How Does a Baseball Bat Work?
Alan M. Nathan
Department of Physics
University of Illinois at Urbana-Champaign
[email protected]
www.npl.uiuc.edu/~a-nathan/pob
SGMA Meeting
Chicago IL
October 12, 2002
SGMA Meeting
Chicago, October 12, 2002
Page 1
The Ball-Bat Collision
z
A violent collision
™ forces large (>8000 lbs!)
™ time is short (<1/1000 sec!)
™ ball compresses, stops, expands
¾ bat compresses ball
¾ ball bends/compresses bat
™ lots of energy dissipated
¾ distortion of ball
¾ vibrations in bat
z
knob end and grip don’t matter!
z
principal focus:
™ large BBS
SGMA Meeting
Chicago, October 12, 2002
Page 2
BBS: What does it depend on?
z Pitched
z Bat
ball speed vball
swing speed vbat
z “Collision
Efficiency” E
™Property of ball and bat
™BESR = E + 1/2
z My
only formula:
™BBS = E vball + (1+E) vbat
SGMA Meeting
Chicago, October 12, 2002
Page 3
BBS: Some Typical Numbers
z
BBS = E vball + (1+E) vbat
™E ≅ 0.20
z
1+E ≅ 1.20
MLB: vball = 90 mph
vbat = 70 mph
™BBS = 0.2 x 90 + 1.2 x 70 = 18 + 84 = 102 mph
z
Slow-pitch softball: vball = 10 mph
vbat = 70 mph
™BBS = 0.2 x 10 + 1.2 x 70 = 2 + 84 = 86 mph
z
Important conclusions:
¾ vbat the most important factor for BBS
¾ performance standard needs to account
SGMA Meeting
Chicago, October 12, 2002
for this
Page 4
BBS: What does E depend on?
z
Energy of bat recoil
™Depends on bat mass/mass distribution (MOI) and
impact location
z
Energy dissipated in ball and bat: COR
™Depends on vball+vbat and impact location
E maximized when recoil & dissipation minimized
SGMA Meeting
Chicago, October 12, 2002
Page 5
Ball-Bat COR
z
Depends on “ball-wall” COR
…which depends on
¾ vrel = vball + vbat
¾ mass of ball
z
Depends on “BPF” (ball-bat COR/ball-wall COR)
…which may depend on
¾ impact location
ƒ vibrations minimized at “sweet spot”
¾ ball-wall COR and compression
¾ vrel
SGMA Meeting
Chicago, October 12, 2002
Page 6
Mass and Mass Distribution
z For
large E
™ more mass in barrel of bat is better
™ mass in handle plays little role
™ physics of this is very well understood
z For
large vbat
™ less mass in barrel of bat is probably better
™ mass in handle probably plays little role
™ not as well understood as we would like
z So,
what to do?
™ assume two effects cancel and ignore
¾Base performance on BPF only
¾NOT my recommendation
Octoberof
12, 2002
™ do more fieldChicago,
studies
bat speed
SGMA Meeting
Page 7
Crisco/Greenwald Batting Cage Study
X
3”
Z
0.8”
ω
45 rad/s
z
x
vbat vs. z
Conclusion: at impact, bat is rotating about knob
SGMA Meeting
Chicago, October 12, 2002
Page 8
Bat Speed vs. MOI
ω
Crisco/Greenwald Batting Cage Study:
knob
(rad/s)
50
y = m1*(m0/1.6)^m2
Value
m1
45.3
m2 -0.30769
Chisq
5.9192
R 0.95907
48
46
Error
0.20659
0.037111
NA
NA
44
42
aluminum
wood
40
1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9
4
2
(10 oz-in )
I
knob
Conclusion: bat speed scales with (1/Iknob)0.3
SGMA Meeting
Chicago, October 12, 2002
Page 9
Conclusions for lab performance testing
z Want
vrel that closely replicates field
z Want
impact location that maximizes
BBS in field
™ NOT COP!
z Want
ball-wall COR and compression
representative of field conditions
SGMA Meeting
Chicago, October 12, 2002
Page 10
COR
COP
0.62
0.60
0.58
0.56
0.54
“normal”
“normal” + 3oz in knob
0.52
25
26
27
28
29
30
31
distance from knob (inches)
32
Conclusion: COP is completely irrelevant
SGMA Meeting
Chicago, October 12, 2002
Page 11
A Possible Testing Procedure
z
Decide on “standard field conditions”:
™ ball (ball-wall COR; compression)
™ vball,field and vbat,field (which depends on bat!)
¾ vrel,field
= vball,field+ vbat,field
z
Measure vf,lab for vball,lab = vrel,field
z
Calculate BBS = vf,lab + vbat,field
z
Repeat at different impact locations until
maximum BBS obtained
Note: procedure based on sound science except
for selection of vbat,field
SGMA Meeting
Chicago, October 12, 2002
Page 12
Summary of Important Points
z
Performance (BBS) depends on
™Bat swing speed
™Bat mass and mass distribution
™Ball-bat COR
z
For laboratory testing, careful attention must be
paid to
™Parameters of ball (COR, compression)
™Selection of impact location(s)
™Relative ball-bat speed
More field tests needed to elucidate bat swing
speed
SGMA
Meeting
Chicago, October 12, 2002
Page 13
z