Physics behind table tennis - can we use science to improve our game? 🏓 🏓 🏓

How can we use physics to improve the way we play table tennis? Just like all other occurrences in the universe, physics can help us understand more about the action. Using the physical concepts of force, velocity, acceleration, displacement, work and energy, we sought to find how variations in spin, height, take-off velocity and acceleration can help us better under the physics behind table tennis. 

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 racquet, 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.However, things will not be exactly the same depending on where one finds oneself on the earth’s surface. Moreover, the weight of the ball can vary depending on whether you play in a position near the poles or at a locality on the equator. However this is really quite inconsequential when one considers that the official 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. But, far more significant variations occur in air pressure when we take into account the height above sea level, for instance. They share an inverse relation of proportionality (height above sea level ∝ 1/air pressure). 

Firstly, when investigating the physics behind the power in our shots, to increase power, we need to do more work. Thus, striking the ball with greater force meant doing more work. Power increases when we do more work or take less time in our shots. 

P = W/t (P=power, W=work, t=time)

W= f*d (f=force applied, d=displacement) 

∴ P = f*(d/t) = f*v (v=velocity). 

Next, to maximize acceleration in shots, the two ways we could do so would include:

1) decreasing initial velocity,

2) increasing final velocity.

Since we have no control over the initial velocity (it depends on our opponent), we need to strike the ball as hard as we can. However, when facing a shot, the initial velocity is in the opposite direction (having a negative value) thus it is added to our velocity. The time remains fixed. 

a= (v-u)/t (a=acceleration, v= final velocity, u= initial velocity, t= time)

When talking about energy, it has to be conserved. Thus, there is a transfer of energy from the body of the player to the ball through the racquet. 

PE = mgh (PE= potential energy, m= mass of ball, g= acceleration due to gravity, h= height of ball). 

This explains why a serve with a high ball toss is more dangerous than one tossed only 6 inches high. The energy gained by the high toss can be converted to spin or speed when struck by the racket. 

KE = ½* m*v2 (KE= kinetic energy, m= mass of ball, v= velocity of ball)

This formula shows that the faster you hit the ball, the more energy the shot will have. Moreover, If the mass of the racquet is high, then it will also result in more energy in the shot.

Next, we can focus on the trajectory of the ball with three different situations (topspin, no spin, and backspin). After leaving the racquet regardless of the spin, speed or direction, the ball is influenced simply by 3 factors - gravity, air resistance and spin (essentially the Magnus effect). In the case of topspin, gravity and the influence of the spin work together giving a more arched trajectory. 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. 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. In the case of a top-spinning ball, the force of the spin is at right angles to the speed and as a result strengthens the downward pull of gravity. Very strong topspin is essentially of the same magnitude as gravity and the ball will sink much more quickly. However, the case is reversed. In strong backspin, the trajectory will veer upwards - here the power of the spin is stronger than gravity.

Finally, focussing on the frictional forces at play, it is difficult to calculate values as the friction differed according to the racquet and ball used. Moreover, there is a force of friction between the ball and racquet when the shot is made, and another frictional force between the table and the ball which impacts its bounce. Although in principle, the same laws should apply during ball/table contact and in ball/racquet contact, here the two surfaces are dramatically different, varying from smooth and shiny to sticky with more friction. Another important factor to take into consideration is that the racquet is usually used actively while the table’s part is always completely passive.