Force of gravity in sports

All athletic performance is influenced in some way by the force of gravity, a centripetal force ‘by which bodies tend to the centre of the earth’ (Newton.)

This might seem to violate Newton’s First Law; for why should all objects accelerate vertically downwards at the same rate regardless of their masses if, when projected horizontally by an equal force, their accelerations are strictly determined by their masses? The answer lies in the perfect balance of gravitation and inertia; the earth always attracts an object with a force proportional to the mass of that object.

However, although it is true that at a given point on the earth all bodies fall with the same acceleration, the pull of gravity diminishes as the distance increases away from the earth’s centre and is inversely proportional to the square of the distance. There is, therefore, a slight variation in gravitational acceleration between the poles and the equator (where the earth bulges) amounting to 0-54 per cent—just large enough to be detected. (Actually 0-3 per cent of the difference arises because the earth is spinning and, in consequence, a body at the equator tends to move off into space; there is a centrifugal effect.)

To date, most world athletic records have been made in the temperate zones, where the acceleration is 0-36 per cent greater than at the equator. Thus, a 26-ft long jump in Germany would be approximately 14; in. farther in, say, Kenya, and a 255-ft javelin throw in New Zealand is worth another 6-in. in Ecuador.f

The varying gravitational attractions of the sun and moon, which influence the tides, also affect the flight of objects—if only to an infinitesimal extent.

Weight and density

In discussing Newton’s Law of Inertia a distinction was made between mass and weight. The mass of an object is a measure of its inertia, its resistance to change in motion. This is a property which does not change from place to place; an athlete with 180 lb of mass would require just as great a force to obtain a given acceleration in Timbuctoo or Tooting, on the moon as here on earth.

However, because of the slight variation in pull, at the equator an athlete weighs 0-5 per cent less there than in the neighbourhood of the poles. And in the same way, weight, with the pull of gravity, decreases gradually with increasing height above sea-level.

On the moon our athlete would weigh only 30 lb, for the gravitational pull there is about a sixth of the earth’s. (Although the mass of the moon is only an eightieth of the earth’s, its diameter is considerably less and its surface, in consequence, is nearer its centre. Because of the inverse square law, the moon’s gravity, per unit mass, is therefore relatively greater.) When we speak of ‘weight’, therefore, we refer to the force of attraction between an object and the earth—an attraction proportional to the object’s mass. If we hold a 16-lb shot in our hand we must exert a certain muscular force to counteract the earth’s attraction; this we call the shot’s weight, but it can vary, if only fractionally.

Not all 16-lb shots are of the same size. Brass shots (which have a lead core) are smaller for their weight than iron ones; a 16-lb shot made from tungsten would be about the size of a tennis ball. Similarly, athletes of different sizes sometimes weigh the same, and vice versa. Obviously, therefore, objects vary in the ratio of their weight (and mass) to volume; i.e. they differ in their density. It is as though, in a denser body, matter is more closely packed. And, with the human body, the density of different parts will vary, e.g. bone is denser than blood.

Weightlessness

When a man stands erect on the ground, the force of gravity acting on his body (i.e. his weight) is cancelled out by an equal upward force exerted by the ground, i.e. ‘ground reaction’; otherwise, obviously, he would accelerate towards the earth’s centre.. This condition also applies to the various parts of his body which, in the position shown have each to support the body weight above them. Thus, each part experiences a degree of compression which increases from the head downwards. This compression can be altered by a change in posture; e.g. increasing if the man stands on one leg (thereby doubling the vertically upward thrust through that leg) or if he accelerates some part of his body vertically.. However, when he breaks contact with the ground, gaining downward or losing upward speed at a rate of 32 ft per second every second these states of compression, the sensations associated with them and their effect on the neuromuscular interactions controlling posture and directing movement no longer exist, (e.g. in long jumping, a clumsy initial attempt at a hitch-kick can be caused by ‘not knowing where the legs are’—because of a lack of pressure on the receptors of the feet and a resulting poor kinesthetic feed-back). His body, lacking ground reaction, then assumes a condition of transient ‘weightlessness’’’’ and can move its various parts, or objects carried by it, in ways which would otherwise require greater effort—resistance to motion originated in the air being due only to inertia.. Thus, the condition of ‘weightlessness’’ tends to increase mobility at the expense of control.

It is interesting to note that when, after breaking ground contact, a man relaxes completely, he tends naturally to assume a position in which a state of angular equilibrium is reached between the different parts of his body, depending upon the mass and tonus of his various muscles. Note also that a floating swimmer (who must displace a weight of water equal to that of his whole body) does not experience ‘weightlessness’, because his limbs are supported externally—water reaction being substituted for ground reaction.

Centre of gravity

We know that the earth attracts every tiny particle of an object with a gravitational force which is proportional to the mass of each particle. If all these separate attractions are thought of as being added together to make one resultant force—i.e. the weight of the object—the point where this force acts will be the Centre of Gravity.

In analysing track and field techniques such a point is often used to represent mass as a whole: the body mass of the athlete, a piece of apparatus, or the combined mass of athlete and implement, as in the pole vault or a throwing event. It is here that we can consider all the mass of the object to be concentrated; in fact, a centre of mass or weight from which the body could be suspended in perfect balance in any position.

However, it is important to realise that this point need not necessarily divide or be surrounded by equal masses. (Only when a body is of uniform density will its centre of gravity coincide with its centre of volume.) For example, where the weight of the athlete is sixteen times greater than that of the hammer-head (ignoring, for the moment, the matter contained in the wire and the handle) the common Centre of Gravity of man and missile lies sixteen units of distance from the hammer’s own Centre of Gravity, but only one from the athlete’s. It is therefore the product of each mass and its distance—i.e. the moments, or turning effects —which must be equal on either side of, or surrounding, the Centre of Gravity.

Each part has its own Centre of Gravity, lying fairly exactly along the longitudinal axis, always nearer the proximal joint (i.e. the joint nearer the trunk). The tables show the relative average masses (average, since these vary in individuals) of different parts of the body, taking the total mass of the body as 100 per cent.

Here, in an erect position with arms to sides, a man’s Centre of Gravity (S) averages 55.27 per cent of his height, approximately H-inches below the navel, roughly midway between the belly and the back.

Children will average a relatively higher Centre of Gravity in such a position, owing to carrying relatively more weight in their upper body. But, again on average, a woman’s Centre of Gravity in this position will be slightly lower, relative to her height, because of her smaller thorax, lighter arms and narrower shoulders, but heavier pelvis and thighs and shorter legs. But the Centre of Gravity lies higher in the trunk of shorter-legged women than in longer-legged males with correspondingly short trunks—an important point when considering the performances of women in high-jumping, hurdling, the running events and in some gymnastic exercises where the body is supported completely by the arms.

The location of the Centre of Gravity for any particular person, in any given position, changes with inspiration and expiration, upon eating and drinking and with an increase of fat or age.

For our later observations it will be important to know only the approximate position of this point, and to appreciate that it moves always in sympathy with the movements of the different parts of the body. It is, in fact, a most unstable point in the athlete, and yet, despite its almost continuous motion, it seldom leaves the pelvic cavity. in contact with the ground. By moving when in contact with the ground an athlete changes the position of his Centre of Gravity both in relation to his mass and to the ground itself. And this applies whether he is in direct contact or indirect contact.

To give examples: if, from the standing position he raises his right arm horizontally to the side his Centre of Gravity shifts to his right and is raised about 11 in.; and when the other arm is stretched out similarly the Centre of Gravity rises by the same amount again but returns to the body’s centre-line.

Then, when both arms are raised directly overhead it moves an additional 2 in. higher in the trunk. In a crouch starting position an athlete’s Centre of Gravity is lower and brought well forward of the feet, and a pole vaulter who drops his legs while clearing the cross-bar also lowers his Centre of Gravity (if no other movement is involved) while he holds the pole.

In exceptional forms of movement, however, this point can lie outside the body.

As an extreme example of this we can take the exploding of a high-explosive shell in the air. Air resistance apart, the shell’s Centre of Gravity describes a smooth curve both before and after the mid-air explosion, until fragments of it strike other objects. The force of its explosion, working in all directions, leaves the path of its Centre of Gravity unchanged.

This principle of the maintenance of the path of the Centre of Gravity is exemplified in the hitch-kick (i.e. running-in-the-air) style in long-jumping where the athlete cannot alter the flight path of his Centre of Gravity although, for other reasons, his movements have their value.

If the long-jumper were permitted to carry weights, he could gain additional height and speed by throwing them down and back in the air; for, through the two-way action of force, the impulse so derived would also influence his body, but in an opposite direction. (It is interesting to note that in ancient Greek times when weights (halteres) were used in jumping for distance, they were not released in the air but, with the arms, were swung back prior to the landing. Thus the weights were used only to improve the take-off impulse and advance the jumper’s heels in relation to the combined Centre of Gravity of athlete and halteres.)

The modern jumper’s movements in the air, therefore, alter his body position only in relation to his Centre of Gravity; they cannot jet-propel him. When in the air, a part of his body moves one way, some other part moves in an opposite direction, simultaneously, so that the product of masses and distances about the Centre of Gravity is unchanged. If, for example, the head and feet move down then the hips are made to move up.

But it should be noted that the reaction to a movement in the air need not comprise the units of mass and distance which caused it; e.g. when, using a Western Roll , a high-jumper reaches towards the pit with his inside arm the simultaneous reaction can be that of a fractional raising of the rest of the body mass or, to take the other extreme, a pronounced lifting of an even lighter part of the athlete. When the arm action is accompanied by a raising of the other arm, the trunk and hips gain no additional height in relation to the Centre of Gravity; one movement cancels out the beneficial effect of the other. Under such circumstances, therefore, it is important which part of the athlete absorbs the reaction.

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