1、Designation: F2845 10Standard Test Method forMeasuring the Dynamic Stiffness (DS) and CylindricalCoefficient of Restitution (CCOR) of Baseballs andSoftballs1This standard is issued under the fixed designation F2845; the number immediately following the designation indicates the year oforiginal adopt
2、ion 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 This procedure describes a method of measuring thedynamic stiffness (DS)
3、and cylindrical coefficient of restitution(CCOR) of baseballs and softballs providing similar impactforces and ball deformation as are observed in a bat-ballcollision.1.2 This procedure is for a ball that is intended for the gameof baseball or softball.1.3 The test method is based on ball speed meas
4、urementsbefore and after impact with a cylindrical test surface and theimpact force between the ball and impacted surface.1.4 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
5、 onlyand are not considered standard.1.5 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 applica-bility of regulatory lim
6、itations prior to use.2. Referenced Documents2.1 ASTM Standards:2E177 Practice for Use of the Terms Precision and Bias inASTM Test MethodsE691 Practice for Conducting an Interlaboratory Study toDetermine the Precision of a Test Method3. Terminology3.1 Definitions of Terms Specific to This Standard:3
7、.1.1 baseball or softball, nany ball defined by the rulesfor the game of baseball or softball, respectively.3.1.2 cylindrical coeffcient of restitution (CCOR), ntheratio of the rebound to incoming speed of a ball impacting asolid rigid cylinder.3.1.3 dynamic stiffness (DS), na normalized measure oft
8、he ball impact force having units of stiffness (lb/in. or kN/m).It is obtained by dividing the square of the peak force betweenthe ball and impact surface by the ball mass and the square ofthe incoming ball speed.4. Summary of Test Method4.1 A load cell or array of cells is mounted between acylindri
9、cal solid steel impact surface and a rigid wall. The ballspeed is measured before and after impact with the impactsurface and the force is measured throughout the impact event.4.2 Method AThe cylindrical impact surface for softballsis 2.25 6 0.01 in. (57.2 6 0.3 mm) in diameter. The ballinbound spee
10、d is 95 mph (42.5 m/s).4.3 Method BThe cylindrical impact surface for baseballsis 2.62 6 0.01 in. (66.7 6 0.3 mm) in diameter. The ballinbound speed is 115 mph (51.4 m/s).5. Significance and Use5.1 1 The ball dynamic stiffness is a measure of a ballshardness. Its measurement is conducted to represen
11、t bat-ballimpact forces. It is normalized by the ball weight and speed tominimize the influence of manufacturing and test variationsfrom the measure.5.2 The cylindrical coefficient of restitution is a ball prop-erty of relative velocity change caused by impact with acylindrical surface.5.3 This test
12、 method compares the performance of baseballsand softballs after impact with a cylindrical test surface.5.4 Sports associations can use DS and CCOR measure-ments in specifications for official baseballs and softballs.6. Apparatus6.1 Strike Plate:6.1.1 Load CellAdevice capable of measuring force up t
13、o10 kip (45 kN) within 61 %. The peak load-cell reading afterball impact due to oscillation shall not exceed 5 % of themeasured peak impact force.1This test method is under the jurisdiction of ASTM Committee F08 on SportsEquipment and Facilities and is the direct responsibility of Subcommittee F08.2
14、6 onBaseball and Softball Equipment.Current edition approved May 1, 2010. Published June 2010. DOI: 10.1520/F2845-10.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to
15、 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.6.1.2 Impact SurfaceA 4 6 0.1-in. (102 6 2-mm) longsolid steel half cylinder of diameter prescribed by Method A orB.6.1.3 Mountin
16、gThe load cell and impact surface shall besecured to a massive rigid wall, and fastened sufficiently secureto prevent movement during ball impact. Thread-lockingliquids help prevent fasteners from coming loose and reduceload-cell oscillations.6.2 Ball Throwing DeviceA ball throwing device capableof
17、delivering the ball through the electronic speed monitorwithin 61 mph (60.14 in./s, 60.5 m/s) of the desired speed.Balls shall be oriented to impact the strike surface between thestitches.6.3 Electronic Speed Monitors3An electronic ball-speedmeasuring system consisting of two vertical light screensm
18、ounted 12 6 0.03 in. (305 6 0.8 mm) apart, and aphotoelectric sensor located at each screen that triggers atiming device on ball passage to measure the time for the ballto traverse the distance between the two vertical planes beforeand after impact with the strike plate. Accuracy shall be 60.1mph (6
19、0.014 in./s , 60.05 m/s).6.4 Data AcquisitionThe signal from the load cell shall besampled at a frequency of at least 100 kHz while it is in contactwith the ball.7. Preparation of Apparatus7.1 Mount the cylindrical impact surface and load cell on arigid wall. Verify all fasteners are tightened accor
20、ding tolaboratory procedure to minimize load-cell oscillation.7.2 Position the speed monitors so that the first speedmonitor (light screen) is 12 6 0.1 in. (305 6 2 mm) from thestrike plate (see Fig. 1).8. Conditioning8.1 Ball Conditioning and Test-Room Conditioning:8.1.1 Test balls shall be stored
21、in an environmentallycontrolled space for at least 14 days immediately beforetesting.8.1.2 Temperature is to be maintained at 72 6 4F (22 62C).8.1.3 Relative humidity (RH) is to be maintained between40 and 60 %.8.1.4 Temperature and relative humidity are to be measuredand recorded hourly within 0.5F
22、 (0.3C) and 2 % RH overconditioning and test durations.9. Procedure9.1 Select the desired test method according to 4.2 or 4.3.9.2 Set the ball throwing device to the test target speedwithin 6 1 mph (60.14 in./s , 0.5 m/s). Results from shotsabove or below this speed range will not be used.9.3 A mini
23、mum 1-min rest period is required between eachshot. A non-contact temperature sensor shall be used to verifythe ball temperature remains within the specified test-roomtemperature range.9.4 The ball shall be rotated after each impact among itsfour ears or surfaces with maximum spacing between thestit
24、ches.9.5 Verify proper alignment by observing the rebound pathof the ball after impact. The ball rebound angle after impactwith the impact surface should be within 6 5 of the inboundball path.9.6 Compare the impulse from the ball speed and impactforce.9.6.1 Calculate the impulse from the impact forc
25、e by:LF5*Ft!dt (1)where:LF= force impulse, lb-s (N-s), andF(t) = force measurement during impact, lb (N).9.6.2 Calculate the impulse from the ball speeds by:LS5mcLV 1 S! (2)where:LS= speed impulse, lb-s (N-s),m = ball mass, oz (g),3The sole source of supply of the apparatus (IBeam Sensor or equivale
26、nt) knownto the committee at this time is Automated Design Corporation, 1404 Joliet Road,Suite B, Romeoville, IL 60446, http:/ If you are awareof alternative suppliers, please provide this information to ASTM InternationalHeadquarters. Your comments will receive careful consideration at a meeting of
27、 theresponsible technical committee,1which you may attend.FIG. 1 Test ApparatusF2845 102V = incoming speed, mph (m/s),S = outgoing ball speed, mph (m/s), andcL= unit conversion factor, 350.99 US (1000 SI).49.6.3 Calculate the impulse ratio by:K 5LSLF(3)where:K = impulse ratio,LS= speed impulse, lb-s
28、 (N-s), andLF= force impulse, lb-s (N-s).9.7 The speeds and forces from the six valid impacts foreach ball are averaged to determine the DS and CCOR for aball.9.7.1 For an impact to be valid the ball inbound speed andrebound trajectory must be within the allowable respectivetolerance for speed and t
29、rajectory and the impulse ratio mustfall between 0.9 and 1.1.9.7.2 For a ball test result to be valid, the standard deviationof the six impulse ratios of a ball must be less than 0.02.9.7.3 For cases of excessive invalid hits due to the impulseratio requirements, check light-gate and load-cell calib
30、rationsand ball-weight measurement.9.7.4 Formula:DS 5cS6mFSK1F1V1D21SK2F2V2D21SK3F3V3D21SK4F4V4D21SK5F5V5D21SK6F6V6D2G(4)CCOR 516FV1S11V2S21V3S31V4S41V5S51V6S6G(5)where:DS = dynamic stiffness, lb/in (kN/m),CCOR = cylindrical coefficient of restitution,V = incoming speed, mph (m/s),S = outgoing ball
31、speed, mph (m/s),F = peak impact force, lb (N),m = ball mass, oz (g), andcS= unit conversion factor - 19.943 US (1 SI).510. Report10.1 Report the following information:10.1.1 Name of test facility and test operator,10.1.2 Test date,10.1.3 Hourly measurements of test conditions including:10.1.3.1 Rel
32、ative humidity and temperature of the ball-conditioning and test-room environments,10.1.3.2 Number of days ball was in conditioning environ-ment.10.1.4 Test equipment used for this method.10.1.5 Test ball information including weight, circumfer-ence, model and manufacturer.10.1.6 For each impact (in
33、cluding invalid impacts) ballinbound speed, rebound speed, CCOR, peak force and DS.10.1.7 Any important observations including but not exclu-sively, damage to the ball, unusual noises or vibrations and thenumber of invalid impacts for each ball.10.1.8 Respective calibration dates for load cells and
34、veloc-ity timers.11. Precision and Bias611.1 The precision of this test method is based on aninterlaboratory study conducted in 2009. Five laboratoriesparticipated in this study. Each of the labs was asked to reportthree replicate test results for eighteen different balls (nine setsof two). After co
35、mpleting their measurements on the first set,the laboratories sent their nine balls to a second laboratory foranother round of testing (Round 2). Every “test result” reportedrepresents a single determination or measurement. PracticeE691 was followed for the design and analysis of the data.11.1.1 Rep
36、eatability limit (r)Two test results obtainedwithin one laboratory shall be judged not equivalent if theydiffer by more than the “r” value for that material; “r” is theinterval representing the critical difference between two testresults for the same material, obtained by the same operatorusing the
37、same equipment on the same day in the samelaboratory.11.1.1.1 Repeatability limits are listed in Tables 1-3 below.11.1.2 Reproducibility limit (R)Two test results shall bejudged not equivalent if they differ by more than the “R” valuefor that material; “R” is the interval representing the criticaldi
38、fference between two test results for the same material,obtained by different operators using different equipment indifferent laboratories.11.1.2.1 Reproducibility limits are listed in Tables 1-3below.11.1.3 The above terms (repeatability limit and reproduc-ibility limit) are used as specified in Pr
39、actice E177.11.1.4 Any judgment in accordance with statements 11.1.1and 11.1.2 would have an approximate 95 % probability ofbeing correct.11.2 BiasAt the time of the study, there was no acceptedreference material suitable for determining the bias for this testmethod, therefore no statement on bias i
40、s being made.11.3 The precision statement was determined through sta-tistical examination of 1080 results, from five laboratories, onnine sets of ball samples. To judge the equivalency of two testresults, it is recommended to choose a sample material closestin characteristics to the test material.12
41、. Keywords12.1 ball elasticity; ball hardness; baseball; cylindrical co-efficient of restitution; dynamic stiffness; softball4The conversion factor is found from (16 oz/lb)(32.174 ft/s2)(1 mi/5280 ft)(3600s/hr) = 350.99 (oz/lb s)(mi/hr) US or (1000 g/kg) = 1000 SI.5The conversion factor is found fro
42、m (16 oz/lb)(386.088 in/s2)(1 mi/63360in)2(3600 s/hr)2= 19.943 (oz/in lb)(mi/hr)2US or (1000 g/kg)(1 kN/1000 N)=1SI.6Supporting data have been filed at ASTM International Headquarters and maybe obtained by requesting Research Report RR:F08-1010.F2845 103TABLE 1 Dynamic Stiffness (lb/in.)Sample Avera
43、ge RepeatabilityStandardDeviationReproducibilityStandardDeviationRepeatabilityLimitReproducibilityLimitxsrsRrRBall 1 Round 1 6943.2 243.2 425.4 680.9 1191.2Ball 1 Round 2 6744.3 114.1 433.1 319.6 1212.8Ball 2 Round 1 6783.4 117.3 317.8 328.5 889.8Ball 2 Round 2 6554.0 113.8 314.0 318.7 879.3Ball 3 R
44、ound 1 8190.8 135.1 499.5 378.3 1398.5Ball 3 Round 2 8117.6 233.2 626.1 652.9 1753.1Ball 4 Round 1 7186.5 115.1 332.8 322.1 931.8Ball 4 Round 2 7080.3 203.2 356.4 569.0 997.9Ball 5 Round 1 8539.3 166.5 609.2 466.3 1705.8Ball 5 Round 2 8356.7 205.2 650.9 574.6 1822.5Ball 6 Round 1 8111.8 128.3 568.5
45、359.2 1591.9Ball 6 Round 2 8254.4 329.7 526.8 923.3 1475.1Ball 7 Round 1 8025.8 146.2 575.5 409.3 1611.3Ball 7 Round 2 7870.2 353.8 582.4 990.8 1630.9Ball 8 Round 1 7778.4 114.5 583.8 320.6 1634.6Ball 8 Round 2 7738.9 421.0 627.5 1178.9 1757.0Ball 9 Round 1 7419.5 122.6 582.9 343.2 1632.1Ball 9 Roun
46、d 2 7064.9 159.5 348.0 446.5 974.4TABLE 2 Mass (ounces)Sample Average RepeatabilityStandardDeviationReproducibilityStandardDeviationRepeatabilityLimitReproducibilityLimitxsrsRrRBall 1 Round 1 4.9641 0.0068 0.0262 0.0191 0.0734Ball 1 Round 2 4.9539 0.0018 0.0240 0.0052 0.0673Ball 2 Round 1 4.9080 0.0
47、090 0.0231 0.0251 0.0646Ball 2 Round 2 4.9067 0.0032 0.0295 0.0090 0.0825Ball 3 Round 1 5.2238 0.0062 0.0264 0.0174 0.0739Ball 3 Round 2 5.2254 0.0030 0.0354 0.0083 0.0991Ball 4 Round 1 5.1245 0.0089 0.0356 0.0250 0.0996Ball 4 Round 2 5.1196 0.0032 0.0349 0.0089 0.0977Ball 5 Round 1 5.2575 0.0069 0.
48、0303 0.0193 0.0849Ball 5 Round 2 5.2505 0.0019 0.0165 0.0053 0.0463Ball 6 Round 1 5.1193 0.0461 0.0462 0.1291 0.1294Ball 6 Round 2 5.1161 0.0027 0.0202 0.0077 0.0564Ball 7 Round 1 5.0294 0.0048 0.0491 0.0133 0.1376Ball 7 Round 2 5.0402 0.0032 0.0456 0.0089 0.1276Ball 8 Round 1 5.1135 0.0056 0.0437 0
49、.0157 0.1223Ball 8 Round 2 5.1052 0.0039 0.0205 0.0108 0.0574Ball 9 Round 1 5.1613 0.0058 0.0392 0.0161 0.1097Ball 9 Round 2 5.1467 0.0107 0.0220 0.0300 0.0616F2845 104ASTM 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 the validity of any such patent rights, and the riskof infringement of such rights, are entirely their own responsibility.This standard is subject to revis
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