1. Can a curveball be hit farther than a fastball? Some Aerodynamics mg Fd FL (Magnus)  Drag: Fd = ½ CDAv2 “Lift”: FL = CMARv (in direction leading edge is turning) CD, CM ~ 0.2-0.5 NSBP Meeting, February 18, 2005

Measurements of Lift and Drag Joe Hopkins, Lance Chong, Hank Kaczmarski, AMN Motion Capture System Two-wheel pitching machine Baseball with reflecting dot NSBP Meeting, February 18, 2005

Experiment: MoCap Data y z y = ½ ayt2 topspinay>g NSBP Meeting, February 18, 2005

Effect of Spin on Baseball Trajectory 77’ Hubbard: CL based on wind tunnel and other experimental data Adair: Lift is “differential drag”lift is small whenever drag is not changing much with v (such as near 100 mph) All calculations done assuming no spin-dependent drag and constant angular velocity of ball (no “spin-down”). Lift … scales approx. linearly with  has major effect on trajectory NSBP Meeting, February 18, 2005

Oblique Collisions: Putting Spin on the Ball Sliding friction … reduces transverse velocity increases  sliding-to-rolling transition Results Balls hit to left/right break toward foul line Topspin gives tricky bounces in infield Pop fouls behind the plate curve back toward field Backspin keeps fly ball in air longer f NSBP Meeting, February 18, 2005

Undercutting the ball  backspin Ball100 downward Bat 100 upward D = center-to-center offset trajectories Undercut too much: popup with lots of backwpin Undercut too little: low trajectory with little backspin More friction does not help NSBP Meeting, February 18, 2005

Fastball: spin reverses Curveball: spin doesn’t reverse   larger for curveball Undercut too much: popup with lots of backwpin Undercut too little: low trajectory with little backspin More friction does not help NSBP Meeting, February 18, 2005

In summary…. Can a curveball be hit farther than a fastball? Higher pitch speed  higher hit ball speed on fastball But…more backspin on curve ball Net result: curveball goes farther by a little bit Mont Hubbard, AJP 71, 1152-1162 (2003) See also February 2005 issue of AJP for a debate: Hubbard vs. Adair NSBP Meeting, February 18, 2005

Physics Description of Ball-Bat Collision forces large (>8000 lbs!) time is short (<1/1000 sec!) ball compresses, stops, expands bat compresses ball ball bends/compresses bat lots of energy dissipated distortion of ball vibrations in bat ball-bat COR related to energy dissipation why is aluminum better? Courtesy of CE Composites NSBP Meeting, February 18, 2005

NSBP Meeting, February 18, 2005

Wood versus Aluminum Aluminum has thin shell Less mass in barrel easier to swing and control  but less effective at transferring energy  Hoop modes trampoline effect larger COR  This summarizes the important properties of bats NSBP Meeting, February 18, 2005

The “Trampoline” Effect: A Simple Physical Picture Two springs mutually compress each other KE  PE  KE PE shared between “ball spring” and “bat spring” 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” 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? NSBP Meeting, February 18, 2005

“Trampoline” Effect tennis ball/racket strings Softball/bat DEMO: DEAD BALL ON FLOOR, bongo paddle SUPERBALL ON FLOOR,bongo paddle The issue: springiness of surface. Bat compresses ball, ball compresses bat--same size force--which one gives depends on how easily compressed. NCAA: e<.228 Wood bat, for given force, compresses 2% of ball. Or…only 2% of energy in collision is stored in bat, rest is in ball. Makes no difference how much of energy stored in bat is returned Al bat: 10% in COR==>7 mph==>35’ or more Just like tennis racket....looser strings gives a higher ball speed! All sorts of tricks.....thinner wall..etc. More later. new rule changes in NCAA: e<.228 Better bat: a tennis racket Better ball: spherical metallic shell NSBP Meeting, February 18, 2005

Experimental Modal Analysis Impact hammer (force transducer) 35 points along length Accelerometer fixed location on barrel FFT Analyzer Frequency Response Function (accel / force) Dan Russell, Kettering U. NSBP Meeting, February 18, 2005

Hoop Modes of Hollow Bats Lowest hoop mode… --that annoying “ping” --“trampoline effect” NSBP Meeting, February 18, 2005

COR correlated with fhoop Energy left in hoop vibrations... Wood bat ~30’ on long fly ball Each .01 of COR1.6/1.25 in vf, or 1.3 mph6’ on fly ball Courtesy of Dan Russell www.kettering.edu/~drussell/bats NSBP Meeting, February 18, 2005

Summary: Why Does Aluminum Outperform Wood? Trampoline effect reduces energy dissipation More pop Longer fly ball NSBP Meeting, February 18, 2005

Final Summary Physics of baseball is a fun application of basic (and not-so-basic) physics Check out my web site if you want to know more www.npl.uiuc.edu/~a-nathan/pob a-nathan@uiuc.edu Go Red Sox! NSBP Meeting, February 18, 2005