1. The Science of Baseball Alternative models
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The Science of Baseball Alternative models
A. Terry Bahill
Emeritus Professor of
Systems Engineering
University of Arizona
©, , Bahill

2. Reference
Terry Bahill, The Science of Baseball: Modeling Bat-Ball Collisions and the Flight of the Ball, Springer Nature, NY, NY, 2018
Chapters 5

3. State the problem 4/25/2019 © 2017 Bahill 4/25/2019
Begin with the end in mind
Steven Covey and Omega Alpha Association
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4. Product Position Statement
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Product Position Statement
For engineers and students of the science of baseball, who want to understand bat-ball collisions and the flight of the ball, this book The Science of Baseball presents equations for the speed and spin of the bat and ball after the collision in terms of those same four variables before the collision.
Unlike existing books on the physics of sports, this book uses only simple Newtonian axioms and the conservation laws. It also contains alternative models for bat-ball collisions and the flight of the ball.
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7. Alternative models
Purpose: This module will present four alternatives to the BaConLaw model and explain why each might be used for a different purpose.
BaConLaw model
Effective Mass model
Sliding Pin model
Spiral Center of Mass model
Collision with Friction model
Ball in Flight model
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8. Modeling
This book is about modeling and simulation of bat-ball collisions and the flight of the ball.
A model is a simplified representation of some aspect of a real system.
A simulation is an implementation of a model, often on a digital computer.
Models are ephemeral: they are created, they explain a phenomenon, they stimulate discussion, they foment alternatives and then they are replaced by new models.
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9. BaConLaw model
Fundamental axiom for the BaConLaw model is a free-end collision.
The bat acts as if no one is holding onto its knob.
Imagine the bat laying on a sheet of ice and you are looking down on top of it.
Then a baseball slams into the bat at 80 mph.
This collision produces a translation and a rotation of the bat about its center of mass.
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10. Coefficient of restitution
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11. Kinetic energy lost
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12. The input/output equations
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13. Simplified equations
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14. Rule of thumb
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15. Effective mass model Assume a free-end collision
Purpose: This section presents the bat Effective Mass model, which is the most popular physics model for bat-ball collisions.
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16. Batted-ball speed
Using the coefficient of restitution and conservation of linear momentum yields
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17. Simplified batted-ball speed
Compare this to the BaConLaw model
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18. Spiral center of mass model
This model is for the swing of the bat
The BaConLaw and Effective Mass models are only for the collision
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19. New type of data
Recent studies of bat and ball speed have used multiple video cameras and commercial prepackaged software to measure and compute bat speed
These computer-camera system overlay pitch trajectories on television replays
On television, the batted-ball speed is often called the exit speed, the exit velocity or the launch speed
Instead of computing the speed and rotation of the center of mass of the bat, as in the free-end collision models, they compute the speed of the knob of the bat
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20. Linear, angular and total bat speeds for 20,000 swings by male professional batters
Variable
SI units
Baseball units
Linear knob speed,
4.5 m/s,
10.1 mph,
Angular rotation speed,
41 rad/s,
387 rpm,
Total speed at the center of mass
27.9 m/s,
62.3 mph,
Total speed at the sweet spot
33.3 m/s,
74.5 mph,
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21. Sliding pin model Not a free-end collision
Batter is holding the knob end
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22. Sliding pin joint
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23. Purpose The Sliding Pin model models a new type of data
Previously the input data were the translational and rotational velocities at the center of mass of the bat.
The Sliding Pin model will use the translational and rotational velocities at the knob.
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24. A new coefficient of restitution
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25. The input/output equations
The 14 page derivation process is the same as for the
BaConLaw model.
The equations may look the same, but they are different.
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26. Simplified equations
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27. Sliding Pin simulation
SI units (m/s, rad/s)
Baseball units (mph, rpm)
Inputs
-37.1
-83.0
209
2000
4.5 10 41
387
0.453 
0.453
Outputs
37.2
83.4 -7
-17 18
175
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29. Comparison of Sliding Pin and BaConLaw models
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Comparison of Sliding Pin and BaConLaw models
Sliding Pin model 
SI units (m/s, rad/s)
Baseball units (mph, rpm)
Inputs
-37.1
-83.0
209
2000
4.5 10 41
387
 0.453
0.453
Outputs
37.2
83.4 -7
-17 18
175
 BaConLaw model
SI units
Baseball units
Inputs
-37
-83
209
2000 23 52 32
309 28 62
 0.465
0.465
Outputs 41 92 11 24 1 7
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30. Collision with friction
Newton’s axioms and Conservation of Momentum
both yield the same equation
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31. Purpose
To present the Collision with Friction model, which our modeling technique can not handle, because our model is only good for a point before the collision and a point after the collision.
It cannot handle behavior during the collision.
The first purpose of this book
to show a complex configuration for which our technique works. The BaConLaw model did this.
to show a configuration for which our technique does not work. The Collision with Friction model does this.
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32. Collision with Friction model
SI units (m/s or rad/s)
Baseball units, mph or rpm
Inputs
-37
-83 28 62
Results
209
2000
222
2126 13
126
-209
-2000
-196
-1874
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33. Actual bat-ball collision
We assumed that the ball slides across the bat
However, it could slip, slide, roll or grip the bat
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34. Summary of Collision with Friction model
Although the equations are consistent, the model is not valid because behavior during the collision is unknown.
Our model is only good for a point before and a point after the collision. It is not valid during the collision.
The BaConLaw model fulfilled part of a purpose of this book: it showed a the most complex configuration for which our technique works.
The Collision with Friction model completed the fulfillment of this purpose by showing a configuration for which our technique was too simple.
This is an important section because few studies show failures. In this section, I show a failure. I tried to model an event, but was unsuccessful. Then I explain why I was unsuccessful.
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35. Summary
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36. BaConLaw model The BaConLaw model assumes a free-end collision
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37. Effective mass model Assumes a free-end collision 4/25/2019
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38. Spiral center of mass model
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39. New type of data Variable SI units Baseball units Linear knob speed,
4.5 m/s,
10.1 mph,
Angular rotation speed,
41 rad/s,
387 rpm,
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40. Sliding pin model
Not a free-end collision
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41. Actual bat-ball collision
We assumed that the ball slides across the bat
However, it could slip, slide, roll or grip the bat
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42. Collision with friction
This collision cannot be modeled using only Newton’s
axioms and the Conservation of Momentum
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