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Experimental Baseball Physics. Alan M. Nathan a-nathan@uiuc.edu webusers.npl.uiuc.edu/~a-nathan/pob Department of Physics University of Illinois. Courtesy, Trey Crisco. Courtesy, Dan Russell. 1927 Yankees: Greatest baseball team ever assembled. 1927 Solvay Conference :
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Experimental Baseball Physics Alan M. Nathan a-nathan@uiuc.edu webusers.npl.uiuc.edu/~a-nathan/pob Department of Physics University of Illinois Courtesy, Trey Crisco Courtesy, Dan Russell
1927 Yankees: Greatest baseball team ever assembled 1927 Solvay Conference: Greatest physics team ever assembled MVP’s The Baseball/Physics Connection
Some Topics I Will Cover • The ball-bat collision • The flight of the baseball
The Ball-Bat Collision vball vbat BBS q=0.20 BBS = q vball + (1+q) vbat z • e:“coefficient of restitution” 0.50 • (energy dissipation—mainly in ball, some in bat) • r mballz2/I6 :bat recoil factor = 0.25 • (momentum and angular momentum conservation) • ---heavier is better but…
Studies of the Collision Efficiency q • Independent of reference frame • Measure in bat rest frame: q=vf/vi • Use q to predict field performance Sports Sciences Laboratory, Washington State University
Independence of End Conditions • strike bat in barrel—look 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
Studies of the Collision Efficiency q • Independent of end conditions Vf (mph) Courtesy, Keith Koenig
q: Field Study vs. Laboratory Crisco, Smith, AMN
f1 = 179 Hz f3 = 1181 Hz f2 = 582 Hz f4 = 1830 Hz frequency time Modal Analysis of a Baseball Bat www.kettering.edu/~drussell/bats.html
Vibrations, COR, and the “Sweet Spot” Strike bat here at ~ node 2 vibrations minimized COR maximized BBS maximized best “feel” + e vf Evib Note: COP is irrelevant to feel and performance
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 “bounce”—confirmed by experiment • …and higher BBS • Also seen in golf, tennis, … demo
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
Regulating Performance of Non-Wood Bats:A Science-Based Approach Used by NCAA BBS = q vball + (1+q) vbat • 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
Batting cage study show how bat speed depends on I for college baseball players • ~ [1/I6]n 0<n<0.5 n 0.3 aluminum wood Crisco, Greenwald, AMN Other studies show bat speed independent of M for fixed I
102 mph max vf 97 mph BESR limit typical wood MOI limit Example: 34” Bats =q+1/2 All bats below horizontal line and to right of vertical line are allowed
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/I6]n 0<n<0.5
What About Juiced Baseballs? Conclusion: No evidence for juiced ball
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
FM Fd Fd=½ CDAv2 mg FM= ½ CLAv2 CL = CMR/v Courtesy, Popular Mechanics direction leading edge is turning Flight of the Baseball • Gravity • Drag (“air resistance”) • Lift (or “Magnus”)
Motion Analysis System ATEC 2-wheel pitching machine Baseball with reflecting dot Measuring Magnus Force Using High-Speed Motion Analysis
~15 ft Joe Hopkins Motion Analysis Geometry
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
Results for Lift Coefficient FL= 1/2ACLv2 S=r/v 100 mph, 2000 rpm S=0.17 Conclusions: --data qualitatively consistent (~20%) --RKA model inconsistent with data
The PITCHf/x Tracking SystemA Quantitative Tool to Study Pitched Baseball Trajectories
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
drag/W=1@~90 mph Example: Drag and Drag Coefficients20k pitches from Anaheim, 2007
Using PITCHf/x to Classify PitchesJon Lester, Aug 3, 2007 @ Seattle spin axis LHP Catcher’s View I: 4-seam fastball II: Slider (?) III: 2-seam fastball IV: Curveball break direction = -90o
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?
Calculations 400 ft/30 ft Range=415-455 Time can resolve See www.hittrackeronline.com 4 s 5 s 7 s
From PITCHf/x to HITf/xBarry Bond’s 756th Home Run • PITCHf/x data tracked hit ball over first 20 ft • Precision measurement of endpoint and time-of-flight • Inferred: v0=112 mph; =270 up; =160to right of dead center; =1186 rpm (backspin) and 189 rpm (sidespin, breaking to center)
Baseball Aerodynamics:Things I would like to know better • Better data on drag • “drag crisis”? • spin-dependent drag? • drag for v>100 mph • Dependence of drag & Magnus on seam orientation, surface roughness, … • Is the spin constant?
Trackman: 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
Monopulse Principle (Phase) Trackman Radar
Steroids 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
To have 10% HR’s, there must be a lot of near-HR’s Elite hitters: HR/BBIP = ~10% Thanks to Roger Tobin
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
Home Run Distances, 2007 www.hittrackeronline.com Delta = distance beyond fence (ft) ~4% per foot Tobin’s Conclusion: increase of BBS by few mph can increase HR rate by 30-50%!
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