Club Certificate2025
ESKILFRA-35270
Centre de Calcul FFVoile
17 rue Henri Bocquillon
75015 Paris
France
Rated boat velocities in knots
Wind Velocity 4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Beat Angles43.4°43.4°41.2°39.7°38.6°38.2°38.2°38.4°39.6°
Beat VMG2.473.404.114.614.854.955.005.024.93
52°3.875.186.096.636.896.997.057.117.10
60°4.125.466.326.817.067.197.257.347.34
75°4.285.636.486.947.237.447.587.737.82
90°4.155.516.426.987.287.537.778.108.30
110°3.955.416.497.087.477.828.108.468.73
120°3.785.216.306.977.407.798.168.859.30
135°3.324.655.766.607.127.537.948.799.96
150°2.733.945.055.986.697.167.548.329.25
Run VMG2.363.424.375.205.926.526.987.708.42
Gybe Angles145.7°145.7°150.5°153.9°160.1°166.9°175.9°177.4°176.8°
APH ToD:577.2CDL: 8.611APH ToT: 1.0395CertNo:25298a
BOAT
ClassX 332DesignerJEPPESEN NielsenBuilderX-YACHTSAge date01/2001Series date10/1994Offset fileX332RE.offData fileF35270_25298a
HULL
Length Overall9.978 mMaximum Beam3.284 mDraft1.825 mDisplacement4,564 kgDLR6.3223IMS DivisionCruiser/RacerDynamic Allowance0.170%Age Allowance0.487%
PROPELLER
InstallationStrutTypeFolding 2 bladesDiameter0.380m
CREW
Maximum weight589 kg(default)Minimum weight459 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail34.3535.05Headsail Luffed30.5430.54Headsail FlyingSymmetric70.7370.73Asymmetric
STORM SAIL AREAS (m²)
Trysail10.10Storm Jib8.75Heavy Weather Jib23.60
SAIL LIMITS
Headsails5Spinnakers4
STABILITY
Righting MomentN/AStability IndexN/A
COMMENTS
2025: NC / 2024: New SPL and sails / Very Small P&E / YANMAR SD20 / From:X332 DK.dxt
The owner and any other person in charge is responsible that boat is complying with her certificate in accordance with RRS 78.1 and ORC Rule 304.
Club Certificate2025
ESKILFRA-35270
Centre de Calcul FFVoile
17 rue Henri Bocquillon
75015 Paris
France
Time Allowances in secs/NM
Wind Velocity 4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Beat VMG1456.11059.8875.0780.7742.2727.5720.6717.4730.9
52°931.0694.8591.2542.8522.7515.0510.8506.6507.4
60°873.7659.9569.5528.8509.7500.9496.3490.8490.7
75°842.1639.5555.7518.6497.7483.9475.1465.5460.6
90°868.3653.3560.3515.6494.6477.9463.1444.3433.9
110°910.7665.0555.0508.8481.8460.4444.2425.6412.5
120°951.2690.5571.1516.3486.3462.0440.9406.9387.0
135°1085.1773.8624.7545.6505.5478.2453.6409.5361.4
150°1320.6912.8712.9602.1538.0502.9477.4432.7389.0
Run VMG1524.81054.0822.9692.0607.9552.4515.8467.6427.6
Selected Courses
Windward / Leeward1488.81056.9849.0736.4675.1639.9618.2592.5579.3
All purpose1122.8813.3668.7595.1556.8534.3518.8497.7484.0
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward707.00.8487
All purpose577.21.0395
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low741.00.8097
Triple Number Coastal/Long Distance Medium573.21.0467
Triple Number Coastal/Long Distance High514.81.1655
Triple Number Windward/Leeward Low953.00.6296
Triple Number Windward/Leeward Medium701.20.8557
Triple Number Windward/Leeward High614.00.9772
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance627.70.9558
Triple Number Coastal/Long Distance Low741.00.8097
Triple Number Coastal/Long Distance Medium573.21.0467
Triple Number Coastal/Long Distance High514.81.1655
Triple Number Windward/Leeward Low953.00.6296
Triple Number Windward/Leeward Medium701.20.8557
Triple Number Windward/Leeward High614.00.9772
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1584.41056.6799.9667.0593.4554.6524.2475.0461.0
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.7469
Downwind "popa"0.8912
70% up, 30% down "Ilhabela"0.7850
30% up, 70% down "Ilhabela-inverso"0.8424
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low741.00.8097
Triple Number Coastal/Long Distance Medium573.21.0467
Triple Number Coastal/Long Distance High514.81.1655
Triple Number Windward/Leeward Low953.00.6296
Triple Number Windward/Leeward Medium701.20.8557
Triple Number Windward/Leeward High614.00.9772
Predominantly Upwind622.80.9634
Predominantly Downwind588.41.0197
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low741.00.8097
Triple Number AP Medium573.31.0465
Triple Number AP High514.81.1655
Triple Number Windward/Leeward Low995.40.6028
Triple Number Windward/Leeward Medium701.20.8557
Triple Number Windward/Leeward High614.00.9772
Single Number Predominant Upwind647.20.9270
Single Number Predominant Reaching575.81.0420
Single Number Predominant Downwind614.60.9762
Predominant Upwind - Low884.80.6781
Predominant Upwind - Low/Med679.50.8830
Predominant Upwind - Medium602.70.9955
Predominant Upwind - Med/High566.91.0584
Predominant Upwind - High552.41.0862
Predominant Downwind Low905.00.6630
Predominant Downwind Low/Med667.70.8987
Predominant Downwind Medium567.21.0579
Predominant Downwind Med/High505.41.1871
Predominant Downwind High469.41.2783
Predominant Reaching Low797.00.7528
Predominant Reaching Low/Med611.30.9815
Predominant Reaching Medium538.51.1142
Predominant Reaching Med/High495.81.2103
Predominant Reaching High470.31.2757
SA/DSPL Upwind23.47SA/DSPL Downwind38.00
Scoring OptionTODTOT
5-Band Windward/Leeward Low1113.30.5389
5-Band Windward/Leeward Low/Med814.20.7369
5-Band Windward/Leeward Medium689.10.8707
5-Band Windward/Leeward Med/High622.30.9642
5-Band Windward/Leeward High594.71.0090
Windward/Leeward 60-40 Low1113.20.5390
Windward/Leeward 60-40 Low/Med821.30.7306
Windward/Leeward 60-40 Medium702.40.8543
Windward/Leeward 60-40 Med/High642.40.9339
Windward/Leeward 60-40 High619.80.9681
5-Band AP Low820.20.7315
5-Band AP Low/Med647.50.9266
5-Band AP Medium565.51.0610
5-Band AP Med/High521.11.1515
5-Band AP High499.01.2024
5-Band SF Bay Tour - Low958.40.6261
5-Band SF Bay Tour - Low/Med778.80.7705
5-Band SF Bay Tour - Medium666.70.9000
5-Band SF Bay Tour - Med/High608.90.9854
5-Band SF Bay Tour - High583.71.0280
Chicago-Mac Upwind0.9002
Chicago-Mac All Purpose0.9235
Chicago-Mac Downwind0.9405
Bayview-Mac Cove Island0.6762
Bayview-Mac Shore0.6818
Harvest Moon Regatta502.21.1947
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance627.70.9558
Triple Number Coastal/Long Distance Low741.00.8097
Triple Number Coastal/Long Distance Medium573.21.0467
Triple Number Coastal/Long Distance High514.81.1655
Triple Number Windward/Leeward Low953.00.6296
Triple Number Windward/Leeward Medium701.20.8557
Triple Number Windward/Leeward High614.00.9772
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1584.41056.6799.9667.0593.4554.6524.2475.0461.0
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance627.70.9558
Triple Number Coastal/Long Distance Low741.00.8097
Triple Number Coastal/Long Distance Medium573.21.0467
Triple Number Coastal/Long Distance High514.81.1655
Triple Number Windward/Leeward Low953.00.6296
Triple Number Windward/Leeward Medium701.20.8557
Triple Number Windward/Leeward High614.00.9772
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1584.41056.6799.9667.0593.4554.6524.2475.0461.0
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance627.7
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1584.41056.6799.9667.0593.4554.6524.2475.0461.0
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low741.00.8097
Triple Number Coastal/Long Distance Medium573.21.0467
Triple Number Coastal/Long Distance High514.81.1655
Triple Number Windward/Leeward Low953.00.6296
Triple Number Windward/Leeward Medium701.20.8557
Triple Number Windward/Leeward High614.00.9772
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating627.70.9558
FinRating, kevyt tuuli1094.10.9140
FinRating, kova tuuli502.00.9960
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low741.00.8097
Triple Number Coastal/Long Distance Medium573.21.0467
Triple Number Coastal/Long Distance High514.81.1655
Triple Number Windward/Leeward Low953.00.6296
Triple Number Windward/Leeward Medium701.20.8557
Triple Number Windward/Leeward High614.00.9772
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.9558
Triple Number Coastal/Long Distance Low0.8097
Triple Number Coastal/Long Distance Medium1.0467
Triple Number Coastal/Long Distance High1.1655
Triple Number Windward/Leeward Low0.6296
Triple Number Windward/Leeward Medium0.8557
Triple Number Windward/Leeward High0.9772
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1584.41056.6799.9667.0593.4554.6524.2475.0461.0
For information
General Purpose Handicap (GPH)647.6
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance627.70.9558
Triple Number Coastal/Long Distance Low741.00.8097
Triple Number Coastal/Long Distance Medium573.21.0467
Triple Number Coastal/Long Distance High514.81.1655
Triple Number Windward/Leeward Low953.00.6296
Triple Number Windward/Leeward Medium701.20.8557
Triple Number Windward/Leeward High614.00.9772
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1584.41056.6799.9667.0593.4554.6524.2475.0461.0
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low741.00.8097
Triple Number Coastal/Long Distance Medium573.21.0467
Triple Number Coastal/Long Distance High514.81.1655
Triple Number Windward/Leeward Low953.00.6296
Triple Number Windward/Leeward Medium701.20.8557
Triple Number Windward/Leeward High614.00.9772
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance627.70.9558
Triple Number Coastal/Long Distance Low741.00.8097
Triple Number Coastal/Long Distance Medium573.21.0467
Triple Number Coastal/Long Distance High514.81.1655
Triple Number Windward/Leeward Low953.00.6296
Triple Number Windward/Leeward Medium701.20.8557
Triple Number Windward/Leeward High614.00.9772
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1584.41056.6799.9667.0593.4554.6524.2475.0461.0
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance627.70.9558
Triple Number Coastal/Long Distance Low741.00.8097
Triple Number Coastal/Long Distance Medium573.21.0467
Triple Number Coastal/Long Distance High514.81.1655
Triple Number Windward/Leeward Low953.00.6296
Triple Number Windward/Leeward Medium701.20.8557
Triple Number Windward/Leeward High614.00.9772
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1584.41056.6799.9667.0593.4554.6524.2475.0461.0
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low741.0
Triple Number Coastal/Long Distance Medium573.2
Triple Number Coastal/Long Distance High514.8
Triple Number Windward/Leeward Low953.0
Triple Number Windward/Leeward Medium701.2
Triple Number Windward/Leeward High614.0
Predominantly Upwind622.8
Predominantly Downwind588.4
Predominantly Reaching564.3
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance627.70.9558
Triple Number Coastal/Long Distance Low741.00.8097
Triple Number Coastal/Long Distance Medium573.21.0467
Triple Number Coastal/Long Distance High514.81.1655
Triple Number Windward/Leeward Low953.00.6296
Triple Number Windward/Leeward Medium701.20.8557
Triple Number Windward/Leeward High614.00.9772
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1584.41056.6799.9667.0593.4554.6524.2475.0461.0
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8097
Triple Number Coastal/Long Distance Medium1.0467
Triple Number Coastal/Long Distance High1.1655
Triple Number Windward/Leeward Low0.6296
Triple Number Windward/Leeward Medium0.8557
Triple Number Windward/Leeward High0.9772
Coastal/Long Distance0.9558
Predominantly Upwind0.9634
Predominantly Downwind1.0197
For information
General Purpose Handicap (GPH)647.6
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)1.0395
Distanseseilas Trippeltall svak vind0.8097
Distanseseilas Trippeltall mellomvind1.0467
Distanseseilas Trippeltall sterk vind1.1655
Pølsebane Trippeltall svak vind0.6296
Pølsebane Trippeltall mellomvind0.8557
Pølsebane Trippeltall sterk vind0.9772
Motvind Singeltall0.9634
Medvind Singeltall1.0197
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low741.00.8097
Triple Number Coastal/Long Distance Medium573.21.0467
Triple Number Coastal/Long Distance High514.81.1655
Triple Number Windward/Leeward Low953.00.6296
Triple Number Windward/Leeward Medium701.20.8557
Triple Number Windward/Leeward High614.00.9772
Coastal/Long Distance627.70.9558
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind622.80.9634
Predominantly Downwind588.41.0197
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore583.21.0288
Cape Doctor Coastal488.11.2292
Triple Number Coastal/Long Distance Low741.00.8097
Triple Number Coastal/Long Distance Medium573.21.0467
Triple Number Coastal/Long Distance High514.81.1655
Triple Number Windward/Leeward Low953.00.6296
Triple Number Windward/Leeward Medium701.20.8557
Triple Number Windward/Leeward High614.00.9772
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8097
Triple Number Coastal/Long Distance Medium1.0467
Triple Number Coastal/Long Distance High1.1655
Triple Number Windward/Leeward Low0.6296
Triple Number Windward/Leeward Medium0.8557
Triple Number Windward/Leeward High0.9772
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8097
Triple Number Coastal/Long Distance Medium1.0467
Triple Number Coastal/Long Distance High1.1655
Triple Number Windward/Leeward Low0.6296
Triple Number Windward/Leeward Medium0.8557
Triple Number Windward/Leeward High0.9772
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance627.70.9558
Triple Number Coastal/Long Distance Low741.00.8097
Triple Number Coastal/Long Distance Medium573.21.0467
Triple Number Coastal/Long Distance High514.81.1655
Triple Number Windward/Leeward Low953.00.6296
Triple Number Windward/Leeward Medium701.20.8557
Triple Number Windward/Leeward High614.00.9772
Predominantly Upwind622.80.9634
Predominantly Downwind588.41.0197
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1584.41056.6799.9667.0593.4554.6524.2475.0461.0
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance627.70.9558
Triple Number Coastal/Long Distance Low741.00.8097
Triple Number Coastal/Long Distance Medium573.21.0467
Triple Number Coastal/Long Distance High514.81.1655
Triple Number Windward/Leeward Low953.00.6296
Triple Number Windward/Leeward Medium701.20.8557
Triple Number Windward/Leeward High614.00.9772
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1584.41056.6799.9667.0593.4554.6524.2475.0461.0
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low741.00.8097
Triple Number AP Medium573.31.0465
Triple Number AP High514.81.1655
Triple Number Windward/Leeward Low995.40.6028
Triple Number Windward/Leeward Medium701.20.8557
Triple Number Windward/Leeward High614.00.9772
Single Number Predominant Upwind647.20.9270
Single Number Predominant Reaching575.81.0420
Single Number Predominant Downwind614.60.9762
Predominant Upwind - Low884.80.6781
Predominant Upwind - Low/Med679.50.8830
Predominant Upwind - Medium602.70.9955
Predominant Upwind - Med/High566.91.0584
Predominant Upwind - High552.41.0862
Predominant Downwind Low905.00.6630
Predominant Downwind Low/Med667.70.8987
Predominant Downwind Medium567.21.0579
Predominant Downwind Med/High505.41.1871
Predominant Downwind High469.41.2783
Predominant Reaching Low797.00.7528
Predominant Reaching Low/Med611.30.9815
Predominant Reaching Medium538.51.1142
Predominant Reaching Med/High495.81.2103
Predominant Reaching High470.31.2757
SA/DSPL Upwind23.47SA/DSPL Downwind38.00
Scoring OptionTODTOT
5-Band Windward/Leeward Low1113.30.5389
5-Band Windward/Leeward Low/Med814.20.7369
5-Band Windward/Leeward Medium689.10.8707
5-Band Windward/Leeward Med/High622.30.9642
5-Band Windward/Leeward High594.71.0090
Windward/Leeward 60-40 Low1113.20.5390
Windward/Leeward 60-40 Low/Med821.30.7306
Windward/Leeward 60-40 Medium702.40.8543
Windward/Leeward 60-40 Med/High642.40.9339
Windward/Leeward 60-40 High619.80.9681
5-Band AP Low820.20.7315
5-Band AP Low/Med647.50.9266
5-Band AP Medium565.51.0610
5-Band AP Med/High521.11.1515
5-Band AP High499.01.2024
5-Band SF Bay Tour - Low958.40.6261
5-Band SF Bay Tour - Low/Med778.80.7705
5-Band SF Bay Tour - Medium666.70.9000
5-Band SF Bay Tour - Med/High608.90.9854
5-Band SF Bay Tour - High583.71.0280
Chicago-Mac Upwind0.9002
Chicago-Mac All Purpose0.9235
Chicago-Mac Downwind0.9405
Bayview-Mac Cove Island0.6762
Bayview-Mac Shore0.6818
Harvest Moon Regatta502.21.1947
Club Certificate2025
ESKILFRA-35270
Centre de Calcul FFVoile
17 rue Henri Bocquillon
75015 Paris
France
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassX 332MeasurementHIN949Plan reviewHull constructionCoredCarbon rudderNoLight stanchionsNoTrim tabNo
LOA9.978Max. Beam3.284Draft1.825Displacement4,564Wetted area22.70IMS L9.127LSM08.970Acc. length9.978Sink (kg/mm) 16.90
VCGD-0.008VCGM0.047RM Rated (kg·m) 101.6Limit of positive stability(°) N/AStability IndexN/ADefault crew weight589Declared crew weightN/A
PROPELLER
Propeller TypeFolding 2 blades
InstallationStrutTwin screwNoHydro generatorNo
PRD0.380PBWPIPA0.0033
EDL2.018ST10.040ST2
ST3ST40.112ST50.285
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerNoMainsail furlerNoArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders2Rotating mastNo
P12.900IG13.177ISP13.192MDT10.115MDL10.163MDT20.100MDL20.130TL1.612MW0.163GO0.175
E4.470J3.550BAS1.725FSD0.028SFJ0.286SPL3.750WPLTPSBD0.150MWT116.20MCG4.580
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodVCG entered directlyVCG entered-0.008Flotation Date01/01/2013
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Club Certificate2025
ESKILFRA-35270
Centre de Calcul FFVoile
17 rue Henri Bocquillon
75015 Paris
France
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateCommentM40.151.001.722.853.7434.3525/03/2024Médium
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateCommentG24.8212.45NoNo 30.5425/03/2024Médium
SYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLAreaMeas.DateCommentS312.9012.9012.906.706.1070.7325/03/2024Médium
CRUISER/RACER REQUIREMENTS*
Accommodation length10.0 mTable area0.44 m²Headroom1.70 mMinimum number of berths4Personal gear stowage0.16 m³Fresh water capacity80 lMinimum number of seats in cockpit4Food stowage0.24 m³Fuel capacity50 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.