1、Designation: F2398 10An American National StandardStandard Test Method forMeasuring Moment of Inertia and Center of Percussion of aBaseball or Softball Bat1This standard is issued under the fixed designation F2398; the number immediately following the designation indicates the year oforiginal adopti
2、on or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope1.1 Method for determining the moment of inertia (MOI),the center of percussio
3、n (COP), and the balance point (BP) ofbaseball and softball bats. These physical properties are used inTest Method F1881, Test Method F1890, and Test MethodsF2219.1.2 The MOI, COP, and BP are measured in the laboratoryon test equipment meeting the requirements defined in this testmethod.1.3 The valu
4、es stated in inch-pound units are to be regardedas the standard.1.4 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the appli
5、ca-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2F1881 Test Method for Measuring Baseball Bat Perfor-mance FactorF1890 Test Method for Measuring Softball Bat Perfor-mance FactorF2219 Test Methods for Measuring High-Speed Bat Perfor-mance3. Terminology3.1 De
6、finitions of Terms Specific to This Standard:3.1.1 balance point (BP), nthe distance to the center ofmass measured from the distal end of the bat.3.1.2 center of percussion (COP), nalso known as thecenter of oscillation. Forces and impacts at this location willnot induce reactions at the pivot point
7、, 6 in. (152 mm) from thedistal end of the bat.3.1.3 cycle, none complete oscillation of a pendulumsupported at the pivot point, 6 in. (152 mm) from the distal endof the bat.3.1.4 moment of inertia (MOI), nalso known as the massmoment of inertia, the measure of the bats resistance tochanges in its r
8、otation rate about the pivot point, 6 in. (152mm) from the distal end of the bat.3.1.5 period, nthe time required for a pendulum to oscil-late through one complete cycle.4. Significance and Use4.1 This test method offers a laboratory means to measurethe inertial properties of bats, specifically weig
9、ht, balancepoint, center of percussion, and MOI, in support of other testmethods including the ASTM standards referenced in thisdocument.4.2 Use of this test method can provide sports governingbodies the means to establish rules regarding the physicalproperties of bats, specifically MOI.5. Apparatus
10、5.1 Bat MOI Test Apparatus:5.1.1 Ruler, suitable for measuring lengths up to 42 in.(1067 mm) to the nearest 0.03 in. (0.8 mm).5.1.2 Weight Scales, suitable for measuring weight up to 48oz (1364 g) to the nearest 0.0035 oz (0.1 g).5.1.3 Electronic Timer, suitable device sufficiently accuratefor measu
11、ring time to the nearest 1 s (0.000001 s).5.1.4 Pendulum StandA frame with a pivoting bat collar-clamp large enough to allow a bat held in a vertical position toswing freely (see Fig. 1).5.1.5 Bat Collar-ClampA lightweight clamp or collar thatcan hold the weight of a bat and provide a fixed pivot lo
12、cation.The clamp shall be rotationally balanced and have a maximumMOI of 4 oz-in.2(80 kg-mm2) measured about the bat pivotlocation (see Fig. 1). The MOI of the clamp shall not changewith the diameter of the bat being tested.6. Calibration and Standardization6.1 Calibration RodThe calibration rod sha
13、ll be 1 in.(25.4 mm) in diameter by 34 in. (864 mm) long, solidaluminum.1This test method is under the jurisdiction of ASTM Committee F08 on SportsEquipment and Facilities and is the direct responsibility of Subcommittee F08.26 onBaseball and Softball Equipment.Current edition approved May 1, 2010.
14、Published June 2010. Originallyapproved in 2004. Last previous edition approved in 2004 as F2398 041. DOI:10.1520/F2398-10.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, re
15、fer to the standards Document Summary page onthe ASTM website.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.6.2 Target Calibration MOIMeasure the length and theweight of the calibration rod. Compute the target calibrationrod MOI us
16、ing Eq. 1:IT5 WcHLc2121 SLc2 dD2J 1 Ic(1)where:IT= target MOI of the calibration rod, oz-in.2(kg-mm2)Wc= measured weight of the calibration rod, oz (kg)Lc= measured length of the calibration rod, in. (mm)d = pivot distance (6 in. or 152 mm)Ic= MOI of the clamp about its pivot point, oz-in.2(kg-mm2)6
17、.3 Balance Point CalibrationFollowing 7.1, the BP ofthe calibration rod shall be Lc/2 6 0.05 in. (1 mm). If the BPof the calibration rod is outside the allowed range, then checkthe calibration of the scales and support fixture.6.4 Mass Moment of Inertia CalibrationUsing the mea-sured properties of t
18、he calibration rod from 6.2 and 6.3 andfollowing 7.2 and 7.3, the measured MOI of the calibration rodshould be within 650 oz-in.2(916 kg-mm2) of the target MOI,IT. If the MOI of the calibration rod is outside the allowedrange, then check the clamp location and timer calibration.7. Procedure7.1 Deter
19、mination of BPMeasure and record the overallbat length to the nearest 0.06 in. (1.5 mm). Place the bat levelon the BP fixture as shown in Fig. 2. Record the measuredweights (W6and W24) to the nearest 0.035 oz (1.0 g). Calculatethe BP relative to the distal end of the bat knob using Eq 2:FIG. 1 MOI F
20、ixtureFIG. 2 Balance Point FixtureF2398 102BP 56W61 24W24Wt(2)where:BP = BP from distal end of the bat knob, in. (mm)W6= weight of the bat measured 6 in. from the knob, oz(g)W24= weight of the bat measured 24 in. from the knob, oz(g)Wt=W6+W24= total weight of the bat, oz (g)7.2 Determination of COP:
21、7.2.1 Test SetupApply the clamp to the bat handle so thatthe pivot location (point of the vee on underside of the clamp)is 6 6 0.03 in. (152 6 0.8 mm) from the distal end of the bat(see Fig. 1). Hang the bat in the stand making sure the bathangs vertically and can swing freely about the pivots. If t
22、hebat does not hang vertically, correct by centering the batbetween the pivots.7.2.2 Bat TestRotate the bat about the pivot to an angle of5 from the vertical. Release the bat and allow it to swing freely(see Fig. 1). Allow the bat to swing through five cycles (that is,settle into simple pendulum osc
23、illation). Start the electronictimer when bat reaches the fifth swing cycle. Stop the timeronce the bat has completed fifteen full cycles. The timer shallbe triggered by a light beam broken by the path of the bat at thebottom of the pendulum arc. Do not use these results if thestandard deviation of
24、the last 10 period measurements isgreater than 0.001 s. Determine and record the average periodfor the bat, T, using Eq 3:T 5110p61 p71 . 1 p15! (3)where:T = average period (s), andpi= period of the ithoscillation (s)7.2.3 COP LocationCalculate and record the bat COPrelative to the 6-in. pivot point
25、 location using Eq 4:COP 5T2g4p2(4)where:g = gravity or 386.1 in./s2(9806 mm/s2)7.3 Determination of MOI:7.3.1 MOICalculate and record the MOI of the bat to thenearest 1 oz-in.2(18 kg-mm2) using Eq 5:I 5 WtBP a!COP Ic(5)where:Wt= total weight of the bat (oz or kg)a = distance from distal end to the
26、pivot point, a = 6 in.(152.4 mm)8. Report8.1 Report the following information:8.1.1 Name of the test operator and test facility,8.1.2 Test date,8.1.3 Test equipment used for this test method,8.1.4 Bat model, length, weight tested, and any otherpertinent data, such as condition of the bat or modifica
27、tion tothe bat,8.1.5 W6,W24, and Wt,8.1.6 Balance point,8.1.7 Measured periods, average period, and8.1.8 Bat COP, MOI, and MOI of bat pivot support.9. Precision and Bias9.1 Precision and bias evaluations have not been conductedfor this test method. When such data are available, a precisionand bias s
28、ection will be added.10. Keywords10.1 balance point, BP; baseball bat; bat; center of percus-sion, COP; moment of inertia, MOI; softball batASTM International takes no position respecting the validity of any patent rights asserted in connection with any item mentionedin this standard. Users of this
29、standard are expressly advised that determination of the validity of any such patent rights, and the riskof infringement of such rights, are entirely their own responsibility.This standard is subject to revision at any time by the responsible technical committee and must be reviewed every five years
30、 andif not revised, either reapproved or withdrawn. Your comments are invited either for revision of this standard or for additional standardsand should be addressed to ASTM International Headquarters. Your comments will receive careful consideration at a meeting of theresponsible technical committe
31、e, which you may attend. If you feel that your comments have not received a fair hearing you shouldmake your views known to the ASTM Committee on Standards, at the address shown below.This standard is copyrighted by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-
32、2959,United States. Individual reprints (single or multiple copies) of this standard may be obtained by contacting ASTM at the aboveaddress or at 610-832-9585 (phone), 610-832-9555 (fax), or serviceastm.org (e-mail); or through the ASTM website(www.astm.org). Permission rights to photocopy the standard may also be secured from the ASTM website (www.astm.org/COPYRIGHT/).F2398 103
