Title: Experimental Baseball Physics
1Experimental 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
2The Baseball/Physics Connection
3Some Topics I Will Cover
- The ball-bat collision
- The flight of the baseball
4The 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
5Studies 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
6Independence 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
7Studies of the Collision Efficiency q
- Independent of end conditions
Vf (mph)
Courtesy, Keith Koenig
8q Field Study vs. Laboratory
Crisco, Smith, AMN
9Modal Analysis of a Baseball Bat www.kettering.edu
/drussell/bats.html
10Vibrations, 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
11Aluminum 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
12Softball Data and Model
Russell, Smith, AMN
Wood
change kbat
change kball
- Conclusions
- COR of Al bat can be significantly higher
- essential physics is understood
13Regulating Performance of Non-Wood BatsA
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
14Batting cage study show how bat speed depends on
I for college baseball players
aluminum
wood
Crisco, Greenwald, AMN
Other studies show bat speed independent of M for
fixed I
15Example 34 Bats
q1/2
All bats below horizontal line and to right of
vertical line are allowed
16What About Corked Bats?or..What was Sammy
thinking?
no trampoline effect!
- Conclusion
- No increase in BBS
- increase in swing speed
- decrease in collision efficiency
17What About Juiced Baseballs?
Conclusion No evidence for juiced ball
18Putting 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
19High-Speed VersionWork in Progress
20Flight of the Baseball
- Gravity
- Drag (air resistance)
- Lift (or Magnus)
21Measuring Magnus Force Using High-Speed Motion
Analysis
22Motion 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
24Typical Data and Fit
25Results 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
26The PITCHf/x Tracking SystemA Quantitative Tool
to Study Pitched Baseball Trajectories
27How 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
28Example Bonds 756
29Example Drag and Drag Coefficients20k pitches
from Anaheim, 2007
30Using PITCHf/x to Classify PitchesJon 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
31How 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?
32Calculations
400 ft/30 ft Range415-455 Time can resolve
See www.hittrackeronline.com
4 s
5 s
7 s
33From PITCHf/x to HITf/xBarry 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)
34Baseball AerodynamicsThings 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?
35Trackman The Wave of the Futuresee
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
36Trackman Radar
- Monopulse Principle (Phase)
37thanks to Fredrik Tuxen, CTO of Trackman
38Steroids and Home Run Productonsee 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
39Elite hitters HR/BBIP 10
Thanks to Roger Tobin
40Change 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
41Home Run Distances, 2007 www.hittrackeronline.com
4 per foot
Tobins Conclusion increase of BBS by few mph
can increase HR rate by 30-50!
42Work 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