baseball and bat performance standards

NCAA Research Committee June 13, 2001

Baseball and Bat Performance Standards

Alan M. NathanDepartment of Physics

University of Illinois at [email protected]

NCAA Research CommitteeOmaha, NE

June 13, 2001


Outline

Introduction

General Principles

Current NCAA and ASTM Procedures

A New Proposal

Need for Additional Research

Summary/Conclusions


Introduction The main issue:

how to devise laboratory tests to predict field performance

The approach: Study problem with model for ball-bat collision Model constrained by

physics principlesdata intelligent guessing

Compare with available data


General Principles

Lab: Given vball , vbat

measure vf

determine eA

Field: Given vball , vbat , eA

predict vf

vball vbat

vf

batAballAf ve1 ve v

eA = “collision efficiency” = BESR-1/2


Properties of eA

vball

eAvball

batAballAf ve1 ve v

For bat initially at rest…eA = vf/vball

BESR = vf/vball + 1/2 -1 eA +1

at “sweet spot”, eA 0.2 (BESR 0.7) vbat much more important than vball


Properties of eA

(or BESR) It depends on...

inertial properties (mball, Mbat, CM, MOI, impact point)COR of ball+bat

impact pointvrel = vball + vbat

but weakly

It does not depend on...vball or vbat individually

only vrel

support on knob end free, clamped, pivoted, hand-held

vball vbat

vf


Typical Example34”/31 oz wood batvball = 90 mphknob = 45 rad/s

Conclusions:• location of vf ,MAX depends on

* the bat (eA)* the swing (vbat)

• COP not relevant

batAballAf ve1 ve v

20

40

60

80

100

0.00

0.05

0.10

0.15

0.20

0.25

0 2 4 6 8 10 12 14

eAv (mph)

distance from tip (inches)

vf

eA

vbat

COP


What Does eA Depend On?

= +

r bat recoil factor (inertial properties)

e ball-bat COR 0.5 = BPF e0

e0 ball-wall COR

r1r-e eA

I

bm Mm r

CMbat,

2ball

bat

ballfree

. .CM .

b

Free

pivot .

x

.

Ixm r

pivotbat,

2ball

pivot

Pivoted


-0.1

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14distance from tip (inches)

eA

er

COP CM

flexible

rigid

r1r-e eA

Example: Free Wood Bat


r1r-e eA

Free vs. Pivoted

conclusions:• eA ~ independent of knob end (support, mass, …)• e (or BPF) not!• should be tested experimentally

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10distance from tip (inches)

eA

efree

epivoted

COP


-0.2

-0.1

0

0.1

0.2

0 5 10 15

eA


wood: BPF=0.99aluminum: BPF=0.97aluminum: BPF=1.07

0

0.1

0.2

0.3

0.4

0.5

0 5 10 15

e



40

50

60

70

80

90

100

0 5 10 15

vf (mph)



BPF vs. BESR vs. vf


80

85

90

95

100

105

110

2 3 4 5 6 7 8 9

vf (mph)

z (inches)

Dot is COP

Simulations of Aluminum Bats(34”, 31 oz)


Dependence on Impact Speed

0.18

0.19

0.2

0.21

0.22

0.23

100 110 120 130 140 1500.45

0.46

0.47

0.48

0.49

0.50

0.51

eA

vrel

(mph)

mph 10

0.008 ve

rel

A

NOTE: effect mainly due to ball-wall COR (e0)

0.40

0.45

0.50

0.55

0.60

60 80 100 120 140equivalent impact speed (mph)

COR

Briggs, 1945

UML/BHM

Lansmont

MLB specs

MLB/UML

COR Measurements

Lansmont/CPD


Review of Current NCAA Procedure

Standard swing: vball = 70 mph vbat = 66 mph @ z=6”vrel = 136 mph

BHM swings bat Measure vf and infer BESR Require vf,max 97 mph

eA,max 0.228 BESR 0.728

v vvv e

batball

batfA


Good Features of NCAA Procedure

Use of BESR (eA) as performance metric better than BPF as predictor pf performance

Metric applied at optimum impact point not at some arbitrary point (COP, …)

vrel = 136 mph approximates game conditions far better than old ASTM method although 160 mph is better


Possible Problems

Problems of principlenot subjected to scientific scrutiny

“peer review” high torque of BHM may excite vibrations in bat

Problems of procedurenormalization of eA to bat speedcorrection for non-standard ball COR


BHM Swing vs. Batter Swing

Much higher torque with BHM wood bats break possible excitation of “diving board mode”

15 Hz very rough estimate

v=3 mph more study needed

measure vibrationcross check with other techniques

0

10

20

30

40

50

60

70

0 0.05 0.1 0.15 0.2

V (mph)

time (sec)


Problem with vbat Normalization

v vvv einfer

ve1 ve vmeasure

batball

batfA

batAballAf

• must use vbat at actual impact point• should not use vbat at z=6”

* unless impact point is there• example: suppose vf,max at z=7” or 5” and eA=0.220

* inferred eA=0.193 @ 7” and 0.247 @ 5”* this is a significant error (but easily fixed)

4.3 mph in a 90+70 collision


Problem with COR Correction

For a given ball, measure vf in 70+68 (138 mph) collision with standard bat at z=6” rsb=0.2278; if vf=94 mph e0,sb=0.459 (@125 mph)

x vf - 94

For bat being tested with this ball, adjust eA

eA= x/vrel (should this be -x/vrel?)

This is at best an approximation


Better COR Correction

• infer e0 of ball with standard bat (using rsb)• measure eA of same ball with bat under test• use r to infer e• scale e by e0,sb/e0

• used scaled e and r to recompute eA

NOTE:-even this procedure is approximate-need experiments to check consistency


Review of Proposed ASTM Procedure

Project ball on stationary bat at 140 mph bat pivot point is 6” from knob

Measure vball and vf for impact at COP

Use measured ball-wall COR e0 andmeasured inertial properties of bat r to

infer BPF

Use BPF as metric/predictor of performance

0

vv

err1

BPF ball

f


Comments on ASTM Procedure The Good:

completely transparent procedure that is easily checked by any interested observer

does not attempt to measure speed of struck bat, unlike old ASTM procedure

vrel approximates game conditionsmeasures ball-wall COR with same apparatus

The Bad:use of BPF as metric (eA is better)

restriction to measurements at COP


Proposed New Procedure Use the best features of the current NCAA and the

proposed ASTM procedures fire ball at stationary bat at 150 mph

eliminates possible complications of BHMmakes entire process easily understood by all

measure vball and vf to get eA = vf/vball

measure over broad enough range to cover vf,max

need to define standard conditionscorrect eA for ball-wall COR

need to measure ball-wall COR at what velocity? More on this later.

need to measure inertial properties of bat (r)


Proposed New Procedure

use eA and standard swing to predict vf,max

regulate size of vf,max


z

x

Crisco/Greenwald Batting Cage Study

Z0.8”

X3”

45 rad/s

vbat vs. z

The Standard Swing

70 mph@ 28”


Standard Conditionsvball = 90 mph knob = 45 rad/s

vrel = 160 mph @ z=6”

20

40

60

80

100

0.00

0.05

0.10

0.15

0.20

0.25

0 2 4 6 8 10 12 14

eAv (mph)


vf

eA

vbat

COP


Standard Conditionse0 = 0.46

•Need ball-wall COR at appropriate speed•If ball-bat collision is at vrel

*ball-wall collision should be at same center-of-mass energy*150 mph ~134 mph

•Should be checked experimentally

rvrel


0.5

0.55

0.6

0.65

0.7

0.75

0.8

2 3 4 5 6 7 8 9 10

M5BESR

distance from barrel (inches)

0.5

0.55

0.6

0.65

0.7

0.75

0.8

2 3 4 5 6 7 8 9 10

WoodBESR

distance from barrel (inches)

Crisco/Greenwald Batting Cage vs. Lansmont Laboratory


0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

23 24 25 26 27 28 29 30 31

eA

distance from knob (inches)

Ball 22,COR=.526pivot about 5.76"v

initial=100 mph

rigid bat

flexible bat

Lansmont Tests of R161 Wood Bat

Lansmont Measurements vs. Calculations


0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.05 0.1 0.15 0.2 0.25 0.3

BPF

distance from barrel (m)

Crisco/Greenwald Batting Cage Data(wood)

calculation

Crisco/Greenwald Batting Cage vs. Calculations


I-n knob

•n=0 •constant bat speed

•n=0.5 •constant bat energy

•data •n=0.31 0.04•constant “bat+batter”

energy, with Ibatter104 oz-in2

v(6”) = 1.2 x 10-3 mph/oz-in2 (vf=1.5 0.3 mph)

40

42

44

46

48

50

1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9Iknob

(104 oz-in2)

knob

(rad/s)

y = m1*(m0/1.6)^m2ErrorValue

0.2065945.3m1 0.037111-0.30769m2

NA5.9192ChisqNA0.95907R

Crisco/Greenwald Batting Cage Study:bat speed versus MOI


Areas for more Experiments More extensive wood-aluminum comparisons BHM vs. stationary vs. field comparisons COR: flat vs. cylindrical Collision time vs. vrel

COR vs. vrel (recoil effect) vbat vs. M, MOI, zCM, … COR correction to eA

eA for free vs pivoted bat off-axis effects


Summary of Important Points

Much of the physics of ball-bat collision well understoodbasic principlesmodels constrained by good data

This understanding can be applied to the issue of bat and ball standards

Laboratory measurements can predict field performance

More research needed in some areas

baseball and bat performance standards

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