Leg stiffness and mechanical energeticprocesses during jumping on asprung surface

ADAMANTIOS ARAMPATZIS, GERT-PETER BRUGGEMANN, and GASPAR MOREY KLAPSING

German Sport University of Cologne, Institut for Biomechanics, 50933 Cologne, GERMANY

ABSTRACT

ARAMPATZIS, A., G-P. BRUGGEMANN, and G. M. KLAPSING. Leg stiffness and mechanical energetic processes during jumpingon a sprung surface.Med. Sci. Sports Exerc., Vol. 33, No. 6, 2001, pp. 923–931.Purpose: The purposes of this study were: a) toexamine the effect of verbal instructions given to the subjects on the control of lower extremity stiffness and b) to determine the effectof leg stiffness on mechanical energetic processes during drop jumps on a sprung surface.Methods: A total of 10 female athletesperformed a series of drop jumps on a sprung surface from heights of 20 and 40 cm. The instructions given to the subjects were a) “jumpas high as you can” and b) “jump high a little faster than at your previous jump.” The jumps were performed at each height until theathlete could not achieve a shorter ground contact time. Four jumps per subject per height were analyzed. The ground reaction forceswere measured using a “Kistler” force plate (1000 Hz). The athletes’ body positions were recorded using a high-speed (250 Hz) videocamera. The deformation of the sprung surface was determined by another high-speed camera operating at 500 Hz. Surface EMG wasused to measure muscle activity in five leg muscles.Results: The contact time showed high correlation with leg stiffness as well aswith ankle and knee stiffness. The change in leg stiffness was not due to the duration of the preactivation but rather to the level ofactivation during this phase. An increase in leg stiffness caused an increase in the energy stored and recovered in and by the sprungsurface and a decrease of the energy produced by the subjects.Conclusions:By influencing contact time through verbal instructions,it is possible to control leg stiffness. Maximal vertical take-off velocity of the center of mass and maximal take-off body energy canbe achieved having different levels of leg stiffness. The maximization of mechanical power is achieved by optimal leg stiffness valuesand leg muscle preactivation levels.Key Words: JOINT STIFFNESS, MECHANICAL ENERGY, MECHANICAL POWER, DROPJUMPS, VISCO-ELASTIC

I n many sports, there is an exchange of mechanicalenergy between the human body and elastic or visco-elastic surfaces (2,11,13,14,23,25,30). Humans adjust

their behavior depending on the surface characteristics(11,13,14) and are able to vary their sport performance(3,26). In response to a different surface stiffness, humanschange their leg stiffness (11,13,14). On the other hand, legstiffness influences oxygen consumption during running(5,15,21). Running velocity influences ankle stiffness (28),and the stretch-shortening cycle-induced fatigue causeschanges in knee stiffness and take-off velocity during dropjumps (17,18). From this, we can conclude that the stiffnessof the lower extremities influences athletic performance invarious sport activities. The relationship between leg stiff-ness and performance during explosive movements on asprung surface has not yet been reported in the literature.Leg stiffness can be influenced by stride frequency whilerunning (10) or hopping frequency when bouncing in place(9,12,13). These findings support the idea that it is possibleto control leg stiffness by means of the ground contact timeand consider its effects on mechanical energetic processes

during drop jumps (jumping down from a raised platformand upon landing, executing a vertical jump) on a sprungsurface. The purposes of this study were: a) to examine theeffect of verbal instructions given to the subjects on thecontrol of lower extremity stiffness and b) to determine theeffect of the leg stiffness on mechanical energetic processesduring drop jumps on a sprung surface.

METHODS

A total of 10 female athletes (height: 1.706 0.07 m,weight: 61.226 3.65 kg) participated in this study. In-formed written consent was obtained from all subjects inaccordance with the policy statement of the American Col-lege of Sports Medicine. The subjects performed drop jumps(DJ) from two different heights (20 and 40 cm) on a sprungsurface. Two different heights were chosen because of itspossible influence on jumping performance (20). Thesprung surface (403 60 cm) was mounted on a force plate(Kistler). The materials and structure of the sprung surfacewere similar to those of gymnastic tumbling floors (Fig. 1).For control purposes, the subjects were instructed to keeptheir hands on their hips during the drop jumps. The in-structions given to the subjects were a) “jump as high as youcan” and b) “jump high a little faster (with relation to groundcontact time) than your previous jump.” The ground contacttime was measured and checked after every jump using the

0195-9131/01/3306-0923/$3.00/0MEDICINE & SCIENCE IN SPORTS & EXERCISE®Copyright © 2001 by the American College of Sports Medicine

Received for publication October 1999.Accepted for publication August 2000.

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force plate data. The jumps were performed at each heightuntil the athlete could not achieve a shorter ground contacttime. The contact times of the first jumps of each athletetended to be longer than 200 ms. In the case that it wasshorter than 200 ms, the subject was instructed to performanother jump with a longer contact time. Four jumps persubject per height were analyzed. The selection of the jumpsto be analyzed was based on contact time. The first jumpwas supposed to have a contact time over 200 ms and thefourth jump the shortest contact time. The second and thirdjumps should have contact times less than 200 ms beingbetween 7 and 15 ms shorter than the previous jump.

The human body was represented by using a 15 segmenttwo-dimensional human body model (2). The masses andmoments of inertia of the various segments were calculatedusing the data provided by Zatsiorsky and Seluyanov (31).The ground reaction force was measured using a force plate(Kistler, 1000 Hz). The movement of the athlete was cap-tured using a high-speed (250 Hz) digital camera (RedlakeMotionscope 250 C). The optical axis of the camera wasapproximately perpendicular to the plane of motion. Toimprove the quality of the video analysis, six reflectivemarkers (radius 10 mm) were used to mark joint positions.The markers were fixed on the following body landmarks:the tip of the foot at the height of the metatarsals, lateralmalleolus, lateral epicondylus, greater trochanter, and C7vertebrae. These markers defined the position of the feet,lower legs, upper legs, and torso. The head and arm position

in relation to the body remains constant in this model (Fig.2). The stiffness of the sprung surface was determined bymeans of a static load test (up to 2000 N) measuring verticaldeformation (KSurf582.41 kN·m-1). The linear relationshipbetween force and deformation was considerably high (r2 50.99). The effective mass of the sprung surface (12,13) was1.9 kg. To determine the deformation of the sprung surfaceduring the drop jumps, a reflective marker placed under thesurface was used (Fig. 1). The motion of this marker wascaptured by a digital camera (Kodak SR-500 C) operating at500 Hz. This camera captured a 63 10 cm2 area. The videorecordings were digitized using the Peak-Motus automatictracking system. The two-dimensional coordinates weresmoothed using a fourth-order low-pass Butterworth filterwith a cut-off frequency of 15 Hz for the recordings at 250Hz and with a cut-off frequency of 24 Hz for those recordedat 500 Hz (19).

The vertical velocity of the subject’s center of massduring the support phase was calculated through integrationof the vertical ground reaction force:

Vz(t) 5 VzTD 1EtTD

tTO~Fz(t) 2 mszs(t) 2 mg!

mz dt

Vz: vertical velocity of the subject’s center of massVzTD: vertical velocity of the subject’s center of mass at

touch-down (this was calculated using the video data)Fz: vertical ground reaction forcems: effective mass of the sprung surface

TABLE 1. Support time (tsupport), leg stiffness (KLeg), ankle stiffness (KAnkle), knee stiffness (KKnee), and sprung surface stiffness (Ksurf) during drop jumps from 20 cm [Mean(SD), N 5 10].

Parameter(DJ 20 cm) Group 1 Group 2 Group 3 Group 4

tsupport [ms] 227 (24) 188 (9)1 175 (7)1,2 165 (7)1,2,3

KLeg [kNzm21] 27.66 (8.36) 47.86 (7.58)1 60.71 (10.21)1,2 80.94 (16.81)1,2,3

r2KLeg 0.95 (0.05) 0.97 (0.02) 0.96 (0.02) 0.96 (0.03)

KAnkle [Nzmz°21] 9.80 (2.96) 15.73 (4.90)1 19.27 (4.04)1,2 22.94 (8.36)1,2

r2KAnkle 0.92 (0.07) 0.98 (0.02)1 0.98 (0.01)1 0.98 (0.02)1

KKnee [Nzmz°21] 27.52 (18.54) 55.84 (20.86)1 68.59 (32.36)1 —r2

KKnee 0.88 (0.08) 0.81 (0.15) 0.87 (0.13) —Ksurf [kNzm21] 80.91 (8.81) 85.19 (8.56) 80.19 (9.38) 80.21 (8.71)r2

Ksurf 0.99 (0.05) 0.99 (0.04) 0.99 (0.03) 0.99 (0.03)1 Statistically significant (P , 0.05) difference between group 1 and group 2, group 1 and group 3, and group 1 and group 4.2 Statistically significant (P , 0.05) difference between group 2 and group 3, and group 2 and group 4.3 Statistically significant (P , 0.05) difference between group 3 and group 4.

FIGURE 1—The sprung surface.

FIGURE 2—Modeled representation of the human body during dropjumps on a sprung surface.

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zs: vertical acceleration of the sprung surfacem: mass of the subjectg: acceleration of gravityThe total vertical motion of the center of mass of the

subject (DSz tot) during the support phase was calculated byintegration of the velocity of the subject’s center of mass.Then the change of the subject’s center of mass positionrelative to the surface was calculated as follows:

DSz subj5 DSz tot 2 DSz surf

DSz surf: vertical deformation of the sprung surfaceDSz subj: vertical change of the subject’s center of mass

position relative to the surfaceThe total mechanical power was calculated by multiplying

the vertical ground reaction force with the vertical velocity ofthe subject’s center of mass. The total mechanical work wascalculated by integrating the total mechanical power over time.The strain energy of the sprung surface was calculated byintegration of the vertical ground reaction force over the ver-tical deformation of the surface. Mechanical work done by thesubjects was obtained from the difference between total me-chanical work and strain energy in the surface. The whole

energy of the human body was defined as of the sum of thepotential and kinetic energies of the 15 segment model (Fig. 2).The joint moments and the mechanical power of the jointmoments were calculated through inverse dynamics (16). Todetermine the force application point under the feet, two flex-ible pressure distribution insoles from “Paromed” were usedduring the drop jumps.

The leg stiffness was approximated using a linear spring.Stiffness of the ankle and knee joints were each approximatedby rotational springs. The stiffness values were calculated bymeans of linear regression equations. For the leg stiffness, theequations presented the relationship between the verticalground reaction force and the vertical positional changes of thecenter of mass of the subject relative to the surface (DSz subj).For the stiffness at the knee and ankle joints, it showed therelationship between the moment and change in joint angle.The regression equation was applied only while ankle and kneejoint angles were reducing (negative phase).

Surface electromyography (EMG) was used to measuremuscle activity (1000 Hz) in five muscles (gastrocnemiuslateralis, gastrocnemius medialis, tibialis anterior, vastus

FIGURE 3—Vertical force (FZ) vs downward displacement of center of mass (DSz subj), joint movement (MAnkle, MKnee) vs angular displacementfor ankle (DQAnkle) and knee (DQKnee) during the negative phase of the drop jumps an a sprung surface (N 5 10).

TABLE 2. Support time (tsupport), leg stiffness (KLeg), ankle stiffness (KAnkle), knee stiffness (KKnee), and sprung surface stiffness (Ksurf) during drop jumps from 40 cm [Mean(SD), N 5 10].

Parameter(DJ 40 cm) Group 1 Group 2 Group 3 Group 4

tsupport [ms] 217 (15) 186 (9)1 173 (7)1,2 164 (6)1,2,3

KLeg [kNzm21] 30.90 (8.68) 48.00 (11.18)1 55.39 (7.82)1,2 62.46 (9.97)1,2

r2KLeg 0.92 (0.07) 0.96 (0.02) 0.96 (0.02) 0.96 (0.02)

KAnkle [Nzmz°21] 12.30 (6.77) 13.98 (2.99) 16.13 (4.80) 17.74 (4.35)1,2

r2KAnkle 0.96 (0.03) 0.93 (0.10) 0.97 (0.03) 0.96 (0.04)

KKnee [Nzmz°21] 22.08 (8.37) 46.23 (22.48)1 79.89 (32.28)1,2 121.08 (44.16)1,2,3

r2KKnee 0.85 (0.08) 0.90 (0.07) 0.86 (0.10) 0.88 (6.29)

Ksurf [kNzm21] 85.01 (9.55) 84.86 (9.58) 85.41 (7.97) 85.47 (9.72)r2

Ksurf 0.99 (0.04) 0.99 (0.01) 0.99 (0.02) 0.99 (0.02)1 Statistically significant (P , 0.05) difference between group 1 and group 2, group 1 and group 3, and group 1 and group 4.2 Statistically significant (P , 0.05) difference between group 2 and group 3, and group 2 and group 4.3 Statistically significant (P , 0.05) difference between group 3 and group 4.

LEG STIFFNESS AND MECHANICAL ENERGY Medicine & Science in Sports & ExerciseT 925

lateralis, and hamstring) of the left leg. Preamplified, bipolarelectrodes with a 2-cm inter-electrode distance were placedon the muscle belly. The EMG data were rectified andsmoothed a using a second-order Butterworth filter with acut-off frequency of 10 Hz (8). The linear envelope EMGdata were normalized as follows:

EMGNk 5EMGFk

Maxkz 100

EMGNk: normalized EMG-Data from k-MuscleEMGFk: linear envelope EMG-Data from k-MuscleMaxk: Maximum linear envelope EMG-Data from k-

Muscle of each athlete during the trial in which the athletedemonstrated the highest leg stiffness.

The preactivation time and the integral of the preactivationsignal (IEMGPA) were calculated from the normalized EMGdata. The onset for the preactivation time of every muscle wasconsidered to be at the point when the normalized EMG valueexceeded the mean value plus 2 standard deviations of thenormalized EMG signal when the given muscle was relaxed.

The observation window for the relaxed muscle signal was 200ms. The problem with the on-off times of muscle activation arethoroughly discussed by DeLuca (6). The purpose of this studywas not to develop a method for on-set/off-set EMG analysisbut rather to use a method that consistently defines on-set timesfor group comparison.

The synchronization of the kinematic, dynamic, andEMG data was achieved by starting the measurementsystems at the same time. All analyzed jumps were dividedinto four groups. Group 1 contained the jump from eachsubject with the longest contact time. Group 4 contained thejumps with the shortest contact times. Groups 2 and 3contained the two remaining jumps from each subject thatwere assigned to the given groups based on contact time.The differences among groups were checked using a non-parametric test for several dependent samples (Friedmantest). At those parameters where differences were found, anonparametric test for two dependent samples (Wilcoxontest) was applied to assess the differences between the

FIGURE 4—Leg stiffness (KLeg), maximum vertical ground reaction force (FZmax) and vertical sinking of the center of mass (DSz subj) during dropjumps on a sprung surface (mean6 SD,N 5 10). (1) Statistically significant (P < 0.05) difference between group 1 and group 2, group 1 and group3, and group 1 and group 4; (2) statistically significant (P < 0.05) difference between group 2 and group 3, and group 1 and group 4; (3) statisticallysignificant (P < 0.05) difference between group 3 and group 4.

FIGURE 5—Strain energy of the sprung surface (Esurf), energy of the subject (Esubj), and total energy (Etot) during the negative phase of the dropjumps on a sprung surface (mean6 SD,N 5 10). (1) Statistically significant (P < 0.05) difference between group 1 and group 2, group 1 and group3, and group 1 and group 4; (2) statistically significant (P < 0.05) difference between group 2 and group 3, and group 1 and group 4; (3) statisticallysignificant (P < 0.05) difference between group 3 and group 4.

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groups. The level of significance was set atP , 0.05.Pearson’s correlation coefficients were calculated to exam-ine the relationships between the different parameters.

RESULTS

Leg stiffness, ankle stiffness, and knee stiffness were influ-enced by the duration of the ground contact (Tables 1 and 2).Shorter ground contact times caused higher leg stiffness values(DJ20 cm: r5 20.82,P , 0.01; DJ40 cm: r5 20.89,P ,

0.01). At both jumping heights, the relationship between thevertical ground reaction force and the vertical positionalchange of the subject’s center of mass (DSz subj) showed a highlinearity (r2KLeg 5 0.926 0.07 to r2KLeg 5 0.976 0.02,Tables1 and 2 and Fig. 3). The relationship between moment andchange in angle of the ankle (r2

KAnkle 5 0.926 0.07 to r2KAnkle

5 0.98 6 0.02) and of the knee (r2KKnee 5 0.81 6 0.15 to

r2KKnee5 0.906 0.07,Tables 1 and 2) showed a similar linearbehavior. Leg stiffness influenced the vertical ground reactionforce as well as the vertical lowering of the subject’s center of

FIGURE 6—Total energy of the human body at the take off (Ebody TO), energy loss in sprung surface (Eloss), energy of the subject (Esubj), energyof the sprung surface (Esurf), and total energy (Etot) during the positive phase of the drop jumps on a sprung surface (mean6 SD, N 5 10). (1)Statistically significant (P < 0.05) difference between group 1 and group 2, group 1 and group 3, and group 1 and group 4; (2) statistically significant(P < 0.05) difference between group 2 and group 3, and group 1 and group 4; (3) statistically significant (P < 0.05) difference between group 3 andgroup 4.

FIGURE 7—Force-deformation curves of the sprung surface (N 5 10).

LEG STIFFNESS AND MECHANICAL ENERGY Medicine & Science in Sports & ExerciseT 927

mass (Fig. 4). The leg stiffness also had an effect on the amountof energy transmitted to the sprung surface (Fig. 5). Higher legstiffness values caused an increase in the amount of energytransmitted to the sprung surface (DJ20 cm: r5 0.88, P ,0.01; DJ40 cm: r5 0.87,P , 0.01). Conversely, an increasein leg stiffness caused a decrease in the energy absorbed by thesubjects during the negative phase of the drop jumps (DJ20 cm:r 5 20.84,P , 0.01; DJ40 cm: r5 20.73,P , 0.01; Fig. 5).

The total energy of the subject’s body at the instant oftake-off and its vertical take-off velocity didn’t showstatistically significant differences in the first threegroups (Fig. 6). Both values decreased significantly ingroup 4. The energy delivered by the subjects during thepositive phase of the drop jump showed statistically sig-nificant differences between the groups (Fig. 6). In group1, the amount of energy delivered by the subjects was thehighest. Furthermore, the mechanical power of the sub-jects during the positive phase only showed significantdifferences in group 4 (Fig. 6). An increase in leg stiff-ness caused an increase in the amount of energy deliveredby the sprung surface and higher mean mechanical powervalues during the positive phase of the drop jump (DJ20

cm: rEsurf 5 0.84,P , 0.01; rPmean surf5 0.88,P , 0.01;DJ40 cm: rEsurf 5 0.84,P , 0.01; rPmean surf5 0.90,P ,0.01). The total mechanical power (subject plus surface)during the positive phase of the drop jump had the bestvalues in group 3 (Fig. 6). The loss of energy duringground contact due to the visco-elasticity of the sprungsurface was about 246 8.2% of the energy transmitted tothe surface (Figs. 6 and 7). All four groups showedsignificant differences in the joint moments as well as inthe mechanical power of the ankle and the knee joints(Fig. 8). At the ankle joint the highest values wereachieved in groups 3 and 4. At the knee it was in groups1 and 2. Clear differences in the amplitude of the changein knee angle could be seen (Figure 8). The amplitudedecreased continuously from group 1 to group 4.

The preactivation time of the analyzed muscles was notgreatly influenced by the different movement execution(Tables 3 and 4 and Fig. 9). The IEMG during preactivationshowed clear differences (Tables 5 and 6). Groups 3 and 4showed higher values than groups 1 and 2. At the dropjumps from 20 cm height, a significant relationship betweenleg stiffness and IEMGPA of the gastrocnemius lateralis (r5

FIGURE 8—Maximum moment at the ankle and knee joints (MAnkle max, MKnee max), maximum mechanical power at the ankle and knee joints(P

Ankle max, PKnee max), and change in ankle and knee angles (DQAnkle, DQKnee) during drop jumps on a sprung surface (mean6 SD, N 5 10). (1)

Statistically significant (P < 0.05) difference between group 1 and group 2, group 1 and group 3, and group 1 and group 4; (2) statistically significant(P < 0.05) difference between group 2 and group 3, and group 1 and group 4; (3) statistically significant (P < 0.05) difference between group 3 andgroup 4.

TABLE 3. Preactivation time during drop jumps from 20 cm [Mean (SD), N 5 10].

Muscle Group 1 Group 2 Group 3 Group 4

Gastr. lat.[ms] 72 (48) 90 (46)1 108 (44)1 114 (43)1

Gastr. med.[ms] 128 (34) 147 (44) 150 (36) 154 (32)Tib. anter.[ms] 125 (68) 93 (73) 66 (73) 47 (45)1

Vast. lat.[ms] 50 (43) 68 (49) 81 (41) 102 (55)1

Hamstr.[ms] 99 (34) 119 (24) 124 (34) 113 (29)1 Statistically significant (P , 0.05) difference between group 1 and group 2, group 1 and group 3, and group 1 and group 4.2 Statistically significant (P , 0.05) difference between group 2 and group 3, and group 2 and group 4.3 Statistically significant (P , 0.05) difference between group 3 and group 4.

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0.53, P , 0.01), gastrocnemius medialis (r5 0.55, P ,0.01) and the vastus lateralis (r5 0.71,P , 0.01) could beestablished. In drop jumps from 40 cm a similar relationshipwas found between leg stiffness and IEMGPA of the gas-trocnemius lateralis (r5 0.53, P , 0.01) and the vastuslateralis (r5 0.71,P , 0.01).

DISCUSSION

In drop jumps on a sprung surface, leg stiffness, anklestiffness, and knee stiffness during the negative phase can beapproximated using three springs (one linear and two rota-tional springs). This is illustrated by the high linear rela-tionship between force and change in position of the centerof mass and between moment and change in angle (Tables1 and 2 and Fig. 3). The stiffness of the lower extremities ofthe athletes was changed by giving the instruction “jumphigh faster.” Also, changes in the level of muscle activationduring the preactivation phase were observed. Basing onthese findings, it can be argued that the athletes developeda higher muscle activation in response to the given instruc-tion. This higher muscle activation caused changes in thestiffness of the lower extremities, and this way also causedhigher maximal ground reaction forces and lower verticaldownward displacement of the center of masses duringground contact, as well as shorter contact times. Theseresults are in accordance with those reported by Nigg andLiu (24). Nigg and Liu (24) studied the effect of musclestiffness on impact forces during running by means of asimplified model of the human body. They found that in-

creasing stiffness also increases impact forces and lowersthe maximal vertical displacement of the upper body.

The leg stiffness is influenced by both ankle and kneestiffness (Tables 1 and 2). The correlations between leg andjoint stiffness are higher at the knee (DJ20 cm: rAnkle 50.52,P , 0.01, rKnee5 0.69,P , 0.01; DJ40 cm: rAnkle 50.18, NS, rKnee 5 0.74,P , 0.01). It seems as if the kneejoint plays a very important role in adjusting leg stiffness.This assumption is supported by the relationship betweenleg stiffness and the IEMG during the preactivation phase ofthe gastrocnemii and the vastus lateralis. Also the changes inthe joint angles, due to the different performances of thedrop jumps, are higher at the knee than at the ankle (Fig. 8).These results are in accordance with those presented byStefanyshyn and Nigg (27), Derrick et al. (7), and Aram-patzis et al. (4). Arampatzis et al. (4) reported that up toa running velocity of 6.5 m·s-1, leg stiffness is mainlyinfluenced by changes in knee stiffness. Stefanyshyn andNigg (27) found greater differences in both energy absorp-tion and energy production at the knee joint between run-ning and sprinting. Derrick et al. (7) reported that the stridelength has a greater influence on the energy absorption at theknee joint in comparison to the ankle joint.

The leg stiffness has a positive influence on the amount ofenergy stored in the sprung surface and hence in the amountof energy flowing back during the positive phase (Fig. 6).The energy transmitted to the sprung surface is 25–45% ofthe total body energy decrease experienced by the subjectduring the negative phase. The amount of energy flowingback from the sprung surface to the subject is between 20%

FIGURE 9—Normalized EMG-activation during drop jumps on a sprung surface (N 5 10, the x-axis is normalized as follows:2100 until 0%represents the flight phase, 0 until 100% represents the support phase).

TABLE 4. Preactivation time during drop jumps from 40 cm [Mean (SD), N 5 10].

Muscle Group 1 Group 2 Group 3 Group 4

Gastr. lat.[ms] 81 (28) 82 (39) 90 (44) 98 (32)Gastr. med.[ms] 125 (35) 160 (32) 140 (32) 145 (42)Tib. anter.[ms] 124 (73) 119 (59) 154 (62) 96 (70)Vast. lat.[ms] 52 (48) 52 (27) 70 (57) 59 (22)Hamstr.[ms] 124 (38) 115 (50) 109 (28) 118 (43)

1 Statistically significant (P , 0.05) difference between group 1 and group 2, group 1 and group 3, and group 1 and group 4.2 Statistically significant (P , 0.05) difference between group 2 and group 3, and group 2 and group 4.3 Statistically significant (P , 0.05) difference between group 3 and group 4.

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and 35% of the total energy delivered to the human bodyduring the positive phase. In spite of this, the total bodyenergy and the vertical take-off velocity of the center ofmass don’t differ significantly in the first three groups. Infact, group 4 shows the lowest values for both parameters.The reason is that in group 4 the energy delivered by thesubject during the positive phase was considerably lower(Fig. 6). These results show: a) the maximization of thevelocity of the center of mass and of the total body energyat take-off is not achieved by maximizing the energy trans-mitted to the sprung surface, and b) there are diverse per-formance strategies leading to a maximization of the take-off velocity and the maximal total body energy at take-off.Anderson and Pandy (1) found a similar phenomenon withinthe muscle-tendon-complex by means of a simulation modelof countermovement jumps. An increase in the energy trans-mitted to the tendon led to a reduction of the energy pro-duced by the contractile elements. The achieved jump heightremained almost the same (1). Also Voigt et al. (29) werenot able to find any correlation between the total positivework done or the jump height and the energy transmitted tothe tendons during drop jumps. Our results differ from thosereported by Sanders and Allen (26). Sanders and Allen (26)measured higher jump heights during drop jumps on asprung surface when reducing the energy absorbed by thesubject during the negative phase and through an increase ofthe energy transmitted to the sprung surface. This relation-ship could not be confirmed in this study (Figs. 5 and 6).

The mean and maximal total mechanical power during thepositive phase of the drop jumps are influenced by leg stiffnessand show highest values in group 3 (Fig. 6). This indicates thatthere is an optimal leg stiffness value to maximize the mechan-ical power during the positive phase of the drop jumps on avisco-elastic sprung surface. The increase in total mechanicalpower seen until group 3 results from the higher mechanicalpower of the sprung surface (Fig. 6). On the other hand, thedecrease seen in group 4 results from the lower mechanicalpower achieved by the subject. The produced mechanicalpower decreases considerably (mostly at the knee joint, Fig. 8).

This means that the total mechanical work and the total me-chanical power are dependent on both the behavior of theenergy storing system (sprung surface) and the behavior of theenergy producing system (subject).

The preactivation times of the studied muscles did notchange in relation to the changes in leg stiffness (Tables 3 and4 and Fig. 7). The IEMG of the preactivation phase showeddifferences and was related to the leg stiffness (Tables 5 and 6).This may indicate that not the amount of time of the preacti-vation but rather the activation level causes the change in legstiffness. Although it is possible to change leg stiffness byaltering the body geometry at touch down (11), this is not thefact in this study because no differences in ankle, knee, or hipangles could be found between the four groups. Nielsen et al.(22) also reported that ankle stiffness was dependent on theamount of muscle activity during plantar flexion. Anyway, thehighest mechanical power values are not achieved by a max-imal activation of the leg muscles. For example, the gastroc-nemius medialis and the vastus lateralis showed the highestIEMG during the preactivation phase in group 4 (Tables 5 and 6).The take-off parameters of group 4 were lower than those of group3 (Fig. 6). It appears that maximization of mechanical power is notachieved by a maximum activation but rather an optimum acti-vation of the leg muscles during the preactivation phase.

From this we can conclude: The leg stiffness during dropjumps on a sprung surface can be controlled through thecontact time. The energy transmitted to the sprung surface,the energy produced by the subject during the positivephase, and the total mechanical power during the positivephase during drop jumps are influenced by leg stiffness. Anincrease in leg stiffness causes an increase in the energytransmitted to and recovered from the sprung surface andsimultaneously a decrease in the energy produced by thesubjects. Therefore, it is possible to achieve maximal verticaltake-off velocity of the center of mass and maximal take-offbody energy by creating different levels of leg stiffness. Themaximization of mechanical power is achieved by optimal legstiffness values and by the amount of activation of the legmuscles during the preactivation phase.

TABLE 5. Integrated EMG during the preactivation phase of the drop jumps from 20 cm [Mean (SD), N 5 10].

Muscle Group 1 Group 2 Group 3 Group 4

Gastr. lat.[% s] 1.42 (0.98) 2.75 (1.84)1 3.62 (1.56)1,2 3.60 (1.52)1,2

Gastr. med.[% s] 3.83 (2.00) 4.31 (2.10) 6.71 (2.47)1,2 7.87 (2.1)1,2

Tib. anter.[% s] 4.08 (2.10) 3.74 (2.28) 5.77 (3.40) 4.68 (2.24)Vast. lat.[% s] 0.92 (0.40) 1.19 (0.58) 2.31 (1.22)1,2 2.97 (1.09)1,2

Hamstr.[% s] 2.49 (1.70) 4.27 (2.21)1 5.26 (2.72)1 5.02 (2.28)1

1 Statistically significant (P , 0.05) difference between group 1 and group 2, group 1 and group 3, and group 1 and group 4.2 Statistically significant (P , 0.05) difference between group 2 and group 3, and group 2 and group 4.3 Statistically significant (P , 0.05) difference between group 3 and group 4.

TABLE 6. Integrated EMG during the preactivation phase of the drop jumps from 40 cm [Mean (SD), N 5 10].

Muscle Group 1 Group 2 Group 3 Group 4

Gastr. lat.[% s] 1.76 (0.69) 2.56 (1.71)1 2.40 (1.15)1 3.01 (1.22)1

Gastr. med.[% s] 4.86 (1.69) 5.51 (2.64) 5.26 (1.50) 6.41 (1.60)1,3

Tib. anter.[% s] 4.60 (2.54) 4.36 (2.46) 3.53 (2.11)1 3.43 (1.94)2

Vast. lat.[% s] 1.65 (0.40) 1.97 (0.89)1 1.73 (0.72)1 2.34 (0.75)1,2,3

Hamstr.[% s] 3.32 (1.80) 3.32 (1.77) 3.67 (1.98) 4.24 (2.61)1 Statistically significant (P , 0.05) difference between group 1 and group 2, group 1 and group 3, and group 1 and group 4.2 Statistically significant (P , 0.05) difference between group 2 and group 3, and group 2 and group 4.3 Statistically significant (P , 0.05) difference between group 3 and group 4.

930 Official Journal of the American College of Sports Medicine http://www.acsm-msse.org

Address for correspondence: Adamantios Arampatzis,German Sport University of Cologne, Institut for Biomechanics,

Carl-Diem-Weg 6, 50933 Cologne, Germany; E-mail: Arampatzis@hrz.dshs-koeln.de.

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APPENDIX. Nomenclature.

DSz subj : vertical displacement of the subject’s center of mass relative to the sprung surface during the downward movement of the center of massEsurf : strain energy of the sprung surfaceEsubj : energy (mechanical work) of the subjectEtot : total energy (mechanical work) (surface plus subject)Eloss : energy loss in sprung surfacePsurf : mechanical power of the sprung surfacePsubj : mechanical power of the subjectPtot : total mechanical power (surface plus subject)Ebody TO : total energy of the human body at take offVz TO : vertical take off velocity of the subject’s center of massnegative phase : From touch down until maximal compression of the sprung surfacepositive phase : From maximal compression of the sprung surface until take offDQAnkle, DQKnee : change in ankle and knee angles from touch down until maximal joint flexion

LEG STIFFNESS AND MECHANICAL ENERGY Medicine & Science in Sports & ExerciseT 931