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Experimental Baseball Physics

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Experimental Baseball Physics Alan M. Nathan a-nathan_at_uiuc.edu webusers.npl.uiuc.edu/~a-nathan/pob Department of Physics University of Illinois Courtesy, Trey Crisco – PowerPoint PPT presentation

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Title: Experimental Baseball Physics


1
Experimental Baseball Physics
Alan M. Nathan a-nathan_at_uiuc.edu webusers.npl.uiuc
.edu/a-nathan/pob Department of
Physics University of Illinois
Courtesy, Trey Crisco
Courtesy, Dan Russell
2
The Baseball/Physics Connection
3
Some Topics I Will Cover
  • The ball-bat collision
  • The flight of the baseball

4
The Ball-Bat Collision
BBS q vball (1q) vbat
z
e coefficient of restitution ? 0.50
(energy dissipationmainly in
ball, some in bat) r ? mballz2/I6 bat recoil
factor ? 0.25 (momentum and angular momentum
conservation) ---heavier is better but
5
Studies of the Collision Efficiency q
  • Independent of reference frame
  • Measure in bat rest frame qvf/vi
  • Use q to predict field performance

Sports Sciences Laboratory, Washington State
University
6
Independence of End Conditions
  • strike bat in barrellook at response in handle
  • handle moves only after 0.6 ms delay
  • collision nearly over by then
  • nothing on knob end matters
  • size, shape
  • boundary conditions
  • hands!
  • confirmed experimentally

7
Studies of the Collision Efficiency q
  • Independent of end conditions

Vf (mph)
Courtesy, Keith Koenig
8
q Field Study vs. Laboratory
Crisco, Smith, AMN

9
Modal Analysis of a Baseball Bat www.kettering.edu
/drussell/bats.html
10
Vibrations, COR, and the Sweet Spot
at node 2 vibrations minimized COR
maximized BBS maximized best feel

e
vf
Evib
Note COP is irrelevant to feel and performance
11
Aluminum Bats and the Trampoline Effect A
Simple Physical Picture
  • Two springs mutually compress each other
  • KE ? PE ? KE
  • PE shared between ball spring and bat spring
  • sharing depends on kball/kbat
  • PE in ball mostly dissipated (80!)
  • PE in bat mostly restored
  • Net effect less overall energy dissipated
  • ...and therefore higher ball-bat COR
  • more bounceconfirmed by experiment
  • and higher BBS
  • Also seen in golf, tennis,

demo
12
Softball Data and Model
Russell, Smith, AMN
Wood
change kbat
change kball
  • Conclusions
  • COR of Al bat can be significantly higher
  • essential physics is understood

13
Regulating Performance of Non-Wood Bats A
Science-Based Approach Used by NCAA
  • Specify maximum q
  • approx. same as for wood bats of similar wt.
  • implies bats swung alike will perform alike
  • Specify minimum MOI to limit bat speed
  • smaller than wood
  • Together, these determine a maximum BBS
  • gap between wood and aluminum ? 5
  • does that mean aluminum should be banned?
  • an issue many are struggling with

BBS q vball (1q) vbat
14
Batting cage study show how bat speed depends on
I for college baseball players
  • 1/I6n
  • 0ltnlt0.5
  • n ? 0.3

aluminum
wood
Crisco, Greenwald, AMN
Other studies show bat speed independent of M for
fixed I
15
Example 34 Bats
q1/2
All bats below horizontal line and to right of
vertical line are allowed
16
What About Corked Bats? or..What was Sammy
thinking?
no trampoline effect!
  • Conclusion
  • No increase in BBS
  • increase in swing speed
  • decrease in collision efficiency
  • 1/I6n
  • 0ltnlt0.5

17
What About Juiced Baseballs?
Conclusion No evidence for juiced ball
18
Putting spin on the ball Low speeds
no spin
topspin
backspin
Cross AMN
  • Conclusions
  • slide-then-roll model approximately works
  • curveball is hit with more backspin than fastball

19
High-Speed Version Work in Progress
20
Flight of the Baseball
  • Gravity
  • Drag (air resistance)
  • Lift (or Magnus)

21
Measuring Magnus Force Using High-Speed Motion
Analysis
22
Motion Analysis Geometry
23
  • Motion Capture System
  • 10 Eagle-4 cameras
  • 700 frames/sec
  • 1/2000 shutter
  • EVaRT 4.0 software
  • www.motionanalysis.com
  • Pitching Machine
  • project horizontally
  • 50-110 mph
  • 1500-4500 rpm

24
Typical Data and Fit
25
Results for Lift Coefficient
FL 1/2?ACLv2 Sr?/v 100 mph, 2000
rpm ?S0.17
Conclusions --data qualitatively consistent
(20) --RKA model inconsistent with data
26
The PITCHf/x Tracking System A Quantitative Tool
to Study Pitched Baseball Trajectories
27
How Does PITCHf/x Work?
  • Two video cameras track baseball in 1/60-sec
    intervals
  • usually high home and high first
  • third CF camera used establishes ht. of strike
    zone
  • Pattern-recognition software to identify blobs
  • Camera calibration to convert pixels to (x,y,z)
  • 9-parameter fit to trajectory
  • constant acceleration for x(t),y(t),z(t)
  • Use fit to calculate lots of stuff
  • The full trajectory
  • The break
  • Drag and Magnus forces

28
Example Bonds 756
29
Example Drag and Drag Coefficients 20k pitches
from Anaheim, 2007
30
Using PITCHf/x to Classify Pitches Jon Lester,
Aug 3, 2007 _at_ Seattle
spin axis
LHP Catchers View
I 4-seam fastball II Slider (?) III 2-seam
fastball IV Curveball
break direction ?-90o
31
How Far Did That Home Run Travel?
  • Ball leaves bat
  • Hits stands D from home plate, H above ground
  • How far would it have gone if no obstruction?

32
Calculations
400 ft/30 ft Range415-455 Time can resolve
See www.hittrackeronline.com
4 s
5 s
7 s
33
From PITCHf/x to HITf/x Barry Bonds 756th Home
Run
  • PITCHf/x data tracked hit ball over first 20 ft
  • Precision measurement of endpoint and
    time-of-flight
  • Inferred v0112 mph ?270 up ?160 to right
    of dead center ?1186 rpm (backspin) and 189 rpm
    (sidespin, breaking to center)

34
Baseball Aerodynamics Things I would like to
know better
  • Better data on drag
  • drag crisis?
  • spin-dependent drag?
  • drag for vgt100 mph
  • Dependence of drag Magnus on seam orientation,
    surface roughness,
  • Is the spin constant?

35
Trackman The Wave of the Future see
www.trackmangolf.com
  • Doppler radar to measure radial velocity
  • 3-detector array to measure phase
  • two angles
  • Sidebands gives spin magnitude
  • Result
  • in principle, full trajectory can be
    reconstructed, including spin and spin axis
  • already in use for golf, currently being adapted
    for baseball

36
Trackman Radar
  • Monopulse Principle (Phase)

37
thanks to Fredrik Tuxen, CTO of Trackman
38
Steroids and Home Run Producton see Roger Tobin,
AJP, Jan. 2008
  • Steroids increases muscle mass
  • Increased muscle mass increases swing speed
  • Increased swing speed increase BBS
  • Increased BBS means longer fly balls
  • Longer fly balls means more home runs

39
Elite hitters HR/BBIP 10
Thanks to Roger Tobin
40
Change in range distribution when batted ball
speed increased by 3
Baseline
3 change in BBS gives 50 increase in HR rate!
3 speed increase
Thanks to Roger Tobin
41
Home Run Distances, 2007 www.hittrackeronline.com
4 per foot
Tobins Conclusion increase of BBS by few mph
can increase HR rate by 30-50!
42
Work in Progress
  • Collision experiments calculations to elucidate
    trampoline effect
  • New studies of aerodynamics using Trackman and
    PITCHf/x
  • Experiments on high-speed oblique collisions
  • A book, with Aussi Rod Cross

Thanks for the invitation and your attention
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