Club Certificate2025
Easy ElevenCRO 2742
Hrvatski jedriličarski savez
Osječka 11
21000 Split
CROATIA
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 Angles44.6°44.6°42.6°40.9°39.7°38.9°38.4°38.8°39.5°
Beat VMG2.563.594.445.085.565.855.986.086.06
52°4.075.566.687.498.028.338.498.618.64
60°4.375.907.007.768.248.548.738.888.95
75°4.596.147.237.968.418.738.999.339.49
90°4.426.097.388.228.709.009.189.6110.00
110°4.466.177.518.368.889.339.7410.3410.77
120°4.325.997.328.218.779.239.6910.6211.48
135°3.795.346.657.688.378.869.3110.2511.44
150°3.114.475.706.767.638.268.719.4810.29
Run VMG2.693.874.945.856.617.197.678.459.11
Gybe Angles142.1°142.1°146.0°148.9°150.4°153.0°158.1°163.8°162.9°
APH ToD:502.3CDL: 11.909APH ToT: 1.1945CertNo:171/25
BOAT
ClassDufour 470DesignerFelciBuilderDufourAge date01/2021Series date01/2021Offset fileDufour470perf.offData fileCRO2742
HULL
Length Overall13.990 mMaximum Beam4.740 mDraft2.589 mDisplacement13,508 kgDLR6.1734IMS DivisionCruiser/RacerDynamic Allowance0.310%Age Allowance0.130%
PROPELLER
InstallationStrutTypeFolding 3 bladesDiameter0.410m
CREW
Maximum weight999 kg(default)Minimum weight849 kg ✱ when appliedNon Manual PowerCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail66.4167.46Headsail Luffed50.4350.43Headsail FlyingSymmetricAsymmetric147.02147.02 (All asymmetric spinnakers with SHW/SFL > 85%)
STORM SAIL AREAS (m²)
Trysail20.18Storm Jib16.75Heavy Weather Jib45.22
SAIL LIMITS
Headsails7Spinnakers5
STABILITY
Righting MomentN/AStability IndexN/A
COMMENTS
SPL = 5.24
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
Easy ElevenCRO 2742
Hrvatski jedriličarski savez
Osječka 11
21000 Split
CROATIA
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 VMG1405.41003.3811.6708.2646.9615.7602.4592.1594.3
52°885.0648.0538.6480.8449.0432.4424.2418.1416.5
60°823.2610.2514.1464.0436.9421.6412.5405.2402.5
75°784.5586.1498.0452.4427.9412.2400.3385.7379.4
90°815.1591.1487.7438.2413.8400.2392.3374.6359.9
110°807.1583.2479.6430.7405.5386.1369.6348.1334.2
120°833.4600.5491.7438.3410.7390.1371.6339.0313.7
135°949.1673.7541.1469.1430.1406.5386.7351.3314.6
150°1158.3805.0631.6532.8471.7435.6413.5379.9350.0
Run VMG1337.5929.5729.3615.2544.5500.6469.4426.2395.0
Selected Courses
Windward / Leeward1371.1966.4770.4661.7595.7558.1535.9509.2494.6
All purpose1032.3738.5598.7524.1481.3456.4440.4419.3405.3
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward627.10.9568
All purpose502.31.1945
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low668.60.8974
Triple Number Coastal/Long Distance Medium499.11.2021
Triple Number Coastal/Long Distance High436.51.3746
Triple Number Windward/Leeward Low868.40.6909
Triple Number Windward/Leeward Medium622.90.9633
Triple Number Windward/Leeward High531.41.1290
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance549.51.0920
Triple Number Coastal/Long Distance Low668.60.8974
Triple Number Coastal/Long Distance Medium499.11.2021
Triple Number Coastal/Long Distance High436.51.3746
Triple Number Windward/Leeward Low868.40.6909
Triple Number Windward/Leeward Medium622.90.9633
Triple Number Windward/Leeward High531.41.1290
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1454.7962.7722.6593.4515.1473.9445.1400.8384.9
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.8433
Downwind "popa"0.9965
70% up, 30% down "Ilhabela"0.8841
30% up, 70% down "Ilhabela-inverso"0.9450
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low668.60.8974
Triple Number Coastal/Long Distance Medium499.11.2021
Triple Number Coastal/Long Distance High436.51.3746
Triple Number Windward/Leeward Low868.40.6909
Triple Number Windward/Leeward Medium622.90.9633
Triple Number Windward/Leeward High531.41.1290
Predominantly Upwind544.11.1027
Predominantly Downwind514.71.1657
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low668.60.8974
Triple Number AP Medium499.21.2019
Triple Number AP High436.51.3746
Triple Number Windward/Leeward Low907.90.6609
Triple Number Windward/Leeward Medium622.90.9633
Triple Number Windward/Leeward High531.41.1290
Single Number Predominant Upwind568.41.0556
Single Number Predominant Reaching500.11.1998
Single Number Predominant Downwind538.51.1142
Predominant Upwind - Low818.80.7328
Predominant Upwind - Low/Med610.00.9836
Predominant Upwind - Medium523.01.1472
Predominant Upwind - Med/High478.61.2538
Predominant Upwind - High461.71.2995
Predominant Downwind Low807.70.7428
Predominant Downwind Low/Med588.41.0196
Predominant Downwind Medium493.81.2151
Predominant Downwind Med/High437.71.3707
Predominant Downwind High406.31.4768
Predominant Reaching Low720.10.8332
Predominant Reaching Low/Med537.01.1173
Predominant Reaching Medium462.11.2984
Predominant Reaching Med/High420.91.4256
Predominant Reaching High398.01.5074
SA/DSPL Upwind20.42SA/DSPL Downwind37.30
Scoring OptionTODTOT
5-Band Windward/Leeward Low1018.70.5890
5-Band Windward/Leeward Low/Med735.20.8161
5-Band Windward/Leeward Medium610.00.9836
5-Band Windward/Leeward Med/High540.11.1108
5-Band Windward/Leeward High511.31.1735
Windward/Leeward 60-40 Low1026.10.5847
Windward/Leeward 60-40 Low/Med744.00.8065
Windward/Leeward 60-40 Medium620.40.9671
Windward/Leeward 60-40 Med/High553.41.0842
Windward/Leeward 60-40 High527.91.1366
5-Band AP Low739.60.8113
5-Band AP Low/Med575.71.0423
5-Band AP Medium490.61.2229
5-Band AP Med/High443.01.3544
5-Band AP High420.51.4268
5-Band SF Bay Tour - Low875.70.6852
5-Band SF Bay Tour - Low/Med701.60.8551
5-Band SF Bay Tour - Medium586.21.0236
5-Band SF Bay Tour - Med/High522.81.1477
5-Band SF Bay Tour - High496.51.2085
Chicago-Mac Upwind1.0166
Chicago-Mac All Purpose1.0473
Chicago-Mac Downwind1.0702
Bayview-Mac Cove Island0.7484
Bayview-Mac Shore0.7536
Harvest Moon Regatta431.91.3891
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance549.51.0920
Triple Number Coastal/Long Distance Low668.60.8974
Triple Number Coastal/Long Distance Medium499.11.2021
Triple Number Coastal/Long Distance High436.51.3746
Triple Number Windward/Leeward Low868.40.6909
Triple Number Windward/Leeward Medium622.90.9633
Triple Number Windward/Leeward High531.41.1290
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1454.7962.7722.6593.4515.1473.9445.1400.8384.9
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance549.51.0920
Triple Number Coastal/Long Distance Low668.60.8974
Triple Number Coastal/Long Distance Medium499.11.2021
Triple Number Coastal/Long Distance High436.51.3746
Triple Number Windward/Leeward Low868.40.6909
Triple Number Windward/Leeward Medium622.90.9633
Triple Number Windward/Leeward High531.41.1290
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1454.7962.7722.6593.4515.1473.9445.1400.8384.9
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance549.5
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1454.7962.7722.6593.4515.1473.9445.1400.8384.9
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low668.60.8974
Triple Number Coastal/Long Distance Medium499.11.2021
Triple Number Coastal/Long Distance High436.51.3746
Triple Number Windward/Leeward Low868.40.6909
Triple Number Windward/Leeward Medium622.90.9633
Triple Number Windward/Leeward High531.41.1290
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating549.51.0920
FinRating, kevyt tuuli998.91.0011
FinRating, kova tuuli423.01.1822
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low668.60.8974
Triple Number Coastal/Long Distance Medium499.11.2021
Triple Number Coastal/Long Distance High436.51.3746
Triple Number Windward/Leeward Low868.40.6909
Triple Number Windward/Leeward Medium622.90.9633
Triple Number Windward/Leeward High531.41.1290
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance1.0920
Triple Number Coastal/Long Distance Low0.8974
Triple Number Coastal/Long Distance Medium1.2021
Triple Number Coastal/Long Distance High1.3746
Triple Number Windward/Leeward Low0.6909
Triple Number Windward/Leeward Medium0.9633
Triple Number Windward/Leeward High1.1290
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1454.7962.7722.6593.4515.1473.9445.1400.8384.9
For information
General Purpose Handicap (GPH)568.6
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance549.51.0920
Triple Number Coastal/Long Distance Low668.60.8974
Triple Number Coastal/Long Distance Medium499.11.2021
Triple Number Coastal/Long Distance High436.51.3746
Triple Number Windward/Leeward Low868.40.6909
Triple Number Windward/Leeward Medium622.90.9633
Triple Number Windward/Leeward High531.41.1290
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1454.7962.7722.6593.4515.1473.9445.1400.8384.9
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low668.60.8974
Triple Number Coastal/Long Distance Medium499.11.2021
Triple Number Coastal/Long Distance High436.51.3746
Triple Number Windward/Leeward Low868.40.6909
Triple Number Windward/Leeward Medium622.90.9633
Triple Number Windward/Leeward High531.41.1290
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance549.51.0920
Triple Number Coastal/Long Distance Low668.60.8974
Triple Number Coastal/Long Distance Medium499.11.2021
Triple Number Coastal/Long Distance High436.51.3746
Triple Number Windward/Leeward Low868.40.6909
Triple Number Windward/Leeward Medium622.90.9633
Triple Number Windward/Leeward High531.41.1290
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1454.7962.7722.6593.4515.1473.9445.1400.8384.9
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance549.51.0920
Triple Number Coastal/Long Distance Low668.60.8974
Triple Number Coastal/Long Distance Medium499.11.2021
Triple Number Coastal/Long Distance High436.51.3746
Triple Number Windward/Leeward Low868.40.6909
Triple Number Windward/Leeward Medium622.90.9633
Triple Number Windward/Leeward High531.41.1290
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1454.7962.7722.6593.4515.1473.9445.1400.8384.9
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low668.6
Triple Number Coastal/Long Distance Medium499.1
Triple Number Coastal/Long Distance High436.5
Triple Number Windward/Leeward Low868.4
Triple Number Windward/Leeward Medium622.9
Triple Number Windward/Leeward High531.4
Predominantly Upwind544.1
Predominantly Downwind514.7
Predominantly Reaching489.2
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance549.51.0920
Triple Number Coastal/Long Distance Low668.60.8974
Triple Number Coastal/Long Distance Medium499.11.2021
Triple Number Coastal/Long Distance High436.51.3746
Triple Number Windward/Leeward Low868.40.6909
Triple Number Windward/Leeward Medium622.90.9633
Triple Number Windward/Leeward High531.41.1290
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1454.7962.7722.6593.4515.1473.9445.1400.8384.9
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8974
Triple Number Coastal/Long Distance Medium1.2021
Triple Number Coastal/Long Distance High1.3746
Triple Number Windward/Leeward Low0.6909
Triple Number Windward/Leeward Medium0.9633
Triple Number Windward/Leeward High1.1290
Coastal/Long Distance1.0920
Predominantly Upwind1.1027
Predominantly Downwind1.1657
For information
General Purpose Handicap (GPH)568.6
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)1.1945
Distanseseilas Trippeltall svak vind0.8974
Distanseseilas Trippeltall mellomvind1.2021
Distanseseilas Trippeltall sterk vind1.3746
Pølsebane Trippeltall svak vind0.6909
Pølsebane Trippeltall mellomvind0.9633
Pølsebane Trippeltall sterk vind1.1290
Motvind Singeltall1.1027
Medvind Singeltall1.1657
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low668.60.8974
Triple Number Coastal/Long Distance Medium499.11.2021
Triple Number Coastal/Long Distance High436.51.3746
Triple Number Windward/Leeward Low868.40.6909
Triple Number Windward/Leeward Medium622.90.9633
Triple Number Windward/Leeward High531.41.1290
Coastal/Long Distance549.51.0920
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind544.11.1027
Predominantly Downwind514.71.1657
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore499.01.2024
Cape Doctor Coastal409.51.4653
Triple Number Coastal/Long Distance Low668.60.8974
Triple Number Coastal/Long Distance Medium499.11.2021
Triple Number Coastal/Long Distance High436.51.3746
Triple Number Windward/Leeward Low868.40.6909
Triple Number Windward/Leeward Medium622.90.9633
Triple Number Windward/Leeward High531.41.1290
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8974
Triple Number Coastal/Long Distance Medium1.2021
Triple Number Coastal/Long Distance High1.3746
Triple Number Windward/Leeward Low0.6909
Triple Number Windward/Leeward Medium0.9633
Triple Number Windward/Leeward High1.1290
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8974
Triple Number Coastal/Long Distance Medium1.2021
Triple Number Coastal/Long Distance High1.3746
Triple Number Windward/Leeward Low0.6909
Triple Number Windward/Leeward Medium0.9633
Triple Number Windward/Leeward High1.1290
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance549.51.0920
Triple Number Coastal/Long Distance Low668.60.8974
Triple Number Coastal/Long Distance Medium499.11.2021
Triple Number Coastal/Long Distance High436.51.3746
Triple Number Windward/Leeward Low868.40.6909
Triple Number Windward/Leeward Medium622.90.9633
Triple Number Windward/Leeward High531.41.1290
Predominantly Upwind544.11.1027
Predominantly Downwind514.71.1657
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1454.7962.7722.6593.4515.1473.9445.1400.8384.9
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance549.51.0920
Triple Number Coastal/Long Distance Low668.60.8974
Triple Number Coastal/Long Distance Medium499.11.2021
Triple Number Coastal/Long Distance High436.51.3746
Triple Number Windward/Leeward Low868.40.6909
Triple Number Windward/Leeward Medium622.90.9633
Triple Number Windward/Leeward High531.41.1290
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1454.7962.7722.6593.4515.1473.9445.1400.8384.9
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low668.60.8974
Triple Number AP Medium499.21.2019
Triple Number AP High436.51.3746
Triple Number Windward/Leeward Low907.90.6609
Triple Number Windward/Leeward Medium622.90.9633
Triple Number Windward/Leeward High531.41.1290
Single Number Predominant Upwind568.41.0556
Single Number Predominant Reaching500.11.1998
Single Number Predominant Downwind538.51.1142
Predominant Upwind - Low818.80.7328
Predominant Upwind - Low/Med610.00.9836
Predominant Upwind - Medium523.01.1472
Predominant Upwind - Med/High478.61.2538
Predominant Upwind - High461.71.2995
Predominant Downwind Low807.70.7428
Predominant Downwind Low/Med588.41.0196
Predominant Downwind Medium493.81.2151
Predominant Downwind Med/High437.71.3707
Predominant Downwind High406.31.4768
Predominant Reaching Low720.10.8332
Predominant Reaching Low/Med537.01.1173
Predominant Reaching Medium462.11.2984
Predominant Reaching Med/High420.91.4256
Predominant Reaching High398.01.5074
SA/DSPL Upwind20.42SA/DSPL Downwind37.30
Scoring OptionTODTOT
5-Band Windward/Leeward Low1018.70.5890
5-Band Windward/Leeward Low/Med735.20.8161
5-Band Windward/Leeward Medium610.00.9836
5-Band Windward/Leeward Med/High540.11.1108
5-Band Windward/Leeward High511.31.1735
Windward/Leeward 60-40 Low1026.10.5847
Windward/Leeward 60-40 Low/Med744.00.8065
Windward/Leeward 60-40 Medium620.40.9671
Windward/Leeward 60-40 Med/High553.41.0842
Windward/Leeward 60-40 High527.91.1366
5-Band AP Low739.60.8113
5-Band AP Low/Med575.71.0423
5-Band AP Medium490.61.2229
5-Band AP Med/High443.01.3544
5-Band AP High420.51.4268
5-Band SF Bay Tour - Low875.70.6852
5-Band SF Bay Tour - Low/Med701.60.8551
5-Band SF Bay Tour - Medium586.21.0236
5-Band SF Bay Tour - Med/High522.81.1477
5-Band SF Bay Tour - High496.51.2085
Chicago-Mac Upwind1.0166
Chicago-Mac All Purpose1.0473
Chicago-Mac Downwind1.0702
Bayview-Mac Cove Island0.7484
Bayview-Mac Shore0.7536
Harvest Moon Regatta431.91.3891
Club Certificate2025
Easy ElevenCRO 2742
Hrvatski jedriličarski savez
Osječka 11
21000 Split
CROATIA
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassDufour 470Measurement25/09/2021HINPlan reviewHull constructionSolidCarbon rudderNoLight stanchionsNoTrim tabNo
LOA13.990Max. Beam4.740Draft2.589Displacement13,508Wetted area46.85IMS L13.163LSM012.981Acc. length14.000Sink (kg/mm) 36.87
VCGD0.300VCGM0.312RM Rated (kg·m) 447.7Limit of positive stability(°) N/AStability IndexN/ADefault crew weight999Declared crew weightN/A
PROPELLER
Propeller TypeFolding 3 blades
InstallationStrutTwin screwNoHydro generatorNo
PRD0.410PBWPIPA0.0007
EDLST1ST2
ST3ST4ST5
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerNoMainsail furlerNoArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders3Rotating mastNo
P18.300IG18.300ISP19.540MDT10.155MDL10.280MDT20.155MDL20.280TL0.000MW0.280GO0.280
E6.300J5.100BAS1.340FSD0.040SFJ0.200SPLWPLTPS5.900BD0.250MWTMCG
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodVCG entered directlyVCG entered0.300Flotation Date06/10/2021
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Club Certificate2025
Easy ElevenCRO 2742
Hrvatski jedriličarski savez
Osječka 11
21000 Split
CROATIA
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment10.201.212.203.915.1566.4129/09/2021
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment10.100.731.422.824.235.5617.90YesNo 50.4313/09/202520.060.671.312.684.095.5216.79NoNo 45.6707/10/2024Charter sails
ASYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLRatioAreaMeas.DateComment120.2617.3418.809.369.4899%147.0209/10/2021
CRUISER/RACER REQUIREMENTS*
Accommodation length14.0 mTable area0.66 m²Headroom1.89 mMinimum number of berths6Personal gear stowage0.24 m³Fresh water capacity240 lMinimum number of seats in cockpit6Food stowage0.36 m³Fuel capacity130 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.