1. Modeling the Ball-Bat Collision
Alan M.
University of Illinois

2. Outline
1. Introduction 2. Physics-based collision model 3. Some interesting results 4. What’s Next?

3. 1. Introduction: The Goals
Primary: Use parameters of ball-bat contact to predict batted ball outcome
Contact: Bat speed, direction, orientation, location. Pitch speed, direction, spin rate & axis
Outcome: Exit velocity, launch angle, direction, spin rate & axis
Secondary: Reverse engineer to infer contact from outcome

4. 2. Creating a Physics-Based Model of Ball-Bat Collision
Philosophy: How to do “real-world” physics
Create a model for the collision
Constrain the model using fundamental principles
Determine unknown parameters from controlled experiments
Confront model with real-world data
Iterate as needed

5. 2. Creating a Physics-Based Model of Ball-Bat Collision
Additional philosophy on doing “real-world” physics
Simpify geometry to identify the essential physics
w/o extraneous details
Obtain model parameters
Then relax simplifying assumptions to examine realistic situations

6. 2. Creating a Physics-Based Model of Ball-Bat Collision
Simplfying assumptions
Hit ball off tee
Reduce to 2D geometry
NOTE: “offset” and “CL” are equivalent
attack angle AA
offset E
centerline angle CL
vbat

7. Experiment: Swing Bat on Stationary Ball; Measure EV,LA,spin
Click here for article AA E CL

8. Forces on Ball f vball vbat Normal force (N) acts along centerline
“normal COR” eN
Frictional force (f) acts tangential to surface
“tangential COR” eT
Launch angle lies between AA and CL
Backspin due to f
In absence of friction (f=0)
LA=CL
spin=0
EV=k*cos(CL-AA)
but closer to CL

9. Some Results from Experiment
EV largest when AA lines up with CL
“squared up”
~k*cos(CL-AA)
Spin depends on how AA and DA line up with CL
small when squared up
~c*sin(CL-AA)
LA depends mostly on CL (or offset) and less on AA N f
vbat
vball

10. Analogy with golf
In both cases, LA determined
mainly by CL

11. Final Words On Experiments
Experiments have taught us some important features regarding dependence of batted ball on CL and AA
They have also determined good values for the two unknown parameters: eN and eT
We can now proceed with confidence to a more realistic situation
Model should work well for most batted ball parameters
Exception: spin rate, which is sensitive to things omitted from model

12. More Realistic SituationAA
descent angle DA E CL
vpitch
vbat
Ball is moving
Velocity
Descent angle
Spin
Bat is oriented
Tilt out of horizontal plane
“tilt angle”
Rotated horizontally
“fan angle”
Altogether 4 angles

13. Some Observations There are 4 different independent variables
CL, AA, fan, tilt
There are 5 different dependent variables
EV, LA, SA, spin rate, spin axis
Many ways to display the data
I will show only a few

14. Observation 1 (fan=tilt=0):
Max EV when AA=CL AA
squared up
topspin
low spin
Spend lots of time here.
EV-CL: makes sense
Backspin, topspin
backspin

15. Observation 2 (fan=tilt=0):
Launch angle for max EV related to attack angle
A potential tool to study batter tendencies
AA=15
AA=5
AA=25

16. Example: Stanton vs. Gallo
Similar max EV ~ 116 mph
LA for peak EV very different ~ 50 vs. 220
different attack angle & HR/BB
wOBA=0.404
wOBA=0.522

17. 3: Attack Angle and Timing
Example: Joey Gallo
Attack Angle=190
Descent Angle=60
Bat Speed = 80 mph
Suppose mis-timed by ±3 ms ±4”
CL angle changes by ±200 (E by ±1”)
That’s huge!

18. Observation 4 (fan0, tilt=0):
EV is stronger function of LA than SA
Why the difference? AA CL
vbat
Note: Slope of EV vs AA is small; slope of spin vs AA is large.

19. line drives curve toward foul line
Observation 5 (fan0, tilt=0):
Origin of sidespin
Fan angle
line drives curve toward foul line
450
-450 00 f
Note: Slope of EV vs AA is small; slope of spin vs AA is large.
But balls hit up the middle slice. Why?

20. Tilt angle: converts backspin to sidespin
Origin of sidespin
Tilt angle: converts backspin to sidespin
Balls hit to CF slice to opposite field
Slice to opposite field > hook to pull field
Confirmed by Statcast
Tilt 00
300
Note: Slope of EV vs AA is small; slope of spin vs AA is large.

21. Summary
Physics-based model for ball-bat collision developed w/empirical parameters from experiments
Model qualitatively accounts for many observations from Statcast
EV, LA, spin axis
Spin rate more problematic
Future developments
Using motion analysis to develop model further
Figure out why spin rate overpredicted
Reverse engineer
Develop tools to analyze batter tendencies
Thanks to Lloyd Smith, Jeff Kensrud, Rawlings