## The Physics of Baseball Argonne National Laboratory 19 July 2006 Porter W Johnson Illinois Institute of Technology ABSTRACT

Baseball is our national sport, and it also has broad international appeal. It is by far the oldest organized professional sport. Its development reflects the history of our nation, as well our increasing technological sophistication. The application of physical principles to baseball is considered. Dynamical issues in pitching, hitting, fielding, and running will be examined.

A Few Important Parameters
• The Baseball
1. Mass: 0.15 kilograms
2. Diameter: 0.1 meters
3. Force of gravity: 1.2 Newtons (down)
4. Force of air resistance (ignore rotation, seams, etc):
opposite direction to velocity & proportional to air density
1. Below 25 meters/sec
laminar flow: F proportional to v
2. 25-40 meters/sec: linear in v
3. above 40 meters/sec quadratic in v
4. Air resistance balances gravity
40 meters/sec / terminal speed
• The Bat
1. Single solid piece of hardwood, non-laminated
2. Mass: 0.85 - 1.25 kilograms
3. Length: 0.80-0.95 meters
• The Field
1. Pitcher-Batter: 18 meters
2. Base-to-base: 28 meters
3. Home Run distances (typical): 90 - 120 meters
• Various Speeds
1. Speed of Pitched ball: 30 - 45 meters/sec
2. Speed of Hit ball: 0 - 60 meters/sec
3. Rotational speed: (pitcher): 0 - 3000 rpm
4. Rotational speed: (batter): 0 - 5000 rpm
5. Speed of runners: up to 10 meters/sec
• Various Times
1. Travel from pitcher to batter: 0.45 - 0.60 sec
2. Runner from base to base: 3-4 sec
3. Time of flight of baseball: 0 - 6 sec
• Various Distances
1. Maximum pop-up height: 50 meters
2. Maximum hit distance: 150 meters
3. Maximum throw by outfielder: 100 meters
• Weather and Geography: P = r  R T / M
Only  r  matters:  so the ball travels further at
1. High temperature (Phoenix)
2. Low atmospheric pressure (Denver)
3. High relative humidity (H20 displaces N2)
Highlights in the History of Baseball
 1839 Alexander Doubleday allegedly invented baseball in Cooperstown New York 1865 Overhand pitching legalized 1876 National League organized 1900 American League organized World Series begun 1919 Chicago White Sox scandal 1920 “Live ball” era “Spitball” banned 1927 Babe Ruth hits 60 home runs in a season 1932 Leagues adopt common baseballs 1935 Night baseball begun 1941 Joe DiMaggio hits safely in 56 consecutive games 1947 Jackie Robinson plays for Brooklyn Dodgers 1961 Roger Maris hits 61 home runs in extended season 1962 Maury Wills steals 104 bases in a season, breaking Ty Cobb’s record of 97 1971 Cowhide substituted for horsehide on baseballs 1972 American Leagues adopts “designated hitter” rule 1984 Pete Rose breaks Ty Cobb’s lifetime record of 4189 hits. (4256 total) 1998 Sammy Sosa and Marc McGwire break Ruth’s Home Run record 2000 Leagues adopt common standards and training programs for umpires 2001 Barry Bonds hits home run #73, averaging one per 6.5 at-bats 2004 Ichiro Suzuki gets 258 hits in a season, breaking George Sisler's 1920 record of 257 hits
For information on the cultural roots of baseball, see the website
http://www.britannica.com/original?content_id=1506&pager.offset=1

Other Sports
• Cricket (batsman, hurler, wicket)
• Soccer (banana kick, archaic refereeing)
• Tennis (collision more elastic)
• Golf (top spin; friendly to technology)
• Frisbee (the people's sport)
• Softball (windmill windup in fast pitch grapefruit game)
• Badminton (why is this here?)
• Lacrosse

Results of World Baseball Tournament: held  03 - 20 March 2006

• First: Japan
• Second: Cuba
• Third-Fourth: Mexico, Korea
• Fifth-Eight: Dominican Republic, Puerto Rico, United States, Venezuela
• Other: Australia, Canada, China, Chinese Taipei, Italy, Netherlands, Panama, South Africa,

Pitching

The pitcher stands less than 20 meters from the batter, and throws the ball at speeds of around 40 meters/sec. In that time the ball drops from its "straight line" path by about 1.2 meters.

Because of the stitches on the baseball there is considerable turbulence affecting its motion, and it may behave somewhat erratically. The complications in the motion of the ball arise from the Prandtl Layer of air that moves with the baseball, and which has a dominating effect on the motion of the ball.

The pitcher may put considerable spin on the baseball, corresponding to about 20 revolutions over its path.

A few pitchers have been able to perfect the knuckleball, which hardly spins at all, and which drifts somewhat arbitrarily in its motion.

Ty Cobb's remembrance of his introduction to Walter Johnson:

"On August 2, 1907, I encountered the most threatening sight I ever saw in the ball field. He was only a rookie, and we licked our lips as we warmed up for the first game of a doubleheader in Washington. Evidently, manager Pongo Joe Cantillon of the Nats had picked a rube out of the cornfields of the deepest bushes to pitch against us. ...

The first time I faced him I watched him take that easy windup-and then something went past me that made me flinch. The thing just hissed with danger. We couldn't touch him...every one of us knew we'd met the most powerful arm ever turned loose in a ball park."

Batting

The batter has about 0.5 seconds to gauge the path of a pitch, and the bat must be at the right place [within about 1 cm] at the right time [within 0.01 seconds] to make solid contact.

The bat-ball collision lasts typically for 0.001 seconds, and the average force on this ball is of order 10,000 Newtons, corresponding to a mass of about 1000 kg [or a ton].

The process of hitting is mysterious, but with God-given quick reflexes and many years of practice, a few players can learn to hit the ball regularly.

Ted Williams said "Hitting is fifty percent above the shoulders" and wrote a book entitled The Science of Hitting, in which he analyzed hitting with detail normally reserved for scientists and scholars.

• A solidly hit baseball may leave the bat with speeds as great as 60 meters/sec, much larger than the speeds with which the pitcher typically throws the ball.
• Because of the presence of significant topspin or backspin, the flight of a hit baseball is difficult to predict.
• The path of a fly ball is strongly influenced by air resistance; in fact, air resistance is just as important as gravity for its motion.
• The ball remains in the air for as long as 5 or 6 seconds, and the outfielder must decide quickly where they should go to catch the ball, if they can.

"Did they tell me how to pitch to Williams? Sure they did. It was great advice, very encouraging. They said he had no weakness, won't swing at a bad ball, has the best eyes in the business, and can kill you with one swing. He won't hit anything bad, but don't give him anything good." - Bobby Shantz

"Willie Mays was never sick, he was never hurt, he never had a bellyache, he never had a toothache; never had a headache. He came to the park every day to put on the uniform and play." - Leo Durocher, manager.

Batting Fundamentals by Ty Cobb
• Don't Grip your bat at the very end.  Also, leave at least an inch or more space between your fingers.
• Stand back of the plate, especially against right hand pitchers. Try to hit the ball to right-center field.
• Don't slug at full speed; but  learn to meet the ball firmly.
• To hit to right or right-center, stand away from the plate.
• The plate is the pitcher's objective and he has to come to it. Use a slightly closed stance, and keep a little more weight on your front foot than back.
• Don't pull a curve ball from a right hander.
• Keep your left elbow cocked on level with your hands or even higher.
• Keep your back leg straight.
• If high fast balls inside really bother you, crouch over from waist and pass them up.
• Against a speedy left-hander don't pull.  But against a left-hander of fair speed, move up in the box, and pull.
• Summary: "A ball bat is a wondrous weapon."

Catcher

Like the conductor of a symphony, the catcher directs defensive play, calls the pitches, and keeps the team focused on getting the batter out.

Also, a good catcher can manage to block the umpire's view of a pitch on the outside corner, to keep the hitter psychologically on guard, and guide the pitcher to success.

The catcher is the ultimate line of defense against a stolen base.  A quick runner can steal a base in just over 3 seconds.  The catcher has a little over a second to catch the pitch and throw it accurately to stop the runner.

The catcher gets more than his share of bumps, bruises, and sprained fingers from foul tips, bad pitches, bats, and aggressive base runners.

Catchers are frequently required to chase after pop-ups behind the plate. These poorly hit pitches usually have a lot of spin, and move erratically, so that pop-ups may be very difficult to catch. A great catcher makes catching them look easy, in spite of the perils of bats, other equipment, dugout steps, fences, screens, and railing.

"Why has our pitching been so great? Our catcher (Yogi Berra) that's why. He looks cumbersome but he's quick as a cat." - Casey Stengel
Fielding

The ball bounces differently in every ball park, and the differences are especially pronounced on artificial turf, on which the ball has a lively bounce.

A third baseman has to knock a ground ball down or block it, grab it, and then throw it to the first baseman --- all before two seconds have passed.

It is somewhat of a mystery as to how outfielders are able to gauge the flight of the ball, since it can vary greatly because of spin, wind conditions, and atmospheric drag.

Baseball Quotations
Source:

"Throwing a fastball to Henry Aaron is like trying to sneak the sun past a rooster." --- Curt Simmons, pitcher

"Hitting against Sandy Koufax is like drinking coffee with a fork." --- Willie Stargell

"Hitting is timing. Pitching is upsetting timing." --- Warren Spahn

"I never saw anyone like Ty Cobb. No one even close to him as the greatest all-time ballplayer. That guy was superhuman, amazing." --- Casey Stengel.

"I never threw an illegal pitch. The trouble is once in a while I toss one that ain't never been seen by this generation." --- Satchel Paige

"I'd go through hell in a gasoline suit to keep playing baseball." --- Pete Rose

"When I came to Detroit I was just a mild-mannered Sunday-school boy." --- Ty Cobb

"He should play in handcuffs." --- A Sports Writer on Willie Mays

"He's got a gun concealed about his person. They can't tell me he throws them balls with his arm." --- Ring Lardner about Walter Johnson

"Ninety percent of baseball is mental, and the other half is physical." --- Yogi Berra

"I'm not sure what the hell charisma is, but I get the feeling it's Willie Mays." --- Ted Kluszewski

"I swing big, with everything I've got. I hit big or I miss big. I like to live as big as I can." --- Babe Ruth

Types of Pitches
1. High Speed
• Cutter / Cut fastball
• Fastball
• Four seam fastball
• Hopping fastball
• Rising fastball
• Sinking fastball
2. Moderate Speed; high spin
• Drop
• Roundhouse Curve
• Screwball
• Sharp-breaking curve
• Slider
3. Seam Orientation Dependent
• Knuckleball
• Scuffed ball
• Spitball
• Split-finger fastball
• Forkball
• Gyroball (Japanese specialty)
4. Off-speed
• Blooper / Eephus Pitch
• Change-up

Baseball Films (my order of preference)
• Biographical
1. The Pride of the Yankees 1943: (Lou Gehrig)
2. Fear Strikes Out 1957 (Jim Piersall)
3. Eight Men Out 1988 (Joe Jackson)
4. Cobb 1994
5. The Rookie 2002 (Jimmy Morris)
• Fictional
1. Bull Durham 1988
2. A League of Their Own 1992
3. Mr. Baseball 1992
4. For the Love of the Game 1999
5. The Natural 1984

Take Me Out to the Ball Game -- Jack Norworth: 1908 version
Source:
http://www.baseball-almanac.com/poetry/po_stmo.shtml
Katie Casey was baseball mad.
Just to root for the home town crew,
Ev'ry sou Katie blew.
On a Saturday, her young beau
Called to see if she'd like to go,
To see a show but Miss Kate said,
"No, I'll tell you what you can do."

"Take me out to the ball game,
Take me out with the crowd.
Buy me some peanuts and cracker jack,
I don't care if I never get back,
Let me root, root, root for the home team,
If they don't win it's a shame.
For it's one, two, three strikes, you're out,
At the old ball game."

Katie Casey saw all the games,
Knew the players by their first names;
Told the umpire he was wrong,
All along good and strong.
When the score was just two to two,
Katie Casey knew what to do,
Just to cheer up the boys she knew,
She made the gang sing this song:

"Take me out to the ball game,
...
For it's one, two, three strikes, you're out,
At the old ball game."

My All Time Baseball Team  Tyrus Cobb left field Honus Wagner shortstop Rogers Hornsby second base Lou Gehrig first base Willie Mays center field Ted Williams right field Yogi Berra catcher Pie Traynor third base Sandy Koufax [left handed pitcher] Bob Feller [right handed pitcher]

And, I feel that the greatest player of all time, according to his proven record to hit, run, throw, bunt, and catch, was Willie Mays.

How to Keep Young   by Satchel Page
• Avoid fried foods, which angry up the blood.
• If you stomach disputes you, lie down and pacify it with cool thoughts.
• Keep the juices flowing by jangling around gently as you move.
• Go very light on the vices, such as carrying on in society.  The social ramble ain't restful.
• Avoid running at all times.
• Don't look back.  Something might be gaining on you.

VOCABULAIRE DU BASEBALL QUÉBÉCOIS
Source:  http://www.duke.edu/~pstewart/baseball.htm
```
champ gauche, centre, droit -- left, center, right field
formation des frappeurs -- batting order
manche (f) -- inning
retrait (m) -- out
point -- run
lanceur -- pitcher
prendre son élan -- wind up (v)
suivi (m), prolongé -- follow-through
retirer sur prises -- strike out (vt)
blanchissage -- shutout (n)
(balle) rapide -- fastball
(balle) courbe -- curve
(balle) glissante -- slider
(balle) jointure, tire-bouchon -- knuckleball
balle papillon -- floater
courbe renversée -- screwball
tombante -- sinker
changment -- change-up
lancer latéral -- sidearm delivery
mauvais lancer -- wild pitch
feinte illégale -- balk
bâton -- bat
bonne balle, en jeu -- fair ball
balle fausse -- foul ball
ricochet (m) -- foul tip
coup retenu, amorti -- bunt (n)
risque-tout -- squeeze play
roulant (m) -- ground ball
chandelle (f), balle retroussée -- popup
ballon sacrifice -- sacrifice fly
flèche (f) -- line drive
coup sûr -- base hit
simple, double, triple -- single, double, triple
(coup de) circuit -- home run
plongeon (m), tete première -- head-first slide
marquer (un point) -- score
coureur coincé, pris en souricière, en trappe -- trapped runner
receveur -- catcher
premier-, deuxième-, troisième-but -- first, second, third baseman
arrête-court -- shortstop
voltigeur -- outfielder
toucher -- tag
double retrait -- double play
relais hors cible -- wild throw
la partie des étoiles -- all-star game
recrue (f) -- rookie
statistique:
point produit -- run batted in
laissés sur but -- left on base
point mérité -- earned run
présence officielle -- at-bat
moyenne offensive, puissance de frappe -- batting average
erreur (f) -- error
balle passée -- passed ball
```
For additional information see The Physics of Baseball on  my website at  this URL:

http://www.iit.edu/~johnsonp/baseball.html