### Wacky Table Tennis

1st Hour Colin Brady, Mauricio Perez, David Matusz

Equipment:
Ping Pong Ball
High Speed Camera
Wii Remote
Duct Tape
Light
Black Marker

Procedure:
First, you have to get all the materials. Then, you have to put black marks evenly on a ping pong ball in order to see the rotation of the ball. Secondly, you must set up a high speed camera and capture the ball after it is struck. Once you have done this continue to capture the hits until you get the one you want. While doing this, duct tape the wii remote to your arm, so you can use it as an acceleramtor.

We will be testing a flat serve, a topspin serve, and a topspin forehand with the ping pong paddle and ball, testing the acceleration and speed of the wrist, hand motion. We will also calculate the speed of the ping-pong ball and it's spin, pending the camera can measure spin.

### Why is Spin Important in Table Tennis?

It is probably easiest to understand how important spin is by first imagining what table tennis would be like if there was no such thing as spin. If you could not spin the ball in table tennis, what would be different?

How Hard You Can Hit

First of all, you would be limited in how hard you could hit the ball. A table tennis table is 9 feet or 2.74 meters long. A top player can hit a ball off the bat at around 175km/hour (although it will slow down a little due to air resistance).

Without boring you with all the physics, this means that the ball will drop due to gravity about one and a half to two centimeters during the time it takes to cross the table. So if the ball is hit at the same height as the top of the net, it will be physically impossible to hit the ball at this speed and still land the ball on the opponent's court - the ball will simply not drop fast enough. It gets worse as the ball gets lower, since the ball must now be hit upwards to get over the net, and then there is only gravity to pull it back down onto the table. (By the way, you could hit the ball as hard as you can virtually straight up in the air, hoping that it will come down on the other side of the table. But practically it's a pretty silly thing to do, and very hard as well - try it sometime!)

The ball could only be hit at full speed and power if the ball was high enough to draw a virtually straight line between the ball and a point on the opponent's side of the table, without the net getting in the way. This is roughly 30cm above the table if the ball is hit at the endline.

Spin is what allows players to hit a table tennis ball hard when the ball is low or below the net, but still land it on the table. By putting heavy topspin on the ball, a player is able to make the ball drop towards the table faster, so that he can hit the ball fast in an upwards direction, but have his heavy topspin pull the ball down onto the other side of the table.

Spin is why the real sport of table tennis is played so much faster and harder than the basement version - the more you can spin the ball, the harder you can hit it and still hit the table!

Variety of Strokes

Secondly, without spin you would lose the ability to curve the ball through the air, and bounce in the direction of the spin when it hits the table. Every stroke would go in a straight line in the direction that the ball is hit - much like a badminton shuttlecock.

Putting topspin on the ball causes the ball to drop faster and kick more forward when it bounces, while backspin makes the ball tend to lift against the force of gravity and slows down the forward bounce. Left sidespin and right sidespin cause the ball to curve to the left and right, and bounce towards these directions when hitting the table. Any combination of two of these spins can be used to achieve strokes that are harder for the opponent to return than a ball with no spin. If the opponent doesn't adjust for the effect of the spin on the flight of the ball and the way it bounces, he's unlikely to even hit the ball!

Spin is the reason why the modern game has much more variety of strokes than the basement version - with spin you have many more choices about what to do with the ball - hit it hard hard or soft, with topspin or backspin, or curve it left or right with sidespin.

Deception

Thirdly, without spin you would lose the ability to deceive the opponent about what spin is on the ball. Every ball would have exactly the same amount of spin - none.

In the modern game, it's possible to deceive the opponent with spin in a couple of ways. Firstly, clever players can trick the opponent about what type of spin is on the ball. This is quite difficult to do during a rally, but more achievable when serving. Secondly, it's possible to make an opponent guess wrong about the amount of spin on the ball, for example making him think the ball has light backspin, when in actual fact the ball has heavy backspin. The opponent would be likely to put the ball in the net.

Spin is the reason why the modern game is much more difficult to play, but also much more rewarding. The ability to vary the spin and deceive your opponent is crucial to success in advanced table tennis. With topspin, the ball is rotating forward so that the top of the ball is moving in the same direction that the ball is travelling. The force exerted on the ball by its spin will be generally downwards (assuming the ball has been hit almost horizontally). This downward force works in the same direction as gravity, causing the ball to dip faster towards the table. It is the effect of topspin that allows advanced players to hit the ball with amazing power from below the net, but still land the ball on the other side of the table. With backspin, the bottom of the ball is moving in the same direction that the ball is travelling. The force exerted on the ball by its spin will be generally upwards (again, assuming the ball has been hit almost horizontally). This upward force works in the opposite direction to gravity, causing the ball to drop more slowly. Since a table tennis ball is light and easily slowed by air, a heavy backspin stroke performed from several feet from the table will often slow down it's forward speed quite noticeably over the opponent's side of the table, then slowly fall onto the playing surface. This 'stop and drop' effect is used by defenders when playing against topspin attacks.

When sidespin is applied, the force on the ball will be parallel to the ground and towards the left or right side. The ball will drop at the same speed as a no-spin ball, but it will curve to the left or the right in the air. Sidespin can be combined with either topspin or backspin to produce a moving ball that is acted on by a combination of both forces. A ball with topspin and sidespin will drop faster and curve to the left or right, while a ball with backspin and sidespin will tend to drop slowly and curve at the same time. Spin is applied to the ball by brushing or skimming the ball instead of making square contact. Think of a line going straight out from the bat in the direction the rubber surface is travelling. If the line goes through the center of the ball when the ball is struck, maximum speed will be given and no spin will be applied. The closer the line is to the edge of the ball, the more spin will be put on the ball, and the less speed. In practice, the line is always somewhere in between these two extremes, giving more spin and less speed the closer the line is to the edge of the ball. The diagram above illustrates the first case, where the ball is struck squarely by the rubber surface, with the direction of motion of the bat going straight through the center of the ball. No spin will be applied by this stroke, but a lot of speed will be given.

The diagram above illustrates the second extreme, where the direction of motion of the rubber surface is almost at the edge of the ball. This stroke will produce a heavy spin on the ball, but not much speed.

The diagram above shows what will happen when the direction the rubber surface is travelling is in between the center and the edge of the ball. The closer the line to the edge of the ball, more spin will be given and less speed , and the closer the line to the center of the ball, more speed will be given and less spin. This means that for the same amount of bat speed, you can generate completely different amounts of spin and speed, just by varying the way you contact the ball.

By adjusting the direction the rubber surface travels vertically or horizontally, you can also change the horizontal speed of the ball. The diagram above shows two strokes that would produce the same speed and spin on the ball. They will not appear to be the same to the opponent though.

Stroke A is a more upward stroke, and will give a return that has more upward speed and less forward speed. The opponent will see this as a slower, high topspin.

Stroke B is a more forward stroke, and will give a return that has more forward speed and less upward speed. The opponent will see this as a faster, low topspin.

Remember that both balls are equally spinny. So this means that a ball that is coming at you faster and lower is not necessarily less spinny than a ball that is coming slower and higher.

Plan

We are going to take a ping-pong ball and do a top spin serve and a flat spin serve and observe the diffierence in roation of the ball. Then we are going to hit a moving ball with a top spin forehand, and a flat forehand. We will be using the accelerrometer to observe how fast you hand moves when hitting the ball to create spin. We will compare the speed when you hit it flat, and when you hit it with spin, comparing how much spin you can put on it while still keeping it at a fast speed.

What We Found

#### Flat Spin Serve

This is a video of a flat spin serve.

In this tracker and graph, you can see how the ping pong ball moves when hitting a flat serve. As you can see once the ball is struck it travels in the x direction consistetntly. The graph looks almost like a prefect diagnol line. In the second graph of the flat serve it shows how the velocity of the ball stays somewhat constant through the 6.5 seconds. In the flat spin serve, the ball does not spin a whole lot.

In this graph and video, it shows an example of a flat serve. From the graphs, the ball moves downward in the y direction, but the velocity changes due to the little amount of spin on the ball. The video shows the ball spinning slightly and allows you to see the direction it is going.
This video and graph shows the ball while being hit with a flat serve again. As you can see the ball moves  very consistently in the x and y directions. The ball moves downward over time in both the x and y directions. In the video you can see how the ball spins.
This graph shows the acceleration of Dave's wrist as he hits a top spin forehand. As you can see his wrist accelerates in the x and y direction very little while hitting the ball. As he strikes the ball AccZ is what accelerates the most. This is due to a diagnol motion while hitting the ball. In order to hit a topspin forehand, you must skim the top of the ball in order to create the spin. The acceleration in the diagnol direction is at first negative. This is because he moves his wrist back and downward in order to get enough power to hit the ball back over the net, and create topspin.

Finding Force
As we all know F=MA.
So we took the acceleration of the ball in the x and y direction and multiplied it by the mass of the ping pong ball.
We got an answer of F= .0027 times 22.75
Which gives us the force of the ball in the x direction.
It equals .061425 N
the ball in the y direction F= .027 times 24.78
which gives us the force of the ball in the y direction which equals .0066906 N

Mass
the ping pong ball is .0027Kg

Acceleration
In the y direction it equals 24.78
in the x direction it equals 22.75

Velocity
The velocity of the ball is distance over time
the y direction velocity equals  2.533
the x direction velocity equals  3.922

Momentum

The momentum equation is
p=mv
so fro y it is 2.533 times .0027
for x it s .0027 times 3.922
so the momentum of the ball in the y direction is .0068391
and the momentum of the ball in the x direction is .0105894

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#### Topspin Serve

This video will show the ball being hit with a topspin serve.

This graph above shows the acceleration of Dave's wrist as he hits a topspin serve.His wrist accelerates in a sort of crazy motion because he unfortunately was moving around alot and wasn't still. That and the fact that Mauricio prematurely launched the wiimote and then turned it off late there is a little too much data in it. But as is evident he initially wound up and then hit the ping pong ball... the data collected afterwards is from his motion after before Mauricio turned off the program.

Finding Force
As we all know F=MA.
So we took the acceleration of the ball in the x and y direction and multiplied it by the mass of the ping pong ball.
We got an answer of F= .0027 times 1.72
Which gives us the force of the ball in the x direction.
It equals .004644 N
the ball in the y direction F= .0027 times 2.433
which gives us the force of the ball in the y direction which equals .0065691 N

Mass
the ping pong ball is .0027Kg

Acceleration
In the y direction it equals 2.433
in the x direction it equals 1.724

Velocity
The velocity of the ball is distance over time
the y direction velocity equals  .3314
the x direction velocity equals  .4027

Momentum

p=mv
for the y it is 2.433 times .0027
for x it is 1.724 times .0027
The momentum of the ball in the y direction =8.9478 E -4
the momentum of the ball in the x direction =.00108729
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#### Topspin Serve

This video shows the ball being hit by a topspin serve.

This shows the ball's velocity in the x and y direction.
This graph is from another topspin serve. It shows Dave's wrist as he hits it. It looks strange because Dave could not stand still, but it is evident where he hit it. You can see the x go up and then a green and red spike down, showing him hitting the ball.

Finding Force

Force of the ball in the y direction =.0027 times 1.16
which equals .003132 N
force of the ball in the x direction = .0027 times 1.179
which equals .0046413 N

Acceleration

in the y direction it equals 1.16
in the x direction it equals 1.179

Mass

The ball weighs .0027Kg

Velocity

The velocity in the y direction =1.792
the velocity in the x direction =6.195

Momentum

P=MV

for y it was .0027 times 1.792
for x it was .0027 times 6.195
The momentum of the ball in the y direction = .0048384
the momentum of the ball in the x direction =.0167265
_________________________________________________________________________________________________________________________________________

#### Return

This video shows us hitting a topspin return.

The graphs show that once the ball was hit, it traveled upwards in the y and x directions. It shows the velocity of the ball in both directions.
This graph shows the velocity of the ball in the y direction. As you can see its a pretty straight line. The velocity is indicated by using d divided by t.
This graph shows the acceleration of the ball in the y direction. Which would be upward. By using the equation we find that a is the accelereation.
This graph shows the acceleration of Dave's wrist as he hits a topspin return. As you can see his wrist accelerates in the z and y directions. But the x direction is different because he pulls his arm back to hit the ball. While he pushes his arm upward in a diagnol motion to get spin on the ball.

Mass

The mass of the ping pong ball is .0027Kg

Acceleration = 2.154 in the y direction
and 6.719 in the x direction

Force
F=MA
F in the y direction equals .0027 times 2.154
F in the y direction for the topspin return = .0058158

for force in the x direction we take .0027 times 6.719
so the force in the x direction equals .0181413

Velocity

In the y direction v = 1.138
In the x direction v = 2.336

Momentum
for y its  .0027 times 1.138
for x it is.0027 times 2.336

The momentum of the ball in the y direction = .0030726
and in the x direction = .0063072

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Steve Dickie,
Oct 20, 2008, 7:42 AM