (HT) is called “Ergojump” (Bosco,1983). This electronic apparatus is made up of aresistive (or capacitative) platform connected by acable to a digital timer (±0,001 s) which is able torecord the flight time as it is triggered, during ajump, by the feet of the subject at the moment ofrelease from the platform, and will be stopped at themoment of touch down. In addition, the averagemechanical power produced in watts/kg is calculated.

ELEVATION OF THE CENTER OF GRAVITYDURING SJ AND CMJThe jump performance during SJ and CMJ can bequantified by calculating the elevation of the centerof gravity. The height of jump is calculated from the time offlight (tf) measured directly with the Ergojump(Bosco et al., 1983).The basis of this calculation is described inAsmussen and Bonde-Petersen (1974) and heresummarized: in the flight the subject will take offwith a certain vertical release velocity (vf), whichwill decrease and become zero at the top of the jump.During the subsequent downward movement, thevelocity will again increase and reach the same value

calculated using the recorded flight time (t f)according to the method of Asmussen and Bonde-Petersen (1974) as follows:

hf = (g·tf2)/8 [m] (4)

The displacement of CG during contact period (hc)can be estimated assuming that the vertical velocityfrom the lowest point of the CG to the releaseincreases linearly. If the release velocity is vv and thecontact time is tc, the elevation of CG during thecontact period (hc) is:

hc = (vv/2)·(tc/2) [m] (5)

Because the vertical release velocity and impactvelocity are equal in a harmonic jump, the verticalvelocity (vv) can be written as follows:

vv = (g·tf)/2 [m/s] (6)

where tf is the flight time between jumps. Applyingthe formulas (5) and (6) we can rewrite thedisplacement (hc) as follows:

hc = (g·tf·tc)/8 [m] (7)

As the total displacement of CG is the sum of hc andhf, we can write:

h = [(g·tf·tc)/8]+[ (g·tf2)/8]

h = (g·tf·tt)/8 [m] (8)

Where tf = flight time of one jump; tt = total time ofone jump (tt = tc + tf). The total work performed(formula 2) during a vertical jump can now bewritten as follows:

W = (m·g2·tf·tt)/8 [J] (9)

Assuming that the time of the positive work phase(tpos) during contact can be an half of the total contacttime (tpos = 1/2tc), the average mechanical power of thepositive work phase per body mass is:

Power = [(m·g2·tf·tt)/8]/(m·1/2tc)

Power = (g2·tf·tt)/(4·tc) [watts/kg] (10)

In the jump series the Ergojump (Bosco-System) issumming the total flight time (Tt) of all (n) jumps,and therefore the average flight time (tf) for one jumpis:

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tf = Tf/n [s] (11)

If in the jump series (including n jumps) the totalperformance time (Tf) is e.g. 10 s, then the averagetotal time(tt) is:

tt = Tt/n

tt = 10/n [s] (12)

The contact time in a jump series is the totalperformance time minus the total flight times. Thenthe average contact time (tc) in one jump is:

tc = (Tc - Tf)/n

tc = Tv/n [s] (13)

Now substituting the individual flight times for theaverage flight times the average mechanical power ina jump series can be written as follows:

Power = (g2·Tf·Tt)/(4·n·Tc) [watts/kg] (14)

If the total time is e.g. 10 s the last formula iswritten:

Power = (g2·Tf·10)/4·n(10·Tt) [watts/kg] (15)

REFERENCES

Asmussen E, Bonde-Petersen F (1974) Storage of elasticenergy in skeletal muscles in man. Acta Physiol Scand91: 385-393

Bosco C, Luhtanen P, Komi PV (1983) A simple methodfor measurement of mechanical power in jumping. Eur JAppl Physiol 50: 273-282

Bosco C., Komi P.V. (1979) Potentiation of themechanical behaviour of the human skeletal musclethrough prestretching. Acta Physiol. Scand., 106:467-472. 1979.

Hill A.V. (1938). The heat of shortening and the dynamicconstants of muscle. Proc. Roy. Soc. B., 126:136-195.

Bosco C. (1985). Elasticità muscolare e forza esplosivanelle attività fisico-sportive. Società Stampa Sportiva-Roma.

Fitts R.H., McDonald K.S., Schluter J.M. (1991). Thedeterminants of skeletal muscle force and power: theiradaptability with changes in activity pattern. J. Biomech.,24(1):111-122.

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