Forces and physics in athletics

Force

In athletics all motion is derived from force—force from the muscle contractions, from gravity, from the friction and upthrust of the ground and the resistance of the air. In this sport we are concerned mostly with the use of force for changing the state of motion of athletes and their implements—slowing them down, stopping or speeding them up.

However, there can be force without motion. For example, a javelin or pole can be gripped tightly without its moving; a tennis ball can be flattened a little by squeezing. Force can, therefore, bring about, or tend to bring about, a change of shape in a body, causing stresses within, which are the result of its attempt to regain its original shape; and forces do not affect motion when their resultant is zero.

Force can be felt but not seen. But its effects can be seen and measured, and it can be described and determined in terms of its magnitude, direction and point of application. Like velocity and momentum, therefore, it is a vector quantity, and can be analysed by the use of a parallelogram.

Magnitude. Force is usually measured inpound-wt, apound-wtbeing approximately the pull of gravity on a standard pound of mass at sea level, latitude 45°. Internally, the athlete obtains his force through the contraction of muscle fibres. Each fibre, though sometimes several inches in length, is not more than a fraction of an inch in diameter. At rest, these fibres are soft, flabby and easily stretched, but on receiving nerve impulses they shorten, changing in effect from a piece of perished rubber to a contracted steel spring.

The magnitude of muscle force is in direct proportion to the size and number of fibres contracting, is inversely proportional to the speed of contraction (i.e. the faster the contraction, the smaller the force exerted) and is usually greatest when the muscle is fully extended.

In muscles with straight parallel fibres (e.g. the sartorius) force potential can be estimated by measuring the proportional fibre cross section (proportional, not actual, because muscle also contains blood vessels, connective tissues, inter-spaces, etc.) in terms of pounds per square inch.

However, in muscles with a ‘belly’ (e.g. the gastrocnemius) maximum force, for a given length and weight, can be much greater—but at the expense of less shortening; because the fibres run obliquely and, therefore, for only a fraction of the muscle’s full anatomical length. In this case the cross section is usually impossible to define.

In a letter to the author, the distinguished physiologist, Professor A. V. Hill (University of London) suggests an average muscle force, in man, of 126 pounds per square inch (physiologists are not agreed on a definite figure).

Through training, an athlete cannot increase the number of fibres within a muscle but he can increase its force potential by increasing their diameter. Here, the two-way effect of force is again in evidence, since a muscle pulls as powerfully upon its origin as on its insertion, but in an opposite direction

In athletics we are seldom, if ever, concerned with the measurement of force of a single muscle, but rather think in terms of a whole movement, momentarily involving the total force of several muscle groups working against the resistance of the ground , a missile (e.g. in discus throwing) or, sometimes, against some other part of the body.

Certainly, in athletic movement, no muscle—and not even a single muscle group—works alone, for all the muscles of the body are more or less in constant demand, supporting, guiding and generally contributing to force and the control of movement.

Direction. When athletic efficiency is at its best force has been properly directed both internally and externally. The direction of the force exerted by a single muscle depends upon the relation of the moving bone’s long axis to the muscle-insertion. The angle between the muscle’s line of pull and the long axis of this bone (the axis being a straight line from the bone’s mid-point at either end) is known

C as the angle of pull, an angle which, with body movement, is constantly changing.

From a purely mechanical point of view, a muscle’s most effective pull will be at right angles to the moving bone; but as muscle fibres at such an angle are seldom fully stretched, the greatest effective force is usually obtained when the angle of pull is more acute. It would seem, therefore, that physiological laws sometimes work in opposition to mechanical ones, which points to the futility of trying to analyse athletic techniques on a mechanical basis, muscle by muscle.

As with the assessing of the magnitude of force, it is therefore more convenient to consider an athlete’s total, resultant body force exerted against the resistance of the ground or apparatus. In running, for example, this should be done in such a way as to produce mainly horizontal movement; at take-off in high-jumping force must be directed mainly in a downward direction, so that the athlete shall be thrown almost vertically; and in throwing events the direction of total body force will determine the angle at which the missiles are thrown.

Point of application. The effect of force varies with the point of its application. This characteristic is discussed more fully later. Meanwhile, it is sufficient to say that, internally, force is applied to the bone levers at the points where muscles originate or are inserted. As to the total force of propulsion in running and jumping, it is applied where the feet contact the ground and, in shot putting, where the missile touches the hand. The point of application and the direction of force may be combined in the one concept: the line of action.

Accelerated motion

As already stated, in track and field athletics we are mostly concerned with the use of force to change the state of motion of athletes and their implements. In this connection, two simple experiments should help to clarify its effects.

First, two 8-lb shots are placed on a smooth, horizontal surface, and between them is set a compressed spring which cannot expand because it is tied. When the thread is broken the spring drives both shots apart with equal force and they ‘collide simultaneously with two wooden blocks set, beforehand, at equal distances from the shots’ original positions. From this it can be seen that when equal forces are applied against equal masses they produce the same change in velocity, and experiments prove that accelerations given to a body are proportional to the magnitude of the force.

Then, one of the shots is replaced by a 16-lb missile and the experiment is repeated. Now, the larger shot is given only half the acceleration of the smaller one and, in a given time, it travels only half the distance. From this we can conclude that when equal forces impart accelerations to unequal masses, the product ofrnass and acceleration is the same; which gives us our measurement of force = mass X acceleration.

Therefore, under otherwise identical conditions, the acceleration of athletes and their apparatus depends upon their masses which, in turn, are measures of inertia, resistance to motion.

To provide equal acceleration in unequal masses, the forces applied must be proportional to the masses; for example, if there are two runners, one weighing 250 lb and the other 125 lb, the heavier athlete must exert twice the force of the lighter athlete to produce the same acceleration.

Frictional forces apart, any force will accelerate any mass. For example, but for the resistance of air and water a docker leaning against the side of an Atlantic liner, unmoored, could give it motion with which to cross to America—but he would have to lean in the right direction and the crossing would take a long time! In practice, of course, liners can be moved only when the force acting on them in a given direction is greater than the frictional and other forces opposing; and so it is with athletes and their apparatus.

Just as the Force of Gravity is responsible for a constant free-fall acceleration which, in 1, 2, 3 units of time produces vertical dis tances in the proportions of 1, 4, 9 so does a similar relationship between time and distance apply to an object or athlete moving in any direction as a result of the application of any constant force in that direction.

Impulse

The change in speed of an athlete, discus, shot, javelin or hammer does not merely depend upon the force applied, but also upon the time for which it operates, its impulse. In starting from blocks, for example, an athlete should adjust his position not only to increase his driving force but also to lengthen the time during which it is exerted, thus increasing his starting velocity. And in the throwing events, also, the best techniques are those in which maximum muscular force is exerted for the longest possible time.

The same change in speed (and, therefore, the same impulse) can be produced by a small force acting for a long time, or a very large force acting for a short time. However, in athletics, an increase in force often requires a more rapid action, resulting in a decrease in time of operation—unless the distance over which the force operates is increased.

The impulse of a force is equal to the momentum (mass X velocity) of the mass moved from rest by the force. Of academic interest only, the impulse given to a high-jumper at take-off is also given to the earth, but in an opposite direction. Their momenta are therefore equal. Likewise, an athlete’s momentum from the blocks in a sprint start is equal but opposite to the earth’s, for the impulse is the same. In fact, the concept of momentum is often used as equivalent to that of impulse.

In the analysis of athletic movement it is often convenient to distinguish between a controlled impulse due to direct muscular effort and joint leverage, as with the leg-drive in sprint-starting, and a transmitted impulse produced, for example, by the bracing of a comparatively unyielding leg against the ground during the initial stages of a high-jump take-off, where its magnitude and direction cannot be determined through muscular action of the leg itself. Almost invariably, in track and field athletic techniques transmitted impulses (of, usually, two or more times body weight) precede the smaller controlled impulses. Because it involves force, impulse is a vector quantity.

Effective force

In track and field athletics there are many examples of the impossibility of exerting full force against a fast-moving object, for the feet (in running) and the hand (in throwing) cannot be moved fast enough. In such cases, the speed of movement of the source of resistance reduces not only the ability to apply muscular effort, but also the time for which that effort can be applied. These two factors may place quite a low limit to the size of the effective force, i.e. the force ‘received’ by the ground or implement. For this reason, in most athletic events, acceleration has its greatest value at the beginning, when the athlete’s body and/or the missile he holds is moving slowly.

Sprinting is a good example. At the start, where the opposing force of air resistance is small because the athlete’s movement over the ground is comparatively slow, most of the considerable horizontal force of his leg drive is effective in producing a marked change in speed. But as his speed increases the opposing forces also increase, and therefore a progressively smaller fraction of his limited leg drive is available to add to his speed.

It is difficult to exert a forceful backward thrust against the ground which, to the athlete, appears to be moving in an opposite direction. Top speed is reached when the effective force of the leg drive equals all the opposing forces. Up to this point in the race his speed has increased, but by a progressively diminishing degree. For, with each stride taken, foot contact is of shorter and shorter duration; impulse is successively reduced and even without an actual reduction in horizontal thrust (and reduction is certain) each successive increase in speed is smaller.

A second example can be taken from shot putting where, as soon as the movement across the circle begins, pressure between the shot and the athlete’s fingers increases; for force is being applied to accelerate it, and this pressure will always be equal to the force exerted. A further increase in applied force would result in another increase in pressure, but in practice shot putters find the pressure reduced in the final arm-thrust; they find it easier to move, whereas if it were possible to impart a constant acceleration it would be as difficult to put at the end as at the beginning. This is because of the difficulty of ‘keeping up with’ the shot.

In fact, to be able to accelerate his body or a throwing implement an athlete must be capable of moving at a greater speed than the ground or the missile moving away from him. And the greater his speed, in comparison, the greater his effective force will be. Clearly, then, the ability of an athlete to apply force depends not only upon strength but also upon speed.

Summation of forces

From a purely mechanical point of view it is immaterial whether a succession of forces is applied one by one or simultaneously; the resultant is the same. However, where human beings are concerned the strongest parts of the body are the heaviest, and have a correspondingly greater inertia: consequently they are less speedy in their movements. With the athlete it is a question of using the different muscles when they are capable of sufficient speed to apply full force.

This calls for a definite sequence and timing of body forces. The strong but slower muscles surrounding the body’s Centre of Gravity should begin, followed by the trunk and thighs, and end up with the weaker, lighter but faster extremities. When the forces are properly harnessed, therefore, movement flows outward simultaneously from the centre of the body.

Of course, the sequence in which an athlete uses the different parts of his body is partly dependent upon the nature of the construction of the human body; and the timing of the various movements can be influenced by the strength of these parts.

In jumping and throwing activities, where an athlete or a missile is raised against the force of gravity, it is particularly important to apply the different body forces as quickly as possible, otherwise speed in a vertical direction will be lost. Ideally, in this summation of forces, they should be applied so that the various joints, having attained top speed, continue at that speed in support of the movements which follow. It follows that, ideally, all the forces should end together as well.

When the fulcra are permitted to lose speed the final, resultant velocity is reduced. Much more common in athletics, when the body forces are hurried and so are not applied long enough, or are omitted altogether, total velocity again suffers.

Opposing forces, parallelogram and resolution of forces

As already stated the qualities determining a force are its magnitude, direction and point of application. Force is a vector quantity, therefore, which can be represented diagrammatically by straight lines, as can motion. Indeed, as, in athletics, all motion is derived through the application of force.

A line can be drawn, called a force vector, with one end representing the point of application, its direction and arrowhead coinciding with the direction of the force, and its length containing as many units of length as the force has units of force.

Opposing forces. In tug o’ war the reactions to the forces exerted on the ground are represented by vector lines, both horizontal, which can be replaced by a single line—a resultant—representing the 50 lb acting towards the right. When two forces are acting in opposite directions, therefore, the resultant has the direction of the larger force.

Parallelogram of forces. But when several forces acting at a point are not directly opposed and parallel, the problem is more difficult. Forces, like velocities, do not disturb each other; each is separate, and for purposes of analysing movement in athletics it is often convenient to treat them as such.

To take, for example, the directing of a runner’s propulsive, muscular force against gravity and air resistance, the effective point of action of these three forces is the athlete’s Centre of Gravity —a point where, it can be assumed, all the mass of his body is concentrated.

At a constant speed these three forces balance each other.

Both gravity (CA) working vertically downwards, and air resistance (CB) acting horizontally against the runner are represented by force vectors. Using these as two sides of a parallelogram, the missing sides are constructed geometrically and a diagonal is drawn from the point of origin—i.e. the Centre of Gravity—to the opposite corner (CD). This line represents in both length and direction the magnitude and direction of the combined opposing forces. The propulsive muscular force required to maintain a constant speed is therefore represented by the line CE. This, an equilibrant needed to balance the other forces, is not necessarily to be identified with the angle of the trunk—the runner’s ‘body-lean’—but none the less the need for greater emphasis on horizontal force when air resistance is increased.

Where more than two forces act upon a point the resultant of two forces is first obtained in the manner already described and then this is combined vector by vector, until a resultant—a single force that can replace them all—is found.

Resolution of forces. E.g a long-jumper is shown just about to leave the ground. In this example, the line of action of the force driving him into the air is from his jumping foot (the point of application) through his Centre of Gravity. The two effects of this force are to project him vertically and accelerate him forward. We know that these component forces may be regarded separately, but in what proportions are they represented? The problem is the reverse of that discussed already.

Again, the geometrical parallelogram method is used; but either the directions or magnitudes of both components, or the direction and magnitude of one component, must be known in advance, otherwise the problem is capable of many different solutions. In this case we know the directions of the components. Two lines are then produced from the point of application (i.e. the foot), one vertical and the other horizontal, and a parallelogram is then made whose diagonal is the vector of the takeoff force. The length of each of these lines in comparison with that of the diagonal represents the magnitude of the components in relation to the take-off drive.

If the take-off force is known, of course, then the line of action can be drawn in units of length corresponding to the units of force, and from the length of the component vectors the magnitude of the horizontal and vertical forces can be calculated.

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