This is not the place to explain in detail what deviations the ball is submitted to under consideration of the distance-time behaviour. However, basically it can be said of the so-called ballistic curves (taking into account of friction losses in the air and on the ground with a given form of the ball) that the horizontal velocities of the tennis ball are high as compared with the vertical velocities (exception: high lobs). The reason for this is that the length of the tennis court is very great, whereas the height of fall is not very considerable. A consequence of this is that friction hardly influences the vertical movement of the ball, whereas the horizontal velocity of the ball is considerably reduced by the air resistance (R v2). Although friction proportionally grows with the square of velocity, the decrease in ball velocity is insignificant (up to 4 %). The loss in vertical height, however, is almost identical. Since, however, only the vertical movement is interesting for time orientation, the 'ideal' law of gravitation is almost fulfilled.
Things are different with balls with forward spin (drive/topspin) or backward spin (slice). The so-called ´Magnus effect´, which is characterised by a combination of very high horizontal velocities and high rotational velocities (identical level of direction), changes the behaviour of the ball. In this case the vertical distance-time-law deviates from this phenomenon, and with the simultaneous appearance of spin, the horizontal velocity is responsible for the ball falling to the ground faster or slower. A physical explanation for this is that gravitation is superimposed upon by another force which has its origin in the spin. This means as far as perception is concerned that one sees the ball rising or falling as if in a slow-motion or fast-motion film. Such a ball with 'higher gravitation' has to be corresponded to by the movement of the racket face with a changed vertical velocity. It must be mentioned here that e,g. the topspin, which falls down faster and thus helps to save time, later loses this time again by reaching a higher maximum during bounding (later as far as time is concerned). The importance of this physical fact is that it makes possible for the player to let his movements as far as time and space are concerned be guided by the vertical movements of the ball.
In accordance with the possibility theorem of perception, which implies the idealised movement, and the invariance of gravitation, which even exists under ballistic conditions, there is the possibility to determine the relationship between object and subject as regards time and space. 'Timing' can be defined. Perception and movement can be related to each other. The structural problem of form is solved with the example of a concrete movement. The required unit of perception and movement (see Rudel 1977, teaching film) can be expressed in a 'graspable' relationship.
In order to explain once again the connecting character of gravitation as far as perception and movement are concerned, it must once more be stated which perception and which movement are meant. The movement is the flight of the ball with its invariance in the vertical aspect and the movement af the racket face. They are connected in the 'guiding-beam movement' of the racket face, in the 'sticking', in the simultaneous 'drawing', or whatever image one uses.
1.3 Contact movement racket face - ball
It has already been mentioned that the player's movement is the establishment of a relation between himself and the ball. This relation is established evem before the player touches the ball with the racket face by orienting to the opponent's stroke and the behaviour of the ball during the flight. The better the player adapts his movements to the behaviour of the approaching ball as far ds space and time are concerned, the more exactly ('timed') can the stroke be performed. The demands on the relationship to be described must encompass all space-time relations between player and ball before, during and after hitting the ball. In doing so, the contact movement between racket face and ball is helpful.
Just imagine the following situation: Two players are standing opposite each other, one of them perpendicularly strikes the ball up to the height of his head. It is the other player's task to catch the falling ball with the racket face so that the ball does not hounce.
From this the following movement sequences are developed:
• striking perpendicularly downward when the ball is rising or falling above net height;
• striking perpendicularly upward when the ball is falling for the first time;
• hitting perpendicularly upward after the ball has touched the ground and is rising again (figure 3);
• hitting perpendicularly upward after the ball has touched the ground and is falling for the second time.
Figure 3 : Half-volley - vertical aspect
In order to catch the ball smoothly, the velocity of the movement of the racket face must correspond with the velocity of the ball. If the player right from the time of his partner's stroke tries to follow the vertical movement of the ball with his racket face, the approach to identical height when the ball falls can easily be achieved. In order to perform this movement, the space-time-relation can be determined. In doing so, the 'timing' of the racket face movement represents the performance of the movement of the whole body. This acquired vertical contact behaviour is also used when performing the movement sequences mentioned above:
• When striking downward: in doing so, the racket face first all follows the upward movement of he ball; during the strike it moves downward·. This movement goes hand in hand with an upward-downward movement (smash/service) of the player.
• When striking upward: first of all, the racket face follows the upward movement of the ball, then it moves downwards, and after this, during the strike, upward again. In doing so the racket face causes the player to make a downward-upward movement with a rhythmical change (volley, half-volley, groundstroke).It does not matter how high the hitter strikes the ball, the timespace relations remain constant.·The movement rhythms created for the strokes mentioned above can be transferred to:
• all smashes and services
(hitting zone during the first rise and first fall above net height)
• all volleys (hitting zone during the first fall of the ball)
• all groundstrokes.
(hitting zone during the second fall after bouncing (figure·4).
| Movement Rhythms | Strokes | Moment of hitting | Racket face movement (vert.) |
| 1 | smash /service | during the 1 rise a. first fall above net height | upward - downward |
| 2 | volley | during the first fall | upward - downward - upward |
| 3 | half-volley | during the rise after bouncing | upward - downward - upward |
| 4 | groundstroke | during the second fall after bouncing | upward - downward - upward |
Figure