)OURNALO( APPLIED BIOMCCHANItS, T9%. U. J38-J5a© l')% hy Human Kinelics Publishers. Inc.

Differences BetweenOne-Foot and Two-Foot

Vertical Jump Performances

Peter F. Vitit and Richard N. Hinrichs

The purpose of this investigation was to quantify the differences between one- andtwo-f[X)i venical jumping performances. Fourteen subjects peribnned both jump styieswilh a four-step, self-paced approach. While overall jump and reach height weresimilar hetween one-fool and iwo-foot jumps, the strategies employed to achieve ihe.seresults were nolahly differetit. One-f(H)t jumps benefited from tin increased takeoffheight that was largely aitribuiahle to ihe elevalion of the free swinging leg. Further, itwas suggested thai the actions of this limb may have helped slow the rate of exteasionof tiie support leg during the propulsion phase. Greater flight heights were achievedduring two-fmtt jumps, as expected, but the magnitude of this difference was onlyaboul 9 cm. Il was suggested that factors assix-iated with Ihe development of musculartension, vertical velocity at touchdown, and horizontal approach speed may have allcontributed to the unexpecledly small differences hi flight height between one-footand two-foot jumping performances.

Jumping is a fundamental aspect of several sports including ba.sketball. volleyball,and irack and field. In addiiion. venical jumping ha.s often been used as a cmde melhodforevaluuting anaerobic muscle power(Fox, Bowers. & Foss, 1988; Sargent. 1921). Thus,jumping has received a great deal of attention from researchers in biomechanics and physi-ology. A va.sl body of literature has documented numerous investigations of jumping me-chanics and the determinant factors o! jumping performance. While several researchershave examined biomechanical aspects of either one-foot vertical jumping (Dapena, 1980a,1980b; Dapena & Chung. 1988; Dapena. McDonald. & Cappaert, 1990) or two-foot ver-tical jumping (Ae & Shibukawa, 1980; Bobbert, Mace, Schinkelshoek, Huijing. & IngenSchenau. 1986; Coutts, 1982; Harman. Rosenstein. Frykman. & Rosenstein, 1990; Komi& Bosco. 1978). few have specifically investigated the differences between the Iwo styles.Therefore, the purpose of this investigation was to quantify the differences between one-and two-foot maximum effort vertical jumping performances. It was expected that one-foot jumps would benefit from ihe actions of the free swinging leg during the groundsupport phase and from the elevation of this limb at the instant of takeoff. Two-foot jumps,with essentially twice the available leg musculature to produce vertical impul.ses againstthe ground, were expected to produce greater vertical velocities at takeoff and, therefore,greater elevations of the whole body center of mass (CM) during the flight phase.

The authors are with the Exercise and Sport Research Institute, Arizona State University,Tempe. AZ 85287-0404.

338

Vertical lump Performances 339

Review of Literature

Soest, Roebroek. Bobbert., Huijing. and Ingen Schenau (1985) compared one- and two-foot vertical jumping performances among 10 competitive male volleyball aihletes. Alljumps were performed from a standing start with a countermovement but without the useof an arm swing. In one-foot jumps, swinging ofthe contralateral leg was prohibited. Onewould expect that one-foot jump heights would be half the value of two-foot jump heightssince only half of the total leg musculature is allowed to produce vertical impulses againstthe ground. However. Soest etal. concluded that one-foot jump height was 58.5% of two-fool jump height—a value significantly greater than 509c. The authors suggested that thedifference between one- and two-foot jumps was attributable to a neural mechanism thatinhibited the expression of maximal strength during the iwo-foot jumps (Soest etal.. 1985).This inhibiting mechanism, sometimes called the "bilateral deficit." has also been demon-strated in more simple tasks including unilateral versus simultaneous bilateral isometricleg extension activities (Howard & Enoka. 1991; Koh, Grabiner, & Clough. 1993; Schantz,Muritani. Karlson, Johansson. & Lundh, 1989; Vandervoort. Sale, & Moro/.. 1984).

Saunders {1980) examined the effects of approach speed on one- and two-foot ver-tical jump performances. In the study, 3 volleyball players and 3 basketball players wereasked to complete two-foot and one-foot jumps, respectively. During each of 10 jumps,athletes were asked to initiate approach runs of various speeds. These approach runs wereexpressed as a percentage of each athlete's maximum sprinting speed. Saunders (1980)concluded that vertical velocities of two-foot jumps increased with approach speeds up to50-60% of maximum sprint speed. Similariy. vertical velocities of one-foot jumps in-creased with approach speeds up to 60-70% of maximum sprint speed. In both cases,vertical jump peribrmances decreased after the "optimal" approach speeds were exceeded.Dapena et al. (1990) reported similar decrements in high-jump performances when opti-mal approach speeds were exceeded.

In general, however, studies have shown that vertical jump performance increaseswhen an approach run precedes the jump. Healy (1977) reported that one-half-step andtwo-step approaches yielded significantly greater vertical jump heights than did jumpsperformed without an approach. Overall, il was found that the two-.siep approach yieldedthe greatest jump height compared to the other approach conditions. Kayambashi (1977)reported that three-step and four-step approaches resulted in greater jump heights than didtwo-step approaches. Similarly, Enoka (1971) reported that jumps following approachruns of one. three, and five steps resulted in higher jump and reach scores than jumpsinitiated from a standing position.

With regard to more conventional standing two-foot vertical jump performances,several researchers have demonstrated that a properly performed countermovement willcontribute to significant increa.ses in jump height (Asmussen & Bonde-Petersen. 1974;Cavagna. Dusman. & Margaria, 1968; Harman et al., 1990; Komi & Bosco, 1978). Dur-ing the descent of the countermovement, the hips, knees, and ankles are flexed into posi-tions which stretch the muscles that will later act to extend those same joints. It has beentheorized that besides improving the force-producing capacities of the muscle itself, thecountermovement utilizes some of the elastic properties of muscles and tendons (Bobbertet al., 1986; Komi & Bosco, 1978); increases the distance over which force can be ex-erted, thereby prolonging the upward propulsion phase (Anderson & Pandy, 1993; Pandy& Zajac. 1991; Zajac, 1993); and takes up some ofthe mu.scular slack that is associatedwith the initial stages of the development of muscular tension {Ingen Schenau, 1984;Zajac, 1993).

340 Vint and Hinrichs

Dapena and Chung (1988) noted that during one-foot high-jump performances, ver-tical velocity ofthe CM was positive throughout all but the first 0.01 s ofthe takeoff phaseof the jump. The fact that the CM moved upward despite continued flexion of the supportleg seemed to indicate that the mechanism by which one-foot jumps load the support legmusculature is not at all similar to the traditional counlermovement action that is oftenperformed during two-foot jumps. Rather, Dapena and Chung (1988) suggested that one-foot jumps may have derived a beneficial eccentric loading effect from the radial motionof the CM moving over the base of support. The radial motions of the segmental andwhole-body centers of mass, with respect to the support foot, may have helped developfaster eccentric or slower concentric conditions of the support leg musculature. This wouldhave helped maintain the active musculature in a more favorable region of the force-veloeity relationship (Fenn & Marsh. 1935; Komi. 1973: Perrine & Edgerton, 1978).

Deterministic Factors of Vertical Jumping

In a maximal-effort venical jump performance, the goal of the ta.sk is simply to jump andreach as high a.s possible. In the absence of air resistance and other external forces, theupward projection of the whole-body CM is completely determined by the vertical veloc-ity at the instant of takeoff and the acceleration due to gravity. However, this quantity doesnot completely describe ihe overall jump and reach height thai is observed.

A simple deterministic model (Hay & Reid, 1988) can be used to show that themaximum heighl to which an individual can jump and reach may be described by ihe sumof four lesser heights: takeoff height, flight height reach height, and loss height (see Fig-ure I). Takeoff height may be defined as the height of the CM at the instant the individualleaves the ground. Flight height refers lo the actual height to which the CM is elevatedduring the in-llight phase of the jump. Reach height describes the veriical distance fromthe CM to the fingertips at the instant the maximum jump and reach height is evaluated.Loss height refers to the difference between the peak height ofthe CM and the height ofthe CM at the instant the maximum jump and reach height is evaluated. This last factorcan usually be attributable to a mistiming ofthe final reach.

In standing two-foot vertical jumps (with arm swing and countermovement), take-off height, flight height, and reach height account for4l*3i. 17%, and 42% ofthe overalljump and reach height. re.spective!y. Loss height is negligible, accounting for about 0.2%of the overall jump and reach height (Hinrichs & Vint, 1994). It may be surprising to notethat the contribution of flight height is so much smaller than that of takeoff height andreach heighl. Regardless, it is clear that an overwhelming percentage of the overall jumpand reach height is determined not by the vigorous muscular effort required to propel thebody upward but simply by the position and orientation ofthe body about the CM at theinstant of takeoff and again when the maximum height is evaluated.

Procedures

Fourteen male physical education students (mean age 22.5 years; height 181.6 cm andmass 80.1 kg with shoes on) volunteered to participate as subjects in the experiment. In-formed consent was obtained from each subject prior to testing. Following a brief warm-upand stretching period, each subject was asked to perform a block of five one-foot and fivetwo-foot maximum-effort vertical jumps. For both jump styles, subjects were allowed to usea four-step, self-paced approach run-up. Jump iind reach heights were measured for each trialusing a simple vertical jump height measuring device (Vertec, Sports Imports, Columbus,OH). Subjects were asked to jump and reach as high as possible and contact the Vertec with

Vertical Jump Performances 341

Jump and ReachHeight

Takeoff Heighl Flight Height Reach Height Loss Heighl

Jump and Reach

Height FlighiHeight

CM

Takeoff Height

Reach Height

Figtire I — Deterministic model and illustration of simple factors that determini; overall jumpand reach height (following guidelines of Hay & Reid, 1988). Note that relative proportions ofthe four subheight.s are drawn approximately to scale. Refer to Table I for exact proportions.From "Vertical ,|umping Performance: One-Foot Vs. Two-Foot Takeoff Techniques," byP. Vint, 1996. Performance and Conditioning for Volleyball, 3, pp. 4-7. Copyright 1996 byConditioning Pre.s.s, P.O. Box 6819, Lincoln, NE 68506.

their dominant hand. For each jump style and for each subject, the trial that yielded thehighest measured jump and reach height was considered for further analysis.

Two-dimensional video data were collected at 60 Hz in the sagittal plane. A Panasonicmodel D5100 video camera was placed approximately 30 ni away from the subjects in aneffort to reduce perspective error. Selected jumps were digitized with the Peak Perfor-mance motion measurement system (Englewood, CO). Digitizing began approximately10 video fields before the last heei strike of the approach and ended approximately 10video fields after the vertical jump and reach measurement device was contacted. If. dur-ing two-foot jumps, subjects planted one foot and then the other, digitizing was initiatedapproximately 10 video fields before the final heel strike ofthe first foot to contact theground. This asynchronous foot planting technique (termed the "step-close" technique byCoutts, 1982) was observed to be the norm rather than the exception.

Mathematical Model and Body Segment Parameters

Twenty-one points were used to define a 14-segment model ofthe body. In addition, thefingertip ofthe dominant hand was digitized at the in.stant the Vertec was contacted. Seg-

542 Vim and Hinrichs

mental masses and center of mass locations obtained from the mean data of Clauser,McConville. and Young (1969) as adjusted by HinHchs (1990) were used to compute thewhole-body CM location throughout the entire trial. The centers of mass for various sys-tem.s of segments were computed from the general equation:

P=(Im,P,)/(Sm,) (1)

where m, is the mass of the i"" segment, and P, and P are the vectors locating the centers ofmass of the i'" segment and the system of segments, respectively, relative to the fixedO;XY reference frame. The various systems of segments that were defmed in this studyincluded the head and trunk, right arm, left arm, both ann.s, right leg, left leg, both legs,and ihe whole body.

Smoothing and Differentiation

Raw two-dimensional data were rotated into a true vertical-horizontal lab reference frame.To reduce the endpoint effects of the Butterworth digital filter, all coordinate data werepadded with 20 points on either side of the original array using a linear extrapolationscheme (Smith, 1989). Horizontal (X) and vertical (Y) coordinates of each data pointwere smoothed with a fourth order, zero-lag Butterworth digital filter (Winter. Sidwell. &Hobson. 1974). Cutoff frequencies ranged from 3.25 to 9.75 Hz and were selected auto-matically by an algorithm ba.sed on the method of Wells and Winter (1980). All velocity

& Nelson. 1973). Velocity data were not subjected to further smoothing.

Kinematic Factors

Takeoff height, flight height, reach height, and loss height were calculated using the ver-tical position ofthe CM at the appropriate events. Average horizontal approach speed wascalculated over approximately the last O.I s prior to the final heel strike of the approach.Similarly, average horizontal fiight speed was calculated over approximately the last 0.1 sprior to the instant the Vertec was contacted.

Segmental Contributions to Lift

The relative momentum approach of Ae and Shibukawa (1980) was used to determine thecontributions ofthe arms, head and trunk, and legs to the change in vertical momentum ofthe body during the propulsion phase of the jump. The change in vertical momentum willbe hereafter referred to as "lift" and will be used to represent the net impulse from the verticalforces over the propulsion phase (Hinrichs, Cavanagh, & Williams. 1987). For both jumpstyles, the propulsion phase was defined by the interval between the instant of zero verticalvelocity of the CM during the ground support phase and the instant of takeoff.

The relative momentum for each ami, each leg, and the head and trunk were com-puted as follows:

+ m VssN/H + m^ (2)

+ m^VH (3)

(4)

^^ (5)

Vertical Jump Performances 343

where m represents mass, v represents velocity, and the subscripts A and T denote thearms, and the trunk and head, respectively. Equation 2 was used to compute the relativemomentum of the right and left arms separately. For each leg during two-foot jumps, andfor the support leg during one-foot jumps, relative momentum was calculated from Equa-tion 4, where the subscripl SL denotes the support leg. For the free swinging leg duringone-foot jumps, relative momentum was calculated from Equation 5, where the subscriptFL denotes the free swinging leg. The subscripts SSN and H, preceded by a slash, wereused to indicate the velocities relative to the supersternale and hips (midpoint between theright and left hip), respectively (e.g., v / j;; describes the relative velocity of the center ofmass of the entire arm segment with respect to the supersternale).

In Equations 2-5, the terms with a solid underline were considered to be the mo-mentum generated by the support leg or legs, while those with a dotted underline definedthe momentum generated by the trunk. The arms were left only with the momentum asso-ciated with the motion of the arms relative to the supersternale (m^v^ssN)' During one-footjumps, the momentum of the free swinging leg was determined solely by the relativemotion of the free swinging leg with respect to hips (mpLVpuH). Rather than using themidpoint of the shoulders {Ae & Shibukawa, 1980) or the chin-neck intersect (Hinrichs eta!., 1987), we designated the supersternale as the reference point for defining the relativemotion of the arms. This assignment was more consistent with the chosen set of bodysegment parameters (Hinrichs, 1990). Further details about the methods involved in deter-mining the relative segmental contributions to vertical impulse may be found in Ae andShibukawa (1980) and Hinrichs et al. (1987).

Radial and Vertical Motions

In order to investigate the mechanisms responsible for loading the support leg muscula-ture, we analyzed the radial and vertical motions of the body throughout the ground sup-port phase. The radial motion methodology was adapted from Dapena and Chung (1988)to accommodate an analysis of one-foot and two-foot jumps.

Analysis of the radial motions of the segmental and whole-body centers of massdependsonthedefinitinnof a single hinge point over which the body rotates. For one-footjumps, the hinge point was defined by the average of the X coordinates of the heel and toeof the support leg when the foot was firmly planted on the ground (Figure 2a). For two-foot jumps, the hinge point wa.s defined by the average of the X coordinates of the heeland toe points of both feel when they were both firmly planted on the ground (Figure 2b).For both jump styles, the Y coordinate of the hinge point was defined as zero throughoutthe duration of the support phase.

Throughout the duration of the ground support phase of the jump, the radial direc-tion vector was defined by a segment that originated at the hinge and terminated at thewhole-body center of mass. Position vectors were defined from the hinge to the centers ofmass of each of the various systems of segments. In addition, for one-foot jumps, a posi-tion vector was defined from the hinge to the hip of the support leg. For two-foot jumps, asimilar vector was defined from the hinge to the midpoint of the right and left hip. Themagnitude of each position vector was projected onto the radial direction vector using thedot product relationship. This projected magnitude was defined as the radial distance foreach of the segments or points of interest. Radial velocities were obtained from finitedifference differentiation of the radial distance arrays. The radial velocity of the whole-body center of mass may be described by the sum nf the radial velocities of the individualsystems of segments. Therefore, segmental contributions to the radial velocity of the whole-body center of mass (VRf;) were determined by the relationship shown in Equation 6:

Vint and Hinrichs

Figure 2 — Stick figure rcpresenlations of typical (a) one-foot and (b) two-foot jumpperformances (representative subject left-handed). Horizontal spacing between adjacent .stickligure.s has been exaggerated lor clarity. Trajectory of whole-b<Kly center nf mass has beenoverlaid on .stick figure profiles. Tnsets illu.strate location of hinge point during ground supportphase for typical (al one-foot jump and (bl two-foot jump performances. Fnim "VerticalJumping Performance: One-Foot Vs. Two-Foot Takeoff Techniques." by P. Vint. 1996,Performance and Conditioning for Volleyball, 3, pp. 4-7. Copyright 1996 by Conditioning Press,P.O. Box 6819, Lincoln. NE 68506.

Vertical Jump Performances 345

VR 3 = I(V,,-mi/M) (6)

where V, , represents the radial velocity of the center of mass of the i"" system of seg-ments, mi represents the mass of the i"' system of segments, and M represents the wholebody mass (Dapena & Chung, 1988). The m /M term in Equation 6 is included to ensurethat the segmental contributions to the whole-body radial velocity are weighted appro-priately.

Statistical Analysis

Matched-pairs / tests were performed on selected means to detect significant differencesbetween one-foot and two-foot jumping performances (SPSS, Chicago, IL). Twenty-fivestatistical tests were conducted in all. In an effort to compromise between the effects ofType I and Type II errors, the overall, experiment-wise confidence level was chosen at0.10. The Bonferroni procedure (Stevens. 1990) was used to adjust the confidence levelft)r each test from 0.1 to 0.0042 (the latter derived from I - [ 1 - 0.11"-').

Results

Table I summarizes some of the basic performance characteristics of one-foot and two-foot jumps. Both the absolute and relative magnitudes of these deterministic factors weresimilar to those observed for standing two-foot jumps (Hinrichs & Vint, 1994). Takeoffheight was significantly higher in one-foot jumps, while flight height was significantlyhigher for two-foot jumps. Overall jump and reach height, reach height, and loss heightwere not different between jump styles (p = .7, .9, and .07, respectively).

Mean horizontal approach velocities were 3.77 ±0.41 m • s' and 3.41 ± 0.55 m • s ' forone-foot and two-foot jumps, respectively. Although one-foot jumps tended to be some-what faster, the difference between jump styles was not statistically significant(p = .06). Compared to two-foot jumps, one-foot jumps carried significantly more hori-zontal velocity into the flight phase (/? < .0042). Horizontal fiight velocity was 1.88 ±0.1m • s"' for one-foot jumps and 1,01 ± 0.22 m • s ' for two-foot jumps.

Table I Mean and STD Values (in meters) for Basic Deterministic Factors of VerticalJumping During One- and Two-Foot Jumps, Plus Percentages of Overall Jump andReach Height

One-foot Two-footM STD % M STD %

Overall height 3.08 0.11 100.0 3.07 0.10 100.0Takeoff height 1.34 0.06 43.5 1.24* 0.05 40.4Flight height 0.45 0.06 14.6 0.54t 0.08 17.6Reach height 1.29 0.05 41.9 1.29 0.04 42.0Loss height 0.003 0.003 0.0 0.006 0.006 0.0

Note. Statistical tests were only performed on the absolute height values. *Two-footsignificantly less than one-foot (j) < .0042). tTwo-foot significantly greater than one-foot

346 Vint and Hinrichs

Table 2 Mean and STD Values for Segmental Contributions to Lift During PropulsionPhase of Jump (Values Expressed in Absolute Units and as Percentages of Total Whole-Body Lift)

Whole bodyHead and trunkReach armLowered armSum of armsSupport leg(s)Free swinging legSum of legs

Absolute lift (N • s)

One-footM

234.5020.016,648.99

15.62207.55-8.00*

199.55

STD

26.4623.715.512.456.72

23.077.94

23.91

Two-footM

259.43-19.21*

7.842.50*

10.34268.911NA268.9 It

STD

29.7316.674.515.228.46

30.17

30.17

Percentage of total lift (%)

One-footM

100.008.102.783.856.64

88.96-3.3885.58

STD

0.009.782.241.092,728.983.329.93

Two-footM

100.00-7.51

3.010.913.92

103.83NA103.83

STD

0.006.481.691.973.255.78

5,78

Note. Statistical tests were only performed on the absolute lift values, *Two-foot signifi-cantly less than one-foot (p < .0042). tTwo-foot significantly greater than one-foot (p <.0042). |One-foot significantly less than zero (p < .0042).

Segmentat Contributions to Lift

In general, the results of the segmental contribution analysis were in agreement with thefindings of Ae and Shibukawa (1980) (see Table 2 and Figure 3). Although two-foot jumpstended to produce greater lift during the propulsion phase than did one-foot jumps, thisdifference was not statistically significant (p = .02).

The arms contributed vei7 little to total lift, yielding only about 7% and 4% duringone-foot and two-foot jumps, respectively. For both jump styles, the greatest contribu-tions to lift were derived from the legs. Surprisingly, during one-foot jumps, the free swing-ing leg actually had a slightly negative contribution to lift (-3.38 ± 3.32%). In almostevery circumstance, this was attributable to the sign of the mpLVpL*,, term (Equation 5)switching from a positive value at the beginning ofthe propulsion pha.se (just after touch-down) to a negative value at the Instant of takeoff. For two-foot jumps, the combinedcontributions ofthe legs actually exceeded 100%. This was made possible by the negativecontribution of the head and trunk.

Vertical and Radial Motions

The radial distance and radial velocity profiles were very similar between jump styles(see Table 3 and Figures 4 and 5). For both one- and two-foot jumps, the radial distancedecrea.sed to a minimum value during the first half of the ground .support phase and thenincreased until takeofl. This trend resulted in highly negative radial velocities at heel strikethat gradually increased to zero and finally reached highly positive values at takeolT.

In contra.st. the CM height and vertical velocity profiles demonstrated notabledifferences between styles. One-foot jumps displayed virtually no lowering of the CMduring the ground support phase (mean lowering 0.002 ± 0.003 m). Any decrea.ses in CM

11 .1* . 1 I '

Vertical Jump Performances 347

I

Head and TrunkRighl Arm (non-dominflnt)Lef) Arm |dominanl)Righl Leg (support)Left Leg (free swinging)CM

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

Time (s)

1

350 ,-mv.

Head MKl Trunk

3 0 0 | - _D— Righl Aim (non-dominani)

—o— Left Arm (dominani)_ —a—Sum of Legs

CM

0.00 0.05 0.10 0,15 0.20

Time (s)

0.25 0.30 0.35

Figure 3 — Relative vertical momenta, or lift, during the propulsion phase for typical (a) one-(<M>t and (b) two-foot jumps (representative subject left-handed). Time t = 0.0 s represents thein.stant of (Inal heel strike of the approach. Interval between dotted vertical lines deflnes timeover which lift was calculated (mv ^ = initial vertical momt'ntum; mv = final vertical momentum).

348 Vint and Hitirichs

IIS~" ^^ t/^

c o o c

(N r-1 r —

8 CO -O O— O Ol

o d d o

o o c o

c> a <D ~S (^ d d

o c o

— r-; q r4

•^ P —

d d d d

•5: ^ii U (L>

t:oa.

IT3 C

.2

I. 2 . CQ

1

11 2 —

1s =111

1> t-. o

Vertical lump Performances

a 2.0

1.5

^ 1.0

0.5

0.0

349

0.00

Vertical

Radial

0.05 O.IO 0.15 0.20 0.25 0.30 0.35

Time (s)

b 2.0

1.5

(D 1.0o

0.5

0.0

Vertical

Radial

0.00 0.05 0.10 0,15 0.20 0.25 0.30

Time (s)

0.35

Figure 4 — Radial distance and height of CM throughout ground support phase of typical (a)one-foot and (b) two-foot jump trials (representative subject left-handed). Time t = O.U srepresents the instant of final heel strike of the approach. See Table 3 for definitions of T,,T2,and T,.

Vint and Hinrichs

-30.00 0.05 0.10 0.15 0.20

Time (s)

0.25 0.30 0.35

0.00 0.05 0.10 0.15 0.20 0.25

Time (s)

0.30 0.35

Figure 5 — Radial and vertical velocity of CM throughout ^niund support phase of typical (a)one-fiKit and (b) two-foot jump trials (representative subject left-handed). Time t = 0.0 srepre.sents the instant of final het'l strike of the approach. See Table 3 for dennitioas of T,, T ,and T..

Vertical Jump Performances 351

height that did occur during one-foot jumps did so within the first 0.014 ± 0.018 s afterheel strike. Conversely, two-foot jumps elicited a mean lowering of 0.064 ± 0.023 mthrough the first 0.! 11 ± 0.023 s. Peak negative vertical velocities for one-foot and two-foot jumps during the ground support phase were-0.05 ±0.17 m s ' and-0.93 ± 0.24 m• s"', respectively {p < .(K)42).

At the instant of final heel strike during the approach for two-foot jumps, both theradial and vertical velocitie.s of the CM were negative. One-foot jumps, by contrast, dis-played negative radial velocity but negligible vertical velocity at heel strike. For bothjump styles, the CM was already moving upward with appreciable vertical velocity by thetime the minimum radial distance was achieved. At this time, the vertical velocity for one-foot jumps was about twice that of two-foot jumps. By takeoff, however, the verticalvelocity for two-foot jumps had surpa.ssed that for one-foot jumps.

The relative radial velocity of the CM with respect to the hip of the support leg wasexpected to indicate the state of activity of the support leg musculature. According toDapena and Chung (1988),

For a given radial velocity of the CM. the faster that body segments move radiallyaway from the foot, the faster the hip joint will move radially toward the foot, ortheslower it will move radially away from the foot. Therefore, positive radial motionsof the body segments will put the leg muscles in faster eccentric or slower concen-tric conditions, thus enabling them to exert larger tensions, (p. 293)

Segmental contributions to the radial velocity of the CM were derived from Equation 6and were expressed relative to the radial velocity of the hip (see Figure 6).

For one-foot and two-foot jumps, the radial velocity of the CM with respect to thehip (or hips) (VRC;^,) was negative throughout approximately the first quarter of the groundsupport phase and then remained positive until takeoff. Early in the ground support phasefor one-foot jumps, the sum of the negative contributions of the arms and free swingingleg was greater than the sum of the positive contributions of the head and trunk and thesupport leg. Later, when V^Q^H was positive, the positive contributions of the head andtrunk, the arms, and the free swinging leg outweighed the mode.st negative contributionsof the support leg.

The paitem of segmental contributions to V^ ;,,, was very similar for two-foot jumps.The main differences between jump styles were found in the contributions of the legs.Figure 6b shows that the contribution of the left leg was initially positive and then becamenegative toward the end. This was likely due to the asynchronous step-close foot planttechnique (Coutts, 1982) used by most subjects during two-foot jumps. For example, dur-ing most of the two-foot jump trials, left-handed subjects were found to plant the left footand then the right foot. In a similar manner, right-handed subjects typically employed aright-left foot planting technique.

Discussion

The purpose of this study was to quantify the differences between one-foot and two-footvertical jump performances. Fourteen male subjects were asked to complete maximaleffort one-foot and two-foot vertical jumps using a four-step, self-paced running approach.Two-dimensional video data were used to study jumping performances from the last stepof the approach through the instani that the maximum jump and reach height was reached.

The simple deterministic model presented in Figure I indicates that the overall jumpand reach height depends upon the height and vertical velocity of the CM at takeoff and

352

a

'cfl

sloc

ityR

adia

l

>

1.50

1.25

1.00

0.75

0.50

0,25

0.00

-0,25

Vint and Hinrichs

-0.50

—o— Head and Trunk—Q— Righi Atm {nun-dnmiiumt)—0— Left Ann (dominml)—a— Righi Log (juppon)—V— Left Leg (free swinging)

CM w.r.l. Right Hip

\

0.00 0.05 0.10 0.15 0,20 0.25 0.30 0.35

Time (s)

loci

ty (

>

ladi

al

<u

HI

1.50

1.25

1,00

0,75

0.50

0.25

0.00

-0.25

-0.50

—o— Head and Tnuik—a— Right Arm (nun—o— t.en Arm {dominanl)- i — Rifiht Leg—17— Left Lag^ ^ CM w.r.l Mid-tiip

0.00 0.05 0,10 0,15 0.20 0.25 0.30 0.35

Time (s)

Figure 6 — Segmental contributions to the relative radial velocity of the CM with respect toIhe (a) hip of the support leg throughout the ground support pha.se of a typical one-fotit jumptrial and |b) mid-hip throughout the ground .support pha.se of a typical two-foot jump trial(representative subject left-handed). Time t = 0.0 s represents Ihe instant of Final heel strike ofIhe approach. Positive values indicate segment i.s contributing to slower concentric or fastereccentric conditions of support leg musculature. Negative values indicate segment Ls contributingto a cushioning effect.

Vertical jump Performances 353

upon the position and orientation of the body about the CM at the instant the maximumheight is evaluated. The results of this study indicate that while overall jump and reachheights were similar between one-foot and two-foot jumps, strategies employed to achievethese results were notably different.

During one-foot jumps, subjects benefited from an increased takeoff height thatwas largely attributable to the elevation of the free swinging leg. This conclusion is sup-ported by the fact that at takeoff, the height of the CM of the free swinging leg was 0.35 mhigher than the CM of the support leg. In addition, it appeared that there was a slightlygreater degree of extension in the support leg during one-foot jumps. At takeoff, the aver-age height of the CM of the .support leg (or legs) was 0.74 ± 0.04 m and 0.71 ± 0.03 in forone-foot and two-foot jumps, respectively. During two-foot jumps, subjects were able toachieve greater flight heights, perhaps due to the greater availability of musculature thatcould be recruited tn generate vertical impulse against the ground. This issue will be dis-cussed in greater detail later. Reach heights were virtually identical between jump styles.Loss heights were negligible for both jump styles and were similar in magnitude to thosefound in standing two-foot jump performances (Hinrichs & Vint, 1994). In addition, al-though one-foot jumps carried significantly faster horizontal velocity throughout the in-Illght phase of the jump, subjects did not differ between jump .styles in their ability tocoordinate the final reach with the apex of the CM.

The relative momentum approach of Ae and Shibukawa (1980) was used toquantify segmental contributions to the change in vertical momentum, or lift, during thepropulsion phase of jumping. Although whole-body lift was not statistically differentbetweenjump styles, there was a strong tendency for more lift to be produced during two-foot jumps ip = .02). While this tendency was consistent with the greater flight heightsobserved for two-foot jumps, the lack of significance may be explained as a Type II errorarising from the stringent ex peri ment-wise confidence level (a = .0042).

In general, the legs were the greatest contributors to lift for both jump styles. Thesummation of the lift derived from both legs was about 86% and 104% for one-foot andtwo-foot jumps, respectively. For one-foot jumps, the free-swinging leg was found tohave a negative contribution to lift. While this finding may .seem somewhat surprising, itshould be recalled ihat the lift contributed by the free swinging leg is solely detennined bythe mFLVpuHterm in Equation 5. At the final heel strike of the approach, the relative verti-cal velocity of the free swinging leg with respect to the hip of the same leg was approxi-mately zero. Throughout the majority of the ground support phase, this leg was swingingupward with a velocity greater than that of the hip. However, immediately before takeoff,the free swinging leg decelerated to a speed that was slower than the hip of the same leg(see Figure 3a).

The fact that the free swinging leg had a negative contribution to lift during one-foot jumps does not necessarily mean that it had a deleterious effect on overall perfor-mance. During the time when the free swinging leg was accelerating upward, it wouldhave exerted a downward force on the torso. This downward force would have slowed therate of extension of the support leg. thereby maintaining these muscles in a more favor-able portion of the force-velocity curve and facilitating the development of greater mus-cular tension (Fenn & Marsh, 1935; Perrine & Edgerton, 1978). Near takeoff, the freeswinging leg decelerated and exerted an upward force on the torso. Although this upwardforce would have tended to reduce the force-developing capacities of the support leg mus-culature, it would have done so at a time when the support leg was near full extension andwas in a poor position to develop further propulsive forces. (It is also possible that Ihisupward force was responsible for the slightly greater support leg extension and, hence, the

354 Yini and Hinrichs

increased takeoff height observed during one-foot jumps.) This mechanism has been usedto describe the contribution of the arm .swing during standing two-foot jumps (Harman etal., 1990) and may also be used to account for ihc relatively small contribution ol ihe armsto overall lift in the present study. We therefore suggest that care be taken when interpret-ing result.^ obtained from the Ae and Shibukawa (1980) relative momentum methodology.While this approach is both intuitively and computationally appealing, investigators mustalso consider the dynamic effects of the limbs throughout the activity of interest.

Previously, the radial motion methodology had been used exclusively to study themechanics of the high-jump approach (Dapena & Chung. 1988). In the pre.sent investiga-tion, this methodology was adapted to study the function of the approach during one- andIwo-foot jumps. Although we provided a somewhat different definition for the hinge point,the patterns of the radial motions of segmental and whole-body centers of mass were verysimilar to those presented by Dapena and Chung (1988). While one-foot jumps displayedvirtually no lowering of the CM during the ground support phase, two-foot jumps demon-strated a pattern ol' CM lowering that was consistent with traditional countermovementactions. However, both jump styles displayed highly negative radial velocities at heelstrike that gradually increased to 7£ro and finally reached highly positive values at takeoff. Ithas been suggested that radial velocity profiles are consistent with the well-known stretch-shortening cycle for previously stretched muscle (Dapena & Chung. 1988). If this is true, itappears that both one-toot and two-foot jumps may benefil from this mechanism.

While the radial motions of the CM can provide some information about the gen-eral conditions of the support leg musculature, Ihe radial velocity of the hip of the supportleg can provide a better source of this informalion (Dapena & Chung. 1988). The differ-ence between radial velocity of the CM and radial velocity of the hip is attributable to therelative motion of the body segments about the hip. The relative radial velocity of the CMwith respect to the hip (V f ,) can then be used to understand how various body segmentscontribute lo development of tension in the support leg musculature. Computationally,this is accomplished by expressing both sides of Equation 6 with respect to the radialvelocity of the hip. For both one-foot and two-foot jumps, the initial negative values forVRG/H indicated that the radial motions of the body segments had a net cushioning effectearly in the ground support pha.se (see Figure 6). For one-foot jumps, this was cau.sed bynegative contribulions of the arms and free swinging leg that essentially overrode thepositive contributions of the head and trunk and the support leg. For two-foot jumps, thiscushioning effect was caused by the radial motions of the arms and the first foot to plantduring the ground support phase. It is conceivable that this was one of the reasons whymost of our subjects adopted an asynchronous foot-planting technique in preference to asimultaneous landing technique. Coutts (1982) suggested that while the asynchronous (or"step-close") landing technique does not offer any distinct advantage over the .simulta-neous (or "hop") landing technique in the development of vertical velocity at takeoff, itmay help to reduce peak impact forces and attenuate ihe impact impulse by increasingground contact time. This, in turn, may help to reduce the predisposition for injury. Futurestudies should investigate the advantages and disadvantages of these landing strategies asthey relate to vertical jump performances.

For both jump styles, when V cyn became and then remained positive, radial mo-tions of the body .segments may have helped place the muscles of the support leg (orlegs) in either faster eccentric or slower concentric conditions (Dapena & Chung. 1988).This again would have allowed the leg extensor muscles to develop greater forces andtherefore increase the vertical impulses against the ground. This finding is important inthat it helps to explain the results of previous research demonstrating that vertical jump

Vertical lump Performances 355

performance increases when the jump is preceded by a running approach (e.g., Enoka,1971).

With essentially twice the available leg musculature, two-foot jumps were expectedto demonstrate a clear superiority in the development of vertical velocity at takeoff. How-ever, while the difference between one-foot and two-foot flight height was statisticallysignificant, the magnitude of this difference was only 9 cm or about 179f. Why was thisdifference so small? After all, Soest et al. (1985) demonstrated a difference of nearly 40%in jump height between one-foot and two-foot standing jumps. Although it is impossibleto completely ascertain the source of the unexpectedly small differences in flight height, anumber of explanations for this finding may be plausible.

One of the most obvious explanations for this difference is that the support legmusculature was probably more active during one-toot jumps. Since the weight of thebody was unchanged betweenjump conditions, one-foot jumps would have required oneleg to support the entire body weight. Two-foot jumps, conversely, would have allowedthe weight to be distributed across two legs. This would have resulted in a greater muscu-lar tension, per suppon leg, during one-foot jumps compared to two-foot jumps. It islikely that this inerease in tension would have been due to relatively greater neural activa-tion of the support leg musculature during one-foot jumps.

Soest et al. (1985) suggested that the differences between one-foot and two-footvertical jumps were consistent with ihe literature related to the bilateral deficit phenom-enon. A complete discussion of the manifestations of the bilateral deficit is beyond thescope of the present investigation (for excellent reviews, see Ohtsuki, 1994, and Archontides& Eazey. 1993); however, we will note that a number of investigators have reported thatIhe strength developed during simultaneous bilateral exercise is significantly lower thanthe sum of that developed during unilateral efforts (Howard & Enoka, 1991; Schantz etai., 1989; Vandervoort et al., 1984). In addition, there is evidence suggesting that thebilateral deficit increases with increasing movement speed (Vandervoort et al.. 1984;Vandervoort. Sale, & Moroz, 1987). It has been suggested ihat Ihe bilateral deficit may beattributable to a decreased neural drive that results in an inability to fully recruit large,high-threshold motor units during maximal voluntary contractions (Koh et al., 1993;Vandervoort et al.. 1984, 1987). A closer inspection of the Soest et al. (1985) data revealedthat the angular velocities of the hip and knee were notably greater during two-foot jump-ing performances. Therefore, in addition to eliciting the force reduction that would beexpected from the well-known force-velocity properties of muscle, faster leg extensionsduring two-foot jumps may have also suffered from an increased inhibition in the expres-sion of maximum force due to the nature of the bilateral deficit phenomenon. The.se speed-dependent issues may have played a significant role in the findings of Soest et al. (1985)and should be considered when comparing independent unilateral and simultaneous bilat-eral performances.

In the present study, it was suggested that radial motion parameters would betterindicate the state of the support leg musculature. At takeofT. the radial vel(K;ity of the CMwas significantly faster for two-foot jumps (see Table 3). Therefore, it is conceivable thattwo-foot jumps were subject to decreases in musculature tension that would have beenbrought about by the force-velocity relationship and the movement speed dependence ofthe bilateral deficit. However, during the time when the CM was moving in the positiveradial direction (between times T, and T,), the average radial velocities of the CM were1.86 m • s 'and 1.85 m • .s ' for one-foot and two-foot jumps, respectively. Since the aver-age radial velocities of the CM were virtually identical, it seems unlikely that these speed-related factors played a significant role in limiting two-foot jump performances.

356 Vint and Hinrichs

Another possible explanation for the relatively small difference in flight height isthat one-foot jumps were simply more effective in developing propulsive impulses againstthe ground. One-foot jumps displayed virtually no lowering of the CM during the groundsupport phase. In fact, the magnitude of the peak negative velocity was only -0.05 ± 0.17m s ' andthLs was overcome in the finst 0.014 ±0.018 s after heel strike. Therefore, sincevirtually no effort was required to stop the downward moiion of the CM. more energycould be expended to propel the body upward. Any beneficial effects that may have beenderived from the radial motions of the body would have helped to provide higher impulsesagainst the ground while lhe body was already moving upward. Two-foot jumps, whileprobably deriving eccentric loading effects early in lhe ground support phase from theradial and vertical motions of the body, still had to overcome the downward momentum ofthe body before efforts could be made to directly increase the vertical velocity in thedesired direction. This fact alone may have put the two-foot jumps in a less than idealsituation for propelling the body upward.

Horizontal approach speeds were 3.77 m • s ' and 3.41 m • s ' for one-foot and two-toot jumps, respectively. While these values were not statistically different (p = .06), therewas clearly a trend lor one-footjumps to employ faster approaches. This would imply thatthe kinetic energy carried into the ground support phase would have also tended to begreater for one-foot jumps. If a portion of this increased energy could be stored and subse-tjuently reutilized during the takeoff phase, this would afford one-foot jumps an advan-tage over two-foot jumps. In this study, subjects were allowed to use a four-step, self-paced approach. It i.s conceivable that had subjects been permitted to use an unconstrainedrun-up, there would have been a greater difference in the approach speed and hence in theinitial kinetic energy between Jump styles.

Although the overall jump and reach heights were virtually identical between jumpstyles, the manners in which these results were achieved were notably different. One-foot jumps benefited from an increased takeoff height that was largely attributable tothe elevation of the free swinging teg. Further, it was suggested that the actions of thislimb may have helped slow ihe rate of extension of the support leg during the propul-sion pha.se. This would have resulted in the development of higher muscular tensionsand therefore greater flight heights than would have otherwise been expected. Two-footjumps were expected to produce greater vertical velocities at takeoff and, therefore,greater elevations of the whole-body center of mass (CM) during the flight phase. Al-though greater flight heights were achieved during two-ftx)t jumps, the magnitude of thisdifference was only about 9 cm. Factors associated with the development of musculartension, vertical velocity at touchdown, and horizontal approach speed may have all con-tributed to the unexpectedly small differences in flight height between one-foot and two-foot jumping performances.

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A cknowledgmen ts

We would like to express our sincere thanks to John DeWitt, Tony Marsh, Scott McLean,Rachel Seidler, Chris Sherwood, Dr. Phil Martin, and Steve D" Amico for their assistance throughoutvarious stages of this project. We also wish to thank Dr. James G. Hay from the University of Iowaand Dr. Jesus Dapena from Indiana University for their valuable comments throughout the develop-ment of this manuscript.

Peter Vint is now with the Deptinment of Exercise and Sport Science, University of NorthCarolina at Greensboro, 250 HHP Building, Greensboro. NC 27412-5001. Richard Hinrichs is withthe Exercise and Sport Research Institute, Arizona State University, Tenupe., AZ 85287-0404.