Club Certificate2025
CymbalNOR 15220
Norges Seilforbund
Sognsveien 73
0854 OSLO
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°41.5°40.2°38.9°38.4°38.1°38.8°
Beat VMG2.223.093.804.334.755.055.205.275.21
52°3.504.775.736.416.867.157.317.427.42
60°3.745.056.006.657.057.317.497.637.67
75°3.885.226.186.827.217.477.687.978.09
90°3.725.156.267.027.467.757.978.208.43
110°3.775.216.347.107.547.888.208.789.20
120°3.635.036.156.957.437.808.148.799.50
135°3.164.475.596.487.117.527.868.539.24
150°2.603.784.855.756.517.087.478.108.72
Run VMG2.253.274.204.985.696.326.877.618.20
Gybe Angles144.4°144.4°147.2°151.9°155.9°165.1°175.0°178.8°179.0°
APH ToD:587.3CDL: 8.909APH ToT: 1.0217CertNo:666743
BOAT
ClassBavaria 37 CruiserDesignerJAKOPIN&JAKOPINBuilderBavaria YachtbauAge date01/2006Series date01/2004Offset fileBAVA37CL.OFFData file666743
HULL
Length Overall11.200 mMaximum Beam3.802 mDraft1.953 mDisplacement6,930 kgDLR7.0795IMS DivisionCruiser/RacerDynamic Allowance0.390%Age Allowance0.487%
PROPELLER
InstallationStrutTypeFolding 2 bladesDiameter0.400m
CREW
Maximum weight681 kg(default)Minimum weight551 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail30.6730.88Headsail Luffed36.9636.96Headsail FlyingSymmetricAsymmetric75.3975.39 (All asymmetric spinnakers with SHW/SFL > 85%)
STORM SAIL AREAS (m²)
Trysail10.16Storm Jib9.20Heavy Weather Jib24.83
SAIL LIMITS
Headsails5Spinnakers4
✱ Asymmetric may be tacked on the pole
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
CymbalNOR 15220
Norges Seilforbund
Sognsveien 73
0854 OSLO
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 VMG1624.91165.8948.4832.1757.9712.8692.5682.6690.9
52°1027.7754.2628.3561.7524.6503.8492.4485.3485.1
60°961.6712.3599.7541.4510.5492.3480.9471.7469.6
75°926.8689.2582.8527.8499.1481.7468.7451.5445.0
90°966.7699.5574.8512.5482.6464.4451.8438.9426.8
110°955.8690.8567.4507.2477.5456.7439.0410.2391.3
120°991.6715.8585.8518.3484.3461.7442.5409.7378.8
135°1137.9804.9643.8555.4506.4478.7457.9422.0389.5
150°1384.3953.2742.5626.4552.8508.5482.1444.6412.7
Run VMG1598.21100.6857.4722.5632.9569.5523.8473.1439.2
Selected Courses
Windward / Leeward1610.51133.2902.9777.3695.4641.1608.1577.9565.1
All purpose1215.3868.4703.4615.5563.2530.4510.1487.5474.2
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward729.00.8231
All purpose587.31.0217
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low785.90.7635
Triple Number Coastal/Long Distance Medium584.11.0272
Triple Number Coastal/Long Distance High506.71.1842
Triple Number Windward/Leeward Low1018.00.5894
Triple Number Windward/Leeward Medium726.40.8260
Triple Number Windward/Leeward High605.00.9917
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance642.10.9344
Triple Number Coastal/Long Distance Low785.90.7635
Triple Number Coastal/Long Distance Medium584.11.0272
Triple Number Coastal/Long Distance High506.71.1842
Triple Number Windward/Leeward Low1018.00.5894
Triple Number Windward/Leeward Medium726.40.8260
Triple Number Windward/Leeward High605.00.9917
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1710.51129.9847.5697.0602.7550.7515.6468.1451.7
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.7251
Downwind "popa"0.8607
70% up, 30% down "Ilhabela"0.7611
30% up, 70% down "Ilhabela-inverso"0.8150
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low785.90.7635
Triple Number Coastal/Long Distance Medium584.11.0272
Triple Number Coastal/Long Distance High506.71.1842
Triple Number Windward/Leeward Low1018.00.5894
Triple Number Windward/Leeward Medium726.40.8260
Triple Number Windward/Leeward High605.00.9917
Predominantly Upwind635.40.9443
Predominantly Downwind601.90.9969
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low785.90.7635
Triple Number AP Medium584.21.0271
Triple Number AP High506.71.1842
Triple Number Windward/Leeward Low1064.80.5635
Triple Number Windward/Leeward Medium726.40.8260
Triple Number Windward/Leeward High605.00.9917
Single Number Predominant Upwind663.30.9046
Single Number Predominant Reaching586.31.0234
Single Number Predominant Downwind630.50.9516
Predominant Upwind - Low958.00.6263
Predominant Upwind - Low/Med714.70.8395
Predominant Upwind - Medium610.80.9824
Predominant Upwind - Med/High553.81.0835
Predominant Upwind - High535.31.1209
Predominant Downwind Low956.20.6275
Predominant Downwind Low/Med692.90.8659
Predominant Downwind Medium576.81.0402
Predominant Downwind Med/High505.21.1877
Predominant Downwind High470.21.2760
Predominant Reaching Low850.40.7056
Predominant Reaching Low/Med631.70.9498
Predominant Reaching Medium540.51.1102
Predominant Reaching Med/High489.11.2268
Predominant Reaching High465.71.2885
SA/DSPL Upwind18.49SA/DSPL Downwind28.99
Scoring OptionTODTOT
5-Band Windward/Leeward Low1195.20.5020
5-Band Windward/Leeward Low/Med861.90.6961
5-Band Windward/Leeward Medium710.00.8451
5-Band Windward/Leeward Med/High615.90.9741
5-Band Windward/Leeward High580.91.0329
Windward/Leeward 60-40 Low1201.40.4994
Windward/Leeward 60-40 Low/Med871.80.6882
Windward/Leeward 60-40 Medium722.60.8303
Windward/Leeward 60-40 Med/High632.70.9483
Windward/Leeward 60-40 High601.90.9969
5-Band AP Low872.00.6881
5-Band AP Low/Med676.00.8876
5-Band AP Medium573.61.0460
5-Band AP Med/High514.11.1670
5-Band AP High489.11.2268
5-Band SF Bay Tour - Low1026.90.5843
5-Band SF Bay Tour - Low/Med823.20.7288
5-Band SF Bay Tour - Medium684.00.8772
5-Band SF Bay Tour - Med/High601.10.9982
5-Band SF Bay Tour - High570.41.0520
Chicago-Mac Upwind0.8699
Chicago-Mac All Purpose0.8947
Chicago-Mac Downwind0.9125
Bayview-Mac Cove Island0.6373
Bayview-Mac Shore0.6421
Harvest Moon Regatta505.01.1881
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance642.10.9344
Triple Number Coastal/Long Distance Low785.90.7635
Triple Number Coastal/Long Distance Medium584.11.0272
Triple Number Coastal/Long Distance High506.71.1842
Triple Number Windward/Leeward Low1018.00.5894
Triple Number Windward/Leeward Medium726.40.8260
Triple Number Windward/Leeward High605.00.9917
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1710.51129.9847.5697.0602.7550.7515.6468.1451.7
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance642.10.9344
Triple Number Coastal/Long Distance Low785.90.7635
Triple Number Coastal/Long Distance Medium584.11.0272
Triple Number Coastal/Long Distance High506.71.1842
Triple Number Windward/Leeward Low1018.00.5894
Triple Number Windward/Leeward Medium726.40.8260
Triple Number Windward/Leeward High605.00.9917
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1710.51129.9847.5697.0602.7550.7515.6468.1451.7
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance642.1
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1710.51129.9847.5697.0602.7550.7515.6468.1451.7
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low785.90.7635
Triple Number Coastal/Long Distance Medium584.11.0272
Triple Number Coastal/Long Distance High506.71.1842
Triple Number Windward/Leeward Low1018.00.5894
Triple Number Windward/Leeward Medium726.40.8260
Triple Number Windward/Leeward High605.00.9917
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating642.10.9344
FinRating, kevyt tuuli1173.80.8520
FinRating, kova tuuli492.81.0146
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low785.90.7635
Triple Number Coastal/Long Distance Medium584.11.0272
Triple Number Coastal/Long Distance High506.71.1842
Triple Number Windward/Leeward Low1018.00.5894
Triple Number Windward/Leeward Medium726.40.8260
Triple Number Windward/Leeward High605.00.9917
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.9344
Triple Number Coastal/Long Distance Low0.7635
Triple Number Coastal/Long Distance Medium1.0272
Triple Number Coastal/Long Distance High1.1842
Triple Number Windward/Leeward Low0.5894
Triple Number Windward/Leeward Medium0.8260
Triple Number Windward/Leeward High0.9917
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1710.51129.9847.5697.0602.7550.7515.6468.1451.7
For information
General Purpose Handicap (GPH)665.6
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance642.10.9344
Triple Number Coastal/Long Distance Low785.90.7635
Triple Number Coastal/Long Distance Medium584.11.0272
Triple Number Coastal/Long Distance High506.71.1842
Triple Number Windward/Leeward Low1018.00.5894
Triple Number Windward/Leeward Medium726.40.8260
Triple Number Windward/Leeward High605.00.9917
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1710.51129.9847.5697.0602.7550.7515.6468.1451.7
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low785.90.7635
Triple Number Coastal/Long Distance Medium584.11.0272
Triple Number Coastal/Long Distance High506.71.1842
Triple Number Windward/Leeward Low1018.00.5894
Triple Number Windward/Leeward Medium726.40.8260
Triple Number Windward/Leeward High605.00.9917
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance642.10.9344
Triple Number Coastal/Long Distance Low785.90.7635
Triple Number Coastal/Long Distance Medium584.11.0272
Triple Number Coastal/Long Distance High506.71.1842
Triple Number Windward/Leeward Low1018.00.5894
Triple Number Windward/Leeward Medium726.40.8260
Triple Number Windward/Leeward High605.00.9917
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1710.51129.9847.5697.0602.7550.7515.6468.1451.7
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance642.10.9344
Triple Number Coastal/Long Distance Low785.90.7635
Triple Number Coastal/Long Distance Medium584.11.0272
Triple Number Coastal/Long Distance High506.71.1842
Triple Number Windward/Leeward Low1018.00.5894
Triple Number Windward/Leeward Medium726.40.8260
Triple Number Windward/Leeward High605.00.9917
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1710.51129.9847.5697.0602.7550.7515.6468.1451.7
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low785.9
Triple Number Coastal/Long Distance Medium584.1
Triple Number Coastal/Long Distance High506.7
Triple Number Windward/Leeward Low1018.0
Triple Number Windward/Leeward Medium726.4
Triple Number Windward/Leeward High605.0
Predominantly Upwind635.4
Predominantly Downwind601.9
Predominantly Reaching572.7
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance642.10.9344
Triple Number Coastal/Long Distance Low785.90.7635
Triple Number Coastal/Long Distance Medium584.11.0272
Triple Number Coastal/Long Distance High506.71.1842
Triple Number Windward/Leeward Low1018.00.5894
Triple Number Windward/Leeward Medium726.40.8260
Triple Number Windward/Leeward High605.00.9917
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1710.51129.9847.5697.0602.7550.7515.6468.1451.7
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7635
Triple Number Coastal/Long Distance Medium1.0272
Triple Number Coastal/Long Distance High1.1842
Triple Number Windward/Leeward Low0.5894
Triple Number Windward/Leeward Medium0.8260
Triple Number Windward/Leeward High0.9917
Coastal/Long Distance0.9344
Predominantly Upwind0.9443
Predominantly Downwind0.9969
For information
General Purpose Handicap (GPH)665.6
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)1.0217
Distanseseilas Trippeltall svak vind0.7635
Distanseseilas Trippeltall mellomvind1.0272
Distanseseilas Trippeltall sterk vind1.1842
Pølsebane Trippeltall svak vind0.5894
Pølsebane Trippeltall mellomvind0.8260
Pølsebane Trippeltall sterk vind0.9917
Motvind Singeltall0.9443
Medvind Singeltall0.9969
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low785.90.7635
Triple Number Coastal/Long Distance Medium584.11.0272
Triple Number Coastal/Long Distance High506.71.1842
Triple Number Windward/Leeward Low1018.00.5894
Triple Number Windward/Leeward Medium726.40.8260
Triple Number Windward/Leeward High605.00.9917
Coastal/Long Distance642.10.9344
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind635.40.9443
Predominantly Downwind601.90.9969
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore568.91.0546
Cape Doctor Coastal478.21.2547
Triple Number Coastal/Long Distance Low785.90.7635
Triple Number Coastal/Long Distance Medium584.11.0272
Triple Number Coastal/Long Distance High506.71.1842
Triple Number Windward/Leeward Low1018.00.5894
Triple Number Windward/Leeward Medium726.40.8260
Triple Number Windward/Leeward High605.00.9917
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7635
Triple Number Coastal/Long Distance Medium1.0272
Triple Number Coastal/Long Distance High1.1842
Triple Number Windward/Leeward Low0.5894
Triple Number Windward/Leeward Medium0.8260
Triple Number Windward/Leeward High0.9917
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7635
Triple Number Coastal/Long Distance Medium1.0272
Triple Number Coastal/Long Distance High1.1842
Triple Number Windward/Leeward Low0.5894
Triple Number Windward/Leeward Medium0.8260
Triple Number Windward/Leeward High0.9917
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance642.10.9344
Triple Number Coastal/Long Distance Low785.90.7635
Triple Number Coastal/Long Distance Medium584.11.0272
Triple Number Coastal/Long Distance High506.71.1842
Triple Number Windward/Leeward Low1018.00.5894
Triple Number Windward/Leeward Medium726.40.8260
Triple Number Windward/Leeward High605.00.9917
Predominantly Upwind635.40.9443
Predominantly Downwind601.90.9969
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1710.51129.9847.5697.0602.7550.7515.6468.1451.7
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance642.10.9344
Triple Number Coastal/Long Distance Low785.90.7635
Triple Number Coastal/Long Distance Medium584.11.0272
Triple Number Coastal/Long Distance High506.71.1842
Triple Number Windward/Leeward Low1018.00.5894
Triple Number Windward/Leeward Medium726.40.8260
Triple Number Windward/Leeward High605.00.9917
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1710.51129.9847.5697.0602.7550.7515.6468.1451.7
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low785.90.7635
Triple Number AP Medium584.21.0271
Triple Number AP High506.71.1842
Triple Number Windward/Leeward Low1064.80.5635
Triple Number Windward/Leeward Medium726.40.8260
Triple Number Windward/Leeward High605.00.9917
Single Number Predominant Upwind663.30.9046
Single Number Predominant Reaching586.31.0234
Single Number Predominant Downwind630.50.9516
Predominant Upwind - Low958.00.6263
Predominant Upwind - Low/Med714.70.8395
Predominant Upwind - Medium610.80.9824
Predominant Upwind - Med/High553.81.0835
Predominant Upwind - High535.31.1209
Predominant Downwind Low956.20.6275
Predominant Downwind Low/Med692.90.8659
Predominant Downwind Medium576.81.0402
Predominant Downwind Med/High505.21.1877
Predominant Downwind High470.21.2760
Predominant Reaching Low850.40.7056
Predominant Reaching Low/Med631.70.9498
Predominant Reaching Medium540.51.1102
Predominant Reaching Med/High489.11.2268
Predominant Reaching High465.71.2885
SA/DSPL Upwind18.49SA/DSPL Downwind28.99
Scoring OptionTODTOT
5-Band Windward/Leeward Low1195.20.5020
5-Band Windward/Leeward Low/Med861.90.6961
5-Band Windward/Leeward Medium710.00.8451
5-Band Windward/Leeward Med/High615.90.9741
5-Band Windward/Leeward High580.91.0329
Windward/Leeward 60-40 Low1201.40.4994
Windward/Leeward 60-40 Low/Med871.80.6882
Windward/Leeward 60-40 Medium722.60.8303
Windward/Leeward 60-40 Med/High632.70.9483
Windward/Leeward 60-40 High601.90.9969
5-Band AP Low872.00.6881
5-Band AP Low/Med676.00.8876
5-Band AP Medium573.61.0460
5-Band AP Med/High514.11.1670
5-Band AP High489.11.2268
5-Band SF Bay Tour - Low1026.90.5843
5-Band SF Bay Tour - Low/Med823.20.7288
5-Band SF Bay Tour - Medium684.00.8772
5-Band SF Bay Tour - Med/High601.10.9982
5-Band SF Bay Tour - High570.41.0520
Chicago-Mac Upwind0.8699
Chicago-Mac All Purpose0.8947
Chicago-Mac Downwind0.9125
Bayview-Mac Cove Island0.6373
Bayview-Mac Shore0.6421
Harvest Moon Regatta505.01.1881
Club Certificate2025
CymbalNOR 15220
Norges Seilforbund
Sognsveien 73
0854 OSLO
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassBavaria 37 CruiserMeasurementHINPlan reviewHull constructionSolidCarbon rudderNoLight stanchionsNoTrim tabNo
LOA11.200Max. Beam3.802Draft1.953Displacement6,930Wetted area28.80IMS L10.054LSM09.928Acc. length11.200Sink (kg/mm) 22.11
VCGD0.128VCGM0.227RM Rated (kg·m) 169.2Limit of positive stability(°) N/AStability IndexN/ADefault crew weight681Declared crew weightN/A
PROPELLER
Propeller TypeFolding 2 blades
InstallationStrutTwin screwNoHydro generatorNo
PRD0.400PBWPIPA0.0032
EDL1.400ST10.048ST20.170
ST30.170ST40.098ST50.295
RIG
Forestay tensionAftInner stayNone FittedMast materialSingle headsail furlerNoMainsail furlerArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders2Rotating mastNo
P12.700IG13.560ISP13.700MDT10.110MDL10.210MDT20.000MDL20.000TL0.000MW0.000GO0.000
E4.570J4.010BAS1.700FSDFoilSFJ0.000SPL4.080WPLTPS0.000BD0.000MWT0.00MCG0.000
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodRM estimatedFlotation Date01/01/2015
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Club Certificate2025
CymbalNOR 15220
Norges Seilforbund
Sognsveien 73
0854 OSLO
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment403-2014052217000.050.681.312.493.5530.6722/05/2014Rulleseil
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment403-2014052217100.070.000.000.000.005.8512.50NoNo 36.9622/05/2014
ASYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLRatioAreaMeas.DateComment990-20190521170913.4812.0212.756.967.6491%75.3929/04/2019
CRUISER/RACER REQUIREMENTS*
Accommodation length11.2 mTable area0.55 m²Headroom1.77 mMinimum number of berths5Personal gear stowage0.20 m³Fresh water capacity130 lMinimum number of seats in cockpit5Food stowage0.30 m³Fuel capacity74 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.