1、Designation: F2398 11An 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 standard. The values given in parentheses are mathematicalconversions to SI units that are provided for information onlyand are not considered standard.1.4 This standard does not purport to address all of thesafety concerns, if any, associated with
5、its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2F1881 Test Method for Measuring Baseball Bat Perfor-mance FactorF1890
6、 Test Method for Measuring Softball Bat Perfor-mance FactorF2219 Test Methods for Measuring High-Speed Bat Perfor-mance3. Terminology3.1 Definitions of Terms Specific to This Standard:3.1.1 balance point (BP), nthe distance to the center ofmass measured from the knob end of the bat.3.1.2 center of p
7、ercussion (COP), nalso known as thecenter of oscillation. Forces and impacts at this location willnot induce reactions at the pivot point, 6 in. (152 mm) from theknob end of the bat.3.1.3 cycle, none complete oscillation of a pendulumsupported at the pivot point, 6 in. (152 mm) from the knob endof t
8、he bat.3.1.4 moment of inertia (MOI), nalso known as the massmoment of inertia, the measure of the bats resistance tochanges in its rotation rate about the pivot point, 6 in. (152mm) from the knob end of the bat.3.1.5 period, nthe time required for a pendulum to oscil-late through one complete cycle
9、.4. Significance and Use4.1 This test method offers a laboratory means to measurethe inertial properties of bats, specifically weight, 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
10、provide sports governingbodies the means to establish rules regarding the physicalproperties of bats, specifically MOI.5. Apparatus5.1 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
11、 weight up to 48oz (1361 g) to the nearest 0.0035 oz (0.1 g).5.1.3 Electronic Timer, suitable device sufficiently accuratefor measuring 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 fr
12、eely (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 location.The clamp shall be rotationally balanced and have a maximumMOI of 4 oz-in.2(73 kg-mm2) measured about the bat pivotlocation (see Fig. 1). The MOI of the clamp sha
13、ll not changewith the diameter of the bat being tested.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 April 1, 2011. Published May 2
14、011. Originallyapproved in 2004. Last previous edition approved in 2010 as F2398 10. DOI:10.1520/F2398-11.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standa
15、rds Document Summary page onthe ASTM website.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.6. Calibration and Standardization6.1 Calibration RodThe calibration rod shall be 1 6 0.01in. (25.4 6 0.25 mm) in diameter by 34 6 0.1 in. (
16、864 6 2.5mm) long, solid aluminum.6.2 Target Calibration MOIMeasure the length and theweight of the calibration rod. Compute the target calibrationrod MOI using 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
17、, 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)6.3 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 out
18、side the allowed range, check thecalibrations of the scales and support fixture.6.4 Mass Moment of Inertia CalibrationUsing the mea-sured properties of the 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 th
19、e 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 Determination of BP:7.1.1 Measure and record the overall bat length to thenearest 0.06 in. (1.5 mm). Place the bat level on the BP fixtureas shown in Fi
20、g. 2. Record the measured weights (W6and W24)to the nearest 0.035 oz (1.0 g). Calculate the BP relative to theknob end of the bat using Eq 2:BP 56W61 24W24Wt(2)where:BP = BP from knob end of the bat, in. (mm)W6= weight of the bat measured 6 in. (152 mm) from theknob, oz (g)W24= weight of the bat mea
21、sured 24 in. (610 mm) fromthe knob, oz (g)Wt=W6+W24= total weight of the bat, oz (g)7.2 Determination of COP:7.2.1 Apply the clamp to the bat handle so that the pivotlocation (point of the vee on underside of the clamp) is 6 60.03 in. (152 6 0.8 mm) from the knob end of the bat (see Fig.1). Hang the
22、 bat in the stand making sure the bat hangsvertically and can swing freely about the pivots. If the bat doesnot hang vertically, correct by centering the bat between thepivots.7.2.2 Rotate the bat about the pivot to an angle of 5 fromthe vertical. Release the bat and allow it to swing freely (seeFig
23、. 1). Allow the bat to swing through five cycles (that is,settle into simple pendulum oscillation). Start the electronictimer when bat reaches the fifth swing cycle. Stop the timeronce the bat has completed 15 full cycles. The timer shall betriggered by a light beam broken by the path of the bat at
24、theFIG. 1 MOI FixtureF2398 112bottom of the pendulum arc. Do not use these results if thestandard deviation of 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= peri
25、od of the ithoscillation (s)7.2.3 Calculate and record the bat COP relative to the 6-in.(152-mm) pivot point 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 Calculate and record the MOI of the bat to the nearest1 oz-in.2(18 kg-mm2) using
26、Eq 5:I 5 WtBP a!COP Ic(5)where:Wt= total weight of the bat (oz or kg)a = distance from knob end to the 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
27、Bat model, length, weight tested, and any otherpertinent data, such as condition of the bat or modification 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 evalu
28、ations have not been conductedfor this test method. When such data are available, a precisionand bias section 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 valid
29、ity of any patent rights asserted in connection with any item mentionedin this standard. Users of this 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 subje
30、ct to revision at any time by the responsible technical committee and must be reviewed every five years 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 Headquart
31、ers. Your comments will receive careful consideration at a meeting of theresponsible technical committee, 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
32、 is copyrighted by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959,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/).FIG. 2 Balance Point FixtureF2398 113
