The rubbers used in teble tennis have two important element. The first one is the kind of rubber sheet, and The second one is the thickness of it.
Furthermore, the rubber sheet has two categories.
The first one is the surface side of rubber sheet which frictional resistance is low.
The second one is the inverted side of rubber sheet which frictional resistance is high.
When using the surface side, "the momentum of flying" is high but "the momentum of spin" is low.
On the other hand. When using the inverted side, "the momentum of flying" is high and "the momentum of spin" also is high.
Spin range depends heavily on the type of rubber. To win games, it is necessary to know about the rubber causing the spin.
You have to know not only the feature of your own rubber but also of the opponent's.
If you do not know those features, you will not be able to win matches. Because you cannot control the ball flight as you intended.
The rubbers have the following thickness. "Thin", "Medium", "Thick", "MAX". Thicker rubbers will be heavier.
Comparing the swing speed using the "Thin" and the "Thick", the "Thin" is easy to swing since the rubber is lighter.
The "Thin" and "Thick" are differences in thickness. However, whether does thickness selection only depend on the difference in weight?
I wonder why players choose the thickness.
I wanted to have some criteria, and thought but roughly,
what relations occur between the thickness of rubber and the ball movement when the ball is bounced by the rubber.
Placing the "Thick" and "Thin" of the same rubber material on the table, and dropping the ball from the same height.
How will the difference happen between the heights of bounce?
Maybe you would think that the "Thick" gets higher. However, the result is the same. What does this mean?
The ball that fell to the rubber stores the strain energy inside the rubber by contracting the rubber.
And in the process of restoring the shrinked rubber, it releases its energy and bounces the ball.
Therefore, the fact that both of the rebound height are the same indicates the amount of energy stored inside those rubbers is also the same.
However, since the thickness of each rubber is different, the stress inside the rubber is different.
Thin rubber has more internal stress than thick rubber.
In the calculation result, when the rubber thickness is twice, the internal stress becomes 1 / √ 2.
Conversely, when the rubber thickness is half, the internal stress becomes √2 times. Relation between rubber thickness and strain energy in case of using the same rubber was shown below as reference.
The frictional force is F = μN, if the load is N and the proportional constant is μ.
The force applied to the rubber by the ball is F = μσA, where A is the contact area of the rubber and the ball, and σ is the stress.
As a result, If the rubber is thick, it is difficult for the ball to spin, and if the rubber is thin, the ball is easy to spin.
Although, we will mention controlling of ball flight with spin composition at later section, thin rubber is easy to spin, and
thin rubber is easy to control large direction change.
So why do players choose a thicker rubber?
Actually, the strain limit of the "Thick" is greater than that of the "Thin".
Since the "Thick" can accumulate larger energy, players are able to fly the ball farther.
However, since the rubber becomes heavy, it is not suitable for striking near the table where fast swing speed is required.
On the other hand, thin rubber is light, so it is suitable for hitting near the table,
but it is not suitable for hitting away from the table because it is not able to fly the ball away.
It is important to know "the type and thickness of the rubber" of a opponent.
Because you become possible to predict the spin type of the opponent's service, a countermeasure of it can take easily.
Sometimes, some players are using "MAX" near the table.
So you should be able to make game advantageously against this opponent if you choose fast rally.
On manufacturer's website have posting "the correlation diagram of speed and spin" indicating their rubber performance.
In many case their Figures indicate by the spin on the horizontal axis and the speed on the vertical axis.
But in my Figure indicates by the speed on the horizontal axis and the spin on the vertical axis.
This Figure makes it intuitively to visualize the flight trajectory.
The following figure is simulated the speed and spin of the above rubbers as parameter.
The ball's trajectory is determined when it leaves from the rubber due to the Magnus effect.
According to this figure, the player using the "TSP Hurricane" that tends to get caught in the net indicates that it is recommended to use the "Butterfly Tenergy 64".
The "Nittaku Tyrano" may be too fly. the "Butterfly Sreiver" will become a ball that is easy to attack.
By using "the trajectory simulator of the ball by the table tennis rubbers",
you will become possible to compare the flight trajectory of various rubbers.
<Reference>
Relation between rubber thickness and strain energy
Supposing that a pressure P is applied in the vertical direction to a rubber which have the fixed cross-sectional area of A0 and the initial thickness of l0,
and as a result, it shrinks by dλ in the action direction.
The Work dW due to the pressure P is as follws.
dW = P dλ
W = ∫0λ P dλ
σ = Eε
σ = P/A0
ε = λ/l0
P = EA0λ/l0
W = ∫0λ P dλ = ∫0λ E A0/l0 λ dl
= E/2 A0/l0 λ2
Let the subscript of the standard rubber thickness is 1 ,
the subscript of the rubber which is twice of the standard thickness is 2 .
Let us compare the rubber internal stress when W 1 = W 2 .
λ12/l1 = λ22/l2
λ2 = √(l2/l1) λ1
= √(2l1/l1) λ1 = √2 λ1
that is
σ1 = Eλ1/l1
σ2 = Eλ2/l2 = E√2 λ1/ 2l1 = (E/√2) λ1/l1 = (1/√2) σ1
That is, when the rubber thickness is twice, the internal stress is 1 / √ 2. Conversely,
when the rubber thickness is half, the internal stress becomes √2 times.
When the rubber thickness is n times,
it becomes
σn = (1/√n) σ1
