A Biomechanical Analysis of the Last Stride, Touchdown ... · Last Stride, Touchdown, and Takeoff Characteristics of the Men's Long Jump Adrian Lees, Philip Graham-Smith, and Neil

JOURNAL OF APPLIED BIOMECHANICS, 1994,10, 61-78 O 1994 by Human Kinetics Publishers, Inc.

A Biomechanical Analysis of the Last Stride, Touchdown, and Takeoff

Characteristics of the Men's Long Jump

Adrian Lees, Philip Graham-Smith, and Neil Fowler

This study was concerned with the measurement of performance variables from competitors in the men's long jump final of the World Student Games held in Sheffield, England, in July 1991. Several performances of 10 finalists were recorded on cine film at 100 Hz. Resulting sagittal plane kinematic data were obtained for the last stride, touchdown, and takeoff for a total of 27 jumps. It was confirmed that takeoff velocity was a function of touchdown velocity, and that there was an increase in vertical velocity at the expense of a reduction of horizontal velocity. It was concluded that there was evidence for mechanisms which may be termed mechanical, biomechanical, and muscular. The former relates to the generation of vertical velocity by the body pivoting over the base of support during the compression phase, and a lifting of the arms and free leg during the lift phase; the second is the elastic reutilization of energy; and the third is the contribution by concentric muscular contraction.

The long jump is an event that requires an athlete to jump as far as possible from a fast run up into a pit of sand. The distance jumped is largely determined by the flight distance (Hay, 1986), and this is determined by the height, speed, and angle of projection of the center of mass (CM) at takeoff. The speed and angle of projection are determined by the combination of horizontal and vertical velocity. The horizontal velocity is developed through the approach run, which is usually of sufficient length for the athlete to be close to maximum speed at the takeoff board. The vertical velocity is generated during contact with the board. If we assume that the athlete is able to generate maximum speed close to the board, the problem of long jumping becomes one of generating vertical velocity from the board. The adjustments made by the athlete approaching the board enable this vertical velocity to be generated.

The adjustments made by athletes during the latter stages of approach have been consistently reported in recent studies (Bruggemann & Susanka, 1987;

Adrian Lees, Philip Graham-Smith, and Neil Fowler are with the Sports Biomechan- ics Laboratory, School of Human Sciences, Liverpool John Moores University, Liverpool, U.K. L3 3AF.

62 Lees, Graham-Smith, and Fowler

Glossary

Performance variables CM-center of mass H-height of CM A-leg angle to the vertical defined by the line from the CM to the ankle joint %horizontal distance from the CM to the ankle joint S-speed VX-horizontal velocity VY-vertical velocity

Key positions TOLS-takeoff last stride TD--touchdown MKF-maximum knee flexion TO-takeoff

Key phases TOLS-TD-period of last stride TD-TO--period of contact phase TD-MIC-period of compression phase MKF-TO--period of lift phase

Hay & Nohara, 1990; Lees, Fowler, & Derby, 1993; Nixdorf & Bruggemann, 1990). Typically these are

0 an approach speed that peaks within the last two strides, a last-but-one stride slightly longer than that found during the immediately preceding part of the approach, a marked lowering of the CM during the contact phase of the last stride, a last stride that is slightly shorter than the last-but-one stride,

o a touchdown leg that is placed well in front of the body, and a vigorous upward lift of the free (lead) leg, arms, and torso.

The adjustments also alter other measurable parameters. For example, the time of flight in the last-but-one stride tends to increase while for the last stride it tends to decrease, in relation to the trends noted for the respective stride lengths.

The lowering of the CM has been explained as (a) minimizing the downward vertical velocity so as to maximize the effect of the vertical impulse and (b) increasing the vertical distance over which the CM is worked. The large touchdown distance has been explained as (a) enabling an increase in the time period during which vertical impulse can be generated, (b) increasing the range of movement through which the hip extensor muscles may work, and (c) placing the leg in a position to enable it to be stretched and store elastic energy.

The stretching of the leg musculature enables a storage of elastic energy and increased muscle force through eccentric action. The contribution of the elastic recoil mechanism has not been specifically isolated, but its importance

Analysis of Men's Long Jump 63

in the performance of the long jump seems not to be in doubt (e.g., Witters, Bohets, & Van Copenolle, 1992).

These adjustments have been noted in the literature and individual explanations given, but a well-stated theory linking them all together and explaining their relationship with the generation of vertical velocity has been curiously absent from the literature. In a companion paper, Lees et al. (1993) attempted to interpret these movements in this regard. The interpretation revolves around identification of four mechanisms operating in the generation of vertical velocity during the contact between touchdown (TD) and maximum knee flexion (MKF) marking the compression phase, and MKF and takeoff (TO) marking the lift phase. It was suggested that during the compression phase the CM pivots over the foot, generating vertical velocity via a purely mechanical mechanism. It was also suggested that during the lift phase vertical velocity was generated by upward momentum of the arms, free leg, and torso, by a release of stored elastic energy, and by a release of muscle chemical energy during the concentric contraction. The latter three mechanisms could not be isolated, but the former mechanism accounted for over 60% of the vertical velocity at takeoff. This places it as the single most important mechanism acting to create vertical velocity. It is enhanced by the ability of the touchdown leg to resist flexion.

In studying high jumping, Dapena and Chung (1988) prefer to use the radial velocity of the CM with respect to the position of foot placement (pivot point) as an indicator of the division between the compression and lift phases. This is probably more appropriate in the high jump due to the marked leg placement in front of the CM (about 60" to the vertical) and a marked backward lean of the body. Their interpretation of the mechanisms operating in that event was that the leg placement evoked a stretch reflex and reuse of elastic energy, which increased the forces muscles would be able to exert in the second phase. While they recognized the importance of the leg extensor muscles, their emphasis was placed on putting them in a fast eccentric condition so as to enhance the second (lift) phase of the movement. This contrasts with the view of Lees et al. (1993), who emphasized eccentric muscular leg strength for resisting leg flexion so as to enhance the mechanical pivot mechanism during the first (compression) phase of the movement.

The movements made prior to touchdown can be seen as placing the body in the correct position to take advantage of the mechanical mechanism operating during the compression phase. In order for the body to successfully pivot over the foot to gain vertical velocity the leg must be placed well in front of the CM. Experimental data suggest an angle of the leg to the vertical of about 25-30'. In order for this position to be attained, the CM must be in a low position. The CM is placed in a low position by the action of the last two strides. The longer than normal last-but-one stride leads to a s m d increase in horizontal velocity and a small lowering of the CM by virtue of an increase in the touchdown distance at the start of the last stride (Hay & Nohara, 1990). The CM lowers markedly during contact of the last stride, and this low position is maintained to enable a suitably large touchdown distance of the touchdown foot. In this position the body can pivot over the leg to gain vertical velocity providing it is sufficiently able to resist flexion. This interpretation of the action explains all of the observed phenomena.

The identification of several mechanisms responsible for generating vertical velocity helps to explain the equivocal correlations found between approach and


takeoff parameters with jump distance. The importance of horizontal velocity is well established for the long jump, and over a wide range of speeds a relationship with jump distance appears to exist (Hay, 1993). However, for elite athletes performing at their maximum speeds, such relationships are equivocal. Some studies (e.g., Hay, Miller, & Cantema, 1986; Hay & Nohara, 1990; Nixdorf & Bruggemann, 1990) have reported significant positive relationships. Others (e.g., Bruggemann & Susanka, 1987, for men) have reported weak positive relationships, and others still (e.g., Koh & Hay, 1990; Lees et al., 1993; Nixdorf & Bruggemann, 1990, for women) have reported no significant relationships. The utilization of horizontal velocity to generate vertical velocity during the compression phase depends on appropriate body position, leg position, and eccentric leg strength. Failure in any one of these could impoverish an otherwise expected relationship.

The purpose of this study was to present data on elite male long jumpers and to identify the essential characteristics of technique as related to the model of long jumping outlined previously. It was also intended to extend the database on the touchdown to takeoff phase with particular reference to a consolidation of an understanding of the mechanisms operating in the generation of vertical velocity.

Method

Subjects

Twelve male long jumpers were filmed during their competitive performances in the men's long jump final during the 1991 World Student Games (WSG). All performances were filmed at 100 Hz with one Locam camera placed perpendicular to the runway, about 7 m from the takeoff board, such that the foot contact during touchdown of the last stride was visible and about 1 m after the takeoff board. This ensured that sufficient film frames were available for analysis after takeoff into the jump to calculate projection parameters adequately. Judges were asked to cooperate, and they agreed to place themselves so that they were not in the field of view of the camera. Despite this, several problems arose with other competitors, television camera crew, and security personnel encroaching into the field of view, and trials were lost due to the need to change film in the camera. There were 27 legal trials analyzed in total. Two competitors completed only one successful jump each and these were not recorded; hence data from 10 competitors were available. In total there was one successful jump recorded from two competitors, two jumps from one competitor, three jumps from five competitors, and four jumps from two competitors. No data were available for the standard anthropometric measurements of body height and mass.

Analysis Procedures

The film was analyzed with an 11-segment biomechanical model defined by 18 points. The segmental data used were those proposed by Dempster (1955) for adult males. Data were smoothed with a Butterworth second-order filter with padded end points and a cutoff frequency of 8 Hz. First and second derivatives were calculated by direct differentiation (Lees, 1980). Derived parameters such as kinetic energies were computed on the basis of a whole body model (Lees et


al., 1993). The results of repeatability trials, which were conducted by three different experimenters, are also reported in that study. The error associated with displacement measures was typically 3%, velocities 5%, angles 8%, and angular velocities 16%.

Statistical procedures used were Pearson's product moment correlation coefficient for establishing relationships, Student's t test for establishing differences, and Shapiro-Wilks's test for establishing the nonnormality of data sets. A level of significance of p < .O1 was used unless otherwise stated.

Results

The definition of touchdown (TD) was taken as the first clear frame in which the foot was in contact with the ground. Similarly, the definition of takeoff (TO) was taken as the first frame in which the foot was clear of the ground. A typical path of the center of mass during the touchdown last stride (TDLS), takeoff last stride (TOLS), touchdown, and takeoff into the jump is shown in Figure 1. Also marked on the figure is the point of maximum knee flexion (MKF) during the contact phase. It can be seen from this that the trajectory is exceptionally flat over the flight phase of the last stride and shows no appreciable reduction at touchdown. It appears to rise immediately from touchdown through maximum knee flexion to takeoff, with the majority of the increase occurring between the last two events.

Figure 2 shows the corresponding velocity components for a typical performance with the same events marked. It can be seen that there is a small downward vertical velocity at touchdown, which becomes positive very soon after. This

WSG MEN 8.18 m

Time (S)

Figure 1 - The height of the center of mass during the last stride and the takeoff into the jump.

Lees, Graham-Smith, and Fowler

WSG MEN 8.W m

e Horizontal Vet

A vertical Vel n

3

Time (s)

Figure 2 - The horizontal and vertical velocities of the center of mass during the last stride and the takeoff into the jump. The events of last stride touchdown (TDLS), last stride takeoff (TOLS), touchdown (TD), maximum knee flexion (MKF), and takeoff (TO) are shown.

rises to a peak and starts to fall at takeoff. This reduction is due to the fact that maximum vertical velocity in upward projections of the body are reached before the foot leaves the ground as rapid plantar flexion contributes very little to an increase in upward motion (e.g., Bobbert, Huijing, & Van Ingen Schenau, 1987; Lees & Fahmi, in press). It is clear that there is a reduction in horizontal velocity as a result of contact with the ground, but this is smooth rather than sudden as would be expected for an impact. The smoothing of the data is the result of the data processing routines used. Satisfactory results are generally produced with the processing routines as used here, but they are not usually expected to faithfully reproduce the kinematic characteristics of impact.

The measures of distance jumped are given in detail in Table 1. These data were tested for nonnormality and yielded a test statistic W = .942. A second group was formed using the best performance for each performer (n = lo), and this yielded a test statistic W = .925. Both of these values were nonsignificant at the p = .O1 level, indicating that the data sets could not be established as nonnormal. Therefore these data and other derived variables were considered to be normal.

Data were obtained from each analysis to define a range of variables associated with the technique of long jumping, as outlined in the introduction. The group means and standard deviations for the selection of variables for the last stride, touchdown, maximum knee flexion, and takeoff are given in Table 2. Further characteristics derived from these data, such as changes in velocities,


Table 1 Descriptive Data for Jump Distances

Round1 subject

Official distance (m)

Toe to board (m)

Effective distance (m)

positions, and energies during the contact phase are given in Table 3. In these tables two sets of data are given. One is for the whole group of 27 analyses and the second is for the best performance of each of the 10 competitors. The latter data set is presented for comparability with other published data. The presentation of the former data set was preferred in this study as the focus of interest was in establishing mechanisms of performance, which should be apparent from all legal jumps and not just the best jumps. A comparison between the means of the two data sets using Student's t test showed that there were not any significant differences between any of the measure or derived variables.

In this study all of the velocities used refer to instantaneous velocities. For comparison, the average velocity calculated over the flight time of the last stride


Table 2 Descriptive Data for Last Stride (LS), Touchdown (TD), Maximum Knee Flexion (MKF), and Takeoff (TO)

Variable

HTOLS 1.13 0.06 1.12 0.08 Length (last stride) 2.10 0.10 2.08 0.09 Average speed (last stride) 9.93 0.49 10.02 0.45

sm 9.88 0.55 9.96 0.51 v x m 9.88 0.56 9.96 0.52 v y m -0.15 0.33 -0.06 0.35 Hm 1.10 0.05 1.10 0.45 Ankle velocity (TD) 3.26 1.03 3.19 0.96 Knee angle (TD) 165.9 3.9 166.9 4.69 Knee flexion velocity (TD)" -6.76 2.63 -6.69 2.32 Hip angle (TD) 146.9 7.5 149.3 8.2

Dm 0.45 0.10 0.45 0.06

Am 24.7 3.70 24.8 3.70

SWKF 9.18 0.42 9.17 0.42

v x ~ ~ 8.97 0.40 8.93 0.39

v y m 1.87 0.34 1.96 0.42

HMKF 1.14 0.51 1.15 0.06 Knee angle (MKF) 144.1 5.14 144.9 6.4 Hip angle (MKF) 157.8 6.92 159.6 8.7

DMKF 0.01 0.06 -0.00 0.06

A m 0.49 3.41 -0.17 3.31

STO 9.26 0.51 9.25 0.50

v x m 8.75 0.51 8.74 0.50 v y m 3.01 0.29 3.02 0.32

Hm 1.33 0.05 1.34 0.06 Knee angle (TO) 172.5 3.1 171.9 2.6 Hip angle (TO) 195.1 6.5 193.9 6.9

Dm -0.44 0.04 -0.42 0.04

Am -22.5 2.25 -2 1.6 2.42 Projection angle (TO) 19.0 1.78 19.1 2.06

Contact time (TD-TO) 0.120 0.012 0.118 0.010

Peak knee flexion velocity (TD-TO) -9.93 1.31 -9.90 1.17 Peak knee extension velocity (TD-TO) 10.80 1.53 10.42 1.92 Min. hip extension velocity (TD-TO)b 2.31 1.96 2.17 2.37 Peak hip extension velocity (TD-TO) 7.42 1.50 7.04 1.77

Note. Units are times in s; distances in m; velocities in m - s-'; angles in degrees; angular velocities in rad . s-'. "Extension velocity is defined as positive, and flexion velocity is defined as negative.

most cases hip flexion does not occur during the period from TD-TO, but continues to extend from its TD position. The mean value indicates that the hip is showing an extension velocity during this period.


Table 3 Derived Changes From TD Through MKF to TO (N = 22)

Variable

Projectile distance 7.99 0.71 7.99 0.72

STD-MKF ~m-To

STD-~O

v x T P ~ O

VXMKF-TO vxTth~O

VYrnMKF VYMKF-TO v y m m

% of VYmTo achieved at MKF

Knee angle (TD-MKF) Knee angle (MKF-TO) Knee angle (TD-TO)

Kinetic energy (TD) Kinetic energy (MKF) Kinetic energy (TO) Potential energy (TD-MKF) Potential energy (MKF-TO) Work done (TD-MKF) Work done (MKF-TO)

Note. Units are times in s; distances in m; velocities in m . s-'; angles in degrees; angular velocities in rad . s-'. Units for energies and work are J . kg-'. H is the height of the center of mass. KE and PE are the total body kinetic and potential energies, respec- tively.

is given in Table 2. The average velocity agrees well with the estimate of velocity at touchdown. The slightly smaller touchdown velocity is due to the smoothing of the data as noted previously.

The model of long jumping referred to in the introduction leads to the expectation of relationships between certain variables. These relate speed of approach and takeoff parameters to distances jumped and are given in Table 4. In addition, the low CM position at touchdown (H,) and a large touchdown distance (Dm) and angle (A,) suggest that a specific mechanism is operating in the compression phase. Therefore we would expect to find relationships between


Table 4 Correlation Coefticients Between Various Measures of Jump Distance and Last Stride (LS), Touchdown (TD), and Takeoff (TO) Variables

Variables n = 27 n = 10

Official distance vs. Sm vs. average speed (LS) vs. S, VS. Hm vs. projection angle (TO)

Effective distance vs. Sm vs. average speed (LS) vs. S, VS. Hm vs. projection angle (TO)

Projectile distance vs. Sm vs. average speed (LS) vs. Sm VS. HTo vs. projection angle (TO)

touchdown angle and vertical velocity changes from TD to MKF (the compression phase) and from MKF to TO (the lift phase) ranges of movement and measures of leg angle. These are tabulated in Table 5.

Discussion

This study was concerned with the clarification of a model for long jump performance and the identification of mechanisms operating in the performance of the long jump, rather than the further profiling of elite performance. These mechanisms should operate on all successful jumps performed during competition and not just the best jump for each performer. Therefore this study presents data on all of those successful jumps for each competitor. Although the pitfalls of combining several jumps by one performer are outlined by Hay (1987), these are counteracted in the generation of correlational data by using the degrees of freedom determined by the number of competitors rather than the number of jumps analyzed. For comparison with other published data, descriptive characteristics are given in Table 6 for the best performance of each finalist (n = 10) and for the whole group (n = 27).

The data for the 1983 TAC are from Hay et al. (1986), the 1987 Rome World Championships from Bruggemann and Susanka (1987), and the 1988 Seoul Olympics from Nixdorf and Bruggemann (1990). The average figures from this study compare well with other elite performance groups. In particular it is noted that the WSG athletes produce a similar angle of projection but a lower

Analysis of Men's Long Jump

Table 5 Correlations Between Selected Variables Relating to the Model of the Long Jump

Variable n = 27 n = 10

Am vs. Dm VS. H, vs. contact time (TD-TO) vs. ankle velocity (TD) vs. knee flexion velocity (TD) vs. hip angle (TD) VS. H,.To vs. VYT0 vs. VXmm vs. vx,,

VYTD-MKF VS. A, VS. STD VS. VXm.MKF vs. knee angle (TD-MKF) vs. peak knee flexion velocity VS. WmF-rn vs. VY,,

V ~ M W - K I VS. ATD vs. Sm vs. VX,,, vs. knee angle (MKF-TO) vs. peak knee extension velocity vs. hip angle (MKF-TO)

v y ~ ~ o vs. A, vs. Sm VS. VXnMKF vs. knee flexion velocity (TD) vs. hip angle (MKF)

Hm-TO VS. HMW., VS. VYTo vs. Sm vs. projection angle

takeoff velocity. As a result they achieve shorter jump distances. No differences are apparent between the two WSG Sheffield data sets.

From the descriptive data in Table 2 (n = 27 group), several characteristics of the long jump technique can be seen. The CM of the body seems to have achieved its lowest point at touchdown with a drop of about 3 cm from its position at takeoff last stride. As the CM is dropping at touchdown there is a


Table 6 Comparison of Takeoff Variables for Men's Long Jump From Recent Major Championships

Official Projection distance (m) angle (") S, (m/s) H, (m)

1983 TAC - 20.2 9.46 - 1987 Rome WC 8.30 20.7 9.6 - 1988 Seoul Olympics 8.18 19.8 9.6 - 1991 Sheffield WSG (N = 10)" 7.80 19.1 9.25 1.34 1991 Sheffield WSG (N = 27)b 7.67 19.0 9.26 1.33

%est performance. bWhole group.

residual negative vertical velocity of -0.15 m . s-I. The low position of the CM also enables the touchdown leg to be placed well in front of it, as indicated by the DTD value of 0.45 m and an extended knee angle of 166". The corresponding angle of touchdown ATD (defined by a line from the CM to the ankle joint) is 24.7", which is within the range quoted by Alexander (1990) as optimum on the basis of a theoretical model. These data are similar to that for the best jumps with the exception of the vertical velocity, which has lower negative value in the smaller group at -0.06 m . s-I, but these were not significantly different.

The mean velocity of the ankle joint at touchdown has a value of 3.26 m . s-', which gives it a backward velocity relative to the CM. This value is close to that found by Koh and Hay (1990), and it is concluded that all subjects use an active landing (i.e., one in which the leg is swept backward as it contacts the ground). It is important to keep the landing leg stiff, and so any "active" or "pawing" action is best made with an extension of the hip rather than flexion of the knee joint. Flexion of the knee would increase the backward velocity of the foot relative to the CM but would put the leg in a weaker position to absorb impact. However, too great a backward velocity of the foot will lead to a reduced Dm and so compromise the ability of the athlete to generate vertical velocity.

In order to present velocity profiles within the contact phase of the long jump, maximum knee flexion is chosen as a suitable indication of the point at which the leg goes from compression (by way of eccentric muscular action) to extension (by way of concentric muscular contraction). At maximum knee flexion the knee joint has a mean angle of 144". The horizontal velocity has dropped by 0.90 m . s-' to 8.97 m . s-', and the vertical velocity has increased by 2.02 m . s-' to 1.87 m . s-I. The height of the CM has increased by only 0.044 m. What is noticeable in these data is that there is a large increase in vertical velocity for very little increase in vertical height. This is the result of the very large impact force generated at contact (Ramey, 1972). Over 64% of the final vertical velocity has been achieved by maximum knee flexion, and confirms that the mechanical mechanism operating during the compression phase is the most important feature of the long jump takeoff. In order to promote this, the athlete must possess a strong leg that will resist yielding over this phase and it must be placed well in front of the body to allow the center of mass to pivot over it.


Therefore the low position of the CM at touchdown is seen as a necessary precursor for generating the correct position in which this mechanism can operate.

Using a whole body model for the assessment of energy changes we calculated that for the whole group, the mean energy at touchdown is 49.0 J . kg-' and by maximum knee flexion this has decreased to 42.7 J . kg-'. There has been relatively little work done in raising the center of mass over this phase, and so most of the energy (6.3 J . kg-') is lost from the initial kinetic energy and does not appear in measurable mechanical form. This energy amounts to about 500 J for a typical 80-kg male. Of such a quantity of energy, some is dissipated by negative muscular work and some stored in the elastic structures of the takeoff leg. With structures capable of storing at least 100 J during running (Ker, Bennett, Bibby, Kester, & Alexander, 1987) and probably more for the long jump where the extension forces are much greater, it is likely that the reutilization of this energy will play an additional role in further increasing vertical velocity at takeoff. It is noted that the best jumpers attain higher energy and dissipate more energy than the group as a whole although these differences are not significant. There is relatively little work done during the lift phase. An average gain of 2.7 J . kg-' (equivalent to 200 J for an 80-kg male) is recorded, which indicates an efficiency factor of some 40%. Some of this energy would come from concentric muscular action during the lift phase, and so the true efficiency factor for reutilization of elastic energy will be smaller. Witters et al. (1992) noted rather poor efficiencies for long jumpers.

From maximum knee flexion to takeoff the mean horizontal velocity was reduced by 0.22 m . s-'. During this time the vertical velocity increased by 1.12 m . s-' and the height of the center of mass increased by 0.19 m. Quite why the horizontal velocity should continue to decrease after maximum knee flexion was not clear. This could be because the CM is still behind the point of support at maximum knee flexion and there is still some braking to be done as the whole body continues to pivot over the foot. Although the distance of the ankle joint in front of the center of mass is small (DM,, = 0.01 m) the center of pressure could be located at the head of the metatarsals and this might be at least 0.15 m ahead of the CM in this position. The same mechanical mechanism as described previously could still be operating and so continue to help increase the vertical velocity after maximum knee flexion has been reached. The small reduction in horizontal velocity after MKF represents over 150 J of energy for an 80-kg male, and this energy could contribute to the energy gained during the lift phase. If this were the case then the efficiency for the return of stored elastic energy would be even lower than suggested. These figures are guidelines only but would indicate that the elastically stored energy is possibly a minor contributor to long jump performance. If this is the case, it has consequences for the type of training regimens that are recommended to athletes.

It was supposed that including several jumps per performer would mean that the collection of jumps would be more widely spread. This might be expected to have some effect on the establishment of relationships that may only be apparent if investigated over a wider performance spectrum. In elite performances, variables typically cannot be controlled, their ranges are narrow, and spurious relationships can be generated. This problem might also be compounded by the rather large tolerances expected in some of the variables measured for this type of data (Lees et al., 1993). Despite these impediments, it might be argued that


if relationships exist they should be considered to have some meaning. It should be emphasized here that the relationships found should be considered to be casual rather than causal (as used by Hay & Miller, 1985). They remain casual until such time as they can be linked with some theory predicting a relationship, and if they support that theory they may be considered to be evidence of a cause-effect relationship.

Relationships between various measures of distance and touchdown and takeoff variables are given in Table 4. The highest and most consistent relationships appear between measures of jump distance and touchdown speed. These are significant for all estimates of distance and are consistent with some reports in the literature. Relationships between jump distances and takeoff parameters are in the main poor. This latter finding is best explained by the fact that projectile distance is determined by three interacting variables and not one independent variable. Some significant relationships are found but these are not sufficiently consistent to suppose that they represent a causal factor. Further explanations are that there may be an element of performance within the flight and landing phases that is important, or simply that there is insufficient range in the variables used to establish satisfactory relationships.

The expected relationships between approach velocity and distance for elite jumpers would hold providing other aspects of their technique are sound. Indeed, the existence of this relationship indicates that the technique demonstrated by the group is generally sound. For example, such a relationship would not be expected for sprinters, who have the capability to generate speed but not the technique or strength to jump well. Other aspects of technique are to do with the placement of the touchdown leg well in front of the CM, and this is enhanced by a low CM position at touchdown to enable the jumper to pivot over the foot, thereby gaining vertical velocity. In order to make the most of this mechanism the touchdown leg must be strong and must resist too much flexion. Consequently, relationships would be expected between measures of technique and leg angular kinematics (Table 5).

A key variable is the angle of the line made by the center of mass and the ankle joint at touchdown (A,). The model for the long jump outlined previously suggests that the body should pivot over the foot thereby generating vertical velocity. The high correlation between A, and DTD suggests that either is an adequate measure of this aspect of technique. The negative relationship with the height of the CM (H,) is confirmation that a low CM height leads to a large AT,. Although a large A, should enable the foot to be in contact with the ground longer and so a positive relationship would be expected with the time of contact from touchdown to takeoff, no such relationship is found. This is probably due to the low spread in the time of contact data. The larger the value of A, the more the leg is stretched forward at touchdown and the less able it is to sweep backward in the active-style landing leading to a positive relationship with the absolute velocity of the ankle. The existence of an optimum A, (Alexander, 1990) implies that there are negative consequences if it is too large. If this is the case there will be a greater braking effect. This braking effect can presumably be minimized if the leg is swept backward relative to the CM at touchdown, and so a compromise between ATD and ankle velocity at TD must be reached. A minor relationship (p < .lo) is found with knee flexion velocity at touchdown, suggesting that a larger ATD could be associated with a higher knee flexion


velocity. This curious relationship is better seen in the context of the stronger negative relationship between A, and hip angle (TD). As Am increases, hip angle reduces (i.e., becomes more flexed), suggesting that leg extension at TD is achieved primarily by hip flexion and that knee flexion remains a preparation for impact. Consequently, hip mobility and strength are likely to be important performance characteristics. A larger A, leads expectedly to a larger range in height moved by the CM (H,,). This greater range of movement leads to a greater vertical takeoff velocity VYTo but does not appear to lead to a reduction in horizontal velocity either over the compression phase (VXTO.MKF) or during the whole of the contact phase (VXm.ro).

The generation of vertical velocity is known to be important in long jumping and this also enables the various mechanisms acting to be more clearly established. It has been argued that the main mechanical mechanism operating during the compression phase is the pivoting of the CM over the foot. Consequently, relationships between vertical velocity changes from touchdown to maximum knee flexion (VYTD-MKF) and other parameters representing touchdown technique would be expected. Surprisingly, VYTDMKF shows no relationship with A,, STD, or horizontal velocity loss (VXm.m) during this phase. A second requirement for successful pivoting over the foot is a resistance of the leg to flex at the knee. No significant relationships were found with knee angle and angular velocities either. A lack of expected relationships suggests that the mechanisms operating during the compression phase may be more complex than first thought. This suggests that there may be other actions taking place not measured during this analysis, for example, motions in the frontal plane, which would only be uncov- ered by a full three-dimensional analysis. The vertical velocity gained during the compression phase dominates the total vertical velocity gain (VY,,), and the larger this is the lower is the vertical velocity gain from MKF to TO, as indicated by an inverse relationship with VYmF,.

The vertical velocity from maximum knee flexion to takeoff VYMm-To represents the actions made during the lift phase. At this stage no relationships would be expected with ATD, S,, and horizontal velocity loss VXW.~~ , and none are found. The lack of relationships with the change in knee angle (MKF-TO), peak knee extension velocity, and change in hip angle (MKF-TO) suggests that the actions other than joint extensions made by the athlete are important in generating vertical velocity during this phase. The emphasis in long jump technique is on the actions of the free leg, arms, and torso, and these would appear to be more important. It also questions the importance placed on the storage and reutilization of elastic energy, which presumably has the greatest effect around the knee.

The total gain in vertical velocity during contact (VYm,o) shows no relationship with A,, S,, and velocity loss during compression (VXm-MKF). The VYmTDm shows a strong relationship with knee flexion velocity (TD). There is no particular feature of the model that would predict this relationship other than the small link between A, and knee flexion velocity (TD) noted previously. This might be evidence of the link between A, and vertical velocity gain expected but not found. An interesting inverse relationship is that the hip angle at MKF indicates that a higher vertical velocity change is related to a smaller hip angle at MKF. This might be the case if the smaller hip angle provided for a greater

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touchdown. In the data here, the CM is at its lowest position at touchdown. This enables the touchdown leg to be placed well in front of the CM close to the expected range of 25-30". This enables the CM to pivot over the foot and as a result obtain over 64% of the final vertical velocity by maximum knee flexion. The touchdown leg sweeps backward relative to the CM, which may reduce the braking effect of this leg action. There is a corresponding loss of horizontal velocity of 0.90 m . s-' by maximum knee flexion, or 80% of the total horizontal velocity loss. There is clearly a trade between these two velocity components but a close link between them cannot be established, suggesting that other factors are also important during the compression.

To ensure the pivot mechanism can operate there is a clear requirement for the body to resist flexion at touchdown thereby rendering it more effective. As approach speed increases leg strength must also increase to be able to control the higher forces of impact. Relationships between measures of leg kinematics and vertical velocities generated were in the main fairly poor. This was a disappointing observation but could be accounted for by the factors outlined previously. Their failure to make a substantial appearance does not affect the rational basis for an expectation of their existence. However, a lack of expected relationships might indicate that other mechanisms, for example hip action, may operate. Identifying their presence and quantifying their effect remains a challenge for the future.

References

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Nixdorf, E., & Bruggemann, G.P. (1990). Biomechanical analysis of the long jump. In G.-P. Bruggemann & B. Glad (Eds.), Scientific research project at the Games of the XXIVth OlympiaLCSeoul 1988 (pp. 263-302). Monaco: International Athletic Foundation.

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Acknowledgments

This study was partly funded by the National Coaching Foundation. The authors wish to express their appreciation to Dave Derby for digitizing the film.

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