Physics and Baseball: A Report to Red Sox Nation

1
Physics and BaseballA Report to Red Sox Nation
Alan Nathan, University of Illinois
2
A good book to read.
Prof. Bob Adair
the physics of baseball is not the clean,
well-defined physics of fundamental matters.
Hence conclusions must depend on approximations
and estimates. But estimates are part of the
physicists repertoire... The physicists
model of the game must fit the game. Baseball
is not rocket science. Its much harder.
3
The Baseball/Physics Connection
4
Topics I Will Cover

• The ball-bat collision
• How a bat works
• Wood vs. aluminum
• The flight of the baseball
• Drag, lift, and all that
• New tools for baseball analysis

5
You can observe a lot by watching---Yogi Berra

• forces large, time short
• gt8000 lbs, lt1 ms
• ball compresses, stops, expands
• like a spring KE?PE?KE
• bat recoils
• lots of energy dissipated
• distortion of ball
• vibrations in bat

6
What Determines Batted Ball Speed?

• pitch speed
• bat speed
• collision efficiency a property of the ball
  and bat
• BBS q vpitch (1q) vbat
• typical numbers q 0.2 1q 1.2
• example 85 70 gives 101 mph (400)
• vbat matters much more than vpitch!
• Each mph of bat speed worth 6 ft
• Each mph of pitch speed worth 1 ft

7
Kinematics of Ball-Bat Collision
BBS q vpitch (1q) vbat
1. m/Meff ball mass/effective bat mass ? 0.25
bat recoil 2. e elasticity of collision ?
0.50 energy dissipation For m/Meff ltlt1 and
e?1, q?1
8
1. Effective Bat Mass

• Meff ? Swing Weight related to MOI about the
  handle
• Larger ? less recoil to bat ? larger q
• Larger ? smaller swing speed

Batters seem to prefer lower MOI bats sacrificing
power for quickness
Cross and AMN, Sports Technology 2, 7-15 (2009)
9
Is There an Advantage to Corking a Bat?
Sammy Sosa, June 2003
Based on best experimental data available for
harder hit no for frequency of good contact
probably
10
e ball-bat coefficient of restitution (bbcor)

• 1 - e2 fraction of CM energy dissipated
• 75!
• Joint property of ball and bat
• Most of energy loss is in ball
• But the bat matters
• Vibrations decrease e
• Trampoline effect increase e

11
Vibrations and the ball-bat collision

outside
sweet spot
12
Studying the Vibrations of a Baseball
Bat www.kettering.edu/drussell/bats.html
13
Dynamics of the Bat-Ball Collision AMN, AJP 68,
979-990 (2000)
20

• Solve eigenvalue problem for normal modes
• Model ball-bat force F
• Expand y in normal modes
• Solve coupled equations of motion for ball, bat
• Energy budget
• KE of ball (batted ball speed)
• recoil of bat
• dissipation in ball
• vibrations in bat

14
Vibrations, BBCOR, and the Sweet Spot

at node 2 vibrations minimized COR
maximized BBS maximized best feel
e
vf
Evib
15
Independence of End Conditions

• strike bat on barrellook at movement in handle
• handle moves only after 0.6 ms delay
• collision nearly over by then
• nothing on knob end matters
• size, shape, hands, grip
• boundary conditions
• confirmed experimentally

Batter could drop bat just before contact and it
would have no effect on ball!!!
16
BBCOR and the Trampoline Effect(hollow bats)
The Ping!
Lowest Hoop (or wineglass) Mode
17
The Trampoline Effect A Simple Physical
Picture

• BBCOR increases with
• elasticity of ball (0.5)
• elasticity of bat (1)
• relative stiffness kball/kbat
• BBCOR(Al)/BBCOR(wood)
• unregulated, can be very large
• Little League lt1.15
• NCAA lt 1.0 (!)

change kbat
18
Forces on a Spinning Baseball in Flight
FM

• Drag slows ball down
• Magnus mg deflects ball from straight line

FD
mg
19
Real vs. Physics 101 Trajectory Effect of
Drag and Magnus
20
What do we know about CD?(mainly from pitch
tracking)

• Depends on .
• v0 (Reynolds Number)
• surface roughness?
• seam orientation?
• spin?

• Good approximation
• Cd 0.350.05 in range 60-100 mph
• No steep drag crisis
• More dedicated experiments in progress

21
What do we know about CL?(mainly from
high-speed motion analysis)

• Depends on .
• spin parameter S ? R?/v
• v _at_ fixed S?
• best evidence is no, in region of 50-100 mph
• seam orientation?

Good approximation CL? S ? R?/v in range
0.05-0.30
22
New tools to study flight of baseball

• PITCHf/x and HITf/x
• Video tracking
• TrackMan
• Doppler radar tracking

23
PITCHf/x and HITf/x
Marv White, Physics, UIUC, 1969

• Two video cameras _at_60 fps
• high home and high first
• tracks every pitch in every MLB ballpark
• all data publicly available on web!
• tracks initial trajectory of batted ball
• Used for analysis, TV broadcasts, MLB Gameday,
  etc.

24
TrackMan

• Doppler radar to measure radial velocity
• dr/dt ? r(t)
• 3-detector array to measure phase
• two angles ?(t), ?(t)
• Together these give full 3D trajectory
• Spin modulates to give sidebands
• spin frequency ?

25
So what good is a physicist in all this?

• Minimal parametrization of the trajectory
• Constant acceleration works very well for pitched
  ball
• Constant jerk works for most batted balls
• Keeping everyone honest
• Laws of physics cannot be violated
• Recognizing and dealing with imperfect data
• Measurements have uncertainties!

26
Baseball AnalysisUsing PITCHf/x to discover
how pitchers do what they do
Hitting is timing. Pitching is upsetting
timing.
27
Ex 1 Mariano Rivera Why is he so good??
Three Reasons Location, Location, Location
28
Ex 2 Late Break Truth or MythMariano
Riveras Cut Fastball
29
Ex 2a What makes an effective slider
Josh Kalk, THT, 5/22/08
This slider is very effective since it looks like
a fastball for over half the trajectory, then
seems to drop at the last minute (late break).
side view
30
Ex 3 A Pitchers Repertoire
Catchers View
31
Ex 4 Jon Lester vs. Brandon Webb
15 inches
Brandon Webb is a sinkerball pitcher Almost no
rise on his fastball
32
Ex 5 The Knuckleball
Tim Wakefield is a knuckleball pitcher Chaotic
Movement
33
Ex 5 Ubaldo Jimenez Pitching at High Altitude
vf/v0
"Every time that I come here to San Diego, it's
always good. Everything moves different. The
breaking ball is really nasty, and my fastball
moves a lot. So I love it here."
Denver
Denver
Denver
Denver
34
Learning About Batted Balls

• HITf/x
• Initial part of trajectory
• All April 2009 data available
• TrackMan
• Full trajectory
• Limited data from StL, Sept. 2009

35
TrackMan Data from StL, 2009
R vs. v0
R vs. ?0
USEFUL BENCHMARK 400 ft _at_ 103 mph 5 ft per mph
peaks _at_ 25o-35o
36
What Constitutes a Well-Hit Ball?
w/o home runs
home runs
V0gt90
37
Putting Spin on Batted Balls

• in front or behind ? sidespin
• sideways Magnus force
• fly balls break toward foul pole

38

• undercutting/overcutting ? backspin/topspin
• Magnus force is up/down
• Topspin makes line drives nose-dive
• Backspin keeps fly ball in air longer
• Tricky popups to infield

39
Paradoxical PopupsAJP 76, 723-729 (2008)
40
Combining HITf/x with Hittracker

• HITf/x ? v0,?,?
• Hittracker (Greg Rybarczyk, hittrackeronline.com)
• Landing point
• Flight time
• Together these constrain the full trajectory

41
(No Transcript)
42
HITf/x hittracker Analysis The carry of a
fly ball

• Motivation does the ball carry especially well
  in the new Yankee Stadium?
• carry (actual distance)/(vacuum distance)
• for same initial conditions

43
HITf/x hittracker Analysis4354 HR from 2009
Denver
Cleveland
Yankee Stadium
44
Work in Progress

• Collision experiments calculations to elucidate
  trampoline effect
• New studies of drag and Magnus
• Experiments on high-speed oblique collisions
• To quantify spin on batted ball

45
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
• go.illinois.edu/physicsofbaseball
• a-nathan_at_illinois.edu
• I am living proof that knowing the physics
  doesnt help you play the game better!

_at_ Red Sox Fantasy Camp, Feb. 1-7, 2009
46
HITf/x hittracker Analysis4354 HR from 2009
47
CD One Final Thought
PFX
TM
PFX-TM
Correlations suggestive of variations in
baseball
48
Extract sidespin vs. ? from trajectory
CF
RF
LF
RF
LF
RF
LHH
RHH
?

• Balls break toward foul pole
• Break increases with angle
• Ball hit to CF slices
• LHH/RHH asymmetry
• Tilt in bat

49
Is the Baseball Juiced? Is COR larger than it
used to be?

• Measurements with high-speed cannon
• CORrebound speed/initial speed
• 1975 vs. 2004

• 1975 and 2004 equal to few
• No evidence for juiced ball

50
Example Pitching at High Altitude
Denver
Toronto
Toronto
Denver
PITCHf/x data contain a wealth of information
about drag and lift!