CCL-K6 Final 2009-02-24 corr 2015-01-05 - BIPM · • Customs clearance and shipping delays. • Last minute withdrawal of one NMI. • Re-commissioning of pilot laboratory closure

CIPM CCL Key comparison: Calibration of CMM 2-D Artifacts 1/162

CCL-K6 Final 2009-02-24 corr 2015-01-05.docx 10/27/2008

Centro Nacional de Metrología

CIPM Key Comparison

CCL KC-6

Calibration

of

Coordinate Measuring Machine (CMM)

Two-dimensional (2-D) Artifacts

(Ball Plates & Bore Plates)

Final Report



1 Introduction ................................................................................................................. 4

2 Organization ............................................................................................................... 4

2.1 Participants .......................................................................................................... 5

2.2 Initial Schedule .................................................................................................... 7

2.3 Problems during circulation .................................................................................. 7

2.4 Final Timetable and Circulation Scheme .............................................................. 8

3 Description of the Standards ....................................................................................... 9

3.1 Artifacts ............................................................................................................... 9

4 Measurement instructions ......................................................................................... 11

4.1 Traceability ........................................................................................................ 11

4.2 Measurands ....................................................................................................... 11

4.3 Measurement instructions .................................................................................. 13

5 Measurement methods and instruments used by the participants ............................. 13

6 Stability and condition of the artifacts ........................................................................ 14

7 Claimed Uncertainties ............................................................................................... 16

8 Measurement Results ............................................................................................... 16

8.1 Steel Ball Plate .................................................................................................. 16

8.2 ZERODUR Bore Plate ....................................................................................... 16

9 Measurement Results in Cylindrical Coordinates ...................................................... 35

9.1 Ball Plate ........................................................................................................... 35


10 Key Comparison Reference Value (KCRV) Determination .................................... 53

10.1 Outlier elimination process ................................................................................. 53

10.2 Uncertainty of the KCRV .................................................................................... 54

10.3 KCRV determination for the Steel Ball Plate ...................................................... 56

10.4 KCRV determination for the ZERODUR Bore Plate ........................................... 57

11 Participants results with respect to KCRV ............................................................. 59

11.1 Steel Ball Plate Results ..................................................................................... 59


11.3 Average Normalized Errors for the Steel Ball Plate ............................................ 59

11.4 Average Normalized Errors for the ZERODUR Bore Plate ................................. 59

11.5 Birge Ratio Calculation ...................................................................................... 61

11.6 Birge Ratio for the Measuring Elements of the Steel Ball Plate .......................... 61

11.7 Birge Ratio for the Measuring Elements of the ZERODUR Bore Plate ............... 61

12 Conclusions .......................................................................................................... 87



12.1 On the results of the comparison ....................................................................... 87

12.2 Suggestions for future comparisons of this kind ................................................. 87

13 Acknowledgements ............................................................................................... 88

14 References ............................................................................................................ 89

Appendix .......................................................................................................................... 90

Equivalences of participant laboratories results (i) with respect to reference values (R) ... 91

Pairwise equivalences between results of participant laboratories i and j ....................... 105



1 Introduction

The metrological equivalence of national measurement standards and calibration certificates issued by National Metrology Institutes (NMIs) is established by a set of key comparisons chosen and organized by the Consultative committees of the CIPM or by the regional organizations in collaboration with the consultative committees.

At its meeting in 1997, the Consultative Committee for Length (CCL) identified several key comparisons in the field of dimensional metrology. In particular, it decided that comparisons on CMM 1-D and CMM 2-D artifacts should be carried out. The Centro Nacional de Metrología (CENAM), was designated as pilot laboratory for the CMM 2-D artifact comparison. It was proposed to start it once the 1-D would be finished. However, at the 1998 meeting, the Chairman of the Working Group in Dimensional Metrology (WGDM), Dr. Jim Pekelsky, urged to start it as soon as possible.

This report of the comparison was circulated among the participants as Draft B v 0.5 and after review and approval by all of them became the final report. It comprises all information about the comparison measurement results (Draft A). In addition, the choice of a Key Comparison Reference Value (KCRV), its estimated uncertainty, the performance of each participant with respect to this value and the Birge ratio of the different measurands of each artifact is presented.

2 Organization

Following the Guidelines to CIPM key comparisons [1] the choice of artifacts and a preliminary list of participants was made, as well as circulation scheme. Then a technical protocol was written [2] by Edgar Arizmendi and Miguel Viliesid from the pilot NMI, CENAM, and sent to the participants.



2.1 Participants

No. COUNTRY REGION CONTACT PERSON / ADDRESS

1 AUSTRALIA APMP Nicholas BROWN

National Metrology Institute of Australia (NMIA1)

Division of Telecommunications and Industrial Physics

National Measurement Laboratory (Room B24E)

Bradfield Rd.

West Lindfield

NSW 2070

Tel. +612-9413-7157, Fax +612-9413-7474

e-mail: [email protected]

2 CANADA SIM Kostadin DOYTCHINOV

Institute for National Measurement Standards

National Research Council Canada (INMS-NRC)

Montreal Rd. M-36

Ottawa, K1A 0R6

Tel. +1-613-991-0265, Fax +1-613-952-1394


3 CHINA APMP Shen SHAOXI

National Institute of Metrology (NIM)

No. 18 Bei San Huan Dong Lu

Beijing.


4 CZECH REPUBLIC EUROMET Vit ZELENY

Czech Metrology Institute (CMI)

V botanice 4

150 72 Praha 5

http://www.cmi.cz/ tel. (+420 2) 57321312, fax. (+420 2) 57328077

[email protected]

5 FRANCE EUROMET Georges-Pierre VAILLEAU

Bureau National de Metrologie-Laboratorie National de'Essais

(BNM-LNE)

Division 32 – Metrologie dimensionelle

1, rue G Boissier

75724 Paris Cedex 15

FRANCE

tel 33 1 40 43 38 24, fax 33 1 40 43 37 37


6 GERMANY EUROMET Heinrich SCHWENKE

5.32 Laboratorium für Koordinatenmessgeraete / CMM-Section

Physikalisch-Technische Bundesanstalt (PTB)

Bundesallee 100

38116 Braunschweig

Fon ++49/531/5925320, Fax ++49/531/5925305


7 JAPAN APMP Tomizo KUROSAWA

National Metrology Institute of Japan (NMIJ2)

1-1-4, Umezono, Tsukuba, Ibaraki 305-8563

Japan

Phone: +81 298 61 4041, Fax: +81 298 61 4042


1 Formerly, CSIRO.

2 Formerly, National Research Laboratory of Metrology, NRLM.



8 NETHERLANDS EUROMET Robbert BERGMANS

Netherlands Meetinstituut VSL B.V. (NMi VSL)

Department of Mechanics

Shoemakerstraat 97

P.O. Box 654

2600 AR Delft

Tel.: 31 15 269 15 00, Fax: 31 15 261 29 71


9 RUSSIA COOMET Valery LYSSENKO

Head of Department of geometrical measurement

VNIIMS

46, Ozernaya

Moskow

119361, Russia

Phone +7 095 4373429, Fax +7 095 4375666

E-mail: [email protected].

10 SOUTH AFRICA3 SADCMET John. R. HANNAFORD

National Metrology Laboratory

CSIR Building 5

Meiring Naude Rd. Brummeria

Pretoria 0001

Tel. +27-12-841-4799, Fax +27-12-841-4458


11 UNITED KINGDOM EUROMET Andrew LEWIS

Centre for Basic, Thermal and Length Metrology

National Physical Laboratory (NPL)

Teddington ,Middlesex, TW11 0LW

Tel: +44 20 8943 6124, Fax: +44 20 8943 2945

email: [email protected]

12 UNITED STATES SIM Jack STONE

National Institute of Standards and Technology (NIST)

Precision Engineering Division

Metrology Bldg. (220), R. A107

MET B113

Gaithersburg, MD 20899-0001

Tel. +1-301-975-5638


13 MEXICO (PILOT) SIM Miguel VILIESID or Edgar ARIZMENDI Centro Nacional de Metrología (CENAM) Jefe de División Metrología Dimensional Apartado Postal1 – 100 Centro Querétaro, Qro 76000 Mexico Tel. +52 4 11-0500 ext.: 3277 or 3282 Fax +52 42 11 0577 e-mail: [email protected] e-mail: [email protected]

Table 1.- List of participants of comparison CCL-K6.

3 This laboratory withdrew form the comparison after receiving the artifacts for

measurement and did not report any results.



2.2 Initial Schedule

An initial time schedule was drawn as shown in Table 2. The circulation of artifacts should have taken place within a 24 month period starting on January 2001 with the participation of 13 NMIs from the five Regional Metrology Organizations (RMO).

Region NMI Country Period

Pilot Laboratory

SIM

CENAM Mexico

NIST USA 01-02-05 to 01-05-04

EUROMET BNM-LNE France 01-05-07 to 01-06-15

PTB Germany 01-06-18 to 01-07-27

CMI Czech Republic4

01-07-30 to 01-09-14

COOMET VNIIMS Russia 01-09-17 to 01-10-26

EUROMET NPL United Kingdom

01-10-29 to 01-12-07

Pilot Laboratory CENAM Mexico6 01-12-10 to 02-01-31

APMP NIM China6 02-02-04 to 02-03-29

NRLM Japan 02-04-01 to 02-05-10

CSIRO Australia 02-05-13 to 02-06-21

SADCMET CSIR South Africa 02-06-24 to 02-08-02

Euromet NMi Netherlands 02-08-05 to 02-09-13

SIM

Pilot Laboratory

NRC Canada 02-09-16 to 02-10-25

CENAM Mexico 02-10-28 to 02-12-06

Table 2.- Initial timetable for the comparison.

2.3 Problems during circulation

Several problems arose during the circulation of the artifacts:

• A few countries were skipped at their initial allocated period and had to be scheduled a new time period after due to custom clearance problems or heavy working load agenda at that NMI at the initial allocated period.

• Official holidays coincided with some participants designated measurement period.

4 This country was allocated a longer period of time for holiday reasons.



• Breakdown of the pilot’s CMM. The machine was out of service for more than two years.

• Unscheduled control measurements made by a designated co-pilot laboratory performed in place of those the pilot laboratory was unable to carry out because their CMM was out of service.

• Re-measurement by one laboratory after detecting problems with their reported measurements.

• Customs clearance and shipping delays.

• Last minute withdrawal of one NMI.

• Re-commissioning of pilot laboratory closure measurements.

• Other delays of some participants.

2.4 Final Timetable and Circulation Scheme

The final circulation scheme and timetable is shown in table 3.

Mexico 1 2001-01-30 Japan 2002-06-13

USA 1 2001-05-04 Australia 2002-10-14

France 2001-06-15 South Africa 2002-11-30

Germany 2001-07-27 Netherlands 2003-01-30

Czech Rep. 2001-09-14 China 2003-04-15

UK 2001-12-07 Russia 2003-12-15

USA 2 2002-01-30 Canada 2004-02-15

China 2002-03-15 USA 3 2004-04-15

Mexico 2 2004-08-25

Table 3.- Final circulation scheme and timetable.



3 Description of the Standards

3.1 Artifacts

The measurement artifacts are the following:

Ball Plate

Make: KOBA

Serial Number: 970224,

Material: Steel frame with ceramic balls.

Thermal expansion coefficient of steel, α = 11.5 × 10-6 K-1 at 20 °C.

Dimensions (mm):

Figure 1.- Ball plate description

5

21 25

13 420

420

85

125

295

210

85

Sphere φ 22

83

24

Fixture points

S1

S3

S2



Bore Plate

Serial Number: NONE

Material: ZERODUR

Thermal expansion coefficient of ZERODUR: 0 at 20 °C.

Dimensions (mm):

Figure 2.- Bore plate description.

500

400

50

500 400

50

Aluminum frame Zerodur plate

50 30

20 S3

S2 S1



4 Measurement instructions

4.1 Traceability

Length measurements should have been independently traceable to the latest realization of the mètre as set out in the current ”Mise en Pratique”. This means that the length unit should have been transferred to the ball and bore plates with the CMM by one of the following methods: laser interferometer, gauge blocks, ball beams, ball bar or step gauges. Whatever the instrument or standard used, traceability to the definition of the length unit should have been achieved through calibrations performed in house. Temperature measurements should be made using the International Temperature Scale of 1990 (ITS-90).

4.2 Measurands

Ball Plate. - The object reference plane was defined by the center of balls number 1, 5 and 21. The origin of object coordinate system was the center of ball number 1. The X-axis of the object reference system was defined by the line that passes through the center of ball number 1 and the center of ball number 5. The direction from the origin to ball number 5 defines the positive X-axis direction. The Y-axis is defined was the orthogonal line that passes through the center of ball number 1. The positive direction was from ball number 1 to ball number 21. The measurands of the ball plate are the coordinates of each ball center with respect to the origin of object coordinate system (Fig.3) with the plate lying horizontally and fixed as described in section 4.3.3.

Figure 3.- Ball plate coordinate system.

Xobj

Yobj

Ball 1 (0,0,0) Ball 5 (x,0,0)

Ball 21 (x,y,0)

1 5

21 25

13



Bore Plate.- A plane for the bore plate should have been determined by measuring three or more points wide spread over one of the plate's faces (for example, three points located at the vicinity of three bores in the corners). This plane should have been translated into the plate's symmetry plane in the z direction, half the plate's nominal thickness (thickness should not be measured). This plane is the object reference plane. The origin of object coordinate system lies on the object reference plane and was the center point of the bore at the corner where the yellow sticker appears. The X-axis of the object reference system was defined by the line that passes through the origin and the center of the last bore in the X direction, as shown by the yellow sticker. The direction from the origin to the last bore in the row defined the positive X-axis direction. The Y-axis was defined as the orthogonal line that passes through the origin of the object coordinate reference system and the positive direction was the one shown by the yellow sticker (figure 4). The measurands of the bore plate were the center coordinates of each bore with respect to the object coordinate system with the plate lying horizontally and fixed as described in section 4.3.4.

The thermal expansion coefficient used should have been the quoted values for each plate. Laboratories should report the temperatures at which the length measurements were made. Laboratories should only measure the artifacts at a

temperature of (20 ± 0,3) °C.

Figure 4.- Bore plate coordinate system.

Yobj

Xobj

Bore (0,0) Bore (x,0)

Bore (x,y)



4.3 Measurement instructions

4.3.1. Each laboratory was free to use its own measuring method. However, measurements were to be reported in the object reference coordinate system described in 4.2. Appendix A5 in the protocol described a measurement method that could be used. Before measurement, the artifacts should have been inspected for damage. Special attention was to be paid to the measurement surfaces and form elements (balls or bores). Any scratches rust spots or other damages should have been documented. Appendix A1 contained a form that should have been filled and sent upon reception quoting the state of the artifacts as received.

4.3.2. Before measurement, the plates and supports were to be cleaned. The form elements should have been cleaned with special care individually as well as the measuring surfaces in the vicinity of all probing points.

4.3.3. Included with the ball plate, there were three fixtures to mount it in horizontal position: one conical, one with a V-grove and a flat one. Three hemispherical supports were screwed to the ball plate (points S1, S2 and S3 of Fig. 1). The three supports should have been fixed to the CMM table as to support each of the hemispheres in the following order. Firstly, the cone base should be attached to the support point S1. Secondly, the V-grove base should be attached to point S2, with the grove aligned towards the cone. Finally, the plane base should be attached to point S3.

4.3.4. Included with the bore plate, there were three identical fixtures to mount it in horizontal position. The three fixtures should have been screwed to the edges of the bore plate in the points S1, S2 and S3 shown Fig. 2. It was intended that the plate lay horizontal over the CMM table.

4.3.5. The measurement results should have been corrected to the reference temperature of 20 °C using the values of the thermal expansion coefficient provided by the pilot laboratory.

4.3.6. No other measurements were to be attempted by the participants and the artifacts should not be used for any purpose other than described in this document. The artifacts could not be given to any party other than the participants in the comparison.

4.3.7. If for any reason a laboratory was not able to make all the measurements of one or both artifacts, it is still encouraged to report the rest of the results. Foreseeing this possibility, the laboratory could have chosen to make only the determination of the position of peripheral form elements, for example.

5 Measurement methods and instruments used by the participants

Out of the twelve final participants, eight applied the recommended reversal method described in Appendix 5 of the protocol. These were: NMIA, INMS-NRC, NIM, CMI, BNM-LNE, PTB, VNIIMS and CENAM. The other five used their own custom methods. All custom methods incorporated the use of a laser interferometer or that of interferometric scales.



NMIJ-AIST combined the reversal method of Appendix 5 with interferometric measurements of the central ball rows crossing the ball plate at the center and

then applied a correction to the previous measurements. They did something similar with the bore plate but used a couple of bore lines crossing on X and Y directions.

NMi also used a laser interferometer to measure each row of balls in the X direction, then rotated the plate and measured each row in Y direction, then measured all the 45 º diagonals in one direction and finally all the other rows in the other diagonal direction.

NPL made the dimensional measurements conventionally with the CMM probe and CMM scales. However, they made additional measurements with an interferometric set-up to correct for CMM scale errors. The measurements were made on the comparison artifact by measuring the two ball or bore central lines on X and Y directions. The method is similar to that applied by NMIJ, with the additional feature that the target probe is not only tracked by a displacement interferometer, but also by a column reference interferometer; and that both positions bare double beam and therefore it corrects for tilt in the two directions.

Finally, NIST used a CMM fully equipped with interferometric scales replacing the original ones, and they did not apply the reversal method but rather measured twice in 90º different orientations and the data is combined to separate CMM from artifact errors. The measurements are repeated four times and linear drift is also corrected.

Table 4 summarizes the methods applied.

6 Stability and condition of the artifacts

There were no major reports of damage of the artifacts. However, the following remarks were made. PTB reported two minor damages in bores 12 (coordinates (3,2)) and 48 ((5,8)) of the ZERODUR bore plate not influencing measurements. CMI reported light scratches on the conical edges of the same bores 12 and 48; NPL reported damage to the casing of the ball plate with no consequences to the artifact; and CSIRO reported minor scratches and marks in both artifacts and specifically on bores 26, 34 and 48 of the bore plate. INMS-NRC commented they detected unusually large error in bore 12. However they did not attribute it to any damage but rather suspected that the bore plate could rock inside its aluminum frame when moving in the X-direction at certain acceleration in CMMs with moving tables. No comments were reported on the steel ball plate.

The pilot laboratory, CENAM and the copilot laboratory, NIST, performed control measurements during the exercise. Considering the modulus r of the x and y coordinates reported for the center of all balls with respect to the center of ball 1, figure 5 shows the deviation from the nominal r distance to each ball center. The graph shows the deviations from nominal position for each measuring element with

ball 20 having the largest of about 0.15 µm.

Among the whole set of measurements, for all measuring elements and for the five participations of both laboratories, the mean of the variations between any



combination of two stets of measurements in time was 0.132 µm; and the largest

value was 0.579 µm occurring at ball 22 between CENAM set of measurements number 1 (2001-01-30) and NIST set of measurements number 3 (2004-04-15).

If the simple mean of these five sets of measurements is taken as reference value, all results appear to be consistent in terms of the average normalized error for the 24 measuring elements in the artifact (all average En values between 0.36 and 0.87), as well as in terms of the declared uncertainties by each laboratory averaged over all 24 measuring elements (in average the reference value crosses well within the standard uncertainty bar of the laboratory).

Figure 5 shows no visible trend in any of the balls, nor the deviations change significantly through the control measurements and therefore we conclude the artifact behaved reasonably well during the comparison exercise and no drift may be inferred out of the measurements performed by the pilot laboratories.

Similarly, figures 6, 7 and 8 show the same kind of plots for the ZERODUR bore plate. As there are 61 bores in this case, the graph had to be split into three. While in the steel ball plate all deviations from nominal are positive, here most of them

are negative and the largest one is of around 0.15 µm also (bore 58). Among the whole set of measurements, for all measuring elements and for the five participations of both laboratories, the mean of the variations between any

combination of two stets of measurements in time was 0.141 µm; and the largest

value being 0.590 µm occurring at ball 53 between CENAM set of measurements number 1 (2001-01-30) and NIST set of measurements number 1 (2001-11-15).

If the simple mean of these five sets of measurements is taken as reference value, all results appear to be consistent in terms of the average normalized error for the 60 measuring elements in the artifact (all average En values between 0.39 and 0.61), as well as in terms of the declared uncertainties by each laboratory averaged over all 60 measuring elements (in average the reference value crosses the standard uncertainty bar of the laboratory).

Figures 6 through 8 show no visible trend in any of the balls, nor the deviations change significantly through the control measurements and therefore we conclude the artifact behaved reasonably well during the comparison exercise and no drift may be inferred out of the measurements performed by the pilot laboratories.

Figure 9 show the control measurement results made by the pilot laboratories for the central ball 13 and for the corner balls 5, 21 and 25 of the steel ball plate along with the claimed uncertainties for the modulus r of the x and y coordinates reported with their uncertainties at k = 1. A visual inspection shows that correspondence is good for the central ball 13 and for the ball 5 that lays over the X-axis (y = 0). Ball 25 shows very good correspondence between the NIST measurements and good between the CENAM ones, however, the correspondence between laboratories is not as good. In any case, this is certainly due to laboratory equipment and conditions and not due to artifact changes. Ball 21 shows less good agreement but it does not seem significant to invalidate any results as discussed above.

Figure 10 shows similar plots for the measurements made by the pilot laboratories of the central bore 35 and of the corner bores 9, 53 and 61 of the ZERODUR bore plate. Exception made of bore 53; the other three bores are in very good agreement between the five measurements. Bore 53 presents very good correspondence between the NIST measurements and good correspondence between the CENAM ones. There is poor correspondence between the results



obtained between the two laboratories. However, this must be attributed to changes in the laboratories conditions and equipment and not to the artifacts. Again, this does not seem to invalidate the results as discussed above.

7 Claimed Uncertainties

Uncertainties were quoted in different ways. Most laboratories quoted two equations, one for the steel ball plate and one for the ZERODUR bore plate. However, some quoted only one equation for both and one laboratory preferred to state a linear equation instead of the suggested equation of the form

222)( lbalu += . Another laboratory stated values in X and Y for each of the

coordinates of each geometrical feature of the plates without stating an equation. A quadratic curve was adjusted by the pilot to these points just to be able to compare it to the rest of the participants.

For the Steel Plate, claimed standard uncertainty equations had a relatively wide

spread with an mean value of 0.206 µm and a standard deviation of this mean of

0,023 µm at L = 0 mm; and a mean of 0.621 µm and standard deviation of 0.112

µm at L = 1000 mm. For the ZERODUR bore plate some participants estimated a smaller uncertainty and the correspondent respective values for the mean and the

standard deviation were 0.215 µm and 0.023 µm at L = 0 mm; and 0.536 µm and

0.112 µm at L = 1000 mm.

Table 5 shows the quoted standard uncertainty equations for each participant along with the values that these equations take at L = 0 mm and L = 1000 mm. For the laboratories that quoted different equations for each plate, both equations appear.

Figure 11 shows the plot of the steel ball plate standard uncertainty equations and figure 12 plots those of the ZERODUR bore plate.

8 Measurement Results

8.1 Steel Ball Plate

Table 6 shows the measurement results of the comparison as stated by the participants. It was not required to state the Z coordinates but most laboratories reported them and they are also shown along with the X and Y coordinates. However, they are not used in any calculations. The table is split in four parts, a, b, c and d.

8.2 ZERODUR Bore Plate

Table 7 shows the measurement results of the comparison as stated by the participants. The table is split in three parts, a, b, c and d.



Table 4.- Participant countries, name of institute, method to obtain traceability, calibration method and reported temperature variation during measurements.

COUNTRY LABORATORY MEASUREMENT INSTRUMENT

TRACEABILITY MEASUREMENT METHOD

Temperature span during measurements (ºC)

AUSTRALIA NMIA (CSIRO) LEITZ PMM866 Cal. laser interf. + cal. length bar + cal. sphere

Appendix 5 of protocol Ball p.: 19.6 to 20.2 Bore p.: 20.0 to 20.3

CANADA INMS-NRC MITUTOYO LEGEX #707

Calibrated gauge blocks Appendix 5 of protocol Ball p.: 20.020 to 20.050 Bore p.: 20.020 to 20.056

CHINA NIM LEITZ (B&Sh) PMM12106MG with laser interferometer

Laser interf. calibrated against MeP laser

Appendix 5 of protocol 19.7 to 20.3

CZECH REPUBLIC

CMI SIP CMM 5 Calibrated gauge blocks Appendix 5 of protocol 19.9 to 20.1

FRANCE BNM-LNE SIP CMM 5/SIP Concerto


Appendix 5 of protocol Not quoted

GERMANY PTB CMM LEITZ PMM 866 + laser interferometer


Appendix 5 of protocol Ball p.:20.05 TO 20.25 Bore p.: not quoted

JAPAN NMIJ-AIST (NRLM)

LEITZ (B&Sh) PMM866P + laser interferometer

Laser interf. calibrated against MeP laser?

Appendix 5 + own method with interferometer

Ball p.: 19.863 to 20.079 Bore p.: 19.816 to 20.077

NETHERLANDS NMi ZEISS UC550 + laser interferometer in X and Y/ UMESS-Basic


Own method with interferometer

Ball p.: 19.78 to 20.17 Bore p.: 20.02 to 20.39

RUSSIA VNIIMS ZEISS UPCM 850 Calibrated gauge blocks Appendix 5 of protocol Not quoted

UNITED KINGDOM

NPL LEITZ PMM12106 custom high accuracy/ QUINDOS

Gauge blocks + step gauge + cal. laser interferometer + cal. shpere

Combination of modified App. 5 + own method with interferometer

Ball p.: 19.972 to 20.120 Bore p.: 19.1 to 20.1

UNITED STATES NIST MOORE M48 with interferometric scales


Own modified app. 5 method

18.8 to 20.2

MEXICO (PILOT) CENAM SIP CMM5L/ CONCERTO

Calibrated step gauge Appendix 5 of protocol 19.87 to 19.95



Figure 5.- Ball plate measurements reported as deviations from nominal modulus r (µm) performed by pilot laboratory, CENAM, and co-pilot NIST at different dates.

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.016

Desviation from nominal (mm)

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

2001-01-30 2001-11-15 2002-12-15 2004-01-09 2004-08-25

Ball



Figure 6.- Bore plate measurements reported as deviations from nominal modulus r (µm) of the first 20 bores performed by pilot, CENAM, and co-pilot NIST at different dates.

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

Deviation from nominal (mm)

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

2001-01-30 2001-11-15 2002-12-09 2004-01-09 2004-08-25

Bore



Figure 7.- Bore plate measurements reported as deviations from nominal modulus r (µm) of bores 21 to 40 performed by pilot, CENAM, and co-pilot NIST at different dates.

-0.18

-0.16

-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02


21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

Bore

2001-01-30 2001-11-15 2002-12-15 2004-01-09 2004-08-25



Figure 8.- Bore plate measurements reported as deviations from nominal modulus r (µm) of the last 21 bores performed by pilot, CENAM, and co-pilot NIST at different dates.

-0.16

-0.15

-0.14

-0.13

-0.12

-0.11

-0.1

-0.09

-0.08

-0.07

-0.06


41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

61

Bore

2001-01-30 2001-11-15 2002-12-15 2004-01-09 2004-08-25



Figure 9.- Center ball 13 and corner balls 5, 21 and 25 deviations from nominal modulus r (µm) performed by pilot, CENAM, and co-pilot

NIST at different control dates along with claimed standard uncertainties.

BALL 21

-0.20

0.00

0.20

0.40

0.60

0.80

NIST1 NIST2 NIST3 CENAM1 CENAM2

Lab.

Dev. (um)

BALL 25

-0.20

0.00

0.20

0.40

0.60

0.80

1.00


Lab.

Dev. (um)

BALL 13

-0.40

-0.20

0.00

0.20

0.40

0.60


Lab.

Dev. (um)

BALL 5

-0.40

-0.20

0.00

0.20

0.40

0.60


Lab.

Dev. (um)



Figure 10.- Center bore 35 and corner bores 9, 53 and 61 deviations from nominal modulus r (µm) performed by pilot, CENAM, and co-pilot NIST at different control dates along with claimed standard uncertainties.

Ball 53

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80


Lab.

Dev. (um)

Ball 61

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60


Lab.

Dev. (um)

Ball 35

-0.40

-0.20

0.00

0.20

0.40

0.60


Lab.

Dev. (um)

Ball 9

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0.50


Lab.

Dev. (um)



Country Claimed Combined Standard Uncertainty as quoted

uc (µµµµm)

L = 0

uc (µµµµm)

L = 1 m

Australia

Ball P.: u lc ( ) = 22 )1000/*12.1(31.0( L+ L in

mm

Bore P.: u lc ( ) = 22 )1000/*91.0(31.0( L+ L in

mm

0.31

1.162

0.961

Canada Ball P.: u

2c=0.15

2+0.00047

2L

2 µm, L in mm

Bore P.: u2

c=0.552+0.00041

2L

2 µm, L in mm 0.15

0.493

0.437

China Ball P.:

2262 )1059.0()14.0()( Lmluc−×+= µ

Bore P.:2262 )1037.0()14.0()( Lmluc

−×+= µ 0.14

0.606

0.396

Czech Rep.

Ball P.: u lc ( ) = √ 0,352 + 0,40

2 ⋅ l2

Bore P.: u lc ( ) = √ 0,352 + 0,36

2 ⋅ l2

0.35 0.532

0.502

France Ball P.: =)(Lu c √√√√(470 nm)

2 + (1,43⋅ L)

2 + 0,3 µm . L

Bore P.: =)(Lu c √√√√(470 nm) 2 + (0,85⋅ L)

2 + 0,3 µm . L

0.47 1.602

1.115

Germany Ball P.: ))1035.0(2.0()( 262 Lmluc

−×+= µ

Bore P.: ))1025.0(2.0()( 262 Lmluc−×+= µ

0.20 0.403

0.320

Japan Ball P.: u= sqrt(126^2 + 248/L) ^2 [nm] Bore P.: u= sqrt(119^2 + 215/L) ^2 [nm] 0.119

0.278

0.246

Nether-lands

Did not state equations. Equations adjusted by pilot:

Ball P.: u lc ( ) = 22 )*00047.0(16.0( L+

Bore P.: u lc ( ) = 22 )*00047.0(16.0( L+

0.169 0.507

United Kingdom

Ball P.: u lc ( ) = √√√√0.222 + (0.44⋅⋅⋅⋅ l)2

µm

Bore P.: u lc ( ) = √√√√0.222 + (0.33⋅⋅⋅⋅ l)2

µm 0.22

0.492

0.397

Russia mkmllUc 2610225,1128,0)( −⋅+= 0.128 1.232

USA 1 For both: u lc ( ) = ±±±± 0.089 + 0.05 * L 0.089 0.139

USA

2 and 3

For both u lc ( ) = ±±±± 0.057 + 0.066 * L 0.057 0.123

Mexico

1 and 2

Ball P.: ( ) ( )2243,027,0 Lmuc += µ

Bore P.: ( ) ( )2233,027,0 Lmuc += µ

0.27

0.508

0.426

Table 5.- Claimed uncertainty equations of participants. All uncertainties are combined standard uncertainties.





Figure 11.- Claimed Standard Uncertainty Curves of participants for the Steel Ball Plate. X-axis in millimeters and Y-axis in micrometers.

Figure 12.- Claimed standard uncertainty curves of participants for the ZERODUR Bore Plate. X-axis in millimeters and Y-axis in micrometers.



NMI NMIA (CSIRO) INMS-NRC NIM CMI

Bola X Y Z X Y Z X Y Z X Y Z

1 0.0000 0.0000 0.0000 0.000000 0.000000 0.000001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

2 83.0040 -0.0002 -0.0022 83.004171 -0.000270 -0.003599 83.0040 -0.0003 -0.0029 83.0040 -0.0003 0.0022

3 166.0071 -0.0004 0.0026 166.007767 -0.000573 0.000961 166.0074 -0.0006 0.0016 166.0073 -0.0005 0.0032

4 249.0074 -0.0005 -0.0007 249.008478 -0.000695 -0.002129 249.0080 -0.0006 -0.0014 249.0080 -0.0007 0.0021

5 332.0086 0.0000 0.0000 332.010194 0.000000 0.000000 332.0094 0.0000 0.0000 332.0098 0.0000 0.0000

6 0.0055 83.0002 -0.0039 0.005536 83.000822 -0.004256 0.0057 83.0008 -0.0042 0.0054 83.0007 -0.0004

7 83.0081 82.9996 -0.0044 83.008309 83.000209 -0.006318 83.0084 83.0001 -0.0056 83.0080 83.0000 0.0021

8 166.0116 82.9999 0.0005 166.012191 83.000437 -0.001572 166.0119 83.0004 -0.0007 166.0118 83.0003 0.0031

9 249.0125 83.0009 0.0041 249.013566 83.001397 0.002146 249.0133 83.0014 0.0029 249.0132 83.0012 0.0021

10 332.0114 83.0016 0.0162 332.013045 83.002112 0.015599 332.0126 83.0020 0.0157 332.0125 83.0019 -0.0001

11 0.0059 166.0013 -0.0049 0.006031 166.002327 -0.005345 0.0059 166.0024 -0.0051 0.0058 166.0023 -0.0008

12 83.0074 166.0014 0.0027 83.007626 166.002490 0.001188 83.0075 166.0025 0.0020 83.0073 166.0024 0.0017

13 166.0114 166.0011 -0.0156 166.012128 166.002196 -0.017542 166.0118 166.0023 -0.0165 166.0117 166.0021 0.0027

14 249.0128 166.0023 0.0159 249.013883 166.003323 0.014193 249.0134 166.0035 0.0149 249.0136 166.0033 0.0019

15 332.0128 166.0035 0.0340 332.014338 166.004621 0.033286 332.0137 166.0046 0.0335 332.0140 166.0045 -0.0003

16 0.0079 249.0010 -0.0028 0.008000 249.002414 -0.003109 0.0081 249.0024 -0.0028 0.0077 249.0024 -0.0005

17 83.0100 249.0013 -0.0110 83.010140 249.002712 -0.012570 83.0102 249.0026 -0.0116 83.0100 249.0027 0.0021

18 166.0137 249.0009 0.0114 166.014381 249.002225 0.008866 166.0141 249.0022 0.0103 166.0142 249.0023 0.0034

19 249.0147 249.0022 0.0262 249.015783 249.003563 0.024343 249.0154 249.0036 0.0253 249.0153 249.0036 0.0025

20 332.0143 249.0029 0.0502 332.015828 249.004260 0.049374 332.0152 249.0042 0.0495 332.0153 249.0043 0.0001

21 0.0059 332.0003 -0.0001 0.005879 332.002093 0.000000 0.0062 332.0020 0.0000 0.0057 332.0020 0.0000

22 83.0065 331.9995 0.0107 83.006722 332.001245 0.009620 83.0069 332.0011 0.0102 83.0065 332.0013 0.0024

23 166.0098 331.9993 0.0271 166.010457 332.001049 0.025086 166.0105 332.0009 0.0261 166.0102 332.0011 0.0034

24 249.0105 332.0003 0.0456 249.011516 332.002084 0.044170 249.0114 332.0020 0.0447 249.0110 332.0020 0.0029

25 332.0120 332.0015 0.0735 332.013471 332.003268 0.073019 332.0131 332.0030 0.0730 332.0130 332.0033 0.0005

Table 6 a.- Coordinates of the center of the balls for the 25 balls of the steel ball plate. All values in millimeters.



Table 6 b.- Coordinates of the center of the balls for the 25 balls of the steel ball plate. All values in millimeters.

NMI BNM-LNE PTB NMIJ (NRLM) NMi


1 0.000000 0.000000 / 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.000000 0.000000 0.000008

2 83.003900 -0.000075 / 83.0040 -0.0003 -0.0019 83.0042 -0.0002 -0.0024 83.003964 -0.000412 -0.001628

3 166.007513 -0.000388 / 166.0077 -0.0005 0.0026 166.0077 -0.0005 0.0022 166.007648 -0.000769 0.003329

4 249.008363 -0.000688 / 249.0083 -0.0007 -0.0006 249.0083 -0.0006 -0.0010 249.008194 -0.000845 -0.000365

5 332.009913 0.000000 / 332.0100 0.0000 0.0000 332.0100 0.0000 0.0000 332.009931 0.000000 -0.000055

6 0.005425 83.000788 / 0.0054 83.0008 -0.0039 0.0056 83.0007 -0.0040 0.005437 83.000764 -0.005309

7 83.008063 83.000050 / 83.0082 83.0001 -0.0040 83.0083 83.0001 -0.0047 83.008293 83.000027 -0.005088

8 166.012025 83.000363 / 166.0122 83.0004 0.0007 166.0122 83.0003 0.0002 166.012178 83.000289 0.000418

9 249.013525 83.001338 / 249.0135 83.0013 0.0046 249.0134 83.0013 0.0040 249.013451 83.001288 0.003167

10 332.012800 83.001975 / 332.0130 83.0020 0.0163 332.0129 83.0019 0.0162 332.012788 83.002137 0.014889

11 0.005763 166.002475 / 0.0059 166.0023 -0.0049 0.0060 166.0023 -0.0049 0.005676 166.002165 -0.006099

12 83.007350 166.002388 / 83.0076 166.0025 0.0031 83.0077 166.0024 0.0028 83.007392 166.002375 0.002780

13 166.011875 166.002238 / 166.0121 166.0022 -0.0151 166.0121 166.0021 -0.0153 166.011983 166.002273 -0.015055

14 249.013775 166.003400 / 249.0139 166.0033 0.0162 249.0138 166.0032 0.0160 249.013719 166.003267 0.015481

15 332.014200 166.004388 / 332.0143 166.0045 0.0342 332.0142 166.0044 0.0340 332.014146 166.004386 0.032599

16 0.007863 249.002575 / 0.0078 249.0025 -0.0028 0.0081 249.0023 -0.0027 0.007671 249.002205 -0.003664

17 83.010025 249.002800 / 83.0101 249.0028 -0.0106 83.0102 249.0026 -0.0107 83.009867 249.002450 -0.010698

18 166.014300 249.002463 / 166.0144 249.0023 0.0121 166.0144 249.0022 0.0122 166.014205 249.002178 0.012169

19 249.015750 249.003700 / 249.0157 249.0036 0.0265 249.0157 249.0035 0.0264 249.015721 249.003456 0.026486

20 332.015713 249.004338 / 332.0157 249.0042 0.0503 332.0157 249.0041 0.0502 332.015637 249.004031 0.049150

21 0.005888 332.002025 / 0.0058 332.0020 0.0000 0.0060 332.0017 0.0000 0.005823 332.001610 -0.000146

22 83.006613 332.001263 / 83.0066 332.0013 0.0111 83.0068 332.0010 0.0109 83.006429 332.000944 0.012220

23 166.010488 332.001138 / 166.0104 332.0011 0.0279 166.0105 332.0008 0.0277 166.010268 332.000823 0.029031

24 249.011500 332.002075 / 249.0114 332.0021 0.0460 249.0115 332.0017 0.0457 249.011333 332.001892 0.046791

25 332.013350 332.003213 / 332.0134 332.0032 0.0737 332.0133 332.0028 0.0735 332.013125 332.002922 0.073444



Table 6 c.- Coordinates of the center of the balls for the 25 balls of the steel ball plate. All values in millimeters.

5 This laboratory did not report the final result but sent the whole set of measurements in every position. The pilot laboratory

calculated the best estimate as the arithmetic mean of the set of measurements.

NMI VNIIMS5 NPL NIST 1 CENAM 1


1 0.000000 0.000000 0.000000 0 0 0 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

2 83.0038 -0.0003 -0.0025 83.00396 -0.00031 -0.00033 83.0040 -0.0003 -0.0001 83.0038 -0.0002 -0.0022

3 166.0072 -0.0006 0.0020 166.00762 -0.00051 0.00524 166.0075 -0.0006 0.0051 166.0075 -0.0005 0.0023

4 249.0075 -0.0008 -0.0011 249.00827 -0.00065 0.00126 249.0082 -0.0008 0.0013 249.0082 -0.0008 -0.0008

5 332.0087 0.0000 0.0000 332.0099 0 0 332.0099 0.0000 0.0000 332.0100 0.0000 0.0001

6 0.0053 83.0000 -0.0041 0.00543 83.00071 -0.00439 0.0053 83.0007 -0.0042 0.0056 83.0008 -0.0041

7 83.0076 82.9995 -0.0047 83.00814 83.00004 -0.00274 83.0080 83.0000 -0.0026 83.0082 83.0002 -0.0046

8 166.0112 82.9998 -0.0001 166.01206 83.00035 0.00303 166.0119 83.0002 0.0027 166.0121 83.0004 0.0001

9 249.0122 83.0008 0.0037 249.01339 83.00129 0.00598 249.0133 83.0010 0.0058 249.0135 83.0013 0.0041

10 332.0114 83.0012 0.0162 332.01275 83.00206 0.01578 332.0128 83.0018 0.0157 332.0132 83.0018 0.0163

11 0.0060 166.0007 -0.0052 0.00591 166.00225 -0.00555 0.0058 166.0022 -0.0055 0.0060 166.0023 -0.0050

12 83.0073 166.0009 0.0024 83.00751 166.00237 0.00452 83.0074 166.0023 0.0042 83.0075 166.0024 0.0026

13 166.0115 166.0005 -0.0160 166.01198 166.0022 -0.01267 166.0118 166.0019 -0.0133 166.0120 166.0019 -0.0157

14 249.0125 166.0020 0.0159 249.01373 166.00328 0.01773 249.0136 166.0030 0.0173 249.0137 166.0033 0.0159

15 332.0127 166.0030 0.0340 332.01403 166.0045 0.03335 332.0140 166.0043 0.0331 332.0143 166.0045 0.0341

16 0.0081 248.9999 -0.0030 0.00787 249.00244 -0.00322 0.0079 249.0023 -0.0033 0.0078 249.0024 -0.0021

17 83.0098 249.0001 -0.0111 83.00997 249.00272 -0.00858 83.0101 249.0027 -0.0079 83.0099 249.0028 -0.0111

18 166.0135 248.9998 0.0113 166.01422 249.00224 0.01556 166.0142 249.0022 0.0143 166.0141 249.0022 0.0113

19 249.0145 249.0011 0.0261 249.01564 249.00364 0.02851 249.0156 249.0034 0.0278 249.0155 249.0037 0.0264

20 332.0141 249.0019 0.0503 332.01558 249.00427 0.04955 332.0157 249.0041 0.0493 332.0157 249.0043 0.0504

21 0.0061 331.9980 0.0000 0.00587 332.00192 0 0.0058 332.0019 0.0000 0.0059 332.0022 0.0001

22 83.0064 331.9973 0.0109 83.00653 332.00123 0.01355 83.0067 332.0011 0.0130 83.0067 332.0014 0.0106

23 166.0097 331.9972 0.0274 166.01039 332.00103 0.03151 166.0103 332.0007 0.0306 166.0103 332.0009 0.0269

24 249.0102 331.9983 0.0459 249.01146 332.00205 0.04843 249.0113 332.0017 0.0480 249.0114 332.0019 0.0456

25 332.0117 331.9994 0.0741 332.01333 332.00313 0.07338 332.0133 332.0030 0.0732 332.0136 332.0032 0.0734



Table 6 d.- Coordinates of the center of the balls for the 25 balls of the steel ball plate. All values in millimeters.

6 These values were control values performed by the pilot and co-pilot laboratories.

NMI NIST 26 NIST 3

6 CENAM 2

6

Bola X Y Z X Y Z

1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

2 83.0040 -0.0003 -0.0018 83.0041 -0.0001 -0.0009 83.0041 -0.0002 -0.0030

3 166.0076 -0.0006 0.0035 166.0077 -0.0004 0.0042 166.0076 -0.0005 0.0010

4 249.0083 -0.0007 -0.0003 249.0084 -0.0006 0.0006 249.0083 -0.0006 -0.0021

5 332.0100 0.0000 0.0000 332.0100 0.0000 0.0000 332.0099 0.0000 0.0000

6 0.0053 83.0008 -0.0045 0.0055 83.0006 -0.0043 0.0053 83.0007 -0.0044

7 83.0081 83.0001 -0.0047 83.0083 83.0001 -0.0036 83.0082 83.0001 -0.0058

8 166.0120 83.0004 0.0008 166.0122 83.0003 0.0015 166.0121 83.0004 -0.0015

9 249.0134 83.0012 0.0037 249.0135 83.0013 0.0048 249.0135 83.0014 0.0020

10 332.0129 83.0019 0.0157 332.0129 83.0020 0.0156 332.0131 83.0021 0.0151

11 0.0059 166.0022 -0.0057 0.0060 166.0022 -0.0056 0.0057 166.0022 -0.0053

12 83.0075 166.0023 0.0030 83.0076 166.0023 0.0032 83.0074 166.0023 0.0012

13 166.0120 166.0020 -0.0148 166.0121 166.0017 -0.0148 166.0120 166.0021 -0.0177

14 249.0138 166.0030 0.0162 249.0138 166.0032 0.0160 249.0138 166.0033 0.0133

15 332.0142 166.0042 0.0334 332.0142 166.0044 0.0325 332.0142 166.0045 0.0319

16 0.0079 249.0023 -0.0033 0.0079 249.0023 -0.0034 0.0080 249.0022 -0.0029

17 83.0101 249.0026 -0.0103 83.0101 249.0024 -0.0102 83.0099 249.0024 -0.0126

18 166.0143 249.0021 0.0125 166.0143 249.0020 0.0129 166.0142 249.0020 0.0090

19 249.0157 249.0033 0.0269 249.0156 249.0034 0.0263 249.0154 249.0034 0.0231

20 332.0158 249.0039 0.0498 332.0157 249.0041 0.0484 332.0155 249.0041 0.0473

21 0.0059 332.0018 0.0000 0.0058 332.0020 0.0000 0.0058 332.0021 0.0000

22 83.0067 332.0009 0.0122 83.0068 332.0008 0.0119 83.0064 332.0010 0.0092

23 166.0104 332.0007 0.0289 166.0104 332.0006 0.0290 166.0102 332.0007 0.0243

24 249.0115 332.0017 0.0472 249.0114 332.0017 0.0462 249.0114 332.0018 0.0423

25 332.0135 332.0028 0.0739 332.0133 332.0030 0.0720 332.0135 332.0031 0.0700



Table 7 a.- Coordinates of center of bores for bores of the ZERODUR bore plate. All values in mm.

NMI NMIA (CSIRO) INMS-NRC NIM CMI

Bore x y x y x y x y

1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

2 49.9829 0.0139 49.9830 0.0138 49.9829 0.0139 49.9829 0.0138

3 99.9701 0.0276 99.9701 0.0275 99.9700 0.0276 99.9701 0.0274

4 149.9541 0.0338 149.9540 0.0338 149.9542 0.0340 149.9541 0.0338

5 199.9430 0.0306 199.9429 0.0306 199.9428 0.0308 199.9431 0.0305

6 249.9271 0.0294 249.9270 0.0294 249.9268 0.0296 249.9271 0.0294

7 299.9126 0.0203 299.9128 0.0203 299.9125 0.0204 299.9129 0.0203

8 349.9063 0.0043 349.9064 0.0043 349.9061 0.0044 349.9068 0.0044

9 399.8976 0.0000 399.8979 0.0000 399.8975 0.0000 399.8981 0.0000

10 -0.0081 50.0079 -0.0080 50.0079 -0.0080 50.0078 -0.0080 50.0076

11 49.9841 50.0188 49.9844 50.0188 49.9843 50.0189 49.9843 50.0187

12 100.0036 49.9983 100.0039 49.9984 100.0037 49.9984 100.0039 49.9983

13 149.9970 50.0167 149.9972 50.0167 149.9974 50.0169 149.9973 50.0165

14 199.9775 50.0219 199.9775 50.0220 199.9774 50.0221 199.9777 50.0219

15 249.9515 50.0337 249.9517 50.0338 249.9515 50.0339 249.9518 50.0337

16 299.9354 50.0238 299.9356 50.0240 299.9353 50.0240 299.9357 50.0239

17 349.8818 49.9902 349.8821 49.9904 349.8818 49.9904 349.8824 49.9903

18 399.9021 49.9994 399.9024 49.9996 399.9019 49.9995 399.9025 49.9997

19 0.0080 100.0020 0.0081 100.0020 0.0081 100.0017 0.0081 100.0017

20 50.0092 99.9865 50.0092 99.9865 50.0091 99.9865 50.0091 99.9865

21 349.9108 100.0196 349.9110 100.0198 349.9107 100.0196 349.9112 100.0197

22 399.8780 99.9864 399.8782 99.9867 399.8777 99.9864 399.8782 99.9867

23 0.0200 150.0039 0.0201 150.0041 0.0200 150.0039 0.0200 150.0038

24 50.0312 149.9510 50.0312 149.9512 50.0311 149.9511 50.0310 149.9511

25 349.8830 150.0050 349.8831 150.0054 349.8828 150.0053 349.8833 150.0054

26 399.8688 149.9698 399.8690 149.9703 399.8686 149.9700 399.8691 149.9703

27 0.0255 199.9476 0.0256 199.9482 0.0255 199.9479 0.0256 199.948

28 50.0223 199.9266 50.0222 199.9272 50.0221 199.9271 50.0222 199.9271

29 349.8784 199.9807 349.8784 199.9816 349.8781 199.9814 349.8786 199.9815

30 399.8693 199.9480 399.8694 199.9488 399.8690 199.9486 399.8695 199.9488

31 0.0327 249.9366 0.0328 249.9373 0.0327 249.9371 0.0327 249.9374

32 50.0209 249.9043 50.0208 249.9050 50.0207 249.9049 50.0207 249.9049

33 100.0357 249.9431 100.0355 249.9439 100.0355 249.9438 100.0355 249.9439

34 150.0242 249.9113 150.0239 249.9121 150.0242 249.9121 150.024 249.9122

35 199.9698 249.8637 199.9697 249.8645 199.9696 249.8646 199.9697 249.8646

36 249.9074 249.8801 249.9072 249.8809 249.9070 249.8809 249.9072 249.8809

37 299.8910 249.8888 299.8911 249.8898 299.8908 249.8897 299.8912 249.8899

38 349.8633 249.9501 349.8634 249.9511 349.8631 249.9510 349.8636 249.9513

39 399.8699 249.9258 399.8700 249.9268 399.8696 249.9266 399.8701 249.9269

40 0.0418 299.9535 0.0418 299.9543 0.0417 299.9540 0.0417 299.9542

41 49.9996 299.8896 49.9995 299.8905 49.9994 299.8903 49.9994 299.8904

42 349.8806 299.9170 349.8806 299.9181 349.8803 299.9179 349.8809 299.9181

43 399.8795 299.9011 399.8796 299.9022 399.8792 299.9019 399.8797 299.9021

44 0.0205 349.9271 0.0204 349.9280 0.0204 349.9277 0.0203 349.9278

45 50.0165 349.9158 50.0164 349.9167 50.0163 349.9165 50.0163 349.9166

46 99.9813 349.8776 99.9810 349.8786 99.9809 349.8784 99.9811 349.8785

47 149.9571 349.8638 149.9566 349.8647 149.9569 349.8647 149.9566 349.8647

48 199.9357 349.8704 199.9355 349.8715 199.9355 349.8714 199.9356 349.8714

49 249.9023 349.8751 249.9020 349.8762 249.9019 349.8761 249.9021 349.8763

50 299.8845 349.8976 299.8844 349.8987 299.8842 349.8985 299.8846 349.8987

51 349.9175 349.8727 349.9175 349.8740 349.9172 349.8737 349.9177 349.874

52 399.8959 349.8911 399.8959 349.8923 399.8956 349.8920 399.896 349.8923

53 0.0246 399.9185 0.0246 399.9192 0.0245 399.9188 0.0245 399.9191

54 50.0189 399.9133 50.0186 399.9140 50.0186 399.9137 50.0185 399.9138

55 100.0169 399.8869 100.0167 399.8875 100.0166 399.8872 100.0167 399.8874

56 149.9894 399.8689 149.9890 399.8694 149.9892 399.8693 149.989 399.8695

57 199.9540 399.8666 199.9538 399.8674 199.9537 399.8672 199.9538 399.8672

58 249.9384 399.8612 249.9381 399.8620 249.9379 399.8617 249.9381 399.862

59 299.9379 399.8599 299.9377 399.8607 299.9375 399.8604 299.9379 399.8607

60 349.9188 399.8833 349.9188 399.8842 349.9185 399.8838 349.9191 399.8841

61 399.8935 399.8880 399.8936 399.8889 399.8932 399.8885 399.8936 399.8889



NMI BNM-LNE PTB NMIJ (NRLM) NMi


1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

2 49.9832 0.0138 49.9829 0.0139 49.9827 0.0139 49.9829 0.0139

3 99.9704 0.0276 99.9699 0.0276 99.9698 0.0275 99.9699 0.0278

4 149.9544 0.0339 149.9537 0.0339 149.9535 0.0338 149.9536 0.0340

5 199.9435 0.0306 199.9428 0.0306 199.9425 0.0306 199.9427 0.0308

6 249.9276 0.0295 249.9270 0.0294 249.9265 0.0294 249.9266 0.0296

7 299.9135 0.0204 299.9127 0.0203 299.9123 0.0203 299.9123 0.0203

8 349.9073 0.0044 349.9064 0.0044 349.9059 0.0044 349.9059 0.0044

9 399.8990 0.0000 399.8977 0.0000 399.8972 0.0000 399.8972 0.0000

10 -0.0078 50.0080 -0.0080 50.0079 -0.0080 50.0078 -0.0080 50.0080

11 49.9847 50.0189 49.9843 50.0188 49.9842 50.0187 49.9843 50.0189

12 100.0042 49.9986 100.0037 49.9984 100.0036 49.9982 100.0036 49.9987

13 149.9978 50.0169 149.9969 50.0167 149.9968 50.0166 149.9971 50.0169

14 199.9782 50.0220 199.9774 50.0219 199.9771 50.0218 199.9774 50.0222

15 249.9523 50.0339 249.9516 50.0338 249.9512 50.0337 249.9515 50.0339

16 299.9364 50.0242 299.9355 50.0239 299.9350 50.0239 299.9352 50.0240

17 349.8832 49.9904 349.8820 49.9903 349.8815 49.9902 349.8816 49.9904

18 399.9035 49.9996 399.9021 49.9995 399.9016 49.9994 399.9018 49.9996

19 0.0082 100.0020 0.0081 100.0018 0.0081 100.0017 0.0082 100.0021

20 50.0098 99.9864 50.0092 99.9864 50.0091 99.9863 50.0093 99.9867

21 349.9120 100.0199 349.9109 100.0196 349.9104 100.0196 349.9105 100.0198

22 399.8792 99.9866 399.8779 99.9864 399.8774 99.9864 399.8775 99.9866

23 0.0203 150.0041 0.0201 150.0041 0.0201 150.0039 0.0200 150.0044

24 50.0317 149.9512 50.0312 149.9512 50.0311 149.9510 50.0310 149.9514

25 349.8844 150.0054 349.8831 150.0053 349.8826 150.0052 349.8827 150.0056

26 399.8701 149.9700 399.8688 149.9701 399.8683 149.97 399.8685 149.9703

27 0.0259 199.9481 0.0256 199.9482 0.0256 199.9478 0.0253 199.9484

28 50.0227 199.9271 50.0222 199.9271 50.0221 199.9269 50.0219 199.9274

29 349.8795 199.9816 349.8783 199.9815 349.8779 199.9812 349.8780 199.9816

30 399.8705 199.9487 399.8691 199.9487 399.8686 199.9485 399.8689 199.9488

31 0.0330 249.9370 0.0329 249.9373 0.0328 249.937 0.0326 249.9374

32 50.0213 249.9050 50.0208 249.905 50.0206 249.9047 50.0205 249.9051

33 100.0360 249.9440 100.0355 249.9439 100.0353 249.9436 100.0353 249.9440

34 150.0246 249.9121 150.0239 249.9121 150.0235 249.9117 150.023666 249.912308

35 199.9704 249.8645 199.9695 249.8645 199.9692 249.8642 199.9693 249.8646

36 249.9081 249.8809 249.9072 249.8809 249.9068 249.8805 249.9070 249.8810

37 299.8921 249.8898 299.891 249.8897 299.8905 249.8894 299.8907 249.8898

38 349.8644 249.9511 349.8634 249.951 349.8629 249.9507 349.8630 249.9512

39 399.8710 249.9266 399.8699 249.9267 399.8693 249.9264 399.8695 249.9268

40 0.0421 299.9543 0.0419 299.9542 0.0418 299.9539 0.0416 299.9544

41 50.0001 299.8904 49.9996 299.8904 49.9994 299.8901 49.9992 299.8904

42 349.8816 299.9179 349.8806 299.9179 349.8801 299.9176 349.8802 299.9180

43 399.8807 299.9020 399.8794 299.902 399.8788 299.9017 399.8791 299.9021

44 0.0207 349.9279 0.0205 349.9279 0.0205 349.9276 0.0205 349.9280

45 50.0169 349.9167 50.0165 349.9167 50.0163 349.9164 50.0163 349.9166

46 99.9816 349.8787 99.981 349.8785 99.9808 349.8781 99.9808 349.8785

47 149.9573 349.8647 149.9564 349.8647 149.9562 349.8643 149.9563 349.8647

48 199.9364 349.8714 199.9355 349.8713 199.9351 349.871 199.9352 349.8715

49 249.9030 349.8761 249.9021 349.876 249.9017 349.8757 249.9017 349.8762

50 299.8854 349.8987 299.8843 349.8985 299.884 349.8982 299.8840 349.8987

51 349.9186 349.8740 349.9174 349.8738 349.917 349.8734 349.9170 349.8737

52 399.8970 349.8922 399.8959 349.8922 399.8952 349.8918 399.8953 349.8922

53 0.0249 399.9189 0.0246 399.919 0.0246 399.9185 0.0246 399.9191

54 50.0192 399.9137 50.0188 399.9138 50.0186 399.9134 50.0186 399.9138

55 100.0172 399.8876 100.0167 399.8873 100.0164 399.8869 100.0164 399.8873

56 149.9896 399.8694 149.9889 399.8693 149.9886 399.8689 149.9886 399.8694

57 199.9545 399.8671 199.9538 399.8671 199.9534 399.8667 199.9533 399.8674

58 249.9390 399.8617 249.9383 399.8617 249.9377 399.8613 249.9378 399.8618

59 299.9387 399.8604 299.9378 399.8604 299.9373 399.8601 299.9372 399.8606

60 349.9198 399.8838 349.9189 399.8838 349.9184 399.8833 349.9181 399.8838

61 399.8947 399.8884 399.8934 399.8886 399.8929 399.8882 399.8927 399.8887

Table 7 b.- Coordinates of center of bores for bores of the ZERODUR bore plate. All values in mm.



Table 7 c.- Coordinates of center of bores for bores of the ZERODUR bore plate. All values in mm.

NMI VNIIMS5 NPL NIST 1 CENAM 1


1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

2 49.9834 0.0136 49.9828 0.0138 49.9829 0.0138 49.9830 0.0139

3 99.9708 0.0273 99.9698 0.0275 99.9699 0.0275 99.9700 0.0276

4 149.9549 0.0337 149.9536 0.0338 149.9539 0.0338 149.9540 0.0340

5 199.9443 0.0306 199.9427 0.0306 199.9430 0.0305 199.9429 0.0306

6 249.9287 0.0294 249.9267 0.0296 249.9270 0.0293 249.9268 0.0294

7 299.9148 0.0204 299.9124 0.0205 299.9127 0.0202 299.9127 0.0204

8 349.9088 0.0044 349.9059 0.0044 349.9063 0.0042 349.9062 0.0043

9 399.9008 0.0000 399.8973 0.0000 399.8977 0.0000 399.8976 0.0000

10 -0.0083 50.0079 -0.0080 50.0077 -0.0081 50.0078 -0.0081 50.0079

11 49.9846 50.0188 49.9843 50.0187 49.9843 50.0188 49.9844 50.0188

12 100.0046 49.9983 100.0037 49.9983 100.0037 49.9984 100.0036 49.9983

13 149.9984 50.0167 149.9969 50.0167 149.9971 50.0167 149.9971 50.0168

14 199.9792 50.0221 199.9773 50.0220 199.9775 50.0218 199.9774 50.0219

15 249.9538 50.0341 249.9514 50.0338 249.9516 50.0336 249.9515 50.0338

16 299.9381 50.0243 299.9352 50.0239 299.9354 50.0237 299.9355 50.0239

17 349.8849 49.9907 349.8816 49.9903 349.8819 49.9901 349.8820 49.9904

18 399.9053 49.9995 399.9018 49.9995 399.9021 49.9995 399.9022 49.9994

19 0.0077 100.0016 0.0082 100.0018 0.0080 100.0021 0.0080 100.0018

20 50.0097 99.9863 50.0093 99.9863 50.0092 99.9866 50.0092 99.9865

21 349.9138 100.0199 349.9105 100.0198 349.910762 100.019657 349.9107 100.0197

22 399.8812 99.9864 399.8775 99.9866 399.877846 99.986573 399.8781 99.9864

23 0.0195 150.0037 0.0199 150.0040 0.019801 150.004299 0.0199 150.0040

24 50.0315 149.9508 50.0309 149.9511 50.030907 149.951343 50.0311 149.9511

25 349.8858 150.0053 349.8828 150.0056 349.882998 150.005431 349.8830 150.0052

26 399.8721 149.9700 399.8686 149.9702 399.868735 149.970283 399.8689 149.9701

27 0.0248 199.9479 0.0253 199.9481 0.025252 199.948417 0.0256 199.9481

28 50.0222 199.9268 50.0220 199.9270 50.021983 199.927322 50.0222 199.9271

29 349.8809 199.9814 349.8780 199.9815 349.878188 199.981435 349.8785 199.9814

30 399.8723 199.9485 399.8689 199.9488 399.869138 199.948808 399.8693 199.9487

31 0.0321 249.9370 0.0326 249.9371 0.032665 249.937441 0.0327 249.9371

32 50.0207 249.9045 50.0206 249.9048 50.020698 249.905136 50.0209 249.9048

33 100.0364 249.9435 100.0353 249.9437 100.03542 249.943985 100.0353 249.9437

34 150.0250 249.9118 150.0236 249.9120 150.023762 249.912196 150.0237 249.9119

35 199.9712 249.8641 199.9691 249.8645 199.969533 249.864553 199.9697 249.8644

36 249.9090 249.8805 249.9068 249.8810 249.907161 249.880949 249.9074 249.8807

37 299.8931 249.8893 299.8906 249.8898 299.890947 249.889785 299.8912 249.8896

38 349.8659 249.9507 349.8629 249.9511 349.863308 249.951006 349.8633 249.9508

39 399.8731 249.9265 399.8690 249.9272 399.869793 249.926781 399.8699 249.9265

40 0.0412 299.9538 0.0416 299.9542 0.041662 299.954498 0.0417 299.954

41 49.9995 299.8900 49.9992 299.8902 49.999347 299.8906 49.9995 299.8904

42 349.8832 299.9174 349.8802 299.9178 349.880482 299.917863 349.8806 299.9178

43 399.8828 299.9019 399.8790 299.9019 399.879407 299.902082 399.8796 299.9019

44 0.0200 349.9273 0.0203 349.9278 0.020374 349.928131 0.0204 349.9277

45 50.0163 349.9160 50.0162 349.9165 50.016296 349.916806 50.0166 349.9166

46 99.9811 349.8779 99.9807 349.8784 99.980929 349.878668 99.981 349.8783

47 149.9570 349.8640 149.9561 349.8646 149.956373 349.86479 149.9567 349.8644

48 199.9365 349.8706 199.9350 349.8713 199.935429 349.871401 199.9357 349.8711

49 249.9034 349.8752 249.9015 349.8760 249.901928 349.87598 249.902 349.8759

50 299.8863 349.8980 299.8839 349.8986 299.884252 349.898494 299.8846 349.8983

51 349.9199 349.8731 349.9170 349.8736 349.917366 349.873651 349.9174 349.8735

52 399.8992 349.8919 399.8953 349.8921 399.895707 349.892149 399.8958 349.8918

53 0.0240 399.9181 0.0243 399.9189 0.024499 399.91929 0.0246 399.9187

54 50.0187 399.9130 50.0184 399.9137 50.018639 399.914055 50.0188 399.9136

55 100.0171 399.8867 100.0163 399.8872 100.016593 399.887599 100.0166 399.8871

56 149.9897 399.8686 149.9885 399.8692 149.98885 399.869495 149.9891 399.8692

57 199.9550 399.8666 199.9532 399.8672 199.953683 399.867273 199.9539 399.8669

58 249.9397 399.8614 249.9375 399.8617 249.938041 399.861732 249.9383 399.8616

59 299.9398 399.8602 299.9371 399.8604 299.937616 399.86046 299.9379 399.8603

60 349.9211 399.8835 349.9180 399.8836 349.918548 399.883808 349.9188 399.8837

61 399.8965 399.8883 399.8927 399.8885 399.893284 399.888745 399.8936 399.8885



Table 7 d.- Coordinates of center of bores for bores of the ZERODUR bore plate. All values in mm.

7 These values were control values performed by the pilot and co-pilot laboratories.

NMI NIST 27 NIST 3

7 CENAM 2

7

Bore x y x y x y

1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

2 49.9829 0.0139 49.9829 0.0138 49.9829 0.0136

3 99.9700 0.0275 99.9699 0.0275 99.9700 0.0275

4 149.9538 0.0338 149.9538 0.0338 149.9537 0.0338

5 199.9429 0.0306 199.9429 0.0306 199.9426 0.0305

6 249.9270 0.0295 249.9269 0.0295 249.9266 0.0293

7 299.9127 0.0204 299.9126 0.0204 299.9124 0.0202

8 349.9063 0.0043 349.9062 0.0044 349.9062 0.0044

9 399.8977 0.0000 399.8976 0.0000 399.8976 0.0000

10 -0.0081 50.0079 -0.0081 50.0079 -0.0080 50.0079

11 49.9843 50.0188 49.9843 50.0188 49.9842 50.0189

12 100.0037 49.9984 100.0037 49.9985 100.0035 49.9984

13 149.9970 50.0168 149.9970 50.0168 149.9968 50.0167

14 199.9775 50.0220 199.9774 50.0220 199.9772 50.0220

15 249.9516 50.0338 249.9516 50.0338 249.9513 50.0338

16 299.9354 50.0239 299.9354 50.0239 299.9354 50.0239

17 349.8819 49.9903 349.8818 49.9903 349.8819 49.9903

18 399.9021 49.9996 399.9020 49.9996 399.9020 49.9997

19 0.0081 100.0020 0.0081 100.0020 0.0080 100.0017

20 50.0092 99.9865 50.0092 99.9865 50.0091 99.9863

21 349.910813 100.019773 349.910749 100.019782 349.9106 100.0197

22 399.87793 99.986584 399.877857 99.98659 399.8778 99.9864

23 0.019841 150.004259 0.019865 150.004239 0.0200 150.0039

24 50.030982 149.951301 50.030983 149.951281 50.0310 149.9510

25 349.883075 150.005515 349.883031 150.005519 349.8828 150.0053

26 399.868836 149.970288 399.868799 149.970264 399.8687 149.9700

27 0.025213 199.948346 0.025257 199.948338 0.0254 199.9481

28 50.021944 199.927256 50.021969 199.927242 50.0221 199.9271

29 349.878192 199.981532 349.878151 199.981533 349.8782 199.9814

30 399.869138 199.94879 399.869089 199.948795 399.8691 199.9488

31 0.032564 249.9374 0.032584 249.937425 0.0326 249.9371

32 50.020554 249.905092 50.020593 249.905104 50.0207 249.9049

33 100.035257 249.943954 100.035306 249.943967 100.0352 249.9437

34 150.023599 249.912237 150.023631 249.912209 150.0235 249.9119

35 199.969303 249.86465 199.969293 249.864644 199.9693 249.8645

36 249.906989 249.881127 249.906987 249.88111 249.9068 249.8809

37 299.890822 249.889912 299.890815 249.889919 299.8908 249.8897

38 349.863199 249.95111 349.863162 249.951118 349.8630 249.9511

39 399.869726 249.92678 399.869665 249.926793 399.8696 249.9269

40 0.041557 299.954444 0.041614 299.954454 0.0416 299.9541

41 49.999233 299.890531 49.999255 299.890529 49.9992 299.8904

42 349.880469 299.917965 349.88037 299.917976 349.8804 299.9179

43 399.879411 299.902072 399.87928 299.902073 399.8792 299.9022

44 0.020321 349.928165 0.020337 349.928165 0.0203 349.9277

45 50.016218 349.916846 50.016238 349.916851 50.0161 349.9164

46 99.980852 349.878678 99.980864 349.878674 99.9807 349.8783

47 149.956315 349.864814 149.956297 349.864843 149.9562 349.8644

48 199.935303 349.871491 199.935268 349.871529 199.9353 349.8712

49 249.901853 349.87615 249.901801 349.876195 249.9017 349.8759

50 299.884249 349.898654 299.884168 349.898699 299.8841 349.8984

51 349.917335 349.873787 349.917264 349.873819 349.9172 349.8736

52 399.895725 349.892197 399.895619 349.892213 399.8955 349.8920

53 0.024433 399.919279 0.024428 399.919279 0.0244 399.9189

54 50.018582 399.914031 50.018576 399.914041 50.0185 399.9136

55 100.016517 399.887565 100.016525 399.887596 100.0164 399.8872

56 149.988749 399.869529 149.988751 399.869573 149.9886 399.8692

57 199.953555 399.867398 199.953522 399.867411 199.9535 399.8671

58 249.937973 399.861931 249.937926 399.861938 249.9378 399.8617

59 299.937593 399.8606 299.937527 399.860621 299.9374 399.8605

60 349.918547 399.883927 349.918443 399.883932 349.9183 399.8838

61 399.893295 399.888751 399.893174 399.888788 399.8931 399.8887



9 Measurement Results in Cylindrical Coordinates

As the measurand of the comparison was the distance of each measuring element to the reference element, the pilot laboratory converted the x and y coordinates stated by the participants to the corresponding polar coordinates, distance modulus

r and angle θ.

9.1 Ball Plate

Tables 9 a and 9 b report these values. Only the modulus r is considered for the

comparison. θ is reported just for information.

Graphs 13 a through 13 d show the laboratories deviations from nominal values of the respective ball for each of the 25 balls and all the participant laboratories along with their corresponding claimed standard uncertainty. The laboratory number correspondence in these graphs and tables and those that follow is given according to table 8.


Table 10 reports these values. Only the modulus r is considered for the

comparison. Angle θ is omitted.

Graphs 14 a through 14 d show the deviation from nominal values of the respective bores for each of the 61 bores and all the participant laboratories along with their corresponding claimed standard uncertainty. The laboratory coding is according to table 8.

No. NMI Country No. NMI Country

1 NMIA (CSIRO) Australia 7 NMIJ (NRLM) Japan

2 INMS-NRC Canada 8 NMi Netherlands

3 NIM China 9 VNIIMS Russia

4 CMI Czech Rep. 10 NPL United Kingdom

5 BNM-LNE France 11 NIST USA (1)

6 PTB Germany 12 CENAM Mexico (1)

Table 8.- Laboratory number coding fro following graph representation..



Table 9 a.- Coordinates of center of balls for the steel ball plate with respect to ball 1 in polar coordinates r and θ. r in mm and θ in degrees.

Country

Ball r θθθθ r θθθθ r θθθθ r θθθθ r θθθθ r θθθθ1 0.0000 #¡DIV/0! 0.000000 -32.005316 0.0000 #¡DIV/0! 0.0000 #¡DIV/0! 0.000000 #¡DIV/0! 0.0000 #¡DIV/0!

2 83.0040 -0.0001 83.004171 -0.000187 83.0040 -0.0002 83.0040 -0.0002 83.003900 -0.000052 83.0040 -0.0002

3 166.0071 -0.0001 166.007767 -0.000198 166.0074 -0.0002 166.0073 -0.0002 166.007513 -0.000134 166.0077 -0.0002

4 249.0074 -0.0001 249.008478 -0.000160 249.0080 -0.0001 249.0080 -0.0002 249.008363 -0.000158 249.0083 -0.0002

5 332.0086 0.0000 332.010194 0.000000 332.0094 0.0000 332.0098 0.0000 332.009913 0.000000 332.0100 0.0000

6 83.0002 89.9960 83.000822 89.995968 83.0008 89.9959 83.0007 89.9961 83.000788 89.996045 83.0008 89.9961

7 117.3852 44.9970 117.385749 44.997099 117.3857 44.9970 117.3854 44.9971 117.385462 44.997129 117.3856 44.9971

8 185.6040 26.5634 185.604742 26.563427 185.6045 26.5635 185.6043 26.5634 185.604560 26.563429 185.6047 26.5634

9 262.4812 18.4342 262.482357 18.434259 262.4821 18.4343 262.4819 18.4342 262.482300 18.434249 262.4823 18.4342

10 342.2292 14.0360 342.230935 14.036024 342.2305 14.0360 342.2304 14.0360 342.230664 14.036012 342.2309 14.0360

11 166.0013 89.9978 166.002327 89.997708 166.0024 89.9978 166.0023 89.9978 166.002475 89.997801 166.0023 89.9978

12 185.5982 63.4330 185.599280 63.433039 185.5992 63.4331 185.5991 63.4331 185.599065 63.433101 185.5993 63.4330

13 234.7683 44.9981 234.769580 44.998181 234.7694 44.9983 234.7692 44.9982 234.769431 44.998232 234.7696 44.9982

14 299.2727 33.6890 299.274151 33.689044 299.2738 33.6891 299.2739 33.6891 299.274103 33.689067 299.2742 33.6890

15 371.2003 26.5646 371.202175 26.564637 371.2016 26.5647 371.2018 26.5646 371.201948 26.564615 371.2021 26.5646

16 249.0010 89.9980 249.002414 89.997949 249.0024 89.9979 249.0024 89.9980 249.002575 89.997980 249.0025 89.9980

17 262.4734 71.5629 262.474826 71.562971 262.4747 71.5630 262.4748 71.5630 262.474872 71.563001 262.4749 71.5630

18 299.2691 56.3077 299.270584 56.307746 299.2704 56.3078 299.2705 56.3078 299.270738 56.307784 299.2707 56.3078

19 352.1511 44.9985 352.152857 44.998489 352.1526 44.9985 352.1525 44.9985 352.152930 44.998508 352.1528 44.9985

20 415.0132 36.8689 415.015219 36.868971 415.0147 36.8690 415.0148 36.8690 415.015173 36.868989 415.0151 36.8690

21 332.0003 89.9988 332.002093 89.998775 332.0020 89.9987 332.0020 89.9988 332.002025 89.998773 332.0020 89.9988

22 342.2189 75.9625 342.220605 75.962538 342.2205 75.9625 342.2206 75.9626 342.220596 75.962556 342.2206 75.9626

23 371.1910 63.4334 371.192900 63.433429 371.1928 63.4334 371.1928 63.4335 371.192993 63.433431 371.1929 63.4334

24 415.0065 53.1288 415.008577 53.128879 415.0084 53.1289 415.0082 53.1289 415.008560 53.128880 415.0085 53.1289

25 469.5284 44.9990 469.530739 44.999014 469.5303 44.9990 469.5304 44.9991 469.530615 44.999020 469.5306 44.9990

NMIA (CSIRO) INMS-NRC BNM-LNENMI CMI PTB



Country NMIJ (NRLM) NMi VNIIMS NPL NIST 1 CENAM 1

Ball r θθθθ r θθθθ r θθθθ r θθθθ R θθθθ r θθθθ

1 0.0000 #¡DIV/0! 0.000000 #¡DIV/0! 0.0000 #¡DIV/0! 0.0000 #¡DIV/0! 0.000000 #¡DIV/0! 0.0000 #¡DIV/0!

2 83.0042 -0.0001 83.003964 -0.000284 83.0038 -0.0002 83.0040 -0.0002 83.004005 -0.000203 83.0038 -0.0001

3 166.0077 -0.0002 166.007648 -0.000265 166.0072 -0.0002 166.0076 -0.0002 166.007525 -0.000193 166.0075 -0.0002

4 249.0083 -0.0001 249.008194 -0.000194 249.0075 -0.0002 249.0083 -0.0001 249.008230 -0.000178 249.0082 -0.0002

5 332.0100 0.0000 332.009931 0.000000 332.0087 0.0000 332.0099 0.0000 332.009908 0.000000 332.0100 0.0000

6 83.0007 89.9959 83.000764 89.996036 83.0000 89.9961 83.0007 89.9960 83.000720 89.996106 83.0008 89.9959

7 117.3857 44.9971 117.385609 44.997042 117.3847 44.9971 117.3855 44.9971 117.385424 44.997134 117.3857 44.9971

8 185.6047 26.5634 185.604664 26.563388 185.6036 26.5634 185.6046 26.5634 185.604367 26.563394 185.6046 26.5634

9 262.4822 18.4342 262.482214 18.434244 262.4809 18.4342 262.4822 18.4342 262.481950 18.434206 262.4823 18.4342

10 342.2307 14.0360 342.230691 14.036038 342.2291 14.0359 342.2306 14.0360 342.230616 14.035980 342.2310 14.0360

11 166.0023 89.9977 166.002165 89.997830 166.0007 89.9977 166.0023 89.9977 166.002173 89.997805 166.0023 89.9977

12 185.5992 63.4330 185.599072 63.433087 185.5977 63.4329 185.5991 63.4331 185.599046 63.433078 185.5991 63.4331

13 234.7695 44.9982 234.769532 44.998219 234.7679 44.9980 234.7695 44.9982 234.769178 44.998188 234.7693 44.9982

14 299.2740 33.6890 299.273983 33.689052 299.2723 33.6890 299.2740 33.6891 299.273720 33.689032 299.2740 33.6891

15 371.2020 26.5646 371.201898 26.564618 371.2000 26.5645 371.2018 26.5646 371.201710 26.564619 371.2021 26.5646

16 249.0023 89.9979 249.002205 89.998024 248.9999 89.9979 249.0024 89.9980 249.002329 89.997981 249.0024 89.9980

17 262.4747 71.5630 262.474490 71.563010 262.4722 71.5629 262.4748 71.5630 262.474776 71.562981 262.4748 71.5630

18 299.2706 56.3077 299.270448 56.307769 299.2681 56.3076 299.2705 56.3078 299.270457 56.307767 299.2704 56.3078

19 352.1528 44.9985 352.152737 44.998484 352.1502 44.9984 352.1528 44.9985 352.152611 44.998492 352.1528 44.9985

20 415.0150 36.8690 415.014928 36.868961 415.0124 36.8689 415.0150 36.8690 415.015000 36.868965 415.0151 36.8690

21 332.0017 89.9988 332.001610 89.998785 331.9980 89.9987 332.0019 89.9988 332.001915 89.998789 332.0022 89.9988

22 342.2204 75.9625 342.220242 75.962573 342.2167 75.9624 342.2205 75.9626 342.220434 75.962542 342.2208 75.9625

23 371.1927 63.4334 371.192612 63.433440 371.1891 63.4333 371.1929 63.4334 371.192552 63.433427 371.1927 63.4334

24 415.0083 53.1288 415.008313 53.128883 415.0048 53.1287 415.0085 53.1289 415.008188 53.128871 415.0084 53.1289

25 469.5303 44.9990 469.530250 44.999014 469.5268 44.9988 469.5305 44.9990 469.530415 44.999003 469.5308 44.9990

9 b.- Coordinates of center of balls for the steel ball plate with respect to ball 1 in polar coordinates r and θ. r in mm and θ in degrees.



Figure 13 a.- Laboratory deviations from nominal values for balls 2 to 7. Laboratory numbers according to table 8. All deviations from nominal values are in µm. The drawing in the top left side shows the position of the corresponding ball in the plate.

BALL 2

3.0

3.5

4.0

4.5

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

BALL 3

3.0

3.5

4.0

4.5

5.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

BALL 4

6.5

7.0

7.5

8.0

8.5

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

BALL 5

8.0

9.0

10.0

11.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

BALL 6

-0.5

0.0

0.5

1.0

1.5

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

BALL 7

4.0

5.0

6.0

7.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)



Figure 13 b.- Laboratory deviations from nominal values for balls 8 to 13. Laboratory numbers according to table 8. All deviations from nominal values are in µm. The drawing in the top left side shows the position of the corresponding ball in the plate.

BALL 8

9.0

10.0

11.0

12.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

BALL 9

11.0

12.0

13.0

14.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

BALL 10

11.0

12.0

13.0

14.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

BALL 11

0.0

1.0

2.0

3.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

BALL 12

3.5

4.5

5.5

6.5

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

BALL 13

8.0

9.0

10.0

11.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)



Figure 13 c.- Laboratory deviations from nominal values for balls 14 to 19. Laboratory numbers according to table 8. All deviations from nominal values are in

µm. The drawing in the top left side shows the position of the corresponding ball in the plate.

BALL 14

11.0

12.0

13.0

14.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

BALL 15

12.5

13.5

14.5

15.5

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

BALL 16

-0.5

0.5

1.5

2.5

3.5

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

BALL 17

2.5

3.5

4.5

5.5

6.5

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

BALL 18

6.5

7.5

8.5

9.5

10.5

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

BALL 19

10.5

11.5

12.5

13.5

14.5

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)



Figure 13 d.- Laboratory deviations from nominal values for balls 20 to 25. Laboratory numbers according to table 8. All deviations from nominal values are in


BALL 20

12.00

13.00

14.00

15.00

16.00

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

BALL 21

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

BALL 22

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

BALL 23

1.0

2.0

3.0

4.0

5.0

6.0

7.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

BALL 24

4.0

5.0

6.0

7.0

8.0

9.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

BALL 25

7.0

8.0

9.0

10.0

11.0

12.0

13.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)



Table 10.- Modulus r of the position of each bore with respect to bore 1 in mm.

NMI NMIA (CSIRO) INMS-NRC NIM CMI BNM-LNE PTB NMIJ (NRLM) NMi VNIIM5

NPL NIST 1 CENAM 1

Bore r r r r r r r r r r r

1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0 0 0.000000 0.0000 0.0000 0.000000

2 49.9829 49.9830 49.9829 49.9829 49.9832 49.9829 49.98270193 49.98287493 49.983402 49.9828 49.9829 49.983002

3 99.9701 99.9701 99.9700 99.9701 99.9704 99.9699 99.96980378 99.96989287 99.970804 99.9698 99.9699 99.970004

4 149.9541 149.9540 149.9542 149.9541 149.9544 149.9537 149.9535038 149.9536449 149.954904 149.9536 149.9539 149.954004

5 199.9430 199.9430 199.9428 199.9431 199.9435 199.9428 199.9425023 199.9426904 199.944302 199.9427 199.9430 199.942902

6 249.9271 249.9270 249.9268 249.9271 249.9276 249.9270 249.9265017 249.9266117 249.928702 249.9267 249.9270 249.926802

7 299.9126 299.9128 299.9125 299.9129 299.9135 299.9127 299.9123007 299.9123377 299.914801 299.9124 299.9127 299.912701

8 349.9063 349.9064 349.9061 349.9068 349.9073 349.9064 349.9059 349.905892 349.908800 349.9059 349.9063 349.906200

9 399.8976 399.8979 399.8975 399.8981 399.8990 399.8977 399.8972 399.897225 399.900800 399.8973 399.8977 399.897600

10 50.0079 50.0079 50.0078 50.0076 50.0080 50.0079 50.00780064 50.00797563 50.007901 50.0077 50.0078 50.007901

11 70.7127 70.7130 70.7129 70.7128 70.7132 70.7129 70.71273294 70.71289419 70.713086 70.7128 70.7129 70.712945

12 111.8059 111.8062 111.8060 111.8061 111.8065 111.8060 111.8058139 111.806058 111.806753 111.8060 111.8060 111.805859

13 158.1163 158.1165 158.1168 158.1165 158.1171 158.1162 158.1160975 158.1164444 158.117647 158.1162 158.1164 158.116445

14 206.1388 206.1388 206.1387 206.1390 206.1395 206.1387 206.138354 206.1387593 206.140464 206.1386 206.1388 206.138669

15 254.9100 254.9102 254.9101 254.9103 254.9109 254.9101 254.909736 254.9100443 254.912364 254.9100 254.9101 254.910050

16 304.0783 304.0785 304.0783 304.0786 304.0794 304.0784 304.077942 304.0781585 304.081066 304.0781 304.0783 304.078435

17 353.4350 353.4353 353.4350 353.4356 353.4364 353.4352 353.4346957 353.4347758 353.438132 353.4348 353.4350 353.435219

18 403.0157 403.0160 403.0155 403.0161 403.0171 403.0157 403.015173 403.0153855 403.018857 403.0153 403.0157 403.015768

19 100.0020 100.0020 100.0017 100.0017 100.0020 100.0018 100.0017003 100.0021413 100.001600 100.0018 100.0021 100.001800

20 111.7954 111.7955 111.7954 111.7954 111.7956 111.7953 111.7952158 111.795676 111.795484 111.7953 111.7955 111.795439

21 363.9251 363.9254 363.9250 363.9255 363.9263 363.9252 363.924729 363.92486 363.928081 363.9248 363.9251 363.925045

22 412.1889 412.1891 412.1886 412.1892 412.1901 412.1888 412.1883249 412.188486 412.192011 412.1885 412.1888 412.189004

23 150.0039 150.0041 150.0039 150.0038 150.0041 150.0041 150.0039013 150.0043553 150.003701 150.0040 150.0043 150.004001

24 158.0773 158.0775 158.0773 158.0773 158.0776 158.0775 158.0772386 158.0775488 158.077175 158.0773 158.0775 158.077333

25 380.6831 380.6834 380.6830 380.6835 380.6845 380.6833 380.6827995 380.6830683 380.685780 380.6831 380.6833 380.683167

26 427.0667 427.0671 427.0666 427.0672 427.0680 427.0668 427.0663394 427.0666484 427.069897 427.0667 427.0668 427.066936

27 199.9476 199.9482 199.9479 199.9480 199.9481 199.9482 199.9478016 199.9484136 199.947902 199.9481 199.9484 199.948102

28 206.0895 206.0900 206.0899 206.0899 206.0901 206.0899 206.0897276 206.0901459 206.089655 206.0898 206.0901 206.089946

29 402.9977 402.9982 402.9978 402.9983 402.9991 402.9980 402.9975499 402.9978728 403.000254 402.9978 402.9979 402.998170

30 447.0734 447.0739 447.0734 447.0740 447.0748 447.0736 447.0730364 447.0734461 447.076346 447.0734 447.0737 447.073752

31 249.9366 249.9373 249.9371 249.9374 249.9370 249.9373 249.9370022 249.9373531 249.937002 249.9371 249.9374 249.937102

32 254.8612 254.8619 254.8618 254.8618 254.8620 254.8619 254.8615693 254.8619703 254.861393 254.8616 254.8620 254.861726

33 269.2187 269.2193 269.2192 269.2193 269.2196 269.2193 269.2189897 269.2193657 269.219306 269.2190 269.2194 269.219083

34 291.4840 291.4845 291.4847 291.4847 291.4849 291.4845 291.4839761 291.4845829 291.484834 291.4843 291.4845 291.484251

35 320.0309 320.0315 320.0315 320.0316 320.0319 320.0314 320.0309351 320.0313209 320.032107 320.0311 320.0314 320.031404

36 353.4031 353.4036 353.4034 353.4036 353.4042 353.4036 353.4029895 353.4035071 353.404545 353.4034 353.4036 353.403555

37 390.3576 390.3583 390.3580 390.3584 390.3590 390.3581 390.3575595 390.3579795 390.359493 390.3579 390.3581 390.358225

38 429.9760 429.9767 429.9764 429.9770 429.9775 429.9766 429.9760473 429.9764308 429.978488 429.9763 429.9766 429.976431

39 471.5494 471.5500 471.5496 471.5502 471.5508 471.5499 471.5492154 471.5495834 471.552491 471.5494 471.5498 471.549777

40 299.9535 299.9543 299.9540 299.9542 299.9543 299.9542 299.9539029 299.9543749 299.953803 299.9542 299.9545 299.954003

41 304.0292 304.0300 304.0298 304.0299 304.0300 304.0300 304.0296237 304.0299063 304.029541 304.0297 304.0301 304.029936

42 460.8326 460.8333 460.8329 460.8335 460.8339 460.8331 460.832563 460.8329046 460.834787 460.8328 460.8330 460.833073

43 499.8443 499.8450 499.8445 499.8450 499.8458 499.8447 499.84406 499.8445164 499.847380 499.8444 499.8448 499.844820

44 349.9271 349.9280 349.9277 349.9278 349.9279 349.9279 349.9276006 349.9279866 349.927301 349.9278 349.9281 349.927701

45 353.4724 353.4733 353.4730 353.4731 353.4733 353.4733 353.4729371 353.4731277 353.472541 353.4731 353.4733 353.473178

46 363.8827 363.8835 363.8833 363.8835 363.8838 363.8834 363.8830104 363.8834147 363.882900 363.8833 363.8836 363.883258

47 380.6466 380.6472 380.6473 380.6472 380.6475 380.6471 380.6466739 380.6471035 380.646713 380.6469 380.6472 380.646963

48 402.9685 402.9693 402.9692 402.9693 402.9697 402.9691 402.9686847 402.9691345 402.969032 402.9689 402.9692 402.969069

49 429.9578 429.9585 429.9584 429.9587 429.9591 429.9585 429.9579806 429.9583451 429.958562 429.9581 429.9583 429.958318

50 460.8243 460.8251 460.8248 460.8252 460.8257 460.8249 460.8244393 460.8248281 460.825784 460.8246 460.8248 460.824906

51 494.8264 494.8273 494.8269 494.8275 494.8281 494.8271 494.8265382 494.8267814 494.828377 494.8267 494.8270 494.826892

52 531.3572 531.3581 531.3576 531.3581 531.3588 531.3580 531.3571705 531.3574791 531.360247 531.3574 531.3578 531.357622

53 399.9185 399.9192 399.9188 399.9191 399.9189 399.9190 399.9185008 399.9191028 399.918101 399.9189 399.9193 399.918701

54 403.0292 403.0298 403.0296 403.0296 403.0296 403.0297 403.0292643 403.0296746 403.028880 403.0295 403.0299 403.029488

55 412.2049 412.2055 412.2052 412.2054 412.2057 412.2053 412.2048193 412.2052338 412.204795 412.2051 412.2055 412.205062

56 427.0737 427.0741 427.0740 427.0741 427.0743 427.0739 427.0734332 427.0738699 427.073539 427.0737 427.0741 427.073890

57 447.0737 447.0743 447.0741 447.0742 447.0744 447.0741 447.0735286 447.0740706 447.074155 447.0738 447.0742 447.073931

58 471.5487 471.5492 471.5489 471.5492 471.5494 471.5491 471.5484208 471.5488829 471.549566 471.5487 471.5490 471.548993

59 499.8507 499.8512 499.8508 499.8513 499.8515 499.8510 499.8504611 499.8508057 499.852041 499.8506 499.8509 499.850981

60 531.3660 531.3666 531.3662 531.3668 531.3670 531.3664 531.3657312 531.3659109 531.367660 531.3657 531.3662 531.366296

61 565.5309 565.5316 565.5311 565.5316 565.5321 565.5313 565.5306393 565.5308309 565.533256 565.5307 565.5313 565.531346



Figure 14 a.- Laboratory deviations from nominal values for 2 through 7. Laboratory numbers according to table 8. All deviations from nominal values are in µm. The drawing in the top left side shows the position of the corresponding ball in the plate

Bore 2

-17.5

-17.0

-16.5

-16.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore3

-30.5

-30.0

-29.5

-29.0

-28.5

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 4

-47.0

-46.5

-46.0

-45.5

-45.0

-44.5

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 5

-58.0

-57.5

-57.0

-56.5

-56.0

-55.5

-55.01 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 6

-74.5

-73.5

-72.5

-71.5

-70.51 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 7

-88.5

-87.5

-86.5

-85.5

-84.51 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)



Figure 14 b.- Laboratory deviations from nominal values for 8 through 13. Laboratory numbers according to table 8. All deviations from nominal values are in

µm. The drawing in the top left side shows the position of the corresponding ball in the plate

Bore 8

-95.0

-94.0

-93.0

-92.0

-91.0

-90.01 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 9

-103.0

-102.0

-101.0

-100.0

-99.0

-98.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 10

7.0

7.5

8.0

8.5

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 11

1.5

2.0

2.5

3.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 12

2.0

2.5

3.0

3.5

4.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 13

2.0

2.5

3.0

3.5

4.0

4.5

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)



Figure 14 c.- Laboratory deviations from nominal values for 14 through 19. Laboratory numbers according to table 8. All deviations from nominal values are in


Bore 14

-17.0

-16.5

-16.0

-15.5

-15.0

-14.5

-14.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 15

-41.5

-41.0

-40.5

-40.0

-39.5

-39.0

-38.5

-38.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 16

-60.5

-60.0

-59.5

-59.0

-58.5

-58.0

-57.5

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 17

-119.0

-118.0

-117.0

-116.0

-115.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 18

-0.50

0.50

1.50

2.50

3.50

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 19

1.0

1.5

2.0

2.5

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)



Figure 14 d.- Laboratory deviations from nominal values for 20 through 25. Laboratory numbers according to table 8. All deviations from nominal values are in


Bore 20

-8.5

-8.0

-7.5

-7.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 21

-81.0

-80.0

-79.0

-78.0

-77.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 22

-123.0

-122.0

-121.0

-120.0

-119.0

-118.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 23

3.0

3.5

4.0

4.5

5.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 24

-37.5

-37.0

-36.5

-36.0

-35.5

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 25

-106.0

-105.0

-104.0

-103.0

-102.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)



Figure 14 e.- Laboratory deviations from nominal values for 26 through 31. Laboratory numbers according to table 8. All deviations from nominal values are in


Bore 26

-134.0

-133.0

-132.0

-131.0

-130.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 27

-53.0

-52.5

-52.0

-51.5

-51.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 28

-66.50

-66.00

-65.50

-65.00

-64.50

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 29

-116.0

-115.5

-115.0

-114.5

-114.0

-113.5

-113.0

-112.5

-112.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 30

-141.0

-140.0

-139.0

-138.0

-137.0

-136.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 31

-64.0

-63.5

-63.0

-62.5

-62.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)



Figure 14 f.- Laboratory deviations from nominal values for 32 through 37. Laboratory numbers according to table 8. All deviations from nominal values are in


Bore 32

-90.5

-90.0

-89.5

-89.0

-88.5

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 33

-40.0

-39.5

-39.0

-38.5

-38.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 34

-64.0

-63.5

-63.0

-62.5

-62.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 35

-125.5

-125.0

-124.5

-124.0

-123.5

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 36

-151.0

-150.5

-150.0

-149.5

-149.0

-148.5

-148.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 37

-156.0

-155.0

-154.0

-153.0

-152.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)



Figure 14 g.- Laboratory deviations from nominal values for 38 through 43. Laboratory numbers according to table 8. All deviations from nominal values are in


Bore 38

-141.0

-140.0

-139.0

-138.0

-137.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 39

-151.00

-150.00

-149.00

-148.00

-147.00

-146.00

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 40

-47.0

-46.5

-46.0

-45.5

-45.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 41

-109.5

-109.0

-108.5

-108.0

-107.5

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 42

-146.0

-145.0

-144.0

-143.0

-142.0

-141.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 43

-157.0

-156.0

-155.0

-154.0

-153.0

-152.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)



Figure 14 h.- Laboratory deviations from nominal values for 44 through 49. Laboratory numbers according to table 8. All deviations from nominal values are in


Bore 44

-73.5

-73.0

-72.5

-72.0

-71.5

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 45

-81.5

-81.0

-80.5

-80.0

-79.5

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 46

-123.0

-122.5

-122.0

-121.5

-121.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 47

-142.5

-142.0

-141.5

-141.0

-140.5

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 48

-145.0

-144.5

-144.0

-143.5

-143.0

-142.5

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 49

-159.0

-158.5

-158.0

-157.5

-157.0

-156.5

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)



Figure 14 i.- Laboratory deviations from nominal values for 50 through 55. Laboratory numbers according to table 8. All deviations from nominal values are in


Bore 50

-153.5

-153.0

-152.5

-152.0

-151.5

-151.0

-150.5

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 51

-149.0

-148.5

-148.0

-147.5

-147.0

-146.5

-146.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 52

-151.0

-150.0

-149.0

-148.0

-147.0

-146.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 53

-83.0

-82.0

-81.0

-80.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 54

-84.5

-84.0

-83.5

-83.0

-82.5

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 55

-106.5

-106.0

-105.5

-105.0

-104.5

-104.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)



Figure 14 j.- Laboratory deviations from nominal values for 56 through 61. Laboratory numbers according to table 8. All deviations from nominal values are in


Bore 56

-1.0

-0.5

0.0

0.5

1.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 57

-140.5

-140.0

-139.5

-139.0

-138.5

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 58

-151.0

-150.5

-150.0

-149.5

-149.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 59

-150.0

-149.5

-149.0

-148.5

-148.0

-147.5

-147.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 60

-142.0

-141.5

-141.0

-140.5

-140.0

-139.5

-139.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)

Bore 61

-155.0

-154.0

-153.0

-152.0

-151.0

1 2 3 4 5 6 7 8 9 10 11 12

Lab.

Dev. (um)



10 Key Comparison Reference Value (KCRV) Determination

10.1 Outlier elimination process

The KCRV was determined as the simple mean of the largest subset of laboratories which had “consistent” results8. To establish the largest subset of laboratories that had “consistent” results, an iterative elimination process was applied. To start the process, all participants were considered to calculate the simple mean. At each step, to judge whether a participant was a candidate to be eliminated, two values of the participants were compared and used as criteria:

10.1.1 The RMS9 value ( RMSjδ ) of each laboratory (j = 1,2,],m) difference ( ijδ ) between

its value on element i ( ijr ) with respect to the simple mean for that element ( ir ) over all

measuring elements (i= 2, 3, 4, ], n). In other words, let:

iijij rr −=δ (10.1)

Where:

mrr

m

j

iji ∑=

=1

, the mean of the i measuring element for m laboratories taken

in account to calculate it;

i= 2, 3, 4, ], n , the number of measuring element10;

j= 1, 2, 3,], m, the number of laboratory.

Then the RMS deviation of laboratory j is given by:

∑=

−=n

i

ijRMSj n2

2 )1/(δδ (10.2)

Once all RMSjδ j = 1,2,],m are obtained, they are sorted in decreasing order

(order k). The first values, with the largest RMSδ values are candidates to be

eliminated.

8 Consistency is quoted because it is not checked in a rigorous statistical way but rather by the

parameters that are described herein.

9 Root Mean Square Value.

10 It always starts at i = 2 because measuring element 1 is always the reference.



10.1.2 The second criterion is the average normalized error, jE , for all n

measuring elements of each laboratory j with respect to the simple mean. In other words, let:

ijuE ijij δδ= (10.3)

Where ijδ is calculated from 10.1 and ij

uδ is the standard uncertainty of the

difference and is calculated by:

222 2ijiijij rrr u

muuu −+=δ (10.4)

Where: ijr

u is the uncertainty on measuring element i of laboratory j;

iru is the uncertainty of the mean of measuring element i.

Then: )1(

2

−= ∑=

nEE

n

i

ijj (10.5)

According to the definition of this normalized error, the participants with jE

values greater than 1 are prone to be eliminated.

Figure 15 summarizes the elimination process. At each step the simple mean is

calculated. The participant in the first place (k=1) of the ordered list of RMSδ values is

taken as candidate to be eliminated. Then its corresponding E value is tested. If it is also the largest and it is grater than 1, this laboratory is eliminated. Then the process is repeated until all laboratories participating in the calculation of the simple mean have

average normalized errors E under 1.

10.2 Uncertainty of the KCRV

For the KCRV, both the internal and external uncertainties were taken in account. The

internal uncertainty (intir

u ) is given as the uncertainty combination of the declared

standard uncertainties of the participants contributing to calculate the simple mean:

For i = 1, 2, 3,], n (10.6)

Where n is the number of measuring elements and m’ the number of laboratories contributing to the mean.

∑=

='

1

2

2int '

1m

j

ijr um

ui



And the external uncertainty (extr i

u ) is given by the standard deviation of the simple mean

(ir

S ). Therefore, the final uncertainty on the reference value is:

Figure 15.- Flow chart of outlier elimination process.

22

int extrrr iiiuuu += (10.7)

Finally, a least-squares curve of the uncertainty as a function of length l of the form 10.8 was adjusted:

222)( lbalu += (10.8)

Where u(l) is in µm and l in mm.

Start

m = no. of

participants

Set in decreasing

order (k)

for k = 1,2,=,m

Eliminate lab. k

m = m - 1

Is

? 1>kE

Stop

NoNo

k = 1

k = k + 1

Calculate

jEj = 1,2,=,m

RMSjδand

Yes

Calculate the

simple mean

for m

participants

Is the

corresponding

the largest?

kE

Yes

RMSkδ

Start

m = no. of

participants

Set in decreasing

order (k)

for k = 1,2,=,m

Eliminate lab. k

m = m - 1

Is

? 1>kE

Stop

NoNo

k = 1

k = k + 1

Calculate

jEj = 1,2,=,m

RMSjδand

Yes

Calculate the

simple mean

for m

participants

Is the

corresponding

the largest?

kE

Yes

RMSkδ



10.3 KCRV determination for the Steel Ball Plate

For the steel ball plate the number of participants contributing to the simple mean reference value determination was 10. The iteration process as describe in section 10.1 was stopped after two iterations. The corresponding uncertainty on the reference value was obtained according to 10.2.

In the first iteration, the criteria values shown in Table 11 were obtained. As the largest

values of both correspond to laboratory number 9 and its E was greater than 1, this laboratory was eliminated. The process was repeated for a second time (Table 12) and,

once again the laboratory which had the largest E value also had the largest RMSδ value

and it was greater than 1, laboratory number 1. Therefore, it was eliminated.

Table 11.- RMSδ and E values obtained at

the first elimination iteration for the Steel Ball Plate.

Laboratory

RMSδ

(µm) E

1 1.203 2.45

2 0.279 1.09

6 0.228 0.80

7 0.137 0.63

12 0.224 0.56

3 0.149 0.50

11 0.093 0.43

10 0.141 0.42

8 0.113 0.39

4 0.134 0.30

5 0.226 0.30


the second elimination iteration for the Steel Ball Plate

The process was stopped after two iterations as there were no more E values greater than 1 (table 13). Thus, this set of laboratories is considered to be in good consistency.

Parameters a2 and b2 of the adjusted uncertainty curve of the reference value, of the form 10.8 obtained were:

a2 = 5,706 x 10-3 and b2 = 6,868 x 10-8

Laboratory

RMSδ

(µm) E

9 1.984 3.27

1 1.029 1.96

2 0.444 1.44

6 0.400 1.16

7 0.277 1.06

12 0.385 0.88

10 0.315 0.78

3 0.268 0.72

8 0.219 0.65

11 0.217 0.65

5 0.398 0.49

4 0.261 0.48



Laboratory

RMSδ

(µm) E

11 0.139 0.77

2 0.170 0.72

3 0.178 0.56

7 0.107 0.50

8 0.142 0.46

6 0.113 0.44

4 0.159 0.36

12 0.139 0.36

5 0.122 0.17

10 0.050 0.17

1 1.323 2.54

9 2.281 3.87

Table 13.- Final RMSδ and E values for the Steel Ball Plate. At the end the

corresponding RMSδ and E values of those laboratories excluded from the

calculation of the reference value are also shown, with respect to that reference value.

10.4 KCRV determination for the ZERODUR Bore Plate

In this case, the number of participants contributing to the simple mean reference value determination was 9. The iteration process as describe in section 10.1 was stopped after three iterations. The corresponding uncertainty on the reference value was obtained according to 10.2.

In the first iteration, the criteria values shown in Table 14 were obtained. As the largest

values of both correspond to laboratory number 9 and its E value was greater than 1, this laboratory was eliminated. The process was repeated for a second time (Table 15).

In this case the laboratory which had the largest E value - laboratory number 7 - was not

the one with the largest RMSδ . According to the algorithm, the second one on the list with

largest RMSδ was picked which corresponded to laboratory number 5. The E value of the

later was greater than 1 therefore, it was eliminated.

On the third iteration (Table 16) it was laboratory number 7 which had the largest E and

RMSr values and E was also greater than 1. Therefore it was eliminated.

Table 17 shows the parameter RMSδ and E values at the end of the iteration process. It

ma y be observed that all E values are smaller than 1. Therefore, the process was stopped and the nine corresponding laboratories were retained to calculate the reference value.

Parameters a2 and b2 of the adjusted uncertainty curve of the reference value, of the form 10.8 obtained were:

a2 = 5,308 x 10-3 and b2 = 7,091 x 10-8



Laboratory

RMSδ

(µm) E

9 1.460 2.077

7 0.527 2.018

11 0.226 0.997

10 0.374 0.992

1 0.437 0.848

5 0.603 0.839

3 0.262 0.745

8 0.338 0.689

6 0.162 0.490

2 0.144 0.469

12 0.164 0.366

4 0.166 0.351


the first elimination iteration for the ZERODUR Bore Plate.

Table 16.- RMSδ and E values obtained at the

third elimination iteration for the ZERODUR Bore Plate.

Laboratory

RMSδ

(µm) E

7 0.416 2.002

5 0.722 1.008

10 0.256 0.814

1 0.377 0.733

11 0.157 0.716

2 0.180 0.642

4 0.255 0.586

3 0.152 0.569

8 0.220 0.489

6 0.094 0.319

12 0.093 0.261

Table 15.- RMSδ RMSr and E values obtained

at the second elimination iteration for the ZERODUR Bore Plate.

Table 17.- Final RMSδ and E values for

the ZERODUR Bore Plate. At the end the

corresponding RMSδ and E

values of those laboratories excluded from the calculation of the reference value are also shown, with respect to that reference value.

Laboratory

RMSδ

(µm) E

7 0.348 1.862

2 0.242 0.947

11 0.175 0.915

4 0.321 0.759

1 0.340 0.657

10 0.190 0.627

6 0.127 0.482

3 0.121 0.445

8 0.177 0.420

12 0.109 0.307

Laboratory

RMSδ

(µm) E

2 0.205 0.789

10 0.225 0.767

11 0.152 0.724

1 0.365 0.717

4 0.287 0.682

3 0.130 0.526

8 0.190 0.444

6 0.102 0.374

12 0.099 0.295

9 1.630 2.275

5 0.759 0.966

7 0.387 1.926



11 Participants results with respect to KCRV

In this section we present the results of every participant with respect to the reference values chosen in Section 10. Due to the large number of measurands, it is not possible to present the results of all participants in the same plot. Therefore, a plot of the results of each participant as a function of length for every measuring element of the two artifacts is shown.

11.1 Steel Ball Plate Results

Figures 16 through 27 show the participants results as deviations to the KCRV. Under each uncertainty bar the number of the corresponding ball is indicated. Table 18 shows the nominal distances of each of the measuring elements. When two balls are at the same distance, the first one is shown with a full dot and continuous uncertainty bars, while the second one is shown with the contour and dashed uncertainty bars. The blue lines show the standard uncertainty of the reference value calculated as described in Section 10.2 and with the parameter values of Section 10.3. The laboratories uncertainty bars are shown at k = 1.


Figures 28 through 39 show the participants results as deviations to the KCRV. The number of bore is not indicated due to lack of space. Table 19 shows the nominal distances of each of the measuring elements and from these values the number may be deduced. When two bores are at the same distance, the first one is shown with a full dot while the second one is shown with the contour and dotted uncertainty bars. In the only two cases there is a third measuring element at the same distance, the uncertainty bars are shown dotted. The blue lines show the standard uncertainty of the reference value calculated as described in section 10.2. The laboratories uncertainty bars are shown at k = 1.

11.3 Average Normalized Errors for the Steel Ball Plate

In table 13, the Average Normalized Error of the participants contributing to the reference value as well as that of those laboratories excluded in the calculation of that value are shown.

11.4 Average Normalized Errors for the ZERODUR Bore Plate

In table 17, the Average Normalized Error of the participants contributing to the reference value as well as that of those excluded with respect to that value are shown.



Ball Nominal r (mm) Ball

Nominal r (mm)

1 0.00 14 299.26

2 83.00 15 371.19

3 166.00 16 249.00

4 249.00 17 262.47

5 332.00 18 299.26

6 83.00 19 352.14

7 117.38 20 415.00

8 185.59 21 332.00

9 262.47 22 342.22

10 342.22 23 371.19

11 166.00 24 415.00

12 185.59 25 469.52

13 234.76

Table 18.- Nominal distances r of balls in the Steel Ball Plate (rounded to two decimal places).

Bore Nominal r (mm) Bore

Nominal r (mm) Bore

Nominal r (mm) Bore

Nominal r (mm)

1 0.00 16 304.14 31 250.00 46 364.01

2 50.00 17 353.55 32 254.95 47 380.79

3 100.00 18 403.11 33 269.26 48 403.11

4 150.00 19 100.00 34 291.55 49 430.12

5 200.00 20 111.80 35 320.16 50 460.98

6 250.00 21 364.01 36 353.55 51 494.97

7 300.00 22 412.31 37 390.51 52 531.51

8 350.00 23 150.00 38 430.12 53 400.00

9 400.00 24 158.11 39 471.70 54 403.11

10 50.00 25 380.79 40 300.00 55 412.31

11 70.71 26 427.20 41 304.14 56 427.20

12 111.80 27 200.00 42 460.98 57 447.21

13 158.11 28 206.16 43 500.00 58 471.70

14 206.16 29 403.11 44 350.00 59 500.00

15 254.95 30 447.21 45 353.55 60 531.51

61 565.69

Table 19.- Nominal distances r of bores in the ZERODUR Bore Plate (rounded to two decimal places).



11.5 Birge Ratio Calculation

The Birge Ratio is defined as:

inti

i

r

extr

Bu

uR =

(11.1)

Where intiru and extr i

u are calculated according to Section 10.2.

The Birge Ratio of each measuring element i was calculated from the sub-set of laboratories m’ contributing to the KCRV. The Birge Ratio has an expectation value of 1 if the number of laboratories m’ is large. If RB < 1 , it means that the uncertainties declared by the participants have been conservative with respect to their performance; while if RB > 1 , the participants have underestimated their uncertainty.

11.6 Birge Ratio for the Measuring Elements of the Steel Ball Plate

Table 20 shows the Average Birge Ratio values for all the measuring elements of the Steel Ball Plate. Note that all values are quite smaller than 1.

11.7 Birge Ratio for the Measuring Elements of the ZERODUR Bore

Plate

Table 21 shows the Average Birge Ratio values for all the measuring elements of the ZERODUR Bore Plate. Note that most values are smaller than 1.

Ball Birge Ratio Ball

Birge Ratio

2 0.46 14 0.43

3 0.53 15 0.51

4 0.49 16 0.34

5 0.62 17 0.37

6 0.19 18 0.34

7 0.49 19 0.36

8 0.53 20 0.45

9 0.46 21 0.53

10 0.60 22 0.43

11 0.34 23 0.41

12 0.34 24 0.41

13 0.49 25 0.49

Table 20.- Birge Ratio for the measuring elements of the Steel Ball Plate. Note all values are smaller than one.



Bore Birge Ratio Bore

Birge Ratio Bore

Birge Ratio Bore

Birge Ratio

2 0.24 17 0.91 32 0.87 47 0.78

3 0.41 18 0.81 33 0.88 48 0.88

4 0.85 19 0.67 34 0.85 49 0.80

5 0.55 20 0.47 35 0.73 50 0.82

6 0.65 21 0.75 36 0.52 51 0.96

7 0.67 22 0.84 37 0.84 52 0.88

8 0.91 23 0.73 38 0.86 53 0.83

9 0.90 24 0.43 39 0.82 54 0.71

10 0.47 25 0.54 40 1.03 55 0.68

11 0.34 26 0.62 41 1.01 56 0.53

12 0.45 27 0.98 42 0.87 57 0.58

13 0.68 28 0.76 43 0.80 58 0.61

14 0.41 29 0.68 44 1.02 59 0.72

15 0.41 30 0.66 45 1.01 60 1.02

16 0.59 31 0.97 46 0.96 61 0.93

Table 21.- Birge Ratio for the measuring elements of the ZERODUR Bore Plate. Note most values are smaller than one.



Figure 16.- Results of laboratory number 1 for the 25 balls of the Steel Ball Plate as a function of length with respect to the reference value. The blue lines represent the reference value uncertainty. All uncertainties shown are at k = 1.

Laboratory 1

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

0 50 100 150 200 250 300 350 400 450 500

(mm)

(um)

1

2,6

7

3,11 8,12

13

4,169,1714,18

5,2110,22

19

15,23

20,24

25




Laboratory 2

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0 50 100 150 200 250 300 350 400 450 500

(mm)

(um)

1

2,6

7

3,11

8,1213

4,16

9,1714,18

5,21

10,2219 15,23

20,24

25




Laboratory 3

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0 50 100 150 200 250 300 350 400 450 500

(mm)

(um)

1

2,6

7

3,118,12

13

4,16

9,17

14,18

5,21

10,22

19

15,2320,24

25

1




Laboratory 4

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0 50 100 150 200 250 300 350 400 450 500

(mm)

(um)

1

2,6

7

3,11 8,12134,169,17

14,185,21

10,22

19

15,23

20,24

25




Laboratory 5

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 50 100 150 200 250 300 350 400 450 500

(mm)

(um)

1

2,67 3,11

8,1213

4,169,17 14,18

5,2110,22

19

15,2320,24

25




Laboratory 6

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0 50 100 150 200 250 300 350 400 450 500

(mm)

(um)

1 2,6 73,13

8,1213

4,169,17

14,18

5,21

10,2219

15,23

20,24

25




Laboratory 7

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0 50 100 150 200 250 300 350 400 450 500

(mm)

(um)

1

2,6

7

3,11

8,12 13

4,16

9,17

14,18

5,21

10,22

19

15,23

20,24

25




Laboratory 8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0 50 100 150 200 250 300 350 400 450 500

(mm)

(um) 1

2,6

7

3,11

8,12

13

4,16

9,17

14,18

5,21

10,22

19

15,23

20,24

25




Laboratory 9

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1.0

0 50 100 150 200 250 300 350 400 450 500

(mm)

(um)

1

7

13

19

25

2,6

3,118,12

4,169,17

14,18

5,2110,22

15,23 20,24




Laboratory 10

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0 50 100 150 200 250 300 350 400 450 500

(mm)

(um)

1

7

1319

252,6 3,11

8,12

4,16

9,1714,18 5,21

10,22 15,23

20,24




Laboratory 11

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0 50 100 150 200 250 300 350 400 450 500

(mm)

(um)

1

7

13

19

25

2,6

3,11

8,12

4,16

9,17

14,18

5,21

10,22

15,23

20,24




Laboratory 12

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

0 50 100 150 200 250 300 350 400 450 500

(mm)

(um)

1

2,6

7

3,11

8,124,16

9,17

14,18

5,21

10,22

20,24

13

19

25

15,23



Figure 28.- Results of laboratory number 1 for the 61 bores of the ZERODUR Bore Plate as a function of length with respect to the reference value. The blue lines represent the reference value uncertainty. All uncertainties shown are at k = 1.

Laboratory 1

-1.40

-1.20

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 100 200 300 400 500 600

(mm)

(um)




Laboratory 2

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0 100 200 300 400 500 600

(mm)

(um)




Laboratory 3

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0 100 200 300 400 500 600

(mm)

(um)




Laboratory 4

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 100 200 300 400 500 600

(mm)

(um)




Laboratory 5

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

0 100 200 300 400 500 600

(mm)

(um)




Laboratory 6

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0 100 200 300 400 500 600

(mm)

(um)




Laboratory 7

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0 100 200 300 400 500 600

(mm)

(um)




Laboratory 8

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 100 200 300 400 500 600

(mm)

(um)



Figure 36.- Results of laboratory number 9 for the 61 bores of the ZERODUR Bore Plate as a function of length with respect to the reference value. The blue lines represent the reference value uncertainty. All uncertainties shown are at k = 1

Laboratory 9

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

5.00

0 100 200 300 400 500 600

(mm)

(um)



.


Laboratory 10

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0 100 200 300 400 500 600

(mm)

(um)




Laboratory 11

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0 100 200 300 400 500 600

(mm)

(um)




Laboratory 12

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0 100 200 300 400 500 600

(mm)

(um)



12 Conclusions

12.1 On the results of the comparison

• The comparison was a valuable exercise and produced valid results as the artifacts proved to be stable throughout the comparison exercise. Therefore, the results obtained may be taken as a proof of the performance of the participants in CMM 2-D standard calibrations.

• Out of the twelve participants, ten ( 83%) were in good agreement for the Steel Ball Plate and nine (75%) for the ZERODUR Bore Plate. Out of these values the KCRV was determined.

• The Birge Ratios obtained for the measuring elements of both artifacts proved that there is consistency between the results obtained ant the declared uncertainties of the participants.

• It would seem that the uncertainty declarations are rather conservative. This is also because of the fact that the method proposed in the protocol and the custom methods adopted by some laboratories were quite redundant and there was a self cancelling effect; and also because the variability measuring elements geometries – spheres and cylinders – is rather small. It must be stressed that uncertainties obtained by the same laboratories, with the same equipment and with the same operating conditions for more complex geometries and with no redundancy may be quite larger.

• The results on the Steel Ball Plate were slightly better than those on the ZERODUR Bore Plate. This may have the several explanations:

o The Steel Ball Plate had smaller dimensions Than the ZERODUR one.

o The center of a sphere (Steel Ball Plate) is uniquely defined whereas the center of a cylinder (ZERODUR Bore Plate) is not, even though the depth coordinate was given.

o Temperature variations affected probably more the measurement in the ZERODUR Bore plate because most machines made on granite or Steel would expand in the same proportion than the Steel Ball Plate while the ZERODUR would not.

12.2 Suggestions for future comparisons of this kind

• Although the artifacts are heavy and relatively fragile, they were well protected in their casings and did not suffer during the whole circulation. It may be said that these artifacts are well suited for this kind of exercise provided they are properly packed.

• It should be pointed out that this comparison was a relatively expensive one when compared to others due to:

o The cost of the artifacts themselves and the casings.

o The cost of insurance.



o The cost of shipping due to the weight and volume of the artifacts.

o The man-hours required by the participants to measure.

This is something not to be neglected in future comparison organizations of this kind.

• It should also be pointed out that it was a long exercise and it spanned through almost four years, although the initial time schedule was supposed to take two years only. The main reason for delay was the breakdown of the pilot laboratory’s CMM but there were other delays related to the participants. It is advised in the future that participants stick strictly to their allocated period.

• It is a comparison that has many measurands and therefore, it is complex to analyze or summarize each laboratory’s performance.

• Some improvements may be suggested for future protocols. If the measurand is the distance between items, then this should have been reported by the participants instead of the x and y coordinates. Instead, the pilot laboratory made these transformations and there was a rounding error involved in this transformation as most laboratories reported X and Y results rounded only to one tenth of a micrometer.

13 Acknowledgements

� Dr. H. Kunzman, H. Schwenke and their institution, PTB, for having lent a very valuable artifact for the comparison exercise.

� Dr. J. Stone and his institution, NIST, for

• their support on shipping back and forth the artifacts and the corresponding burdensome customs and administrative arrangement required;

• and for having served as copilots of the caparison performing measurements in three different occasions.

� M. E. Arizmendi, head of the CMM Lab at CENAM for

• collaborating on the preparation of the protocol,

• performing the control measurements,

• gathering all the participants data and transforming it into a homogeneous and comparable database;

• as well as for his comments on the exercise performance.



14 References

[1] T.J. Quinn, Guidelines for key comparisons carried out by Consultative Committees, BIPM, 1997, Paris

[2] R. Thalmann, Calibration of long gauge blocks by interferometry - Instructions and technical protocols, OFMET, Wabern, 1999.

[3] Lewis, Calibration of long artefacts - Technical Protocol, NPL, Teddington, 2000.

[4] O. Jusko, Calibration of Ball Bars and a Step Gauge - Technical Protocol, PTB, Braunschweig, 1998.

[5] Guideline for the DKD-calibration test plates in the form of ball and bores plates, DKD (Draft version), Braunschweig, 1992.

[6] Decker, J. E., Atschuler J., et al., Stage One: Calibration of Gauge Blocks by Optical Interferometry, Report on SIM 4.2 Regional Comparison, Ottawa, Canada, 2005.

Kruger O. A., CCL-K3 Calibration of angle standards, Draft B7 Report, August 2007.



Appendix



Equivalences of participant laboratories results (i) with respect to reference values (R) The equivalences of each laboratory i (i = 1, =,12) measurements with respect to the

corresponding reference values (R) for every measuring element on the steel ball plate and on

the ZERODUR bore plate were calculated. The equivalences are determined by two values, the

difference between the laboratory result (i) and the reference value (R), DiR, of each element;

and the uncertainty of this difference, UiR. They are given by the following equations:

�� = �� − �� (A1)

Where: ri is the laboratory’s result and

rR is the reference value.

�� = 2 ∙ �1 − 1 ′� �� + ��

(A2)

Where: ui is the uncertainty of laboratory i,

uR is the uncertainty of the reference value and

m’ is the number of laboratories taken in account in

the calculation of the reference value.

In the case of the steel ball plate, m’ = 10 and in the case of the ZERODUR bore plate m’ = 9.

This calculation was performed for every measuring element k (k = 25 for the steel ball plate and

k = 61 for the ZERODUR bore plate). For both artifacts DiR = 0 for measuring elements number

1 (k = 1) by definition.

All results are given by laboratory number according to the following table.

No. NMI Country No. NMI Country

1 NMIA (CSIRO) Australia 7 NMIJ (NRLM) Japan

2 INMS-NRC Canada 8 NMi Netherlands

3 NIM China 9 VNIIMS Russia

4 CMI Czech Rep. 10 NPL United Kingdom

5 BNM-LNE France 11 NIST USA (1)

6 PTB Germany 12 CENAM Mexico (1)



Steel Ball Plate

The following tables show the values of DiR and UiR for each laboratory i (i = 1,..,12) and for each measuring element k (k = 1,...,25). They are followed by plots11 of these values shown as a function of the nominal distances of the measuring elements for each laboratory. The dots represent DiR according to equation A1 for the different measuring elements and the blue curves represent UiR according to equation A2.

11

Please note that for all plots where laboratory number 8 is involved, the uncertainty curves are not smooth. This is due to the fact that this laboratory did not state an uncertainty equation as a function of length, but rather stated individual uncertainty values for each measuring element. For measuring elements at a same distance, the values were not equal. Those plotted are those corresponding to the first number of element at that distance.



D ik U ik D ik U ik D ik U ik D ik U ik D ik U ik D ik U ik

(µµµµm) (µµµµm) (µµµµm) (µµµµm) (µµµµm) (µµµµm) (µµµµm) (µµµµm) (µµµµm) (µµµµm) (µµµµm) (µµµµm)

1 0.0000 0.6073 0.0004 0.3222 0.0000 0.3222 0.0000 0.6810 0.0000 0.9045 0.0000 0.4084

2 0.0000 0.6339 0.1711 0.3335 0.0000 0.3335 0.0000 0.6853 -0.1000 0.9800 0.0000 0.4144

3 -0.4673 0.7077 0.1999 0.3651 -0.1673 0.3651 -0.2673 0.6980 -0.0543 1.0990 0.1327 0.4319

4 -0.8335 0.8160 0.2443 0.4125 -0.2335 0.4125 -0.2335 0.7187 0.1295 1.2492 0.0665 0.4596

5 -1.3046 0.9470 0.2898 0.4709 -0.5046 0.4709 -0.1046 0.7467 0.0084 1.4207 0.0954 0.4957

6 -0.5604 0.6339 0.0619 0.3335 0.0396 0.3335 -0.0604 0.6853 0.0271 0.9800 0.0396 0.4144

7 -0.4094 0.6594 0.1694 0.3443 0.1563 0.3443 -0.1973 0.6896 -0.1177 1.0247 0.0148 0.4203

8 -0.6050 0.7306 0.1639 0.3751 -0.1131 0.3751 -0.2473 0.7022 -0.0181 1.1321 0.1552 0.4376

9 -0.9839 0.8359 0.1845 0.4213 -0.0669 0.4213 -0.2250 0.7228 0.1268 1.2758 0.0913 0.4649

10 -1.4842 0.9643 0.2362 0.4787 -0.2230 0.4787 -0.3443 0.7506 -0.0351 1.4429 0.1650 0.5006

11 -0.9990 0.7077 0.0277 0.3651 0.1010 0.3651 0.0010 0.6980 0.1760 1.0990 0.0010 0.4319

12 -0.9484 0.7306 0.1275 0.3751 0.0801 0.3751 -0.0987 0.7022 -0.0871 1.1321 0.1249 0.4376

13 -1.1263 0.7955 0.1634 0.4035 0.0050 0.4035 -0.2071 0.7146 0.0142 1.2217 0.1464 0.4542

14 -1.3036 0.8932 0.1651 0.4468 -0.1388 0.4468 -0.0833 0.7349 0.1178 1.3510 0.1663 0.4805

15 -1.6135 1.0143 0.2629 0.5012 -0.3166 0.5012 -0.0930 0.7623 0.0358 1.5070 0.1753 0.5152

16 -1.3963 0.8160 0.0177 0.4125 0.0037 0.4125 0.0037 0.7187 0.1787 1.2492 0.1037 0.4596

17 -1.3303 0.8359 0.0538 0.4213 -0.0338 0.4213 -0.0022 0.7228 0.1006 1.2758 0.1243 0.4649

18 -1.4285 0.8932 0.0514 0.4468 -0.1250 0.4468 0.0137 0.7349 0.2048 1.3510 0.1246 0.4805

19 -1.6159 0.9812 0.1139 0.4863 -0.1310 0.4863 -0.2017 0.7545 0.1872 1.4647 0.0812 0.5055

20 -1.8286 1.0926 0.2101 0.5367 -0.3287 0.5367 -0.1887 0.7812 0.1645 1.6067 0.0713 0.5386

21 -1.6463 0.9470 0.1465 0.4709 0.0537 0.4709 0.0537 0.7467 0.0787 1.4207 0.0537 0.4957

22 -1.6715 0.9643 0.0750 0.4787 -0.0222 0.4787 0.0748 0.7506 0.0662 1.4429 0.0990 0.5006

23 -1.7425 1.0143 0.1162 0.5012 0.0016 0.5012 0.0464 0.7623 0.2092 1.5070 0.1358 0.5152

24 -1.8534 1.0926 0.1834 0.5367 0.0466 0.5367 -0.1934 0.7812 0.1666 1.6067 0.1266 0.5386

25 -2.0499 1.1937 0.2403 0.5828 -0.2114 0.5828 -0.0700 0.8071 0.1160 1.7345 0.1421 0.5697

65

Ball

1 2 3 4





1 0.0000 0.2828 0.0000 0.1511 0.0000 0.6954 0.0000 0.4439 0.0000 0.2266 0.0000 0.5341

2 0.2000 0.2888 -0.0360 0.3695 -0.2000 0.7183 -0.0400 0.4514 0.0050 0.2365 -0.2000 0.5401

3 0.1327 0.3060 0.0807 0.4508 -0.3673 0.7828 0.0527 0.4731 -0.0423 0.2539 -0.0673 0.5578

4 0.0665 0.3328 -0.0395 0.5251 -0.7335 0.8798 0.0365 0.5073 -0.0035 0.2773 -0.0335 0.5861

5 0.0954 0.3670 0.0264 0.5188 -1.2046 1.0000 -0.0046 0.5515 0.0034 0.3054 0.0954 0.6236

6 -0.0604 0.2888 0.0036 0.4345 -0.7604 0.7183 -0.0504 0.4514 -0.0404 0.2365 0.0396 0.5401

7 0.0856 0.2946 0.0290 0.3790 -0.8337 0.7404 -0.0700 0.4588 -0.1556 0.2429 0.0856 0.5461

8 0.1105 0.3116 0.0859 0.4059 -1.0075 0.8031 0.0077 0.4801 -0.2106 0.2590 0.0658 0.5636

9 -0.0036 0.3379 0.0410 0.4614 -1.3001 0.8980 -0.0163 0.5138 -0.2231 0.2816 0.0913 0.5916

10 0.0438 0.3716 -0.0074 0.5464 -1.5812 1.0160 -0.0629 0.5575 -0.0828 0.3091 0.3106 0.6288

11 0.0010 0.3060 -0.1340 0.4180 -1.5990 0.7828 -0.0490 0.4731 -0.1260 0.2539 0.0010 0.5578

12 0.0801 0.3116 -0.0800 0.4056 -1.4404 0.8031 -0.0317 0.4801 -0.1059 0.2590 -0.0093 0.5636

13 0.0757 0.3276 0.1153 0.4139 -1.4799 0.8613 0.0616 0.5006 -0.2382 0.2729 -0.1364 0.5806

14 0.0276 0.3527 -0.0026 0.4573 -1.7197 0.9504 0.0138 0.5330 -0.2658 0.2938 -0.0001 0.6078

15 0.0412 0.3851 -0.0134 0.5347 -1.9266 1.0626 -0.0662 0.5753 -0.2012 0.3199 0.1753 0.6441

16 -0.0963 0.3328 -0.1913 0.4469 -2.4963 0.8798 0.0437 0.5073 -0.0673 0.2773 0.0037 0.5861

17 -0.0338 0.3379 -0.2814 0.4199 -2.5320 0.8980 0.0073 0.5138 0.0041 0.2816 0.0611 0.5916

18 0.0414 0.3527 -0.0851 0.4215 -2.4547 0.9504 -0.0252 0.5330 -0.0756 0.2938 -0.1250 0.6078

19 0.0104 0.3762 -0.0058 0.4720 -2.5351 1.0318 0.0670 0.5635 -0.1317 0.3127 0.0104 0.6339

20 0.0114 0.4067 -0.0804 0.5557 -2.5886 1.1360 0.0173 0.6037 -0.0082 0.3369 0.1313 0.6687

21 -0.2463 0.3670 -0.3363 0.5057 -3.9463 1.0000 -0.0263 0.5515 -0.0313 0.3054 0.2537 0.6236

22 -0.1435 0.3716 -0.2878 0.4359 -3.8300 1.0160 0.0141 0.5575 -0.0957 0.3091 0.2203 0.6288

23 -0.0878 0.3851 -0.1710 0.4820 -3.6655 1.0626 0.0687 0.5753 -0.2314 0.3199 -0.0878 0.6441

24 -0.1334 0.4067 -0.0800 0.5468 -3.6334 1.1360 0.1226 0.6037 -0.2052 0.3369 -0.0334 0.6687

25 -0.2114 0.4351 -0.2489 0.6455 -3.7469 1.2314 0.0431 0.6413 -0.0834 0.3591 0.2836 0.7018

127 8 9 10 11

Ball



-2.50

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 100 200 300 400 500

Laboratory 1

UiR

UiR

l (mm)

DiR( µµ µµm)

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 100 200 300 400 500

Laboratory 2

UiR

UiR

l (mm)

DiR( µµ µµm)

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 100 200 300 400 500

Laboratory 3

UiR

UiR

l (mm)

DiR( µµ µµm)

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 100 200 300 400 500

Laboratory 4

UiR

UiR

l (mm)DiR( µµ µµm)



-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

0 100 200 300 400 500

Laboratory 5

UiR

UiR

l (mm)

DiR( µµ µµm)

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 100 200 300 400 500

Laboratory 6

UiR

UiR

l (mm)

DiR( µµ µµm)

-0.50

-0.40

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0.50

0 100 200 300 400 500

Laboratory 7

UiR

UiR

l (mm)

DiR( µµ µµm)

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 50 100 150 200 250 300 350 400 450 500

Laboratory 8

UiR

UiR

l (mm)DiR( µµ µµm)



-5.00

-4.00

-3.00

-2.00

-1.00

0.00

1.00

2.00

0 50 100 150 200 250 300 350 400 450 500

Laboratory 9

UiR

UiR l (mm)

DiR( µµ µµm)

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 50 100 150 200 250 300 350 400 450 500

Laboratory 10

UiR

UiR

l (mm)

DiR( µµ µµm)

-0.40

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0 50 100 150 200 250 300 350 400 450 500

Laboratory 11

UiR

UiR

l (mm)

DiR( µµ µµm)

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 50 100 150 200 250 300 350 400 450 500DiR ( µµ µµm)

l (mm)

Laboratory 12

UiR

UiR



ZERODUR BORE Plate The following tables show the values of DiR and UiR for each laboratory i (i = 1,..,12) and for each measuring element k (k = 1,...,61). They are followed by plots12 of these values shown as a function of the nominal distances of the measuring elements for each laboratory. The dots represent DiR according to equation A1 for the different measuring elements and the blue curves represent UiR according to equation A2.

12




1 -0.0002 0.6024 0.0014 0.3182 -0.0002 0.3015 -0.0002 0.6759 -0.0002 0.8981 -0.0002 0.4043

2 -0.0019 0.6091 0.0555 0.3216 -0.0019 0.3047 -0.0019 0.6772 0.2981 0.9312 -0.0019 0.4059

3 0.1217 0.6286 0.0825 0.3317 0.0217 0.3140 0.1216 0.6813 0.4217 0.9705 -0.0783 0.4105

4 0.1895 0.6599 0.0635 0.3479 0.2896 0.3290 0.1895 0.6881 0.4896 1.0153 -0.2104 0.4181

5 0.1223 0.7014 0.0723 0.3694 -0.0776 0.3489 0.2223 0.6975 0.6223 1.0649 -0.0777 0.4286

6 0.2036 0.7514 0.0962 0.3953 -0.0964 0.3729 0.2036 0.7094 0.7036 1.1187 0.1036 0.4417

7 -0.0206 0.8083 0.1779 0.4249 -0.1206 0.4003 0.2794 0.7237 0.8794 1.1761 0.0794 0.4571

8 0.0385 0.8707 0.1499 0.4573 -0.1615 0.4304 0.5385 0.7402 1.0385 1.2366 0.1385 0.4748

9 -0.0294 0.9376 0.2725 0.4921 -0.1294 0.4628 0.4706 0.7589 1.3706 1.2998 0.0706 0.4943

10 0.0690 0.6091 0.0434 0.3216 -0.0311 0.3047 -0.2311 0.6772 0.1689 0.9312 0.0689 0.4059

11 -0.1384 0.6157 0.1010 0.3250 0.0738 0.3079 -0.0677 0.6786 0.3565 0.9468 0.0030 0.4074

12 -0.1473 0.6350 0.1719 0.3350 -0.0131 0.3171 0.1211 0.6827 0.5236 0.9806 -0.0131 0.4120

13 -0.1063 0.6660 0.0745 0.3511 0.3365 0.3319 0.1151 0.6895 0.7159 1.0230 -0.2011 0.4196

14 0.0162 0.7072 0.0814 0.3724 -0.0323 0.3517 0.2102 0.6989 0.7195 1.0713 -0.0808 0.4301

15 -0.0771 0.7568 0.0990 0.3981 -0.0378 0.3755 0.2171 0.7107 0.7466 1.1242 0.0406 0.4431

16 -0.0423 0.8133 0.1787 0.4275 -0.1081 0.4027 0.2700 0.7250 1.0098 1.1810 0.0727 0.4585

17 -0.1124 0.8753 0.2340 0.4597 -0.0841 0.4326 0.4958 0.7415 1.3019 1.2410 0.0998 0.4761

18 -0.0041 0.9419 0.2900 0.4944 -0.1902 0.4648 0.4300 0.7601 1.4099 1.3038 0.0083 0.4956

19 0.1149 0.6286 0.0755 0.3317 -0.1851 0.3140 -0.1851 0.6813 0.1149 0.9705 -0.0851 0.4105

20 0.0023 0.6350 0.0558 0.3350 -0.0424 0.3171 -0.0424 0.6827 0.1813 0.9806 -0.0871 0.4120

21 -0.0031 0.8891 0.2337 0.4669 -0.0993 0.4393 0.4089 0.7453 1.2331 1.2541 0.0930 0.4801

22 0.0852 0.9547 0.3147 0.5010 -0.2058 0.4710 0.3520 0.7637 1.2979 1.3157 -0.0118 0.4994

23 -0.1474 0.6600 0.0260 0.3479 -0.1474 0.3290 -0.2474 0.6881 0.0527 1.0153 0.0526 0.4181

24 -0.1137 0.6660 0.0669 0.3511 -0.0505 0.3319 -0.0822 0.6895 0.2342 1.0230 0.0760 0.4196

25 -0.1268 0.9115 0.1515 0.4785 -0.1924 0.4501 0.3066 0.7515 1.3176 1.2752 0.0834 0.4866

26 -0.1044 0.9755 0.2269 0.5119 -0.2215 0.4811 0.3520 0.7698 1.1830 1.3351 0.0009 0.5057

27 -0.4982 0.7014 0.0568 0.3694 -0.1982 0.3489 -0.0982 0.6975 0.0018 1.0649 0.1018 0.4286

28 -0.4330 0.7071 0.0870 0.3724 0.0035 0.3516 0.0278 0.6989 0.1491 1.0713 0.0278 0.4301

29 -0.2441 0.9419 0.2136 0.4944 -0.1572 0.4648 0.3265 0.7601 1.1575 1.3038 0.0660 0.4956

30 -0.1788 1.0041 0.2587 0.5267 -0.1788 0.4949 0.3579 0.7782 1.2075 1.3615 -0.0446 0.5144

Ball

1 2 3 654




(µµµµm) (µµµµm) (µµµµm) (µµµµm) (µµµµm) (µµµµm) (µµµµm) (µµµµm) (µµµµm) (µµµµm) (µµµµm) (µµµµm)31 -0.5779 0.7514 0.0812 0.3953 -0.0779 0.3729 0.2221 0.7094 -0.1779 1.1187 0.1221 0.4417

32 -0.5339 0.7567 0.0996 0.3981 0.0152 0.3755 0.0152 0.7107 0.2310 1.1242 0.1329 0.4431

33 -0.5295 0.7726 0.1352 0.4063 0.0460 0.3831 0.1389 0.7147 0.4175 1.1404 0.1389 0.4474

34 -0.4530 0.7982 0.0913 0.4197 0.2329 0.3955 0.2157 0.7211 0.4388 1.1662 0.0785 0.4544

35 -0.4213 0.8328 0.1343 0.4376 0.1564 0.4121 0.2189 0.7301 0.5782 1.2001 0.0158 0.4640

36 -0.3353 0.8753 0.1002 0.4597 -0.0525 0.4326 0.0889 0.7415 0.7254 1.2409 0.0889 0.4761

37 -0.5141 0.9246 0.2047 0.4853 -0.0917 0.4564 0.3437 0.7552 0.9711 1.2875 0.0620 0.4905

38 -0.4636 0.9797 0.1972 0.5140 -0.1032 0.4831 0.4781 0.7710 1.0127 1.3389 0.1409 0.5070

39 -0.3290 1.0396 0.2784 0.5452 -0.1594 0.5121 0.4236 0.7889 1.0278 1.3943 0.1480 0.5253

40 -0.6334 0.8083 0.1474 0.4249 -0.1334 0.4003 0.0666 0.7237 0.1666 1.1761 0.0666 0.4571

41 -0.6717 0.8132 0.1844 0.4275 -0.0141 0.4027 0.0845 0.7250 0.1996 1.1809 0.1174 0.4585

42 -0.4620 1.0240 0.2593 0.5371 -0.1040 0.5045 0.4817 0.7842 0.8830 1.3799 0.1238 0.5205

43 -0.4023 1.0814 0.3209 0.5670 -0.1623 0.5324 0.3577 0.8018 1.0977 1.4327 0.0577 0.5384

44 -0.6936 0.8707 0.2016 0.4573 -0.0936 0.4304 0.0064 0.7402 0.1064 1.2366 0.1064 0.4748

45 -0.7161 0.8754 0.1927 0.4597 -0.0514 0.4327 0.0476 0.7415 0.2315 1.2410 0.1749 0.4761

46 -0.6630 0.8890 0.1977 0.4669 -0.0037 0.4393 0.1474 0.7452 0.4770 1.2540 0.1199 0.4801

47 -0.4972 0.9114 0.1593 0.4785 0.2512 0.4501 0.1330 0.7515 0.4088 1.2752 0.0543 0.4866

48 -0.6190 0.9419 0.2189 0.4943 0.1500 0.4648 0.1996 0.7601 0.5966 1.3037 0.0632 0.4956

49 -0.5058 0.9796 0.2013 0.5140 0.0755 0.4831 0.3545 0.7710 0.7148 1.3389 0.1103 0.5070

50 -0.5200 1.0239 0.2741 0.5371 -0.0319 0.5045 0.3803 0.7842 0.9009 1.3799 0.0332 0.5205

51 -0.5460 1.0739 0.3439 0.5631 -0.0510 0.5288 0.5147 0.7994 1.1511 1.4258 0.1611 0.5361

52 -0.4588 1.1289 0.3659 0.5917 -0.0919 0.5554 0.4066 0.8167 1.0934 1.4761 0.2655 0.5535

53 -0.4567 0.9377 0.2615 0.4921 -0.1567 0.4628 0.1433 0.7589 -0.0567 1.2998 0.0433 0.4943

54 -0.4090 0.9420 0.2100 0.4944 -0.0493 0.4648 0.0375 0.7601 0.0251 1.3038 0.0747 0.4956

55 -0.3057 0.9547 0.2614 0.5010 -0.0875 0.4710 0.1308 0.7637 0.4461 1.3157 0.0338 0.4994

56 -0.2130 0.9756 0.1279 0.5119 0.0912 0.4811 0.2083 0.7698 0.3254 1.3351 -0.0141 0.5057

57 -0.3283 1.0041 0.2471 0.5267 0.0741 0.4949 0.1189 0.7782 0.3425 1.3615 0.0294 0.5144

58 -0.2478 1.0396 0.2423 0.5452 -0.0889 0.5121 0.2715 0.7889 0.4942 1.3943 0.1231 0.5253

59 -0.2640 1.0814 0.3065 0.5670 -0.1041 0.5324 0.3759 0.8018 0.6160 1.4327 0.0759 0.5384

60 -0.2418 1.1289 0.3943 0.5917 -0.0631 0.5554 0.5578 0.8167 0.7930 1.4761 0.2004 0.5535

61 -0.2600 1.1813 0.4322 0.6190 -0.1185 0.5808 0.4471 0.8336 0.8714 1.5239 0.0936 0.5703

Ball

1 2 3 4 5 6





1 -0.0002 0.2675 -0.0002 0.1457 -0.0002 0.6902 -0.0002 0.4397 -0.0002 0.2222 -0.0002 0.5296

2 -0.2019 0.2696 -0.0289 0.4896 0.4980 0.6985 -0.1120 0.4416 -0.0049 0.2274 0.0981 0.5311

3 -0.1783 0.2758 -0.0892 0.5923 0.8216 0.7230 -0.1683 0.4472 -0.0333 0.2355 0.0217 0.5359

4 -0.4105 0.2858 -0.2694 0.6596 0.9895 0.7620 -0.3005 0.4565 -0.0415 0.2464 0.0896 0.5436

5 -0.3777 0.2992 -0.1896 0.7119 1.4223 0.8135 -0.1977 0.4692 0.1033 0.2597 0.0223 0.5543

6 -0.3964 0.3156 -0.2864 0.7627 1.8036 0.8753 -0.2064 0.4850 0.0786 0.2749 -0.0964 0.5678

7 -0.3206 0.3345 -0.2836 0.8197 2.1794 0.9453 -0.2706 0.5037 0.0794 0.2919 0.0794 0.5838

8 -0.3615 0.3556 -0.3695 0.8905 2.5385 1.0219 -0.3215 0.5249 0.0485 0.3103 -0.0615 0.6021

9 -0.4294 0.3785 -0.4044 0.8008 3.1706 1.1038 -0.3294 0.5483 0.1086 0.3299 -0.0294 0.6227

10 -0.0311 0.2696 0.1439 0.6723 0.0690 0.6985 -0.1411 0.4416 0.0090 0.2274 0.0690 0.5311

11 -0.1384 0.2717 0.0228 0.5211 0.2151 0.7068 -0.0748 0.4435 0.0065 0.2304 0.0737 0.5327

12 -0.1920 0.2778 0.0522 0.5532 0.7472 0.7310 -0.0533 0.4491 0.0289 0.2379 -0.1473 0.5374

13 -0.3276 0.2877 0.0193 0.5967 1.2218 0.7696 -0.2043 0.4584 -0.0538 0.2484 0.0202 0.5452

14 -0.3961 0.3010 0.0092 0.6434 1.7139 0.8207 -0.1512 0.4710 0.0283 0.2614 -0.0808 0.5558

15 -0.3712 0.3173 -0.0629 0.6912 2.2567 0.8819 -0.1496 0.4867 0.0282 0.2765 -0.0575 0.5692

16 -0.4204 0.3362 -0.2039 0.7429 2.7031 0.9515 -0.2182 0.5053 -0.0216 0.2934 0.0727 0.5852

17 -0.4093 0.3572 -0.3293 0.8044 3.0272 1.0276 -0.3471 0.5264 -0.0706 0.3117 0.1139 0.6035

18 -0.5003 0.3800 -0.2878 0.8902 3.1836 1.1090 -0.3390 0.5498 -0.0023 0.3312 0.0951 0.6240

19 -0.1851 0.2758 0.2559 0.6316 -0.2851 0.7230 -0.1051 0.4472 0.1989 0.2356 -0.0851 0.5359

20 -0.2213 0.2778 0.2389 0.5671 0.0471 0.7310 -0.1810 0.4491 0.0537 0.2379 0.0023 0.5374

21 -0.3877 0.3618 -0.2568 0.7724 2.9638 1.0444 -0.2806 0.5312 -0.0240 0.3157 -0.0718 0.6077

22 -0.4969 0.3843 -0.3358 0.8494 3.1897 1.1245 -0.3586 0.5544 -0.0222 0.3349 0.1822 0.6280

23 -0.1474 0.2858 0.3066 0.6322 -0.3474 0.7621 -0.0474 0.4565 0.2516 0.2464 -0.0474 0.5436

24 -0.1454 0.2877 0.1648 0.5991 -0.2085 0.7696 -0.1296 0.4584 0.1189 0.2484 -0.0505 0.5452

25 -0.4156 0.3695 -0.1468 0.7553 2.5649 1.0718 -0.0689 0.5390 0.0412 0.3223 -0.0479 0.6145

26 -0.5024 0.3916 -0.1934 0.8283 3.0556 1.1500 -0.1594 0.5619 0.0043 0.3410 0.0945 0.6347

27 -0.2982 0.2992 0.3138 0.6434 -0.1983 0.8135 0.0017 0.4692 0.3187 0.2597 0.0018 0.5543

28 -0.1905 0.3010 0.2278 0.6246 -0.2633 0.8206 -0.1590 0.4710 0.1905 0.2614 0.0278 0.5558

29 -0.4301 0.3800 -0.1072 0.7503 2.2737 1.1090 -0.2242 0.5498 -0.0635 0.3312 0.1900 0.6240

30 -0.5813 0.4014 -0.1716 0.8223 2.7280 1.1848 -0.2146 0.5722 0.0377 0.3494 0.1342 0.6439

Ball

127 8 9 10 11




(µµµµm) (µµµµm) (µµµµm) (µµµµm) (µµµµm) (µµµµm) (µµµµm) (µµµµm) (µµµµm) (µµµµm) (µµµµm) (µµµµm)31 -0.1779 0.3156 0.1731 0.6662 -0.1780 0.8753 -0.1279 0.4850 0.2631 0.2749 -0.0779 0.5678

32 -0.2006 0.3173 0.2005 0.6439 -0.3770 0.8819 -0.1319 0.4867 0.2462 0.2765 -0.0436 0.5692

33 -0.2140 0.3226 0.1620 0.6194 0.1019 0.9014 -0.1583 0.4919 0.1880 0.2813 -0.1211 0.5736

34 -0.4703 0.3311 0.1364 0.6156 0.3875 0.9330 -0.1959 0.5003 0.0898 0.2889 -0.1959 0.5809

35 -0.4058 0.3428 -0.0200 0.6280 0.7658 0.9755 -0.2247 0.5119 0.0778 0.2992 0.0627 0.5909

36 -0.4767 0.3572 0.0408 0.6561 1.0790 1.0275 -0.1161 0.5264 0.0960 0.3117 0.0890 0.6035

37 -0.5142 0.3740 -0.0941 0.7013 1.4193 1.0878 -0.1378 0.5437 0.0757 0.3261 0.1516 0.6186

38 -0.4403 0.3930 -0.0568 0.7582 2.0007 1.1550 -0.2055 0.5634 0.0696 0.3422 -0.0567 0.6360

39 -0.5198 0.4138 -0.1517 0.8297 2.7556 1.2280 -0.3523 0.5853 0.1002 0.3597 0.0420 0.6555

40 -0.2334 0.3345 0.2386 0.6985 -0.3335 0.9454 0.0166 0.5037 0.3646 0.2919 -0.1334 0.5838

41 -0.2114 0.3362 0.0712 0.6561 -0.2936 0.9514 -0.1457 0.5053 0.2731 0.2934 0.1010 0.5852

42 -0.4511 0.4084 -0.1095 0.7929 1.7724 1.2090 -0.2580 0.5795 0.0101 0.3552 0.0587 0.6503

43 -0.6023 0.4284 -0.1459 0.8551 2.7178 1.2789 -0.2963 0.6008 0.1125 0.3719 0.1577 0.6694

44 -0.1936 0.3556 0.1924 0.7471 -0.4936 1.0220 0.0364 0.5249 0.3374 0.3103 -0.0936 0.6022

45 -0.1504 0.3572 0.0402 0.6529 -0.5464 1.0276 -0.0288 0.5265 0.2509 0.3117 0.0900 0.6035

46 -0.3197 0.3618 0.0847 0.6192 -0.4295 1.0443 -0.0724 0.5312 0.2619 0.3157 -0.0724 0.6077

47 -0.3922 0.3695 0.0374 0.6301 -0.3528 1.0717 -0.1611 0.5390 0.1263 0.3223 -0.1033 0.6145

48 -0.3957 0.3799 0.0540 0.6610 -0.0484 1.1089 -0.1712 0.5498 0.1157 0.3312 -0.0112 0.6240

49 -0.3663 0.3930 -0.0018 0.7029 0.2149 1.1550 -0.1989 0.5634 -0.0059 0.3422 -0.0292 0.6360

50 -0.3898 0.4084 -0.0010 0.7556 0.9551 1.2090 -0.2087 0.5795 -0.0026 0.3552 0.0766 0.6503

51 -0.4046 0.4258 -0.1614 0.8167 1.4340 1.2698 -0.2420 0.5980 0.0317 0.3698 -0.0510 0.6669

52 -0.5247 0.4451 -0.2161 0.9017 2.5515 1.3365 -0.2848 0.6187 0.0867 0.3858 -0.0731 0.6855

53 -0.4567 0.3785 0.1453 0.8196 -0.8567 1.1038 -0.0567 0.5483 0.3333 0.3299 -0.2567 0.6227

54 -0.3470 0.3800 0.0633 0.6471 -0.7315 1.1090 -0.1113 0.5498 0.3078 0.3312 -0.1237 0.6240

55 -0.4270 0.3844 -0.0126 0.6708 -0.4512 1.1246 -0.1336 0.5544 0.2979 0.3349 -0.1845 0.6280

56 -0.4940 0.3916 -0.0572 0.7025 -0.3886 1.1500 -0.2564 0.5619 0.1509 0.3410 -0.0375 0.6347

57 -0.5072 0.4014 0.0348 0.7391 0.1189 1.1848 -0.2031 0.5722 0.1318 0.3494 -0.1047 0.6439

58 -0.5341 0.4138 -0.0719 0.7839 0.6108 1.2280 -0.2797 0.5853 0.0130 0.3597 0.0383 0.6555

59 -0.4641 0.4284 -0.1195 0.8376 1.1160 1.2789 -0.3401 0.6008 0.0135 0.3719 0.0559 0.6694

60 -0.5052 0.4451 -0.3254 0.9062 1.4233 1.3365 -0.5560 0.6187 -0.0254 0.3858 0.0592 0.6855

61 -0.5428 0.4636 -0.3512 1.0133 2.0735 1.4000 -0.5216 0.6387 0.1141 0.4011 0.1643 0.7036

11 12

Ball

7 8 9 10



-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 100 200 300 400 500 600

Laboratory 1

UiR

l (mm)

DiR( µµ µµm)

UiR

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 100 200 300 400 500 600

Laboratory 2

UiR

l (mm)

DiR( µµ µµm)

UiR

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 100 200 300 400 500 600

Laboratory 3

UiR

l (mm)

DiR( µµ µµm)

UiR

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 100 200 300 400 500 600

Laboratory 4

UiR

l (mm)

DiR( µµ µµm)

UiR



-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

0 100 200 300 400 500 600

Laboratory 5

UiR

l (mm)

DiR( µµ µµm)

UiR

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 100 200 300 400 500 600

Laboratory 6

UiR

l (mm)

DiR( µµ µµm)

UiR

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0 100 200 300 400 500 600

Laboratory 7

UiR

l (mm)

DiR( µµ µµm)

UiR

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 100 200 300 400 500 600

Laboratory 8

UiR

l (mm)

DiR( µµ µµm)

UiR



-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

0 100 200 300 400 500 600

Laboratory 9

UiRl (mm)

DiR( µµ µµm) UiR

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 100 200 300 400 500 600

Laboratory 10

UiR

l (mm)

DiR( µµ µµm)

UiR

-0.50

-0.40

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0.50

0 100 200 300 400 500 600

Laboratory 11

UiR

l (mm)

DiR( µµ µµm)

UiR

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 100 200 300 400 500 600

Laboratory 12

UiR

l (mm)

DiR( µµ µµm)

UiR



Pairwise equivalences between results of participant laboratories i and j The equivalences of laboratory i (i = 1, =,12) measurements and laboratory j (j, j = 1, =,12, j ≠ i) measurements for every measuring element on the steel ball plate and on the ZERODUR bore plate were calculated. The equivalence is determined by two values, the difference between laboratory j result with respect to laboratory i result, Dij , of each element; and the uncertainty of this difference, Uij. They are given by the following equations:

(A3)

Where: ri is the result of laboratory i rj is the result of laboratory j.

(A4)

Where: ui is the uncertainty of laboratory I and uj is the uncertainty of laboratory j. This calculation was performed for every measuring element k (k = 25 for the steel ball plate and k = 61 for the ZERODUR bore plate). For both artifacts Dij = 0 for measuring element number 1 (k = 1) by definition.

Steel Ball Plate The following tables show the values of Dij and Uij for each laboratory i (i = 1,..,12) and for each measuring element k (k = 1,...,25). They are followed by plots13 of these values shown as a function of the nominal distances of the measuring elements for each laboratory. The dots represent Dij according to equation A3 and the blue curves represent Uij according to equation A4.

13




D ij U ij D ij U ij D ij U ij D ij U ij D ij U ij D ij U ij


1 0.0000 0.6888 0.0000 0.6888 0.0000 0.9351 0.0000 1.1261 0.0000 0.7378 0.0000 0.6693

2 0.0000 0.7177 0.0000 0.7177 0.0000 0.9557 -0.1000 1.2077 0.0000 0.7631 0.2000 0.6958

3 0.4673 0.7981 0.3000 0.7981 0.2000 1.0150 0.4130 1.3531 0.6000 0.8344 0.6000 0.7700

4 0.8335 0.9167 0.6000 0.9167 0.6000 1.1069 0.9630 1.5444 0.9000 0.9412 0.9000 0.8799

5 1.3046 1.0606 0.8000 1.0606 1.2000 1.2239 1.3130 1.7666 1.4000 1.0731 1.4000 1.0139

6 0.5604 0.7177 0.6000 0.7177 0.5000 0.9557 0.5875 1.2077 0.6000 0.7631 0.5000 0.6958

7 0.4094 0.7455 0.5657 0.7455 0.2121 0.9759 0.2917 1.2612 0.4242 0.7876 0.4950 0.7214

8 0.6050 0.8232 0.4919 0.8232 0.3578 1.0341 0.5870 1.3947 0.7603 0.8568 0.7155 0.7932

9 0.9839 0.9386 0.9171 0.9386 0.7589 1.1243 1.1107 1.5786 1.0752 0.9612 0.9803 0.9003

10 1.4842 1.0796 1.2612 1.0796 1.1399 1.2397 1.4492 1.7956 1.6492 1.0906 1.5280 1.0317

11 0.9990 0.7981 1.1000 0.7981 1.0000 1.0150 1.1750 1.3531 1.0000 0.8344 1.0000 0.7700

12 0.9484 0.8232 1.0286 0.8232 0.8497 1.0341 0.8613 1.3947 1.0733 0.8568 1.0286 0.7932

13 1.1263 0.8942 1.1314 0.8942 0.9192 1.0891 1.1405 1.5090 1.2728 0.9208 1.2021 0.8591

14 1.3036 1.0014 1.1649 1.0014 1.2203 1.1752 1.4214 1.6760 1.4700 1.0186 1.3313 0.9588

15 1.6135 1.1347 1.2969 1.1347 1.5205 1.2860 1.6493 1.8793 1.7889 1.1416 1.6547 1.0831

16 1.3963 0.9167 1.4000 0.9167 1.4000 1.1069 1.5750 1.5444 1.5000 0.9412 1.3000 0.8799

17 1.3303 0.9386 1.2965 0.9386 1.3281 1.1243 1.4309 1.5786 1.4546 0.9612 1.2965 0.9003

18 1.4285 1.0014 1.3035 1.0014 1.4422 1.1752 1.6333 1.6760 1.5532 1.0186 1.4700 0.9588

19 1.6159 1.0983 1.4849 1.0983 1.4142 1.2554 1.8031 1.8240 1.6970 1.1079 1.6263 1.0491

20 1.8286 1.2210 1.5000 1.2210 1.6400 1.3597 1.9932 2.0097 1.9000 1.2219 1.8400 1.1638

21 1.6463 1.0606 1.7000 1.0606 1.7000 1.2239 1.7250 1.7666 1.7000 1.0731 1.4000 1.0139

22 1.6715 1.0796 1.6492 1.0796 1.7462 1.2397 1.7376 1.7956 1.7705 1.0906 1.5280 1.0317

23 1.7425 1.1347 1.7441 1.1347 1.7888 1.2860 1.9516 1.8793 1.8783 1.1416 1.6547 1.0831

24 1.8534 1.2210 1.9000 1.2210 1.6600 1.3597 2.0200 2.0097 1.9800 1.2219 1.7200 1.1638

25 2.0499 1.3324 1.8385 1.3324 1.9799 1.4566 2.1659 2.1773 2.1920 1.3261 1.8385 1.2682

1-7

Ball

1-2 1-3 1-4 1-5 1-6





1 0.0000 0.6200 0.0000 0.9468 0.0000 0.7603 0.0000 0.6450 0.0000 0.8222 -0.0004 0.4243

2 -0.0360 0.7370 -0.2000 0.9822 -0.0400 0.7861 0.0050 0.6736 -0.2000 0.8460 -0.1711 0.4384

3 0.5480 0.8454 0.1000 1.0815 0.5200 0.8588 0.4250 0.7487 0.4000 0.9136 -0.3672 0.4782

4 0.7940 0.9786 0.1000 1.2293 0.8700 0.9680 0.8300 0.8583 0.8000 1.0163 -0.4778 0.5381

5 1.3310 1.0852 0.1000 1.4105 1.3000 1.1029 1.3080 0.9910 1.4000 1.1448 -0.7944 0.6122

6 0.5640 0.7754 -0.2000 0.9822 0.5100 0.7861 0.5200 0.6736 0.6000 0.8460 -0.0223 0.4384

7 0.4384 0.7639 -0.4243 1.0164 0.3394 0.8111 0.2538 0.6997 0.4950 0.8691 -0.0131 0.4520

8 0.6909 0.8393 -0.4025 1.1127 0.6127 0.8818 0.3944 0.7719 0.6708 0.9350 -0.2770 0.4908

9 1.0249 0.9593 -0.3162 1.2568 0.9677 0.9884 0.7608 0.8785 1.0752 1.0357 -0.2514 0.5493

10 1.4768 1.1147 -0.0970 1.4345 1.4213 1.1209 1.4014 1.0085 1.7948 1.1620 -0.4592 0.6221

11 0.8650 0.8264 -0.6000 1.0815 0.9500 0.8588 0.8730 0.7487 1.0000 0.9136 0.0733 0.4782

12 0.8685 0.8391 -0.4919 1.1127 0.9168 0.8818 0.8425 0.7719 0.9391 0.9350 -0.0474 0.4908

13 1.2417 0.8995 -0.3535 1.2012 1.1879 0.9472 0.8881 0.8376 0.9899 0.9966 -0.1584 0.5267

14 1.3010 1.0067 -0.4160 1.3359 1.3174 1.0472 1.0378 0.9365 1.3035 1.0916 -0.3039 0.5816

15 1.6001 1.1515 -0.3130 1.5043 1.5474 1.1730 1.4123 1.0592 1.7889 1.2121 -0.5795 0.6508

16 1.2050 0.9344 -1.1000 1.2293 1.4400 0.9680 1.3290 0.8583 1.4000 1.0163 -0.0140 0.5381

17 1.0489 0.9379 -1.2017 1.2568 1.3376 0.9884 1.3345 0.8785 1.3914 1.0357 -0.0876 0.5493

18 1.3435 0.9892 -1.0262 1.3359 1.4034 1.0472 1.3529 0.9365 1.3035 1.0916 -0.1764 0.5816

19 1.6101 1.0913 -0.9192 1.4582 1.6829 1.1385 1.4842 1.0257 1.6263 1.1789 -0.2449 0.6318

20 1.7482 1.2304 -0.7600 1.6138 1.8460 1.2552 1.8204 1.1387 1.9600 1.2913 -0.5387 0.6960

21 1.3100 1.0782 -2.3000 1.4105 1.6200 1.1029 1.6150 0.9910 1.9000 1.1448 -0.0927 0.6122

22 1.3837 1.0593 -2.1586 1.4345 1.6856 1.1209 1.5757 1.0085 1.8918 1.1620 -0.0972 0.6221

23 1.5715 1.1253 -1.9230 1.5043 1.8112 1.1730 1.5111 1.0592 1.6547 1.2121 -0.1146 0.6508

24 1.7734 1.2259 -1.7800 1.6138 1.9760 1.2552 1.6482 1.1387 1.8200 1.2913 -0.1368 0.6960

25 1.8010 1.3641 -1.6970 1.7558 2.0930 1.3619 1.9665 1.2414 2.3335 1.3947 -0.4517 0.7547

Ball

1-11 1-12 2-31-101-8 1-9





1 -0.0004 0.7616 -0.0004 0.9867 -0.0004 0.5000 -0.0004 0.3918 -0.0004 0.3000 -0.0004 0.7759

2 -0.1711 0.7684 -0.2711 1.0657 -0.1711 0.5094 0.0289 0.4016 -0.2071 0.4694 -0.3711 0.8012

3 -0.4672 0.7887 -0.2542 1.1927 -0.0672 0.5365 -0.0672 0.4297 -0.1192 0.5535 -0.5672 0.8726

4 -0.4778 0.8213 -0.1148 1.3544 -0.1778 0.5789 -0.1778 0.4728 -0.2838 0.6379 -0.9778 0.9801

5 -0.3944 0.8648 -0.2814 1.5398 -0.1944 0.6336 -0.1944 0.5273 -0.2634 0.6538 -1.4944 1.1133

6 -0.1223 0.7684 -0.0348 1.0657 -0.0223 0.5094 -0.1223 0.4016 -0.0583 0.5276 -0.8223 0.8012

7 -0.3667 0.7752 -0.2871 1.1133 -0.1545 0.5186 -0.0838 0.4112 -0.1404 0.4819 -1.0030 0.8256

8 -0.4112 0.7953 -0.1820 1.2282 -0.0087 0.5453 -0.0534 0.4386 -0.0780 0.5173 -1.1714 0.8951

9 -0.4095 0.8276 -0.0577 1.3831 -0.0932 0.5870 -0.1881 0.4810 -0.1435 0.5840 -1.4846 1.0002

10 -0.5805 0.8709 -0.2712 1.5639 -0.0711 0.6410 -0.1924 0.5346 -0.2436 0.6813 -1.8174 1.1311

11 -0.0267 0.7887 0.1483 1.1927 -0.0267 0.5365 -0.0267 0.4297 -0.1617 0.5241 -1.6267 0.8726

12 -0.2263 0.7953 -0.2146 1.2282 -0.0027 0.5453 -0.0474 0.4386 -0.2075 0.5170 -1.5679 0.8951

13 -0.3706 0.8148 -0.1492 1.3247 -0.0170 0.5707 -0.0877 0.4645 -0.0481 0.5356 -1.6433 0.9596

14 -0.2485 0.8464 -0.0474 1.4644 0.0012 0.6107 -0.1375 0.5046 -0.1678 0.5906 -1.8848 1.0583

15 -0.3559 0.8888 -0.2271 1.6333 -0.0876 0.6628 -0.2218 0.5560 -0.2763 0.6797 -2.1895 1.1827

16 -0.0140 0.8213 0.1610 1.3544 0.0860 0.5789 -0.1140 0.4728 -0.2090 0.5678 -2.5140 0.9801

17 -0.0560 0.8276 0.0468 1.3831 0.0705 0.5870 -0.0876 0.4810 -0.3352 0.5481 -2.5858 1.0002

18 -0.0377 0.8464 0.1534 1.4644 0.0732 0.6107 -0.0100 0.5046 -0.1364 0.5602 -2.5061 1.0583

19 -0.3156 0.8769 0.0733 1.5875 -0.0327 0.6483 -0.1034 0.5418 -0.1197 0.6196 -2.6490 1.1486

20 -0.3987 0.9178 -0.0455 1.7414 -0.1387 0.6975 -0.1987 0.5900 -0.2905 0.7123 -2.7987 1.2642

21 -0.0927 0.8648 -0.0677 1.5398 -0.0927 0.6336 -0.3927 0.5273 -0.4827 0.6423 -4.0927 1.1133

22 -0.0002 0.8709 -0.0088 1.5639 0.0240 0.6410 -0.2185 0.5346 -0.3628 0.5861 -3.9050 1.1311

23 -0.0699 0.8888 0.0929 1.6333 0.0196 0.6628 -0.2040 0.5560 -0.2872 0.6344 -3.7817 1.1827

24 -0.3768 0.9178 -0.0168 1.7414 -0.0568 0.6975 -0.3168 0.5900 -0.2634 0.7046 -3.8168 1.2642

25 -0.3103 0.9570 -0.1243 1.8802 -0.0981 0.7435 -0.4517 0.6344 -0.4892 0.8094 -3.9872 1.3700

Ball

2-72-4 2-5 2-6 2-8 2-9





1 -0.0004 0.5325 -0.0004 0.3488 -0.0004 0.6177 0.0000 0.7616 0.0000 0.9867 0.0000 0.5000

2 -0.2111 0.5432 -0.1661 0.3617 -0.3711 0.6267 0.0000 0.7684 -0.1000 1.0657 0.0000 0.5094

3 -0.1472 0.5738 -0.2422 0.3902 -0.2672 0.6529 -0.1000 0.7887 0.1130 1.1927 0.3000 0.5365

4 -0.2078 0.6216 -0.2478 0.4312 -0.2778 0.6944 0.0000 0.8213 0.3630 1.3544 0.3000 0.5789

5 -0.2944 0.6829 -0.2864 0.4817 -0.1944 0.7487 0.4000 0.8648 0.5130 1.5398 0.6000 0.6336

6 -0.1123 0.5432 -0.1023 0.3617 -0.0223 0.6267 -0.1000 0.7684 -0.0125 1.0657 0.0000 0.5094

7 -0.2394 0.5536 -0.3249 0.3717 -0.0838 0.6356 -0.3536 0.7752 -0.2740 1.1133 -0.1414 0.5186

8 -0.1563 0.5837 -0.3745 0.3988 -0.0981 0.6614 -0.1342 0.7953 0.0950 1.2282 0.2683 0.5453

9 -0.2008 0.6307 -0.4076 0.4388 -0.0932 0.7024 -0.1581 0.8276 0.1937 1.3831 0.1581 0.5870

10 -0.2991 0.6912 -0.3190 0.4884 0.0744 0.7561 -0.1213 0.8709 0.1880 1.5639 0.3881 0.6410

11 -0.0767 0.5738 -0.1537 0.3902 -0.0267 0.6529 -0.1000 0.7887 0.0750 1.1927 -0.1000 0.5365

12 -0.1592 0.5837 -0.2334 0.3988 -0.1368 0.6614 -0.1789 0.7953 -0.1673 1.2282 0.0447 0.5453

13 -0.1018 0.6124 -0.4017 0.4234 -0.2998 0.6863 -0.2121 0.8148 0.0092 1.3247 0.1414 0.5707

14 -0.1514 0.6573 -0.4310 0.4608 -0.1653 0.7259 0.0555 0.8464 0.2566 1.4644 0.3051 0.6107

15 -0.3291 0.7156 -0.4641 0.5080 -0.0876 0.7780 0.2236 0.8888 0.3524 1.6333 0.4919 0.6628

16 0.0260 0.6216 -0.0850 0.4312 -0.0140 0.6944 0.0000 0.8213 0.1750 1.3544 0.1000 0.5789

17 -0.0465 0.6307 -0.0497 0.4388 0.0073 0.7024 0.0316 0.8276 0.1344 1.3831 0.1581 0.5870

18 -0.0765 0.6573 -0.1270 0.4608 -0.1764 0.7259 0.1387 0.8464 0.3298 1.4644 0.2496 0.6107

19 -0.0469 0.6994 -0.2456 0.4950 -0.1034 0.7635 -0.0707 0.8769 0.3182 1.5875 0.2121 0.6483

20 -0.1927 0.7544 -0.2183 0.5388 -0.0787 0.8131 0.1400 0.9178 0.4932 1.7414 0.4000 0.6975

21 -0.1727 0.6829 -0.1777 0.4817 0.1073 0.7487 0.0000 0.8648 0.0250 1.5398 0.0000 0.6336

22 -0.0609 0.6912 -0.1707 0.4884 0.1453 0.7561 0.0970 0.8709 0.0884 1.5639 0.1213 0.6410

23 -0.0475 0.7156 -0.3476 0.5080 -0.2040 0.7780 0.0447 0.8888 0.2075 1.6333 0.1342 0.6628

24 -0.0608 0.7544 -0.3886 0.5388 -0.2168 0.8131 -0.2400 0.9178 0.1200 1.7414 0.0800 0.6975

25 -0.1971 0.8057 -0.3237 0.5791 0.0433 0.8599 0.1414 0.9570 0.3274 1.8802 0.3536 0.7435

Ball

2-10 2-11 2-12 3-4 3-5 3-6





1 0.0000 0.3918 0.0000 0.3000 0.0000 0.7759 0.0000 0.5325 0.0000 0.3488 0.0000 0.6177

2 0.2000 0.4016 -0.0360 0.4694 -0.2000 0.8012 -0.0400 0.5432 0.0050 0.3617 -0.2000 0.6267

3 0.3000 0.4297 0.2480 0.5535 -0.2000 0.8726 0.2200 0.5738 0.1250 0.3902 0.1000 0.6529

4 0.3000 0.4728 0.1940 0.6379 -0.5000 0.9801 0.2700 0.6216 0.2300 0.4312 0.2000 0.6944

5 0.6000 0.5273 0.5310 0.6538 -0.7000 1.1133 0.5000 0.6829 0.5080 0.4817 0.6000 0.7487

6 -0.1000 0.4016 -0.0360 0.5276 -0.8000 0.8012 -0.0900 0.5432 -0.0800 0.3617 0.0000 0.6267

7 -0.0707 0.4112 -0.1273 0.4819 -0.9900 0.8256 -0.2263 0.5536 -0.3118 0.3717 -0.0707 0.6356

8 0.2236 0.4386 0.1990 0.5173 -0.8944 0.8951 0.1208 0.5837 -0.0975 0.3988 0.1789 0.6614

9 0.0632 0.4810 0.1078 0.5840 -1.2333 1.0002 0.0506 0.6307 -0.1562 0.4388 0.1581 0.7024

10 0.2668 0.5346 0.2156 0.6813 -1.3582 1.1311 0.1601 0.6912 0.1402 0.4884 0.5336 0.7561

11 -0.1000 0.4297 -0.2350 0.5241 -1.7000 0.8726 -0.1500 0.5738 -0.2270 0.3902 -0.1000 0.6529

12 0.0000 0.4386 -0.1601 0.5170 -1.5205 0.8951 -0.1118 0.5837 -0.1860 0.3988 -0.0894 0.6614

13 0.0707 0.4645 0.1103 0.5356 -1.4849 0.9596 0.0566 0.6124 -0.2432 0.4234 -0.1414 0.6863

14 0.1664 0.5046 0.1362 0.5906 -1.5809 1.0583 0.1525 0.6573 -0.1270 0.4608 0.1387 0.7259

15 0.3578 0.5560 0.3032 0.6797 -1.6100 1.1827 0.2504 0.7156 0.1154 0.5080 0.4919 0.7780

16 -0.1000 0.4728 -0.1950 0.5678 -2.5000 0.9801 0.0400 0.6216 -0.0710 0.4312 0.0000 0.6944

17 0.0000 0.4810 -0.2476 0.5481 -2.4982 1.0002 0.0411 0.6307 0.0379 0.4388 0.0949 0.7024

18 0.1664 0.5046 0.0399 0.5602 -2.3297 1.0583 0.0998 0.6573 0.0494 0.4608 0.0000 0.7259

19 0.1414 0.5418 0.1252 0.6196 -2.4041 1.1486 0.1980 0.6994 -0.0007 0.4950 0.1414 0.7635

20 0.3400 0.5900 0.2482 0.7123 -2.2600 1.2642 0.3460 0.7544 0.3204 0.5388 0.4600 0.8131

21 -0.3000 0.5273 -0.3900 0.6423 -4.0000 1.1133 -0.0800 0.6829 -0.0850 0.4817 0.2000 0.7487

22 -0.1213 0.5346 -0.2656 0.5861 -3.8078 1.1311 0.0364 0.6912 -0.0735 0.4884 0.2425 0.7561

23 -0.0894 0.5560 -0.1726 0.6344 -3.6671 1.1827 0.0671 0.7156 -0.2330 0.5080 -0.0894 0.7780

24 -0.1800 0.5900 -0.1266 0.7046 -3.6800 1.2642 0.0760 0.7544 -0.2518 0.5388 -0.0800 0.8131

25 0.0000 0.6344 -0.0375 0.8094 -3.5355 1.3700 0.2546 0.8057 0.1280 0.5791 0.4950 0.8599

Ball

3-7 3-8 3-9 3-10 3-11 3-12





1 0.0000 1.1720 0.0000 0.8062 0.0000 0.7440 0.0000 0.7000 0.0000 1.0010 0.0000 0.8268

2 -0.1000 1.2385 0.0000 0.8110 0.2000 0.7481 -0.0360 0.7865 -0.2000 1.0199 -0.0400 0.8327

3 0.2130 1.3475 0.4000 0.8253 0.4000 0.7602 0.3480 0.8365 -0.1000 1.0746 0.3200 0.8500

4 0.3630 1.4897 0.3000 0.8486 0.3000 0.7800 0.1940 0.8898 -0.5000 1.1600 0.2700 0.8782

5 0.1130 1.6565 0.2000 0.8801 0.2000 0.8069 0.1310 0.8948 -1.1000 1.2699 0.1000 0.9162

6 0.0875 1.2385 0.1000 0.8110 0.0000 0.7481 0.0640 0.8226 -0.7000 1.0199 0.0100 0.8327

7 0.0795 1.2791 0.2121 0.8158 0.2828 0.7521 0.2263 0.7930 -0.6364 1.0384 0.1273 0.8385

8 0.2292 1.3784 0.4025 0.8300 0.3578 0.7642 0.3332 0.8119 -0.7603 1.0922 0.2549 0.8558

9 0.3518 1.5153 0.3162 0.8531 0.2214 0.7839 0.2659 0.8510 -1.0752 1.1763 0.2087 0.8838

10 0.3092 1.6784 0.5093 0.8845 0.3881 0.8107 0.3369 0.9141 -1.2369 1.2848 0.2813 0.9215

11 0.1750 1.3475 0.0000 0.8253 0.0000 0.7602 -0.1350 0.8173 -1.6000 1.0746 -0.0500 0.8500

12 0.0116 1.3784 0.2236 0.8300 0.1789 0.7642 0.0188 0.8118 -1.3416 1.0922 0.0671 0.8558

13 0.2213 1.4633 0.3536 0.8440 0.2829 0.7761 0.3224 0.8206 -1.2728 1.1434 0.2687 0.8727

14 0.2011 1.5883 0.2496 0.8667 0.1109 0.7955 0.0807 0.8526 -1.6364 1.2240 0.0971 0.9001

15 0.1288 1.7419 0.2683 0.8976 0.1342 0.8219 0.0796 0.9102 -1.8336 1.3286 0.0268 0.9373

16 0.1750 1.4897 0.1000 0.8486 -0.1000 0.7800 -0.1950 0.8410 -2.5000 1.1600 0.0400 0.8782

17 0.1028 1.5153 0.1265 0.8531 -0.0316 0.7839 -0.2792 0.8268 -2.5298 1.1763 0.0095 0.8838

18 0.1911 1.5883 0.1109 0.8667 0.0277 0.7955 -0.0987 0.8319 -2.4684 1.2240 -0.0388 0.9001

19 0.3889 1.6999 0.2828 0.8889 0.2121 0.8145 0.1959 0.8682 -2.3334 1.2996 0.2687 0.9268

20 0.3532 1.8413 0.2600 0.9190 0.2000 0.8403 0.1082 0.9303 -2.4000 1.3986 0.2060 0.9629

21 0.0250 1.6565 0.0000 0.8801 -0.3000 0.8069 -0.3900 0.8864 -4.0000 1.2699 -0.0800 0.9162

22 -0.0086 1.6784 0.0243 0.8845 -0.2183 0.8107 -0.3626 0.8456 -3.9048 1.2848 -0.0606 0.9215

23 0.1628 1.7419 0.0894 0.8976 -0.1342 0.8219 -0.2173 0.8768 -3.7118 1.3286 0.0224 0.9373

24 0.3600 1.8413 0.3200 0.9190 0.0600 0.8403 0.1134 0.9244 -3.4400 1.3986 0.3160 0.9629

25 0.1860 1.9701 0.2121 0.9482 -0.1414 0.8653 -0.1789 1.0007 -3.6769 1.4911 0.1131 0.9977

Ball

4-104-5 4-6 4-7 4-8 4-9





1 0.0000 0.8268 0.0000 0.8841 0.0000 1.0216 0.0000 0.9732 0.0000 0.9400 0.0000 1.1814

2 -0.0400 0.8327 -0.2000 0.8894 0.1000 1.0968 0.3000 1.0511 0.0640 1.0788 -0.1000 1.2591

3 0.3200 0.8500 0.2000 0.9053 0.1870 1.2173 0.1870 1.1741 0.1350 1.2248 -0.3130 1.3983

4 0.2700 0.8782 0.2000 0.9312 -0.0630 1.3711 -0.0630 1.3298 -0.1690 1.3970 -0.8630 1.5828

5 0.1000 0.9162 0.2000 0.9663 0.0870 1.5484 0.0870 1.5080 0.0180 1.5568 -1.2130 1.7988

6 0.0100 0.8327 0.1000 0.8894 0.0125 1.0968 -0.0875 1.0511 -0.0235 1.1054 -0.7875 1.2591

7 0.1273 0.8385 0.2828 0.8948 0.1326 1.1419 0.2033 1.0973 0.1467 1.1257 -0.7159 1.3102

8 0.2549 0.8558 0.3131 0.9106 0.1733 1.2510 0.1286 1.2083 0.1040 1.2390 -0.9895 1.4383

9 0.2087 0.8838 0.3162 0.9363 -0.0356 1.3985 -0.1304 1.3574 -0.0859 1.3972 -1.4270 1.6160

10 0.2813 0.9215 0.6548 0.9712 0.2001 1.5715 0.0788 1.5312 0.0276 1.5883 -1.5462 1.8270

11 -0.0500 0.8500 0.0000 0.9053 -0.1750 1.2173 -0.1750 1.1741 -0.3100 1.2118 -1.7750 1.3983

12 0.0671 0.8558 0.0894 0.9106 0.2120 1.2510 0.1673 1.2083 0.0072 1.2389 -1.3532 1.4383

13 0.2687 0.8727 0.0707 0.9261 0.1322 1.3428 0.0615 1.3012 0.1011 1.3282 -1.4941 1.5486

14 0.0971 0.9001 0.0832 0.9514 0.0485 1.4762 -0.0901 1.4355 -0.1204 1.4680 -1.8374 1.7106

15 0.0268 0.9373 0.2683 0.9857 0.1395 1.6381 0.0054 1.5979 -0.0492 1.6451 -1.9624 1.9087

16 0.0400 0.8782 0.0000 0.9312 -0.0750 1.3711 -0.2750 1.3298 -0.3700 1.3665 -2.6750 1.5828

17 0.0095 0.8838 0.0632 0.9363 0.0237 1.3985 -0.1344 1.3574 -0.3820 1.3826 -2.6326 1.6160

18 -0.0388 0.9001 -0.1387 0.9514 -0.0801 1.4762 -0.1634 1.4355 -0.2898 1.4560 -2.6595 1.7106

19 0.2687 0.9268 0.2121 0.9760 -0.1061 1.5941 -0.1768 1.5539 -0.1930 1.5827 -2.7223 1.8547

20 0.2060 0.9629 0.3200 1.0096 -0.0932 1.7420 -0.1532 1.7018 -0.2450 1.7480 -2.7532 2.0362

21 -0.0800 0.9162 0.2000 0.9663 -0.0250 1.5484 -0.3250 1.5080 -0.4150 1.5520 -4.0250 1.7988

22 -0.0606 0.9215 0.1455 0.9712 0.0329 1.5715 -0.2097 1.5312 -0.3540 1.5499 -3.8962 1.8270

23 0.0224 0.9373 -0.1342 0.9857 -0.0733 1.6381 -0.2969 1.5979 -0.3801 1.6269 -3.8746 1.9087

24 0.3160 0.9629 0.1600 1.0096 -0.0400 1.7420 -0.3000 1.7018 -0.2466 1.7449 -3.8000 2.0362

25 0.1131 0.9977 0.3536 1.0420 0.0262 1.8757 -0.3274 1.8352 -0.3649 1.9028 -3.8629 2.2005

Ball

4-11 4-12 5-6 5-7 5-8 5-9





1 0.0000 1.0379 0.0000 0.9567 0.0000 1.0841 0.0000 0.4728 0.0000 0.4000 0.0000 0.8198

2 0.0600 1.1129 0.1050 1.0365 -0.1000 1.1560 0.2000 0.4781 -0.0360 0.5363 -0.2000 0.8421

3 0.1070 1.2342 0.0120 1.1602 -0.0130 1.2729 0.0000 0.4937 -0.0520 0.6046 -0.5000 0.9058

4 -0.0930 1.3897 -0.1330 1.3156 -0.1630 1.4237 0.0000 0.5188 -0.1060 0.6727 -0.8000 1.0031

5 -0.0130 1.5693 -0.0050 1.4927 0.0870 1.5990 0.0000 0.5519 -0.0690 0.6739 -1.3000 1.1252

6 -0.0775 1.1129 -0.0675 1.0365 0.0125 1.1560 -0.1000 0.4781 -0.0360 0.5880 -0.8000 0.8421

7 0.0477 1.1582 -0.0378 1.0831 0.2033 1.1996 0.0707 0.4834 0.0141 0.5448 -0.8485 0.8639

8 0.0257 1.2682 -0.1925 1.1944 0.0839 1.3058 -0.0447 0.4989 -0.0693 0.5693 -1.1628 0.9261

9 -0.1431 1.4174 -0.3499 1.3430 -0.0356 1.4507 -0.0949 0.5236 -0.0503 0.6196 -1.3914 1.0214

10 -0.0279 1.5926 -0.0478 1.5157 0.3456 1.6219 -0.1213 0.5565 -0.1724 0.6986 -1.7463 1.1416

11 -0.2250 1.2342 -0.3020 1.1602 -0.1750 1.2729 0.0000 0.4937 -0.1350 0.5778 -1.6000 0.9058

12 0.0555 1.2682 -0.0188 1.1944 0.0778 1.3058 -0.0447 0.4989 -0.2048 0.5690 -1.5652 0.9261

13 0.0474 1.3610 -0.2524 1.2871 -0.1506 1.3959 -0.0707 0.5139 -0.0311 0.5789 -1.6263 0.9844

14 -0.1040 1.4961 -0.3836 1.4207 -0.1179 1.5274 -0.1387 0.5380 -0.1689 0.6193 -1.8860 1.0746

15 -0.1020 1.6602 -0.2370 1.5819 0.1395 1.6880 -0.1342 0.5700 -0.1887 0.6912 -2.1019 1.1894

16 -0.1350 1.3897 -0.2460 1.3156 -0.1750 1.4237 -0.2000 0.5188 -0.2950 0.6067 -2.6000 1.0031

17 -0.0933 1.4174 -0.0964 1.3430 -0.0395 1.4507 -0.1581 0.5236 -0.4057 0.5859 -2.6563 1.0214

18 -0.2299 1.4961 -0.2804 1.4207 -0.3298 1.5274 -0.0832 0.5380 -0.2097 0.5904 -2.5793 1.0746

19 -0.1202 1.6156 -0.3189 1.5382 -0.1768 1.6443 -0.0707 0.5610 -0.0870 0.6365 -2.6163 1.1577

20 -0.1472 1.7656 -0.1728 1.6848 -0.0332 1.7915 -0.0600 0.5918 -0.1518 0.7139 -2.6600 1.2650

21 -0.1050 1.5693 -0.1100 1.4927 0.1750 1.5990 -0.3000 0.5519 -0.3900 0.6627 -4.0000 1.1252

22 -0.0520 1.5926 -0.1619 1.5157 0.1541 1.6219 -0.2425 0.5565 -0.3868 0.6061 -3.9291 1.1416

23 -0.1404 1.6602 -0.4405 1.5819 -0.2970 1.6880 -0.2236 0.5700 -0.3068 0.6467 -3.8013 1.1894

24 -0.0440 1.7656 -0.3718 1.6848 -0.2000 1.7915 -0.2600 0.5918 -0.2066 0.7061 -3.7600 1.2650

25 -0.0728 1.9012 -0.1994 1.8168 0.1676 1.9248 -0.3536 0.6211 -0.3910 0.7989 -3.8891 1.3639

Ball

5-10 5-11 5-12 6-7 6-8 6-9





1 0.0000 0.5946 0.0000 0.4378 0.0000 0.6720 0.0000 0.2520 0.0000 0.7586 0.0000 0.5071

2 -0.0400 0.6019 0.0050 0.4451 -0.2000 0.6783 -0.2360 0.4352 -0.4000 0.7816 -0.2400 0.5139

3 -0.0800 0.6233 -0.1750 0.4598 -0.2000 0.6968 -0.0520 0.5122 -0.5000 0.8469 -0.0800 0.5341

4 -0.0300 0.6573 -0.0700 0.4812 -0.1000 0.7265 -0.1060 0.5838 -0.8000 0.9458 -0.0300 0.5660

5 -0.1000 0.7021 -0.0920 0.5085 0.0000 0.7662 -0.0690 0.5751 -1.3000 1.0690 -0.1000 0.6079

6 -0.0900 0.6019 -0.0800 0.4451 0.0000 0.6783 0.0640 0.4975 -0.7000 0.7816 0.0100 0.5139

7 -0.0849 0.6091 -0.1704 0.4503 0.0707 0.6845 -0.0566 0.4438 -0.9192 0.8040 -0.1556 0.5207

8 -0.1476 0.6302 -0.3658 0.4642 -0.0894 0.7028 -0.0246 0.4681 -1.1180 0.8676 -0.1029 0.5406

9 -0.1075 0.6639 -0.3143 0.4853 0.0000 0.7323 0.0446 0.5202 -1.2965 0.9644 -0.0126 0.5722

10 -0.2280 0.7083 -0.2479 0.5123 0.1455 0.7718 -0.0512 0.6025 -1.6250 1.0854 -0.1067 0.6137

11 -0.0500 0.6233 -0.1270 0.4598 0.0000 0.6968 -0.1350 0.4802 -1.6000 0.8469 -0.0500 0.5341

12 -0.1565 0.6302 -0.2308 0.4642 -0.1342 0.7028 -0.1601 0.4678 -1.5205 0.8676 -0.1118 0.5406

13 -0.0849 0.6506 -0.3847 0.4771 -0.2828 0.7207 0.0396 0.4745 -1.5556 0.9269 -0.0141 0.5598

14 -0.1525 0.6833 -0.4321 0.4971 -0.1664 0.7495 -0.0302 0.5149 -1.7473 1.0180 -0.0139 0.5903

15 -0.2415 0.7265 -0.3766 0.5232 0.0000 0.7880 -0.0546 0.5896 -1.9677 1.1334 -0.1073 0.6306

16 -0.0600 0.6573 -0.1710 0.4812 -0.1000 0.7265 -0.0950 0.5064 -2.4000 0.9458 0.1400 0.5660

17 -0.1170 0.6639 -0.1202 0.4853 -0.0633 0.7323 -0.2476 0.4795 -2.4982 0.9644 0.0411 0.5722

18 -0.1498 0.6833 -0.2002 0.4971 -0.2496 0.7495 -0.1265 0.4798 -2.4961 1.0180 -0.0666 0.5903

19 -0.0141 0.7144 -0.2128 0.5160 -0.0707 0.7772 -0.0163 0.5276 -2.5456 1.1016 0.0566 0.6194

20 -0.0540 0.7559 -0.0796 0.5409 0.0600 0.8145 -0.0918 0.6092 -2.6000 1.2090 0.0060 0.6579

21 -0.0800 0.7021 -0.0850 0.5085 0.2000 0.7662 -0.0900 0.5619 -3.7000 1.0690 0.2200 0.6079

22 -0.0849 0.7083 -0.1948 0.5123 0.1213 0.7718 -0.1443 0.4923 -3.6865 1.0854 0.1576 0.6137

23 -0.0671 0.7265 -0.3672 0.5232 -0.2236 0.7880 -0.0832 0.5367 -3.5777 1.1334 0.1565 0.6306

24 -0.0040 0.7559 -0.3318 0.5409 -0.1600 0.8145 0.0534 0.6001 -3.5000 1.2090 0.2560 0.6579

25 -0.0990 0.7952 -0.2256 0.5645 0.1414 0.8501 -0.0375 0.6986 -3.5355 1.3076 0.2546 0.6943

Ball

6-12 7-8 7-9 7-106-10 6-11





1 0.0000 0.3085 0.0000 0.5959 0.0000 0.7155 0.0000 0.4400 0.0000 0.1780 0.0000 0.5400

2 -0.1950 0.3161 -0.4000 0.6016 -0.1640 0.8185 -0.0040 0.5685 0.0410 0.3987 -0.1640 0.6488

3 -0.1750 0.3289 -0.2000 0.6183 -0.4480 0.9160 -0.0280 0.6379 -0.1230 0.4795 -0.1480 0.7099

4 -0.0700 0.3463 -0.1000 0.6451 -0.6940 1.0382 0.0760 0.7097 0.0360 0.5507 0.0060 0.7743

5 -0.0920 0.3677 0.0000 0.6810 -1.2310 1.1367 -0.0310 0.7205 -0.0230 0.5336 0.0690 0.7831

6 0.0200 0.3161 0.1000 0.6016 -0.7640 0.8533 -0.0540 0.6175 -0.0440 0.4659 0.0360 0.6921

7 -0.2411 0.3208 0.0000 0.6072 -0.8627 0.8424 -0.0990 0.5782 -0.1846 0.4075 0.0566 0.6572

8 -0.3211 0.3326 -0.0447 0.6237 -1.0934 0.9099 -0.0783 0.6062 -0.2965 0.4311 -0.0201 0.6814

9 -0.2195 0.3495 0.0949 0.6504 -1.3411 1.0197 -0.0572 0.6612 -0.2640 0.4816 0.0503 0.7299

10 -0.1266 0.3706 0.2668 0.6860 -1.5738 1.1647 -0.0555 0.7449 -0.0754 0.5618 0.3180 0.8055

11 -0.1270 0.3289 0.0000 0.6183 -1.4650 0.8985 0.0850 0.6126 0.0080 0.4452 0.1350 0.6873

12 -0.1860 0.3326 -0.0894 0.6237 -1.3604 0.9098 0.0483 0.6059 -0.0259 0.4307 0.0707 0.6812

13 -0.3140 0.3430 -0.2121 0.6399 -1.5952 0.9645 -0.0537 0.6200 -0.3535 0.4344 -0.2517 0.6932

14 -0.2934 0.3588 -0.0277 0.6659 -1.7171 1.0632 0.0164 0.6653 -0.2632 0.4721 0.0025 0.7331

15 -0.2424 0.3790 0.1342 0.7006 -1.9132 1.1989 -0.0528 0.7420 -0.1878 0.5445 0.1887 0.8023

16 0.0290 0.3463 0.1000 0.6451 -2.3050 0.9967 0.2350 0.6475 0.1240 0.4678 0.1950 0.7177

17 0.0379 0.3495 0.0949 0.6504 -2.2506 0.9995 0.2887 0.6296 0.2856 0.4373 0.3425 0.7015

18 -0.1170 0.3588 -0.1664 0.6659 -2.3697 1.0467 0.0599 0.6385 0.0094 0.4335 -0.0399 0.7089

19 -0.1421 0.3735 0.0000 0.6909 -2.5293 1.1419 0.0728 0.6885 -0.1259 0.4794 0.0163 0.7534

20 -0.0196 0.3925 0.1200 0.7245 -2.5082 1.2732 0.0978 0.7695 0.0722 0.5598 0.2118 0.8272

21 0.2150 0.3677 0.5000 0.6810 -3.6100 1.1301 0.3100 0.7100 0.3050 0.5194 0.5900 0.7735

22 0.0478 0.3706 0.3638 0.6860 -3.5422 1.1117 0.3020 0.6590 0.1921 0.4417 0.5081 0.7268

23 -0.1436 0.3790 0.0000 0.7006 -3.4945 1.1738 0.2397 0.7007 -0.0604 0.4868 0.0832 0.7643

24 -0.0718 0.3925 0.1000 0.7245 -3.5534 1.2689 0.2026 0.7624 -0.1252 0.5499 0.0466 0.8205

25 0.1280 0.4103 0.4950 0.7566 -3.4980 1.4009 0.2920 0.8571 0.1655 0.6488 0.5325 0.9083

Ball

7-11 7-12 8-9 8-10 8-11 8-12





1 0.0000 0.8400 0.0000 0.7373 0.0000 0.8964 0.0000 0.4746 0.0000 0.6966 0.0000 0.5686

2 0.1600 0.8630 0.2050 0.7619 0.0000 0.9179 0.0450 0.4834 -0.1600 0.7040 -0.2050 0.5757

3 0.4200 0.9284 0.3250 0.8276 0.3000 0.9793 -0.0950 0.5028 -0.1200 0.7259 -0.0250 0.5915

4 0.7700 1.0283 0.7300 0.9257 0.7000 1.0739 -0.0400 0.5318 -0.0700 0.7610 -0.0300 0.6153

5 1.2000 1.1537 1.2080 1.0472 1.3000 1.1938 0.0080 0.5688 0.1000 0.8075 0.0920 0.6463

6 0.7100 0.8630 0.7200 0.7619 0.8000 0.9179 0.0100 0.4834 0.0900 0.7040 0.0800 0.5757

7 0.7637 0.8853 0.6781 0.7845 0.9192 0.9388 -0.0856 0.4902 0.1556 0.7114 0.2411 0.5812

8 1.0152 0.9492 0.7969 0.8482 1.0733 0.9989 -0.2182 0.5088 0.0581 0.7330 0.2764 0.5964

9 1.2839 1.0471 1.0771 0.9441 1.3914 1.0918 -0.2068 0.5373 0.1075 0.7678 0.3143 0.6199

10 1.5183 1.1705 1.4984 1.0634 1.8918 1.2100 -0.0199 0.5739 0.3735 0.8139 0.3934 0.6506

11 1.5500 0.9284 1.4730 0.8276 1.6000 0.9793 -0.0770 0.5028 0.0500 0.7259 0.1270 0.5915

12 1.4087 0.9492 1.3345 0.8482 1.4311 0.9989 -0.0742 0.5088 0.0224 0.7330 0.0966 0.5964

13 1.5415 1.0091 1.2417 0.9070 1.3435 1.0557 -0.2998 0.5262 -0.1980 0.7541 0.1018 0.6107

14 1.7334 1.1017 1.4539 0.9970 1.7196 1.1440 -0.2796 0.5533 -0.0139 0.7879 0.2657 0.6333

15 1.8604 1.2196 1.7253 1.1106 2.1019 1.2572 -0.1351 0.5887 0.2415 0.8329 0.3766 0.6632

16 2.5400 1.0283 2.4290 0.9257 2.5000 1.0739 -0.1110 0.5318 -0.0400 0.7610 0.0710 0.6153

17 2.5393 1.0471 2.5361 0.9441 2.5930 1.0918 -0.0032 0.5373 0.0538 0.7678 0.0569 0.6199

18 2.4296 1.1017 2.3791 0.9970 2.3297 1.1440 -0.0505 0.5533 -0.0998 0.7879 -0.0494 0.6333

19 2.6021 1.1871 2.4034 1.0794 2.5456 1.2259 -0.1987 0.5789 -0.0566 0.8203 0.1421 0.6548

20 2.6060 1.2973 2.5804 1.1849 2.7200 1.3322 -0.0256 0.6125 0.1140 0.8637 0.1396 0.6835

21 3.9200 1.1537 3.9150 1.0472 4.2000 1.1938 -0.0050 0.5688 0.2800 0.8075 0.2850 0.6463

22 3.8442 1.1705 3.7343 1.0634 4.0503 1.2100 -0.1099 0.5739 0.2062 0.8139 0.3160 0.6506

23 3.7342 1.2196 3.4341 1.1106 3.5777 1.2572 -0.3001 0.5887 -0.1565 0.8329 0.1436 0.6632

24 3.7560 1.2973 3.4282 1.1849 3.6000 1.3322 -0.3278 0.6125 -0.1560 0.8637 0.1718 0.6835

25 3.7901 1.3988 3.6635 1.2817 4.0305 1.4307 -0.1266 0.6441 0.2404 0.9050 0.3670 0.7108

Ball

9-10 9-11 9-12 10-11 10-12 11-12



-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

0 50 100 150 200 250 300 350 400 450 500

Equivalence Lab. 2 vs Lab. 1

Uij

l (mm)

Dij( µµ µµm) Uij

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

0 50 100 150 200 250 300 350 400 450 500

Equivalence Lab. 3 vs Lab 1

Uij

l (mm)

Dij( µµ µµm)

Uij

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij

-2.50

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

0 50 100 150 200 250 300 350 400 450 500

Equivalence Lab.5 vs Lab. 1

Uij

l (mm)Dij( µµ µµm) Uij



-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)


-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij

-3.00

-2.50

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij



-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

0 50 100 150 200 250 300 350 400 450 500

Equivalence lab. 10 vs Lab. 1

Uij

l (mm)


-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

0 50 100 150 200 250 300 350 400 450 500


Uij l (mm)

Dij( µµ µµm)

Uij

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij



-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij

-2.50

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)Dij( µµ µµm)

Uij



-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij

-5.00

-4.00

-3.00

-2.00

-1.00

0.00

1.00

2.00

0 50 100 150 200 250 300 350 400 450 500


Uij l (mm)


-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij



-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 50 100 150 200 250 300 350 400 450 500


Uij


Uij

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 50 100 150 200 250 300 350 400 450 500

Equivalence Lab.4 vs Lab.3

Uij

l (mm)

Dij( µµ µµm)

Uij

-2.50

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

0 50 100 150 200 250 300 350 400 450 500

Equivalence Lab. 5 vs Lab.3

Uij

l (mm)

Dij( µµ µµm)

Uij

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 50 100 150 200 250 300 350 400 450 500


Uij


Uij



-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 50 100 150 200 250 300 350 400 450 500

Eqivalence Lab. 8 vs Lab. 3

Uij

l (mm)

Dij( µµ µµm)

Uij

-5.00

-4.00

-3.00

-2.00

-1.00

0.00

1.00

2.00

0 50 100 150 200 250 300 350 400 450 500


Uij l (mm)


-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 50 100 150 200 250 300 350 400 450 500


Uij


Uij



-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 50 100 150 200 250 300 350 400 450 500

Eqivalence Lab. 11 vs Lab. 3

Uij

l (mm)

Dij( µµ µµm)

Uij

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij

-2.50

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 50 100 150 200 250 300 350 400 450 500


Uij


Uij



-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij

-5.00

-4.00

-3.00

-2.00

-1.00

0.00

1.00

2.00

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 50 100 150 200 250 300 350 400 450 500


Uij


Uij



-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij

-2.50

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij

-2.50

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij



-2.50

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij

-5.00

-4.00

-3.00

-2.00

-1.00

0.00

1.00

2.00

3.00

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij

-2.50

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

0 50 100 150 200 250 300 350 400 450 500


Uij


Uij



-2.50

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij

-5.00

-4.00

-3.00

-2.00

-1.00

0.00

1.00

2.00

0 50 100 150 200 250 300 350 400 450 500


Uijl (mm)

Dij( µµ µµm)

Uij



-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 50 100 150 200 250 300 350 400 450 500


Uij


Uij



-4.00

-3.00

-2.00

-1.00

0.00

1.00

2.00

0 50 100 150 200 250 300 350 400 450 500


Uijl (mm)

Dij( µµ µµm)

Uij

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij

-0.50

-0.40

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0.50

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 50 100 150 200 250 300 350 400 450 500


Uij


Uij



-4.00

-3.00

-2.00

-1.00

0.00

1.00

2.00

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 50 100 150 200 250 300 350 400 450 500


Uij


Uij



-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

5.00

0 50 100 150 200 250 300 350 400 450 500


Uijl (mm)

Dij( µµ µµm)

Uij

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

5.00

0 50 100 150 200 250 300 350 400 450 500


Uij l (mm)

Dij( µµ µµm)

Uij

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

5.00

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij



-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 50 100 150 200 250 300 350 400 450 500


Uij

l (mm)

Dij( µµ µµm)

Uij



ZERODUR Bore Plate The following tables show the values of Dij and Uij for each laboratory i (i = 1,..,12) and for each measuring element k (k = 1,...,60). They are followed by plots14 of these values shown as a function of the nominal distances of the measuring elements for each laboratory. The dots represent Dij according to equation A3 and the blue curves represent Uij according to equation A4.

14






1 0.0016 0.6888 0.0000 0.6803 0.0000 0.9351 0.0000 1.1261 0.0000 0.7378 0.0000 0.6641

2 0.0574 0.6960 0.0000 0.6873 0.0000 0.9402 0.3000 1.1591 0.0000 0.7438 -0.2000 0.6707

3 -0.0392 0.7171 -0.1000 0.7081 -0.0001 0.9553 0.3000 1.2041 -0.2000 0.7616 -0.3000 0.6899

4 -0.1260 0.7510 0.1000 0.7413 0.0000 0.9801 0.3000 1.2599 -0.4000 0.7903 -0.6000 0.7209

5 -0.0501 0.7961 -0.2000 0.7856 0.1000 1.0137 0.5000 1.3251 -0.2000 0.8287 -0.5000 0.7621

6 -0.1073 0.8505 -0.3000 0.8390 0.0000 1.0553 0.5000 1.3983 -0.1000 0.8757 -0.6000 0.8121

7 0.1985 0.9126 -0.1000 0.9000 0.3000 1.1041 0.9000 1.4784 0.1000 0.9300 -0.3000 0.8693

8 0.1114 0.9810 -0.2000 0.9672 0.5000 1.1591 1.0000 1.5644 0.1000 0.9902 -0.4000 0.9323

9 0.3019 1.0543 -0.1000 1.0393 0.5000 1.2194 1.4000 1.6552 0.1000 1.0555 -0.4000 1.0002

10 -0.0256 0.6960 -0.1000 0.6874 -0.3000 0.9402 0.1000 1.1591 0.0000 0.7438 -0.1000 0.6707

11 0.2393 0.7031 0.2121 0.6943 0.0706 0.9453 0.4949 1.1764 0.1414 0.7498 0.0000 0.6771

12 0.3192 0.7240 0.1342 0.7149 0.2683 0.9604 0.6708 1.2164 0.1342 0.7674 -0.0447 0.6962

13 0.1807 0.7576 0.4427 0.7479 0.2213 0.9850 0.8222 1.2700 -0.0949 0.7959 -0.2214 0.7270

14 0.0652 0.8023 -0.0485 0.7917 0.1940 1.0184 0.7033 1.3338 -0.0970 0.8341 -0.4123 0.7679

15 0.1761 0.8563 0.0393 0.8448 0.2942 1.0599 0.8237 1.4060 0.1177 0.8808 -0.2942 0.8175

16 0.2210 0.9181 -0.0657 0.9054 0.3124 1.1084 1.0522 1.4854 0.1151 0.9348 -0.3781 0.8743

17 0.3464 0.9860 0.0283 0.9721 0.6081 1.1632 1.4142 1.5706 0.2121 0.9947 -0.2970 0.9370

18 0.2941 1.0591 -0.1860 1.0439 0.4341 1.2234 1.4140 1.6610 0.0124 1.0597 -0.4961 1.0045

19 -0.0394 0.7171 -0.3000 0.7081 -0.3000 0.9554 0.0000 1.2042 -0.2000 0.7616 -0.3000 0.6899

20 0.0535 0.7240 -0.0447 0.7149 -0.0447 0.9604 0.1790 1.2164 -0.0894 0.7674 -0.2236 0.6962

21 0.2369 1.0011 -0.0961 0.9869 0.4121 1.1755 1.2362 1.5894 0.0961 1.0081 -0.3846 0.9509

22 0.2295 1.0730 -0.2910 1.0576 0.2668 1.2350 1.2127 1.6782 -0.0970 1.0722 -0.5821 1.0175

23 0.1734 0.7510 0.0000 0.7414 -0.1000 0.9801 0.2000 1.2600 0.2000 0.7903 0.0000 0.7209

24 0.1807 0.7576 0.0632 0.7478 0.0316 0.9849 0.3480 1.2699 0.1897 0.7959 -0.0316 0.7269

25 0.2783 1.0256 -0.0656 1.0110 0.4333 1.1956 1.4443 1.6198 0.2101 1.0299 -0.2888 0.9736

26 0.3313 1.0960 -0.1170 1.0802 0.4565 1.2542 1.2874 1.7064 0.1053 1.0928 -0.3979 1.0387

27 0.5551 0.7961 0.3000 0.7856 0.4000 1.0137 0.5001 1.3251 0.6000 0.8287 0.2000 0.7621

28 0.5201 0.8023 0.4365 0.7917 0.4608 1.0184 0.5821 1.3337 0.4608 0.8341 0.2425 0.7678

29 0.4578 1.0590 0.0869 1.0439 0.5706 1.2233 1.4016 1.6610 0.3102 1.0597 -0.1860 1.0045

30 0.4375 1.1273 0.0000 1.1110 0.5367 1.2807 1.3864 1.7448 0.1342 1.1209 -0.4025 1.0677

31 0.6591 0.8505 0.5000 0.8390 0.8000 1.0553 0.4000 1.3983 0.7000 0.8757 0.4000 0.8121

32 0.6335 0.8563 0.5491 0.8447 0.5491 1.0598 0.7649 1.4060 0.6668 0.8808 0.3333 0.8174

33 0.6647 0.8736 0.5756 0.8617 0.6684 1.0733 0.9470 1.4285 0.6684 0.8959 0.3156 0.8334

34 0.5442 0.9016 0.6859 0.8892 0.6687 1.0954 0.8918 1.4645 0.5315 0.9204 -0.0173 0.8592

35 0.5556 0.9394 0.5777 0.9264 0.6402 1.1255 0.9995 1.5124 0.4371 0.9536 0.0155 0.8940

36 0.4355 0.9859 0.2828 0.9721 0.4242 1.1631 1.0607 1.5706 0.4242 0.9946 -0.1415 0.9369

37 0.7188 1.0400 0.4225 1.0252 0.8578 1.2075 1.4852 1.6375 0.5761 1.0427 0.0000 0.9869

38 0.6609 1.1005 0.3604 1.0846 0.9417 1.2580 1.4764 1.7119 0.6045 1.0968 0.0233 1.0429

39 0.6074 1.1664 0.1696 1.1494 0.7526 1.3139 1.3568 1.7925 0.4770 1.1561 -0.1908 1.1039

40 0.7808 0.9126 0.5000 0.9001 0.7000 1.1041 0.8000 1.4785 0.7000 0.9300 0.4000 0.8693

41 0.8561 0.9180 0.6576 0.9053 0.7562 1.1084 0.8713 1.4853 0.7891 0.9347 0.4603 0.8742

42 0.7213 1.1492 0.3580 1.1325 0.9437 1.2992 1.3450 1.7715 0.5857 1.1406 0.0109 1.0880

43 0.7231 1.2124 0.2400 1.1947 0.7600 1.3533 1.5000 1.8486 0.4600 1.1977 -0.2000 1.1467

44 0.8952 0.9810 0.6000 0.9672 0.7000 1.1591 0.8000 1.5644 0.8000 0.9903 0.5000 0.9324

45 0.9088 0.9860 0.6647 0.9722 0.7637 1.1632 0.9475 1.5707 0.8909 0.9947 0.5657 0.9370

46 0.8608 1.0010 0.6593 0.9869 0.8104 1.1754 1.1401 1.5893 0.7829 1.0080 0.3434 0.9509

47 0.6565 1.0256 0.7484 1.0110 0.6302 1.1956 0.9060 1.6197 0.5515 1.0298 0.1050 0.9735

48 0.8379 1.0590 0.7690 1.0438 0.8186 1.2233 1.2155 1.6609 0.6822 1.0597 0.2232 1.0045

49 0.7071 1.1005 0.5813 1.0846 0.8602 1.2580 1.2206 1.7119 0.6161 1.0968 0.1395 1.0429

50 0.7941 1.1492 0.4881 1.1325 0.9003 1.2992 1.4209 1.7715 0.5532 1.1406 0.1302 1.0880

51 0.8898 1.2042 0.4949 1.1866 1.0606 1.3462 1.6970 1.8386 0.7071 1.1902 0.1414 1.1390

52 0.8247 1.2647 0.3669 1.2460 0.8654 1.3986 1.5522 1.9123 0.7243 1.2451 -0.0659 1.1952

53 0.7181 1.0544 0.3000 1.0393 0.6000 1.2195 0.4000 1.6553 0.5000 1.0555 0.0000 1.0002

54 0.6190 1.0591 0.3597 1.0439 0.4465 1.2234 0.4341 1.6611 0.4837 1.0597 0.0620 1.0045

55 0.5671 1.0731 0.2182 1.0577 0.4365 1.2350 0.7519 1.6782 0.3395 1.0722 -0.1213 1.0175

56 0.3410 1.0960 0.3043 1.0802 0.4213 1.2542 0.5384 1.7064 0.1989 1.0928 -0.2810 1.0387

57 0.5755 1.1273 0.4025 1.1110 0.4472 1.2807 0.6708 1.7448 0.3578 1.1209 -0.1789 1.0677

58 0.4902 1.1664 0.1590 1.1494 0.5194 1.3139 0.7420 1.7925 0.3710 1.1561 -0.2862 1.1039

59 0.5705 1.2124 0.1600 1.1947 0.6400 1.3533 0.8800 1.8486 0.3400 1.1977 -0.2000 1.1467

60 0.6361 1.2647 0.1787 1.2461 0.7996 1.3986 1.0348 1.9123 0.4421 1.2451 -0.2634 1.1952

61 0.6921 1.3224 0.1414 1.3028 0.7071 1.4490 1.1314 1.9825 0.3536 1.2976 -0.2828 1.2488

1-71-61-5

Ball

1-2 1-3 1-4





1 0.0000 0.6200 0.0000 0.9468 0.0000 0.7603 0.0000 0.6450 0.0000 0.8222 -0.0016 0.4104

2 -0.0270 0.7986 0.4999 0.9576 -0.1100 0.7664 -0.0030 0.6528 0.1000 0.8279 -0.0574 0.4141

3 -0.2109 0.8860 0.6999 0.9892 -0.2900 0.7845 -0.1550 0.6729 -0.1000 0.8447 -0.0608 0.4250

4 -0.4589 0.9578 0.8000 1.0397 -0.4900 0.8138 -0.2310 0.7044 -0.1000 0.8719 0.2261 0.4425

5 -0.3120 1.0248 1.3000 1.1067 -0.3200 0.8531 -0.0190 0.7457 -0.1000 0.9088 -0.1499 0.4660

6 -0.4900 1.0963 1.6000 1.1872 -0.4100 0.9012 -0.1250 0.7953 -0.3000 0.9540 -0.1926 0.4946

7 -0.2630 1.1772 2.2000 1.2787 -0.2500 0.9566 0.1000 0.8518 0.1000 1.0065 -0.2985 0.5274

8 -0.4080 1.2725 2.5000 1.3791 -0.3600 1.0183 0.0100 0.9140 -0.1000 1.0653 -0.3114 0.5637

9 -0.3750 1.2492 3.2000 1.4865 -0.3000 1.0851 0.1380 0.9806 0.0000 1.1293 -0.4019 0.6029

10 0.0750 0.9362 0.0000 0.9576 -0.2100 0.7664 -0.0600 0.6528 0.0000 0.8279 -0.0744 0.4141

11 0.1612 0.8252 0.3534 0.9682 0.0635 0.7725 0.1449 0.6597 0.2121 0.8335 -0.0272 0.4177

12 0.1994 0.8616 0.8944 0.9995 0.0939 0.7905 0.1762 0.6794 0.0000 0.8502 -0.1850 0.4285

13 0.1256 0.9143 1.3281 1.0496 -0.0980 0.8196 0.0525 0.7105 0.1265 0.8773 0.2620 0.4460

14 -0.0070 0.9764 1.6977 1.1160 -0.1673 0.8586 0.0121 0.7514 -0.0970 0.9139 -0.1137 0.4693

15 0.0141 1.0452 2.3338 1.1958 -0.0725 0.9064 0.1053 0.8007 0.0196 0.9589 -0.1368 0.4977

16 -0.1616 1.1217 2.7455 1.2868 -0.1759 0.9615 0.0207 0.8568 0.1151 1.0112 -0.2868 0.5303

17 -0.2169 1.2093 3.1396 1.3865 -0.2348 1.0228 0.0417 0.9185 0.2263 1.0697 -0.3181 0.5664

18 -0.2837 1.3184 3.1877 1.4934 -0.3349 1.0894 0.0019 0.9849 0.0992 1.1335 -0.4802 0.6054

19 0.1410 0.9161 -0.4000 0.9892 -0.2200 0.7845 0.0840 0.6730 -0.2000 0.8447 -0.2606 0.4250

20 0.2366 0.8716 0.0448 0.9995 -0.1833 0.7905 0.0514 0.6794 0.0000 0.8502 -0.0982 0.4285

21 -0.2537 1.1951 2.9669 1.4086 -0.2774 1.0365 -0.0209 0.9322 -0.0687 1.0828 -0.3330 0.5744

22 -0.4210 1.2964 3.1044 1.5138 -0.4438 1.1022 -0.1074 0.9976 0.0970 1.1458 -0.5205 0.6129

23 0.4540 0.9368 -0.2001 1.0398 0.1000 0.8138 0.3990 0.7044 0.1000 0.8720 -0.1734 0.4426

24 0.2785 0.9160 -0.0948 1.0496 -0.0159 0.8195 0.2326 0.7104 0.0632 0.8773 -0.1174 0.4460

25 -0.0200 1.1983 2.6917 1.4445 0.0579 1.0588 0.1680 0.9545 0.0788 1.1042 -0.3439 0.5875

26 -0.0889 1.2955 3.1601 1.5473 -0.0550 1.1232 0.1088 1.0185 0.1990 1.1660 -0.4483 0.6252

27 0.8120 0.9726 0.2999 1.1067 0.5000 0.8531 0.8170 0.7457 0.5000 0.9088 -0.2551 0.4660

28 0.6608 0.9625 0.1697 1.1159 0.2740 0.8586 0.6235 0.7514 0.4608 0.9139 -0.0836 0.4693

29 0.1369 1.2165 2.5178 1.4934 0.0199 1.0894 0.1807 0.9849 0.4342 1.1334 -0.3709 0.6054

30 0.0072 1.3113 2.9069 1.5931 -0.0358 1.1520 0.2165 1.0469 0.3131 1.1938 -0.4375 0.6421

31 0.7510 1.0231 0.3999 1.1872 0.4500 0.9012 0.8410 0.7953 0.5000 0.9540 -0.1591 0.4946

32 0.7344 1.0106 0.1569 1.1958 0.4020 0.9063 0.7801 0.8006 0.4903 0.9589 -0.0844 0.4976

33 0.6916 1.0046 0.6315 1.2213 0.3713 0.9218 0.7176 0.8164 0.4084 0.9735 -0.0892 0.5068

34 0.5894 1.0204 0.8404 1.2626 0.2570 0.9468 0.5428 0.8419 0.2571 0.9972 0.1417 0.5216

35 0.4013 1.0539 1.1871 1.3181 0.1966 0.9807 0.4991 0.8762 0.4840 1.0295 0.0221 0.5416

36 0.3761 1.1039 1.4143 1.3864 0.2191 1.0228 0.4313 0.9185 0.4242 1.0696 -0.1527 0.5664

37 0.4201 1.1704 1.9334 1.4655 0.3764 1.0720 0.5898 0.9676 0.6658 1.1167 -0.2963 0.5952

38 0.4068 1.2493 2.4644 1.5539 0.2582 1.1274 0.5332 1.0226 0.4069 1.1700 -0.3004 0.6277

39 0.1772 1.3418 3.0846 1.6500 -0.0233 1.1880 0.4292 1.0824 0.3710 1.2286 -0.4377 0.6631

40 0.8720 1.0857 0.2999 1.2788 0.6500 0.9567 0.9980 0.8519 0.5000 1.0066 -0.2808 0.5274

41 0.7429 1.0590 0.3781 1.2867 0.5260 0.9615 0.9448 0.8567 0.7727 1.0112 -0.1985 0.5303

42 0.3524 1.3052 2.2343 1.6249 0.2039 1.1722 0.4721 1.0668 0.5207 1.2132 -0.3633 0.6538

43 0.2564 1.3896 3.1200 1.7170 0.1060 1.2306 0.5148 1.1243 0.5600 1.2698 -0.4832 0.6879

44 0.8860 1.1640 0.2000 1.3791 0.7300 1.0183 1.0310 0.9140 0.6000 1.0653 -0.2952 0.5637

45 0.7563 1.1018 0.1697 1.3865 0.6873 1.0229 0.9670 0.9186 0.8061 1.0697 -0.2442 0.5664

46 0.7478 1.0900 0.2335 1.4085 0.5906 1.0365 0.9250 0.9322 0.5906 1.0827 -0.2015 0.5744

47 0.5346 1.1139 0.1444 1.4444 0.3361 1.0588 0.6235 0.9545 0.3939 1.1041 0.0919 0.5875

48 0.6730 1.1568 0.5706 1.4933 0.4477 1.0893 0.7346 0.9849 0.6078 1.1334 -0.0689 0.6054

49 0.5040 1.2123 0.7207 1.5539 0.3069 1.1273 0.4999 1.0225 0.4766 1.1700 -0.1258 0.6276

50 0.5191 1.2800 1.4751 1.6249 0.3113 1.1721 0.5174 1.0668 0.5966 1.2132 -0.3060 0.6538

51 0.3846 1.3578 1.9800 1.7051 0.3040 1.2230 0.5777 1.1168 0.4949 1.2624 -0.3949 0.6835

52 0.2427 1.4561 3.0103 1.7931 0.1740 1.2791 0.5455 1.1718 0.3857 1.3169 -0.4579 0.7161

53 0.6020 1.2629 -0.4000 1.4866 0.4000 1.0851 0.7900 0.9807 0.2000 1.1294 -0.4181 0.6029

54 0.4723 1.1480 -0.3225 1.4934 0.2976 1.0894 0.7168 0.9849 0.2853 1.1335 -0.2594 0.6054

55 0.2932 1.1727 -0.1455 1.5139 0.1721 1.1022 0.6036 0.9976 0.1212 1.1458 -0.3489 0.6129

56 0.1558 1.2090 -0.1755 1.5473 -0.0434 1.1232 0.3639 1.0185 0.1755 1.1660 -0.0367 0.6252

57 0.3631 1.2543 0.4473 1.5931 0.1252 1.1520 0.4602 1.0469 0.2236 1.1938 -0.1730 0.6421

58 0.1759 1.3105 0.8586 1.6500 -0.0318 1.1880 0.2608 1.0824 0.2862 1.2286 -0.3312 0.6631

59 0.1445 1.3776 1.3801 1.7171 -0.0761 1.2306 0.2776 1.1243 0.3200 1.2698 -0.4106 0.6879

60 -0.0837 1.4592 1.6651 1.7931 -0.3142 1.2792 0.2164 1.1718 0.3010 1.3169 -0.4574 0.7161

61 -0.0912 1.5726 2.3335 1.8770 -0.2616 1.3329 0.3741 1.2243 0.4243 1.3692 -0.5507 0.7474

2-31-8 1-9 1-10 1-11 1-12

Ball





1 -0.0016 0.7616 -0.0016 0.9867 -0.0016 0.5000 -0.0016 0.3829 -0.0016 0.3000 -0.0016 0.7759

2 -0.0574 0.7635 0.2426 1.0210 -0.0574 0.5023 -0.2574 0.3857 -0.0844 0.5803 0.4425 0.7848

3 0.0392 0.7694 0.3392 1.0626 -0.1608 0.5091 -0.2608 0.3940 -0.1717 0.6814 0.7392 0.8110

4 0.1260 0.7790 0.4261 1.1107 -0.2739 0.5203 -0.4740 0.4073 -0.3329 0.7507 0.9260 0.8528

5 0.1500 0.7922 0.5501 1.1645 -0.1499 0.5356 -0.4499 0.4253 -0.2619 0.8065 1.3501 0.9082

6 0.1073 0.8089 0.6074 1.2231 0.0073 0.5546 -0.4927 0.4474 -0.3826 0.8617 1.7073 0.9747

7 0.1015 0.8289 0.7015 1.2861 -0.0985 0.5770 -0.4985 0.4730 -0.4615 0.9240 2.0015 1.0503

8 0.3886 0.8519 0.8886 1.3526 -0.0114 0.6024 -0.5114 0.5016 -0.5194 1.0008 2.3886 1.1333

9 0.1981 0.8777 1.0981 1.4224 -0.2019 0.6305 -0.7019 0.5327 -0.6769 0.9187 2.8981 1.2219

10 -0.2744 0.7635 0.1255 1.0210 0.0256 0.5023 -0.0744 0.3857 0.1006 0.7586 0.0256 0.7848

11 -0.1687 0.7655 0.2555 1.0374 -0.0980 0.5046 -0.2394 0.3885 -0.0781 0.6110 0.1141 0.7936

12 -0.0508 0.7713 0.3517 1.0735 -0.1850 0.5114 -0.3639 0.3967 -0.1197 0.6441 0.5753 0.8195

13 0.0406 0.7809 0.6414 1.1191 -0.2756 0.5226 -0.4021 0.4100 -0.0552 0.6896 1.1474 0.8610

14 0.1288 0.7941 0.6381 1.1715 -0.1622 0.5378 -0.4775 0.4279 -0.0722 0.7395 1.6325 0.9159

15 0.1181 0.8108 0.6476 1.2292 -0.0584 0.5567 -0.4703 0.4498 -0.1619 0.7915 2.1577 0.9819

16 0.0913 0.8307 0.8312 1.2915 -0.1059 0.5790 -0.5991 0.4753 -0.3826 0.8483 2.5245 1.0570

17 0.2617 0.8537 1.0678 1.3575 -0.1342 0.6043 -0.6433 0.5037 -0.5633 0.9155 2.7932 1.1393

18 0.1400 0.8794 1.1199 1.4268 -0.2817 0.6323 -0.7903 0.5347 -0.5778 1.0075 2.8935 1.2276

19 -0.2606 0.7694 0.0394 1.0627 -0.1606 0.5091 -0.2606 0.3940 0.1804 0.7200 -0.3606 0.8110

20 -0.0982 0.7713 0.1255 1.0734 -0.1429 0.5114 -0.2771 0.3967 0.1831 0.6575 -0.0087 0.8195

21 0.1752 0.8589 0.9993 1.3719 -0.1407 0.6101 -0.6215 0.5101 -0.4906 0.8855 2.7300 1.1576

22 0.0373 0.8845 0.9832 1.4400 -0.3265 0.6377 -0.8116 0.5406 -0.6505 0.9684 2.8749 1.2445

23 -0.2734 0.7790 0.0267 1.1107 0.0266 0.5203 -0.1734 0.4074 0.2806 0.7237 -0.3734 0.8529

24 -0.1491 0.7809 0.1673 1.1191 0.0091 0.5225 -0.2123 0.4100 0.0978 0.6919 -0.2754 0.8610

25 0.1551 0.8675 1.1661 1.3952 -0.0681 0.6194 -0.5671 0.5205 -0.2983 0.8712 2.4134 1.1872

26 0.1252 0.8929 0.9561 1.4614 -0.2260 0.6467 -0.7292 0.5505 -0.4202 0.9500 2.8288 1.2721

27 -0.1550 0.7922 -0.0550 1.1645 0.0450 0.5356 -0.3550 0.4253 0.2569 0.7389 -0.2551 0.9082

28 -0.0593 0.7941 0.0621 1.1714 -0.0593 0.5378 -0.2776 0.4279 0.1407 0.7211 -0.3503 0.9158

29 0.1129 0.8794 0.9438 1.4268 -0.1476 0.6323 -0.6438 0.5347 -0.3209 0.8699 2.0601 1.2276

30 0.0991 0.9044 0.9488 1.4907 -0.3033 0.6591 -0.8400 0.5639 -0.4303 0.9473 2.4693 1.3099

31 0.1409 0.8089 -0.2590 1.2231 0.0409 0.5546 -0.2591 0.4474 0.0919 0.7665 -0.2592 0.9747

32 -0.0844 0.8108 0.1314 1.2292 0.0333 0.5567 -0.3002 0.4498 0.1009 0.7453 -0.4766 0.9818

33 0.0037 0.8163 0.2823 1.2469 0.0037 0.5629 -0.3492 0.4569 0.0268 0.7235 -0.0333 1.0029

34 0.1245 0.8253 0.3475 1.2752 -0.0128 0.5730 -0.5616 0.4685 0.0451 0.7228 0.2962 1.0370

35 0.0846 0.8378 0.4439 1.3124 -0.1184 0.5869 -0.5401 0.4842 -0.1542 0.7389 0.6315 1.0829

36 -0.0113 0.8537 0.6252 1.3574 -0.0113 0.6043 -0.5770 0.5037 -0.0594 0.7710 0.9788 1.1393

37 0.1390 0.8726 0.7664 1.4089 -0.1427 0.6249 -0.7188 0.5266 -0.2988 0.8205 1.2146 1.2046

38 0.2808 0.8945 0.8155 1.4657 -0.0563 0.6485 -0.6375 0.5524 -0.2540 0.8821 1.8035 1.2776

39 0.1453 0.9191 0.7494 1.5270 -0.1303 0.6746 -0.7981 0.5808 -0.4301 0.9587 2.4772 1.3569

40 -0.0808 0.8289 0.0192 1.2861 -0.0808 0.5771 -0.3808 0.4731 0.0912 0.8042 -0.4809 1.0504

41 -0.0998 0.8307 0.0153 1.2914 -0.0670 0.5790 -0.3958 0.4753 -0.1132 0.7636 -0.4780 1.0569

42 0.2224 0.9126 0.6237 1.5110 -0.1355 0.6677 -0.7104 0.5733 -0.3688 0.9211 1.5131 1.3362

43 0.0368 0.9368 0.7769 1.5695 -0.2632 0.6932 -0.9232 0.6007 -0.4668 0.9884 2.3969 1.4122

44 -0.1952 0.8519 -0.0952 1.3527 -0.0952 0.6025 -0.3952 0.5016 -0.0092 0.8586 -0.6953 1.1333

45 -0.1452 0.8537 0.0387 1.3575 -0.0179 0.6044 -0.3432 0.5037 -0.1525 0.7680 -0.7391 1.1394

46 -0.0504 0.8589 0.2793 1.3718 -0.0778 0.6100 -0.5174 0.5101 -0.1130 0.7377 -0.6273 1.1575

47 -0.0263 0.8675 0.2495 1.3952 -0.1051 0.6194 -0.5515 0.5204 -0.1219 0.7510 -0.5121 1.1872

48 -0.0193 0.8794 0.3776 1.4268 -0.1557 0.6323 -0.6147 0.5347 -0.1649 0.7842 -0.2673 1.2275

49 0.1532 0.8945 0.5135 1.4656 -0.0909 0.6485 -0.5675 0.5524 -0.2031 0.8289 0.0137 1.2776

50 0.1062 0.9126 0.6268 1.5110 -0.2409 0.6677 -0.6639 0.5733 -0.2751 0.8851 0.6810 1.3362

51 0.1708 0.9336 0.8072 1.5619 -0.1828 0.6898 -0.7485 0.5971 -0.5052 0.9502 1.0902 1.4023

52 0.0407 0.9572 0.7275 1.6177 -0.1004 0.7144 -0.8906 0.6235 -0.5821 1.0395 2.1856 1.4749

53 -0.1181 0.8778 -0.3181 1.4224 -0.2181 0.6305 -0.7181 0.5327 -0.1161 0.9372 -1.1182 1.2220

54 -0.1725 0.8794 -0.1849 1.4268 -0.1353 0.6323 -0.5570 0.5347 -0.1467 0.7711 -0.9415 1.2277

55 -0.1306 0.8845 0.1848 1.4400 -0.2276 0.6378 -0.6884 0.5407 -0.2739 0.7952 -0.7126 1.2445

56 0.0803 0.8929 0.1974 1.4615 -0.1420 0.6467 -0.6219 0.5505 -0.1851 0.8281 -0.5165 1.2721

57 -0.1283 0.9044 0.0954 1.4907 -0.2177 0.6591 -0.7544 0.5639 -0.2124 0.8668 -0.1282 1.3099

58 0.0292 0.9191 0.2518 1.5270 -0.1192 0.6746 -0.7764 0.5808 -0.3143 0.9143 0.3685 1.3569

59 0.0695 0.9368 0.3095 1.5696 -0.2305 0.6932 -0.7705 0.6007 -0.4260 0.9714 0.8096 1.4122

60 0.1635 0.9572 0.3987 1.6177 -0.1939 0.7145 -0.8995 0.6235 -0.7197 1.0438 1.0291 1.4749

61 0.0150 0.9802 0.4393 1.6708 -0.3386 0.7382 -0.9750 0.6487 -0.7833 1.1551 1.6414 1.5441

2-8 2-9

Ball

2-4 2-5 2-6 2-7





1 -0.0016 0.5325 -0.0016 0.3488 -0.0016 0.6177 0.0000 0.7539 0.0000 0.9808 0.0000 0.4883

2 -0.1674 0.5351 -0.0604 0.3538 0.0426 0.6200 0.0000 0.7557 0.3000 1.0152 0.0000 0.4903

3 -0.2508 0.5428 -0.1158 0.3634 -0.0608 0.6266 0.0999 0.7610 0.4000 1.0566 -0.1000 0.4964

4 -0.3640 0.5554 -0.1050 0.3773 0.0261 0.6376 -0.1000 0.7697 0.2000 1.1042 -0.5000 0.5063

5 -0.2699 0.5726 0.0311 0.3951 -0.0499 0.6526 0.3000 0.7817 0.7000 1.1573 0.0000 0.5199

6 -0.3026 0.5940 -0.0177 0.4162 -0.1927 0.6714 0.3000 0.7969 0.8000 1.2152 0.2000 0.5369

7 -0.4485 0.6191 -0.0985 0.4402 -0.0985 0.6937 0.4000 0.8150 1.0000 1.2771 0.2000 0.5569

8 -0.4714 0.6475 -0.1014 0.4666 -0.2114 0.7192 0.7000 0.8360 1.2000 1.3427 0.3000 0.5797

9 -0.6019 0.6788 -0.1639 0.4950 -0.3019 0.7475 0.6000 0.8596 1.5000 1.4112 0.2000 0.6049

10 -0.1844 0.5351 -0.0344 0.3538 0.0256 0.6200 -0.2000 0.7557 0.2000 1.0152 0.1000 0.4903

11 -0.1758 0.5377 -0.0944 0.3572 -0.0273 0.6222 -0.1415 0.7574 0.2827 1.0315 -0.0707 0.4923

12 -0.2252 0.5454 -0.1430 0.3663 -0.3192 0.6288 0.1342 0.7627 0.5367 1.0673 0.0000 0.4984

13 -0.2788 0.5579 -0.1282 0.3800 -0.0542 0.6398 -0.2214 0.7714 0.3795 1.1125 -0.5376 0.5083

14 -0.2326 0.5750 -0.0531 0.3975 -0.1622 0.6547 0.2425 0.7834 0.7518 1.1642 -0.0485 0.5218

15 -0.2486 0.5963 -0.0708 0.4185 -0.1565 0.6735 0.2549 0.7985 0.7844 1.2212 0.0784 0.5387

16 -0.3969 0.6213 -0.2003 0.4423 -0.1059 0.6957 0.3781 0.8167 1.1179 1.2825 0.1808 0.5587

17 -0.5811 0.6496 -0.3046 0.4685 -0.1201 0.7211 0.5798 0.8376 1.3859 1.3474 0.1838 0.5814

18 -0.6290 0.6809 -0.2923 0.4969 -0.1949 0.7494 0.6202 0.8611 1.6000 1.4156 0.1985 0.6066

19 -0.1806 0.5428 0.1234 0.3634 -0.1606 0.6266 0.0000 0.7610 0.3000 1.0566 0.1000 0.4964

20 -0.2368 0.5454 -0.0021 0.3663 -0.0535 0.6288 0.0000 0.7627 0.2237 1.0673 -0.0447 0.4984

21 -0.5143 0.6560 -0.2578 0.4744 -0.3056 0.7269 0.5082 0.8424 1.3324 1.3616 0.1923 0.5865

22 -0.6733 0.6869 -0.3369 0.5023 -0.1325 0.7549 0.5578 0.8657 1.5037 1.4285 0.1940 0.6115

23 -0.0734 0.5555 0.2256 0.3773 -0.0734 0.6376 -0.1000 0.7697 0.2000 1.1042 0.2000 0.5063

24 -0.1965 0.5579 0.0520 0.3800 -0.1174 0.6398 -0.0316 0.7714 0.2848 1.1125 0.1265 0.5083

25 -0.2204 0.6665 -0.1103 0.4839 -0.1995 0.7363 0.4990 0.8502 1.5100 1.3846 0.2757 0.5950

26 -0.3863 0.6969 -0.2226 0.5112 -0.1323 0.7640 0.5735 0.8734 1.4045 1.4496 0.2224 0.6196

27 -0.0551 0.5726 0.2619 0.3951 -0.0550 0.6526 0.1000 0.7817 0.2001 1.1573 0.3000 0.5199

28 -0.2461 0.5750 0.1034 0.3975 -0.0593 0.6547 0.0243 0.7834 0.1456 1.1642 0.0243 0.5218

29 -0.4378 0.6808 -0.2771 0.4968 -0.0236 0.7494 0.4837 0.8611 1.3147 1.4156 0.2233 0.6066

30 -0.4733 0.7107 -0.2211 0.5234 -0.1245 0.7766 0.5367 0.8840 1.3863 1.4784 0.1342 0.6307

31 -0.2091 0.5940 0.1819 0.4162 -0.1591 0.6714 0.3000 0.7969 -0.1000 1.2152 0.2000 0.5369

32 -0.2315 0.5963 0.1466 0.4184 -0.1432 0.6735 0.0000 0.7985 0.2158 1.2211 0.1177 0.5387

33 -0.2935 0.6032 0.0529 0.4251 -0.2563 0.6796 0.0928 0.8035 0.3715 1.2386 0.0928 0.5443

34 -0.2872 0.6146 -0.0015 0.4359 -0.2872 0.6897 -0.0172 0.8118 0.2059 1.2664 -0.1544 0.5533

35 -0.3590 0.6301 -0.0564 0.4505 -0.0716 0.7036 0.0625 0.8232 0.4218 1.3031 -0.1406 0.5658

36 -0.2164 0.6496 -0.0042 0.4685 -0.0113 0.7211 0.1414 0.8376 0.7779 1.3474 0.1414 0.5814

37 -0.3424 0.6726 -0.1290 0.4895 -0.0530 0.7419 0.4353 0.8549 1.0627 1.3979 0.1536 0.5999

38 -0.4027 0.6989 -0.1277 0.5130 -0.2539 0.7658 0.5812 0.8749 1.1159 1.4538 0.2441 0.6212

39 -0.6307 0.7280 -0.1782 0.5387 -0.2364 0.7924 0.5830 0.8975 1.1872 1.5140 0.3074 0.6448

40 -0.1308 0.6191 0.2172 0.4402 -0.2808 0.6938 0.2000 0.8151 0.3001 1.2772 0.2000 0.5569

41 -0.3300 0.6213 0.0887 0.4422 -0.0834 0.6957 0.0986 0.8167 0.2138 1.2824 0.1315 0.5587

42 -0.5173 0.7203 -0.2492 0.5320 -0.2006 0.7854 0.5857 0.8915 0.9870 1.4983 0.2278 0.6386

43 -0.6172 0.7486 -0.2084 0.5568 -0.1632 0.8114 0.5200 0.9136 1.2600 1.5559 0.2200 0.6616

44 -0.1652 0.6475 0.1358 0.4666 -0.2952 0.7192 0.1000 0.8360 0.2000 1.3427 0.2000 0.5797

45 -0.2215 0.6496 0.0582 0.4685 -0.1027 0.7211 0.0990 0.8376 0.2829 1.3475 0.2263 0.5814

46 -0.2702 0.6560 0.0642 0.4743 -0.2702 0.7269 0.1511 0.8423 0.4808 1.3616 0.1236 0.5865

47 -0.3204 0.6664 -0.0330 0.4838 -0.2626 0.7363 -0.1182 0.8502 0.1576 1.3845 -0.1970 0.5950

48 -0.3902 0.6808 -0.1033 0.4968 -0.2301 0.7493 0.0496 0.8611 0.4465 1.4155 -0.0868 0.6066

49 -0.4001 0.6989 -0.2072 0.5130 -0.2304 0.7658 0.2790 0.8749 0.6393 1.4538 0.0349 0.6212

50 -0.4828 0.7203 -0.2767 0.5320 -0.1975 0.7854 0.4122 0.8915 0.9328 1.4983 0.0651 0.6386

51 -0.5858 0.7449 -0.3122 0.5535 -0.3949 0.8080 0.5657 0.9107 1.2021 1.5484 0.2121 0.6586

52 -0.6507 0.7723 -0.2792 0.5773 -0.4391 0.8333 0.4986 0.9324 1.1853 1.6032 0.3575 0.6809

53 -0.3181 0.6788 0.0719 0.4950 -0.5181 0.7475 0.3000 0.8596 0.1000 1.4113 0.2000 0.6049

54 -0.3214 0.6809 0.0977 0.4969 -0.3338 0.7494 0.0868 0.8611 0.0745 1.4156 0.1240 0.6066

55 -0.3950 0.6869 0.0365 0.5023 -0.4459 0.7549 0.2183 0.8658 0.5336 1.4285 0.1213 0.6115

56 -0.3843 0.6969 0.0230 0.5112 -0.1654 0.7640 0.1170 0.8734 0.2341 1.4496 -0.1054 0.6196

57 -0.4503 0.7107 -0.1153 0.5234 -0.3519 0.7766 0.0447 0.8840 0.2684 1.4784 -0.0447 0.6307

58 -0.5220 0.7280 -0.2293 0.5387 -0.2040 0.7924 0.3604 0.8975 0.5830 1.5140 0.2120 0.6448

59 -0.6466 0.7486 -0.2929 0.5568 -0.2505 0.8114 0.4800 0.9136 0.7201 1.5559 0.1800 0.6616

60 -0.9503 0.7723 -0.4197 0.5773 -0.3350 0.8333 0.6209 0.9324 0.8561 1.6032 0.2634 0.6809

61 -0.9537 0.7987 -0.3181 0.6001 -0.2678 0.8579 0.5657 0.9536 0.9900 1.6553 0.2121 0.7025

Ball

2-10 2-11 2-12 3-4 3-5 3-6





1 0.0000 0.3675 0.0000 0.2800 0.0000 0.7684 0.0000 0.5215 0.0000 0.3318 0.0000 0.6083

2 -0.2000 0.3700 -0.0270 0.5699 0.4999 0.7772 -0.1100 0.5239 -0.0030 0.3365 0.1000 0.6103

3 -0.2000 0.3773 -0.1109 0.6719 0.7999 0.8030 -0.1900 0.5309 -0.0550 0.3453 0.0000 0.6163

4 -0.7000 0.3892 -0.5590 0.7410 0.6999 0.8443 -0.5900 0.5423 -0.3311 0.3577 -0.2000 0.6262

5 -0.3000 0.4054 -0.1120 0.7961 1.5000 0.8990 -0.1200 0.5579 0.1810 0.3735 0.1000 0.6398

6 -0.3000 0.4252 -0.1900 0.8504 1.9000 0.9647 -0.1100 0.5774 0.1750 0.3922 0.0000 0.6568

7 -0.2000 0.4483 -0.1630 0.9116 2.3000 1.0394 -0.1500 0.6004 0.2000 0.4134 0.2000 0.6771

8 -0.2000 0.4741 -0.2080 0.9872 2.7000 1.1213 -0.1600 0.6264 0.2100 0.4368 0.1000 0.7003

9 -0.3000 0.5022 -0.2750 0.9013 3.3000 1.2090 -0.2000 0.6552 0.2380 0.4621 0.1000 0.7261

10 0.0000 0.3700 0.1750 0.7507 0.1000 0.7772 -0.1100 0.5239 0.0400 0.3365 0.1000 0.6103

11 -0.2122 0.3724 -0.0509 0.6009 0.1413 0.7859 -0.1486 0.5262 -0.0672 0.3397 0.0000 0.6123

12 -0.1789 0.3797 0.0653 0.6338 0.7603 0.8115 -0.0402 0.5332 0.0420 0.3479 -0.1342 0.6183

13 -0.6641 0.3916 -0.3172 0.6788 0.8854 0.8524 -0.5408 0.5446 -0.3902 0.3601 -0.3162 0.6282

14 -0.3638 0.4076 0.0415 0.7279 1.7462 0.9066 -0.1189 0.5602 0.0606 0.3757 -0.0485 0.6417

15 -0.3334 0.4274 -0.0251 0.7790 2.2945 0.9718 -0.1118 0.5796 0.0660 0.3942 -0.0196 0.6587

16 -0.3124 0.4503 -0.0958 0.8346 2.8112 1.0460 -0.1102 0.6024 0.0864 0.4153 0.1808 0.6789

17 -0.3253 0.4760 -0.2452 0.9006 3.1113 1.1273 -0.2630 0.6283 0.0134 0.4385 0.1980 0.7020

18 -0.3101 0.5040 -0.0976 0.9915 3.3737 1.2146 -0.1488 0.6570 0.1879 0.4637 0.2853 0.7278

19 0.0000 0.3773 0.4410 0.7110 -0.1000 0.8030 0.0800 0.5309 0.3840 0.3453 0.1000 0.6163

20 -0.1789 0.3797 0.2813 0.6474 0.0895 0.8115 -0.1386 0.5332 0.0962 0.3479 0.0447 0.6183

21 -0.2884 0.4817 -0.1575 0.8695 3.0631 1.1454 -0.1813 0.6342 0.0753 0.4437 0.0275 0.7073

22 -0.2910 0.5094 -0.1300 0.9513 3.3955 1.2312 -0.1528 0.6626 0.1836 0.4685 0.3881 0.7328

23 0.0000 0.3893 0.4540 0.7137 -0.2001 0.8444 0.1000 0.5423 0.3990 0.3577 0.1000 0.6262

24 -0.0949 0.3916 0.2153 0.6811 -0.1580 0.8524 -0.0791 0.5446 0.1694 0.3601 0.0000 0.6281

25 -0.2232 0.4911 0.0456 0.8540 2.7573 1.1747 0.1235 0.6438 0.2336 0.4522 0.1444 0.7159

26 -0.2809 0.5183 0.0281 0.9317 3.2771 1.2586 0.0620 0.6718 0.2258 0.4764 0.3160 0.7412

27 -0.1000 0.4054 0.5120 0.7276 -0.0001 0.8990 0.2000 0.5579 0.5170 0.3735 0.2000 0.6398

28 -0.1940 0.4076 0.2243 0.7093 -0.2668 0.9065 -0.1625 0.5601 0.1870 0.3756 0.0243 0.6417

29 -0.2729 0.5040 0.0500 0.8514 2.4309 1.2146 -0.0670 0.6570 0.0938 0.4637 0.3473 0.7278

30 -0.4025 0.5305 0.0072 0.9278 2.9068 1.2959 -0.0358 0.6845 0.2165 0.4873 0.3130 0.7527

31 -0.1000 0.4252 0.2510 0.7537 -0.1001 0.9647 -0.0500 0.5774 0.3410 0.3922 0.0000 0.6568

32 -0.2157 0.4273 0.1853 0.7320 -0.3922 0.9717 -0.1471 0.5795 0.2310 0.3942 -0.0588 0.6587

33 -0.2600 0.4337 0.1160 0.7090 0.0559 0.9926 -0.2043 0.5859 0.1420 0.4001 -0.1672 0.6643

34 -0.7032 0.4442 -0.0965 0.7073 0.1545 1.0263 -0.4289 0.5963 -0.1431 0.4097 -0.4288 0.6735

35 -0.5622 0.4583 -0.1764 0.7222 0.6094 1.0716 -0.3811 0.6105 -0.0786 0.4226 -0.0937 0.6861

36 -0.4243 0.4760 0.0933 0.7532 1.1315 1.1273 -0.0637 0.6283 0.1485 0.4385 0.1414 0.7020

37 -0.4225 0.4967 -0.0024 0.8016 1.5109 1.1919 -0.0461 0.6495 0.1673 0.4571 0.2433 0.7210

38 -0.3371 0.5201 0.0464 0.8623 2.1039 1.2639 -0.1023 0.6736 0.1727 0.4780 0.0465 0.7428

39 -0.3604 0.5458 0.0076 0.9379 2.9150 1.3423 -0.1929 0.7004 0.2596 0.5009 0.2014 0.7672

40 -0.1000 0.4483 0.3720 0.7899 -0.2001 1.0395 0.1500 0.6004 0.4980 0.4134 0.0000 0.6771

41 -0.1973 0.4503 0.0853 0.7483 -0.2795 1.0459 -0.1315 0.6024 0.2872 0.4153 0.1151 0.6789

42 -0.3471 0.5391 -0.0055 0.9002 1.8764 1.3219 -0.1540 0.6934 0.1141 0.4949 0.1627 0.7608

43 -0.4400 0.5640 0.0164 0.9665 2.8800 1.3969 -0.1340 0.7195 0.2748 0.5169 0.3200 0.7846

44 -0.1000 0.4741 0.2860 0.8428 -0.4000 1.1214 0.1300 0.6264 0.4310 0.4368 0.0000 0.7003

45 -0.0990 0.4760 0.0916 0.7501 -0.4950 1.1274 0.0226 0.6284 0.3024 0.4386 0.1414 0.7020

46 -0.3159 0.4817 0.0885 0.7184 -0.4258 1.1453 -0.0687 0.6342 0.2657 0.4437 -0.0687 0.7072

47 -0.6434 0.4911 -0.2138 0.7309 -0.6040 1.1746 -0.4123 0.6438 -0.1249 0.4521 -0.3545 0.7159

48 -0.5458 0.5040 -0.0960 0.7636 -0.1984 1.2145 -0.3213 0.6570 -0.0344 0.4637 -0.1612 0.7278

49 -0.4417 0.5201 -0.0773 0.8078 0.1395 1.2639 -0.2743 0.6736 -0.0814 0.4780 -0.1046 0.7428

50 -0.3579 0.5391 0.0309 0.8633 0.9869 1.3218 -0.1768 0.6934 0.0293 0.4949 0.1084 0.7608

51 -0.3535 0.5607 -0.1103 0.9278 1.4851 1.3872 -0.1909 0.7161 0.0827 0.5140 0.0000 0.7815

52 -0.4327 0.5847 -0.1242 1.0167 2.6435 1.4589 -0.1929 0.7413 0.1786 0.5352 0.0188 0.8047

53 -0.3000 0.5022 0.3020 0.9202 -0.7000 1.2090 0.1000 0.6552 0.4900 0.4621 -0.1000 0.7261

54 -0.2977 0.5040 0.1126 0.7502 -0.6822 1.2146 -0.0620 0.6570 0.3571 0.4637 -0.0744 0.7278

55 -0.3396 0.5094 0.0749 0.7743 -0.3637 1.2313 -0.0461 0.6626 0.3854 0.4685 -0.0970 0.7328

56 -0.5852 0.5183 -0.1485 0.8071 -0.4798 1.2586 -0.3477 0.6718 0.0597 0.4764 -0.1288 0.7412

57 -0.5814 0.5305 -0.0394 0.8454 0.0448 1.2959 -0.2773 0.6845 0.0577 0.4873 -0.1789 0.7527

58 -0.4452 0.5458 0.0170 0.8926 0.6997 1.3423 -0.1908 0.7004 0.1019 0.5009 0.1272 0.7672

59 -0.3600 0.5640 -0.0154 0.9491 1.2201 1.3970 -0.2360 0.7195 0.1176 0.5169 0.1600 0.7846

60 -0.4421 0.5847 -0.2624 1.0212 1.4864 1.4590 -0.4929 0.7414 0.0376 0.5352 0.1223 0.8047

61 -0.4243 0.6077 -0.2326 1.1326 2.1921 1.5273 -0.4031 0.7658 0.2326 0.5555 0.2828 0.8273

3-11 3-12

Ball

3-7 3-8 3-9 3-10





1 0.0000 1.1720 0.0000 0.8062 0.0000 0.7394 0.0000 0.7000 0.0000 1.0010 0.0000 0.8268

2 0.3000 1.2009 0.0000 0.8074 -0.2000 0.7405 -0.0270 0.8581 0.4999 1.0077 -0.1100 0.8282

3 0.3001 1.2360 -0.1999 0.8110 -0.3000 0.7441 -0.2109 0.9288 0.7000 1.0277 -0.2900 0.8325

4 0.3000 1.2768 -0.4000 0.8169 -0.6000 0.7500 -0.4589 0.9798 0.8000 1.0601 -0.4900 0.8397

5 0.4000 1.3228 -0.3000 0.8251 -0.6000 0.7581 -0.4119 1.0219 1.2000 1.1039 -0.4200 0.8496

6 0.5000 1.3735 -0.1000 0.8355 -0.6000 0.7685 -0.4900 1.0644 1.6000 1.1578 -0.4100 0.8621

7 0.6000 1.4283 -0.2000 0.8480 -0.6000 0.7810 -0.5630 1.1135 1.9000 1.2204 -0.5500 0.8772

8 0.5000 1.4869 -0.4000 0.8626 -0.9000 0.7955 -0.9080 1.1759 2.0000 1.2905 -0.8600 0.8947

9 0.9000 1.5487 -0.4000 0.8791 -0.9000 0.8119 -0.8750 1.1042 2.7000 1.3669 -0.8000 0.9144

10 0.4000 1.2009 0.3000 0.8074 0.2000 0.7405 0.3750 0.9874 0.3000 1.0077 0.0900 0.8282

11 0.4242 1.2147 0.0707 0.8086 -0.0707 0.7417 0.0906 0.8789 0.2828 1.0144 -0.0071 0.8297

12 0.4025 1.2451 -0.1342 0.8122 -0.3131 0.7453 -0.0689 0.9016 0.6261 1.0343 -0.1744 0.8340

13 0.6009 1.2840 -0.3162 0.8181 -0.4427 0.7512 -0.0958 0.9336 1.1068 1.0665 -0.3194 0.8411

14 0.5093 1.3288 -0.2910 0.8262 -0.6063 0.7593 -0.2010 0.9697 1.5037 1.1101 -0.3614 0.8510

15 0.5295 1.3788 -0.1765 0.8366 -0.5883 0.7696 -0.2800 1.0082 2.0396 1.1637 -0.3667 0.8635

16 0.7398 1.4331 -0.1973 0.8491 -0.6905 0.7821 -0.4739 1.0514 2.4331 1.2260 -0.4883 0.8785

17 0.8061 1.4911 -0.3960 0.8637 -0.9051 0.7966 -0.8250 1.1041 2.5314 1.2957 -0.8429 0.8960

18 0.9799 1.5527 -0.4217 0.8802 -0.9303 0.8129 -0.7178 1.1790 2.7536 1.3719 -0.7690 0.9157

19 0.3000 1.2360 0.1000 0.8110 0.0000 0.7441 0.4410 0.9575 -0.1000 1.0277 0.0800 0.8326

20 0.2237 1.2451 -0.0447 0.8122 -0.1789 0.7453 0.2813 0.9112 0.0895 1.0343 -0.1386 0.8340

21 0.8242 1.5039 -0.3159 0.8670 -0.7967 0.7999 -0.6657 1.0788 2.5548 1.3113 -0.6895 0.9000

22 0.9459 1.5644 -0.3638 0.8835 -0.8489 0.8162 -0.6878 1.1453 2.8376 1.3866 -0.7106 0.9196

23 0.3000 1.2768 0.3000 0.8169 0.1000 0.7500 0.5540 0.9593 -0.1001 1.0602 0.2000 0.8397

24 0.3164 1.2839 0.1582 0.8180 -0.0632 0.7511 0.2469 0.9353 -0.1263 1.0665 -0.0474 0.8411

25 1.0110 1.5246 -0.2232 0.8726 -0.7222 0.8053 -0.4534 1.0662 2.2583 1.3369 -0.3755 0.9066

26 0.8310 1.5836 -0.3511 0.8889 -0.8544 0.8215 -0.5454 1.1289 2.7036 1.4108 -0.5115 0.9261

27 0.1000 1.3228 0.2000 0.8251 -0.2000 0.7581 0.4120 0.9694 -0.1001 1.1039 0.1000 0.8496

28 0.1214 1.3288 0.0000 0.8262 -0.2183 0.7593 0.2000 0.9557 -0.2910 1.1100 -0.1868 0.8510

29 0.8310 1.5527 -0.2605 0.8802 -0.7566 0.8129 -0.4337 1.0639 1.9472 1.3719 -0.5507 0.9157

30 0.8497 1.6098 -0.4025 0.8964 -0.9391 0.8290 -0.5295 1.1254 2.3702 1.4440 -0.5724 0.9350

31 -0.4000 1.3735 -0.1000 0.8355 -0.4000 0.7685 -0.0490 0.9889 -0.4001 1.1578 -0.3500 0.8621

32 0.2158 1.3787 0.1177 0.8366 -0.2157 0.7696 0.1853 0.9724 -0.3922 1.1636 -0.1471 0.8635

33 0.2786 1.3942 0.0000 0.8401 -0.3528 0.7731 0.0232 0.9551 -0.0369 1.1810 -0.2971 0.8676

34 0.2231 1.4188 -0.1372 0.8457 -0.6860 0.7787 -0.0793 0.9536 0.1717 1.2093 -0.4117 0.8744

35 0.3593 1.4515 -0.2030 0.8536 -0.6247 0.7866 -0.2388 0.9645 0.5469 1.2478 -0.4436 0.8839

36 0.6364 1.4911 0.0000 0.8637 -0.5657 0.7965 -0.0481 0.9875 0.9900 1.2957 -0.2051 0.8960

37 0.6274 1.5367 -0.2817 0.8758 -0.8578 0.8086 -0.4378 1.0246 1.0756 1.3519 -0.4814 0.9105

38 0.5347 1.5874 -0.3371 0.8900 -0.9184 0.8226 -0.5348 1.0722 1.5227 1.4155 -0.6835 0.9273

39 0.6042 1.6424 -0.2756 0.9060 -0.9434 0.8385 -0.5754 1.1335 2.3320 1.4855 -0.7759 0.9464

40 0.1001 1.4284 0.0000 0.8480 -0.3000 0.7810 0.1720 1.0163 -0.4001 1.2205 -0.0500 0.8772

41 0.1151 1.4330 0.0329 0.8491 -0.2959 0.7821 -0.0133 0.9843 -0.3781 1.2259 -0.2302 0.8785

42 0.4013 1.6280 -0.3579 0.9018 -0.9328 0.8343 -0.5912 1.1026 1.2907 1.4672 -0.7397 0.9414

43 0.7400 1.6808 -0.3000 0.9176 -0.9600 0.8499 -0.5036 1.1569 2.3600 1.5349 -0.6540 0.9602

44 0.1000 1.4869 0.1000 0.8626 -0.2000 0.7955 0.1860 1.0575 -0.5000 1.2905 0.0300 0.8947

45 0.1839 1.4912 0.1273 0.8637 -0.1980 0.7966 -0.0074 0.9852 -0.5940 1.2958 -0.0764 0.8960

46 0.3297 1.5039 -0.0275 0.8670 -0.4670 0.7999 -0.0626 0.9611 -0.5769 1.3113 -0.2198 0.9000

47 0.2758 1.5245 -0.0788 0.8725 -0.5252 0.8053 -0.0956 0.9704 -0.4858 1.3368 -0.2941 0.9065

48 0.3969 1.5526 -0.1364 0.8802 -0.5954 0.8129 -0.1456 0.9950 -0.2480 1.3718 -0.3709 0.9157

49 0.3604 1.5873 -0.2441 0.8900 -0.7207 0.8226 -0.3563 1.0289 -0.1395 1.4155 -0.5533 0.9273

50 0.5206 1.6280 -0.3471 0.9018 -0.7701 0.8343 -0.3812 1.0727 0.5748 1.4672 -0.5889 0.9414

51 0.6364 1.6739 -0.3536 0.9155 -0.9192 0.8479 -0.6760 1.1248 0.9194 1.5260 -0.7566 0.9577

52 0.6867 1.7244 -0.1411 0.9311 -0.9313 0.8633 -0.6228 1.1988 2.1449 1.5912 -0.6914 0.9762

53 -0.2000 1.5487 -0.1000 0.8791 -0.6000 0.8119 0.0020 1.1197 -1.0000 1.3670 -0.2000 0.9144

54 -0.0124 1.5527 0.0372 0.8802 -0.3845 0.8129 0.0258 0.9847 -0.7690 1.3719 -0.1488 0.9157

55 0.3153 1.5644 -0.0970 0.8835 -0.5578 0.8162 -0.1434 1.0031 -0.5820 1.3866 -0.2644 0.9196

56 0.1171 1.5836 -0.2224 0.8889 -0.7023 0.8215 -0.2655 1.0284 -0.5968 1.4108 -0.4647 0.9261

57 0.2236 1.6098 -0.0894 0.8964 -0.6261 0.8290 -0.0841 1.0585 0.0001 1.4440 -0.3220 0.9350

58 0.2226 1.6424 -0.1484 0.9060 -0.8056 0.8385 -0.3434 1.0963 0.3393 1.4855 -0.5512 0.9464

59 0.2401 1.6808 -0.3000 0.9176 -0.8400 0.8499 -0.4954 1.1424 0.7401 1.5349 -0.7160 0.9602

60 0.2352 1.7244 -0.3575 0.9311 -1.0630 0.8633 -0.8833 1.2025 0.8655 1.5912 -1.1138 0.9762

61 0.4243 1.7727 -0.3536 0.9464 -0.9899 0.8784 -0.7983 1.2981 1.6264 1.6538 -0.9687 0.9943

Ball

4-5 4-6 4-7 4-8 4-9 4-10





1 0.0000 0.7223 0.0000 0.8841 0.0000 1.0216 0.0000 0.9697 0.0000 0.9400 0.0000 1.1814

2 -0.0030 0.7244 0.1000 0.8854 -0.3000 1.0542 -0.5000 1.0039 -0.3270 1.0935 0.1999 1.2145

3 -0.1550 0.7284 -0.0999 0.8895 -0.5000 1.0931 -0.6000 1.0445 -0.5109 1.1832 0.3999 1.2623

4 -0.2310 0.7341 -0.1000 0.8961 -0.7000 1.1376 -0.9000 1.0906 -0.7590 1.2597 0.5000 1.3231

5 -0.1190 0.7416 -0.2000 0.9054 -0.7000 1.1870 -1.0000 1.1415 -0.8120 1.3314 0.8000 1.3953

6 -0.1250 0.7507 -0.3000 0.9172 -0.6000 1.2408 -1.1000 1.1968 -0.9900 1.4052 1.1000 1.4772

7 -0.2000 0.7615 -0.2000 0.9313 -0.8000 1.2984 -1.2000 1.2557 -1.1630 1.4855 1.3000 1.5672

8 -0.4900 0.7738 -0.6000 0.9478 -0.9000 1.3594 -1.4000 1.3178 -1.4080 1.5769 1.5000 1.6641

9 -0.3620 0.7877 -0.5000 0.9665 -1.3000 1.4232 -1.8000 1.3827 -1.7750 1.5723 1.8000 1.7667

10 0.2400 0.7244 0.3000 0.8854 -0.1000 1.0543 -0.2000 1.0040 -0.0250 1.1977 -0.0999 1.2145

11 0.0743 0.7258 0.1414 0.8868 -0.3535 1.0697 -0.4949 1.0200 -0.3337 1.1238 -0.1414 1.2326

12 -0.0921 0.7296 -0.2683 0.8908 -0.5367 1.1032 -0.7155 1.0549 -0.4714 1.1706 0.2236 1.2756

13 -0.1688 0.7352 -0.0948 0.8975 -0.9171 1.1454 -1.0435 1.0986 -0.6966 1.2306 0.5059 1.3342

14 -0.1819 0.7426 -0.2910 0.9067 -0.8004 1.1935 -1.1157 1.1482 -0.7103 1.2969 0.9944 1.4050

15 -0.1889 0.7517 -0.2745 0.9185 -0.7060 1.2464 -1.1179 1.2025 -0.8095 1.3675 1.5101 1.4858

16 -0.2917 0.7625 -0.1973 0.9326 -0.9371 1.3034 -1.4303 1.2607 -1.2138 1.4433 1.6933 1.5751

17 -0.5664 0.7748 -0.3818 0.9491 -1.2021 1.3638 -1.7112 1.3223 -1.6311 1.5274 1.7253 1.6712

18 -0.4323 0.7886 -0.3349 0.9678 -1.4016 1.4273 -1.9101 1.3868 -1.6977 1.6286 1.7737 1.7733

19 0.3840 0.7284 0.1000 0.8895 -0.2000 1.0932 -0.3000 1.0445 0.1410 1.2059 -0.4000 1.2623

20 0.0962 0.7296 0.0447 0.8908 -0.2684 1.1032 -0.4026 1.0549 0.0576 1.1780 -0.1342 1.2756

21 -0.4330 0.7776 -0.4807 0.9529 -1.1401 1.3770 -1.6208 1.3357 -1.4899 1.5193 1.7307 1.6923

22 -0.3742 0.7913 -0.1698 0.9714 -1.3097 1.4393 -1.7948 1.3990 -1.6337 1.6133 1.8918 1.7927

23 0.4990 0.7341 0.2000 0.8961 0.0000 1.1377 -0.2000 1.0906 0.2540 1.2439 -0.4001 1.3232

24 0.2011 0.7352 0.0316 0.8975 -0.1582 1.1453 -0.3796 1.0985 -0.0695 1.2318 -0.4427 1.3341

25 -0.2654 0.7822 -0.3545 0.9591 -1.2342 1.3984 -1.7332 1.3575 -1.4644 1.5267 1.2473 1.7267

26 -0.3477 0.7958 -0.2575 0.9775 -1.1821 1.4590 -1.6854 1.4190 -1.3764 1.6165 1.8726 1.8245

27 0.4170 0.7416 0.1000 0.9054 0.1000 1.1870 -0.3000 1.1415 0.3119 1.2916 -0.2001 1.3953

28 0.1627 0.7426 0.0000 0.9067 -0.1214 1.1934 -0.3397 1.1481 0.0787 1.2865 -0.4124 1.4049

29 -0.3899 0.7886 -0.1364 0.9677 -1.0915 1.4273 -1.5876 1.3868 -1.2647 1.5473 1.1162 1.7732

30 -0.3202 0.8020 -0.2236 0.9860 -1.2522 1.4858 -1.7888 1.4461 -1.3792 1.6342 1.5205 1.8679

31 0.0410 0.7507 -0.3000 0.9172 0.3000 1.2408 0.0000 1.1968 0.3509 1.3489 -0.0001 1.4772

32 0.2310 0.7517 -0.0588 0.9185 -0.0981 1.2464 -0.4316 1.2024 -0.0305 1.3413 -0.6080 1.4857

33 0.0492 0.7547 -0.2600 0.9224 -0.2786 1.2626 -0.6315 1.2191 -0.2555 1.3419 -0.3156 1.5111

34 -0.1259 0.7596 -0.4116 0.9288 -0.3603 1.2885 -0.9091 1.2455 -0.3024 1.3617 -0.0513 1.5515

35 -0.1410 0.7663 -0.1561 0.9377 -0.5624 1.3226 -0.9840 1.2803 -0.5982 1.3967 0.1876 1.6055

36 0.0071 0.7748 0.0000 0.9491 -0.6364 1.3638 -1.2021 1.3223 -0.6845 1.4454 0.3536 1.6711

37 -0.2680 0.7849 -0.1920 0.9628 -0.9091 1.4109 -1.4853 1.3701 -1.0652 1.5077 0.4482 1.7467

38 -0.4085 0.7967 -0.5348 0.9788 -0.8718 1.4629 -1.4530 1.4229 -1.0695 1.5804 0.9880 1.8308

39 -0.3234 0.8099 -0.3816 0.9969 -0.8798 1.5191 -1.5476 1.4798 -1.1796 1.6648 1.7278 1.9219

40 0.2980 0.7615 -0.2000 0.9314 -0.1000 1.2985 -0.4000 1.2557 0.0719 1.4142 -0.5001 1.5673

41 0.1886 0.7625 0.0164 0.9326 -0.0822 1.3033 -0.4110 1.2607 -0.1284 1.3952 -0.4932 1.5750

42 -0.4716 0.8064 -0.4230 0.9921 -0.7592 1.5045 -1.3341 1.4650 -0.9925 1.6328 0.8894 1.8981

43 -0.2452 0.8194 -0.2000 1.0099 -1.0400 1.5582 -1.7000 1.5193 -1.2436 1.7101 1.6200 1.9854

44 0.3310 0.7738 -0.1000 0.9478 0.0000 1.3594 -0.3000 1.3178 0.0860 1.4907 -0.6000 1.6641

45 0.2034 0.7748 0.0424 0.9491 -0.0566 1.3639 -0.3819 1.3223 -0.1912 1.4438 -0.7779 1.6712

46 0.1145 0.7776 -0.2198 0.9528 -0.3572 1.3770 -0.7967 1.3357 -0.3923 1.4381 -0.9066 1.6923

47 -0.0067 0.7822 -0.2363 0.9591 -0.3546 1.3983 -0.8010 1.3574 -0.3714 1.4614 -0.7616 1.7266

48 -0.0840 0.7886 -0.2109 0.9677 -0.5334 1.4273 -0.9923 1.3868 -0.5425 1.5008 -0.6450 1.7732

49 -0.3604 0.7967 -0.3836 0.9788 -0.6045 1.4629 -1.0811 1.4229 -0.7166 1.5513 -0.4999 1.8307

50 -0.3829 0.8064 -0.3037 0.9921 -0.8677 1.5045 -1.2907 1.4650 -0.9018 1.6127 0.0542 1.8981

51 -0.4830 0.8177 -0.5657 1.0076 -0.9900 1.5512 -1.5557 1.5123 -1.3125 1.6832 0.2829 1.9740

52 -0.3199 0.8305 -0.4798 1.0252 -0.8279 1.6024 -1.6181 1.5640 -1.3095 1.7714 1.4582 2.0573

53 0.1900 0.7877 -0.4000 0.9665 0.1000 1.4233 -0.4000 1.3827 0.2020 1.5832 -0.8001 1.7667

54 0.2703 0.7886 -0.1612 0.9678 0.0496 1.4273 -0.3721 1.3868 0.0382 1.4940 -0.7566 1.7733

55 0.1671 0.7913 -0.3153 0.9714 -0.4124 1.4394 -0.8732 1.3991 -0.4587 1.5157 -0.8974 1.7927

56 -0.0574 0.7958 -0.2458 0.9775 -0.3395 1.4590 -0.8194 1.4190 -0.3826 1.5480 -0.7139 1.8245

57 0.0130 0.8020 -0.2236 0.9860 -0.3131 1.4858 -0.8497 1.4461 -0.3077 1.5889 -0.2236 1.8679

58 -0.2585 0.8099 -0.2332 0.9969 -0.3710 1.5191 -1.0282 1.4798 -0.5661 1.6397 0.1166 1.9219

59 -0.3624 0.8195 -0.3200 1.0099 -0.5400 1.5582 -1.0801 1.5193 -0.7355 1.7003 0.5001 1.9854

60 -0.5833 0.8305 -0.4986 1.0252 -0.5927 1.6024 -1.2982 1.5640 -1.1185 1.7740 0.6303 2.0574

61 -0.3330 0.8431 -0.2828 1.0425 -0.7778 1.6512 -1.4142 1.6132 -1.2226 1.8750 1.2021 2.1367

5-8 5-9

Ball

4-11 4-12 5-6 5-7





1 0.0000 1.0379 0.0000 0.9567 0.0000 1.0841 0.0000 0.4655 0.0000 0.4000 0.0000 0.8198

2 -0.4100 1.0703 -0.3030 0.9921 -0.2000 1.1151 -0.2000 0.4666 -0.0270 0.6369 0.4999 0.8276

3 -0.5900 1.1092 -0.4550 1.0333 -0.4000 1.1526 -0.1000 0.4701 -0.0109 0.7281 0.8999 0.8506

4 -0.7900 1.1541 -0.5310 1.0797 -0.4000 1.1958 -0.2000 0.4758 -0.0590 0.7900 1.2000 0.8876

5 -0.8200 1.2042 -0.5190 1.1306 -0.6000 1.2442 -0.3000 0.4838 -0.1120 0.8387 1.5000 0.9370

6 -0.9100 1.2589 -0.6250 1.1854 -0.8000 1.2972 -0.5000 0.4938 -0.3900 0.8867 1.7000 0.9968

7 -1.1500 1.3177 -0.8000 1.2437 -0.8000 1.3543 -0.4000 0.5057 -0.3630 0.9412 2.1000 1.0655

8 -1.3600 1.3799 -0.9900 1.3049 -1.1000 1.4150 -0.5000 0.5195 -0.5080 1.0099 2.4000 1.1413

9 -1.7000 1.4453 -1.2620 1.3686 -1.4000 1.4788 -0.5000 0.5350 -0.4750 0.9200 3.1000 1.2229

10 -0.3100 1.0703 -0.1599 0.9921 -0.1000 1.1151 -0.1000 0.4666 0.0750 0.8027 0.0000 0.8276

11 -0.4313 1.0857 -0.3500 1.0085 -0.2828 1.1299 -0.1414 0.4678 0.0198 0.6642 0.2121 0.8353

12 -0.5769 1.1193 -0.4946 1.0439 -0.6708 1.1623 -0.1789 0.4713 0.0653 0.6925 0.7603 0.8581

13 -0.9202 1.1619 -0.7697 1.0877 -0.6957 1.2034 -0.1265 0.4770 0.2204 0.7314 1.4230 0.8948

14 -0.8707 1.2107 -0.6912 1.1372 -0.8004 1.2506 -0.3153 0.4849 0.0900 0.7739 1.7947 0.9438

15 -0.8962 1.2646 -0.7184 1.1911 -0.8041 1.3028 -0.4118 0.4949 -0.1035 0.8180 2.2161 1.0033

16 -1.2281 1.3227 -1.0315 1.2487 -0.9371 1.3593 -0.4932 0.5068 -0.2767 0.8664 2.6304 1.0715

17 -1.6490 1.3845 -1.3725 1.3093 -1.1879 1.4194 -0.5091 0.5205 -0.4291 0.9249 2.9274 1.1469

18 -1.7489 1.4495 -1.4121 1.3727 -1.3148 1.4829 -0.5085 0.5360 -0.2961 1.0081 3.1753 1.2282

19 -0.2200 1.1093 0.0840 1.0334 -0.2000 1.1526 -0.1000 0.4701 0.3410 0.7643 -0.2000 0.8506

20 -0.3623 1.1193 -0.1275 1.0439 -0.1790 1.1623 -0.1342 0.4713 0.3260 0.7050 0.1342 0.8581

21 -1.5137 1.3980 -1.2571 1.3225 -1.3049 1.4326 -0.4807 0.5237 -0.3498 0.8934 2.8708 1.1637

22 -1.6565 1.4618 -1.3201 1.3847 -1.1157 1.4949 -0.4851 0.5390 -0.3240 0.9675 3.2014 1.2438

23 -0.1001 1.1541 0.1989 1.0798 -0.1001 1.1958 -0.2000 0.4758 0.2540 0.7643 -0.4001 0.8876

24 -0.3639 1.1619 -0.1153 1.0877 -0.2848 1.2033 -0.2214 0.4770 0.0888 0.7336 -0.2845 0.8948

25 -1.3865 1.4198 -1.2764 1.3438 -1.3655 1.4539 -0.4990 0.5288 -0.2301 0.8762 2.4816 1.1909

26 -1.3424 1.4820 -1.1787 1.4042 -1.0885 1.5147 -0.5033 0.5440 -0.1943 0.9463 3.0547 1.2694

27 -0.0001 1.2042 0.3169 1.1306 0.0000 1.2442 -0.4000 0.4838 0.2120 0.7740 -0.3001 0.9370

28 -0.3082 1.2107 0.0413 1.1371 -0.1214 1.2505 -0.2183 0.4849 0.2000 0.7563 -0.2910 0.9438

29 -1.3817 1.4494 -1.2209 1.3727 -0.9674 1.4829 -0.4961 0.5360 -0.1733 0.8707 2.2077 1.2282

30 -1.4221 1.5094 -1.1699 1.4308 -1.0733 1.5416 -0.5367 0.5510 -0.1270 0.9397 2.7727 1.3044

31 0.0500 1.2589 0.4410 1.1854 0.1000 1.2973 -0.3000 0.4938 0.0510 0.7944 -0.3001 0.9969

32 -0.3629 1.2645 0.0152 1.1910 -0.2746 1.3027 -0.3334 0.4949 0.0676 0.7733 -0.5099 1.0033

33 -0.5758 1.2811 -0.2294 1.2075 -0.5386 1.3188 -0.3528 0.4982 0.0232 0.7502 -0.0369 1.0224

34 -0.6347 1.3075 -0.3490 1.2336 -0.6347 1.3444 -0.5488 0.5036 0.0579 0.7460 0.3089 1.0534

35 -0.8029 1.3423 -0.5004 1.2680 -0.5155 1.3783 -0.4217 0.5111 -0.0358 0.7568 0.7499 1.0952

36 -0.8415 1.3844 -0.6294 1.3093 -0.6364 1.4194 -0.5657 0.5205 -0.0481 0.7821 0.9900 1.1468

37 -1.1088 1.4326 -0.8954 1.3563 -0.8195 1.4664 -0.5762 0.5319 -0.1561 0.8239 1.3573 1.2070

38 -1.2182 1.4859 -0.9432 1.4081 -1.0694 1.5186 -0.5812 0.5450 -0.1977 0.8775 1.8598 1.2744

39 -1.3801 1.5435 -0.9276 1.4638 -0.9858 1.5750 -0.6678 0.5598 -0.2998 0.9461 2.6076 1.3480

40 -0.1501 1.3177 0.1979 1.2437 -0.3001 1.3544 -0.3000 0.5057 0.1720 0.8239 -0.4001 1.0655

41 -0.3453 1.3227 0.0734 1.2486 -0.0987 1.3592 -0.3288 0.5068 -0.0462 0.7836 -0.4110 1.0715

42 -1.1410 1.5285 -0.8729 1.4493 -0.8243 1.5603 -0.5749 0.5559 -0.2333 0.9103 1.6486 1.3288

43 -1.3940 1.5836 -0.9852 1.5025 -0.9400 1.6143 -0.6600 0.5704 -0.2036 0.9702 2.6600 1.3995

44 -0.0700 1.3800 0.2310 1.3049 -0.2000 1.4150 -0.3000 0.5195 0.0860 0.8692 -0.6000 1.1413

45 -0.2603 1.3845 0.0195 1.3093 -0.1414 1.4195 -0.3253 0.5206 -0.1346 0.7791 -0.7213 1.1469

46 -0.5495 1.3979 -0.2151 1.3225 -0.5495 1.4326 -0.4396 0.5237 -0.0352 0.7472 -0.5494 1.1636

47 -0.5699 1.4198 -0.2825 1.3438 -0.5121 1.4539 -0.4464 0.5288 -0.0168 0.7568 -0.4070 1.1909

48 -0.7678 1.4494 -0.4809 1.3726 -0.6078 1.4828 -0.4589 0.5360 -0.0092 0.7851 -0.1116 1.2281

49 -0.9137 1.4859 -0.7207 1.4081 -0.7440 1.5185 -0.4766 0.5450 -0.1122 0.8240 0.1046 1.2744

50 -1.1095 1.5285 -0.9035 1.4493 -0.8243 1.5603 -0.4230 0.5559 -0.0341 0.8739 0.9219 1.3288

51 -1.3931 1.5765 -1.1194 1.4956 -1.2021 1.6073 -0.5657 0.5684 -0.3225 0.9325 1.2729 1.3903

52 -1.3782 1.6290 -1.0067 1.5462 -1.1665 1.6589 -0.7902 0.5826 -0.4817 1.0155 2.2860 1.4581

53 0.0000 1.4453 0.3900 1.3687 -0.2000 1.4788 -0.5000 0.5350 0.1020 0.9385 -0.9000 1.2230

54 -0.1365 1.4495 0.2826 1.3727 -0.1489 1.4829 -0.4217 0.5360 -0.0114 0.7720 -0.8062 1.2282

55 -0.5797 1.4618 -0.1483 1.3847 -0.6306 1.4950 -0.4608 0.5390 -0.0464 0.7941 -0.4850 1.2438

56 -0.5818 1.4820 -0.1745 1.4042 -0.3629 1.5147 -0.4799 0.5440 -0.0431 0.8238 -0.3744 1.2694

57 -0.5457 1.5094 -0.2107 1.4308 -0.4472 1.5416 -0.5367 0.5510 0.0053 0.8584 0.0895 1.3044

58 -0.7739 1.5435 -0.4812 1.4638 -0.4558 1.5750 -0.6572 0.5598 -0.1951 0.9012 0.4877 1.3480

59 -0.9561 1.5836 -0.6025 1.5025 -0.5600 1.6143 -0.5400 0.5704 -0.1954 0.9529 1.0401 1.3995

60 -1.3490 1.6291 -0.8185 1.5462 -0.7338 1.6589 -0.7055 0.5826 -0.5258 1.0200 1.2230 1.4581

61 -1.3930 1.6791 -0.7573 1.5942 -0.7071 1.7081 -0.6364 0.5964 -0.4448 1.1266 1.9799 1.5229

Ball

5-10 5-11 5-12 6-7 6-8 6-9





1 0.0000 0.5946 0.0000 0.4378 0.0000 0.6720 0.0000 0.2380 0.0000 0.7541 0.0000 0.5002

2 -0.1100 0.5961 -0.0030 0.4406 0.1000 0.6733 0.1730 0.5497 0.6999 0.7625 0.0900 0.5018

3 -0.0900 0.6004 0.0450 0.4448 0.1000 0.6771 0.0891 0.6527 0.9999 0.7871 0.0100 0.5064

4 -0.0900 0.6075 0.1690 0.4504 0.3000 0.6834 0.1411 0.7206 1.4000 0.8264 0.1100 0.5140

5 -0.1200 0.6173 0.1810 0.4574 0.1000 0.6921 0.1880 0.7730 1.8000 0.8786 0.1800 0.5245

6 -0.3100 0.6296 -0.0250 0.4656 -0.2000 0.7032 0.1100 0.8239 2.2000 0.9414 0.1900 0.5376

7 -0.3500 0.6444 0.0000 0.4751 0.0000 0.7164 0.0370 0.8813 2.5000 1.0129 0.0500 0.5532

8 -0.4600 0.6615 -0.0900 0.4858 -0.2000 0.7318 -0.0080 0.9531 2.9000 1.0914 0.0400 0.5712

9 -0.4000 0.6806 0.0380 0.4975 -0.1000 0.7492 0.0250 0.8559 3.6000 1.1755 0.1000 0.5912

10 -0.2100 0.5961 -0.0600 0.4406 0.0000 0.6733 0.1750 0.7354 0.1000 0.7625 -0.1100 0.5018

11 -0.0778 0.5975 0.0035 0.4422 0.0707 0.6746 0.1612 0.5810 0.3535 0.7708 0.0636 0.5033

12 -0.0402 0.6018 0.0420 0.4460 -0.1342 0.6784 0.2442 0.6127 0.9392 0.7951 0.1386 0.5079

13 -0.0032 0.6089 0.1474 0.4515 0.2214 0.6846 0.3469 0.6557 1.5495 0.8341 0.1233 0.5155

14 -0.0703 0.6187 0.1091 0.4583 0.0000 0.6933 0.4053 0.7020 2.1100 0.8858 0.2450 0.5259

15 -0.1902 0.6310 -0.0124 0.4665 -0.0981 0.7044 0.3083 0.7493 2.6279 0.9482 0.2216 0.5390

16 -0.2910 0.6457 -0.0944 0.4760 0.0000 0.7176 0.2165 0.8008 3.1236 1.0192 0.2022 0.5546

17 -0.4469 0.6628 -0.1704 0.4866 0.0141 0.7330 0.0800 0.8625 3.4365 1.0972 0.0622 0.5725

18 -0.3473 0.6819 -0.0105 0.4983 0.0868 0.7503 0.2125 0.9500 3.6838 1.1809 0.1612 0.5925

19 -0.0200 0.6004 0.2840 0.4448 0.0000 0.6771 0.4410 0.6929 -0.1000 0.7871 0.0800 0.5064

20 -0.0939 0.6018 0.1409 0.4460 0.0894 0.6784 0.4602 0.6268 0.2684 0.7951 0.0403 0.5079

21 -0.3736 0.6666 -0.1170 0.4890 -0.1648 0.7365 0.1309 0.8284 3.3515 1.1145 0.1072 0.5766

22 -0.3468 0.6856 -0.0104 0.5005 0.1940 0.7537 0.1611 0.9064 3.6865 1.1969 0.1383 0.5964

23 -0.1000 0.6075 0.1990 0.4504 -0.1000 0.6834 0.4540 0.6924 -0.2001 0.8265 0.1000 0.5140

24 -0.2056 0.6089 0.0429 0.4515 -0.1265 0.6846 0.3101 0.6581 -0.0631 0.8341 0.0158 0.5155

25 -0.1523 0.6730 -0.0421 0.4929 -0.1313 0.7423 0.2688 0.8093 2.9805 1.1426 0.3467 0.5832

26 -0.1603 0.6918 0.0034 0.5043 0.0936 0.7594 0.3090 0.8833 3.5580 1.2231 0.3429 0.6028

27 -0.1000 0.6173 0.2170 0.4574 -0.1000 0.6921 0.6120 0.7022 0.0999 0.8786 0.3000 0.5245

28 -0.1868 0.6186 0.1627 0.4583 0.0000 0.6933 0.4183 0.6826 -0.0727 0.8858 0.0315 0.5259

29 -0.2902 0.6819 -0.1295 0.4983 0.1240 0.7503 0.3229 0.8027 2.7038 1.1809 0.2059 0.5925

30 -0.1699 0.7005 0.0823 0.5095 0.1789 0.7672 0.4097 0.8756 3.3093 1.2590 0.3667 0.6118

31 -0.2500 0.6296 0.1410 0.4656 -0.2000 0.7032 0.3510 0.7236 -0.0001 0.9414 0.0500 0.5376

32 -0.2648 0.6310 0.1133 0.4665 -0.1765 0.7044 0.4010 0.7003 -0.1765 0.9481 0.0686 0.5390

33 -0.2971 0.6351 0.0492 0.4692 -0.2600 0.7080 0.3760 0.6743 0.3159 0.9681 0.0557 0.5433

34 -0.2745 0.6418 0.0113 0.4734 -0.2744 0.7140 0.6067 0.6691 0.8578 1.0003 0.2744 0.5504

35 -0.2406 0.6510 0.0620 0.4793 0.0469 0.7224 0.3859 0.6802 1.1716 1.0438 0.1811 0.5602

36 -0.2051 0.6627 0.0071 0.4866 0.0000 0.7330 0.5176 0.7073 1.5557 1.0971 0.3606 0.5725

37 -0.1997 0.6768 0.0137 0.4952 0.0896 0.7457 0.4201 0.7521 1.9334 1.1591 0.3764 0.5872

38 -0.3464 0.6931 -0.0714 0.5050 -0.1976 0.7605 0.3835 0.8091 2.4410 1.2283 0.2348 0.6041

39 -0.5003 0.7114 -0.0478 0.5160 -0.1060 0.7772 0.3680 0.8816 3.2754 1.3036 0.1675 0.6231

40 -0.0500 0.6444 0.2980 0.4751 -0.2000 0.7164 0.4720 0.7547 -0.1001 1.0130 0.2500 0.5532

41 -0.2631 0.6457 0.1557 0.4760 -0.0164 0.7176 0.2826 0.7104 -0.0822 1.0191 0.0657 0.5546

42 -0.3818 0.7065 -0.1137 0.5131 -0.0651 0.7728 0.3416 0.8435 2.2235 1.2839 0.1931 0.6181

43 -0.3540 0.7245 0.0548 0.5239 0.1000 0.7892 0.4564 0.9065 3.3200 1.3561 0.3060 0.6366

44 -0.0700 0.6615 0.2310 0.4858 -0.2000 0.7318 0.3860 0.8026 -0.3000 1.0915 0.2300 0.5712

45 -0.2037 0.6628 0.0761 0.4866 -0.0848 0.7330 0.1906 0.7039 -0.3960 1.0973 0.1216 0.5725

46 -0.1923 0.6666 0.1420 0.4889 -0.1923 0.7365 0.4044 0.6680 -0.1099 1.1144 0.2472 0.5765

47 -0.2154 0.6730 0.0721 0.4929 -0.1576 0.7423 0.4296 0.6782 0.0394 1.1425 0.2311 0.5832

48 -0.2344 0.6819 0.0525 0.4982 -0.0744 0.7503 0.4497 0.7089 0.3473 1.1808 0.2245 0.5925

49 -0.3092 0.6931 -0.1162 0.5050 -0.1395 0.7605 0.3644 0.7508 0.5812 1.2283 0.1674 0.6041

50 -0.2419 0.7065 -0.0358 0.5131 0.0434 0.7728 0.3889 0.8040 1.3449 1.2839 0.1812 0.6181

51 -0.4031 0.7221 -0.1294 0.5225 -0.2121 0.7871 0.2432 0.8661 1.8386 1.3467 0.1626 0.6342

52 -0.5503 0.7397 -0.1788 0.5329 -0.3387 0.8032 0.3086 0.9537 3.0762 1.4157 0.2399 0.6523

53 -0.1000 0.6806 0.2900 0.4975 -0.3000 0.7492 0.6020 0.8758 -0.4000 1.1755 0.4000 0.5912

54 -0.1861 0.6819 0.2330 0.4983 -0.1985 0.7503 0.4103 0.6943 -0.3845 1.1809 0.2357 0.5925

55 -0.1674 0.6856 0.2641 0.5005 -0.2183 0.7537 0.4145 0.7184 -0.0242 1.1969 0.2934 0.5964

56 -0.2423 0.6918 0.1650 0.5043 -0.0234 0.7594 0.4368 0.7507 0.1054 1.2231 0.2376 0.6028

57 -0.2326 0.7005 0.1024 0.5095 -0.1342 0.7672 0.5420 0.7877 0.6262 1.2590 0.3041 0.6118

58 -0.4028 0.7114 -0.1101 0.5160 -0.0848 0.7772 0.4621 0.8332 1.1449 1.3036 0.2544 0.6231

59 -0.4160 0.7245 -0.0624 0.5239 -0.0200 0.7892 0.3446 0.8880 1.5801 1.3561 0.1240 0.6366

60 -0.7564 0.7397 -0.2258 0.5329 -0.1411 0.8032 0.1798 0.9584 1.9285 1.4158 -0.0508 0.6523

61 -0.6152 0.7569 0.0205 0.5431 0.0707 0.8191 0.1916 1.0700 2.6163 1.4815 0.0212 0.6698

7-9 7-10

Ball

6-10 6-11 6-12 7-8





1 0.0000 0.2972 0.0000 0.5901 0.0000 0.7155 0.0000 0.4400 0.0000 0.1780 0.0000 0.5400

2 0.1970 0.3010 0.3000 0.5914 0.5269 0.8771 -0.0830 0.6631 0.0240 0.5277 0.1270 0.7333

3 0.1450 0.3063 0.2000 0.5954 0.9109 0.9636 -0.0791 0.7520 0.0559 0.6347 0.1109 0.8146

4 0.3690 0.3131 0.5000 0.6018 1.2589 1.0395 -0.0311 0.8135 0.2279 0.7040 0.3590 0.8717

5 0.4810 0.3213 0.4000 0.6108 1.6120 1.1142 -0.0080 0.8628 0.2930 0.7568 0.2120 0.9179

6 0.4750 0.3308 0.3000 0.6221 2.0900 1.1953 0.0800 0.9118 0.3650 0.8073 0.1900 0.9640

7 0.4000 0.3414 0.4000 0.6357 2.4630 1.2869 0.0130 0.9675 0.3630 0.8641 0.3630 1.0169

8 0.4100 0.3531 0.3000 0.6513 2.9080 1.3932 0.0480 1.0374 0.4180 0.9352 0.3080 1.0836

9 0.5380 0.3657 0.4000 0.6689 3.5750 1.3936 0.0750 0.9538 0.5130 0.8330 0.3750 1.0038

10 0.0400 0.3010 0.1000 0.5914 -0.0749 1.0040 -0.2850 0.8237 -0.1350 0.7192 -0.0750 0.8812

11 0.1450 0.3030 0.2121 0.5927 0.1922 0.9036 -0.0977 0.6897 -0.0163 0.5605 0.0509 0.7574

12 0.2209 0.3078 0.0447 0.5967 0.6950 0.9433 -0.1055 0.7180 -0.0232 0.5935 -0.1994 0.7833

13 0.2739 0.3144 0.3479 0.6031 1.2025 1.0016 -0.2236 0.7571 -0.0731 0.6374 0.0009 0.8193

14 0.4244 0.3224 0.3153 0.6121 1.7047 1.0717 -0.1603 0.8002 0.0191 0.6839 -0.0900 0.8593

15 0.3995 0.3318 0.3138 0.6233 2.3196 1.1503 -0.0867 0.8454 0.0911 0.7309 0.0055 0.9015

16 0.3988 0.3423 0.4932 0.6369 2.9070 1.2380 -0.0143 0.8952 0.1823 0.7816 0.2767 0.9483

17 0.3387 0.3539 0.5233 0.6525 3.3565 1.3373 -0.0178 0.9551 0.2587 0.8424 0.4432 1.0051

18 0.4980 0.3665 0.5954 0.6701 3.4713 1.4573 -0.0512 1.0393 0.2855 0.9292 0.3829 1.0854

19 0.3840 0.3063 0.1000 0.5954 -0.5410 0.9913 -0.3610 0.7872 -0.0570 0.6760 -0.3410 0.8471

20 0.2750 0.3078 0.2236 0.5967 -0.1918 0.9524 -0.4199 0.7300 -0.1851 0.6080 -0.2366 0.7943

21 0.3637 0.3565 0.3159 0.6561 3.2206 1.3289 -0.0238 0.9254 0.2328 0.8069 0.1850 0.9769

22 0.4746 0.3689 0.6791 0.6735 3.5255 1.4415 -0.0228 1.0006 0.3136 0.8841 0.5180 1.0484

23 0.3990 0.3131 0.1000 0.6018 -0.6541 1.0202 -0.3540 0.7887 -0.0550 0.6752 -0.3540 0.8485

24 0.2643 0.3144 0.0949 0.6031 -0.3733 1.0031 -0.2944 0.7592 -0.0459 0.6399 -0.2153 0.8212

25 0.4568 0.3607 0.3676 0.6619 2.7117 1.3393 0.0779 0.9101 0.1880 0.7863 0.0988 0.9624

26 0.5067 0.3729 0.5969 0.6793 3.2490 1.4476 0.0339 0.9812 0.1977 0.8594 0.2879 1.0300

27 0.6170 0.3213 0.3000 0.6108 -0.5121 1.0663 -0.3120 0.8001 0.0050 0.6843 -0.3120 0.8591

28 0.3810 0.3224 0.2183 0.6120 -0.4911 1.0590 -0.3868 0.7833 -0.0373 0.6640 -0.2000 0.8435

29 0.3667 0.3665 0.6202 0.6701 2.3809 1.3658 -0.1170 0.9066 0.0438 0.7780 0.2973 0.9591

30 0.6189 0.3784 0.7155 0.6872 2.8997 1.4712 -0.0429 0.9766 0.2093 0.8501 0.3059 1.0255

31 0.4410 0.3308 0.1000 0.6221 -0.3511 1.1285 -0.3010 0.8224 0.0900 0.7047 -0.2510 0.8799

32 0.4468 0.3318 0.1569 0.6233 -0.5775 1.1190 -0.3324 0.8023 0.0457 0.6806 -0.2441 0.8612

33 0.4020 0.3347 0.0928 0.6271 -0.0601 1.1188 -0.3203 0.7809 0.0260 0.6532 -0.2832 0.8413

34 0.5601 0.3395 0.2744 0.6332 0.2510 1.1418 -0.3323 0.7784 -0.0466 0.6467 -0.3323 0.8390

35 0.4837 0.3460 0.4686 0.6417 0.7857 1.1836 -0.2048 0.7908 0.0978 0.6567 0.0827 0.8505

36 0.5728 0.3539 0.5657 0.6525 1.0381 1.2428 -0.1570 0.8176 0.0552 0.6827 0.0481 0.8755

37 0.5899 0.3632 0.6658 0.6654 1.5133 1.3189 -0.0437 0.8607 0.1698 0.7266 0.2457 0.9158

38 0.5099 0.3737 0.3836 0.6804 2.0575 1.4078 -0.1487 0.9154 0.1263 0.7828 0.0001 0.9675

39 0.6200 0.3853 0.5618 0.6973 2.9073 1.5103 -0.2005 0.9849 0.2520 0.8545 0.1938 1.0334

40 0.5980 0.3414 0.1000 0.6357 -0.5721 1.2038 -0.2220 0.8538 0.1260 0.7345 -0.3720 0.9094

41 0.4845 0.3423 0.3124 0.6369 -0.3648 1.1815 -0.2168 0.8153 0.2019 0.6887 0.0298 0.8734

42 0.4612 0.3823 0.5098 0.6928 1.8819 1.4725 -0.1485 0.9496 0.1196 0.8160 0.1682 0.9999

43 0.7148 0.3935 0.7600 0.7094 2.8636 1.5669 -0.1504 1.0106 0.2584 0.8780 0.3036 1.0580

44 0.5310 0.3531 0.1000 0.6513 -0.6860 1.2949 -0.1560 0.9010 0.1450 0.7812 -0.2860 0.9538

45 0.4013 0.3539 0.2404 0.6525 -0.5866 1.2410 -0.0690 0.8147 0.2107 0.6792 0.0498 0.8728

46 0.5816 0.3565 0.2473 0.6561 -0.5143 1.2353 -0.1571 0.7851 0.1772 0.6412 -0.1571 0.8452

47 0.5185 0.3607 0.2889 0.6619 -0.3902 1.2643 -0.1985 0.7958 0.0889 0.6506 -0.1407 0.8551

48 0.5114 0.3665 0.3845 0.6701 -0.1024 1.3128 -0.2252 0.8247 0.0617 0.6808 -0.0652 0.8821

49 0.3604 0.3737 0.3371 0.6804 0.2168 1.3750 -0.1970 0.8643 -0.0041 0.7223 -0.0273 0.9192

50 0.3872 0.3823 0.4664 0.6928 0.9560 1.4502 -0.2077 0.9147 -0.0016 0.7751 0.0775 0.9668

51 0.4363 0.3920 0.3536 0.7072 1.5954 1.5362 -0.0806 0.9739 0.1931 0.8367 0.1103 1.0230

52 0.6114 0.4028 0.4516 0.7235 2.7677 1.6420 -0.0687 1.0570 0.3028 0.9242 0.1430 1.1024

53 0.7900 0.3657 0.2000 0.6689 -1.0020 1.4059 -0.2020 0.9716 0.1880 0.8534 -0.4020 1.0208

54 0.6548 0.3665 0.2233 0.6701 -0.7948 1.3051 -0.1747 0.8123 0.2445 0.6656 -0.1870 0.8705

55 0.7249 0.3689 0.2426 0.6736 -0.4387 1.3314 -0.1210 0.8341 0.3105 0.6900 -0.1719 0.8909

56 0.6449 0.3729 0.4565 0.6793 -0.3313 1.3707 -0.1992 0.8638 0.2081 0.7224 0.0197 0.9188

57 0.6391 0.3784 0.4025 0.6872 0.0842 1.4207 -0.2379 0.8986 0.0971 0.7593 -0.1395 0.9516

58 0.5471 0.3853 0.5724 0.6973 0.6827 1.4826 -0.2078 0.9418 0.0849 0.8045 0.1103 0.9925

59 0.4776 0.3935 0.5200 0.7094 1.2356 1.5563 -0.2206 0.9940 0.1330 0.8588 0.1754 1.0421

60 0.4798 0.4028 0.5644 0.7235 1.7488 1.6448 -0.2306 1.0613 0.3000 0.9291 0.3847 1.1065

61 0.6569 0.4133 0.7071 0.7394 2.4247 1.7631 -0.1704 1.1671 0.4653 1.0413 0.5155 1.2084

Ball

7-11 7-12 8-9 8-10 8-11 8-12





1 0.0000 0.8400 0.0000 0.7373 0.0000 0.8964 0.0000 0.4746 0.0000 0.6966 0.0000 0.5686

2 -0.6100 0.8479 -0.5029 0.7468 -0.3999 0.9038 0.1070 0.4777 0.2100 0.6981 0.1030 0.5711

3 -0.9899 0.8712 -0.8549 0.7722 -0.7999 0.9257 0.1350 0.4830 0.1900 0.7028 0.0550 0.5756

4 -1.2900 0.9086 -1.0310 0.8121 -0.8999 0.9610 0.2590 0.4906 0.3900 0.7105 0.1311 0.5819

5 -1.6200 0.9586 -1.3190 0.8643 -1.4000 1.0084 0.3010 0.5002 0.2200 0.7211 -0.0810 0.5901

6 -2.0100 1.0193 -1.7250 0.9270 -1.9000 1.0662 0.2850 0.5119 0.1100 0.7346 -0.1750 0.6000

7 -2.4500 1.0888 -2.1000 0.9980 -2.1000 1.1329 0.3500 0.5254 0.3500 0.7507 0.0000 0.6116

8 -2.8600 1.1657 -2.4900 1.0758 -2.6000 1.2070 0.3700 0.5406 0.2600 0.7693 -0.1100 0.6247

9 -3.5000 1.2485 -3.0620 1.1589 -3.2000 1.2872 0.4380 0.5575 0.3000 0.7903 -0.1380 0.6394

10 -0.2100 0.8479 -0.0600 0.7468 0.0000 0.9038 0.1500 0.4777 0.2100 0.6981 0.0600 0.5711

11 -0.2899 0.8557 -0.2085 0.7555 -0.1414 0.9112 0.0814 0.4796 0.1485 0.6997 0.0672 0.5727

12 -0.8005 0.8788 -0.7182 0.7804 -0.8944 0.9329 0.0823 0.4846 -0.0939 0.7043 -0.1762 0.5769

13 -1.4261 0.9160 -1.2756 0.8198 -1.2016 0.9680 0.1505 0.4920 0.2245 0.7120 0.0740 0.5831

14 -1.8651 0.9656 -1.6856 0.8716 -1.7947 1.0151 0.1795 0.5016 0.0703 0.7226 -0.1091 0.5912

15 -2.4063 1.0258 -2.2285 0.9337 -2.3141 1.0725 0.1778 0.5131 0.0922 0.7361 -0.0857 0.6011

16 -2.9214 1.0950 -2.7248 1.0042 -2.6304 1.1388 0.1966 0.5266 0.2910 0.7522 0.0944 0.6126

17 -3.3743 1.1714 -3.0978 1.0815 -2.9133 1.2125 0.2765 0.5418 0.4610 0.7707 0.1846 0.6257

18 -3.5226 1.2539 -3.1858 1.1643 -3.0885 1.2924 0.3368 0.5586 0.4341 0.7916 0.0974 0.6403

19 0.1800 0.8712 0.4840 0.7722 0.2000 0.9257 0.3040 0.4830 0.0200 0.7028 -0.2840 0.5756

20 -0.2281 0.8788 0.0066 0.7804 -0.0448 0.9329 0.2348 0.4846 0.1833 0.7043 -0.0514 0.5769

21 -3.2444 1.1884 -2.9878 1.0986 -3.0356 1.2289 0.2566 0.5452 0.2088 0.7750 -0.0478 0.6287

22 -3.5483 1.2697 -3.2119 1.1801 -3.0074 1.3077 0.3364 0.5618 0.5408 0.7957 0.2044 0.6432

23 0.3000 0.9087 0.5990 0.8121 0.3001 0.9611 0.2990 0.4906 0.0000 0.7105 -0.2990 0.5819

24 0.0789 0.9159 0.3274 0.8198 0.1580 0.9680 0.2485 0.4920 0.0791 0.7120 -0.1694 0.5831

25 -2.6338 1.2161 -2.5237 1.1264 -2.6129 1.2557 0.1101 0.5508 0.0210 0.7820 -0.0892 0.6336

26 -3.2151 1.2957 -3.0513 1.2060 -2.9611 1.3329 0.1637 0.5672 0.2540 0.8026 0.0902 0.6479

27 0.2001 0.9586 0.5171 0.8643 0.2001 1.0084 0.3170 0.5002 0.0000 0.7211 -0.3170 0.5901

28 0.1042 0.9655 0.4537 0.8715 0.2910 1.0150 0.3495 0.5015 0.1868 0.7226 -0.1627 0.5912

29 -2.4979 1.2539 -2.3372 1.1642 -2.0837 1.2923 0.1607 0.5586 0.4142 0.7916 0.2535 0.6403

30 -2.9426 1.3312 -2.6904 1.2414 -2.5938 1.3675 0.2522 0.5747 0.3488 0.8120 0.0966 0.6544

31 0.0501 1.0193 0.4411 0.9270 0.1001 1.0663 0.3910 0.5119 0.0500 0.7346 -0.3410 0.6000

32 0.2451 1.0258 0.6232 0.9336 0.3334 1.0725 0.3781 0.5131 0.0883 0.7361 -0.2898 0.6011

33 -0.2602 1.0451 0.0861 0.9535 -0.2231 1.0910 0.3463 0.5169 0.0371 0.7405 -0.3092 0.6043

34 -0.5834 1.0765 -0.2977 0.9855 -0.5834 1.1211 0.2857 0.5230 0.0000 0.7478 -0.2857 0.6095

35 -0.9905 1.1190 -0.6879 1.0286 -0.7030 1.1619 0.3026 0.5313 0.2875 0.7579 -0.0151 0.6167

36 -1.1951 1.1713 -0.9830 1.0814 -0.9900 1.2124 0.2121 0.5418 0.2051 0.7707 -0.0071 0.6257

37 -1.5570 1.2323 -1.3436 1.1427 -1.2676 1.2715 0.2134 0.5541 0.2894 0.7861 0.0759 0.6365

38 -2.2062 1.3008 -1.9312 1.2111 -2.0574 1.3379 0.2750 0.5683 0.1488 0.8039 -0.1263 0.6488

39 -3.1079 1.3755 -2.6554 1.2854 -2.7136 1.4107 0.4525 0.5841 0.3943 0.8240 -0.0582 0.6627

40 0.3501 1.0889 0.6981 0.9981 0.2001 1.1330 0.3480 0.5254 -0.1500 0.7507 -0.4980 0.6116

41 0.1479 1.0949 0.5667 1.0042 0.3946 1.1388 0.4187 0.5266 0.2466 0.7521 -0.1721 0.6126

42 -2.0304 1.3560 -1.7623 1.2660 -1.7137 1.3917 0.2681 0.5799 0.3167 0.8187 0.0486 0.6590

43 -3.0140 1.4278 -2.6052 1.3372 -2.5600 1.4617 0.4088 0.5953 0.4540 0.8384 0.0452 0.6726

44 0.5300 1.1657 0.8310 1.0758 0.4000 1.2070 0.3010 0.5407 -0.1300 0.7693 -0.4310 0.6247

45 0.5176 1.1714 0.7973 1.0815 0.6364 1.2125 0.2797 0.5418 0.1188 0.7707 -0.1609 0.6257

46 0.3571 1.1883 0.6915 1.0985 0.3571 1.2289 0.3343 0.5452 0.0000 0.7750 -0.3343 0.6287

47 0.1917 1.2160 0.4791 1.1263 0.2495 1.2557 0.2874 0.5508 0.0578 0.7819 -0.2296 0.6336

48 -0.1228 1.2538 0.1641 1.1642 0.0372 1.2923 0.2869 0.5586 0.1600 0.7916 -0.1269 0.6403

49 -0.4138 1.3008 -0.2208 1.2111 -0.2441 1.3379 0.1930 0.5683 0.1697 0.8039 -0.0233 0.6488

50 -1.1637 1.3560 -0.9577 1.2660 -0.8785 1.3916 0.2061 0.5799 0.2852 0.8187 0.0792 0.6590

51 -1.6760 1.4185 -1.4023 1.3280 -1.4851 1.4526 0.2737 0.5933 0.1909 0.8358 -0.0827 0.6708

52 -2.8363 1.4873 -2.4648 1.3960 -2.6247 1.5199 0.3715 0.6083 0.2117 0.8551 -0.1598 0.6841

53 0.8000 1.2486 1.1900 1.1590 0.6000 1.2872 0.3900 0.5575 -0.2000 0.7903 -0.5900 0.6394

54 0.6201 1.2539 1.0393 1.1643 0.6078 1.2924 0.4191 0.5586 -0.0124 0.7917 -0.4315 0.6403

55 0.3176 1.2697 0.7491 1.1801 0.2667 1.3077 0.4315 0.5618 -0.0509 0.7958 -0.4824 0.6432

56 0.1321 1.2957 0.5395 1.2060 0.3511 1.3330 0.4073 0.5672 0.2189 0.8026 -0.1884 0.6479

57 -0.3221 1.3312 0.0129 1.2414 -0.2237 1.3675 0.3350 0.5747 0.0984 0.8120 -0.2366 0.6544

58 -0.8905 1.3755 -0.5978 1.2854 -0.5725 1.4107 0.2927 0.5841 0.3180 0.8240 0.0253 0.6627

59 -1.4562 1.4278 -1.1025 1.3373 -1.0601 1.4617 0.3536 0.5953 0.3960 0.8384 0.0424 0.6726

60 -1.9793 1.4873 -1.4488 1.3960 -1.3641 1.5199 0.5306 0.6083 0.6152 0.8551 0.0847 0.6841

61 -2.5951 1.5531 -1.9594 1.4609 -1.9092 1.5843 0.6357 0.6228 0.6859 0.8740 0.0502 0.6971

10-12 11-12

Ball

9-10 9-11 9-12 10-11



-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-2.50

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

0 100 200 300 400 500 600

Equivalence Lab. 5 vsLab. 1

Uij


Uij



-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-3.00

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij



-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 100 200 300 400 500 600


Uij


Uij



-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 100 200 300 400 500 600


Uij

l (mm)

DiR( µµ µµm)

Uij

l (mm)

DiR( µµ µµm)

Uij

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-1.20

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij



-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-1.20

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 100 200 300 400 500 600


Uij


Uij



-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 100 200 300 400 500 600

Equivalence lab. 6 vs Lab. 3

Uij


Uij



-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 100 200 300 400 500 600


Uij


Uij



-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 100 200 300 400 500 600


Uij


Uij



-1.50

-1.00

-0.50

0.00

0.50

1.00

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 100 200 300 400 500 600


Uij


Uij



-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-2.50

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

0 100 200 300 400 500 600


Uij


Uij



-2.50

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-2.50

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

0 100 200 300 400 500 600


Uij


Uij



-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij



-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 100 200 300 400 500 600


Uij


Uij



-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 100 200 300 400 500 600


Uij


Uij



-3.00

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 100 200 300 400 500 600

Equivlance Lab. 10 vs. Lab. 8

Uij

l (mm)

Dij( µµ µµm)

Uij

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 100 200 300 400 500 600

Equivalnce Lab. 11 vs Lab. 8

Uij

l (mm)

Dij( µµ µµm)

Uij

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 100 200 300 400 500 600


Uij


Uij



-4.00

-3.00

-2.00

-1.00

0.00

1.00

2.00

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-4.00

-3.00

-2.00

-1.00

0.00

1.00

2.00

0 100 200 300 400 500 600


Uijl (mm)

Dij( µµ µµm)

Uij

-4.00

-3.00

-2.00

-1.00

0.00

1.00

2.00

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 100 200 300 400 500 600


Uij


Uij



-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 100 200 300 400 500 600


Uij

l (mm)

Dij( µµ µµm)

Uij

Documents

CCL-K6 Final 2009-02-24 corr 2015-01-05 - BIPM · • Customs clearance and shipping delays. • Last minute withdrawal of one NMI. • Re-commissioning of pilot laboratory closure