Sports Science: Jumping (High, Long and Triple)

The laws of mechanics are the basis of a complete understanding of all modern jumping techniques, and a knowledge of these laws is an essential foundation of ability to coach these events.

High-jumping

Spring (which can account for approximately 90 per cent of the height obtained) and lay-out are the key factors in this event.

In good high-jumping, the running approach improves vertical spring and provides horizontal motion for crossing the bar. The take-off movements impart, of first importance, vertical speed to the jumper’s Centre of Gravity; secondly, they initiate most of the rotation required for lay-out. The greater his effective spring, the higher will a jumper raise his Centre of Gravity; but he must so combine horizontal and vertical movement, and adjust his point of take-off, that the high point of the Centre of Gravity’s path is directly over the bar.

Since the use of weights is not permitted by the rules, the modern high-jumper does nothing to disturb the flight curve of his Centre of Gravity ; but by changing position in relation to it he can clear a higher bar. However, in the best jumps the Centre of Gravity’s high point above the bar and the completion of lay-out coincide; and, of course, the athlete gets into and out of his lay-out without knocking the bar down.

Spring and lay-out are the key factors—yet maximum efficiency in one can be obtained only at the expense of the other. All good high-jumping, is therefore a compromise; to obtain economy of lay-out (though never absolute economy) good jumpers drive eccentrically at take-off , slightly reducing their effective spring, but in the process gaining more through their position over the bar. By contrast, poor high-jumpers, anticipating their movements in the air, sacrifice too much spring for their lay-out, or cross the bar in poor positions.

APPROACH. (1) Direction. The direction of approach can greatly influence the component rotations at take-off, and their proportions about the vertical, transverse-horizontal and medial-horizontal axes. Indeed, the approach is so bound up with the jumper’s take-off and subsequent movement in the air that, once habitual, any drastic change to it can mar performance.

An angled approach (i.e. from the side) can be advantageous to all high-jumpers, regardless of style, because (i) it facilitates a greater range of free leg swing at take-off (for the bar is not then at right angles to the jumper’s line of approach), and (ii) it makes possible the throwing of some part of the body over and below the bar before the Centre of Gravity reaches its high point.

However, when the angle is too acute, the athlete travels too much along the bar, at greater heights knocking it off at one point despite clearing it at another. An additional danger is that the lay-out will be anticipated at take-off, exaggerating the lean towards the bar and reducing effective spring. The recommended angle is one of approximately 30-40 deg.

One seldom sees a completely frontal (i.e. 90 deg. angled) approach, though some fine jumpers have commenced from the front before curving in to the bar on the last few strides; this has been done naturally to direct the free leg at take-off and initiate rotational movements required for lay-out. Jumpers who employ a more frontal approach tend to attain the high point of their jump in front of the bar; often, too, their free leg action has to be restricted or modified. (2) Speed. The importance of approach speed increases with (i) the raising of the bar, and (ii) a sharpening of the run-up angle (for then the jumper is inclined to be longer over the bar); it is greater in those styles in which the athlete crosses at an angle—as, for example, in an Eastern Cut-off.

In the sense that a ball, rolling horizontally, changes direction on ar inclined plane, run-up speed in high-jumping cannot be converted vertically; nor, in this respect, should the take-off leg be likened to a stiff pole. For although, initially, the take-off leg straightens, with its foot well in front of the hips, it flexes immediately strain is put upon it. In fact, were it straight and stiff throughout, it could contribute little thrust, because knee joint extension would then be impossible, and the jar would be tremendous.

In all good jumping the take-off foot is placed in front of the athlete at a distance which gives his free leg (in particular) and arms time to assist the thrust from the supporting leg ; with greater approach speed, this foot must be planted even farther forward.

This demands, initially, a backward lean, and a lower hip position; and (provided the jumper is strong and fast enough to use it) it leads to a more favourable pre-spring position.

This long-striding, low preliminary position is best obtained as a result of a marked acceleration over the last few (usually three) strides of the run-up; the approach begins comparatively slowly, with the body pitched forward in a semi-crouch but, during the final acceleration, the hips and legs ‘move ahead’ of a relaxed upper body.

The value of approach speed to spring lies in contributing to range, force and speed beyond what is attainable in a standing highjump. Jumpers should experiment to see if they can benefit from a faster run-up; yet each will possess a ‘critical speed’ beyond which takeoff efficiency will be impaired, varying greatly from jumper to jumper, largely because of variations in strength and intrinsic muscular speed. Some, to gain time to evoke their maximum force at take-off, will use a slow approach; while others can benefit from a faster run-up (and, therefore, a more exaggerated backward lean at the end of it) and still have time to evoke maximum take-off force, the technique now more generally used. For most good high-jumpers a run if only a few strides is necessary. The majority of champions use from seven to nine.

TAKE-OFF. Here, the jumper must (i) impart maximum vertical velocity to his Centre of Gravity commensurate with (ii) acquiring just sufficient body rotation (i.e. total angular momentum) for his lay-out subsequently. (1) Attaining maximum vertical velocity. A jumper projects himself into the air by moving his limbs so that he exerts a force against the ground larger than that supporting his weight; and the reaction to this additional force accelerates him upwards. His vertical velocity also depends upon the time this extra force is applied, i.e. the impulse ; the greater the impulse, the greater the velocity.

In a high-jump take-off, the free leg and both arms are first accelerated upwards against the support of the jumping leg (and, therefore, against the resistance of the ground). Then, with the Centre of Gravity over the jumping foot and already moving upward, an additional impulse is applied through vigorous extension of the trunk and the take-off leg. The important points, here, are: d e f (i) The high jumper obtains no vertical lift by the actual bracing of his take-off leg; but he must possess great strength in that leg— otherwise the upward acceleration of the free leg and arms will be nullified by the downward motion of the rest of his body. (ii) It is the vertical acceleration of the free leg and arms (not the mere fact of their upward movement) which invokes an upthrust from the ground. Here again, it is the athlete who makes the effort to change velocity and the ground which provides the reaction to the change. (iii) The importance of early free leg speed. When a line drawn through the Centre of Gravity of (1) the thigh and (2) the foreleg and foot (and, therefore, of the Centre of Gravity common to both) makes a 30 deg. angle with the downward vertical the vertical component of its velocity is already 50 per cent of its actual velocity; as much as 71 per cent of its actual value when that angle is 45 deg.! (iv) To obtain maximum acceleration of the whole of the free leg in the desired vertical direction the good high jumper straightens this leg as quickly as possible in its swing.

Ideally, the free leg and arms should be moving at their maximum vertical velocity at the instant of take-off; for their acceleration afterwards cannot add to the athlete’s velocity. (Hopper suggests, however, that in good jumping the swinging leg ends its upward acceleration, relative to the athlete’s Centre of

Gravity, when horizontal. It then slows down, changing a downward thrust against the ground into an upward pull. He affirms: ‘The fact seems to be that the proficient jumper is able to time the extension at hip, knee and ankle with the changing upward acceleration of the free limbs, so as to develop at all times the maximum ground reaction that each muscle-group of the take-off leg can handle in turn.’) This points to the need for great strength in the extremity of the takeoff leg, and in those muscles (rarely strengthened sufficiently) which might enable the free leg to accelerate beyond the horizontal. (v) The movements must occur as simultaneously as possible; otherwise (because of the force of gravity) the free leg and/or arms (and, therefore, the Centre of Gravity of the whole body) lose velocity before contact with the ground is broken. (vi) Maximum vertical velocity can be built up only when the accelerations of the different parts of the athlete’s body take place over sufficient range of movement; this applies particularly to the actions of the legs. (vii) The jumper’s Centre of Gravity should be projected from the greatest possible height; at the moment of leaving the ground, the jumping leg and trunk should be fully extended vertically; and, ideally, the free leg and arms should be as shown. (viii) To attain maximum vertical velocity, the up-thrust from the ground must pass through the athlete’s Centre of Gravity. Because of the need to initiate rotation at take-off, however, a slightly eccentric thrust is essential. (ix) Throughout their rapid extension, the trunk and take-off leg must continue to exert the greatest possible effective force against the ground despite the upward movement of the rest of the jumper’s body. (x) Too fast an approach gives insufficient time for the application of the various forces against the ground; vertical velocity is then reduced, as is the take-off angle. (xi) The take-off surface must be firm, or the effect of the various body impulses will be reduced.

What about the effect of ground reaction on a high jumper’s Centre of Gravity (moving in a vertical plane). Here, the curve AB represents the low last stride before take-off (low, because of the importance of not wasting vertical impulse later (at B) in overcoming a dropping of body weight). BC denotes the path of the jumper’s Centre of Gravity as this is influenced by a series of ground reactions while the jumping foot is on the ground. The arrows indicate the relative magnitudes and directions of these residual (i.e. ground reaction less body weight forces at intervals of fa second.

Ground reaction—through a series of controlled impulses —is always exerted at right angles to the direction in which the Centre of Gravity is moving, the effect being to change the latter’s direction without changing its speed developed in the approach. This, though ideal, is impractical.

What actually happens in a good jump, where the need is to build up one very large impulse in a very short time. Now, by means of a braced jumping leg and acceleration of free leg and arms (transmitted impulses) the Centre of Gravity is driven upwards by an average thrust of four times body weight. However, this is only achieved at the expense of Centre of Gravity speed (which, in this case, dropped from 18-2 ft to 14-8 ft per second). In fact, the direction of ground reaction is unfavourable to the speed of the Centre of Gravity until point X is reached—when the forces of this reaction are rapidly diminishing.

It follows, therefore, that good high-jumpers employ forceful, fast and long take-off thrusts. They possess favourable power-weight ratios and, usually, are above average height, flexible and with comparatively long, tapering legs.

A majority of take-off faults in this event are the result of anticipating movement in the air. Indeed, many errors in all forms of motor-learning are errors of anticipation. Good high-jumpers are ‘take-off conscious’; poor ones over-anxious to cross the bar. (2) Acquiring rotation. In even the best high-jumps the time between the instant of take-off and the moment when the body’s Centre of Gravity reaches its high point is too short to permit an origin of lay-out in the air; it must begin on the ground.

For a given style of lay-out, however, the greater the jumper’s spring, the less rotation he requires, for his rotation then acts for a longer period of time. For example, he will need less when projecting his Centre of Gravity 4 ft vertically (0-5 sec) than in raising it only 1-5 ft (0-306 sec).

All three methods of acquiring rotation on the ground are combined in good high-jumping. By checking linear motion (through momentarily fixing the take-off foot), transferring angular momentum (from the arms and free leg) and by thrusting eccentrically to the Centre of Gravity (with the jumping leg) a constant total angular momentum— in magnitude and direction appropriate to the style of crossing the bar —is developed on each jump. This can be resolved in terms of angular momenta about vertical, transverse-horizontal and medial-horizontal axes, which pass through the jumper’s Centre of Gravity, at the instant of take-off.

With one exception, rotations about each of these axes can be acquired in all three methods. Thus, a high-jumper’s free leg swing can impart backward rotation about a transverse-horizontal axis, rotate about a medial-horizontal axis, or twist about a vertical one; or, as usually happens, it can combine all three. Arm action can produce similar effects; granted that the mass and length of an arm are considerably less than that of a leg—but the good high-jumper swings both arms, and their rotational influence on the body is enhanced by virtue of the distance between their axis, the shoulders, and the body’s main axis.

Again, depending upon timing, direction and emphasis, the thrust from the jumping leg can develop rotations about all three axes, or no rotation at all; and by momentarily fixing the take-off foot (i.e. by checking linear movement) a jumper can turn about a transverse-horizontal and/or a vertical axis (though, by this method, rotation about a medial-horizontal axis is not possible).

In building technique, the aim should be to select from the various alternatives according to (a) lay-out requirements, (b) angle and speed of approach and (c) the physique and powers of co-ordination of the athlete. For reasons of initiating rotations, Roll and Straddle jumpers spring from the leg nearer the bar, Scissor and Eastern Cut-off exponents from the outside leg. Each good jumper adjusts his run-up, to suit his particular interpretation of high-jumping form, his strength speed, flexibility and neuromuscular co-ordination.

A second important principle in the building of technique is to rely as much as possible upon transference of angular momentum from the free leg and (to a more limited extent) the arms for the rotational effect; for the more direct the thrust of the take-off leg, through the Centre of Gravity, the greater the impulse available to project the athlete vertically.

In good jumping the approach angle is largely determined by the need for this transfer—an angle of approximately 30-35 deg. for Scissor , Osborn Roll , Straddle and

Arch-straddle lay-outs, but somewhat greater (40-45 deg.) for most Eastern Cut-offs. To develop maximum angular momentum, the free leg swings comparatively straight and accelerates through a wide range.

High-jumpers who use a flexed free-leg swing are more dependent upon eccentric leg thrust for their lay-out, to the greater sacrifice of spring. For although a leg can move with greater angular velocity flexed than straight, experience seems to prove that it cannot do so to the point of developing as much angular momentum, because of its reduced moment of inertia about the hip joint. (Nor, usually, can it accelerate the jumper’s Centre of Gravity over as great a vertical distance, keep him as long over his jumping leg nor provide as high a position of his Centre of Gravity at the instant of take-off.)

Athletes who rely upon a pronounced forward rotation in crossing the bar are usually compelled to restrict their free leg swing—the direction of which (about a transverse-horizontal axis) is often opposed to the required over-all body rotation (i.e. the total angular momentum of the jump). In consequence, they are even more dependent upon the eccentric thrust of the jumping leg.

CLEARANCE. Once contact with the ground has been broken, the high-jumper (who is not permitted the use of weights) does nothing to disturb the flight path of his Centre of Gravity, the parabola of which has been determined previously by his approach speed and take-off spring. In the air, also, he possesses a constant total angular momentum about an axis of momentum (which passes through his Centre of Gravity) fixed in direction.

By altering the position of his body in relation to his Centre of

Gravity, however, he can clear a higher bar; and by changing position about this axis of momentum (i.e. by changing his body’s moment of inertia) he can reduce or increase angular velocity.

Any movement he originates in the air must cause an equal and opposite reaction; clockwise action of one part of his body must produce a counter-clockwise reaction in some other part, and vice versa; but, within limits, the jumper can control the location of the reaction within his body.

The angular velocities of two moving parts of the body about their common axis, i.e. an axis of displacement (which also passes through the body’s Centre of Gravity) are inversely proportional to their moments of inertia. It is important to remember that movement originating in the air often produces action and reaction in horizontal, frontal and sagittal planes, or two of them, simultaneously—though this is by no means always so. (1) Lay-out. A series of jumps (made from the left foot and observed from the pit side of the bar) taken by one athlete. The high point of his Centre of Gravity is the same each time (and is, correctly, directly over the bar); but, through adopting increasingly more economical positions about it, he is able to jump higher and higher.

Progressively, he reduces the gap between his Centre of Gravity and the bar; his best clearances are those where the bar has been raised to the level of—theoretically, even above—his Centre of Gravity. Put another way, the lay-out efficiency on each jump can be assessed by the body mass above and below the bar at this instant; the more mass the jumper has above it, and the higher its position, the poorer is his lay-out. Conversely, the more mass there is below the bar at the high point of the jump, and the nearer it is to the ground, the better is his lay-out provided, of course, that all parts of his body eventually clear the crossbar.

Clearly, position is of little value in jumping for height; and although the Scissor technique is a considerable improvement, there remains a gap of approximately twelve inches between the bar and the jumper’s Centre of Gravity; the upright trunk and raised legs force the seat down and there is little body mass below the bar.

By lying on his side at the high point of the jump an athlete using a Western Roll reduces the gap to approximately six inches ; but there is little mass below bar level, and therefore the space between his Centre of Gravity and the bar is greater than it otherwise would be. An Osborn Roll (i.e. with the back to the bar) is fractionally better, but there still remains little mass below the crossbar. (The many versions of the roll all possess at least some of the lay-out characteristics of these two main variations).

The bar can be moved even closer to the jumper’s Centre of Gravity when he crosses on his back or abdomen ; a complete lay-out in either style possibly saves as much as two inches on position but this lay-out would be unusual in a Modified Scissors jump.

When the trunk and limbs are curved round the bar, the gap is further reduced. Theoretically, such a position can be exaggerated to allow the jumper to pass over the bar while his Centre of Gravity passes beneath ; however, this is not practicable in good high-jumping because it calls for the sacrifice of too much spring; and, of course, to ‘jack’ effectively the athlete would have to be moving much too slowly, horizontally, to clear the bar.

At the high point, the jumper’s hips and abdomen are raised in relation to his Centre of Gravity as a result of the low positions of the head, upper trunk, arms and free leg. In either position it is conceivable that the bar could be raised to the level of the Centre of Gravity’s high point.

The importance of, and difficulty in, reconciling the essential upward spring and lay-out have already been emphasised. Scissor jumps give good take-offs; the free leg movement is efficient and the body is kept over the jumping leg, but the lay-out is poor. A well-executed Eastern Cut-off combines the advantages of a Scissor take-off and an economical lay-out, but it requires exceptional control, suppleness and spring and is made even more difficult because the jumper must throw those parts of the body at take-off farthest away from the bar (i.e. his hips and legs) over first.

Few athletes are happy in a Modified Scissor position , for control over the bar and safe landings are difficult to achieve, though the style gives an excellent take-off.

The Western Roll provides a lay-out demanding no more than average co-ordination and flexibility, nor need it make exceptional demands on take-off spring. The Osborn Roll is better, but more difficult to control. A horizontal Straddle position is better still, but take-off (i.e. rotational) difficulties are increased. An Arch-straddle adds further to the problem of reconciling spring and rotation. (2) Movement originating in the air. Even the best high-jumpers must originate most of the essential turning movement at take-off, for there is so little time to do it in the air. However, certain minor rotations can be originated after contact with the ground has been broken—to the improvement of the jumper’s take-off which, then, needs less of a rotational component. Movement originated off the ground, however, has its equal and opposite reaction within the jumper’s body.

A most outstanding example of this action-reaction is to be found in a well-executed Eastern Cut-off jump. At take-off, through an eccentric thrust from the jumping leg and free leg swing, the jumper rotates backwards mainly about a transverse-horizontal axis and, simultaneously, twists about a vertical axis.

At this instant, also, torsion at the waist is caused by a twisting of the hips and shoulders in opposite directions about the body’s long axis—movements not in parallel planes, however, for the trunk is stretched on the side of the jumping leg and is compressed on the other side by the action of the free leg.

These movements are reversed in the air; the shoulders now twist in the direction of take-off, the hips again moving in opposition; the stomach is turned towards the bar. The lateral stretching of the trunk is also reversed. Thus, the rotation of the hip girdle, turning ‘against’ the upper body, brings the jumping leg to its horizontal position.

Again, the free leg, thrusting towards the pit, now acts in opposition to the head and shoulders which are momentarily forced below bar level. As a result of all these movements, the jumper attains an arched layout over the bar; his hips are raised in relation to his Centre of Gravity because of the low positions of his free leg, head, upper-trunk and arms.

Finally, at great speed, the Cut-offjumper lifts his head, upper body and arms ‘against’ a backward kicking of his free leg ; otherwise (because of his body’s overall rotation) he would strike the bar with his face or chest. He lands on his jumping leg and now faces the crossbar.

By comparison, a Straddle jumper possibly originates less of his turning movement in the air and the style certainly makes fewer demands on his co-ordination, timing and flexibility.

Take-off rotation is again developed by an eccentric thrust from the jumping leg and transference of free-leg and arm angular momentum; rotation about a medial-horizontal axis is marked, with some twisting about a vertical axis, both in the direction of the crossbar.

In comparing the various interpretations of the Straddle style, however, it would seem that rotation about a transverse-horizontal axis is of a less uniform pattern; for whereas, in some Straddles, the angular momentum generated by the free leg swing and arms is more than com- pensated by the jumper’s forward rotation about his take-off foot, resulting in forward rotation about this transverse axis, this is not the case in others, and the athlete therefore leaves the ground with backward rotation about this axis or no rotation at all.

It is suggested, however, that (in the horizontal plane), in general, the axis of momentum in a Straddle jump is at an angle 30-40 deg. to the bar, inclined (because of rotation about a vertical axis) slightly towards the pit. Throughout the jump, therefore, it is at a considerable angle to the jumper’s longitudinal axis.

After take-off the jumping leg hangs momentarily, keeping the hips high in relation to the Centre of Gravity and so helping to advance the leading leg quickly over and beyond the crossbar (important in all the high-jumping styles). Then, as the jumping leg is flexed and the upper body leans towards the bar (so reducing the jumper’s moment of inertia about his axis of momentum), rotation and lay-out are speeded up.

The head and chest barely clear the bar and drop rapidly below the main axis, while the hips and legs are raised above it. In addition, in some interpretations of the style, immediately after crossing the bar, the head and chest are forced even lower, against a downward thrusting of the free leg, to raise the hips and abdomen in relation to the Centre of Gravity and assist with the clearance of the rear (i.e. jumping) leg; this is then lifted, rotated and straightened.

The reaction to these leg and hip movements momentarily checks or, if sufficiently strong, even reverses the turning of the upper body. Finally, with the jumping leg clear, the whole body rotates uniformly, the arms and upper body coming to earth before the legs. Other styles of high-jumping can be analysed similarly.

LANDING. As the high-jumper drops towards the pit he develops kinetic energy, and the greater the distance of his fall, the greater is that energy. To reduce risk of injury the fall should not be too great and, on landing, he should lose kinetic energy as gradually as possible—hence the need for built-up, soft landing areas.

Where the jumper lands on his feet he should flex his leg (or legs) under control: but where it has to be made in some other way the impact can be lessened—the force of landing per square inch reduced—by increasing the area of body contact; and where the kinetic energy is the result of considerable horizontal motion, rolling in the pit (in the same direction as that motion) also reduces the impact of landing. u 100 yards sprint would be compelled in long-jumping to take off at horizontal and vertical velocities much less than might be expected. For, assuming he moves his Centre of Gravity 5 ft horizontally with his jumping foot in contact with the board, at a horizontal velocity of 36 ft per second, his jumping foot would be on the ground only 5/36 second, whereas a study of slow-motion films of 7 ft high-jumpers in action shows they need approximately – second to impart an initial vertical velocity of 16 ft per second.

Efficient long-jumping, like good high-jumping, is therefore something of a compromise. In terms of a competent jumper’s sprinting and high-jumping performances, neither speed nor spring are at a maximum: he reaches the board at a high, but not his top, speed, giving sufficient time for a great (but not his greatest) vertical impulse. In fact, it has been suggested that the proportion of horizontal to vertical take-off velocity in good long-jumping is very approximately 2:1.

The greatest practical angle must always be much less than 45 deg. (the angle sometimes recommended because it is generally known to give a projectile (in vacuo) maximum range in a horizontal plane). Indeed, it is impossible to jump at such an angle without using a very slow approach, or by directing the take-off thrust backwards, at the cost of considerable horizontal speed.

A jumper moving horizontally at 30 ft per second could leave the board at an angle of 45 deg. only if his vertical velocity were also 30 ft per second —when his Centre of Gravity would be raised 14 ft above its take-off height and the jump would measure approximately 56 ft! Again, even if he combined this take-off angle with the ability to raise his Centre of Gravity 4 ft (i.e. at an initial vertical velocity of 16 ft per second), his jump would be only 16 ft!

APPROACH. Ideally, the length of the run-up in long-jumping should be determined by the athlete’s ability to accelerate to top speed, taking an additional three or four strides to prepare for an upward leap from the board. Since research proves that, in making a maximum effort all the way, men sprinters attain this speed approximately 180 ft from the start, ideally the approach must be over 200 ft; indeed, since it can be argued that a long-jumper’s maximum effort is required at the end of the run, not at the beginning, his initial acceleration might well be more gradual and his approach even longer.

In fact, the world’s best long-jumpers to date have seldom exceeded 150 ft in their approach; most have used from 120 ft to 140 ft and a few have barely exceeded 100 ft. In general, it can be said that they have attained, perhaps, no more than 95 per cent of their top sprinting speed. In future, records may be broken by using longer approach runs.

TAKE-OFF. (1) Attaining maximum vertical velocity. The mechanical principles involved in long- and high-jump take-offs are identical; the emphasis at this stage should be on imparting maximum vertical velocity to the jumper’s Centre of Gravity. However, in relation to high-jumping, there are the following differences: (i) In this event the athlete attains a very much greater horizontal speed and does not accelerate into his final take-off stride. Therefore, although initially he places his jumping foot well ahead of his Centre of Gravity, he does not adopt the long, low final striding position of the good high-jumper, for to do so would result in a drastic reduction of essential horizontal speed. (ii) The long-jumper ‘gathers’ for his leap approximately three strides before reaching the board. He then ‘coasts’ on the speed he has already built up, adopts a more erect position (to enable his jumping foot to reach farther forward on take-off) and on the penultimate stride lowers his hips slightly. Although the pattern throughout good long-jumping is by no means consistent, these preparatory movements usually shorten the final stride by from three to nine inches. It would seem, however, that some jump best on a slightly lengthened last stride, while a few athletes use a stride of normal length. (iii) At take-off, the free leg is swung well flexed at the knee, for speed of action. However, his more erect position here gives him a shorter time in contact with the board—and, therefore, a reduced impulse in comparison. A slower approach would give more time but would be offset by a smaller ground reaction and a reduced horizontal speed through the air.

The best long-jumping take-offs are those where resistance to forward motion is minimised and, within limits set by the athlete’s great horizontal speed, a maximum vertical impulse is directed through the Centre of Gravity; the flexed free leg, head, shoulders and arms are first accelerated upwards before an additional vertical impulse is applied through a vigorous straightening of the jumping leg. (2) Rotation. Just as the reaction to the force of a runner’s leg drive is directed eccentrically to his Centre of Gravity (i.e. in all three main planes, sagittal, frontal and horizontal) so doesthjs also apply to a long-jumper’s take-off movements. And just as, for balance when running, clockwise and counter-clockwise moments about the athlete’s Centre of Gravity in each plane must be equal, so is this true of take-off balance in this event.

Balance in the frontal and horizontal planes presents fewer difficulties than balance in the sagittal plane, for the jumper finds the effects of eccentric thrust weaker and, therefore, so much easier to ‘absorb’ and control.

In the sagittal plane, however, there is a strong tendency to forward rotation due to pivoting over and beyond the jumping foot as it rests, momentarily, on the board, and the vertical component of the athlete’s leg thrust as it acts behind the Centre of Gravity.

Backward rotation is encouraged by the horizontal component of the jumper’s leg thrust, its vertical component when acting in front of his Centre of Gravity, and a transference of angular momentum from his free leg swing.

His emphasis on each of these constituent motions, determines whether, in this sagittal plane, the jumper leaves the board with backward rotation, forward rotation or no rotation at all. It would seem that backward rotation can be obtained only by greatly exaggerating the length of the last stride, destroying essential horizontal speed. On the other hand, experience seems to prove that a fast, efficient long-jump take-off produces either no rotation in this plane or—more often —some forward rotation.

FLIGHT. The mechanical principles governing the movements of athletes free in space have already been discussed in some detail and these apply equally to the flight of the long-jumper.

Without the use of weights (not permitted by the rules) he can do nothing to disturb the flight curve of his Centre of Gravity; both linear and angular momenta with which he leaves the ground remain constant in the air (ignoring air resistance). Obviously, therefore, the long-jumper cannot ‘jet propel’ himself in flight and any movement he makes can be concerned only with the efficiency and safety of his landing. (1) Landing position. The best landing position for a long-jumper is one which extends the flight path of his Centre of Gravity as far as possible and provides the greatest possible horizontal distance between his heels and Centre of Gravity, yet without causing him to fall backwards on landing.

To some extent, these factors are incompatible. A jumper adopting the best position for a delayed landing fails to gain maximum horizontal distance with his heels, because, in this position, his hips have receded in relation to his Centre of Gravity. Again, a position giving maximum distance hastens the landing, because the hips are now lower in relation to the Centre of Gravity; and falling backward in the pit is made more probable. Lastly, a position which presents no danger of falling back reduces the distance gained by the heels and brings the jumper to the pit earlier.

In practice, therefore, the best landing position in this event must always be a compromise; the legs are somewhat below the horizontal and the trunk leans slightly forward ; but the greater the jumper’s horizontal speed, the more effective the position he can adopt without falling backwards.

It has been estimated that, for every inch the heels are kept up, a jumper will gain about an inch and a half; all jumpers are aware of the importance of keeping the legs up on landing, and yet in all good long-jumps the legs are dropped immediately prior to landing, a fault usually attributed to abdominal weakness. However, since all parts of a jumper’s body in the air are falling at the same gravitational acceleration of 32 ft per second per second , this explanation cannot be sufficient; for here the legs are not being held up by muscles while other parts of the body are prevented from falling, as happens in hanging, with legs raised horizontally, from a beam or wall-bars; when not in contact with the ground, the athlete can adopt and hold positions which would otherwise cause muscular fatigue.

It is suggested that at this stage of the jump the legs are lowered for one or several of the following reasons: because (i) of forward rotation originated at take-off; (ii) he wishes to avoid sitting back in the pit; (iii) by raising his head and straightening the trunk, dropping his legs in reaction, he feels he is delaying the moment of landing; and (iv) of the tension of the extensor muscles of the body, which may be too strong for his hip flexor and abdominal muscles; only in this sense can the fault be attributed to muscular weakness. d

Even in the best practical landing position, however, it is unlikely that the jumper’s heel will contact the sand beyond an extension of the flight curve of his Centre of Gravity —if, indeed, he can get them even that far in front of his body weight.

Landing efficiency is increased in long-jumping when, immediately before contacting the pit, the arms are behind the jumper , for he then adds to the horizontal distance between his Centre of Gravity and heels , and when he lands he can then throw the arms vigorously forward to assist the forward pivoting of his body, transferring momentum. (2) Movement in flight. The foregoing analysis of the problems of landing and rotation off the board provide the key to the kind of movement in flight of greatest value to the long-jumper.

If he takes off with excessive backward rotation, he should extend his body—’hanging’ —to increase its moment of inertia about at_ransverse-horizontal axis of momentum and so slow down this rotation. Then, immediately before landing, he should ‘jack’ at the hips and so increase his angular velocity, raising and extending his heels in relation to his Centre of Gravity.

With either no rotation or forward rotation off the board about this same axis, however, he will profit from movements which will rotate the body backwards. If he leaves the board with no rotation, by cycling his legs forward, his trunk will automatically turn backwards, for he cannot change his total angular momentum in flight.

With forward rotation off the board, the angular momentum generated by the forward rotations of his legs (and, to lesser degree, his arms) should exceed his total angular momentum; the jumper’s legs and arms must develop sufficient angular momentum not only to ‘take up’ these rotations, but also to turn the trunk and hips backwards in the sagittal plane. But when these arm and leg movements cease, the original body rotation (which cannot be destroyed in the air) reveals itself.

A majority of athletes using this ‘running-in-the-air’ or ‘hitch kick’ style employ a single-stride technique ; yet there is doubt that this displaces body weight sufficiently about the jumper’s Centre of Gravity. Usually, he completes this single stride and attains his landing position too soon, rotating forward again before landing.

It would seem that an extra stride in the air would provide an even better landing position; two strides could give greater displacement, yet without bringing the jumper too quickly into his ‘jacked’ landing position. And, of course, theoret ically, three strides are better still, though no jumper has yet suc ceeded in completing three full strides in the short time between take-off and landing.

With forward rotation off the board, a ‘sail’ jumper speeds up the rotation; by ‘jacking’ quickly after take-off he reduces his moment of inertia about the transverse-horizontal axis and so increases his angular velocity. A ‘hang’ position merely slows this forward rotation by increasing the body’s moment of inertia. As is the case of the ‘sail’ jump, it does nothing to absorb or counteract rotation.

Because of their smaller moments of inertia the arms, even when fully extended, do not possess the turning effect of the legs. Yet, by virtue of the position of the shoulders—a secondary axis, in relation to the jumper’s Centre of Gravity, the location of the main axis—the arms possess a considerable turning effect above the head, particularly where there is a maximum possible distance between the axes.

As the arms are lowered, however, their turning effect on the rest of the body weakens progressively; and if the athlete remains in a fully stretched position they might eventually encourage a forward body rotation. However, in practice, by the time the arms are nearing their lowest position the jumper has already ‘jacked’ in preparation for his landing; the sweep of each arm’s radius of gyration therefore ‘embraces’ the main axis and continues its (now very weak) influence in favour of backward rotation of the whole body.

Certainly, in the sagittal plane the legs are always the principal ‘absorbers’ of body-rotation in long-jumping; the arms—held wide of the body—have more to contribute to balance in the horizontal and frontal planes.

The benefits of a hitch-kick can be exaggerated; men have jumped well without it. Yet, so far as is known, all the world’s 26-ft plus long- jumpers, to date, have employed this technique, although it has sometimes been combined with a ‘hang’

Triple-jumping

The mechanical principles relating to high- and long-jumping are also fundamental to the triple-jump although, of course, the technique of this event differs.

The distance gained in a triple-jump is largely dependent upon the horizontal speed which can be developed in the approach and the extent to which this can be controlled, conserved and evenly apportioned over all three phases—hop, step and jump.

But, on each phase, the triple-jumper must also gain sufficient height at take-off and support his weight on landing. The movements required for this are responsible for opposing horizontal forces of a size which depends upon his mass, velocity, Centre of Gravity angles at takeoff and landing, and skill. The resistance of the air also reduces speed.

As he cannot change his weight, govern air resistance to any significant extent, nor produce a good jump without maximum (controlled) approach speed, he influences his overall jumping distance by controlling his angles of take-off and landing, by skilfully reducing the landing shock, and to a limited degree by driving horizontally on each take-off.

For the conservation of horizontal speed, ideally, the jumper needs a low-angled take-off and a steeply-angled landing, but these are incompatible: take-off and landing angles must always be approximately equal, particularly in the hop and step. Therefore, in the hop, for example, where a good jumper gains his distance mainly on approach speed, a comparatively low take-off angle favours conservation, while the acute angle at which he lands tends severely to check his forward movement.

To reduce this resistance, therefore, the expert triple-jumper moves his leading foot back quickly immediately before landing to reduce its forward speed in relation to the ground , lands with the greatest practicable angle between his leading foreleg and the ground, and then ‘gives’ at the hip, knee and ankle joints. Yet he must stress none of these movements at a cost, subsequently, of essential vertical speed. These principles apply equally to the step technique.

The analysis revealed that, without exception all the jumpers were progressively longer in contact with the ground over the three phases— hop, step and jump—denoting a gradal reduction in horizontal speed. Again, without exception, in terms of time, all were longest in the air during the jump and shortest in the step. In fact, their jumping rhythms were never even. In our hypothetical average jump, for example, the jumper’s Centre of Gravity would rise 15 in. in the hop, only 8 in. in the step and 14 in. in the final phase. These figures also underline the difficulty of gaining height in the step and jump; for the average pressure of the foot on the ground after the hop would be 4 times that of the body weight; after the step, 3-8 times.

Yet this is not to suggest that coaches who advise on even rhythm— ‘ta, ta, ta’—and a successively higher flight are wrong. For in coaching the triple-jump one must teach a higher, longer step than the athlete would do naturally and instil the idea of increased effort from phase to phase. Knowing what actually happens in a good jump a coach may yet correctly tell his athlete to attempt something different —the art, as opposed to the science, of coaching.

The basic principle in the triple-jump is that no one phase must be stressed to the detriment of the overall effort. But there can be no precise ratio of distance between the hop, step and jump because of the differences in athletes (in speed, spring, strength, weight, flexibility, proportions, etc., etc.) Certainly, no triple-jumper apportions his effort in exactly the same way from one jump to the next! However, a 10:7:10 ratio has been found suitable for beginners (e.g. 14 ft 9 in.: 10 ft 5 in.: 14 ft 94- in. for 40 ft), while world performances suggest a 10:8:9 ratio for the much more experienced athlete (e.g. 20 ft ? in.: 16 ft 6 in. : 18 ft 8 in. for 56 ft—i.e. with greater emphasis on the Hop and Step).

Hop. Because of the need to conserve horizontal speed, an expert triple-jumper gains hopping distance mainly as a result of his approach speed; his jumping foot does not reach out as far ahead as in a long-jump take-off nor is his final leg thrust as vertical. He could hop higher and travel much farther in consequence, but only at tremendous cost to speed in the step and jump. In this first phase, in particular, restraint in the apportioning of height and distance (and, therefore, speed) is essential.

If he is to follow the hop with a balanced step of good length, the jumper must keep his body upright in this first phase, his head in natural alignment with the shoulders. To avoid a backward-rotating hitch-kicking movement, the legs should reverse their positions with approximately equal moments of inertia about their hip joints , and to facilitate an ‘active’ landing on the hopping foot this reversing of leg position should occur relatively late in flight.

Here, the expert ‘waits for the ground to come up to him’; until the last possible moment, his leading thigh is held roughly parallel to the ground , for if it is lowered prematurely, his Centre of Gravity will pass quickly over and beyond the landing foot and his supporting leg will be too straight. In consequence, the step phase will be hurried, weakened and shortened.

A jumper who ‘waits for the ground’ lands in a slightly lower position and with greater leg flexion—both favourable to a ‘cushioning’ of the landing and a pronounced forward-upward drive in the step. At the instant of landing the Centre of Gravity should be approximately 1 foot behind the front foot, yet not so far back that the leg ‘buckles’ as a result of the backward thrust of the ground. In fact, the heel lands first, but a good jumper will not be conscious of it; the landing will feel flat-footed. The free leg trails at this stage

The primary function of the arms is to absorb reaction to the powerful, eccentric leg thrust at take-off, to keep the trunk aligned properly. But in so far as action and reaction are interchangeable factors , vigorous arm movement in a sagittal plane can also contribute to the horizontal component of leg thrust on each take-off; and, to a limited extent, the upward acceleration of the arms on each occasion can augment vertical velocity.

Ideally, therefore, the arms should be swung vigorously backwards and forwards in the hop, passing close to the trunk; and this applies also to the step take-off. However, where a jumper leaves the board unbalanced, rotating in a horizontal and/or frontal plane, he must then extend his arms wide of the body in an attempt to produce counter-rotations ; and, to the detriment of his step take-off, he must land with them in this sideways position at the end of the hop.

Step. The figure for the average pressure between foot and ground in landing from the hop in our hypothetical average jump for the twelve experts, gives some indication of the effort required to overcome that pressure and yet acquire new velocity and an optimum take-off angle for an adequate step. With beginners the step is used merely to recover from the hop; they put the next foot to the ground as quickly as they can, and this fault is accentuated when the hop has been too high or the landing foot has been placed too far in front of the body. On the other hand, world-class triple-jumpers rarely step shorter than 14 ft.

The key to developing a good step lies in the use of the free leg at takeoff. Flexed, it should be swung vigorously until its knee is waist high; simultaneously, the other leg should drive hard down and back. Experience proves that in flight a jumper should ‘float’; here again, he should ‘wait for the ground to come up to him’; keeping his front thigh at waist level, yet permitting the rear knee to swing forward to a position beneath its hip.

It has often been suggested that this more vertical rear leg position is easier than trailing it far behind between take-off and landing, for the reason that, otherwise, gravity ‘pulls the leg down’. In flight, however, any body position relative to the Centre of Gravity can be difficult to maintain only by virtue of internal muscular tensions. Since gravity acts on all parts of the body with equal effect, there can be no other reason.

The step landing is the same as for the hop, except that some jumpers swing both arms to the rear before contacting the ground, in order to use a double arm movement in their jump take-off. This arm action is used, usually, with a hang technique. Too vigorous a backward movement of the arms, however, pitches the trunk too far forward for an effective jump; the athlete then falls, rather than springs, into the pit—with considerable forward rotation. The trunk is best kept as erect as possible at this stage.

Jump. Fundamentally, the technique in this final phase is that of the long-jumper, but in comparison, the triple-jumper is a shorter period of time in the air and has less horizontal speed on landing—if his hop and step have been executed correctly. Also, after the two previous phases the control of his jump is more difficult.

With less forward speed on landing, the triple-jumper is in greater danger of sitting back in the pit. Here, a little forward rotation (although never consciously developed in a good jump) might be to the jumper’s advantage; he is also in greater need of movement which will help to pivot him forward over the fulcrum of his heels, i.e. an immediate and pronounced flexing of the legs on landing (reducing his moment of inertia about his heels) and a throwing forward of his arms, to build up and then transfer their momentum. When momentum is transferred mass x velocity of the part equals mass x velocity of the whole.

Sail and hang techniques are usually preferred to a hitch-kick, for the latter needs more time and control than are generally available. In both styles, the legs should be brought through well flexed at the knees before straightening, thereby reducing their moment of inertia about the jumper’s Centre of Gravity, speeding up their movement and diminishing a trunk reaction which would otherwise mar the landing position.

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