Club Certificate2025
GraciaLAT 76
Latvijas Jūras
burāšanas asociācija
Grecinieku street 11A-5, Riga
Riga LV-1050 Latvia
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 Angles44.4°44.4°42.6°41.3°40.7°40.2°39.9°40.3°41.8°
Beat VMG1.962.703.283.693.984.174.254.254.12
52°3.074.154.945.475.816.016.116.166.11
60°3.274.385.165.685.996.186.306.386.36
75°3.374.525.325.856.156.366.516.706.76
90°3.444.685.596.106.356.486.586.897.07
110°3.544.825.746.256.566.827.027.257.43
120°3.404.675.636.206.556.847.107.537.78
135°3.064.245.215.956.386.707.007.588.18
150°2.573.664.645.466.066.426.727.287.87
Run VMG2.213.174.024.765.415.896.266.817.32
Gybe Angles148.2°148.2°152.3°154.3°161.9°168.2°176.3°177.7°177.7°
APH ToD:671.2CDL: 6.392APH ToT: 0.8939CertNo:045/25
BOAT
ClassCARTER 30DesignerRichard CarterBuilderTeligaAge date01/1984Series date12/1975Offset fileCARTER30.OFFData fileLAT-76
HULL
Length Overall9.150 mMaximum Beam3.092 mDraft1.554 mDisplacement3,700 kgDLR9.5395IMS DivisionCruiser/RacerDynamic Allowance0.540%Age Allowance0.487%
PROPELLER
InstallationStrutTypeFolding 3 bladesDiameter0.400m
CREW
Maximum weight400 kg(declared)Minimum weight270 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail16.9417.16Headsail Luffed20.9420.94Headsail FlyingSymmetric63.8463.84Asymmetric
STORM SAIL AREAS (m²)
Trysail4.95Storm Jib6.32Heavy Weather Jib17.06
SAIL LIMITS
Headsails5
✱ One set on the forestay
Spinnakers4
STABILITY
Righting MomentN/AStability IndexN/A
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
GraciaLAT 76
Latvijas Jūras
burāšanas asociācija
Grecinieku street 11A-5, Riga
Riga LV-1050 Latvia
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 VMG1835.21331.11096.8976.3903.9863.0847.5847.3873.8
52°1171.1866.7729.2658.5620.1599.3589.0584.3589.1
60°1101.5821.6697.3634.1601.5582.5571.7564.6565.7
75°1068.4796.9676.3615.6585.3566.5552.9537.5532.4
90°1045.4768.4644.5590.1566.7555.8546.8522.8508.9
110°1017.9747.4627.1576.1548.4528.2513.2496.3484.4
120°1057.6770.5639.9580.8549.7526.2506.7477.9462.7
135°1176.8848.5691.2604.6564.6537.4514.3475.2440.2
150°1403.2982.9776.6658.8594.2560.5535.8494.5457.4
Run VMG1626.71135.0894.7756.8665.2610.9575.3528.6492.1
Selected Courses
Windward / Leeward1730.01233.1995.7866.5784.6736.9711.4687.9682.9
All purpose1317.9954.1784.0696.0645.8616.7599.2579.0570.9
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward822.80.7292
All purpose671.20.8939
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low869.10.6904
Triple Number Coastal/Long Distance Medium666.70.8999
Triple Number Coastal/Long Distance High596.01.0067
Triple Number Windward/Leeward Low1114.40.5384
Triple Number Windward/Leeward Medium817.60.7339
Triple Number Windward/Leeward High709.00.8463
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance729.60.8223
Triple Number Coastal/Long Distance Low869.10.6904
Triple Number Coastal/Long Distance Medium666.70.8999
Triple Number Coastal/Long Distance High596.01.0067
Triple Number Windward/Leeward Low1114.40.5384
Triple Number Windward/Leeward Medium817.60.7339
Triple Number Windward/Leeward High709.00.8463
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1815.91223.3934.5781.4689.4639.7605.1552.2541.2
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.6117
Downwind "popa"0.8129
70% up, 30% down "Ilhabela"0.6608
30% up, 70% down "Ilhabela-inverso"0.7399
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low869.10.6904
Triple Number Coastal/Long Distance Medium666.70.8999
Triple Number Coastal/Long Distance High596.01.0067
Triple Number Windward/Leeward Low1114.40.5384
Triple Number Windward/Leeward Medium817.60.7339
Triple Number Windward/Leeward High709.00.8463
Predominantly Upwind737.20.8139
Predominantly Downwind667.40.8990
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low869.10.6904
Triple Number AP Medium666.80.8998
Triple Number AP High596.01.0067
Triple Number Windward/Leeward Low1163.10.5158
Triple Number Windward/Leeward Medium817.60.7339
Triple Number Windward/Leeward High709.00.8463
Single Number Predominant Upwind768.40.7808
Single Number Predominant Reaching666.00.9010
Single Number Predominant Downwind696.80.8611
Predominant Upwind - Low1071.30.5601
Predominant Upwind - Low/Med816.00.7353
Predominant Upwind - Medium712.30.8424
Predominant Upwind - Med/High660.10.9089
Predominant Upwind - High645.30.9298
Predominant Downwind Low1019.10.5887
Predominant Downwind Low/Med754.90.7948
Predominant Downwind Medium642.30.9341
Predominant Downwind Med/High576.71.0403
Predominant Downwind High542.81.1054
Predominant Reaching Low927.30.6470
Predominant Reaching Low/Med706.60.8492
Predominant Reaching Medium620.00.9678
Predominant Reaching Med/High573.41.0464
Predominant Reaching High548.61.0936
SA/DSPL Upwind15.77SA/DSPL Downwind33.62
Scoring OptionTODTOT
5-Band Windward/Leeward Low1298.20.4622
5-Band Windward/Leeward Low/Med954.00.6289
5-Band Windward/Leeward Medium801.80.7483
5-Band Windward/Leeward Med/High717.90.8358
5-Band Windward/Leeward High691.10.8681
Windward/Leeward 60-40 Low1318.30.4551
Windward/Leeward 60-40 Low/Med975.30.6152
Windward/Leeward 60-40 Medium825.50.7268
Windward/Leeward 60-40 Med/High745.30.8051
Windward/Leeward 60-40 High723.30.8295
5-Band AP Low953.00.6296
5-Band AP Low/Med757.60.7919
5-Band AP Medium656.90.9134
5-Band AP Med/High602.60.9956
5-Band AP High581.11.0325
5-Band SF Bay Tour - Low1126.70.5325
5-Band SF Bay Tour - Low/Med917.60.6539
5-Band SF Bay Tour - Medium779.30.7699
5-Band SF Bay Tour - Med/High704.70.8514
5-Band SF Bay Tour - High680.90.8812
Chicago-Mac Upwind0.7546
Chicago-Mac All Purpose0.7939
Chicago-Mac Downwind0.8307
Bayview-Mac Cove Island0.5796
Bayview-Mac Shore0.5828
Harvest Moon Regatta579.61.0353
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance729.60.8223
Triple Number Coastal/Long Distance Low869.10.6904
Triple Number Coastal/Long Distance Medium666.70.8999
Triple Number Coastal/Long Distance High596.01.0067
Triple Number Windward/Leeward Low1114.40.5384
Triple Number Windward/Leeward Medium817.60.7339
Triple Number Windward/Leeward High709.00.8463
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1815.91223.3934.5781.4689.4639.7605.1552.2541.2
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance729.60.8223
Triple Number Coastal/Long Distance Low869.10.6904
Triple Number Coastal/Long Distance Medium666.70.8999
Triple Number Coastal/Long Distance High596.01.0067
Triple Number Windward/Leeward Low1114.40.5384
Triple Number Windward/Leeward Medium817.60.7339
Triple Number Windward/Leeward High709.00.8463
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1815.91223.3934.5781.4689.4639.7605.1552.2541.2
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance729.6
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1815.91223.3934.5781.4689.4639.7605.1552.2541.2
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low869.10.6904
Triple Number Coastal/Long Distance Medium666.70.8999
Triple Number Coastal/Long Distance High596.01.0067
Triple Number Windward/Leeward Low1114.40.5384
Triple Number Windward/Leeward Medium817.60.7339
Triple Number Windward/Leeward High709.00.8463
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating729.60.8223
FinRating, kevyt tuuli1272.00.7862
FinRating, kova tuuli585.50.8539
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low869.10.6904
Triple Number Coastal/Long Distance Medium666.70.8999
Triple Number Coastal/Long Distance High596.01.0067
Triple Number Windward/Leeward Low1114.40.5384
Triple Number Windward/Leeward Medium817.60.7339
Triple Number Windward/Leeward High709.00.8463
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.8223
Triple Number Coastal/Long Distance Low0.6904
Triple Number Coastal/Long Distance Medium0.8999
Triple Number Coastal/Long Distance High1.0067
Triple Number Windward/Leeward Low0.5384
Triple Number Windward/Leeward Medium0.7339
Triple Number Windward/Leeward High0.8463
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1815.91223.3934.5781.4689.4639.7605.1552.2541.2
For information
General Purpose Handicap (GPH)754.7
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance729.60.8223
Triple Number Coastal/Long Distance Low869.10.6904
Triple Number Coastal/Long Distance Medium666.70.8999
Triple Number Coastal/Long Distance High596.01.0067
Triple Number Windward/Leeward Low1114.40.5384
Triple Number Windward/Leeward Medium817.60.7339
Triple Number Windward/Leeward High709.00.8463
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1815.91223.3934.5781.4689.4639.7605.1552.2541.2
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low869.10.6904
Triple Number Coastal/Long Distance Medium666.70.8999
Triple Number Coastal/Long Distance High596.01.0067
Triple Number Windward/Leeward Low1114.40.5384
Triple Number Windward/Leeward Medium817.60.7339
Triple Number Windward/Leeward High709.00.8463
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance729.60.8223
Triple Number Coastal/Long Distance Low869.10.6904
Triple Number Coastal/Long Distance Medium666.70.8999
Triple Number Coastal/Long Distance High596.01.0067
Triple Number Windward/Leeward Low1114.40.5384
Triple Number Windward/Leeward Medium817.60.7339
Triple Number Windward/Leeward High709.00.8463
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1815.91223.3934.5781.4689.4639.7605.1552.2541.2
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance729.60.8223
Triple Number Coastal/Long Distance Low869.10.6904
Triple Number Coastal/Long Distance Medium666.70.8999
Triple Number Coastal/Long Distance High596.01.0067
Triple Number Windward/Leeward Low1114.40.5384
Triple Number Windward/Leeward Medium817.60.7339
Triple Number Windward/Leeward High709.00.8463
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1815.91223.3934.5781.4689.4639.7605.1552.2541.2
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low869.1
Triple Number Coastal/Long Distance Medium666.7
Triple Number Coastal/Long Distance High596.0
Triple Number Windward/Leeward Low1114.4
Triple Number Windward/Leeward Medium817.6
Triple Number Windward/Leeward High709.0
Predominantly Upwind737.2
Predominantly Downwind667.4
Predominantly Reaching646.5
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance729.60.8223
Triple Number Coastal/Long Distance Low869.10.6904
Triple Number Coastal/Long Distance Medium666.70.8999
Triple Number Coastal/Long Distance High596.01.0067
Triple Number Windward/Leeward Low1114.40.5384
Triple Number Windward/Leeward Medium817.60.7339
Triple Number Windward/Leeward High709.00.8463
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1815.91223.3934.5781.4689.4639.7605.1552.2541.2
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.6904
Triple Number Coastal/Long Distance Medium0.8999
Triple Number Coastal/Long Distance High1.0067
Triple Number Windward/Leeward Low0.5384
Triple Number Windward/Leeward Medium0.7339
Triple Number Windward/Leeward High0.8463
Coastal/Long Distance0.8223
Predominantly Upwind0.8139
Predominantly Downwind0.8990
For information
General Purpose Handicap (GPH)754.7
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)0.8939
Distanseseilas Trippeltall svak vind0.6904
Distanseseilas Trippeltall mellomvind0.8999
Distanseseilas Trippeltall sterk vind1.0067
Pølsebane Trippeltall svak vind0.5384
Pølsebane Trippeltall mellomvind0.7339
Pølsebane Trippeltall sterk vind0.8463
Motvind Singeltall0.8139
Medvind Singeltall0.8990
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low869.10.6904
Triple Number Coastal/Long Distance Medium666.70.8999
Triple Number Coastal/Long Distance High596.01.0067
Triple Number Windward/Leeward Low1114.40.5384
Triple Number Windward/Leeward Medium817.60.7339
Triple Number Windward/Leeward High709.00.8463
Coastal/Long Distance729.60.8223
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind737.20.8139
Predominantly Downwind667.40.8990
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore684.40.8766
Cape Doctor Coastal573.41.0465
Triple Number Coastal/Long Distance Low869.10.6904
Triple Number Coastal/Long Distance Medium666.70.8999
Triple Number Coastal/Long Distance High596.01.0067
Triple Number Windward/Leeward Low1114.40.5384
Triple Number Windward/Leeward Medium817.60.7339
Triple Number Windward/Leeward High709.00.8463
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.6904
Triple Number Coastal/Long Distance Medium0.8999
Triple Number Coastal/Long Distance High1.0067
Triple Number Windward/Leeward Low0.5384
Triple Number Windward/Leeward Medium0.7339
Triple Number Windward/Leeward High0.8463
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.6904
Triple Number Coastal/Long Distance Medium0.8999
Triple Number Coastal/Long Distance High1.0067
Triple Number Windward/Leeward Low0.5384
Triple Number Windward/Leeward Medium0.7339
Triple Number Windward/Leeward High0.8463
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance729.60.8223
Triple Number Coastal/Long Distance Low869.10.6904
Triple Number Coastal/Long Distance Medium666.70.8999
Triple Number Coastal/Long Distance High596.01.0067
Triple Number Windward/Leeward Low1114.40.5384
Triple Number Windward/Leeward Medium817.60.7339
Triple Number Windward/Leeward High709.00.8463
Predominantly Upwind737.20.8139
Predominantly Downwind667.40.8990
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1815.91223.3934.5781.4689.4639.7605.1552.2541.2
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance729.60.8223
Triple Number Coastal/Long Distance Low869.10.6904
Triple Number Coastal/Long Distance Medium666.70.8999
Triple Number Coastal/Long Distance High596.01.0067
Triple Number Windward/Leeward Low1114.40.5384
Triple Number Windward/Leeward Medium817.60.7339
Triple Number Windward/Leeward High709.00.8463
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1815.91223.3934.5781.4689.4639.7605.1552.2541.2
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low869.10.6904
Triple Number AP Medium666.80.8998
Triple Number AP High596.01.0067
Triple Number Windward/Leeward Low1163.10.5158
Triple Number Windward/Leeward Medium817.60.7339
Triple Number Windward/Leeward High709.00.8463
Single Number Predominant Upwind768.40.7808
Single Number Predominant Reaching666.00.9010
Single Number Predominant Downwind696.80.8611
Predominant Upwind - Low1071.30.5601
Predominant Upwind - Low/Med816.00.7353
Predominant Upwind - Medium712.30.8424
Predominant Upwind - Med/High660.10.9089
Predominant Upwind - High645.30.9298
Predominant Downwind Low1019.10.5887
Predominant Downwind Low/Med754.90.7948
Predominant Downwind Medium642.30.9341
Predominant Downwind Med/High576.71.0403
Predominant Downwind High542.81.1054
Predominant Reaching Low927.30.6470
Predominant Reaching Low/Med706.60.8492
Predominant Reaching Medium620.00.9678
Predominant Reaching Med/High573.41.0464
Predominant Reaching High548.61.0936
SA/DSPL Upwind15.77SA/DSPL Downwind33.62
Scoring OptionTODTOT
5-Band Windward/Leeward Low1298.20.4622
5-Band Windward/Leeward Low/Med954.00.6289
5-Band Windward/Leeward Medium801.80.7483
5-Band Windward/Leeward Med/High717.90.8358
5-Band Windward/Leeward High691.10.8681
Windward/Leeward 60-40 Low1318.30.4551
Windward/Leeward 60-40 Low/Med975.30.6152
Windward/Leeward 60-40 Medium825.50.7268
Windward/Leeward 60-40 Med/High745.30.8051
Windward/Leeward 60-40 High723.30.8295
5-Band AP Low953.00.6296
5-Band AP Low/Med757.60.7919
5-Band AP Medium656.90.9134
5-Band AP Med/High602.60.9956
5-Band AP High581.11.0325
5-Band SF Bay Tour - Low1126.70.5325
5-Band SF Bay Tour - Low/Med917.60.6539
5-Band SF Bay Tour - Medium779.30.7699
5-Band SF Bay Tour - Med/High704.70.8514
5-Band SF Bay Tour - High680.90.8812
Chicago-Mac Upwind0.7546
Chicago-Mac All Purpose0.7939
Chicago-Mac Downwind0.8307
Bayview-Mac Cove Island0.5796
Bayview-Mac Shore0.5828
Harvest Moon Regatta579.61.0353
Club Certificate2025
GraciaLAT 76
Latvijas Jūras
burāšanas asociācija
Grecinieku street 11A-5, Riga
Riga LV-1050 Latvia
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassCARTER 30Measurement02/07/2025HINPlan reviewHull constructionSolidCarbon rudderNoLight stanchionsNoTrim tabNo
LOA9.150Max. Beam3.092Draft1.554Displacement3,700Wetted area17.37IMS L7.326LSM07.292Acc. length9.150Sink (kg/mm) 12.41
VCGD0.105VCGM0.103RM Rated (kg·m) 55.5Limit of positive stability(°) N/AStability IndexN/ADefault crew weight439Declared crew weight400
PROPELLER
Propeller TypeFolding 3 blades
InstallationStrutTwin screwNoHydro generatorNo
PRD0.400PBWPIPA0.0006
EDLST1ST2
ST3ST4ST5
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerYesMainsail furlerNoArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders1Rotating mastNo
P10.040IG11.240ISP11.250MDT10.115MDL10.160MDT2MDL2TLNo TaperMWGO0.000
E2.815J3.665BAS1.430FSD0.033SFJ0.045SPL3.820WPLTPSBD0.096MWTMCG
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodRM estimatedFlotation Date02/07/2025
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Club Certificate2025
GraciaLAT 76
Latvijas Jūras
burāšanas asociācija
Grecinieku street 11A-5, Riga
Riga LV-1050 Latvia
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment00.140.581.051.832.4016.9402/07/2025
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment00.070.571.051.932.783.6011.08YesNo 20.9402/07/2025
SYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLAreaMeas.DateComment011.4811.3811.436.736.5963.8402/07/2025
CRUISER/RACER REQUIREMENTS*
Accommodation length9.2 mTable area0.44 m²Headroom1.64 mMinimum number of berths4Personal gear stowage0.16 m³Fresh water capacity64 lMinimum number of seats in cockpit4Food stowage0.24 m³Fuel capacity34 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.