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Experimental Baseball Physics

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Presentation on theme: "Experimental Baseball Physics"— Presentation transcript:

1 Experimental Baseball Physics
Alan M. Nathan webusers.npl.uiuc.edu/~a-nathan/pob Department of Physics University of Illinois Courtesy, Trey Crisco Courtesy, Dan Russell

2 The Baseball/Physics Connection
1927 Yankees: Greatest baseball team ever assembled MVP’s 1927 Solvay Conference: Greatest physics team ever assembled

3 Some Topics I Will Cover
The ball-bat collision The flight of the baseball

4 The Ball-Bat Collision
BBS = q vball + (1+q) vbat vball vbat BBS 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… q=0.20 q is collision efficiency Primary dependence of vf on ball, bat speeds is in the relationship…weaker dependence through e, which depends on rel ball-bat speed. q small implies 1+q>>q, so that vbat matters much more than vball Two mechanisms for losing energy: transfer energy to bat (r), dissipation (e) Inefficient collision (1 for superball on rigid wall, r=0,e=1) Bat speed matters much more than ball speed

5 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

6 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 Calculation but might as well be data. Independence allow measurement in lab

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
f1 = 179 Hz f2 = 582 Hz f3 = 1181 Hz f4 = 1830 Hz time frequency Note: nodes stack up at barrel end-->”sweet spot zone”

10 Vibrations, COR, and the “Sweet Spot”
Strike bat here at ~ node 2 vibrations minimized COR maximized BBS maximized best “feel” + e vf COR vs impact location E-vib vs impact location Vf vs impact location Response in handle vs impact location Sweet spot (feel): close to node 2 (hands insensitive to higher modes; hands are already at node 1) 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 “bounce”—confirmed by experiment …and higher BBS Also seen in golf, tennis, … Ask question: Which give more “power”: tighter strings or looser strings on tennis racket? Then ask (if they get it wrong): can a person bounce higher from a hardwood floor or from a trampoline? demo

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

13 Specify minimum MOI to limit bat speed
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 + (1+q) vbat

14 ~ [1/I6]n 0<n<0.5 n  0.3 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

15 Example: 34” Bats =q+1/2 102 mph MOI limit max vf BESR limit 97 mph typical wood 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/I6]n 0<n<0.5

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 Courtesy, Popular Mechanics
Flight of the Baseball Gravity Drag (“air resistance”) Lift (or “Magnus”) mg Fd FM Courtesy, Popular Mechanics Fd=½ CDAv2 Direction of Fd and Fl. Cd of order 0.5 FM = ½ CLAv CL = CMR/v direction leading edge is turning

21 Measuring Magnus Force Using High-Speed Motion Analysis
ATEC 2-wheel pitching machine Motion Analysis System Baseball with reflecting dot

22 Motion Analysis Geometry
Joe Hopkins ~15 ft

23 Motion Capture System: 10 Eagle-4 cameras 700 frames/sec
1/2000 shutter EVaRT 4.0 software Pitching Machine: project horizontally mph rpm

24 Typical Data and Fit Note: a>g, as expected for topspin
Magnus/Wt = 0.58

25 Results for Lift Coefficient
FL= 1/2ACLv2 S=r/v 100 mph, 2000 rpm S=0.17 Remove Adair curve Make better curve for rest of data 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
No evidence for a sharp drag crisis. mph

30 Using PITCHf/x to Classify Pitches Jon Lester, Aug 3, 2007 @ Seattle
spin axis Show something else LHP Catcher’s 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?

32 400 ft/30 ft Range=415-455 Time can resolve Calculations
See 4 s 5 s 7 s

33 From PITCHf/x to HITf/x Barry 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; =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 v>100 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)
Time gets distance; phase gets angle. Together, these determine position. Must need two angles, implying three receivers.

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 1

39 To have 10% HR’s, there must be a lot of near-HR’s 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
Delta = distance beyond fence (ft) ~4% per foot Tobin’s 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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