1、Designation: F2845 14Standard 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 load cells is mounted between acyl
9、indrical 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.5. Significance and Use5.1 1 The ball dynamic stiffness is a measure of a ballshardness. Its measurement is conducted t
10、o represent 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
11、 This test 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 CellA device capable of measuring
12、 force up to10 kip (45 kN) within 61 %. The peak load-cell reading afterball impact due to oscillation shall not exceed 5 % of themeasured peak impact force.6.1.2 Impact SurfaceA46 0.1-in. (102 6 2-mm) longsolid steel half cylinder. For softballs, the diameter of the half1This test method is under t
13、he 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 March 1, 2014. Published March 2014. Originallyapproved in 2010. Last previous edition approve
14、d in 2011 as F2845 11. DOI:10.1520/F2845-14.2For 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 website.Copyright ASTM In
15、ternational, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1cylinder is 2.25 6 0.01 in. (57.2 6 0.3 mm). For baseballs thediameter of the half cylinder is 2.62 6 0.01 in. (66.7 6 0.3mm).6.1.3 MountingThe load cell and impact surface shall besecured to a massive r
16、igid 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 delivering the ball through the electronic speed monitorwithin 61
17、 mph (60.5 m/s) of the desired speed. Balls shall beoriented to impact the strike surface between the stitches.6.3 Electronic Speed Monitors3An electronic ball-speedmeasuring system consisting of two vertical light screensmounted 12 6 0.03 in. (305 6 0.8 mm) apart, and aphotoelectric sensor located
18、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 (60.05 m/s).6.4 Data AcquisitionThe signal from the load cell shall besampled a
19、t 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 according tolaboratory procedure to minimize load-cell oscillation.7.2 Position the speed monitor
20、s so that the first speedmonitor (light screen) is 12 6 0.1 in. (305 6 3 mm) from thestrike plate (see Fig. 1).8. Calibration and Standardization8.1 Ball Speed GateThe distance between the sensors ofthe speed gates should be measured and recorded. The timersused for speed measurements should be cali
21、brated on at least ayearly basis.8.2 Load CellsThe load cells used to measure the impactforce should be calibrated on at least a yearly basis.9. Conditioning9.1 Ball Conditioning and Test-Room Conditioning:9.1.1 Test balls shall be stored in an environmentallycontrolled space for at least 14 days im
22、mediately beforetesting.9.1.2 Temperature is to be maintained at 72 6 4F (22 62C).9.1.3 Relative humidity (RH) is to be maintained between40 and 60 %.9.1.4 Temperature and relative humidity are to be measuredand recorded hourly within 0.5F (0.3C) and 2 % RH overconditioning and test durations.10. Pr
23、ocedure10.1 Set the ball throwing device to 95 mph (42.5 m/s) forsoftballs and 115 mph (51.4 m/s) for baseballs. Results frominbound speeds exceeding 61 mph (60.5 m/s) of the targetspeed will not be used.10.2 Record the inbound speed, rebound speed, force-timedata and peak impact force.10.3 Aminimum
24、 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.10.4 The ball shall be rotated after each impact among itsfour ears or surfaces with maximum spacing between thestitch
25、es.10.5 Verify proper alignment by observing the rebound pathof the ball after impact. The ball rebound angle after impactwith the impact surface should be within 65 of the inboundball path.10.6 Compare the impulse from the ball speed and impactforce.10.6.1 Calculate the impulse from the impact forc
26、e by:LF5 *t0t1Ft!dt (1)where:LF= force impulse (area under the force-time curve), lb-s(N-s),3The sole source of supply of the apparatus (IBeam Sensor or equivalent) knownto the committee at this time is Automated Design Corporation, 1404 Joliet Road,Suite B, Romeoville, IL 60446, http:/ If you are a
27、wareof alternative suppliers, please provide this information to ASTM InternationalHeadquarters. Your comments will receive careful consideration at a meeting of theresponsible technical committee,1which you may attend.FIG. 1 Test ApparatusF2845 142F(t) = force measurement during impact, lb (N),t0=
28、time when F(t) exceeds 20 lb (89 N) (s), andt1= time after the peak force is reached when F(t) is lessthan 20 lb (89 N) (s).10.6.2 Calculate the impulse from the ball speeds by:LS5mcLV1S! (2)where:LS= speed impulse, lb-s (N-s),m = ball mass, oz (g),V = incoming speed, mph (m/s),S = outgoing ball spe
29、ed, mph (m/s), andcL= unit conversion factor, 350.99 US (1000 SI).410.6.3 Calculate the impulse ratio by:K 5LSLF(3)where:K = impulse ratio,LS= speed impulse, lb-s (N-s), andLF= force impulse, lb-s (N-s).10.7 The speeds and forces from the six valid impacts foreach ball are averaged to determine the
30、DS and CCOR for aball.10.7.1 For an impact to be valid the ball inbound speed andrebound trajectory must be within the allowable respectivetolerance for speed and trajectory and the impulse ratio mustfall between 0.9 and 1.1.10.7.2 For a ball test result to be valid, the standarddeviation of the six
31、 impulse ratios of a ball must be less than0.02.10.7.3 For cases of excessive invalid hits due to the impulseratio requirements, check light-gate and load-cell calibrationsand ball-weight measurement.10.7.4 Formula:DS 5cS6m(i516SKiFiViD2(4)CCOR 516(i516SiVi(5)where:DS = dynamic stiffness, lb/in (kN/
32、m),CCOR = cylindrical coefficient of restitution,Vi= incoming ball speed of the ithtest, mph (m/s),Si= outgoing ball speed of the ithtest, mph (m/s),Fi= peak impact force of the ithtest, lb (N),m = ball mass, oz (g), andcS= unit conversion factor - 19.943 US (1 SI).511. Report11.1 Report the followi
33、ng information:11.1.1 Name of test facility and test operator,11.1.2 Test date,11.1.3 Hourly measurements of test conditions including:11.1.3.1 Relative humidity and temperature of the ball-conditioning and test-room environments,11.1.3.2 Number of days ball was in conditioning environ-ment.11.1.4 T
34、est equipment used for this method.11.1.5 Test ball information including weight,circumference, model and manufacturer.11.1.6 For each impact (including invalid impacts) ballinbound speed, rebound speed, CCOR, peak force and DS.11.1.7 Any important observations including but notexclusively, damage t
35、o the ball, unusual noises or vibrationsand the number of invalid impacts for each ball.11.1.8 Respective calibration dates for load cells and veloc-ity timers.12. Precision and Bias612.1 The precision of this test method is based on aninterlaboratory study conducted in 2009. Five laboratoriespartic
36、ipated in this study. Each of the labs was asked to reportthree replicate test results for eighteen different balls (nine setsof two). After completing their measurements on the first set,the laboratories sent their nine balls to a second laboratory foranother round of testing (Round 2). Every “test
37、 result” reportedrepresents a single determination or measurement. PracticeE691 was followed for the design and analysis of the data.12.1.1 Repeatability limit (r)Two test results obtainedwithin one laboratory shall be judged not equivalent if theydiffer by more than the “r” value for that material;
38、 “r” is theinterval representing the critical difference between two testresults for the same material, obtained by the same operatorusing the same equipment on the same day in the samelaboratory.12.1.1.1 Repeatability limits are listed in Tables 1-3.12.1.2 Reproducibility limit (R)Two test results
39、shall bejudged not equivalent if they differ by more than the “R” valuefor that material; “R” is the interval representing the criticaldifference between two test results for the same material,obtained by different operators using different equipment indifferent laboratories.12.1.2.1 Reproducibility
40、 limits are listed in Tables 1-3.12.1.3 The above terms (repeatability limit and reproduc-ibility limit) are used as specified in Practice E177.12.1.4 Any judgment in accordance with statements 12.1.1and 12.1.2 would have an approximate 95 % probability ofbeing correct.12.2 BiasAt the time of the st
41、udy, there was no acceptedreference material suitable for determining the bias for this testmethod, therefore no statement on bias is being made.12.3 The precision statement was determined through sta-tistical examination of 1080 results, from five laboratories, onnine sets of ball samples. To judge
42、 the equivalency of two testresults, it is recommended to choose a sample material closestin characteristics to the test material.4The 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 foun
43、d from (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 14313. Keywords13.1 ball elasticity; ball h
44、ardness; baseball; cylindrical co-efficient of restitution; dynamic stiffness; softballTABLE 1 Dynamic Stiffness (lb/in.)Sample Average RepeatabilityStandardDeviationReproducibilityStandardDeviationRepeatabilityLimitReproducibilityLimitxsrsRrRBall 1 Round 1 6943.2 243.2 425.4 680.9 1191.2Ball 1 Roun
45、d 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 Round 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.
46、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 8111.8 128.3 568.5 359.2 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 77
47、78.4 114.5 583.8 320.6 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 Round 2 7064.9 159.5 348.0 446.5 974.4TABLE 2 Mass (ounces)Sample Average RepeatabilityStandardDeviationReproducibilityStandardDeviationRepeatabilityLimitReproducibilityLi
48、mitxsrsRrRBall 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 0.0090 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.
49、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 0.0303 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 0.0157 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
