1、Designation: F2398 11 (Reapproved 2015) An 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 yea
2、r oforiginal adoption 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
3、center of percussion (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 test
4、method.1.3 The values 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 an
5、y, associated with 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 Perfo
6、r-mance Factor (Withdrawn 2014)3F1890 Test Method for Measuring Softball Bat PerformanceFactorF2219 Test Methods for Measuring High-Speed Bat Perfor-mance3.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 kn
7、ob 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, 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
8、 in. (152 mm) from the knob 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 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 os
9、cil-late through one complete cycle.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 thisdocume
10、nt.4.2 Use of this test method can 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 We
11、ight Scales, suitable for measuring 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 hel
12、d 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 location.The clamp shall be rotationally balanced and have a maximumMOI of 4 oz-in.2(73 kg-mm2) measured about the bat pivot1This test m
13、ethod is under the jurisdiction of ASTM Committee F08 on SportsEquipment, Playing Surfaces, and Facilities and is the direct responsibility ofSubcommittee F08.26 on Baseball and Softball Equipment.Current edition approved Oct. 1, 2015. Published November 2015. Originallyapproved in 2004. Last previo
14、us edition approved in 2011 as F2398 11. DOI:10.1520/F2398-11R15.2For 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 standards Document Summary page onthe ASTM webs
15、ite.3The last approved version of this historical standard is referenced onwww.astm.org.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1location (see Fig. 1). The MOI of the clamp shall not changewith the diameter of the bat being tes
16、ted.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. (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 u
17、sing Eq. 1:IT5 WcHLc2121SLc22 dD2J1Ic(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.
18、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, check thecalibrations of the scales and support fixture.6.4 Mass Moment of Inertia CalibrationUsing the mea-sured properties of the ca
19、libration 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 Determinat
20、ion 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 Fig. 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 56W6124W24Wt(2
21、)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 measured 24 in. (610 mm) from theknob, 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 th
22、e 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 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 b
23、etween thepivots.FIG. 1 MOI FixtureF2398 11 (2015)27.2.2 Rotate the bat about the pivot to an angle of 5 fromthe vertical. Release the bat and allow it to swing freely (seeFig. 1). Allow the bat to swing through five cycles (that is,settle into simple pendulum oscillation). Start the electronictimer
24、 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 thebottom of the pendulum arc. Do not use these results if thestandard deviation of the last 10 period measurements isgreater
25、 than 0.001 s. Determine and record the average periodfor the bat, T, using Eq 3:T 5110p61p711p15! (3)where:T = average period (s), andpi= period 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 5T2g42(4)where:g = gravi
26、ty 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 Eq 5:I 5 WtBP 2 a!COP 2 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
27、 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 modification tothe bat,8.1.5 W6,W24, and Wt,8.1.6 Balance p
28、oint,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 section will be added.10. Keywords10.1 balance point
29、, BP; baseball bat; bat; center ofpercussion, 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 standard are expressly advised that determination of
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31、our 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 committee, which you may attend. If you feel that your commen
32、ts 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 19428-2959,United States. Individual reprints (single or mu
33、ltiple 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 Copyright Clearance Center, 222Rosewood Drive, Danvers, MA 01923, Tel: (978) 646-2600; http:/ 2 Balance Point FixtureF2398 11 (2015)3
