### Balls of Fury

Duncan Miller
Brian Kaminski
Gust Mareskas
2nd Hour

Our sport...is ping pong. And our project...is spin.

## The Experiment--Overview

We are going to analyze how the spin of a ping pong ball affects its trajectory. Using Mr. Dickie's camera that captures a ridiculous 500 fps, we are going to be able to witness the amount of rpms (revolutions per minute) as the ball travels across the table. In theory, the more induced spin of a ball when it is hit, the more the ball will be move from side to side or up/down. We will be dealing with side spin because this is easier to track (you do not have to deal with gravity's affect in conjunction with the spin).

Materials
Ping pong table
Ping pong ball (with colored quarters)
High Speed Camera
Spotlights
Regular Camera with video
Logger Pro for analysis

Procedure

The ping pong ball will be thrown at the player along the center line. The player will hit the ball, focusing on spinning it left. the ball will strike the player's side of the table before going over the net (which is against the rules of table tennis but the experiment is being performed this way so as to combine the spin from air friction and the spin after hitting the table). The ball will be tracked by two different cameras: Mr. Dickie's high speed camera and another regular one.

## The Data

We will use Mr. Dickie's high speed camera to see how fast the ball is spinning (revolutions per minute). From another camera's view, we will be able to determine the amount of time the ball is in the air. Combining this data, we will be able to estimate the amount of spins of the ball during it's journey. Also, either from the regular camera's view or an observer's measurement (which would be less precise), we will measure the displacement that the ball undergoes from its first bounce on the table to when it bounces on the opponents side. This will be measured as distance from the centerline because, ideally that is where the player will first hit the ball.

Also, from the regular camera, we will also be able to measure both the total time and distance that the ping pong ball travels. We know that the regulated size length of a ping pong table is 9ft. From this, we will be able to determine it's velocity.

In addition, knowing  the ball's diameter, we will know it's circumference. If we know how
fast the ball is spinning (revolutions per minute) and the length of one revolution (circumference), we will theoretically be able to predict how fast arm needs to go sideways when hitting the ball forward.

Unrelated to this data, we know Brian Kaminski's and Duncan Miller's reaction time from the lab we did in class. We know the length of the table and the speed the ball must be traveling to get to the end of the table before the opponent can react. From this, we will be able to determine what makes the perfect smash unreturnable!

Number Crunch
We can already guess that giving the ball more spin will give the ball more displacement. From our data we will be able to find some sort of ratio between the two (something like fifty spins through the air moves the ball one inch to the left).

From Mr. Dickie's high speed camera, we will count the number of frames that it takes to make one revolution. Knowing that it is capturing data at 250 fps, we can do a little dimensional analysis to find its rpms (revolutions per minute). Ultimately combining all of our data, we should be able to find the relationship between arm speed and ball displacement (something like sideways arm speed of 30 mph to the right moves the ball one inch to the left).

Using Logger Pro on the clips from the regular camera, we will be able to determine the ball's total distance traveled (we may have to use pythagorean's theorem) and the amount of displacement from the center. From the regular camera's frames per second, we will be able to find how long it is in the air for.

Here is a sample data table for our experiment

 Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Trial 7 Revolutions per second 41.67 33.33 35.7 38.5 45.5 41.7 38.5 Displacement from the centerline 15.91 cm 33.05 cm 15.36 cm 25.88 cm 33.35 cm 15.29 cm 13.73 cm Total distance traveled from Logger pro or from calculations (using pythagoras) 273.5 cm 295.3 cm 279.6 cm 283.0 cm 295.9 cm 272.6 cm 271.5 cm Total time (from regular camera) from hit to bounce on opposite side .717 s .702 s .700 s .784 s .708 s .752 s .650 s Ball's Velocity 3.81 m/s 4.21 m/s 3.99 m/s 3.648 m/s 4.18 m/s 3.625 m/s 4.18 m/s Ball's Mass 2.47 g 2.47 g 2.47 g 2.47 g 2.47 g 2.47 g 2.47 g Ball's Circumference 12.7 cm 12.7 cm 12.7 cm 12.7 cm 12.7 cm 12.7 cm 12.7 cm Speed of the sphere's rotation(Rotations per second X circumference) 5.29 m/s 4.23  m/s 4.53 m/s 4.89 m/s 5.79 m/s 5.30 m/s 4.89 m/s Speed the hand must be moving sideways to spin the ball that fast (same as above ) 5.29 m/s 4.23 m/s 4.53 m/s 4.89 m/s 5.79 m/s 5.30 m/s 4.89 m/s   Analysis

After gathering all of the data that we needed from the experimental procedure, we can now interpret what all of this means.First of all, we can graph a comparison chart from graphical analysis to see if there is any correlation between the rotations per second and the displacement from the center line.

As you can see from the graph, most of the data points are scattered and there seems to be a relatively low correlation between how fast the ball spins and how much it moves. This doesn't seem to strongly support our original thesis statement that the more revolutions per second, the more the ball will be displaced from the center line. However, such a conclusion makes sense.  As our graph shows, there is in fact a slight positive correlation between the rps and the displacement (the slope is calculated at 0.01), though we expected a steeper line. However, our test was designed to measure the ball's friction with the air. Such friction is minimal and thus doesn't have much of an effect on the direction of the ball in mid-air. Also, we must consider the possibility that Duncan's ping pong skills are not capable of spinning the ball fast enough to see a strong correlation. Indeed, most of a spin's effectiveness in confusing the opponent occurs when the ball hits the paddle, and not fluctuations in the ball's path. Thus we can conclude that the direction of the ball's path, when it is hit, corresponds to the angle of the paddle, and not the amount of spin on the ball. The effectiveness of the spin, thus, occurs when the ball hits the opponent's paddle. The ball travels along the paddle upon contact and goes in an unexpected direction than it would have without the spin.
However, our data can illuminate a number of other conclusions besides the spin versus displacement. First of all, by measuring the ball's circumference (rolling it on a piece of paper and measuring the line for a rotation), we can determine how fast the ball is spinning in meters per second. We do this by mulitplying the circumference in meters by the rotations per second. Knowing how fast the ball is rotating, we can calculate how fast the hand must have been moving for each trial when the ball was hit. Thus, for each trial, when the ball initially rolled against the paddle, the hand was moving as fast as calculated (assuming the ball did not lose much spin from the air).
Also, we have enough data to calculate the momentum, and kinetic energy of the ball during its flight. The mass of the ball, at 2.47 g X the velocity of the ball for each trial gives us the following table of momentum during the ball's flight. Also, the kinetic energy is given by 1/2mv^2. This also adds the table below. Note that the actual hitting of the ball was recorded with a regular camera, not the high speed so it is difficult to measure the time (and therefore the acceleration of the ball) to hit the ball, and thus to caculuate the force. However, with some careful measuring, we estimated that the ball remained on the paddle for 0.03 s. Thus we are able to determine the rest.

 Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Trial 7 Ball's Velocity (m/s) 3.81 4.21 3.99 3.648 4.18 3.625 4.18 Balls' Mass (g) 2.47 2.47 2.47 2.47 2.47 2.47 2.47 Momentum (velocity*mass) (kg*m/s) 0.0094107 0.0103987 0.0098553 0.00901056 0.0103246 0.00895375 0.0103246 Kinetic Energy (1/2 mv^2) 17.927384 21.8892635 19.6613235 16.43526144 21.578414 16.22867188 21.578414 Force (momentum/time) (N) 0.31369 0.346623333 0.32851 0.300352 0.344153333 0.298458333 0.344153333 Total Distance Traveled (cm) 273.5 295.3 279.6 283 295.9 272.6 271.5 Work (force*distance) (N-m) 0.8579422 1.023578703 0.91851396 0.84999616 1.018349713 0.813597417 0.9343763

Finally, given from the lab in class, we know that Brian Kaminski and Duncan Miller's reaction times were measured to approximately 0.3 s. Knowing this, and the length of the table at 9ft, we know that the ball must travel at least an average of 9.13 m/s to make such a smash unreturnable. Given that the ball stays on the paddle for 0.03 seconds, (using F=ma) it would take only 0.752 N of force (not including wind up an follow through) and a good aim to finish an opponent. Spin is just overkill.