1、Designation: F 2398 04e1An 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 F 2398; the number immediately following the designation indicates the year oforiginal ad
2、option or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.e1NOTEFigure 2 editorially corrected in July 2004.1. Scope1.1 This test method co
3、vers a method for determining themoment of inertia (MOI) and balance point (BP) of baseballand softball bats. These physical properties are used in calcu-lations in other key ASTM standards.1.2 The MOI and BP are measured in the laboratory on testequipment meeting the requirements defined in this te
4、stmethod.1.3 The values 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 an
5、d determine the applica-bility of regulatory limitations prior to use.2. Terminology2.1 Definitions of Terms Specific to This Standard:2.1.1 balance point (BP)the distance to the center of massmeasured from the distal end of the bat knob.2.1.2 center of percussion (COP)also known as the centerof osc
6、illation, the length of a simple pendulum with the sameperiod as a physical pendulum, as in a bat oscillating on apivot. Forces and impacts at this location will not induce axialreactions at the pivot point.2.1.3 cycleone complete performance of the oscillation ofthe bat, specifically, one full swin
7、g of the bat.2.1.4 moment of inertia (MOI)a measure of mass distri-bution relative to an axis of rotation. It is the product of themass multiplied by the square of the distance to the mass,summed over the entire bat.2.1.5 periodthe time required for a pendulum to oscillatethrough one complete cycle.
8、3. Significance and Use3.1 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.3.2 Use of this test method can p
9、rovide sports governingbodies the means to establish rules regarding the physicalproperties of bats, specifically MOI.4. Apparatus4.1 Bat MOI Test Apparatus:4.1.1 Ruler, suitable for measuring lengths up to 42 in.(1067 mm) to the nearest 0.031 in. (0.79 mm).4.1.2 Weight Scale, suitable for measuring
10、 weight up to 48oz (1360 g) to the nearest 0.0035 oz (0.1 g).4.1.3 Electronic Timer, suitable device sufficiently accuratefor measuring time to the nearest 1 s (0.000001 s).4.1.4 MOI StandA frame with a pivoting bat collar-clamplarge enough to allow a bat held in a vertical position to swingfreely (
11、see Fig. 1).4.1.5 Bat Collar-ClampA part of the MOI stand thatallows quick accurate mounting of the bat without a variableMOI effect due to the clamp with a maximum MOI of 4oz-in.2(0.8 kg-cm2) measured about the bat pivot location. Alightweight clamp or collar that can hold the weight of a batand pr
12、ovide a fixed pivot location. Collar shall be rotationallybalanced (see Fig. 1).5. Calibration and Standardization5.1 Calibration RodA calibration rod tested at two differ-ent pivot locations shall be used to determine if the MOI standis capable of accurately measuring the MOI of a bat. The rodshall
13、 be a 1-in. (25.4-mm) diameter by 24-in. (609.6-mm) longsteel rod weighing 85.65 oz (2.43 kg). The MOI of this rodmeasured with the pivot location at 8 in. (20.32 cm) should be5487 oz-in.2(1003 kg-cm2) and at a pivot location of 2 in.1This test method is under the jurisdiction of ASTM Committee F08
14、on SportsEquipment and Facilities and is the direct responsibility of Subcommittee F08.26 onBaseball and Softball Equipment and Facilities.Current edition approved May 1, 2004. Published May 2004.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, Uni
15、ted States.(50.8 mm) should be 12 682 oz-in.2(2319.5 kg-cm2). Devia-tions of more than 50 oz-in.2(9.15 kg-cm2), after accounting forthe MOI of the clamp fixture, shall be rectified before bats aretested.6. Procedure6.1 Determination of BPMeasure and record the overallbat length to the nearest 0.0625
16、 in. (1.58 mm). Place bat levelon BP stand as shown in Fig. 2. Record the weight measured bythe 6-in. (Wt6) and the 24-in. (Wt24) scales to the nearest 0.035oz (1.0 g). Eq 1 calculates the BP relative to the distal end ofthe bat knob.BP 5F6Wt6! 1 24Wt24!Wt61 Wt24!G(1)where:BP = BP from distal end of
17、 the bat knob,Wt6= Weight of the bat measured 6 in. from the knob,Wt24= Weight of the bat measured 24 in. from the knob,andWt=Wt6+Wt24= total weight of the bat.6.2 Determination of Bat COP and MOI:6.2.1 Bat MOI Set-UpApply MOI collar-clamp to bathandle so that the pivot location, (point of the vee o
18、n undersideof the clamp) is 6 in. + 0.031 in. (152.4 mm + 0.8 mm) fromthe distal end of the bat knob (see Fig. 1). Hang bat in the MOIstand making sure the bat hangs vertically and can swing freelyabout the pivots. If bat does not hang vertically, correct bycentering the bat to the pivots.FIG. 1 - M
19、OI FixtureFIG. 2 BP FixtureF239804e126.2.2 COP TestRotate the bat about the pivots to an angleof 5 from vertical. Release bat and allow to swing freely (seeFig. 1). Allow bat to swing through five cycles and to settle intosimple pendulum oscillation. Start the electronic timer whenbat reaches the bo
20、ttom of the swing cycle. Stop the timer oncethe bat has completed ten full cycles. The timer shall betriggered by a light beam broken by the path of the bat at thebottom of the pendulum arc. Repeat test five times to minimizetiming errors. Do not use these results if the standard deviationof the fiv
21、e measurements is greater than 0.5 % of the mean.Instead, repeat the five measurements after repeating section6.2.1. Determine and record the average period for the bat,using Eq 2:average period 5 (2)Stime1no. cycles11time2no. cycles21time3no. cycles31time4no. cycles41time5no. cycles5number of tests
22、 5!D6.2.3 COP LocationCalculate and record bat COP rela-tive to the pivot point location stated in 6.2.1 using Eq 3:COP 5Saverage period!2g4p2 D(3)where:COP, in. = (average period)2(9.779) (in./s2),COP, cm = (average period)2(24.839) (cm/s2), andg = acceleration due to gravity, 32.17 ft/s2(9.806m/s2
23、) or 386.1 in/s2(980.6 cm/s2).6.2.4 MOICalculate and record the MOI of the bat to thenearest 0.1 oz-in.2(18.3 g-cm2) using Eq 4:I 5Saverage period!2gWta4p2 D(4)whereWt= Total weight of the bat,a = distance from pivot point to BP, thus a=BP6 in. (15.24 cm),I, oz-in.2= (average period)2(9.779)(Wt(BP 6
24、 in.), andI, g-cm2= (average period)2(24.839)(Wt(BP 15.24cm).7. Report7.1 Report the following information:7.1.1 Name of the test operator and test facility,7.1.2 Test date,7.1.3 Test equipment used for this test method,7.1.4 Bat model, length, weight tested, and any otherpertinent data, such as con
25、dition of the bat or modification tothe bat,7.1.5 Wt6,Wt24, and Wt,7.1.6 Bat BP,7.1.7 Measured periods, average period, and7.1.8 Bat COP and MOI results and MOI of bat pivotsupport.8. Precision and Bias8.1 Precision and bias evaluations have not been conductedfor this test method. When such data are
26、 available, a precisionand bias section will be added.9. Keywords9.1 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 mentionedi
27、n 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 subject to revision at any time by the responsible technical committee and mu
28、st 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 Headquarters. Your comments will receive careful consideration at a meeting of th
29、eresponsible 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 is copyrighted by ASTM International, 100 Barr Harbor Drive, PO Box C70
30、0, 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).F239804e13
