I have decided to begin a diet and exercise program known as lean gains. Of all the diet coaches I have come across online, Andy Morgan of rippedbody.jp seemed to me to have the most thorough method in place to augment the lean gains program, which was originally formulated by Martin Berkhan.
What appealed to me about this particular diet after having tried it for approximately one week was the ease of implementation and the virtual total lack of hunger. Now don’t get me wrong! This isn’t one of those fad diets we could eat all you can look at. It is actually very scientific and mathematical and is based on your basal metabolic rate and cleverly going over and under that on various days according to your activities.
You end up with a daily calorie figure that fluctuate according to whether you weight training or not on specific days. The calories also broken down into macronutrient quantities of protein carbohydrates and fats. The higher calorie days involve more carbohydrates and lower fats. The rest days which have lower calories, are fairly low in carbohydrates and slightly higher in fats, but protein stays high on both days, somewhere around 200 g for me.
One of the interesting things about the diet is its flexibility. There is a skip breakfast, intermittent fasting version, which I actually like. Doing it in this way, you eat two or three large meals after your training session or at some point around lunchtime if you happen to train in the middle of the day. For me, these were quite big meals to get used to but they are very satisfying and leave you feeling full for hours. There is no mucking around with five or six small meals a day. I tried that in the past and eating these mouse sized meals was always very frustrating and left me hungry. I find it much more natural to eat big just a couple of times a day rather than poncing around with silly small meals. It’s very convenient just to cook yourself a couple of big meals rather than all this precooking story in Tupperware baloney you read about on body building websites.
It’s also quite refreshing to see a complete absence of Bro science on Andy Morgan’s website. It’s just down to business, analytical, tracks progress, and if you look at the client testimonials, there is plenty of proof that the system works. But I suppose the best way to test it is to do it yourself. That’s what I intend to do.
The training involves fairly heavy resistance movements such as bench presses, squats and deadlifts, or variations of these according to the clients abilities. There is no cardio required as it is the diet that deals with the fat burning rather than the exercise. The exercise is to stimulate muscle growth and to improve the physique as you lose body fat. There is quite an emphasis actually throughout the site that cardio and aerobic exercise for weight loss is often counter-productive. It can be used sparingly to remove very stubborn body fat, but that is for the later stages of the diet if you are actually having trouble with things like a little bit of extra fat round your lower abs.
Andy links back to Martin Berkhan’s website – leangains.com quite extensively to accentuate and highlight many of the points that are valid in the diet system which may be puzzling to people new to this approach. However, fundamentally, the diet is based on common sense rather than wacko theories. A few pieces of equipment you might need could include digital scales to weigh your food so you know exactly how much your eating. Also you might want to get hold of a good tape measure to keep track of your body dimensions.
In all four throwing events the distance obtained is dependent upon the speed, the angle of release of the missile, and, in the discus and javelin events, certain aerodynamic factors.
An efficient throwing technique is one in which the athlete exerts the forces of his entire body over the greatest range practicable and, therefore, for the longest period of time; for the speed of release in throwing is proportional to the average force exerted through the implement’s Centre of Gravity. Other things being equal, the greater total body force produces the greater speed and the longer throw, since force = mass x acceleration the forces must be exerted against the missile in the proper direction, however—so far as practicable, in the direction of the ultimate throw; for the total effective force in throwing is the sum—the resultant—of all the components of the various body forces acting in that direction. As a general rule, in throwing, however, in the preliminary movements there is more horizontal drive than lift, and in the delivery more lift than horizontal drive. The eventual effect is to release the missile at an appropriate angle to the horizontal.
These two principles are fundamental to correct preliminary movement in throwing—in the run-up, glide or turns. In good throwing they are exemplified in the stretching and powerful recoiling of large muscle-groups; in the driving of body weight from one leg to another and (in the hammer and discus events in particular) in the use of maximum radius of movement in the turns and delivery.
The various forces of the body should be exerted in definite sequence and with proper timing; for the release speed in a good throw will be greater than in a bad one, even if the same effort has been expended and the throws are equal in all other respects.
From a purely mechanical point of view it is immaterial in what order a given set of forces is applied, one by one or simultaneously; the final speed is the same. To accelerate a shot, discus, javelin or hammer, however, each body lever in turn must be capable of moving faster in a given direction than the missile is moving in the same direction; and the faster the lever can move the greater will be its effective force.
In a summation of throwing forces, therefore, the levers of the body should operate so that each can make a maximum, or very near-maximum, contribution to speed. Hence the use of slower but more forceful muscles and levers first (i.e. of the trunk and thighs); while the faster but relatively weaker joints (i.e. of the arms, hands, lower legs and feet) exert their forces after the missile has developed considerable speed. While the feet and hands transmit force during the earlier movements, therefore, their own smaller forces are added only towards the end of a throw. It is important that each lever, having attained top speed, should continue at that speed in support of the movements which follow , bringing about not only a summation of forces, but a summation of rotations, too.
However, there must be no undue delay in the application of the various forces because of forces which tend to retard the missile even before it leaves the thrower’s hand, i.e. gravity (which tends to reduce upward motion) and the friction between the athlete and the ground at the instant of foot contact (which tends to slow the missile horizontally). The vertical forces in particular should be applied as simultaneously as practicable.
Turns, glides and run-ups should be as fast as an athlete can use to good purpose; never so fast that he is unable to exert full body force subsequently in the delivery. In this respect, each athlete possesses his own ‘critical’, optimum speed of preliminary movement.
For maximum speed of release the ground must provide adequate resistance to the thrower’s movements, and for as long as he is in contact with the missile, for the force he can exert against it is limited, very largely, by the counter-thrust of the ground.
Force in a horizontal plane can be lost when both feet are off the ground. As the athlete on the turntable attempts to put the shot, upper and lower parts of his body rotate in opposite directions ; reaction to his movement in a horizontal plane must be absorbed by the turntable and his body, not by the ground. Likewise, force applied vertically in throwing is also dependent upon the resistance of the ground.
As Housden points out, in developing angular momentum in discus throwing the athlete must have some part of each foot or, at least the whole of one foot, in contact with the ground. He recommends the following experiments; first, stand with both feet on the ground and with the right arm back behind the shoulder, swing the arm horizontally, and as it comes to the front of the body, raise the right foot and rise on the left toe. Through a transference of angular momentum from the arm, the body will then turn in the same direction. Then stand with the left foot flat on the ground and repeat the arm movement. There is again a transference of angular momentum. (Here, in both cases, the ball and heel of the foot exert equal and opposite horizontally-directed forces against the ground, which then exerts equal and opposite reactions, forming a couple.)
In a third experiment, stand with only the ball of the left foot in contact with the ground and repeat the arm movement. There will be no transference; (indeed, if the foot rests on a smooth surface, it will rotate towards the arm, in reaction, together with other parts of the body). From this, Housden concludes that a discus thrower is unable to increase his angular momentum from the moment his right foot leaves the ground in the back of the circle until the instant his left foot lands in the front of the circle, and both feet are on the ground again.
Certainly, a thrower can exert his greatest forces when both feet are firmly in contact with the ground. In the shot and javelin events in particular, however, effective contact by the rear leg is broken once it has completed its drive, and contact with the ground is maintained only by the leading foot . It is impor- ry> potation tant to consider the timing of the breaking of this rear leg contact in relation to the movement of the arm, to see how continued maximum horizontal force can be applied to the missile.
Taking shot putting as an example; when the front foot comes to the ground it loses speed. The horizontal force exerted by the ground has then a two-fold effect: it causes both athlete and shot to rotate about this foot, and reduces the forward speed of the Centre of Gravity common to athlete and shot.
This sudden checking force causes an instantaneous change in speed at each point of the putter’s body except one—below which all parts are slowed down, while all parts above this point are speeded up. It is important to realise that when the hand exerts a force on the missile, either above or below this special point, the reaction tends to move the feet forwards or backwards respectively. (When considering the movement of a rigid body, this point is known as the centre of percussion, and its exact position can be calculated. As our shot putter is far from rigid, however, it can only be said that this point will be some distance above the Centre of Gravity.)
By way of illustrating this principle; when a man holds a shot with both hands at arms’ length above his head and, after an upward jump, pushes the shot forward while he is off the ground, his feet should move forward ; but when, under similar circumstances, he thrusts the shot forward at chest height, the reaction should then move them backwards. (By the same token, when the arm circling is executed at the level of the man’s centre of percussion, his feet are unaffected and the movement invokes only the simplest of turntable reactions.)
In shot putting, correct technique requires the rear foot to be firmly in contact with the ground until the arm strikes , permitting the ground to resist the tendency of the feet to move backwards. Once this rear leg has done its work and the arm strikes higher, however, the backward reaction on the hand tends to move the front foot forward and the ground reacts against it, allowing continued maximum force to be exerted.
Throwers who break contact with the ground before the missile leaves the hand may do so for lack of arm and shoulder strength; for a combination of the implement’s inertia and accelerations developed by the legs and trunk may be too much for the arm—whose final action may have to be delayed until the accelerations have been reduced.
Or, again, contact could be broken prematurely to reduce the athlete’s forward motion. Or the feet may be too close together or otherwise incorrectly positioned. Or the arm could be striking too horizontally.
Maximum release speed in throwing (particularly in the shot, discus and javelin events) is influenced by the ‘hinged momenC principle , whereby, on attaining maximum, controlled (i.e. ‘critical’ speed at the end of the preliminary run-up, glide or turns, the front foot is checked.
As we have seen, the checking force at the foot is one of two equal parallel forces acting in opposite directions, producing a turning couple —a forward rotation, a ‘hinged moment’. This checking force also reduces the forward speed of the Centre of Gravity common to thrower and missile.
As the speed of a point on a turning body is directly proportional to its distance from the axis (which, in this case, is the athlete’s front foot) the throwing shoulder will now possess more speed than the Centre of Gravity, but whether or not it is greater than the thrower’s original linear speed depends upon the extent to which the Centre of Gravity slowed down. This, in turn, depends primarly upon the horizontal distance between the Centre of Gravity and the front foot as the latter comes to rest.
In javelin throwing, where this foot is far in advance of the Centre of Gravity , most—if not all—parts of the athlete lose speed at this instant. In so far as there is rotation about the foot, all parts of his body above the Centre of Gravity may move faster but not as fast, perhaps, as his linear speed immediately beforehand.
Such a sacrifice is still worth while to the javelin thrower, however; indeed, it has to be made in good throwing. The front foot must be stretched well ahead of the body in order to provide an effective throwing position and, in view of the thrower’s forward speed, to give sufficient time for the movements of throwing. The writer has seen no mathematical evidence to show that a javelin thrower’s upper body improves its linear speed as a result of the front foot coming to the ground, but if that speed is retained, or only slightly reduced, while the athlete adds his powerful throwing movements, it is obviously of great advantage, subsequently, to the speed of delivery.
In the shot and discus events, however, where (in comparison with the javelin thrower) at this instant the front foot is not excessively in advance of the Centre of Gravity (and where, therefore, there is less checking of forward speed), it seems very likely that there is a point which corresponds to a centre of percussion, with parts of the body above it speeded up; but this point will be changing constantly with changes in body position. (When the base of a rod (i.e. a thin, rigid, uniform rectilinear mass), moving horizontally in a vertical position, is brought to rest the speed of its Centre of Gravity drops by a quarter. If B is twice as far from A as the Centre of Gravity, it will move twice as fast as the Centre of Gravity; so the speed of B is improved by 50 per cent at the instant of checking. The centre of percussion in such a mass is always two-thirds AB from A. In a rigid non-uniform mass, however, the problem is very much more difficult.)
In throwing, the force exerted is to some extent dependent upon the athlete’s mass. In discus throwing, for example, as the arm strikes the tendency is for the rest of the athlete’s body (especially the throwing shoulder) to move downward and backward in reaction, so reducing the effective force and time/range over which force can be applied.
In good throwing, the reaction to the vertical component of the arm’s movement will be counteracted by the up-thrust of the ground, regardless of the thrower’s weight; but the reaction to the horizontal component will cause the upper-body of a comparatively light athlete to move backward more than a heavier thrower, other things being equal. The heavier man can therefore exert more effective force over greater distance.
It follows that an athlete who breaks contact with the ground prematurely in shot putting will in all probability find the error more costly than when throwing a discus since, obviously, the reduction in delivery impulse involves the ratio of missile weight to body weight, i.e. the mass of the missile times its speed, equals the athlete’s mass times his speed in an opposite direction. For this reason it has been argued that the reduction in delivery impulse owing to breaking ground contact before the discus leaves the hand is little more quantitatively significant than a gun’s recoil as a shell is launched.
Sheer mass is also of value in increasing the radius of movement in discus and (particularly) hammer throwing, increasing the missile’s speed. Since the axis of the thrower’s turning movement passes through his feet and the Centre of Gravity (common to athlete and missile) , a heavier athlete brings his shoulders closer to this axis than a lighter thrower.
Angle of release
If a thrower is to obtain maximum distance, it will not be sufficient to give the missile maximum release speed; it must also be thrown at an appropriate angle.
When points of release and landing are the same height above the ground (and aerodynamic factors may be ignored) the optimum angle for the projectile of a missile, regardless of its speed, is one of 45 deg.. In this case, vertical and horizontal component velocities are equal, and the missile also lands at a 45 deg. angle. (Here, distance is as the square of the velocity; so, for example, if the velocity increases by 10 per cent (from, say, 100 to 110 units) the distance will be increased by 21 per cent (from 100 to 121 units).)
It should be noted that the weight of a missile reduces the resultant vertically upward thrust delivered to it. To release, e.g. a shot at this angle, therefore, a thrower must exert a force vertically greater by 16 Ib-wt than the horizontal force.
However, in all four throwing events in field athletics the implement is thrown from a point above the ground and this affects the release angle. Then the optimum angle depends upon height and velocity of projection. In the shot and hammer events (where aerodynamic factors are of no account) the optimum release angle will be less than 45 deg. Theoretically, a missile thrown at this angle will land at an angle with the horizontal equal to the angle its release direction makes with the vertical. For example, a shot released at 41 deg. 40 min. will land at 48 deg. 20 min. (released 7 ft above the ground, at a velocity of 41-3 f.p.s. for a distance of 60 ft measured horizontally from the point of release).
The optimum angles of projection for a put of 60 ft (measured horizontally from the point of release to the point of landing, i.e. not allowing for the distance between the inside edge of the stop-board and the hand (approximately 1 ft)), from release heights of 8 ft, 7 ft and 6 ft, will be 41 deg. 12 min., 41 deg. 40 min. and 41 deg. 54 min. respectively. In hammer throwing the missile is released so close to the ground relative to the distance thrown that, for all practical purposes, 45 deg. can be assumed the proper angle of delivery.
The forces exerted in throwing give greater release speed when they are directed nearer to the horizontal. In fact, a study of the dynamics of shot putting reveals that within certain limits speed of release is more important to an athlete than the use of an optimum angle.
In theory, a shot projected 60 ft from a point 7 ft above the ground must rise to a height of 18 ft 9 in.. Yet most 60 ft shot putters do not put so high and therefore do not release the shot at such optimum angles. It could be said, of course that by contriving to improve their elevation they could put even farther—and this could well be true of some. It seems likely, however, that at such levels of performance the factors responsible for maximum release speed conflict with those that give an optimum angle of delivery. (i) 40 deg. is nearer the average optimum angle than 45 deg; (ii) from 35 deg. upward comparatively little increase is made in putting, for the same velocity; (iii) an increase in height of release from 6 ½ ft to 7 ft gives only an additional 5 to 8 in. in distance; from 7 ft to 8 ft only 9 to 15 in.; (iv) relative increases in velocity very decidedly increase distance. For example, putting from a height of 7 ft, at an angle of 35 deg. at 42 f.p.s., an athlete attains 60 ft 4 in., but gains only 1 ft 4 in. by increasing his angle by 5 deg.; whereas, by returning to an angle of 35 deg. and increasing his speed by only 1 f.p.s. he gains 2 ft 7 in., and as much as 5 ft 2in. for an increase of 2 f.p.s.
The proper use of the strong leg and trunk muscles in throwing plays a vital part not only in releasing the missile at maximum speed, but also in projecting it at a correct angle; in particular, where the angle is too low, leg and trunk action—and not the arm or arms—is almost entirely at fault.
In fact, the emphasis on ‘lifting’ the missile with the legs and trunk during the actual throwing movements should be considerable, especially where comparatively great horizontal speed has first been developed in the run-up or movement across the circle; for the angle of projection will be the product of the preliminary and throwing movements.
In discus and javelin throwing, distance depends upon the speed and angle of release, as with the shot and hammer events, but by virtue of their size and shape, aerodynamic forces also influence the flight of discoi and javelins. These missiles do not describe simple parabolic curves.
As yet, the aerodynamics of discus and javelin throwing have not been worked out in detail, for many unknown factors and variables (not the least variable of which is the thrower himself!) are involved. What follows is therefore no more than an outline of basic, relevant aerodynamic principles, with some comment as to their significance in these events.
General principles. In moving through the air a discus or javelin drives part of that air to the side and pushes some in front of it. This requires work and, therefore, a reduction in kinetic energy and, therefore, speed. The air’s resistance depends upon the shape and size of the missile; generally, the thinner and sharper it is at the front, the smaller is the resistance—which can be further reduced if its cross-section narrows gradually towards the rear, giving a ‘streamlined’ effect.
In front of the missile, therefore, there is a region of increased air pressure, and in its path another region where the air whirls irregularly, causing diminished pressure. The kinetic energy of turbulent air movement in the wake of a discus or javelin accounts for much of the work needed to move it through the air; but the better the stream- lining, the smaller will be this air disturbance. present the same effective cross-section to the on-coming air yet, because of its streamlining, object b has 1/25 the specific resistance of a.)
Air resistance is also dependent upon the speed of the discus or javelin, and is proportional to the square of the velocity.
When a missile is inclined at an angle to the wind the resultant of the forces exerted upon it by the air can then be resolved into vertical (lift) and horizontal (drag) components. The ratio between lift and drag depends upon the angle of attack, i.e. the acute angle between the plane of the discus or javelin and the direction of the relative wind. Even small variations of this angle can sometimes produce abrupt alterations in the lift/drag ratio.
The term relative wind refers to the movement of the air in relation to the missile. All motion is relative; a discus or javelin can be suspended in an air-tunnel with the air flowing past, or it can be moving through still air. A following wind can therefore reduce the speed of the relative wind (lessening lift and drag) and a headwind can increase it (but must not be too strong to be of benefit in these two events).
A relative wind will not always directly oppose the flight-path of the missile’s Centre of Gravity, however; usually, in throwing, air currents are continuously varying in both strength and direction. Nor, always, do the missile’s flight-path and its plane coincide, an angle between being called the angle of incidence; this can be positive (i.e. above the angle of the flight path) or negative (i.e. below that angle). The angle between the plane of the missile and the horizontal is called the attitude angle.
The sizes of the various lifting forces acting on a discus are dependent upon the angle of attack. When the angle is zero the upward forces on the lower surface act only near its leading edge; but as the angle increases these forces also increase, both above and below the discus. When the angle is of a certain size, however, air turbulence forms along the trailing edge and grows markedly with a further increase in angle.
The shape of the discus or javelin and the angle it makes with the direction of the relative wind cause the speed of the air flowing over the missile’s upper surface to be greater than that underneath. As a result, there is a diminished air pressure above the missile and the upward forces acting on it are greater than the downward forces.
All the forces of the air acting on a discus or javelin may be added together to form a resultant which acts at a point called the centre of pressure. This changes position with a change in the angle of attack; as this angle increases, the centre of pressure moves forward and the resultant force increases. Conversely, with an increase in the speed of the relative wind, the centre of pressure moves farther back. There is a limit to which the angle of attack can be increased to advantage, and if that limit is exceeded turbulence behind the missile disturbs the smooth flow of air over its upper surface; the upward force (lift) almost disappears, drag increases and the missile stalls. This limiting angle is called the stalling angle.
The lifting force acting on a discus or javelin in flight therefore depends upon: (i) its shape (which influences the nature of the air-flow past its upper and lower surfaces); (ii) the angle of attack (within limits, the greater angle produces the greater lift); (iii) the surface area (the greater the area, the bigger the total lifting force); (iv) the square of the air speed (for example, lift is four times greater when a javelin is released at 50 m.p.h. than at 25 m.p.h.); (v) air density (the greater the density, the greater the lift).
The flight of the discus. A discus (which experts think a comparatively poor aerodynamic design) ‘performs most efficiently as an airfoil between speeds of 69-8 and 80 feet per second’ (Ganslen), and its spin, in good throwing, provides some gyroscopic stability in flight, keeping the lift/drag ratio relatively constant.
For all its gyroscopic benefit, however, spin itself tends to increase the angle of attack (Housdenf)—a paradox which, perhaps again, shows how, in the analysis of ath letic movement, advantages must be weighed against disadvantages.
To illustrate: when a discus rotates in a clockwise direction its left side meets pressure the air at a greater speed than its right side; the former spins into the air, while the latter moves away from it. Therefore the upward force exerted by the air on the left side is greater and the centre of pressure is to the left. There is therefore a tendency for the discus to turn about the axis XOX1 (clockwise, as seen from X).
This does not happen, however, because of its spin. Assuming an upward pressure exerted somewhere on OY , this turns the discus about the axis OY (clockwise, as seen from Y); for each point on the missile is raised as it moves across OX and continues to rise until it reaches OX1 ; every point on the discus is higher at X1 than at X and, as a result, its front edge tilts upwards. Conversely, a downward force exerted at the centre of pressure will lower this front edge.
The following figures show estimated distances a discus can be thrown for given initial speeds, using combinations of projection and attitude angles (Cooper, Dalzell and Silverman (Purdue University) from wind-tunnel data supplied by Ganslen). Here it has been assumed that spin stabilises a discus, in good throwing, to the point of maintaining a constant attitude angle (the authors claiming that motion picture analysis indicates no appreciable change in this angle throughout flight).
The following conclusions may be drawn from these tables. (1) Speed of release is the factor of greatest importance, as emphasised previously. A small increase in speed in discus throwing gives a comparatively larger increase in distance, however, because the lift on the missile is proportional to the square of its speed. (2) For a given speed, the most important variable is the angle of projection. 150 to 200 ft throwers should project at 35 deg. to 40 deg.; throwers of lesser ability should increase the angle slightly, but never above 45 deg. (3) The attitude angle should be between deg. and deg. At the instant of release, therefore, there should be a negative angle of incidence of approximately 5 deg. to 10 deg. Although, at such an angle, air pressure will tend to depress the front edge of the discus, the ascending half of its flight-path automatically reduces the angle. If the latter tendency is the greater, then the missile moves gradually into alignment with the tangent to the path of its Centre of Gravity— presenting a considerable surface-area to the ground during the descending half of the flight, benefiting by the cushioning effect of the air beneath and, therefore, gaining distance through a gliding motion.
On the other hand, a positive angle of incidence upon release must increase as the discus moves forward and its flight-path curves towards the ground. In addition, air pressure increases this angle, leading to a progressively stronger resistance to forward motion and, eventually, stalling. (The stalling angle for a discus is said to be approximately 30 deg. (Ganslen).)
The greater the speed of the discus upon release, and the stronger the opposing wind, the smaller should be the attitude angle as the discus leaves the hand, to avail the throw of a more favourable lift/drag ratio. Practical experience proves that a discus can be thrown farthest into a wind blowing from front-right , and Pharaoht (Great Britain; 4th, Discus, 1956 Olympic Games) has maintained that the difference between throwing directly into a wind, and with that same wind, varied—for him—from about 5 ft for a wind-speed of 7 m.p.h. to approximately 15 ft at 20 m.p.h., the greater distance being thrown into the wind. Stronger headwinds reduce stability in flight and therefore shorten the distance.
Flight of the javelin. From 1955 to 1961 javelin throwing world records rose primarily through the use of implements of improved aerodynamic design, giving an increased stability and a better lift/drag ratio in flight. They were considered to add as much as 25 ft to a good throw. These ‘glider’ javelins, as they came to be called, were made in several different diameters to suit a thrower’s ability and varying throwing conditions; they possessed a lighter spearhead, a more evenly-distributed surface-area and tapered less towards the tail than previously.
The year 1961 saw the end of this era of javelin throwing, however, because the International Amateur Athletic Federation further revised its specifications so as to limit these aerodynamic features and enforce a stricter uniformity as to the type of javelin used throughout the world. The javelin now permitted has a reduced diameter (a maximum of 30 mm as against the previous 35 mm) and its angle of taper and length of point are also specified. However, the regulations still permit some variation, for the javelin-diameter can vary from 25 mm to 30 mm and its Centre of Gravity can be between 90 cm and 110 cm from the point. Compared with the javelins used prior to 1955, in fact, the present implement remains ‘aerodynamic’.
There is considerable disagreement and ignorance, even among experts, as to the behaviour of an aerodynamic javelin in flight, and little reliable scientific information on this subject at the present time.
A Russian opinion, that of V. L. Kuznetsov, assesses the optimum angle of release for the modern javelin at 28 deg. to 30 deg., ideally with the shaft at this instant in alignment with the tangent to the path of its Centre of Gravity (i.e. with a zero angle of incidence). Certainly, when this improved javelin is released at much greater angles (e.g. at approximately 45 deg., as necessary in throwing the ‘old’ design) the tendency is to give it too great an angle of attack. It then rises and falls abruptly, for its centre of pressure is too far in front of its Centre of Gravity, creating backward rotation and stalling. (These two centres and the distance between them then create a couple whose turning effect is proportional to that distance (i.e. the arm of the couple).)
Some experts are of the opinion that the optimum release-angle of these aerodynamic javelins is nearer 40 deg., with an angle of incidence at this instant of approximately -10 deg.; but they admit that an athlete must be very skilful to use it without creating too great an angle of attack, for in attempting to produce more ‘lift’ in the delivery, the tendency is to raise the head of the javelin. It is easier to control this angle when the delivery is more horizontal, and most athletes prefer to ‘play safe’ in this way.
In an aerodynamically well-designed object the centre of pressure remains comparatively stable in flight; the relatively even distribution of surface-area of the modern javelin is said to reduce the motion of its centre of pressure as it travels through the air. However, even in good throwing it seems certain that this point changes position to some extent—initially, perhaps, acting a little in front of the Centre of Gravity, before moving back during the flight to bring about a slight contrary rotation for landing at a shallow angle.
Rotation of the javelin (in this sagittal plane) is also influenced by the position of the thrower’s grip in relation to the missile’s Centre of Gravity—the point about which rotation must take place in the air. The farther behind this point the grip is (particularly the hand’s last contact with the javelin) the greater will be the tendency for the spearhead to drop prematurely; for the thrower’s upward component of force, and gravity acting through the javelin’s Centre of Gravity, then create a couple.
On the other hand, the closer the grip is to the Centre of Gravity, the smaller will be the rotational effect and the easier it will be for the athlete to exert his final force of delivery correctly. In general, good throwers prefer the Centre of Gravity to be as far away from the spearhead as the rules permit, with their grip as close as possible to the Centre of Gravity.
In the process of releasing a javelin a thrower automatically imparts spin about its long axis—the result of an outward rotation of his elbow and the sequence with which his fingers break contact during delivery. This spin (clockwise, seen from behind, in the case of a right-handed thrower) can possibly give some gyroscopic stability in flight, provided it is of sufficient intensity. However, whereas some experts speak in terms of thirty revolutions per second in a good throw, and regard this spin as important, others deny that much spin is ever developed or has any significance. To summarise: (1) Again, speed of release is the factor of greatest importance as in all other throwing events, and lift on the javelin is proportional to the square of its speed. Within limits, thinner javelins can be selected and used to reduce the drag factor. (2) The optimum angle of release for the ‘aerodynamic’’’ javelins is probably between 35 and 40 deg.; the ‘old’ design of javelin should be released at approximately 45 deg. (3) The attitude angle of the ‘aerodynamic’ javelin at release should possibly be a little less than the release angle; the vital thing, here is not to present too great an angle of attack to the relative wind. Then, in a good throw, the missile will reduce its angle to the horizontal slightly and maintain that angle until it begins to fall, when it again rotates forward to land almost flat, point first. (4) The gliding qualities of the ‘aerodynamic’ javelin are especially valuable in the gaining of distance during the second half of flight.
Hammer. Technique, in good hammer throwing , is designed to release the missile at the greatest possible speed at an optimum angle of approximately 45 deg. from a circle 7 ft in diameter, so that it lands within the prescribed throwing area.
Hammer speed and a rotational pattern are established during (usually two) preliminary swings before the hammer’s speed is markedly increased and its plane of motion is steepened progressively during (usually three) turns
The system of man and hammer rotates about an axis passing through their common Centre of Gravity and the thrower’s contact with the ground. The good thrower works his way across the circle diameter by pivoting alternately on the heel and ball of his left foot. Thus, in the course of making these turns, he moves the common axis from the rear to the front of the circle. Finally, he imparts even greater speed to the hammer-head by lifting it powerfully with his legs and trunk.
As, in any rotation, a hammer’s linear speed will be directly proportional to its distance from the common axis , in good throwing relaxed arms are used merely as a prolongation of the wire shaft, fully extended in the turns and final delivery— pulled out by centrifugal force.
From Newton’s First Law it follows that the hammer would move in a straight path but for the force of gravity and a centripetal (i.e. pulling-in) force exerted by the athlete—a force proportional to the square of the missile’s linear speed. If, for example, the hammer’s speed is doubled, the thrower must then exert four times the centripetal force, automatically increasing an equal but opposite centrifugal (i.e. pulling-out) force.
From turn to turn, therefore , the thrower experiences increased difficulty in maintaining balance and control; for, in a sagittal plane, the hammer’s centrifugal pull and the equal but opposite force from the ground thrusting against his feet tend more and more to rotate him forward.
Because the thrower’s balance in this plane is the product of two pairs of equal forces acting in opposite directions , to counteract this tendency the skilled hammer thrower ‘sits’ in progressively deeper positions from one turn to another, thus increasing the horizontal distance between the force of his weight (acting vertically downwards) and the equal but opposite force passing vertically upwards through his feet. By lowering the Centre of Gravity, this ‘sitting’ also progressively improves the thrower’s stability.
The athlete accelerates the hammer by exerting horizontal and vertical components of force. (1) Horizontally, he is able to apply force only because of the friction between his feet and the ground—through the reactions of the ground to the forces exerted by his feet. This friction also enables the thrower to accelerate the hammer in this plane by movement of the common axis; (e.g. the rotational acceleration of a conker on a string in this plane is possible by virtue of moving such an axis ).
The speed of the hammer-head can be increased horizontally as a result of the thrower’s exerting a centripetal force; as, in good throwing, the arms are extended throughout, such a force can be applied only by moving the common axis. In fact, its movement across the circle is essential to imparting the greatest possible centripetal impulse to the hammer-head, and to this end the weight of the thrower must be maintained over his pivoting leg throughout (for if this axis falls between the feet or over the trailing foot, progression across the circle is impaired).
Tangential acceleration is further improved when the thrower leads the hammer-head. Here he obtains ‘body torque’ through leading markedly with his hips and legs, moving his feet ‘fast and early’ (Cullum) in the turns. In such a case, the apparent radius of hammer movement (i.e. a straight line from the thrower’s left shoulder to the hammer-head) is at an angle to the true radius (i.e. the distance between the hammer-head and the common Centre of Gravity). In fact, whenever the wire shaft is not at right angles to the curve along which the hammer-head is moving, the hammer will be acclerating and, correctly, the thrower will be ‘maintaining contact’ through his left arm (Cullum). (Note the reference to ‘leading’ the hammer-head here, as opposed to ‘trailing’ it. The latter, to a hammer thrower, indicates a bending of the right arm with a resulting shortening of hammer radius; whereas, to ‘lead’ the hammer indicates a trunk twist —infinitely preferable).
To re-emphasise: such methods of accelerating the hammer horizontally are possible only by virtue of the friction between the thrower’s feet and the ground, and this can attain its greatest value when both feet are in contact with the ground and the hammer-head is below the level of the shoulders. (Maximum friction, here, depends on the pressure between the feet and the ground ).
This is particularly true of acceleration through ‘body torque’. Friction will be increased when the common axis leans away from the missile. In that phase of a turn where the thrower pivots on one foot , and with only its outside edge touching the ground, horizontal acceleration can therefore be only very small if, indeed, it is at all possible; for in such a position pressure between foot and ground has a minimum value. (2) Vertically, the hammer can be accelerated upwards and downwards during each successive 360 deg. turn, and in good throwing this vertical acceleration increases progressively from turn to turn— and is of vital importance to the delivery. (i) Vertically upwards. The hammer can be accelerated upwards as soon as the hammer-wire is inclined upwards to the vertical, and this acceleration would appear to attain its maximum value shortly after the hammer-head has passed its lowest point, i.e. off the right foot ). Here, the force applied to the hammer-head is limited by that which the athlete can exert downwards through his feet (preferably both feet simultaneously) against the ground. Therefore, given the position from which to apply such a force, the limiting factor is the strength and speed of the athlete.
The direction of the reaction obtained from the ground will be upward with the hammer at its lowest point and will diminish gradually and change more to the horizontal as the hammer-head rises. (ii) Vertically downward, acceleration is achieved by permitting the body weight to drop just before the hammer-head itself drops in its swings or turns. Here, therefore, the limiting factor to acceleration is the thrower’s weight—whch can be lowered with or without contact with the ground.
First turn Third turn
With a steepening of the plane of hammer movement and a progressive increase in its linear speed from turn to turn, vertical means of acceleration become increasingly important and horizontal means comparatively less so.
When the hammer-head is moving with sufficient speed through the higher ranges of its spiral course, the vertical component of the athlete’s centripetal force sometimes exceeds the weight of his body, and his feet are lifted off the ground as a result.
This is exemplified even in the throwing of world-class hammer throwers, whose feet sometimes leave the ground, momentarily, on their final turn to the detriment of the delivery position. In fact, throwers often jump round on this last turn because the speed of the hammer is too great for their ability to advance their hips and feet in any other way. However, by this means the hips are never so well advanced— relative to the shoulders and hammer-head—as in a suitably fast pivot on one foot; but for this, of course, the thrower needs tremendous speed and dexterity.
Discus. If a discus is to be thrown a maximum distance it must be released with the greatest possible speed at an optimum angle—the latter being influenced quite considerably by the aerodynamic factors discussed already.
In the sense that both are rotational in character, some similarity exists between this event and hammer throwing. Yet, otherwise, they have little in common. For whereas the hammer is slung from a wire which can only transmit force along the direction in which the wire lies, the discus is thrown from an arm, and whenever the thrower’s hand has a firm grasp on the implement there is little limitation to the direction in which that hand can exert force on the discus.
From a position at the rear of the 8 ft 2£in. (2£ m) circle, and with his back to the direction of throw, the athlete executes several (usually no more than three) preliminary swinging movements, using his entire body—not the arm alone. These movements help to prepare him emotionally for the throw and develop a movement pattern important to the efficiency of the turning and throwing movements which follow.
The thrower then shifts his weight over his left (pivoting) foot, turns and drives quickly across the circle. Here, it is important to use just the correct quantity of spin on this pivoting foot; novices often spin too far, to the detriment of their throwing position, subsequently. In driving across the circle it is also important to main- tain a correct relationship between this pivoting foot and the thrower’s Centre of Gravity; the faster the movement across, the farther forward of this foot should be the Centre of Gravity. Through failure to maintain this relationship novice throwers often lose balance falling backwards in the throw. (Ryan.)
In this phase the expert’s shoulders turn through approximately 450 deg. and, correctly, he develops maximum controlled angular and linear velocities. In the turn—part pivot, part jump, part running movement—the axis of movement passes through the common Centre of Gravity and his base—i.e. first his left foot and then the right. A relaxed throwing arm trails fairly wide of the body, encouraging maximum possible radius of movement in the throw which follows; for, for a given angular velocity, the linear speed of the discus will be proportional to its distance from the common axis.
The trailing of the throwing arm also increases the moment of inertia of the upper body relative to the common axis, tending to slow those parts of the body down in their rotation; simultaneously, by keeping the thighs close together in the turn (i.e. reducing their moment of inertia about this axis) the rotation of the lower parts is speeded up. Hence, body torque is built up and maintained. (However, some great throwers build up angular momentum in their hips and legs through a wide leg-sweep during the first half of the turn. When, subsequently, the free leg is pulled in, torque between hips and shoulders is increased—an affect enhanced by a deliberate effort to hold back the upper body by bending the free arm across the chest.)
The expert discus thrower also advances his hips and feet relative to his upper body by stressing the pick-up and rotational movement of his free leg as he drives from the rear of the circle, by getting his right foot to the ground again quickly and by positioning his front foot without delay. And this is achieved without raising his Centre of Gravity unduly, and with both feet off the ground for only an instant—otherwise, when the thrower lands in the front half of the circle, his upper body will have begun to catch up his hips, to the detriment of body torque and the power of his throwing position
The expert also lands on a flexed right leg and with his weight well over it. He then adds to the speed of the discus by trans- total distance in a 60 ft put. Certainly, the glide ought never to be executed to the detriment of power of position and control in the delivery, subsequently; i.e. it should never take up too much of the circle, so cramping the putter’s delivery; or be too fast, to the point of exceeding his ‘critical’ speed.
It can be seen that Rowe’s glide took him rather less than half-way across the circle, permitting a breadth of base suited to his height, horizontal speed and lean over his rear leg.
The actual putting action must begin immediately the athlete’s rear foot comes to rest at the end of the glide, otherwise valuable time will elapse without acceleration being given to the shot. As soon as this rear foot lands, its leg can exert an efficient upward thrust and the trunk and shot can be raised.
However, since maximum body force and maximum rotation of the trunk about its long axis are possible only with the other foot used as tain a correct relationship between this pivoting foot and the thrower’s Centre of Gravity; the faster the movement across, the farther forward of this foot should be the Centre of Gravity. Through failure to maintain this relationship novice throwers often lose balance falling backwards in the throw. (Ryan.)
In this phase the expert’s shoulders turn through approximately 450 deg. and, correctly, he develops maximum controlled angular and linear velocities. In the turn—part pivot, part jump, part running movement—the axis of movement passes through the common Centre of Gravity and his base—i.e. first his left foot and then the right. A relaxed throwing arm trails fairly wide of the body, encouraging maximum possible radius of movement in the throw which follows; for, for a given angular velocity, the linear speed of the discus will be proportional to its distance from the common axis.
The trailing of the throwing arm also increases the moment of inertia of the upper body relative to the common axis, tending to slow those parts of the body down in their rotation; simultaneously, by keeping the thighs close together in the turn (i.e. reducing their moment of inertia about this axis) the rotation of the lower parts is speeded up. Hence, body torque is built up and maintained. (However, some great throwers build up angular momentum in their hips and legs through a wide leg-sweep during the first half of the turn. When, subsequently, the free leg is pulled in, torque between hips and shoulders is increased—an affect enhanced by a deliberate effort to hold back the upper body by bending the free arm across the chest.)
The expert discus thrower also advances his hips and feet relative to his upper body by stressing the pick-up and rotational movement of his free leg as he drives from the rear of the circle, by getting his right foot to the ground again quickly and by positioning his front foot without delay. And this is achieved without raising his Centre of Gravity unduly, and with both feet off the ground for only an instant—otherwise, when the thrower lands in the front half of the circle, his upper body will have begun to catch up his hips, to the detriment of body torque and the power of his throwing position
The expert also lands on a flexed right leg and with his weight well over it. He then adds to the speed of the discus by trans- ferring that weight from rear to front foot, thus shifting the common axis; simultaneously, he stretches and lifts powerfully with legs and trunk and unwinds his upper body and throwing arm through approximately 180 deg. of additional shoulder rotation. All this takes place against a bracing and lifting action of his left leg, the foot of which is placed only slightly to the side of his general line of direction across the circle this foot remains in contact with the ground until the discus has left the hand.
After the left foot meets the ground and the actual throwing movement begins the path of the discus describes a spiral curve, first descending and then rising steeply, but inclining more to the horizontal as the point of release (just in front of the line of the shoulders) is approached. Early in its rise the hand has a firm grasp and during this period can exert a vertical or near-vertical force on the implement. In fact, the lifting of the trunk and legs must take place at this time, while the hand can transmit vertical force.
Later, the upper edge of the discus drops away from the wrist and any force applied through the fingers must then pass through the Centre of Gravity of the implement—otherwise it will wobble, to the detriment of its stability in flight. Consequently, a series of velocities is given to the discus at this stage, beginning vertically but tending towards the horizontal. A combination of these velocities results in the discus starting its flight with a negative angle of incidence.
Shot. The technique of shot putting is simpler than that of each of the other three throwing events, lending itself easily to mechanical analysis through the use of cine film.
By taking cine pictures from a fixed camera set on a continuation of the line dividing the circle into front and rear halves, preferably against accurately-positioned background markings, and focussed on a point approximately 3 ft directly above the middle of the circle, these pictures can be projected, subsequently, frame by frame or at other regular intervals of time, and the path of the shot can be plotted.
Then, provided the camera speed is known, it is possible to calculate the (a) time taken for the put, (b) acceleration of the shot in a sagittal plane, from stage to stage, (c) its path across the circle in this plane, (d) release speed, (e) height of the point of release, (f) and angle of projection; and from (d) (e) and (f) compute (g), the distance of the put.
The purpose of the glide is primarily to give the athlete and the shot horizontal speed prior to the delivery in the front half of the circle. The glide is important, yet not too much importance should be attached to it, as it accounts for only about 7 per cent of the total distance in a 60 ft put. Certainly, the glide ought never to be executed to the detriment of power of position and control in the delivery, subsequently; i.e. it should never take up too much of the circle, so cramping the putter’s delivery; or be too fast, to the point of exceeding his ‘critical’ speed.
It can be seen that Rowe’s glide took him rather less than half-way across the circle, permitting a breadth of base suited to his height, horizontal speed and lean over his rear leg.
The actual putting action must begin immediately the athlete’s rear foot comes to rest at the end of the glide, otherwise valuable time will elapse without acceleration being given to the shot. As soon as this rear foot lands, its leg can exert an efficient upward thrust and the trunk and shot can be raised.
However, since maximum body force and maximum rotation of the trunk about its long axis are possible only with the other foot used as a point of resistance, the front foot should land only fractionally after the rear foot; here, there should be just sufficient rocking motion from one foot to the other to help keep the common Centre of Gravity moving forward. A slight rock will, in fact, help bring the front foot to the ground; on the other hand, with too much weight over the back leg at this stage, and with the front foot poised long in the air, the athlete will lose much, if not all, the speed built up during the glide.
Contrary to the view that the putting action ‘is a movement which begins in the toes and ends in the fingers’, in fact movement begins in the stronger but slower muscles surrounding the athlete’s Centre of Gravity and is then taken up, below the hips, at the knees, ankles and feet, in that order; simultaneously, above the hips, it extends upwards through the putting shoulder, elbow, wrist and fingers. In its summation of forces , therefore, a technically sound putting action can be likened to the throwing of a stone into a pool of water—causing the ripples to flow outward.
Theoretically, there can be no doubt that, throughout the putting movements in the front of the circle, the front foot should be firmly in contact with the ground, providing the necessary resistance for the hand to exert maximum force both vertically and horizontally. The vertical component of force must exceed the force of gravity to ensure continuous, though varying, upward acceleration. Horizontally, as soon as the hand rises above the centre of percussion the backward thrust of the shot on the hand encourages the front foot to move forward.
However, it must be admitted that a majority—if not all—of the world’s 60 ft shot putters do in fact break contact with this front foot fractionally before the missile leaves the hand. This may be to avoid moving beyond the stop-board; for by this means, the athlete reduces some of his forward momentum. Or, the legs may be driving too vertically (possibly because the feet are too close together) or the arm striking too horizontally. Again, this could happen because of the accelerations developed by the legs and trunk—accelerations which may be too great for the strength of the arm; arm action may have to be delayed until these have been reduced, if not completed.
Javelin. The ideal, in this event, is to combine maximum controlled approach-speed with a throwing position which enables maximum force to be applied to the javelin over the greatest possible range , releasing it at an optimum angle. g h I
Throwers are rarely satisfied with their combining of these two largely irreconcilable factors; yet, always, their aim is to obtain an effective throwing position with the javelin already moving fast—and then, with the throwing shoulder travelling at maximum speed relative to the ground, to impart maximum hand speed in relation to the shoulder.
For the greater part of his 14-17 stride (overall) run-up the expert thrower holds the javelin over his shoulder in a position which permits relaxed, balanced running, and accelerates gradually into a horizontal speed governed by his ability to exert full body force, subsequently, in his throwing movements. Approach speed should depend upon body speed and strength.
After 10-12 of these running strides he withdraws and aligns the javelin in preparation for the throw, turning and gradually leaning his trunk to the rear to adopt a powerful pulling position. The change in the angle of the trunk is particularly marked during the so-called ‘cross-step’ immediately prior to the throwing stride , where it is essential that the thrower contacts the ground with his right foot before his body weight moves over and beyond this foot.
Here, in a good throw, the athlete’s grip will be approximately 4 ft behind his Centre of Gravity which, in turn, will be to the rear of his right foot. The line of the leading leg and trunk at this instant will be about 30 deg. to the vertical, but the angle should depend upon the speed of the run-up, the greater speed requiring a greater angle, and vice versa. The thrower coasts through this transition from running to throwing position, yet his strides quicken progressively.
Basically the javelin throwing action can be described as, first, a powerful pull exerted on the missile, followed by a lifting motion, where ‘the thrower attempts to run off and away from the rear leg against the resistance of the frontleg’ (Pugh).
Beginning as the right foot con tacts the ground at the end of the cross-step and with the throwing arm comparatively straight and relaxed, a pull from the shoulder is applied as the weight of the body moves for ward and the front foot reaches out. And as this weight moves ahead of the sup porting foot, the right leg drives hard to add to this pulling movement and keep the right hip, in particular, moving fast into the throw. In good throwing, this transference of weight against the resistance of the front leg occurs without a premature turning of the shoulders to the front; in fact, the hips twist fractionally ahead of the shoulders.
So widespread are the feet in good javelin throwing that the rear leg completes its drive before the front foot contacts the ground. Trunk rotation occurs mainly by virtue of the front foot’s resistance to horizontal motion. A quick turning-in of the rear knee and foot adds to hip speed and coincides with an outward rotation and raising of the throwing elbow which arc essential to a final flail-like arm action.
The javelin and the athlete’s body are maintained in a single vertical plane, with all pulling forces exerted through the length of the implement.
If the trunk is too erect and the throwing base too narrow for the athlete’s approach speed, he will lack sufficient range over which to apply his body forces and will tend quickly to rotate in a sagittal plane over and beyond his front foot in delivery, pulling the javelin down. On the other hand, if he leans back too far and his feet are too widespread, the Centre of Gravity’s forward speed will be reduced excessively , the hips will not pass over the forward foot and, incorrectly, the trunk will pivot about the hips, shortening the radius of movement in a sagittal plane and, again, pulling the javelin down in delivery.
It is difficult to estimate the actual loss in forward speed of the Centre of Gravity due to the impact of the front foot with the ground, but even in a good throw it seems likely that this will be about one quarter of its original horizontal speed, depending upon the efficiency with which the front foot takes up the shock on impact. However, it may well be that the throwing shoulder at least maintains, if not increases, its linear speed, because of its distance above the Centre of Gravity. (M. J. Ellis and H. H. Lockwood agree that the speed of the throwing shoulder increases markedly as the front foot meets the ground, but suggest that this is due to the shoulder’s rapid rotation about the body’s longitudinal axis. In analysing film of one thrower they found that his Centre of Gravity did not describe an arc during the throwing stride, because of his flexed front leg, which kept the Centre of Gravity moving horizontally. They concluded that the hinged effect in this event occurs more in a horizontal than sagittal plane, commenting, ‘Perhaps, whilst the hinged moment effect (in a sagittal plane) is theoretically and mechanically ideal, the stresses that it would place on the thrower are such that the innate protective mechanisms of the body would not allow it to be used, even assuming that the thrower is strong enough to remain rigid.’)
Because, in good throwing, the athlete’s rear foot must break effective contact with the ground before the arm applies its forces, the arm’s first pulling movement, acting at shoulder-level below the point of percussion, must be exerted against the inertia of the thrower’s body, so reducing his forward speed. However, once the front foot meets the ground it remains in contact until the javelin is released, and so provides an essential resistance not only to any vertical component of the force of the arm action, but also to those horizontal components exerted, subsequently, above the point of percussion.
The final flail-like arm action of the good javelin thrower is brought about, first, by outwardly rotating the elbow and raising it higher than the hand grasping the javelin—’leaving that hand behind’ (Pughf)—before quickly extending the forearm and hand to apply further force vertically and through the javelin’s length.
This flailing arm action is superior to a straight-arm, bowling action, because: (i) the muscles acting between the forearm and upper arm, as well as the muscles acting between the shoulder and upper arm, can be used to produce force; (ii) the small moment of inertia of the comparatively light forearm and hand about the elbow joint does not hinder greater angular speed of the forearm relative to the elbow (although, of course, the moment of inertia of the javelin about this joint must also be considered); and (iii) In a straight-arm rotation about the shoulder, angular speed would have to be developed against the considerable moment of inertia of the whole arm and javelin.
Thus, the essential pulling character of a good javelin throw derives from (a) the motion of the body in front of the missile, (b) the body’s rotation in two planes—sagittal and horizontal, and (c) a final flail-like arm action. This pulling movement can take place over as much as 14 ft (Pugh)—from the moment the right foot lands at the end of the cross-step to the instant of release.
An attempt to coach pole vaulting without an understanding of the underlying mechanical principles has been likened to trying to read without a knowledge of the alphabet. There can be few sporting activities with technique as complex; for by planting his pole the vaulter creates a hinged moment which converts primarily linear motion at take-off into angular motion ; and then, simultaneously and interdependently, one pendulum (the athlete) swings from his hands while a second pendulum (pole and athlete) pivots about the base of the pole.
The good vaulter co- ordinates the timing of these two pendulums.
For by bringing the pole D to an upright position with an inadequate body swing he can never clear impressive heights by modern standards , nor can this be done by swinging past and above the grip with the pole failing to attain a vertical position.
In efficient vaulting the athlete effects a compromise between pole speed and body speed; his grip (always the highest possible under the circumstances) and movements on the pole are designed to project his Centre of Gravity high above his top hand just as the pole reaches an almost vertical position.
However, in gaining this height the expert does more than employ these two pendulum movements. He completes and improves the vault by executing a powerful, carefully-timed and well-directed pulling and pushing action, driving his legs and hips upwards.
Approach speed and height of grip
Although, in good vaulting, little speed is required to clear heights up to 13 ft—and some experts, lacking speed and using a relatively low grip, have gone much higher on their ability to develop a powerful pull-push action—nevertheless speed becomes increasingly important as the bar is raised. illustrates this principle. The speeds shown, expressed in terms of a ‘flying’ 100 yards run at uniform speed, are common to the event.
It has been assumed that all the kinetic energy developed in the run-up can be used in raising the Centre of Gravity (common to pole and athlete) whereas, in fact, some kinetic energy must be dissipated by the impact of the pole with the box, some by the backward thrust of the ground on the athlete’s take-off foot and some by transference of momentum between the pole and the athlete and the various parts of his body; in addition, of course, the vaulter must retain sufficient horizontal speed to cross the bar.
Greater approach speed will enable an athlete to use a higher handhold, provided he has the strength to control the greater centrifugal force of his swing. A flexible pole can be held higher than a stiff one; and his height, weight, spring, skill, the direction and strength of the wind, the run-up surface, his general fitness and motivation—all will influence the height of the vaulter’s grasp on the pole.
Experience proves that, speaking generally, a vaulter should aim for a maximum effective grip (i.e. the distance between the top of his higher hand and the ground when the pole is upright in the box) equal to twice his standing height plus at least 4 in. (at least 12 in., when using a fibre-glass pole). This can then be used with maximum controlled speed at each height (which is recommended) or the vaulter can lower his grip and run slower at the easier heights, progressively raising his grip and increasing his speed throughout a competition.
Some of the pole’s speed, and therefore its kinetic energy, developed in the approach is lost at take-off. The takeoff velocity has been resolved into one component acting beneficially, at right angles to the pole , and another directed through the length of the pole into the box. For a given velocity, the greater the angle between pole and ground at takeoff the more effective will be the approach speed (compare Figs. 149tf and 1496); but, of course, this angle can be too great, leaving little for the pole to do.
The good vaulter does not simply run off the ground into his swing, however. He adds to his take-off velocity (Ganslen estimates by as much as 4 ft per second) and directs it at a more favourable angle by jumping; and this is of particular importance when he holds high and the take-off angle between pole and ground is therefore comparatively small (compare Figs. 149« and 1496). Thus he is able to exert maximum force with his hands at right angles to the pole.
Kinetic energy can be retained as a result of the pole’s flexibility; a good pole will ‘give’ as it takes the vaulter’s weight, first assuming a slightly convex bend away from the athlete and then curving laterally (to the left with a left-footed vaulter, and vice versa).
The loss of kinetic energy can also be reduced through an emphasis on forward-upward as opposed to an upward-forward (i.e. a stabbing) movement in planting the pole. The timing is also important: if it is too late or the take-off is too close (i.e. not directly beneath the vaulter’s hands ) he will be snatched prematurely off the ground. Some of the shock can also be absorbed by a partial extension of the arms (never fully stretched, however) at take-off, and by having sand in the box to ‘cushion’ the impact.
In good vaulting, through a pronounced forward-upward take-off drive, the athlete’s chest contacts the pole early in the swing; first he swings from his hands, therefore, and later from his shoulders.
Just as the arm of a metronome oscillates more rapidly as its weight is moved closer to the fulcrum , so, on leaving the ground, does the expert in this event give speed to his pole by extending his body momentarily, keeping his Centre of Gravity close to the pole’s base. This exemplifies the principle of the conservation of angular momentum , for by reducing the moment of inertia, angular velocity is increased proportionately.
This ‘hanging’ movement, in which the vaulter arches his back ‘letting his stomach and hips out’ (Warmerdam)—and which should always be performed in a vertical plane at right angles to the plane of the uprights—is vital to bringing the pole to the vertical only where the highest grip is used commensurate with take-off velocity. With a lower grip there will be neither the necessity nor time for a ‘hang’.
Again, the ‘hang’ position should never be exaggerated beyond the vaulter’s power, later, to raise and flex his legs against gravity and the centrifugal force tending to tear him away from his grip. This is particularly true of the tall, long-legged athlete whose Centre of Gravity is low relative to his hand-hold; he will develop greater centrifugal force than a shorter man swinging with equal angular velocity, and will therefore require more strength and speed.
Nor should the ‘hang’ be held too long or there will not be time in which to raise and turn the body for bar clearance. On the other hand, if it is too short the reaction to the forces involved later, in raising and pulling the body, will act at an angle to the pole and these movements will increase the horizontal distance between the vaulter and the box— both slowing the pole down.
Obviously the vaulter’s movements affect the radii and, therefore, the speeds of both pendulums. So that in addition to the advantages mentioned, by ‘hanging’ momentarily the vaulter increases the moment of inertia of his body about his grip, reducing his angular velocity and staying behind his pole; for if his Centre of Gravity swings too quickly ahead, the pole will lose speed.
Although there must be an element of compromise in the swing of a good vault, it should always be as long delayed as practicable.
When the vaulter’s trunk has swung so that his Centre of Gravity is approximately in line with the base of the pole and his grip, he is then able to exert force without excessively reducing the pole’s speed.
In the process of conserving angular momentum in the swing he has maintained a low position of his Centre of Gravity; it has little vertical speed. But now he must raise it quickly and adopt a position from which he can benefit from a straightening of the pole and further increase vertical speed by pulling and pushing with his arms and by stretching his body; and, ideally, this must be achieved without permitting his Centre of Gravity to move in front of the base-grip line of the pole.
At this stage therefore, and with the vaulter swinging about his grip again, the good performer reduces the moment of inertia of his body, speeding up and raising his hips and legs while keeping his head and upper trunk behind the pole. His legs, flexed vigorously at hips and knees, are pulled in, while, simultaneously, this is counterbalanced by rocking the head and upper body back from extended arms ‘see-saw’ fashion. At the end of the swing-up, therefore, the vaulter’s back is approximately parallel with the ground, with the line of the pole by the left hip. The movement has been described as the beginning of the pull on the pole. It is a pull through the length of the pole initiated by the large muscles of the back, chest, hip flexors and abdominals, with the weaker but faster arm and shoulder muscles taking up and comple- ting the action later.
In performing his swing-up the vaulter does considerable work, resulting in an increase of rotational kinetic energy about his hands. As centrifugal force is propor- tional to the radius of movement times the square of its angular velocity, centri- fugal force might be increased as a result—which perhaps explains why weak athletes find it difficult to keep the head and upper body behind the pole at this stage.
Inevitably, the swing-up reduces the speed of the pole-athlete pendulum, for it increases the distance between the base of the pole (the fulcrum) and the Centre of Gravity common to pole and man. However, this effect can be minimised through correct timing; but if the swing-up occurs too soon, the pole will not carry the athlete to the bar. As we shall see , the timing of this important phase is partly dependent upon the degree of pole flexibility.
Pull, stretch and push
The speed developed in the approach and take-off cannot be sufficient to project a vaulter to maximum heights, perhaps more than 3 ft above his grip on the pole: he must add to his speed by pulling and pushing with his arms and by stretching the original free leg vigorously upwards.
As in the swing-up, the continued raising of body weight lengthens the pole-athlete pendulum and slows it down; in fact, the pull-stretch phase would eventually stop the pole. Under such circumstances the expert conserves what pole speed he can by keeping his Centre of Gravity in line with the pole throughout, or almost so, as in the swing-up. His body spirals upwards about a near-vertical axis, close to the pole.
In good vaulting the pulling and stretching movements begin as top vertical speed is attained in the swing-up, so that one phase flows smoothly into the next. An early pull will ‘kill’ the pole’s speed, and if it is too late the vaulter will rotate too quickly around the bar, dropping his legs rapidly and landing on his back.
The earliest position from which an effective pull-up can take place, assuming adequate vertical speed; the higher the hips are at the moment of initiating it, the more vertical—and therefore the more advantageous—will be the movements which follow.
Pull and stretch should be simultaneous and their forces directed through the length of the pole towards the ground; the pull should be strong and fast and the free leg should be driven vertically in front of the plane of the uprights.
The turn occurs partly as a result of a scissoring leg action, whereby the original free leg is stretched vigorously upwards (vertically by some, and to the left of the pole by others) while the original take-off leg, flexed, ‘cuts’ behind, turning the hips ; and it is due partly to the position of the hands on the pole one above the other, encouraging a twisting of the shoulders in the direction of the grip. Turning speed is related to pulling speed. (When the hands are close together a vaulter swings more effectively, is less likely to turn prematurely (i.e. he ‘stays on his back’), divides the work of his arms more evenly and is more likely to raise his chest a maximum height above his grip on release than with the hands wide apart, However, a gap of approximately 6 in.—while not sufficient to lose these advantages—also permits the take-off leg to swing past the pole without striking it, provides a more favourable leverage for the lower (usually weaker) arm and gives a better balanced position in the pull-up. When using a fibre-glass pole, the vaulter’s grasp should be wider.)
The push is merely a continuation of the pulling action and, like the pull, should be directed through the long axis of the pole towards the ground, against maximum resistance, with the pole (which would otherwise begin to fall back towards the ground) kept close to the athlete.
At first glance it would seem that all parts of the vaulter’s body, and therefore his Centre of Gravity, should rise at maximum vertical speed until he has released the pole; then, having broken contact, he should ‘jack’ (i.e. flex markedly at the hips) to raise his abdomen in relation to his Centre of Gravity, improving his lay-out. Finally, with his hips clear of the bar, he should ‘unjack’ quickly to clear the head, chest and arms, depressing his abdomen and folding back his legs in reaction.
In practice, however, the vaulter must develop a rotation before release, to assist in the raising of the parts of his body still below the bar, and to land feet first in the pit. This rotation is brought about partly by a transference of angular momentum acquired in dropping the legs slightly, but is due, mainly, to a turning couple created by the reaction to his thrust on the pole, acting vertically upwards ); and the force of his weight, acting through his Centre of Gravity, pulling vertically downwards ).
In efficient vaulting, the force of the pole’s upward thrust always exceeds this downward pull. Therefore, although the forces of the couple are equal the athlete’s Centre of
Gravity continues to rise; he releases the pole rotating but still moving upwards.
In this phase also, therefore, a good vault is a compromise. When they have cleared the bar, the hips ‘break’ slightly and the vaulter assumes an arch position at his high point ; and the slight dropping of the legs (in particular, the original take-off leg) takes weight off the shoulders and arms, making it easier to give vertical speed to the upper body which has still to cross the bar. The extent to which a vaulter drops his legs at this stage depends upon the hip and leg elevation obtained previously in the vault and upon his arm and shoulder power (not to mention his sense of self-preservation!).
The modern vaulter ‘jacks’ only in an emergency for this outmoded technique requires more time over the bar than is usually available. Ganslen estimates average horizontal clearance velocity in good vaulting at 6 ft per second—too great to give sufficient time for ‘jacking’ and ‘unjacking’. (The more efficiently the vaulter converts horizontal to vertical movement, however, the greater the period of time for which he is over—and tending to drop on to—the bar, and the faster and more skilful must be his final movements.)
Again, when a vaulter ‘jacks’, still grasping his pole (and, therefore, still indirectly in contact with the ground), he tends merely to pivot about, and lower his Centre of Gravity, instead of continuing to move it upward. Finally, ‘jacking’ involves too much movement at bar level, with chest and thighs in very close proximity with the bar.
Timing and the pole
The timing of a vaulter’s movements will be influenced by the flexibility of his pole. He depends upon its resistance, and yet, if too stiff, it lifts him too rapidly, particularly when he is gripping high; he has to hurry his movements, tending to attain his high point in front of the bar. Also, he is unable to swing directly forward after take-off and often strikes the pole with the thigh of his jumping leg.
On the other hand, if the pole is too springy its bend has the effect of lowering the hand-hold, reducing the moment of inertia of the pole-athlete pendulum and speeding it up, so that there is insufficient time to complete the lifting movements. It may not straighten out in time to be of benefit to the vaulter, and an early pull may even break it. (Even before the introduction of the fibre-glass pole, poles were known to bend as much as 3 ft out of line, lowering the common Centre of Gravity by as much as 7 in.) (Ganslen.)
A reasonable pole-bend (e.g. of approximately 1 ½ ft to 2 ft out of line) permits the use of a higher grasp than is possible with a stiff pole; it takes some of the take-off shock, allows the athlete’s Centre of Gravity to swing directly forward over the box, permits a comparatively gradual rise in the path of the vaulter’s Centre of Gravity (giving sufficient time for his various movements on the pole) and adds to his vertical speed.
The fibre-glass pole
This gives greater height in pole vaulting because it permits the use of a higher grasp and, in bending markedly, stores more energy than poles used hitherto. However, this energy must be given back to the vaulter—and quickly—at the proper time; he must therefore select a pole appropriate to his weight, speed and hand-hold. Its introduction to modern vaulting has brought about the following modifications to the technique: (a) To bend the pole the take-off foot is placed slightly ahead of a vertical line through the top hand at the instant of leaving the ground, and the athlete drives more horizontally. The pole—not the arms— takes the shock of impact. A wider (1-1 ft) grasp encourages this for, then, the top arm is straighter; it also permits a pushing forward of the lower arm and pulling back of the top arm movements, which immediately establish the direction of pole-bend. (b) To retain, and even add to, this bend the vaulter slightly shortens the swinging phase; he lifts his legs viciously and rocks back sooner, so transmitting a large force through his hands into the pole. His wider grasp gives him greater control at this stage, preventing a premature forward trunk swing. (c) To adopt and hold the best position from which to use the released energy when the pole straightens, the vaulter leads with his take-off leg in the shortened swing to avoid turning prematurely; he ‘stays on his back’, with knees, thighs and hips vertical. However, this is no passive position for, as the pole pivots and then straightens, the tendency is for the legs to be driven down; the vaulter must therefore attempt to bring his feet further and further above his head.
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.
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’
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.
It is impossible to excel in hurdling and steeplechasing events without basic sprinting or middle-distance running ability. For these races are won mainly on the ground, and therefore the best method of clearing a hurdle or water jump is that which returns the athlete quickly to the track with a rhythm and effort akin to a running action. Hurdling and water jump techniques are therefore modifications of running form.
To avoid jumping—which checks forward momentum and interrupts the running action—good performers at these events clear the hurdles by using a running step-over action of the front leg, combined with a sideways-swinging rear leg movement. In clearing 2 ft 6 in hurdles neither movement is greatly emphasised; but in the men’s 120 yards race, where the barriers are 3 ft 6 in., even a tall, long-legged athlete has to exaggerate them. The technique of the 440 yards intermediate (3 ft) hurdler falls between these two extremes.
The expert hurdler therefore runs over the obstacles mainly by ‘making room’ with his legs, and in the process raises his Centre of Gravity only a little more than in taking a running stride. Thus, in comparison with their times on the flat, champion high (3 ft 6 in.) hurdlers need no more than about 2-0 sees to clear ten barriers—an average of 0-2 sec per hurdle. The figure is fractionally above 1-0 sec in the men’s 220 yards event (10 x 2 ft 6 in.) and women’s 80 metres race (8 X 2 ft 6 in.). Indeed, a few exceptional hurdlers have taken even less time.
Clearance: the flight-path of the Centre of Gravity. The fastest hurdle clearances are those where the athlete’s Centre of Gravity is raised only slightly more than in taking a running stride—theoretically, with the high point directly above the obstacle and with take-off and landing distances almost equal. (Note that even in a running stride the take-off exceeds the landing distance, i.e. relative to the high point of the Centre of Gravity.)
However, in negotiating the obstacles, hurdlers are compelled to raise their Centres of Gravity even higher, and take-off distances are greater because: (i) their approach speeds do not permit the close take-off; they need more distance in which to raise the leading leg; and by taking off farther away, in consequence, must spring higher to avoid dropping on to the hurdle. The Centre of Gravity therefore attains a higher point, in front of the obstacle ; (ii) although even 3 ft 6 in. hurdles can be cleared with the upper body and hips no higher than in running, this can be achieved only through a higher raising of the hurdler’s Centre of Gravity; for, with the raising of the legs, the hips drop in relation to the Centre of Gravity. If the Centre of Gravity were not so raised, the athlete would hit the obstacle.
Of necessity, therefore, even a highly-efficient clearance takes longer than a normal running stride. The distance it covers is also greater, and this, with the take-off to landing ratio, varies from athlete to athlete and, for any one hurdler, from one clearance to another. Distances and ratios are dependent upon: (i) economy of the clearance position. In efficient high hurdling, a pronounced forward trunk lean and correctly timed arm and leg movement provide a ‘lay-out’ of extreme economy. Here the Centre of Gravity is as near to the hurdle as possible for a quick return to the ground. Conversely, a poor ‘lay-out’ wastes time in the air; (ii) height of the athlete in relation to the height of the hurdle.
Compared with a taller athlete (where both are built proportionately and are equal in all other respects), the Centre of Gravity of a short hurdler moves greater vertical distances and therefore takes more time to rise and fall. In consequence his take-off and landing distances are greater.
He will not be at this disadvantage, however, if (e.g. through abnormally long legs) his Centre of Gravity is the same height above the ground at take-off. Using the same approach speed in both instances, an athlete should cover less ground in clearing a low hurdle than a high one; (iii) approach speed. Theoretically an increase in sprinting speed lengthens both take-off and landing measurements. In fact, however, as a hurdler gathers speed over the first few flights so, successively, are increases in take-off distance matched approximately by landing reductions; ratios change, but the overall distance is constant to within a few inches.
Conversely, as speed is lost take-offs shorten and landings lengthen. All this suggests that greater approach speed, with the concomitant lengthening of the take-off measurement, permits a more horizontal drive and a lower, faster clearance; (iv) leading leg action. The faster the pick-up of the leading leg, the closer can the athlete get to the hurdle and the quicker his clearance can be. (This assumes a set speed of approach.) Accomplished hurdlers use a very fast, high leading leg action; flexion at knee and ankle reduces its moment of inertia about the hip joint, allowing maximum angular velocity; and its quick, high movement imparts speed to the hurdler’s Centre of Gravity.
Through the sluggish action of a longer, heavier leading leg, tall hurdlers sometimes squander their height advantage; their take-off is too far back, with the Centre of Gravity raised too much in consequence. Tall men have the edge in these events, yet, through quicker, more exaggerated movements, athletes of a mere 5 ft 8 in. have demonstrated exceptional efficiency in clearing even high (3 ft 6 in.) hurdles. Often, the short hurdler’s difficulty lies much more in having to stride unnaturally between the obstacles.
A combination of fast, high leading leg action, forward lean (marked in high hurdling) and powerful thrust from the take-off leg gives speed to the Centre of Gravity in a more forward direction; the efficient hurdler drives at the obstacles. In this way, athletes of only fair sprinting ability often maintain good average speeds throughout their races; (v) attaining the correct point of take-off. A hurdle can be cleared efficiently only when the point of take-off is commensurate with approach speed, the subsequent raising and lowering of the Centre of Gravity and quickness in front of the obstacle; and it must be reached without overstriding.
If too close, the hurdler has to jump high to avoid the obstacle, getting his high point beyond it. If he is too far away again he must jump high to avoid dropping on to it. Either way, he wastes time, is too erect, hurries the trailing leg, lands heavily and disturbs his sprinting rhythm.
A slightly shortened stride immediately prior to take-off encourages a good forward drive and body-lean, and can lead to a desirable (if only slight) forward rotation of the whole body before leaving the ground.
Although a hurdler running the 120 yards event in 13-4 sees has an average speed of only 26-8 ft per second (18-2 m.p.h.), at top speed in the race he might clear the hurdles at as much as 32 ft per second, i.e. 21-8 m.p.h. The formula d — %gtz can be used to calculate the time taken for his Centre of Gravity to rise specific distances, i.e. from take-off to the high point, and on this basis to estimate its horizontal motion in that time.
But these figures do not represent take-off distances, for at the instant of leaving the ground the hurdler’s driving foot is approximately 1 ft behind his Centre of Gravity (measured horizontally), and his high point of clearance is in front of the obstacle.
To summarise: it is impracticable to lay down precise distances and ratios. In good hurdling: (i) the Centre of Gravity’s high point is as near, horizontally, to the hurdle as possible and is raised little above a normal running position. Controlling factors, here, are leading leg speed at take-off and the economy of clearance position. Thus, the hurdler spends the shortest possible time off the ground; (ii) the hurdles are cleared at maximum horizontal speed. Therefore, provided condition (i) is fulfilled, the greater the distance between take-off and landing, the better. In assessing clearance efficiency, time and distance should always be considered together.
While hurdling events favour tall athletes, short (5 ft 8 in.-5 ft 10 in.) skilful hurdlers lose less time in clearance than is often supposed, for, to some extent, they make up the disadvantage of an initially lower Centre of Gravity by using a closer take-off.
Clearance: other aspects. The following features of leg action are basic to all good hurdling: (i) a pronounced forward take-off drive (ii) a wide separation of the legs immediately after take-off (greatly assisted by a forward trunk lean ; (iii) a fast leg-pivot (i.e. the front leg’s downward-backward motion co-ordinated with the lateral recovery of the rear leg ; (iv) a landing which flows smoothly into the first of the running strides. The hurdler ‘comes down running’.
In all four phases, front and rear leg movements should be regarded as components of a single action. In this respect, the important points are:
Timing of leg action. Ideally, the legs should move fast and continuously throughout clearance, and should be so timed that the front foot lands only slightly ahead of the Centre of Gravity with the greatest possible backward speed relative to the hips. However, as the leg-pivot cannot begin until the front foot is clear of the hurdle, in high hurdling (and with short hurdlers particularly) there must be a split-second pause after take-off to allow the front foot to get into position for downward movement.
Pivot speed is influenced by horizontal speed, and the time spent off the ground. The greater the horizontal speed, the sooner can the front thigh begin its downward movement and the more delayed, relatively, can be the rear leg recovery. Other things being equal, an athlete with high clearance speed is capable of a better pivot timing than a slower hurdler—and obtains a smoother transition into the sprinting action.
A fast pivot, i.e. one related to the cadence of the running action, is the ideal, but this is possible only when the hurdler spends little time in clearing the obstacles. However, the pivot must always be properly co-ordinated; if it is too fast, the front foot lands too far behind the body and the athlete stumbles into a shortened first stride; if it is too slow, he may fail to clear the rear leg safely, or will land with the front foot too far ahead, checking his forward motion.
In general, a delayed rear leg gives faster and more continuous action, subsequently, and better timing and speed on landing. In fact, an efficient downward front leg movement is largely dependent upon the correct timing of the rear leg; a conscious attempt to ‘claw’ with the leading foot is not recommended. The holding of a forward trunk lean encourages and simplifies this delayed rear leg movement.
Absorbing reaction. The leg movements of hurdling are the cause of greater upper body twisting reactions than in normal running. Yet, these reactions can be channelled and absorbed without upsetting balance and running continuity—a simpler problem for flexible athletes.
At take-off the reaction to leg movement is shared between the ground (which reacts by driving the hurdler forward and upward) and the upper body (which absorbs reaction to the eccentric leg thrust— i.e. in a horizontal plane—by its forward lean and pronounced arm action. (The so-called ‘double-arm action’ is contrary to efficient body mechanics, and is not recommended).
However, the body alone can absorb reaction to leg movement originating in the air; and here, action and reaction are in parallel planes, and possess equal and opposite angular momenta about an axis (of displacement) passing through the hurdler’s Centre of Gravity.
As the leading leg moves down and back and, simultaneously, the rear leg recovers laterally , reaction is absorbed: (i) in the horizontal plane , by holding a forward lean, to increase the horizontal distance between the axis of displacement and the secondary axes of the shoulders. Thus, the arms, swung wide of the body to increase their moments of inertia, take up more reaction than would otherwise be possible. This lean also increases the trunk’s moment of inertia about the axis of displacement, enabling the upper body to absorb any further reaction without markedly twisting out of sprinting alignment; (ii) in the frontal plane , by lowering an extended ‘opposite arm’ in its backward swing, whilst simultaneously raising the other, so preventing an exaggerated upper-body tilt towards the rear leg; reaction to counter-clockwise leg movement is absorbed by clockwise arm movement, and vice versa; (iii) in the sagittal plane by a straightening of the upper body. In this plane the legs may be considered to work in opposition; the ‘unjacking’ of the body is caused only by the action of the front leg, for the other perhaps encourages a weak contrary rotation, weak because of the rear leg’s smaller moment of inertia about the
Centre of Gravity (through which the axis of displacement must pass).
Because of the trunk’s greater moment of inertia about this axis, both range and angular velocity of the trunk are far less than those of the leading leg. Moreover, while the leading leg movement blends with, and is quickened by, an overall forward body rotation (due to an eccentric leg thrust at take-off), this same rotation acts in opposition to the trunk’s reaction. Therefore, although the trunk does straighten to some extent, nevertheless it maintains a forward inclination for balance and acceleration on landing.
In the course of running 3000 metres, clearing twenty-eight 3 ft hurdles and seven water jumps, in terms of energy expenditure the steeplechaser cannot resort to the crisp, exaggerated hurdling movements of the shorter races. However, as steeplechasing standards improve, so does the general efficiency with which the hurdles are negotiated.
It must be emphasised that the proper hurdling of the twenty-eight 3 ft hurdles is more efficient than clearances where the leading foot is placed on top of the hurdles. This latter method may be necessary for those who cannot hurdle but, since the athlete must raise his Centre of Gravity much too high and interrupt his running action, it is uneconomical. And it is slower, as is very obvious when a ‘hurdler’ and ‘stepper’ clear the last three or four hurdles in a close race. The would-be specialist steeplechaser should therefore master hurdling techniques.
In taking the water jump the skilled performer speeds up several strides before take-off and gauges this spot without chopping or changing stride. For it is essential to accelerate beyond average racing speed in order to negotiate this wide (12 ft) obstacle.
He then springs on to the rail, meeting it just above the hollow of the front foot. Now, by maintaining a crouch position over a bent leg, he reduces the body’s moment of inertia about the supporting foot, thus pivoting quickly and easily forward. The leg thrust (primarily horizontal) is powerfully yet smoothly co-ordinated. The trunk straightens, the rear leg is kept trailing momentarily and the arms are raised laterally for balance correction. The landing (about 2 ft from the water’s edge) is made on one foot and the first stride is taken on to dry land.
Experience proves that although, in the early laps, it is possible to clear the water in one leap from the rail, in terms of energy expenditure this becomes increasingly costly as the race proceeds. It is therefore more economical to negotiate the obstacle in the manner described, and to do this throughout the race.
Running, ‘the classical athletic sport’, can be considered both simple and difficult: simple, because it is an instinctive, natural skill performed at some time by all but the most unfortunate; difficult in its mechanical complexity.
No two athletes run in precisely the same way, for people vary in their anatomic structure and body proportion, in strength and flexibility, in posture (often influenced by characteristics of personality) and in their interpretation of some fundamental phase of running action. Moreover, the emphasis on particular aspects of form changes from one running event to another. The ancient Greeks were aware of this; Philostratus speaks of sprinters ‘moving their legs with their arms to achieve speed, as if winged by their hands’; and Aristotle analyses aspects of running in his On the Gait of Animals.
Yet all the many kinds of running, from the shortest sprint to races over the longest distances, share certain basic mechanical principles, a knowledge of which is helpful not only to an understanding of running itself, but in the analysis of other track and field events and sports. For many skills are derived from or are influenced by these innate running movements.
Running movement is brought about by a combination of forces: internally, muscular force, producing a change in ground reaction, as well as overcoming resistance due to muscle viscosity, the tensions of fascia, ligaments, tendons, etc.; externally, the force of gravity, the resistance of the air and the forces exerted by the ground on the runner’s shoe (to ensure that the ground can exert a maximum forward force, the runner wears spiked shoes).
Good running calls for a co-ordinated action of the entire body. However, for the purpose of movement analysis it is convenient to consider it in various parts and phases.
Compared with the locomotion of modern machines, human locomotion is cumbersome and inefficient, for it depends upon the rotation of legs and arms, i.e. approximately 47 per cent of the body’s total mass, and their moments of inertia necessitate the use of tremendous muscular force and expenditure of energy to start, retard, stop or reverse limb movement. In terms of effort economy a wheel mechanism is far better; but Nature uses only rods and levers: arms and legs.
The human body is designed for accuracy of control rather than mere mechanical efficiency, however, and its combined adaptiveness, elasticity and strength have never been equalled by machines. In particular, the three leg levers, articulated on the pelvis, adapt themselves admirably to an enormous variety of postures, efforts and movements, of which running is only one.
Running speed is the product of length and frequency of stride, their ratio changing from one phase of a race to another and from athlete to athlete. Yet these two factors are always interdependent, and maximum running efficiency exists only when they are in correct proportion, depending, mainly, on the weight, build, strength, flexibility and coordination of the runner.
Leg movement, i.e. over two strides. It divides naturally into phases of recovery, when the leg swings from the hip with its foot clear of the ground, and drive, when the foot is in contact with the ground. Both are finely co-ordinated.
Recovery phase. The instant the toes leave the ground the foot, which had been brought momentarily to rest, undergoes an acceleration, when the leg flexes at the hip, knee and ankle joints. This appears to be the result of (i) a reflex mechanism which prevents over- extension and (ii) the forward motion of the thigh causing (iii) a transference of angular momentum to the fore leg. These flexions are marked, particularly, in sprinting.
In this way the mass of the leg is brought closer to the hip axis, reducing the leg’s moment of inertia and increasing angular velocity. The work of pulling the leg mass forward and upward (mainly that of the hip flexors, supported by the abdominals) is also reduced because of the tapering of leg mass; for the arrangement of the muscles ensures that the comparatively light calf and foot, distant from the hip, are easier to accelerate (this principle also applies to the arms).
The co-ordination of both legs is so timed that the flexion of the recovery leg is greatest, and its back-kick highest, fractionally after the front foot meets the ground. The swinging thigh then begins forward-upward movement of great importance to the runner’s drive; in particular, the acceleration of this thigh increases the forward force exerted by the ground, thus increasing the speed with which the Centre of Gravity is moved away from the supporting foot.
At the limit of its forward swing (coinciding with the completion of rear leg drive, thigh movement is reversed, the leg extends from the knee joint and the foot accelerates first forward and then backward. The reversal of thigh movement (brought about primarily by the glutei and hamstring muscles) produces a transference of angular momentum and flail-like action in the fore leg; yet the movement is smooth and neuromuscularly controlled.
It is important to note that in efficient running the leading foot is never stretched grotesquely for a longer stride; stride length is the product of a driving forward of the entire body.
The recovery phase is much more the result of muscular force and control than a pendulum action. It takes longer than the driving phase and for about half the time on each stride, when both feet are off the ground, the legs recover simultaneously. This is in contrast to a walking action, in which the legs swing for not more than half the stride duration, never more than one at a time and contact with the ground is unbroken.
Driving phase. The foot lands: (i) First, on the outside edge, and with the toes pointing slightly outward. It then takes the full weight of the body at a point which varies with the runner’s speed; in sprinting, well up on the ball of the foot , almost flat-footed at very low speeds. As the body passes over the foot, the heel touches the ground lightly. These movements are an instinctive, natural phenomenon. (ii) With its leg flexed at the knee joint, ‘giving’ on impact ; knee and ankle axes are parallel. (iii) Ideally, with a backward speed, relative to the runner’s Centre of Gravity, at least equal to his forward speed over the ground. (iv) In front of the Centre of Gravity; the distance diminishes with an increase in speed.
The optimum position of the feet in running is one in which their inner borders fall approximately along a single straight line. When one foot is placed directly in front of the other, lateral balance is impaired. Too wide a spacing (sometimes due to large thighs or knock knees) encourages a ‘weaving’ running action.
Experts are not agreed on whether the leg’s backward movement can be used to ‘pull’ the runner over the foot before the ‘push’ of the drive. Some say it is impossible, while others rate it purely incidental to grounding the foot quickly for another drive. Still others recommend a deliberate pulling action.
Mechanically, pulling and pushing forces are equally efficient: e.g. it is all the same whether a railway engine pushes or pulls; but with the human machine pushing forces are much stronger. The formation of the leg is unsuited to a pulling force, for the resultant of the ground’s reaction to such a force and the upthrust of the ground on the foot cannot pass through the runner’s Centre of Gravity. Hence, to attempt to accelerate the Centre of Gravity by this means is a waste of effort. Distance runners (who, in conserving a little energy on each stride, save a great deal over the full distance) should therefore reject the ‘pulling’ theory on grounds of effort economy.
As for sprinters, they can obtain and benefit from this second impulse provided the front foot has backward motion, relative to the ground, as touchdown occurs. Obviously, such a method of acceleration becomes progressively more difficult as the athlete gathers forward speed; and at top speed there can be little—if any—relative motion as this foot contacts the track. However, whereas the distance runner permits the lower leg to swing naturally as it approaches the gound, the sprinters need for a rapid striding cadence (at a rate, in good sprinting of about four and a half to five strides per second—it quickens very slightly with a progressive reduction in the stride-impulse) demands an emphasis on getting the front leg quickly under the body for a more immediate leg drive.
As the body moves over the foot the thigh’s backward motion (relative to the hips) is momentarily retarded, while flexion increases at the knee and ankle and the heel drops to touch the ground lightly. This gives the foot more time in which to apply force against the ground and stretches the extensor leg muscles, strengthening and improving their range. The lowering of body weight, also, reduces the athlete’s moment of inertia about the supporting foot, making it easier and quicker to pivot over and beyond.
The supporting leg’s accelerating effect on the runner increases progressively as he moves forward, and the leg is able to direct more of its driving force towards the body. However, it may be that the forward force reaches a maximum and then tapers off before contact with the ground is broken. In good running, the vertical component of this force , is never more than necessary to counteract the pull of gravity on each stride; but it usually exceeds the horizontal thrust component— even in acceleration.
The gluteus maximus, hamstring, quadricep, gastrocnemius and hallucis longus muscles bear the burden of the movement. Extension originates in the stronger but slower muscles surrounding the runner’s Centre of Gravity, and is taken up at the knee, ankle and foot, in that order. All extensions end together with the driving leg ‘athletically straight’, the foot well behind the body —again pointing slightly outward, with the runner breaking contact with the inside front edge.
Eccentric movement. In a normal standing position, a man’s Centre of Gravity is situated approximately at the level of the upper third of the sacrum and, with the raising of various parts of the body, in running at times it is even higher. Relative to the athlete’s Centre of Gravity, leg movement is eccentric, i.e. ‘Off centre’.
Thus, while the force of reac tion to the effective leg drive tran slates, or projects, the body’s
Centre of Gravity, its upward thrust tends to lift, and its for ward thrust pushes forward, the corresponding hip. Likewise, in recovery, the forward-upward swing encourages a retarding and dropping of the hip on the same side of the body. In fact, hip action tends to reduce the thrust received from it or delivered to it. The greater the effective leg drive, the more powerful these tendencies are; and as, in the course of the leg drive, the direction of the thrust or lift changes, so does the proportion of these horizontal and vertical reactions.
However, this hip movement is prevented by muscles and ligaments; e.g. as the body is first supported and then driven forward by one leg, the corresponding gluteus medius and minimus muscles prevent a sagging of the opposite hip. On the contrary, the hips follow the legs.
The reaction cannot be denied, however ; if the pelvis will not assimilate the by-product of eccentric leg thrust, then another part of the body, and/or the ground, must.
Arm and shoulder action
Because of the muscular connections between the pelvis and the upper trunk (e.g. internal oblique and latissimus dorsi muscles) most of this reaction in running is absorbed by the upper body, which can be seen to twist rhythmically in opposition to the leg movement. However, a little is taken up internally and by the ground, and is therefore not apparent.
We have seen that the location of body reaction can be controlled to some limited extent. In different types of running the reaction to the horizontal and vertical components of the eccentric leg thrust is absorbed by: (i) vigorous, but properly directed, arm action ; (ii) the shoulders and arms twisting en bloc, without a pivoting of the arms about the shoulders. This action was exemplified in the style of Emil Zatopek; (iii) a combination of (i) and (ii) above, as is most common to all but the short sprinting events.
Sprinting. In sprinting the accelerations of leg movement required for a striding cadence of four and a half to five times per second (the frequency in top-class competition) and for a powerful leg thrust, are possible only when the shoulders are kept steady about the trunk’s longitudinal axis; because the trunk, with its great inertia, cannot twist and untwist with sufficient rapidity.
In good sprinting the reaction to the horizontal (i.e. twisting) component of the leg thrust is absorbed by the more easily controlled arms, and the shoulders remain steady. However, to ‘take up’ this angular momentum, the arms have to operate with sufficient force and, primarily, in a sagittal (i.e. backward-forward) plane. Force of action is indicated by their radius and angular acceleration, while their range about the shoulders denotes the time/distance of force application. (Arm action will tend to be more effective in absorbing ‘twist’ the greater its distance from the body’s longitudinal axis.)
Both forward and backward arm movements are part of a clockwise or counter-clockwise upper body twist; they work in sympathy with each other, not in opposition. During their forward swings they are kept flexed at about a right angle, giving great angular velocity and co-ordinating with the quick recovery action of the forward-swinging leg. The forward arm movement sets up a backward reaction on the corresponding shoulder, ‘absorbing’ the forward twisting which would otherwise ensue. Of particular importance here is the upper-arm movement in a sagittal plane; a slight cross-body swing of the lower arm is both natural and desirable.
The backward phase of arm action tends to thrust the corresponding shoulder forward. The arm’s effect is at first strengthened and prolonged by a natural straightening at the elbow, corresponding with the longer leverage of the driving leg on the opposite side. But towards the end of its backward movement the arm bends and speeds up again, to match the final, fast stages of leg drive.
The range of arm movement in sprinting is about as much in front of as behind the shoulder axis. It varies with the individual (e.g. thin, small arms might move through a greater arc) and, to a certain extent, from one phase of a sprint to another (emphasised, especially at the start); but, usually, the hands swing no higher than shoulder level to the front, nor more than a foot behind the hip-line to the rear.
While, in all forms of running, the primary function of the upper body is to ‘take up’ reaction to the eccentric leg drive, ‘counterbalancing’ and ‘following’ leg action, in sprinting particularly, the arms may be used to spur on the legs, which speed up and consequently add to their horizontal component of drive; for action and reaction arc interchangeable factors.
Since both arms accelerate upwards and downwards simultaneously (and, in sprinting, with values greater than gravitational acceleration) their upward movement adds to the vertical component of drive; and their downward acceleration coinciding with touch down, lessens the impact between the ground and front foot.
Moreover, by losing upward speed fractionally before the completion of leg drive, they ease the compression of the thrusting leg—and so permit more forceful and freer use of its foot and ankle. Hopper writes: ‘It is in this connection that the vital importance of timing becomes obvious; and one wonders how many pulled muscles and other troubles are due to temporary lack of exact co-ordination between leg and arm action.’
Longer distances. While wishing to maintain as high a speed as possible, those who run longer distances must conserve energy by reducing their effort and frequency of striding. Their weaker leg drive and slower leg swing in recovery develop less angular momentum than in sprinting, and a reduced striding frequency gives the trunk time to take up the reaction to this angular momentum without recourse to forceful and tiring arm movement. Arm action is ‘quieter’ and does not fully compensate; hence the relaxed flowing shoulder-twist and gentle arm movement typical of the distance runner.
Trunk and head positions
Running movement can give maximum efficiency only when the athlete is properly balanced, which depends considerably upon the correct angling of the trunk. The following are relevant factors:
The force of the leg drive and the proportion of its horizontal and vertical components. As previously maintained , for balanced running the moments of the vertical and horizontal components of drive must be adjusted about the runner’s Centre of Gravity, and, at uniform speed, can be considered constant: posture is almost erect though, when a good runner is viewed from the side, there is an illusion of a pronounced forward trunk lean when his driving leg is fully extended ; a fairer view is obtained when he is in mid-stride.
However, in acceleration (i.e. in the gaining or losing of speed) the problem of balance is complicated because of variation in the horizontal component of leg drive. In positive acceleration, for example, the faster a man runs the more difficult it is for him to exert a large force against the ground, which to him, seems to be receding rapidly; he is unable to move his feet fast enough. Thus, the force he exerts and its duration (i.e. the impulse) are successively reduced. (0n leaving the blocks a sprinter will be in contact with the ground for approximately twice as long as when both feet are off the ground. After about ten strides, however, the times will be equal; and, thereafter, will attain a ratio of between 1:1-3 and 1:1-5. Thereafter, at a maximum or near-maximum speed, while he is in contact with the ground in one unit of time he has to counteract the effect of gravity during 13 to 1-5 units—requiring an additional upward thrust of 1-3 to 1-5 times body weight. His vertical component of drive must at all times keep him off the ground for sufficient time for his legs to get into position for the next stride.)
For balance in varying accelerations a runner has constantly to alter the lever-arms of the force components by adjusting the position of his Centre of Gravity in relation to his supporting foot; this he achieves by changing the angle of his trunk. In a phase of great positive acceleration (the result of a large horizontal component of force), as in the first stride from the blocks , a sprinter needs a pronounced forward lean; hence the main justification for a crouched start. But later in his race, with a reduction in the force he can exert, he has to assume a more erect position to avoid toppling forward. (Note: Here it is a vertical component of leg-drive in excess of body weight on each stride which raises the sprinter’s Centre of Gravity progressively towards a normal running position).
By the same token, balanced negative acceleration calls for a backward lean. An exaggerated lean either way reduces the stride length and places an unnecessary strain on the muscles of the trunk.
Rotation in a sagittal plane. So far, it has been convenient to assume the line of thrust from the ground reaction on each stride always to pass through a runner’s Centre of Gravity. Certainly, the resultant effect is as if it did so, and this approach to balance in running is recommended as most practical.
As Hopper has shown, however, ground reaction, besides supporting and propelling the runner, creates angular momentum in a sagittal plane; for when the foot first meets the track both vertical and horizontal components of reaction act in front of his Centre of Gravity, tending to rotate him backwards. But later, when a large vertical component acts behind his Centre of Gravity, the tendency is for the trunk to be rotated forward’, and (particularly in acceleration), to be rotated backward again just before the foot breaks contact, when the vertical component has greatly diminished.
Hopper suggests that, to maintain the trunk in an efficient running position, the legs and arms ‘take up’ these angular momenta. Thus, with the line of thrust from the ground in front of the runner’s Centre of Gravity , foreleg and forearm movements! possess a counter clockwise angular momentum; and with this ground reaction behind, their effect is reversed. Finally, this ‘absorbing’ process is reversed yet again.
But Hopper says, ‘… the transmission of a big force from the ground to the body of the athlete will take place only when the line of its action passes close to both hip and the man’s Centre of Gravity; so it is not surprising that the maximum ground reaction developed… in running does not occur until these conditions are fulfilled.’ position of the Centre of Gravity to the force and direction of ground reaction.
Posture. Hip mobility is of special influence in determining the angle at which the trunk is held in running, because unusual flexibility in these joints enables an athlete to adjust his balance while maintaining a more upright position.
Other postural idiosyncracics can give an illusory, as opposed to real, trunk angle. Round shoulders and a tendency to stoop create an appearance of pronounced forward lean in running , while pigeon-chested or hollow-backed athletes appear to run with an upright carriage.
Posture, a product of heredity, environment and self-expression, is acceptable in an athlete if it permits the proper functioning of respiration, circulation, digestion, etc., and involves no unnecessary tensions or restrictions. In considering its relation to running efficiency these should be the only criteria.
Air resistance. As an athlete runs the resistance of the air not only requires him to do work which, in consequence, restricts his speed; it can also impair his running position; in particular, at top sprinting speed or when running into a strong head wind, air resistance tends to straighten the trunk. Under such circumstances, therefore, he maintains balance by shifting his Centre of Gravity sufficiently far forward to counteract the tendency to rotate backwards. He leans well forward into a strong head wind and is more upright with a following wind. The need for greater emphasis on horizontal force when air resistance is increased has been mentioned already and is illustrated diagrammatically.
Head. By virtue of its weight (approximately a fourteenth of the total mass of the body in an adult) and position on the spine, movements of the head can have considerable effect on other parts of the body. Hence the expression ‘The head is the rudder of the body’.
As a general rule it is better for the balance of the runner for the head to be kept in natural alignment with the shoulders, with the eyes directed to that end. However, a twisting of the head from side to side (i.e. in a horizontal plane) need not upset balance and may even be necessary, sometimes, in middle- and long-distance running.
The effects of a poor head position are often to be seen towards the end of a race, when runners are tiring; throwing it back straightens the trunk and shortens the stride.
Expenditure of energy
For practical coaching purposes the techniques of athletics are best studied through the concept of momentum , since accurate measurement of total mechanical work in athletics is always difficult and is frequently impossible. For this reason, physiologists prefer to analyse in terms of energy, calculating directly from the amount of heat produced during exercise, or indirectly from oxygen consumption and carbon dioxide elimination. Although physiological techniques do not fall within the scope of this article none the less, they are closely related to the mechanics of running; the following information should be useful to coaches and teachers as a background to their study of man, the running machine.
As energy expenditure in running is directly proportional to the square of the speed, there can be no optimum running speed. It has been calculated that the rate of oxygen usage in an average sprinter running ‘all out’, provides energy at the rate of 13 horse-power.
In all forms of running some energy is spent on working against air resistance; as a man runs he drives part of the air to one side, and either carries along or pushes more of it in front of him. This requires work, diminishing his kinetic energy and, therefore, his speed. The force of this air resistence varies as the square of the runner’s speed and is therefore greatest in sprinting. It has been estimated that, in still air, at a speed of 35 ft per second (the top speed of a good sprinter) the force of air resistance is about 3-58 lb.
When an athlete runs, his Centre of Gravity undulates continuously. Off the ground it moves up and down, and while he is in contact energy is used to stop the downward movement of the Centre of Gravity and to give it upward movement again. Because the foot makes contact with the ground almost directly below the Centre of Gravity, the retardation of downward movement can be expected to exceed the following upward acceleration, which occurs when the Centre of Gravity is in front of the foot. If this is so, the time spent in retardation is less than that of acceleration.
When the athlete is not in contact with the ground the vertical movement of his Centre of Gravity is, of course, regulated by the force of gravity. Here, again, the periods spent in upward and downward movement are most probably unequal.
Much more total energy is expended in producing and destroying the kinetic energy in the limbs. Each foot is brought to rest about every sixteen feet and the remainder of each leg is slowed down and speeded up in a continuous cycle of movement. In addition, as the movement is mainly rotary, the direction is continually changing. This means that there is a continual change in the momentum of the legs, and this also applies to the arms.
While the athlete has contact with the ground, part of this total change in momentum is produced by the work done by the driving leg, and accounts for much of the energy expended by this leg. However, when there is no contact with the ground, all change is produced by the transference of momentum from one part of the body to another, at the expense of energy; for there is always a loss of energy in any transference of momentum, because some is transformed into heat.
In consequence, if the work done by the driving leg is not equal to the expenditure of energy during all the movements of a running stride, the runner will slow down. This should serve to emphasise the danger of wasting energy through unnecessary movement and lack of proper relaxation.
Although reference has been made, already, to an average striding cadence of four and a half to five times per second some sprinters have used even greater frequencies. Clearly, an athlete striding only 6 ft at top speed must take as many as six strides in covering 36 ft in one second. Is such a high frequency possible without a reduction in stride length? Have we reached a stage where we can expect faster sprint times only from athletes with longer strides than
Tolan’s? Certainly, the tendency in modern sprinting is for the world’s best to stride between 7 ft and 8 ½ ft.
Leg speed in sprinting is not limited by the neuromuscular mechanism. The mass of the leg, its moment of inertia in recovery, the rate of development of kinetic energy, internal viscosity, the weight of the athlete and the angle of propulsion—these are the limiting factors.
At very high running speeds, especially, muscle movement is extremely uneconomical ; in fact, the efficiency of muscular contraction approaches only 25 per cent. By its very nature, therefore, human locomotion must be wasteful. Yet, through superior balance, relaxation and timing, trained runners can undoubtedly conserve energy and transfer momentum from one part of the body to another, so improving their efficiency. Indeed, the skill accomplished in many sports consists largely of concentrating momentum where it is wanted without unnecessary waste of kinetic energy.
In contradiction to Professor A. V. Hill’s original hypothesis that the fastest time for a given middle or long distance could be attained by running at a constant speed, some physiologists now suggest that the second half of, for example, a mile, should be run faster than the first, with the athlete conserving his anaerobic (i.e. oxygen debt) reserves until comparatively late in the race. And this latter opinion appears to have been substantiated, practically, in the running of a majority of sub four-minute miles so far.
From the point of view of energy expenditure, the writer thinks it very probable that Professor Hill’s conclusion is still valid—but that running with a uniformly accumulating load of oxygen debt, and its chemical consequences, has a more deleterious effect on performance than a less efficient use of energy.
We have seen that a body’s inertia is its resistance to change in motion, and with linear movement mass is the sole measure of that inertia; the greater mass sets up the greater resistance and vice versa.
However, with angular motion the resistance offered to acceleration depends not only upon mass but also upon its distribution about the axis, i.e. the moment of inertia; the closer the mass to the axis, the easier it is to turn. This principle, of great practical application in many problems of human locomotion, explains why one can rotate a limb much more easily about its longitudinal axis than a transverse axis of the same articulation.
In athletics, the distribution of mass can obviously be varied by changing position, by changing shape, about the different axes. For example, flexed or straight, the mass of the arm is the same in both positions and yet it is easier to move in the first position (a) for there its mass is closer to the shoulder-axis. Its moment of inertia is reduced. Likewise, the flexor muscles which pull the recovery leg forward and upward in running have an easier task with the leg bent than with a greater angle at the knee.
For the same reason the total body mass can be turned more easily about / Axis f Axis its longitudinal axis than a transverse one, and with most difficulty about a medial axis; all these axes pass through the Centre of Gravity. Again, an athlete’s resistance to rotation (i.e. his moment of inertia) in pole vaulting is greater with the body extended p. immediately after take off b than in the swing-up, where the legs are well flexed. To find, accurately, the moment of inertia of the body in any position about a given axis, it would be necessary to take each particle separately, multiplying its mass by the square of the distance (measured perpendicularly) to the axis, i.e. its radius; finally, all the separate results should be added together. But since this is obviously not possible, useful if not wholly accurate estimates can be made by using the figures already given for the relative average masses of the human body; in estimating the moment of inertia for each of the body units it must be remembered that each separate part has its own Centre of Gravity, lying fairly exactly along a longitudinal line but always slightly nearer the proximal joint (i.e. the joint nearer the trunk).
A person standing rigidly upright on a frictionless turntable with arms extended horizontally has, about a vertical axis, approximately three times the moment of inertia than in a position where the arms are held to the sides. In the first position he is three times more difficult to turn; i.e. to produce an equal angular acceleration, and with the turning force applied at the same point in both positions, the impulse (force X time) must be three times greater; or an equal impulse must be applied at three times the distance to the axis.
In the arabesque allonge skating and dancing position resistance to turning will be about six times greater and when the body lies on the table horizontally , with the vertical axis passing through its Centre of Gravity, it will be about fourteen times greater. In fact, relative to an axis passing through its Centre of Gravity, the moment of inertia of the body is least about a longitudinal axis, with the arms extended and close together above the head and greatest when turning in a similar position about a medial axis but with arms parallel. But it is greatest of all in a fully extended position with the hands as axis , as in handspring take-off (when, usually, the moment of inertia of the whole body is found by adding (1) the moment of inertia of its mass, supposedly concentrated at its Centre of Gravity, about the main axis and (2) its moment of inertia about a parallel axis through its Centre of Gravity). In fact, the body’s moment of inertia is always greater about an axis not passing through its Centre of Gravity than that about a parallel axis that does.
The angular velocity of a body moving uniformly is the angle through which it turns in a second. If, for example, an arm moves through a right angle in one second, its angular velocity about the shoulder axis is 90 deg. per second. Likewise, if the somersaulting diver turns completely (i.e. through 360 deg.) in two seconds, his angular velocity will be 180 deg. per second. Angular velocity may also be thought of in terms of revolutions per second, and there are other units in which it can be measured.
Angular velocities, like velocities, are rarely uniform in athletic movement, but if we wish to determine the angular velocity of a body at a given instant of acceleration, we must assume it to be moving uniformly for a short time; the shorter thejperiod, the more accurate the calculation will be.
When a turning force ceases to act then, from Newton’s First Law, the body to which it has given velocity will continue to revolve at a uniform rate, or, if brought to rest by force, the body will remain at rest. For example, the diver turns in the air as a result of forces applied on the springboard.
It follows, therefore, that an arm or leg can be moving relative to other parts of an athlete’s body without force acting simultaneously. However, with the human body, because of internal resistances due to opposing muscle forces and the elastic tensions of fascia, ligaments and tendons, where there is motion of such a kind there is usually force acting also. These internal resistances must always be overcome before force can set the various body levers in motion.
As previously mentioned in connection with levers , the linear velocity of a point on a turning body is directly proportional to its distance from the axis. Hence, when the hammer-thrower’s hands are two feet from the axis passing through his base and Centre of Gravity, and the hammer head is six feet away, the hands have only one-third of the linear velocity of the hammer. Again, if two discus throwers turn with equal angular velocities, the athlete with the greater radius of discus movement gives greater speed to the missile.
When the body has angular velocity, its motion may be considered as the linear movement of any point, plus a turning about that point with the same angular velocity. For example: the angular velocity with which a long-jumper rotates about his jumping foot as it rests, momentarily, on the board is equal to that with which he can be considered to turn during the take-off about his moving Centre of Gravity; if he does nothing to counteract it before leaving the ground (and maintains this position in the air), it will be the angular velocity with which he will continue to turn about his Centre of Gravity in flight.
The conservation of angular momentum
The product of a turning body’s moment of inertia and its angular velocity is called its momentum, which, like momentum, is a vector quantity possessing both magnitude and direction and bears the same relationship to impulse as does momentum to impulse.. It is a concept of the utmost importance in analysing turning movement in sport.
According to the law of the conservation of angular momentum, a turning body isolated from external forces, i.e. left completely by itself, will have a constant angular momentum; that is to say, the product of moment of inertia and angular velocity about the axis of momentum is constant.
If it were possible to make a turntable with frictionless ball-bearings and a man standing on it were set in motion by a push, he would continue for ever to revolve with angular momentum, if we ignore air resistance. By the same token, the angular momenta of divers, high-and long-jumpers, etc., whose body masses turn in the air, ‘free’ in space, may, for all practical purposes, be considered constant in magnitude and direction (for the force of gravity, which acts equally on all parts of a revolving body, can be ignored).
Under these conditions the total angular momentum is entirely unaffected by any rotational movements made with the legs, arms or some other part of an athlete. This will be discussed in more detail later.
However, by changing the moment of inertia of body position during spins and rotations it is possible, correspondingly, to speed up or slow down the turning rate. If, for example, the man standing on the revolving turntable increases his resistance to turning three-fold by stretching his arms sideways , then his angular velocity will be three times slower, and if he resumes his first position he will spin at the original rate; but total angular momentum throughout will be unchanged.
The principle is well exemplified in diving. Accepting that, in re lation to a horizontal axis passing through the Centre of Gravity, a ‘straight’ position has approximately three and a half times the moment of inertia of a ‘tuck’ position , if the diver leaves the springboard with just sufficient angular momentum for a complete somersault in the ‘straight’ position it will enable him, should he so choose, to spin from two to two and a half times ‘tucked’. Here allowance is made for the time it takes to adopt the more compact position after leaving the board and a final straightening out prior to entering the water.
This example from diving points to one way in which turning during flight can be controlled in long-jumping. Should the jumper leave the board rotating forward and then ‘jack’ or ‘tuck’ prematurely , his angular velocity is markedly increased thereby and his feet are driven down and back in relation to his Centre of Gravity, for a poor landing. On the other hand, by keeping the body extended in the air, ‘jacking’ at the last moment, this can be averted. Again, a high-jumper twists quickly in the air when his body’s longitudinal axis corresponds closely to his axis of momentum.
Taking another event, a pole vaulter swings slower with his body stretched out just after take-off than when tucked up at the end of the swing, in readiness for his pull-push action.
Ballet dancers and skaters frequently spin at very high speeds. While they are building up angular momentum their arms are stretched out and the free (non-supporting) leg is permitted to swing wide of the body’s vertical axis then, suddenly, the arms and leg are brought in with tremendous effect. A graceful finish and slowing down or stopping are then cunningly combined by again extending the arm and free leg masses.
Good hammer and discus throwers, like the pirouetting dancers and skaters, keep the free leg close to the supporting leg during their turns, thus getting the hips and feet in position quickly, ahead of the rest of the body and the missile.
Again, maintaining balance on ice is the more difficult because of a tendency to rotate (i.e., in a vertical plane), about the body’s Centre of Gravity, as opposed to the feet—where, in the latter case, the moment of inertia is greater.
Determining the axis of momentum
Reference has been made already to an axis of momentum, fixed in direction and about which jumpers, divers, etc., will possess unchanging angular momentum in the air. The position of this axis can be calculated provided the body’s separate momenta about a vertical, transverse-horizontal and medial-horizontal axis at the instant of take-offarc known. Here the principle is applied to a high-jump take-off.
As angular momentum is a vector quantity, each of these three separate turns is represented by a straight line which, in length, is equal to the magnitude of the corresponding angular momentum; all three meet at the athlete’s Centre of Gravity. It has been assumed, for this particular jump, that there is least angular momentum about the vertical axis and most about a medial-horizontal axis; with ackward rotation, also, about a transverse-horizontal axis. However, the turning combinations will vary from style to style, and even from one jump to another by the same athlete.
For a resultant to be found, the direction of each separate turn must also be known. Conventionally, positive direction is that which makes the turning look clockwise and, therefore, each axis is looked along so that this is so , and arrow-heads are then added to point accordingly.
By using the parallelogram method in three dimensions the magnitude and direction of the total angular momentum and the position of the axis of momentum can then be established. The latter, in the case of our high-jumper, will be slightly at an angle to the horizontal and approximately 45 deg. to the crossbar, fixed in direction throughout the jump.
In a somersault dive or long-jump where take-offs are properly balanced, it is not difficult to estimate, from the movements in the air, that the axis of momentum is horizontal. But in many other activities, e.g. high-jumping, it is frequently not perceptible in any but a purely theoretical sense and, in the air, the athlete appears to turn separately, but simultaneously, about his longest and shortest axes; i.e. his axes of minimum and maximum moment of inertia, respectively. In theory it is possible to resolve an athlete’s total angular momentum at any time when he is in the air in space—about either the vertical or horizontal axes previously referred to which remain fixed in direction, or his body’s longitudinal, medial and transverse axes, which change their position relative to the ground as the athlete moves in the air.
As a matter of interest (for it does not arise in track or field events), given sufficient time the human body moving about a prescribed fixed axis will finally settle down to spin with stable equilibrium, selecting its axis of greatest moment of inertia. This, apart perhaps from a small wobbling called nutation (Lat. nutare, to nod), then coincides with the axis of momentum.
An illustration of this principle can sometimes be seen in the circus or on the variety stage where one performer, suspended from a cord gripped by the teeth, is turned by a partner hanging upside down from a trapeze. At first the suspended person revolves rapidly about the body’s long axis but quickly (and automatically) assumes a horizontal position, turning about the body’s ‘preferred’ axis of greatest moment of inertia.
Turns originating on the ground
A careful analysis of track and field techniques shows that, to greater or lesser degree, almost all athletes break contact with the ground during performance, turning momentarily about an axis of momentum. However, it by no means follows that they are always conscious of it, or should be so.
Imperceptible in good running, it nevertheless occurs on each stride and also during well-executed high-hurdle clearances. More obviously it occurs in the jumping events and in the pole vault, as the athlete rotates about the crossbar on releasing the pole.
There are few, if any, good hammer throwers whose two feet do not leave the ground, simultaneously, during the last turn, though doubtless this is something not attempted. In all three of the other throwing events, when well performed, the breaking of contact, with a turn in the air, is important at least to the regaining of balance after the throw if not to the throw itself.
Although, as we shall see later, some turns in athletic movement can originate in the air, nevertheless in track and field athletics most are built up while the runner, jumper or thrower is in contact with the ground, when angular momentum can be acquired in the following three ways: checking linear movement, transference and eccentric thrust. Usually, at least two of these sources are combined.
Checking linear movement. When a body, moving in a straight path, is suddenly checked at an extremity, a hinged moment results and angular momentum is developed. For example: 1. In vaulting over a box the gymnast, after a preliminary run-up, fixes both feet momentarily at take-off, while the rest of his body rotates over and beyond. This turning continues in the air, bringing the head and shoulders down and feet up in relation to his Centre of Gravity. The clockwise body turn illustrated is then reversed when the hands strike the far end. 2. As a result of planting the pole at the end of his approach, the pole vaulter develops angular momentum. He rotates simultaneously about his hands and the end of the pole in the box. 3. The diver’s somersaults can in part be due to checking the feet at take-off on the springboard, as already described. 4. The three previous examples are concerned with angular motion about horizontal axes but, in point of fact, the principle holds for turning about all axes, and sometimes about more than one at a time.
In the javelin event, for example, the thrower checks with his front foot and turns, simultaneously, about a horizontal axis (at the point where this foot meets the ground) and a near-vertical axis (passing through the throwing base and Centre of Gravity). This imparts considerable linear velocity to the throwing shoulder and, subsequently, to the javelin.
As the linear movement of a point on a turning body is directly proportional to its distance from the axis, height can be of particular advantage to a thrower. Assuming, for the moment, that after checking with the front foot the thrower’s Centre of Gravity continues at its previous linear velocity, then the shoulder above it must move considerably faster.
However, checking must cause some loss in forward speed and the more acute the angle between ground and body at the first instant of contact (or, in the pole vault, the smaller the angle between pole and ground) the greater the loss will be. The advantage must be weighed against the disadvantage, as so often in track and field techniques.
Under hinged moment conditions, an athlete’s angular velocity at take-off is identical about both base and Centre of Gravity axes. However, this must not be taken to mean that the angular momenta about these axes are also the same; they are not, for the moments of inertia differ.
In analysing athletic techniques it is usually more convenient to consider take-off angular momentum about the Centre of Gravity as, afterwards, its flight path is more regular than that of the feet and is unaffected by movement of other parts of the body.
Transference. Momentum, linear or angular, can be transferred from one object to another and from a part of an athlete to his whole body.
An example of the transference of linear momentum is if a snooker ball, rolling without ‘side’, strikes one end of a row of balls, its momentum is transferred to the ball at the far end; if two balls are used then, on impact, two balls roll at the other end.
Transference of angular momentum from a part to the whole of the human body can be simply demonstrated. The legs are swung from the hips, unjacking the body and when they are checked in their movement angular momentum transfers to the whole body, which then turns into a sitting position on the table.
Transference can be sudden, as happens when a rotating body part is checked abruptly, or it can be gradual, as the arm, leg, etc., only gradually loses its angular speed. The phenomenon is common to dancing and athletic movement where, often, angular momentum is first developed and stored ‘locally’ while in contact with the ground and used, later, to turn the whole body in the air. The following are examples: (i). In a tour en Pair, the ballet dancer first rotates the arms, shoulders and head in a horizontal plane, with the feet firmly fixed on the floor. Then, as the legs drive him into the air, the effect transfers and his whole body twists. (ii) A good high-jumper’s pronounced free leg swing at take-off builds up much of the angular momentum he will need subsequently for the lay-out over the crossbar. (iii) On the springboard the diver develops angular momentum by swinging his arms. This helps to turn his body in the air. ‘Local’ angular momentum is best built up with the body part extended and accelerating through a considerable arc; maximum angular velocity should be developed before contact with the ground is broken. On transference, the effect on the whole body depends on the distance of the axis of ‘localised’ movement from the body’s main axis, as well as the magnitude of the ‘local’ angular momentum. The turning effect of the arms on the body is all the more powerful because of the distance between the shoulder line and the body’s main axis passing through the diver’s Centre of Gravity. For, in effect, it is the arms’ angular momentum about the main axis which is important.
Eccentric thrust. As, on successive take-offs, an athlete’s line of thrust moves progressively farther from his Centre of Gravity, so will body rotation be easier and the projection of his Centre of Gravity be more difficult. Thus, angular momentum can also be acquired by driving ‘off centre’, i.e. eccentrically.
In track and field athletics this type of thrust is usually applied to an athlete at a point where one foot is in contact with the ground— when its line of action is often at a considerable perpendicular distance to his Centre of Gravity. However, the transmitting of a targe force from the ground to the athlete can take place only when the thrust passes close to his hip, knee and ankle joint and to his Centre of Gravity. Otherwise there is a tendency for these joints to collapse and the thrust develops angular momentum beyond the athlete’s ability to control it. The following are examples of eccentric thrust: (i) By bringing his head and arms forward, as a preliminary to his downward thrust against the springboard, the diver moves his Centre of Gravity slightly forward of his feet. In a good dive the required turning effect is combined with sufficient height off the board. (ii) Although not perceptible in good jumping, part of a high-jumper’s lay-out over the crossbar is due to an eccentric leg thrust at take-off. But the best jumpers sacrifice only a fraction of their upward spring to obtain sufficient rotation. They gain more from their position at the high point than they lose in take-off velocity. (iii) In a gainer (i.e. reverse) dive angular momentum is imparted to the body by means of a final foot thrust, often made with the toes gripping the end of the springboard. This is all the more effective because of its distance from the diver’s Centre of Gravity. (iv) In initiating a front somersault, with no travel, on a trampoline the performer ‘breaks’ at the hips. The reaction of the trampoline thus projects him vertically, with a forward somersault. (Here, the total horizontal momentum generated while the feet are in contact with the trampoline must be zero. This means that if, at this time, he imparts momentum backward to some part of his body, e.g., in rotating the arms clockwise, he must give the rest of his body equal momentum forward, e.g., by shifting his hips horizontally in an opposite direction. Thus the trampoline will have exerted no residual force horizontally.) (The checking of linear momentum is, in fact, caused by an eccentric thrust, whereas a transference of momentum produces such a thrust.)
Turns originating in the air
Action and reaction. While Newton’s Third Law applies to all motion, it is particularly important to an understanding of human and animal movement which begins in the air, ‘free’ in space. For whereas take-off surfaces can ‘absorb’ the reactions to turns originated on the ground, the body alone can do this when initiating movement in the air.
By way of comparison and illustration, we will consider two phases of a pike dive. When the diver drives down on the springboard it reacts with equal force by thrusting upward against his feet; when, as a result, his body is thrown into the air, its linear and angular momenta are equal but opposite to that given to the earth; for impulse and angular impulse are common to both.
But later, when the diver ‘pikes’ in the air , the muscles pulling the trunk down and forward, clockwise, act simultaneously on the thighs, pulling the legs upward in a counter-clockwise direction. Expressed in terms of the contraction of a single muscle, the fibres exert their force equally on origin and insertion, producing rotations on either side of the hip joint that are equal but opposite in their angular momenta. The muscle forces required to stop these rotations are also equal and opposite.
Here are some other examples of this phenomenon. If, the outstretched arm is swung horizontally across the body , the reaction moves the turntable and the standing athlete towards the arm; when the same action is executed after an upward jump the body’s reaction is even more pronounced. (This technique—with the arm lowered in front of the body and raised sideways again to repeat, if necessary— is sometimes used to create twist in dives, so ‘squaring’ the body for entry.)
As the long-jumper brings his legs forward and upward for the landing the hip flexor and abdominal muscles pull his upper body forward and downward. When the hurdler pulls the rear leg across the hurdle rail the contracting muscles simultaneously twist the trunk towards the trailing leg. And when the discus thrower, with both feet momentarily off the ground, twists his hips and legs in advance of his shoulders and the throwing arm , the acting muscles pull the upper parts of his body in an opposite direction.
With such movement, action and reaction occur in the same plane or in planes that are parallel. They will be about an axis, an axis of displacement always at right angles and passing through the athlete’s Centre of Gravity (but not necessarily coinciding with his axis of momentum). Clockwise action produces counter-clockwise reaction, and vice versa, though it is possible that certain very minor reactions to movement can be taken up internally and, therefore, invisibly.
Relative moments of inertia. The angular velocity of the two moving body parts is inversely proportional to their moments of inertia about their common axis. Referring again to the pike dive ; assuming the moment of inertia of arms, head and trunk about the hips to be three times greater than that of the legs, the contracting muscles will impart angular velocities in the ratio of 1:3, i.e., while the trunk rotates through 30 deg. the legs describe a right angle.
If the man on the turntable adopts a sitting position and then repeats the arm experiment, his rotation towards the extended arm is reduced in comparison with the previous example because of his body’s greater moment of inertia about a vertical axis. By the same token, a high-hurdler’s body is less affected by the movements of his trailing leg when he leans forward. On the other hand, a long-jumper preparing for landing will get his heels higher, through quicker and with the minimum of trunk reaction by first bringing the legs forward flexed before extending them. It is therefore possible to control the angular range and speed of reaction to some extent.
We have seen that movement originated in the air cannot disturb an athlete’s Centre of Gravity; thus, in piking , when the upper body and arms and lower legs are brought forward in relation to the Centre of Gravity, the hips, lower trunk and upper parts of the thighs move back, and the product of the masses and their distances about the Centre of Gravity is unchanged.
Control of reaction-location. Within certain limits an athlete can control the location of body reaction. We have seen how the turntable reacts to an arm movement in a horizontal plane; but when both arms are swung in opposite directions simultaneously , the reaction to the movement of one arm is ‘absorbed’ by the other and the turntable does not move. A similar action of the arms after an upward jump will not affect the body. Again, a high-jumper’s clockwise arm sweep could produce a counter-clockwise reaction of the body, or it could be ‘absorbed’ by the other arm or some other part. When a hurdling rear leg movement is performed on a turntable, the reaction swings the table in an opposite direction but if the arms are used correctly, they can absorb this reaction and the table remains still (c). In hurdling, this arm action keeps the trunk facing the front, to the advantage of balance, direction and speed on landing.
Illusions. While, doubtless, a working knowledge of the mechanics of movement improves what has been called ‘the coaching eye’, action and reaction in the air are often difficult for even an experienced person to detect because of rotation or spin developed at take-off. To explain: when a pike dive is well executed it appears that throughout the upward part of the flight the diver brings his upper body down towards fixed legs and then, keeping the arms, head and trunk still, throws the legs back on a fixed trunk to assume a straight position for entry. Trunk and leg motions seem isolated and without reaction. This is because the diver leaves the springboard with forward rota- tion. In piking, as we have seen, the legs are in fact pulled towards the trunk but, in a good dive, their angular velocity is approximately equal to the body’s rotational speed in an opposite direction, thus the legs remain almost vertical as the trunk rotates down and forward.
Conversely, the trunk movement is the more pronounced during the upward flight because it blends with the body’s overall forward rotation off the board. Later, in straightening out, the trunk rotates backward and the legs forward in an approximate ratio of 1:3, but the body’s take- off rotation cancels out the trunk movement while greatly speeding up the movement of the legs. Thus, the diver’s total momentum is first concentrated in the trunk and then, subsequently, in the legs.
The following are examples from track and field athletics. The pole vaulter’s eccentric arm thrust at the top of the vault imparts a rotation (clockwise in our illustration) to his whole body. But as he simultaneously ‘arches’ or ‘jacks’, pulling the trunk and legs in towards each other, the leg movement is the more apparent to an onlooker because it blends with the vaulter’s overall clockwise rotation. But when, on releasing the pole, he ‘unjacks’ his body overall rotation favours the lifting of the arms, head and chest, and the counter-clockwise leg reaction is hardly noticeable, or, perhaps, is completely nullified.
Similarly, the muscles pulling the hurdler’s leading leg towards the ground also straighten up his trunk; at this stage of clearance he, too, ‘unjacks’. But because of taking off with an overall forward rotation his trunk maintains a forward lean for the landing and the leading leg sweeps down and back even more quickly. Likewise, in long- and high-jumping, action and reaction in the air are sometimes difficult to discern and analyse through being ‘superimposed’ upon rotations of the whole body.
We have seen already that an arm or leg can be moving relative to other parts of the body without force acting simultaneously. Theoretically, therefore, force can be applied to a limb while an athlete is in contact with the ground and, relative to the trunk, the limb will go on moving in the air without apparent reaction, for the reaction will have taken place on the ground. However, usually with body movement, where there is motion there is force also, because of the internal resistances which must be overcome.
Exploitation of relative moments of inertia. We know that movement originating in the air cannot change an athlete’s total angular momentum about his axis of momentum because the action of one part of his body is ‘cancelled out’ by the reaction of another. Hence, it might appear that it is impossible to turn the whole body in the air without a point d’appui. However, the following examples will prove to the contrary: (i) If a man, freely falling through space or standing on a frictionless turntable, extends his arms and then swings them horizontally in, say, a clockwise direction, the lower parts of his body will then turn in a counter-clockwise direction. And when he lowers his arms and takes the twist out of his abdominal muscles by turning his shoulders counter-clockwise, a clockwise reaction is produced in his hips and legs. However, now that the moment of inertia of the shoulders and arms is so much smaller than when the arms were extended, the clockwise reaction of his lower body is slight. In consequence, the whole of his body has turned counter-clockwise. (ii) This process—sometimes used at the completion of the twist, in a twisting somersault dive, to bring the hips and legs into line with the upper body—is similar to that which enables a cat or rabbit, dropped from an upside-down position, to twist in the air and land on its feet. During the first stage of its fall the animal ‘pikes’ or bends in the middle and stretches out its hind legs almost perpendicular to an axis passing through its trunk. It then twists the fore part of its body through 180 deg.; the head, fore legs and upper trunk are now ready for the landing. The hind parts react by being displaced through a much smaller angle, because of their much greater moment of inertia about this axis.
During the second stage of the animal’s fall twisting takes place about a new axis parallel to its hind legs , the twist being in the same direction as that of the head and trunk during the first phase. Therefore the hind legs now turn through the larger angle, for the moment of inertia of its upper body about this new axis is much greater. At the completion of this series of movements the animal’s whole body is free from deformation and has turned through 180 deg.. In our illustration the rabbit turns about these two axes of displacement at different times. However, the movements can be—and often are— made simultaneously.
Likewise, when a diver assumes a front-arch position, ‘breaking’ at the hips , extended legs and hips can be used to rotate the trunk in an opposite direction. But to originate twists in the air by this method (and 540 deg. twists can be achieved) the body must be neither too straight nor too ‘piked’; and considerable spinal flexibility is required to continue the movement forward, laterally and backward. (iii) An outstanding example of the use of this principle in sport is seen in the half-twisting somersault, piked, dive. The diver leaves the board with forward rotation and then adopts a pike position. Now he twists his trunk through 90 deg. and then extends his arms sideways.
With the moment of inertia of the head, arms and trunk now greatly increased about the body’s long axis, the legs are momentarily brought into line and twist taken out of the abdominal muscles ; their twist continues until a pike position has again been assumed, but with the legs now on the side of the trunk farthest from take-off.
These leg movements produce no noticeable reaction or change of position in the rest of the diver’s body because of (a) the latter’s greater moment of inertia about the trunk’s long axis, and (b) the illusion created by his forward rotation off the springboard—a rotation in the sagittal plane which tends to conceal his upper body’s reaction to leg movement in that plane.
The diver has again assumed a pike position, but with his body still twisted. He then brings his arms back to their first position, stretched above his head, afterwards completing a 90-deg. trunk turn. Finally, now facing the springboard, he straightens out and enters the water.
Just as animals employ these movements without conscious analysis of the mechanics involved so, too, can athletes. And just as animals do not all conform precisely to the same movement pattern when faced with such problems of balance and safety so, too, in diving and other forms of athletic technique do the methods of exploitation vary from one person to another. In originating twisting movement in the air, for example, there are many variations of head, shoulder, trunk, arm, hip and leg movement available to the flexible, physically-clever performer. (Diving experiments appear to demonstrate that about three-quarters of twisting originating in the air is developed through the use of the spine; only about a quarter through hip movement.)
To re-emphasise: these movements of the whole body in space always take place about axes of displacement which pass through the body’s Centre of Gravity, but which, in most cases, are distinct from its axes of rotation and momentum. They cannot change total angular momentum
Secondary axes. Another type of movement involving the exploitation of relative moments of inertia is concerned with motion of a part of an athlete about an axis at a distance from his Centre of Gravity—a ‘local’ or ‘secondary’ axis.
From Newton’s Third Law it follows that when a man falling freely through space, or standing on a frictionless turntable, twirls an arm in a circle above his head so that its axis of movement corresponds with the body’s longitudinal axis, the angular momentum thus developed is simultaneously compensated for by turning the whole body mass in an opposite direction. In such a circumstance the arm action possesses a constant turning effect on the rest of the body.
Note. The arm’s radius of gyration is the horizontal distance between its axis and a point which represents the ‘mean’ of all the separate moments of inertia of its many parts; a point where, for the purpose of rotation only, we can consider the mass of the arm to be concentrated. It is not the arm’s Centre of Gravity. The circle traced out by this radius will be referred to as the circle of gyration.
When a similar movement is made slightly to the side, however, the turning effect is in proportion to the arm’s distance from the axis of displacement. In reaction, greatest angular displacement is produced when the arm is farthest from this main axis, and least when nearest, but the total rotational effect on the whole body is the same as before.
Should the axis of arm action (now a secondary axis) be moved so far to the side that the arm’s circle of gyration no longer ‘embraces’ the axis of displacement , then part of the arm movement produces a turning effect on the rest of the body contrary to that hitherto; for, relative to the axis of displacement, the arm moves through a sector of the circle of gyration in an opposite direction. However, when the arm is farthest from the body’s main axis its turning effect exceeds that of our two previous examples and, through a 360-deg. arm movement, the angular displacement of the whole body remains the same.
The sector producing a contrary rotation is enlarged. By virtue of the greater distance between these axes it is also more powerful, but so, too, is the arm’s turning effect in an opposite direction. Therefore, through 360 deg. of arm movement, the angular displacement of the whole body is the same as before.
It should be noted that the secondary axis of each rotating arm passes through the shoulder, the main axis passing through the man’s Centre of Gravity.
Here it should be stressed that (i) while the arm movement continues the body can be turned horizontally through any required angle; but when the arm stops, the body stops also; (ii) although the foregoing examples show motion in a horizontal plane, the phenomenon applies to motion in any plane; (iii) such movement cannot change the body’s total angular momentum about its axis of momentum.
In effect, therefore, it is the arm’s momentum about the body’s main axis (passing through the Centre of Gravity) which is significant.
Balance in the air. Movements which exploit relative moments of inertia are of particular importance to the maintenance of an athlete’s balance in the air, for they can be used to counteract embarrassing rotations either originated at take-off or caused by air and wind resistance after contact with the ground has been broken. The following turntable experiment exemplifies this.
IT angular momentum in the same clockwise or counter-clockwise direction is given to the man and turntable before he makes any of the arm movements described under Secondary axes , the reaction to them will create an illusion of reducing total angular momentum or even of reversing its direction, depending upon the efficiency of the arm movements; but when the arm stops, the original angular momentum is again apparent.
Three examples taken from sport follow: (i) A ski jumper with forward rotation in the air (movement hardly conducive to a safe landing!) can move his arms about his shoulders, in the same vertical plane and in the same direction as the embarrassing body rotation, and thus take up some of it, causing his body rotation to slow down. However, when the arm movement stops, the original body rotation again reveals itself.
Factors limiting the value of this action to the ski jumper are (a) working together in a sagittal plane, the arms cannot be swung with full range behind the shoulders and (b) as they move past the trunk they could possibly add to the body’s forward rotation (for the reason given under Secondary axes). (ii) In the hitch-kick long-jumping technique the forward rotation of the arms and the movement of the legs have a forward angular momentum. This may be (a) less than, (b) equal to, or (c) greater than the forward angular momentum with which the jumper left the board, depending upon the take-off angular momentum and the efficiency of his arm and leg movements in the air.
In the first case (a) the arms and legs will take up some of his angular momentum, causing his forward rotation to slow down. In (b) they will take up all his angular momentum, and so his forward rotation will cease temporarily; and in (c) the trunk will automatically rotate backward about the body’s Centre of Gravity, otherwise the jumper will have generated angular momentum in the air, which is impossible. (iii) The long-jumper corrects lateral balance (i.e. his movement in a frontal plane) by the use of his arms. When they are moved about his head in that plane their influence on the rotation of his whole body is the more powerful because of the distance between his shoulders (secondary axes) and his Centre of Gravity (through which must pass his axis of displacement). Depending upon its efficiency, the arm action slows down, stops or even reverses body rotation, yet without changing his total angular momentum; when the arms stop, the rotation of his whole body ‘takes over’ again.
It is sometimes convenient to ‘break down’ movement originating in the air into simultaneous rotation in several planes. Thus, a combination of rear leg recovery and front leg downward drive in hurdling may be considered as simultaneous body rotations and reactions in the three main planes, i.e. horizontal, frontal and sagittal.
We have already seen that, in a horizontal plane, the action of the hurdler’s lower limbs twists his upper body towards the trailing leg ; in a frontal plane it also tilts it down in the direction of this leg ; and in a sagittal plane the reaction rotates him backward, as in a hitch-kick. In all three planes, clockwise motion produces simultaneous counter-clockwise reaction, and vice versa; in each case angular momenta are equal but opposite.
These principles of balance and reaction also apply to certain kinds of movement when an athlete is in contact with the ground. If a man balancing on a beam feels he is falling to one side, he might regain balance by rotating his extended arms in (he some direction, as with the maintenance of lateral balance of the long-jumper in the air , with the difference, however, that when in contact with a beam the movement could, at the same time, displace his Centre of Gravity.
In running, too, the alignment of the body (both on and off the ground) depends to some extent upon such principles.
Gyration and the trading of momentum. We have seen how in many activities the axis of momentum is present in only a theoretical sense, with the athlete turning in the air separately but simultaneously about his body’s longest and shortest axes.
It has been convenient to assume that the axes of momentum and rotation always coincide, but in fact this can be the case only where there has been an angular impulse imparted about either the axis of greatest (i.e. medial) or least (i.e. longitudinal) moment of inertia. Where the athlete develops rotation about his transverse axis or more than one of his principal axes simultaneously , his motion can best be described in terms of a twisting about his longitudinal axis and a gyrating of
Thus the high jumper twists about his longitudinal axis which, at the same time, describes part of a closed conical path about his axis of momentum; and if he maintains the posture shown, this path will not vary and there will be no interchange of momentum between the two motions.
However, through action-reaction in the air an athlete can alter his position relative to his axis of momentum, and so change the direction of his principal axes that he (a) rids himself of the complexities of multi-axial rotation by stabilizing his rotation about only one such axis or, conversely, (b) deliberately brings about gyration.
For example, a gymnast somersaulting forward as he leaves the trampoline (i.e. rotating forward about a horizontal axis of momentum: can originate movement in the air which will change the direction of his principal axes. In consequence, his body absorbs some angular momentum by twisting about its longitudinal axis, simultaneously changing the initial rotation about the transverse axis into the motion illustrated. He ‘trades’ some somersaulting for twisting, although his total angular momentum remains unchanged.
In this case, the initiation of a twisting motion will not alter the rate at which the somersaulting takes place; but, of course, if the twisting is rapid and the cone-angle is therefore much reduced, the motion will not look so much like a somersault. Likewise, by originating movement in the air, our straddle-jumper could bring his longitudinal axis more into line with his axis of momentum and so twist more rapidly away from the bar.
The axis of a revolving body is a straight line, itself at rest in the body, about which all other parts rotate or spin in a plane at right angles. We know that different parts of an athlete have their own axes, the joints, but here we shall consider the revolution of the whole body mass, first, when in contact with the ground and, second, in the air, with contact broken.
Axes when in contact with the ground. There are countless instances in sport where athletes revolve in a vertical or near vertical plane about axes through their points of support. In a handspring for example the gymnast turns first about his hands and then, on returning to ground, about his feet. A cartwheel provides a similar example.
Likewise, take-off movements in jumping and the pivoting of the body on the supporting foot in running can be thought of as rotations of the whole body about an axis at a point where the foot meets the ground. Again, a pole vaulter swings about his hands immediately after take-off, or he and his pole, combined, can be thought of as a mass rotating about the end of the pole in the box—also applicable to a gymnast swinging by his hands on a horizontal bar.
Nor need the extremities always be the point of support although, in track and field athletics, this is most common. In certain gymnastic exercises, for example, it is the head, the shoulders, or the back or buttocks, as in certain tumbling movements.
Motion in a horizontal or near-horizontal plane (i.e. about a vertical or near-vertical axis) is equally common in sport, particularly so in athletics, with the discus and hammer events as outstanding illustrations. With turns of this type the body’s axis passes through the point of support and the athlete’s Centre of Gravity (the latter including clothing worn and any apparatus held).
The ice skater therefore pirouettes about an axis which passes through her Centre of Gravity and the point of the skate in contact with the ice. And in those activities (like the shot, hammer, javelin and discus events) where some turning movements are made with both feet in contact with the ground, the support or base includes both feet and the intervening ground; so, in such cases, an axis can actually fall between the feet and move from one part of the base to another.
Most athletic events combine turning movements about both types of axes.
Axes in the air. For the purpose of analysing the movement of a body (e.g. an athlete or throwing implement) in the air (i.e. without contact with the ground, direct or indirect) it is convenient to consider the rotation about an axis passing through the Centre of Gravity, because of the regularity of that point’s flight path. The position of the axis relative to the ground depends upon turning movement imparted to the body immediately prior to breaking contact, but it will remain fixed in direction throughout the jump or dive until contact is regained, provided air resistance may be disregarded. Thus, the diver , rotates about an axis passing through his % I I
Centre of Gravity, and this axis maintains its direction relative to the ground and water until entry. The high-jumper , rolling or twisting his way over the bar, turns about an axis fixed in direction, but the axis of a spinning discus in flight can be shifted by air resistance. However, in both cases the axis passes through the Centre of Gravity.
It is possible for an athlete to turn about this axis of momentum, as it is called, and, simultaneously, about another axis concerned only with movement originated in flight. But this and other aspects of rotational movement in athletics will be discussed later.
The muscle forces of the human body are applied through a system of levers (bones rotating about their joints) to which the principle of moments, discussed earlier, is fundamental. In analysing movement in sport it is sometimes convenient to regard large segments of an athlete, e.g. an arm, leg or trunk, as a simple lever, in the same way as the use of a piece of apparatus may be analysed in terms of leverage.
The three types of levers are classified according to the arrangement of the fulcrum (axis), the force and the resistance. The fulcra (A) are the joints and through muscle-contraction force is applied at the points where the tendons are attached to the bones (F).
The resistance (R) may be merely the weight of the lever itself or the combined weight of the lever plus a load, like a shoe or throwing implement. However, if (and this would be unusual in track and field athletics) the lever acts in a purely horizontal plane, then the resistance in this plane will be due only to inertia, resistance to change in motion, the pull of gravity being vertical. This resistance might also be a force acting within, or externally against, the body.
First class levers. With this type of lever the fulcrum is situated, ‘see-saw’ fashion, between the applied force and the resistance, both acting in the same direction. The arms (i.e. the distance between force and fulcrum on the one hand and resistance and fulcrum on the other) may be equal or unequal; but if the force arm is longer the lever will favour effective force, and if it is shorter it will gain in speed and range at the expense of force. Hence ‘all that is lost in force is gained in distance, and vice versa’.
In both our examples of first class levers the resist- ance arm is much longer than the force arm, favouring speed and range but not force. This applies to most levers of the body. If, for example, the resistance arm is twelve times longer than the force arm, a triceps force of 96 lb exerts only 8 lb of force on the shot (96 -r 12). But such an arrangement has its compensations, since the muscles shorten slowly, thus developing very high tension.
The interdependence of speed and range of action is illustrated, where a short lever, AB is superimposed on a longer one, AC, both moving with equal angular velocity. The linear velocity of the lever ends is proportional to their radii; therefore, if AC is twice as long as AB, its end will travel twice the distance in a given time, i.e. it will have twice the linear velocity. To take an example from athletics, when a pole vaulter adopts the ‘carry’ position, the downward force he has to exert with his rear hand is many times greater than the force of gravity pulling on the pole in front of his other hand, the fulcrum.
Second class levers. With levers of this class both force and resistance act on the same side of the fulcrum, but in opposite directions and with a longer force arm. It therefore favours force, at the expense of speed and range: a wheelbarrow is another example of a second class lever. But levers of this type are not common in track and field athletics.
The foot is used as a second class lever when a person rises on the toes. When the calf muscles pull on the heels, the body rises. Thus the toes become the fulcrum and the body weight lies between it and the point where force is applied, i.e. the heels, providing one of the few instances where the body’s musculature works at a mechanical advantage. (If the applied force is vertically upward it will evoke a vertically downward reaction which must be added to body weight.)
This is exemplified in progressively loading the calf muscles by rising on the toes, with weights. In this particular exercise the pull of the calf muscles through the heel bone (with the toes as the fixed point) enables a relatively large load to be manipulated easily; for the line of action (through the common Centre of Gravity of body and barbell) is arranged so that it falls close to the fulcrum, viz. the toes.
The closer this line is to the fulcrum, the shorter is the weight arm and the smaller the muscular force required in lifting, and vice versa. The technique of weight lifting (where the aim is to lift the heaviest possible load) therefore requires that the weight arm shall be as short as possible; while the weight trainer (who is primarily concerned with the strengthening effect of the exercise) might attempt to lengthen it, although this could lead to an unstable and even dangerous position
However, when in the exercise the person leans forward sufficiently to move the common Centre of Gravity in front o/the toes, or when the toes and heel are free to move around the ankle joint the calf muscles can then operate the foot as a first class lever. This illustrates how the levers of the body can sometimes be used in more than one way; how, by a change in position, fulcra and points of resistance can be altered. (The muscular effect of this exercise is doubled, of course, when the full body weight is taken by only one leg).
Third class levers. These are by far the most common of body levers. Here the fulcrum is at one end and the resistance at the other, with the force in between. Force and resistance work in opposing directions. Third class levers lack great force of action. When, for example, a 16 lb shot is supported in the hand , the flexor muscles of the upper arm must exert a force of about 160 lb, because the force arm is approximately ten times shorter than the resistance arm. Most of the muscles of the body are inserted near the joint in this fashion, with the resistance at the far end of the bone lever. A weak, long-levered athlete is therefore at a distinct disadvantage, for he can employ his levers against only very light resistances.
Examples of third class leverage are numerous in athletics. Taking, as illustration, movement in the horizontal plane: in the delivery phases of all the throwing events, force is applied between the athlete’s fulcrum (i.e. his axis) and the resistance (the implement). Because of the short lever-arm such movements require great force of muscle action, even where the missile is comparatively light.
Force arms and resistance arms can alter with body movement; e.g. with the humerus held in a vertical position, both arms increase as the elbow bends—keeping the ratio between them (and, therefore, the degree of lifting difficulty) approximately constant. Again, when the forearm is raised from the horizontal both force arm and resistance arm decrease.
In discussing the three classes of lever it has been convenient to assume that force is always applied at right angles, but in the action of muscles on the bone levers this is the exception rather than the rule. In fact, many muscles of the body never pull at an angle exceeding 20 deg.
The more acute the angle of muscle-pull, the farther and faster will a given degree of contraction move the bone, but this, again, is balanced by loss of effective force. Resolving the muscle-pull into two component forces: one, acting at right angles to the bone lever, is beneficial, moving the lever about its fulcrum, the joint ; but the other, acting along the line of the lever towards the joint, stabilises the joint by increasing friction, but makes no contribution to lever motion. Usually, the stabilising component is much larger than the rotary component. Under these circumstances it is fortunate, indeed, that muscles exert their maximum force when stretched, pulling at acute angles.
There is, therefore, an important distinction between mere force of muscle, and strength, which takes the application of force, leverage, also
B H E’c into account. Some athletes, fortunately endowed, possess muscular insertions that are farther from their joints than in the average person; and this, if true of one of their bone levers, appears to apply to them all! Only a very small difference is necessary to give considerable mechanical advantage.
Most of the movement in track and field athletics is of an angular character because the human body, mechanically speaking, comprises a system of levers capable only of rotational motion. And what at first sight often appears to be linear movement is, on analysis, found to be the end product of a series of complex rotations of many parts of the body. It is therefore important, in analysing athletic technique, to be familiar with the principles governing rotational motion.
It is easier to hold a javelin in a horizontal position at its point of balance (i.e. at its Centre of Gravity) than farther down the shaft, and most difficult of all (if not impossible!) to keep it in this position while grasping the tail end.
And yet the javelin weighs no more, and the person holding it does not get progressively weaker! The increasing difficulty is due to the tendency for the javelin to rotate—a tendency which grows with an increase in horizontal distance between the force of its weight, acting through the Centre of Gravity, and the hand.
The following are dynamic examples of the same phenomenon; wheels, revolving doors and propellers are easier to turn when force is applied as far away as possible from their axes—the hub, hinge or shaft. A heavy door is progressively easier to close as one pushes farther and farther away from its hinges. (i) To turn an object, force must be exerted at a distance to its axis, and the greater the distance, the greater will be the rotational or spinning effect. But it is important to note that the distance from the line of action of the force to the axis—the lever-arm, as it is called —must be measured along a perpendicular, i.e. at right angles to the direction of the force. (ii) A larger force will produce a greater turning effect.
The product of the force and the lever-arm is called the moment of the force, or torque, and is used as a measure of this turning effect; and the product of torque and the time for which it acts is known as the impulse.
Horizontal bar exercises. The turning effect of the force of gravity on the swinging gymnast is greater when his body is horizontal, and diminishes progressively as he assumes a more vertical position. Obviously, a change in body position during the swing also increases or decreases the lever arm and influences swinging speed.
Moments in equilibrium. In both horizontal positions the javelin is in equilibrium, because, first, the resultant of all the forces acting on it is zero and, second, clockwise and counter-clockwise moments cancel each other out. It will help to study this in greater detail.
The hand merely exerts an upward force of 1 lb 12 oz— equal to the javelin’s weight. But in the other position this force by itself will not produce equilibrium, even though the sum of the forces is zero. We must refer to the second condition for equilibrium and take the moments into account.
In this position three forces act on the javelin: (1) the forefinger, acting as the axis or fulcrum, exerts an upward force; (2) the javelin’s weight, which has a clockwise moment about this finger; and (3) the downward force exerted by the thumb, which has a counter-clockwise moment. These two moments cancel out each other.
As the sum of all the forces must be zero, the two downward forces (1 lb 12 oz and 21 lb 3 oz) must equal the forefinger’s upward pressure of 22 lb 15£ oz. So the hand exerts two forces; an upward one of 22 lb 15£ oz and a downward one of 21 lb 3 oz. It is hardly surprising that the javelin is more difficult to hold in this position!
From the first position in which the javelin was held it can be seen that an object’s or athlete’s Centre of Gravity is actually a point where the combined moments of the many separate gravitational pulls on all the particles of mass on one side, acting clockwise, equal the combined counter-clockwise moments on the other.
Whenever, at rest, a plumb-line can be dropped from the Centre of
Gravity to fall within the base the various turning effects automatically cancel out—as with the bricks and the balanced athletes.
Balance in acceleration can be maintained by altering the position of the body, thus shifting the Centre of Gravity so as to lengthen or shorten the lever-arms of the component forces applied. For example, the stick remains balanced during linear acceleration when the product of upward force-component and its horizontal distance to the Centre of Gravity is equal to that of the forward component and its distance vertically to the Centre of Gravity.
When the stick leans in the direction of the acceleration its Centre of Gravity is lowered, reducing the lever-arm of the horizontal component of drive and the backward-rotating effect it encourages. Simultaneously, the lever-arm of the vertical component is increased, as is the tendency to rotate the stick forward.
It follows that a sprinter who leans forward too much for the effective force of his leg drive totters, unbalanced, from his marks. Or if he is too upright his legs will seem to move ahead of him and lose their driving effect; this can also happen when a distance runner, surprised by an unexpected challenge, responds without making the necessary adjustment to his body lean. [n efficient running the ratio of forward to upward component of the reaction to leg drive influences the angle of the trunk. At the start, where it is easy to push forcefully backward against the ground, the sprinter needs a pronounced forward lean, but as his speed increases so will the effective force of his drive be reduced, necessitating a progressive modification towards a more erect position. Again, a bounding type of runner, using a comparatively greater vertical drive component may need a more upright carriage to shorten the lever-arm of the force and so reduce the tendency to rotate forward.
It is quite possible for athletes who enjoy exceptional hip mobility and who possess certain postural characteristics to make the necessary adjustments to the position of the Centre of Gravity without employing the more orthodox forward trunk lean—hence their comparatively upright running positions even during acceleration. The great Jesse Owens and E. McDonald Bailey spring readily to mind as good examples of this.
Problems of balance in running and jumping during those phases in which athletes are in contact with the ground are best considered, as in our previous examples, by taking moments about the Centre of Gravity, not the point of support. For, in dealing with the body as a whole, movement on the ground in these events is the combination of a series of linear accelerations whereby clockwise and counter- clockwise turning moments about the point of support cannot be equal.
But if an athlete is balanced in motion, in the sense that there is no turning of the whole body mass, moments about his Centre of Gravity may be considered equal. As a general principle it is usually more convenient to consider an axis passing through the Centre of Gravity in all events where, subsequently, the athlete leaves the ground.
However, in analysing balance in pole vaulting and throwing positions (where the athlete has contact with the ground) it is sometimes convenient to take moments about the base or support, thinking in terms of turning couples. An example follows.
A hammer thrower’s equilibrium in a sagittal plane is the product of two pairs of parallel, equal, forces acting in opposite directions. The hammer’s centrifugal pull and the equal force of the ground thrusting at an angle against the thrower’s feet form one couple tending to rotate him counter-clockwise; the distance at right angles to the line of these parallel forces is the arm of the couple.
In a clockwise direction, however, the force of the thrower’s weight, acting downward through his Centre of Gravity, plus the equal but upward force of the ground under his feet, form a second couple, the arm of which is the horizontal distance between the lines of these two vertically directed forces.
The turning moment of a couple is found by multiplying one of its forces (it should be noted that they are always equal in size) by its arm, and the thrower is balanced when the moments of the two couples are equal.
But as, in spinning, the athlete develops greater velocity in the hammer-head, he automatically increases the centrifugal force and the ground’s horizontal thrust against his feet, both of which tend to rotate him counter-clockwise in a sagittal plane. So he maintains balance by bending his legs and lowering his seat, thereby reducing the arm of this counter-clockwise couple , and increasing the arm of the clockwise one.
Moments in rotation and spin. Just as, with linear acceleration, moments about the support cannot be equal, so it is with angular acceleration, whether the axis is considered to be a point of contact with the ground or the Centre of Gravity.
In analysing a diver’s movements we take moments about his Centre of Gravity. When the reaction to his leg thrust (along a straight line drawn between foot and hip) passes directly through his Centre of Gravity, pure translatory motion occurs, i.e. he leaves the board without rotation. But as, in successive dives he exerts a force at increasing distances to his Centre of Gravity, the effect is as though more is used progressively in imparting a rotation, while less is available to project his body.
In fact, a given reaction (i.e. vertical impulse) to leg-thrust will impart the same vertical speed, and therefore the same height, to a diver’s body, whether directed through his Centre of Gravity or not. But here the difficulty is to exert the same impulse (i.e. force x time) as previously against a rotating body.
To achieve the same height the diver would have to develop a greater thrust from the board; greater still for the rotation. . In both cases the leg-thrust would need to be faster, reducing the time of operation and, consequently, requiring greater thrust.
Eccentric thrusts, are wasteful of energy. Assuming, for the moment, that the diver projects his
Centre of Gravity to the same height in all three dives; the point of application of the thrust moves through the same distance and acquires the same velocity as his Centre of Gravity; but when the same take-off impulse is directed eccentrically this point moves through a greater distance than his Centre of Gravity.
Thus, an impulse exerted through the Centre of Gravity changes a body’s linear kinetic energy while an equal impulse exerted ‘off centre’ changes the body’s linear kinetic energy by the same amount, but also imparts rotational kinetic energy. Hence, unless rotation is required, eccentric thrust is wasteful of energy.
The diver’s rotation off the board is brought about, in fact, by a turning couple; the reaction to his leg thrust, i.e. the force of the springboard, acts vertically upward and the force of his weight, acting through his Centre of Gravity, pulls vertically downward. He obtains this eccentric or sideways thrust about the Centre of Gravity by bringing his head and arms (i.e. just under a fifth of his total body mass) forward beforehand and, in bad diving, by bending forward markedly from his hips.
We have seen that the forces of a couple must be equal and yet, in diving from the springboard,the force of the upward vertical thrust actually exceeds the downward pull on the man’s body. The forces turning him are indeed equal, but it is the excess of force from the board which projects him into the air. If his Centre of Gravity moved downward, i.e. he fell off the board, then the reverse would apply: the force of his body weight would then be greater than that which passed through his feet.
As Orner has written, ‘If a competitor performs a well-executed dive, it will be good because the direction, height and the force of rotation imparted to his body through the diving-board are a close approximation to his exact needs for the correct number of somersaults in the particular position intended and his control in the air will be quite marginal. ‘The picture of a diver jumping from the board steeply without rotation then circling deliberately for a spin, finally halting his rotation completely to dart vertically into the water is pure illusion—and the diver’s art! The illusion is most effectively shattered when a diver errs on take-off by taking too much turning force, and is unable to maintain the impression of ‘stopped’ rotation near the water. ‘Unfortunately, many divers and coaches believe in the possibility of controlling dives fully in the air and are taken in by the illusion. The inevitable result is that they concern themselves mainly with the dive; that is the effects, rather than with the take-off in which errors showing in the dive originate in a proportion of at least 90 per cent.’