All motion in track and field athletics, whether of an athlete’s whole body, a part of it, or the movement of some object of athletic apparatus (like a pole or shot) behaves in accordance with certain well-established principles, and is subject to the same mechanical laws as everything else on earth, animate and inanimate. Motion is of two kinds, linear and angular.
Linear (often referred to as translator) motion is characterised by the progression of a body in a straight line, with all its parts moving the same distance, in the same direction and at the same speed. One seldom sees pure linear motion in track and field events, but it is a factor to be taken into account, none the less. However, in so far as a sprinter’s movements in a 100 yards race can be thought of as being in a straight line, from start to finish (i.e. ignoring the rotational movements of arms and legs and undulations of the trunk), linear movement is apparent, and there are many other such examples in athletics.
Angular motion is far more common in all human and animal locomotion because, mechanically speaking, such motion is dependent upon a system of levers of which they are constructed.
Meanwhile, the chief difference between angular and linear motion is that whereas in angular movement one part of the object—the axis— remains fixed in relation to the others , in linear motion every particle of the object travels the same distance simultaneously, moving from one location to another.
A body can perform linear and angular movements simultaneously: when, during its rotations or angular displacements, its axis moves along a certain path. The motion of a rolling wheel is an example of this. The wheel’s hub moves in linear fashion because of the rotations of the rim: an example of the many objects, including animals and human beings, which move as a whole in a straight path as a result of rotational movement of some part. A sprinter obtains linear movement through the rotary action of his feet; in throwing or putting, the rotational movements of an athlete’s body can be coordinated to impart linear motion to the missile.
In all athletic activities the best results call for a blending of linear and rotational motion; the sprinter’s rotational foot movements must be co-ordinated with the linear vertical motion of his whole body; similarly, the hammer-thrower’s forward movement across the circle must be co-ordinated with his turns.
Uniform and non-uniform motion
The motion of a body is said to be uniform when equal distances are covered in equal times. It is non-uniform when unequal distances are covered in equal times. Thus, a 4 min 16 sec miler running at a perfectly even pace would run with uniform motion (i.e. 16 sec per 110 yards); but a 100 yards sprinter with intermediate times of 5-3 sec (50 yds), 6-2 sec (60 yds), 7-0 sec (70 yds), 8-0 sec (80 yds), and 10-2 sec (100 yds) would be travelling with non-uniform motion.
The sprinter’s motion from 60 to 70 yards would be described as accelerated as he covers the 10 yards distance 0-1 sec faster than the 10 yards immediately preceding (i.e. 50 to 60) and as he loses speed from the 70 yards mark his motion from then on is retarded. These are both loose analogies, since the process of taking even a single running stride can involve acceleration and retardation.
In mechanics a distinction is made between velocity and speed. Velocity includes the direction of travel as well as the rate. A runner may move at a speed of 24 m.p.h., but to state his velocity we must find in which direction he is travelling; he may have a velocity of 24 m.p.h. due north.
The rate of motion or the speed of an object is given in units of length and time. Thus a speed of 24 m.p.h. may also be stated as 35-2 ft per second.
Possessing magnitude and direction, velocity is a vector quality and can therefore be represented diagrammatically by straight lines.
Very rarely in athletics are velocities constant; more often they change in their amount or direction, or both at once. As we have seen, when the velocity of an object (e.g. an athlete or a missile) changes in amount it is said to be retarded (if it continually decreases) or accelerated (if the velocity continually increases).
But the term acceleration is used in mechanics in either the gaining or losing of speed. Whenever the acceleration of an object is opposite in direction to its velocity the term negative acceleration is used, and when acceleration and velocity are in the same direction the acceleration is called positive.
By ‘acceleration’, therefore, is meant the rate of change of velocity.
The following is an example of positive acceleration: let us suppose that an athlete running at a rate of 22 ft per second (i.e. 15 m.p.h.) increases his speed so that it reaches 33 ft per second (i.e. 22 ½ m.p.h.) in 5 sec. His change in speed is 33 minus 22, or 11 ft per second. But this is not his acceleration; it is only the change in velocity.
The change in velocity, 11 ft per second, occurred in 5 sec, so the change in velocity per second is 11 ft per second divided by 5, or 2 ½ ft per second every second. Each second the velocity increased 2 1/5 ft per second. The acceleration—the ‘pick-up’, to use sprinting parlance—was therefore 2s ft per second per second.
Thus every statement of acceleration must contain two units of time: one for velocity and one for the time during which that change in velocity occurred.
What has been said concerns uniform acceleration, but in athletics acceleration is often of a non-uniform character. However, we can only calculate the true value of an acceleration at any instant by taking as a basis the increase of velocity during a period of time, making the latter as small as possible.
Motion of freely falling bodies
As performance in every athletic activity is influenced by the force of gravity, the laws of freely falling bodies apply to all track and field events. Strictly speaking, these laws are applicable only to motion in air-free space, but in athletics for all practical purposes air resistance in falling can be ignored.
The actions of the efficient runner reduce to a minimum the dropping of body weight on each stride and, therefore, the degree of upward movement which would otherwise be wasted on raising it again. The good hurdler takes his obstacles with little to spare in order to return to ground quickly. The high-jumper trains to improve both the power and direction of his take-off drive to gain more height, ‘defying’ gravity. Again, the time during which shots, javelins, hammers and discoi are in flight is largely governed by these same laws.
For a hundred and more centuries, between the earliest civilised man and the time of Galileo, it was believed that heavier things fall faster in proportion to their weight. However, two bodies let fall simultaneously side by side (starting from rest) fall equally quickly, regardless of weight, size or their material. If they are cemented together to form one body this in no way alters the distance fallen in a given period; in fact, a heavy athlete falls no quicker than a light one. And this is so whether or not the fall is directly downward.
The vertical velocity of a freely falling object increases by 32 ft per second every second , and in rising it loses vertical velocity at the same rate. The distance it falls is proportional to the square of the time—i.e. in one unit of time, 1; in two units, 4; in three units, 9 and so on—and can be calculated from the formula d = ½ gt where d is the distance of rise or fall (vertically) measured in feet, g = 32 and / = the time in seconds. In analysing athletic movement it is sometimes useful to know, for example, that an object drops 1 ft in ¼ sec.; 4 ft in I sec; 9 ft in sec; and 16 ft in 1 sec.
An object falling for three seconds will, therefore, drop 144 ft (i.e. 16 ft x 9), will have a final speed of 32 x 3 or 96 ft per sec, and its average speed will be half of this, i.e. 48 ft per sec. The distance it falls in this time will be the average speed multiplied by the time of falling, i.e. 48 x 3 or 144 ft. Released vertically with an initial upward speed of 96 ft per sec from a point 144 ft below its original level, the object will take exactly the same time to reach this level, when its speed will again be zero.
Parallelogram and resolution of velocities
In the course of taking a running stride, high-jumping or releasing a shot (to take only three of countless examples) an athlete imparts to his body and/or the missile two motions simultaneously— one upward and the other forward. These are called component velocities because combined together, they produce a resultant velocity, i.e. the actual velocity of the body or missile. These two simultaneous component motions do not affect each other and can be considered separately, and for the purpose of athletic analysis it is often useful to treat them as such.
If the magnitude of each of these components is known, then both the direction and magnitude of the resultant velocity can be illustrated diagrammatically by the parallelogram method. A spot is first marked on paper representing the point of release (in throwing) or the Centre of Gravity (in running, jumping and vaulting). From this two lines called vectors (from the Latin verb meaning to carry or convey) are drawn at right angles to each other; these indicate the two components, the length of each line from its point of origin to the arrowhead representing the magnitude of each velocity.
Using these as two sides of a parallelogram, the missing sides are constructed by simple geometric methods. A diagonal is finally drawn from the point of origin to the opposite corner, representing in its length and direction both the magnitude and direction of the resultant velocity.
Conversely, when the magnitude and direction of the resultant motion are known it is simple enough to resolve this into its vertical and horizontal components.
Component motions do not always operate at right angles to each other. In determining a resultant the parallelogram method can also be applied when angles are obtuse or acute. Here it is important to note that in the resolving of a resultant either the directions or the 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, since there are many parallelograms with the same diagonal.
Quantities like velocity which have both magnitude and direction (e.g. force, acceleration and momentum), are also called ‘vector quantities’ and can be combined by the parallelogram method. Other qualities (e.g. speed and kinetic energy) which have only size, without specific direction, are called scalars.
Path of projectiles
As soon as throwing implements are released or athletes break contact with the ground they begin to fall, in the sense that gravity then changes their direction of motion. Hence, greater distance in throwing or jumping can be obtained when the initial velocity contains an upward as well as a forward component. For in this case the missile or athlete is in the air longer, permitting greater horizontal travel before return to ground.
In air-free space a combination of inclined-upward initial velocity and gravity causes the object’s Centre of Gravity to describe a perfectly regular curve called a parabola. When the em- phasis is on horizontal motion, as in long-jumping , the curve is long and low, but in the high jump, where vertical movement is stressed, it is short and steep.
It is important to note that in track and field athletics, where neither jet propulsion (where propulsive force is derived from the reaction of escaping gases) nor a mid-air change in weight take place, the movements of an athlete off the ground cannot disturb the smooth curve of his Centre of Gravity.
Again in air-free space the horizontal component remains constant throughout flight; the long-jumper’s forward speed on landing will be the same as at take-off. However, the vertical component, being subject to the laws of freely falling bodies, will be zero at the high point of the jump or throw and then the athlete or missile will fall with gravitational acceleration.
In fact, a jumper or missile may be regarded as having two independent motions ; an initial, uniform inclined-upward motion continuing along the line AB, and a free-fall measured at successive points (here, at ¼ second intervals) along this line.
Note that our high jumper moves horizontally at a steady speed, while a decreasing upward motion to the high point of his jump is matched by an increasing downward motion from then on.
Through the use of vectors , the proportion of a jumper’s horizontal and vertical motion can be illustrated at any point along the flight path of his Centre of Gravity. Thus, at point
A, the tangent AB (I.e the straight line at right angles to the radius of the flight path at this point) represents the athlete’s velocity at that instant; while the vectors AC and AD denote his horizontal and vertical velocities, respectively.
Note that while the horizontal components AC and WY are equal, the vertical velocities (at points A and W) differ not only in direction, but also in magnitude.
In practice, of course, an object in flight pushes air aside, encountering air resistance, a force which slows down motion and blunts the flight path, causing the Centre of Gravity to travel in a curve, somewhat. Air resistance depends upon the size, shape, spin and velocity of the moving object, but in jumping and throwing events it s sufficiently negligible for flight paths to be considered regular, i.e. parabolic.
The optimum angle for the projection of a missile, no matter what its velocity, is 45 deg., when its vertical and horizontal component velocities will be equal. If projected at a greater or lesser angle the object falls short of its maximum range. But 45 deg. is the optimum angle only when the points of release and landing are level which, in track and field athletics, is seldom so.
In releasing the shot from a point 7 ft above the ground, the optimum angle varies with the velocity; a low velocity necessitates the use of a comparatively low release angle, and vice versa. On the other hand, A short man, theoretically, must put more steeply than a tall one and use more velocity to attain a given distance. It is, therefore, upon height and velocity of release that optimum angles depend.
In the long-jump, where the athlete relies mainly on controlled sprinting speed to build up a high take-off velocity, this is done at the expense of vertical speed, horizontal motion being so marked that in the best jumps the athlete’s Centre of Gravity is projected at take-off at an angle below 30 deg.. Here, as in shot putting, the point of projection of the Centre of Gravity is above the landing level.
The release angle in throwing the hammer is only fractionally below 45 deg., but aerodynamic considerations greatly affect release angles in the discus and javelin events.