1 Baseball & Physics: An Intersection of Passions Alan M. Nathan Department of Physics University of Illinois

2 Is this heaven? No, it’s …. Iowa Dyersville, home of the Field of Dreams In my younger days….

But now I just watch and enjoy… …and there’s been a lot to enjoy lately….

4 A good book to read…. “Our goal is not to reform the game but to understand it.” “The physicist’s model of the game must fit the game.” My mentor, Prof. Bob Adair

5 And check out my web site… webusers.npl.uiuc.edu/~pob/a-nathan

6 The Physics of Hitting a Home Run How does a baseball bat work? The flight of a baseball. Leaving the no-spin zone. Putting it all together. And what’s the deal with steroids?

7 “Hitting is timing; pitching is upsetting timing” Hitting the Baseball: the most difficult feat in sports “Hitting is fifty percent above the shoulders” 1955 Topps cards from my personal collection

8 Graphic courtesy of Bob Adair and NYT Hitting and Pitching, Thinking and Guessing

9 “You can observe a lot by watching” Champaign News-Gazette UMass/Lowell --Yogi Berra Easton Sports

10 When ash meets cowhide…. forces large, time short – >8000 lbs, <1 ms ball compresses, stops, expands – like a spring: KE  PE  KE – bat recoils lots of energy dissipated (“COR”) – distortion of ball – vibrations in bat to hit home run…. –large batted ball speed 105 mph  ~400 ft, each additional mph ~ 5-6’ –optimum take-off angle ( ) –lots of backspin

11 What Determines BBS? pitch speed bat speed “collision efficiency”: a property of the ball and bat my only formula BBS = q v pitch + (1+q) v bat typical numbers: q = q = 1.2 example: gives 102 mph (~400”) v bat matters much more than v pitch ! –Each mph of bat speed worth ~6 ft –Each mph of pitch speed worth ~1 ft

12 What does q depend on? 1. Weight of bat in the barrel –Heavier bat more efficient larger q; less recoil to bat –Heavier bat has smaller v bat (usually) –What is ideal bat weight? effect of bat weight on q is easy effect of bat weight on v bat is harder BBS = q v pitch + (1+q) v bat

13 Is There an Advantage to “Corking” a Bat? Based on best experimental data available: …for home run distance: no …for home run frequency: maybe Sammy Sosa, June 2003

14 What does q depend on? 2. Bounciness of ball –“coefficient of restitution” or COR –COR 2 = rebound ht/initial ht –~0.5 for baseball demo

15 What does q depend on? 3.Impact location on bat outside inside sweet spot

16 Vibrations and Broken Bats movie pitcher catcher

17 Aluminum has thin shell –Less mass in barrel --higher bat speed, easier to control --but less effective at transferring energy  --for many bats  cancels »just like corked wood bat –“Hoop modes” trampoline effect “ping” Does Aluminum Outperform Wood? demo YES!

18 Additional Remarks on q can be measured in the lab – regulate non-wood bats (NCAA, ASA, …) “end conditions” don’t matter –Not even the batter’s hands!

19 Aerodynamics of Baseball in Flight Gravity Drag (“air resistance”) “Magnus” force on spinning baseball mg F drag F Magnus 

20 Real vs. “Physics 101” Trajectory: Effect of Drag Reduced distance on fly ball Reduction of pitched ball speed by 8-10 mph Asymmetric trajectory: –Total Distance  1.7 x distance at apex Optimum home run angle ~30 o -35 o

21 Some Effects of Spin Backspin makes ball rise –“hop” of fastball – undercut balls: increased distance, reduced optimum angle of home run Topspin makes ball drop – “12-6” curveball – topped balls nose-dive Breaking pitches due to spin –Cutters, sliders, etc. mg F drag F Magnus 

22 Does a Fastball Rise? Can a ball thrown horizontally rise? Is there a net upward acceleration? Can Magnus force exceed gravity? For this to happen… backspin must exceed 4000 rpm >25 revolutions not physically possible mg F drag F Magnus 

23 What’s the Deal with the Gyroball? Courtesy, Ryutaro Himeno Daisuke Matsuzaka: Does he or doesn’t he? Definitely maybe!

24 What’s the Deal with Denver? High altitude, reduced air density (80% of sea level) –Reduced drag: increases distance –Reduced lift: decreases distance Net effect: –Fly balls travel ~5% farther

25 Leaving the No-Spin Zone

26 Oblique Collisions: Leaving the No-Spin Zone Oblique  friction  spin Familiar Results: Balls hit to left/right break toward foul line Topspin gives tricky bounces in infield Backspin keeps fly ball in air longer Tricky popups to infield

27 Another familiar result: Catcher’s View bat hits under ball: popup to opposite field bat hits over ball: grounder to pull field bat tilted downward

28 Undercutting the ball  backspin Ball10 0 downward Bat 10 0 upward D = center-to-center offset trajectories “vertical sweet spot” What’s this all about?

29 Bat-Ball Collision Dynamics – A fastball will be hit faster – A curveball will be hit with more backspin Aerodynamics – A ball hit faster will travel farther – Backspin increases distance Which effect wins? –Curveball, by a hair! –But I wouldn’t bet the farm on it! Can curveball be hit farther than fastball?

30 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 Steroids and Home Run Producton see Roger Tobin, AJP, Jan. 2008

31 To have 10% HR’s, there must be a lot of near-HR’s Elite hitters: HR/BBIP = ~10% Thanks to Roger Tobin

32 Change in range distribution when batted ball speed increased by 3%: 3% change in BBS gives 50% increase in HR rate! Baseline 3% speed increase Thanks to Roger Tobin

33 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 – Thanks for your attention and go Red Sox!