Mechanics of Table Tennis
Rowden Fullen (2004)
- Trajectory of the Ball
- Absolute Line of Sight
- Smash against Lob
- Flicking the Short Ball
- Service — Speed and Time
- Speed and Spin
- Racket Coverings
- Friction and Bounce
- Bounce on the Table
- Speed, Distance and Time
- Economy of Movement, Key to Speed
- The Radius of the Stroke and Angular Velocity
- The Geometry of the Game
Nothing that happens on a table tennis table is inexplicable as long as you are aware of the basic laws of physics. Once the ball has left the racket, the trajectory and direction is determined by the power and spin fed into the stroke. The trajectory itself is determined by gravity, the air resistance and the influence of the spin. A similar stroke will always produce a similar result in terms of spin, speed and direction. One can of course point out that things will not be exactly the same depending on where one finds oneself on the earth’s surface. The weight of the ball can vary by as much as 0.5% depending on whether you play in a position near the poles or in a locality on the equator. However this is really quite meaningless when you consider that the rules allow a variation of up to 5% in the weight and diameter of the ball and at the most 8% when we are talking about bounce.
Far more significant variations occur in air pressure when we talk about height above sea level for example. At 1000 metres air pressure sinks by 12% and at 3000 metres by up to 30%! This has a major impact on both the air resistance and the effect of the spin on the ball in flight. A major championship event played for example in Mexico City will result in the ball ‘flying’ in an unusual manner and the players must be ready for this, as the trajectory of the ball will not conform to expected criteria. When players talk about a ‘hall’ being slow or fast this is a subjective experience. This can depend on different floor coverings, lighting, acoustics, heat and cold or just the size of the room. It doesn’t mean that the ball is moving in an unusual manner.
Questions relating to materials and the differing spins and effects can be rather more complicated as the manufacturing companies have not tried to create standardised tests to measure exactly what their products can do. Often experienced players or testers (or in some cases not so experienced) categorise rubbers in terms of spin, speed and control, but obviously these classifications are purely subjective. Different players will for example use rubbers in differing ways and one player will often be capable of getting far more out of a particular rubber than another player would. Such ‘subjective’ testing can give some useful information but helps little in giving any base for objective measurement when comparing products from different manufacturers. Also materials and indeed techniques and tactics are constantly in change - it is necessary that we always have an open mind and are ready to look at new ideas and ways of doing things.
2. TRAJECTORY OF THE BALL
After leaving the racket regardless of the spin, speed or direction, the ball is influenced simply by 3 factors - gravity, air resistance and spin (Magnus effect)(See diagrams A and B). In the case of topspin, gravity and the influence of the spin work together giving a more arced trajectory (See Diagram C). With backspin gravity and the spin factors work against each other so that the ball will rise initially in a curve before dropping sharply when gravity predominates over the lessening spin (Diagram D). Gravity is always equally strong and always directed downwards. Air resistance is always against the direction of travel and its effect is strongly influenced by the speed of the ball.
With a speed of 8.5 m/second (30.6 k/hour, 19.125 mph.) the air resistance is about equally as strong as gravity. Air resistance however increases or decreases by the square of the speed. This means that a doubling of the speed to 17m/second (61.2 k/hour) signifies a fourfold increase in air resistance. Halving the speed to 4.25 m/second (15.3 k/hour) would bring about a reduction in air resistance to around one quarter of gravity. In the case of fast counter play an average normal speed would be in the region of 12.5 m/second (45.0 k/hour) which means immediately that it’s always the air resistance which is the dominating factor in the early stages of the ball’s trajectory. (In the case of world records for counter-hitting (of so many shots per minute) an average speed of only around 33kph is achieved).
In the case of a top-spinning ball the force of the spin is at right angles to the speed and the rotational axis and as a result strengthens the downward pull of gravity. Very strong topspin is of the same magnitude as gravity and the ball will sink much more quickly. Note that a pure sidespin ball will have a distinct arc when seen from above. In the case of strong backspin the trajectory will veer upwards - here the power of the spin is stronger than gravity.
3. ABSOLUTE LINE OF SIGHT
Of course it is the player’s own skill and technical knowledge which will determine his or her choice of direction, speed and/or spin. There is however an absolute limit for the all out hard smash where in theory one can utilise a completely straight trajectory.
Below the absolute line of sight the speed element in all no spin or backspin balls will be limited as all such balls will require an arc and some margin for error will be needed in the stroke. The no spin smash is the game’s hardest hit (around 31.1 m/second (measured speed off the racket) or 112 k/hour) and gives the opponent the least possible time to make the return. If balls higher than the absolute line of sight are looped instead, this means a slightly safer shot but at a slower tempo. However the difficulty in switching from topspin to smash often means that many players prefer to spin even in this ‘high ball’ situation.
Under the absolute line of sight topspin is used more than any other stroke as the arced trajectory allows more and more power to be fed into the shot while still retaining a high measure of safety with speed. The absolute line of sight is therefore a useful tool in judging the best stroke to play in any given situation.
OVER ABSOLUTE LINE OF SIGHT
UNDER ABSOLUTE LINE OF SIGHT
- Topspin, backspin or counter-hitting with well judged (and controlled) speed.
Technique for the low ball
Often in the boy’s game even from an early age it is a good idea to work with topspin as this gives high speed and also a high level of safety. With the help of topspin players can have a comfortable margin for error, a lower trajectory and a lower bounce on the opponent’s side of the table.
Backspin with its straighter trajectory often tends to come through nearer to the end of the table. However in spite of this often the peak of the arc is higher and the ball can easily kick up after the bounce (there is also a reduction of speed at this stage) above the dangerous ‘absolute line of sight’, which leaves the defender open to a flat hit kill. It is therefore important that defenders take the ball as early as possible and above table height. Then they have the opportunity of a low ball over the net and a lower ball after the bounce, as the ‘speed’ element tends to take precedence over the effect of the spin and the ball skids through off the table surface. Also the earlier chop will retain more spin as it is in the air for a lesser time between strokes. Length is also crucial for defenders, either very long or very short, so that opponents have little opportunity to smash.
If defenders can introduce a topspin ball back from the table then this is a highly desirable variation, especially sometimes with sidespin. There will be a big difference between the topspin and backspin strokes and even the best of attackers will make mistakes.
4. SMASH AGAINST LOB
We should also look at the scenario where we face high lobbed balls. Here you will often have the opportunity of smashing from 3 areas, as the ball bounces upwards, at the ‘peak’ position or as it is descending (Diagram E). The ‘peak’ position (2) will need something like an overhead tennis smash and will bounce through high and long giving the opponent time to play the return, although the stroke is relatively safe. Killing the descending ball is also quite safe (3) but as you make contact from further back, you have less of the table to aim at and again the opponent has more time even though the trajectory will be flatter.
Theoretically the preferred contact should be as the ball bounces up (1). Here you have the chance to kill absolutely flat and angle the ball well as you are closer to the net - the opponent has very limited time to react. The problem can be that you have much less time yourself to study the spin and to react to any strange bounce. This contact is therefore a little more unsafe and requires practice (a short arm movement is important in this stroke). An interesting alternative is to use topspin from an early timing position - even though this is a slower stroke which gives the opponent time it results in a more curved shot and a ball which drops quickly after the bounce. Other alternatives are the chop smash or a stop ball taken very early.
5. FLICKING THE SHORT BALL
The flick requires some feeling as the ball must be kept as low as possible over the net and yet it is difficult to create speed from a short ball often served with backspin. Good topspin can create a safer stroke but often it is not easy to achieve this over the table. To reach maximum speed over the table the flick should be taken at the ‘peak’ of bounce on every occasion, though the late-timed stroke played more slowly can also open up possibilities.
It is possible to feed in approximately 10 - 15% more speed into the diagonal flick because of the increased distance involved. (Total available distance 3.1m as opposed to 2.7m)
If you wish to flick more safely, with a higher margin then this will require playing the stroke more slowly. Flicking straight and low over the net will result in a maximum speed of around 8.0m/second (28.8 k/hour) but this would drop to 7.0 m/second (25.2 k/hour) if you wished to have a 2cm cushion over the net. Diagonal play would give the higher figure of about 10.0m/second (36.0 k/hour) dropping by 10% (32.4 k/hour or 9.0 m/sec) if the ‘safer’ diagonal stroke were attempted. The flick can often be angled harder and more easily than the counter hit as it is taken closer to the net and with less speed on the incoming ball. However no amount of training can increase the power of the flick beyond what the natural laws allow. The lifting movement (attacking a ball lower than net height) sets the limit and this can only be overcome by the creation of more topspin. However as we have intimated this is extremely difficult in the case of a low over-the-table ball.
If you assume that two top players take the ball about 20 - 25cms off the end of the table then in a rally the ball would reach average speeds of around 12 — 14 m/second (43.2 - 50.4 kms per hour, straight and diagonal respectively). In the case of the safe 2.0 cms over the net stroke, speeds would be around 11.0 and 12.5 m/second. When you compare this with the flick, the latter stroke would not achieve speeds in excess of two-thirds of counter play or around 10.0 m/second (36 kms per hour).
The dominance of the Asian players over the years has occurred primarily because they take the ball early, just after the bounce. European players on the other hand take the ball at ‘peak’ or after the top of the bounce. The difference in usable reaction time gives Asian players a real advantage by preventing opponents from coordinating and organizing their best strategies.
7. SERVICE, SPEED AND TIME
The serve can vary a great deal but the service rules and natural laws impose certain limitations. Because the serve must bounce from one half of the table to the other this means a minimum upwards and downwards movement of around 34 - 35 centimetres (17 + 17). The time frame is approximately 0.38 seconds for a backspin or float serve but this can be reduced in the case of strong topspin. One must bear in mind that the limit for a long serve straight is 2.7 metres but this increases to 3.1 on the diagonal.
The time limit from bounce to bounce is around the same for a long and short service. However in the case of the short serve one must add the time from the racket contact to the first bounce which will add 0.15 - 0.2 seconds. The total time for a short serve can be as long as 0.6 seconds compared with the 0.4 for a long fast serve. The speed for a long fast serve will be very similar to the speeds when flicking - between 8.5 m/second (30.6 k/hour) straight, to up to 10.0 m/second (36.0 k/hour) on the diagonal.
8. SPEED AND SPIN
Strong spin presupposes that sufficient power has been used but spin and ball speed are connected and it therefore follows automatically that high speed will more often than not entail high spin.
The short serve will therefore always have a measurable spin which can be reckoned by the number of revolutions per second, while the long serve can have stronger rotation due to the increased power input. We don’t always experience this on the table as we often play with care against the short serve, however even a small lack of touch can lead to a ball in the net or a high return. Aggressive returns such as flick and long push do not require so much touch and are less sensitive to the spin element on the ball, therefore it is safer to play long if you have learned the technique and if the opponent’s playing style allows this. Also flicks against backspin can use the spin already on the ball and will result in a low dipping shot - long, fast service returns over 8.5 m/second will slow due to air resistance and this again helps when using topspin.
With the help of unusual or deceptive actions the server tries to hide the spin, speed or direction so as to gain an advantage over the opponent, lengthening his reaction time or making it harder for him to read the spin. Bear in mind that the variations to be found in the use of spin, speed, length and placement will often be sufficient to cause problems for opponents and it is important that your players can use the same serve in differing ways and execute differing serves with the same or similar actions.
9. RACKETS AND RACKET COVERINGS
After contact with a blade (without rubbers) the ball will retain on return about 85% of the incoming speed. In the case of a racket with 2.0 mm fast reverse rubber the return speed after the contact will only be about 70% of the incoming ball’s pace. For an attacking player the rubber’s task is to preserve the speed as much as possible (a part of the ball’s energy will always be lost against the surface) and at the same time give the player a good chance to create and vary spin during play. It is obviously important that the outer surface of the rubber has high friction, while the sponge can vary in hardness depending on whether the player needs more spin or speed.
Harder blades and sponges give more speed at the expense of control while softer blades and sponges provide more spin and control as there is a longer contact time on the blade (without gluing you lose between 10 - 20% of the speed and spin). The blade also has its part to play and even under the rubber and sponge it can deform against a hard hit. One can easily see that with a contact speed of up to 31.1 m/second (112 kph. or 70.0 mph.) and a contact time of a thousandth of a second, with a ball weighing 2.7 grams, the impact can be very considerable. If the stroke is not played absolutely cleanly then strong vibrations can be created in the blade with ensuing energy losses. An ‘unclean’ hit always gives slower speed.
Generally we can say that half the racket speed contributes to spin and the other half to speed. What you gain in the one aspect you lose in the other. When looping against a topspin ball the spin must be reversed which requires strong friction and a very closed racket. Looping against backspin means that you play with the spin which needs much less friction but a considerably more open racket angle.
10. FRICTION AND BOUNCE
Irrespective of the ball’s movement in the air, the friction and bounce depend on the material qualities of the racket and of the table. Although in principle the same natural laws should apply during ball/table contact and in ball/racket contact, here the two surfaces are dramatically different, varying from smooth and shiny to sticky with immense friction. Another vitally important factor is that the bat is usually used actively while the table’s part is always completely passive.
The energy which one imparts to the stroke, the motion energy, can be of two types, rotational or speed value. A smash has strong speed value while a loop has a great deal of both values. In the case of ball/table and ball/passive racket the rotational energy can predominate, dramatically slowing the speed value. Perhaps the most important consequence can be that the reversed rotational energy not only returns a much slower ball but also one that can alter direction quite markedly. In the case of the ‘active’ racket a new motion energy will be established.
11. BOUNCE ON THE TABLE
The effect which will occur between the ball and the table is partially because of the bounce N (impact speed and angle) and the spin T (amount and type). There will also of course be energy losses (a reduction in speed of about 10%). The result will be a bounce which can reach a height of approximately 70% of the trajectory’s high point in flight.
The float ball will lose speed after the bounce but will acquire a weak topspin due to the bottom part of the ball being held by the table and the top part rolling forward (Diagram F). In the case of strong topspin the ball will acquire forward energy and this rotational momentum will be converted into extra speed (Diagram G). The speed of the ball’s movement forwards will increase. The result will be a bounce of less than 70% of the highest point in the trajectory, with a lesser spin but an increased speed (in the range of some 15 - 20%). The backspin ball is similar to the float ball - however the big difference will be the spin factor which will have as much effect as the frictional qualities of the table’s surface will allow. Often it can be a question of the ball ‘sliding’ through. Otherwise there will be a clear ‘braking’ effect after the bounce and the ball will slow, kick up a little and hang in the air (it can often kick up above the absolute line of sight).
Sidespin has the rotational values at right angles to the table’s surface which means directly that as the point of the axis is in contact with the table, there is little or no loss of spin. The ball therefore comes through with maximum retained spin.
The friction between the ball and the table will reach a maximum of around 20% of the impact force between the ball and the table - then skidding occurs. In comparison the friction between the ball and the racket is very much stronger and will reach levels of 50% or more. In the case of a passive stroke where the racket scarcely moves then the effect of the spin against the surface will be extreme.
Reverse rubber is very sensitive to spin and the racket must be at the right angle with reference to the incoming spin and speed. A great deal of topspin will require an extremely closed angle but if the speed is also high then the angle will need to be opened up. In the case of the ball’s contact with the racket we are concerned with two types of power. N = Normal power which consists of the bounce and the speed of the ball and T = Tangential power which depends on the spin and the frictional qualities of the racket.
‘Braking’ or frictional forces can have a major effect on the rotational values (spin) and the rotational energy can be changed, exhibiting itself as an increase in speed or as a dramatic change in direction.
The loop is usually executed with maximum racket speed and as thin a contact as possible. The harder one endeavours to strike the ball (with a closed (topspin) racket or open (backspin) racket) then the more spin one will achieve together with speed. Always bear in mind however the old cliché - ‘What one gains in spin one loses in speed and vice versa’.
Interesting effects can also be achieved when one contacts the spinning ball at one of the poles where there is little or no spin - the spin will remain on the return ball but often in a completely unexpected form. This is due to two different axes trying to assert themselves at the same time. A loop against a sidespin ball will result in a topspin return with a sidespin kick.
12. SPEED, DISTANCE AND TIME
Obviously the further you back away from the table the more time you will have to prepare and the more time to set yourself and hit the ball harder. However equally the opponent will have more time (Diagrams H and J). Both show how the ball loses speed over a distance. If two players are each three metres back the total distance between ball contacts is around 9 metres and the ball will slow through the air — this gives over half a second to react which in the case of two fit, skilful players will mean that it will be hard to outmanoeuvre the opponent and win the point.
Diag. H. Choose your initial velocity, say 20 m/second which gives you a mark of around 0.1 seconds on the curved line and a figure of 3 on the baseline. Forget the figures to the left of the 0.1 and work with the right end of the curve. After another 0.2 seconds (0.3) the distance is 7.0, so the ball has travelled 4.0 metres (7.0 - 3.0) and the speed is down to around 11 m/second.
As we can see from (J) there is a big difference looping close to the table and executing a similar stroke three metres back. If we feed in an initial speed of 15 m/second, ball (1) will reach the other end of the table in 0.2 of a second or slightly less and will then have a speed of 10 m/second - ball (2) on the other hand will take around 0.5 of a second and the speed will have dropped to 7.0 m/second. We must also bear in mind that even at relatively slow speeds, say an average of 40 kph, the ball will cover the length of the table in about 0.25 of a second which is the approximate limit of human reaction time for the average player.
There are obviously several advantages in playing closer to the table which many top men are now coming to appreciate in the framework of our much faster modern game (the women have used these advantages for many years).
- The angle of play increases.
- The speed of play increases.
- The time to play decreases.
These aspects mean that the opponent has to cover more of the table and more ground in a lesser time and has to react at a higher speed (the time frame can more than halve). With access to information on time, distances and speed (in relation to the ball) one can easily move into the optimum position to make the best use of time and pressure the opponent. Equally such insight gives perception into one’s own capabilities and how these should develop.
13. ECONOMY OF MOVEMENT — KEY TO SPEED
Explosive speed is an inherited characteristic and players who don’t have it are rather limited in what they can do to train up this aspect. However there is nothing to stop any player only using those patterns which give most economy of movement. It’s elementary for example to understand that quick play requires short strokes so that you can recover for the next ball (not so short however that you fail to play ‘through’ the ball). If in our modern fast game you are attacked hard and have no time, then you must be satisfied with the block return.
Racket recovery is particularly crucial and it’s vital that the racket returns to the neutral position after each stroke so that you are ready to play FH or BH on the next ball. It is equally vital that the elbow drops down after the stroke (especially the BH counter) so that the forearm is in the best possible position to move in either direction.
The ultimate style of the player will dictate which type of movement patterns he or she should use. Close to the table blockers will use many one-step movements or small jump steps. Strong loop players will inevitably use the cross-step to reach the wide ball and defenders should train at moving in and out. However with the modern game both close and deep, movements which retain a square position are preferable. Movement is one of the most critical parts of any young player’s development and yet very few countries in Europe work constructively with footwork patterns at an early age. It is particularly important that you establish a pattern with a young player that can grow with the player, (can a sidestep pattern be easily developed into a cross-step?). It is also a priority in the ‘modern’ game, where we have limited time that footwork is economical, one big step is preferable to many small ones.
Among the world’s elite (especially the Asian players) the FH is still the dominant stroke and many men players will still move more in order to bring this wing into play. (Among the top European men because of the increase in the basic minimal speed many now use the BH from the middle or even from the FH side against the serve. It will be interesting to see if this tactic, which has been common amongst the women for many years, will become the norm in the men’s game).
Perhaps here a warning should be issued to women trying to use the FH over the whole table as some top men do. The women’s game is rather faster as they stand closer to the table, hit the ball earlier and flatter. Often they have less time to move and to react between shots. Also overall their physical capabilities can be reckoned as between 15 - 30% lower than the male. These factors can make the difference between success and failure at top level.
For a top player to execute strong topspin from FH and BH corners with FH and BH consecutively takes around 0.6 of a second. However to do the same with just the FH wing will take almost 1.0 second. This is quite a big time difference at top level. FH play over the whole table is asymmetrical (by this we mean one-sided and unbalanced movement). Symmetrical play is clearly superior from the point of view of economy of movement, the only downside being that the BH topspin is generally less powerful than the FH.
A change to more symmetrical play requires that the BH topspin be of the same quality as the FH. This can be achieved by use of what we call the tennis BH. Here with a quarter rotation backwards, taking the ball off the left hip and using good rotation and very fast forearm action, the stroke can be upgraded to a similar power and speed as the FH. Certainly in the future it is becoming obvious that in the light of the speed of the modern game, play will become more and more ‘symmetrical’ and that this will be the way forward.
14. RADIUS OF THE STROKE AND ANGULAR VELOCITY
A stroke can be executed with a large radius (a straight arm with forward movement) or with a small movement (flick of the wrist). If you use a large action then a small mistake in ‘timing’ will have little significance, however with a small movement the resulting error in placement will be very apparent. Use small movements over the table and the large action further back where you require more power and precision of placement.
In the case of any stroke where an arc is used we can have a positive or negative arc (Diagram I). The positive arc follows the outgoing trajectory of the ball much more closely and as a result has a higher safety margin. The negative arc places much higher demands on exact timing. However in the case of the loop against a backspin ball where the racket angle is much more open the advantages or disadvantages are not so critical.
Many players think that it’s safer and more natural to have a negative arc with the BH topspin and especially where the feet are more parallel with the end of the table. However for those who want to work with the ‘tennis’ BH it’s important that they have the same positive arc on both wings and don’t need to change from one to the other.
15. THE GEOMETRY OF THE GAME
Whether it is a matter of standing right, moving in the right way or placing the ball in the most advantageous position, one can have a great deal of help from pure geometrical analysis. Most players for a start will want to cover around 60 - 65% of the table with the FH side as they can reach further on this wing, and 35 - 40% with the BH.
From the point of view of recovering to the most advantageous position relative to the angle of play, you must assess the total angle available for the opponent’s use and move into a position where your right shoulder is on the centre line (the bisecting line). Obviously when playing the FH from the BH corner playing on the opponent’s BH diagonal gives the most advantageous return angle.
However with the FH serve from the BH corner this can be placed to either corner - it is only necessary that you move to cover the return possibilities the instant after ball contact is made.
In doubles play the same geometry applies - the only difference is that the one who plays the ball doesn’t have to take the return. It is necessary to place the ball in an advantageous position for your partner. A right- and left-handed player complement each other well in this situation as both can often use the FH most of the time. In doubles it is wrong to always try to return to a normal ready position just as it is not profitable if both partners end up wide out on one corner or the other.