Club Certificate2025
HegrenNOR 16365
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 Angles41.8°41.8°39.9°39.2°38.7°38.2°37.9°37.8°39.2°
Beat VMG2.593.474.064.324.464.544.604.654.55
52°3.965.195.926.216.336.406.456.516.49
60°4.185.426.116.386.506.576.636.696.69
75°4.315.566.256.546.716.806.887.007.05
90°4.175.466.236.606.837.007.137.317.45
110°3.875.256.226.676.947.137.297.477.72
120°3.675.076.126.656.997.297.547.888.06
135°3.194.515.616.396.837.197.558.329.20
150°2.593.764.855.806.476.867.227.999.10
Run VMG2.243.264.205.035.766.296.697.358.07
Gybe Angles145.6°145.6°149.8°151.9°160.1°168.7°176.8°177.2°168.5°
APH ToD:611.5CDL: 7.479APH ToT: 0.9812CertNo:676538
BOAT
ClassAphrodite 101DesignerKJAERULFFJAN/ELVSTROMPBuilderBIANCA YACHTSAge date01/1986Series date01/1979Offset fileE111.bofData file676538
HULL
Length Overall9.904 mMaximum Beam2.444 mDraft1.737 mDisplacement3,105 kgDLR6.1724IMS DivisionCruiser/RacerDynamic Allowance0.030%Age Allowance0.487%
PROPELLER
InstallationShaft exposedTypeFolding 2 bladesDiameter0.380m
CREW
Maximum weight330 kg(declared)Minimum weight200 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail24.4124.71Headsail Luffed29.1329.13Headsail FlyingSymmetric59.9459.94Asymmetric
STORM SAIL AREAS (m²)
Trysail7.21Storm Jib5.96Heavy Weather Jib16.07
SAIL LIMITS
Headsails5Spinnakers4
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
HegrenNOR 16365
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 VMG1387.91036.2887.1832.5806.8792.4782.1774.6791.9
52°908.3693.4608.3580.0568.5562.4557.9553.3554.7
60°860.9664.3589.4563.9553.6547.7543.2538.1537.7
75°834.5646.9576.5550.2536.7529.0523.0514.4510.8
90°864.3659.6577.4545.2527.1514.3505.0492.2483.5
110°930.7685.1578.5539.9518.4504.8494.0481.8466.6
120°980.2709.9588.7541.6514.9494.0477.5456.9446.5
135°1126.8799.0642.1563.0527.4500.4476.5432.8391.3
150°1390.2956.9742.3620.4556.6524.6498.7450.8395.6
Run VMG1608.11104.9857.1715.3625.1572.5538.4489.7445.9
Selected Courses
Windward / Leeward1494.31070.6872.1773.9715.9682.4660.3632.2618.9
All purpose1126.1824.4688.4627.0593.9574.3559.9539.6526.2
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward744.40.8060
All purpose611.50.9812
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low756.40.7932
Triple Number Coastal/Long Distance Medium607.90.9870
Triple Number Coastal/Long Distance High555.91.0793
Triple Number Windward/Leeward Low971.30.6177
Triple Number Windward/Leeward Medium739.90.8109
Triple Number Windward/Leeward High655.30.9156
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance663.00.9050
Triple Number Coastal/Long Distance Low756.40.7932
Triple Number Coastal/Long Distance Medium607.90.9870
Triple Number Coastal/Long Distance High555.91.0793
Triple Number Windward/Leeward Low971.30.6177
Triple Number Windward/Leeward Medium739.90.8109
Triple Number Windward/Leeward High655.30.9156
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1598.81074.0822.6701.6632.3594.9565.0518.7506.1
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.7104
Downwind "popa"0.8566
70% up, 30% down "Ilhabela"0.7488
30% up, 70% down "Ilhabela-inverso"0.8068
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low756.40.7932
Triple Number Coastal/Long Distance Medium607.90.9870
Triple Number Coastal/Long Distance High555.91.0793
Triple Number Windward/Leeward Low971.30.6177
Triple Number Windward/Leeward Medium739.90.8109
Triple Number Windward/Leeward High655.30.9156
Predominantly Upwind659.40.9099
Predominantly Downwind614.90.9758
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low756.40.7932
Triple Number AP Medium608.00.9869
Triple Number AP High555.91.0793
Triple Number Windward/Leeward Low1014.20.5916
Triple Number Windward/Leeward Medium739.90.8109
Triple Number Windward/Leeward High655.30.9156
Single Number Predominant Upwind681.80.8800
Single Number Predominant Reaching605.30.9912
Single Number Predominant Downwind642.70.9335
Predominant Upwind - Low884.20.6786
Predominant Upwind - Low/Med705.20.8508
Predominant Upwind - Medium644.40.9311
Predominant Upwind - Med/High613.00.9788
Predominant Upwind - High598.61.0024
Predominant Downwind Low930.50.6448
Predominant Downwind Low/Med692.30.8667
Predominant Downwind Medium595.01.0085
Predominant Downwind Med/High536.31.1187
Predominant Downwind High501.51.1965
Predominant Reaching Low809.10.7416
Predominant Reaching Low/Med634.50.9457
Predominant Reaching Medium570.51.0518
Predominant Reaching Med/High532.91.1260
Predominant Reaching High509.91.1766
SA/DSPL Upwind25.07SA/DSPL Downwind39.48
Scoring OptionTODTOT
5-Band Windward/Leeward Low1127.80.5320
5-Band Windward/Leeward Low/Med843.70.7112
5-Band Windward/Leeward Medium728.40.8238
5-Band Windward/Leeward Med/High664.00.9037
5-Band Windward/Leeward High634.70.9453
Windward/Leeward 60-40 Low1119.60.5359
Windward/Leeward 60-40 Low/Med850.50.7054
Windward/Leeward 60-40 Medium745.30.8050
Windward/Leeward 60-40 Med/High688.10.8720
Windward/Leeward 60-40 High663.60.9042
5-Band AP Low836.40.7174
5-Band AP Low/Med672.90.8917
5-Band AP Medium601.20.9981
5-Band AP Med/High561.81.0680
5-Band AP High540.81.1095
5-Band SF Bay Tour - Low970.40.6183
5-Band SF Bay Tour - Low/Med806.60.7438
5-Band SF Bay Tour - Medium706.40.8493
5-Band SF Bay Tour - Med/High651.40.9211
5-Band SF Bay Tour - High624.80.9603
Chicago-Mac Upwind0.8585
Chicago-Mac All Purpose0.8828
Chicago-Mac Downwind0.9016
Bayview-Mac Cove Island0.6609
Bayview-Mac Shore0.6671
Harvest Moon Regatta535.01.1215
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance663.00.9050
Triple Number Coastal/Long Distance Low756.40.7932
Triple Number Coastal/Long Distance Medium607.90.9870
Triple Number Coastal/Long Distance High555.91.0793
Triple Number Windward/Leeward Low971.30.6177
Triple Number Windward/Leeward Medium739.90.8109
Triple Number Windward/Leeward High655.30.9156
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1598.81074.0822.6701.6632.3594.9565.0518.7506.1
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance663.00.9050
Triple Number Coastal/Long Distance Low756.40.7932
Triple Number Coastal/Long Distance Medium607.90.9870
Triple Number Coastal/Long Distance High555.91.0793
Triple Number Windward/Leeward Low971.30.6177
Triple Number Windward/Leeward Medium739.90.8109
Triple Number Windward/Leeward High655.30.9156
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1598.81074.0822.6701.6632.3594.9565.0518.7506.1
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance663.0
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1598.81074.0822.6701.6632.3594.9565.0518.7506.1
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low756.40.7932
Triple Number Coastal/Long Distance Medium607.90.9870
Triple Number Coastal/Long Distance High555.91.0793
Triple Number Windward/Leeward Low971.30.6177
Triple Number Windward/Leeward Medium739.90.8109
Triple Number Windward/Leeward High655.30.9156
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating663.00.9050
FinRating, kevyt tuuli1109.10.9016
FinRating, kova tuuli544.70.9179
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low756.40.7932
Triple Number Coastal/Long Distance Medium607.90.9870
Triple Number Coastal/Long Distance High555.91.0793
Triple Number Windward/Leeward Low971.30.6177
Triple Number Windward/Leeward Medium739.90.8109
Triple Number Windward/Leeward High655.30.9156
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.9050
Triple Number Coastal/Long Distance Low0.7932
Triple Number Coastal/Long Distance Medium0.9870
Triple Number Coastal/Long Distance High1.0793
Triple Number Windward/Leeward Low0.6177
Triple Number Windward/Leeward Medium0.8109
Triple Number Windward/Leeward High0.9156
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1598.81074.0822.6701.6632.3594.9565.0518.7506.1
For information
General Purpose Handicap (GPH)679.8
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance663.00.9050
Triple Number Coastal/Long Distance Low756.40.7932
Triple Number Coastal/Long Distance Medium607.90.9870
Triple Number Coastal/Long Distance High555.91.0793
Triple Number Windward/Leeward Low971.30.6177
Triple Number Windward/Leeward Medium739.90.8109
Triple Number Windward/Leeward High655.30.9156
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1598.81074.0822.6701.6632.3594.9565.0518.7506.1
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low756.40.7932
Triple Number Coastal/Long Distance Medium607.90.9870
Triple Number Coastal/Long Distance High555.91.0793
Triple Number Windward/Leeward Low971.30.6177
Triple Number Windward/Leeward Medium739.90.8109
Triple Number Windward/Leeward High655.30.9156
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance663.00.9050
Triple Number Coastal/Long Distance Low756.40.7932
Triple Number Coastal/Long Distance Medium607.90.9870
Triple Number Coastal/Long Distance High555.91.0793
Triple Number Windward/Leeward Low971.30.6177
Triple Number Windward/Leeward Medium739.90.8109
Triple Number Windward/Leeward High655.30.9156
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1598.81074.0822.6701.6632.3594.9565.0518.7506.1
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance663.00.9050
Triple Number Coastal/Long Distance Low756.40.7932
Triple Number Coastal/Long Distance Medium607.90.9870
Triple Number Coastal/Long Distance High555.91.0793
Triple Number Windward/Leeward Low971.30.6177
Triple Number Windward/Leeward Medium739.90.8109
Triple Number Windward/Leeward High655.30.9156
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1598.81074.0822.6701.6632.3594.9565.0518.7506.1
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low756.4
Triple Number Coastal/Long Distance Medium607.9
Triple Number Coastal/Long Distance High555.9
Triple Number Windward/Leeward Low971.3
Triple Number Windward/Leeward Medium739.9
Triple Number Windward/Leeward High655.3
Predominantly Upwind659.4
Predominantly Downwind614.9
Predominantly Reaching592.3
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance663.00.9050
Triple Number Coastal/Long Distance Low756.40.7932
Triple Number Coastal/Long Distance Medium607.90.9870
Triple Number Coastal/Long Distance High555.91.0793
Triple Number Windward/Leeward Low971.30.6177
Triple Number Windward/Leeward Medium739.90.8109
Triple Number Windward/Leeward High655.30.9156
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1598.81074.0822.6701.6632.3594.9565.0518.7506.1
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7932
Triple Number Coastal/Long Distance Medium0.9870
Triple Number Coastal/Long Distance High1.0793
Triple Number Windward/Leeward Low0.6177
Triple Number Windward/Leeward Medium0.8109
Triple Number Windward/Leeward High0.9156
Coastal/Long Distance0.9050
Predominantly Upwind0.9099
Predominantly Downwind0.9758
For information
General Purpose Handicap (GPH)679.8
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)0.9812
Distanseseilas Trippeltall svak vind0.7932
Distanseseilas Trippeltall mellomvind0.9870
Distanseseilas Trippeltall sterk vind1.0793
Pølsebane Trippeltall svak vind0.6177
Pølsebane Trippeltall mellomvind0.8109
Pølsebane Trippeltall sterk vind0.9156
Motvind Singeltall0.9099
Medvind Singeltall0.9758
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low756.40.7932
Triple Number Coastal/Long Distance Medium607.90.9870
Triple Number Coastal/Long Distance High555.91.0793
Triple Number Windward/Leeward Low971.30.6177
Triple Number Windward/Leeward Medium739.90.8109
Triple Number Windward/Leeward High655.30.9156
Coastal/Long Distance663.00.9050
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind659.40.9099
Predominantly Downwind614.90.9758
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore622.90.9633
Cape Doctor Coastal530.21.1316
Triple Number Coastal/Long Distance Low756.40.7932
Triple Number Coastal/Long Distance Medium607.90.9870
Triple Number Coastal/Long Distance High555.91.0793
Triple Number Windward/Leeward Low971.30.6177
Triple Number Windward/Leeward Medium739.90.8109
Triple Number Windward/Leeward High655.30.9156
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7932
Triple Number Coastal/Long Distance Medium0.9870
Triple Number Coastal/Long Distance High1.0793
Triple Number Windward/Leeward Low0.6177
Triple Number Windward/Leeward Medium0.8109
Triple Number Windward/Leeward High0.9156
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7932
Triple Number Coastal/Long Distance Medium0.9870
Triple Number Coastal/Long Distance High1.0793
Triple Number Windward/Leeward Low0.6177
Triple Number Windward/Leeward Medium0.8109
Triple Number Windward/Leeward High0.9156
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance663.00.9050
Triple Number Coastal/Long Distance Low756.40.7932
Triple Number Coastal/Long Distance Medium607.90.9870
Triple Number Coastal/Long Distance High555.91.0793
Triple Number Windward/Leeward Low971.30.6177
Triple Number Windward/Leeward Medium739.90.8109
Triple Number Windward/Leeward High655.30.9156
Predominantly Upwind659.40.9099
Predominantly Downwind614.90.9758
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1598.81074.0822.6701.6632.3594.9565.0518.7506.1
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance663.00.9050
Triple Number Coastal/Long Distance Low756.40.7932
Triple Number Coastal/Long Distance Medium607.90.9870
Triple Number Coastal/Long Distance High555.91.0793
Triple Number Windward/Leeward Low971.30.6177
Triple Number Windward/Leeward Medium739.90.8109
Triple Number Windward/Leeward High655.30.9156
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1598.81074.0822.6701.6632.3594.9565.0518.7506.1
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low756.40.7932
Triple Number AP Medium608.00.9869
Triple Number AP High555.91.0793
Triple Number Windward/Leeward Low1014.20.5916
Triple Number Windward/Leeward Medium739.90.8109
Triple Number Windward/Leeward High655.30.9156
Single Number Predominant Upwind681.80.8800
Single Number Predominant Reaching605.30.9912
Single Number Predominant Downwind642.70.9335
Predominant Upwind - Low884.20.6786
Predominant Upwind - Low/Med705.20.8508
Predominant Upwind - Medium644.40.9311
Predominant Upwind - Med/High613.00.9788
Predominant Upwind - High598.61.0024
Predominant Downwind Low930.50.6448
Predominant Downwind Low/Med692.30.8667
Predominant Downwind Medium595.01.0085
Predominant Downwind Med/High536.31.1187
Predominant Downwind High501.51.1965
Predominant Reaching Low809.10.7416
Predominant Reaching Low/Med634.50.9457
Predominant Reaching Medium570.51.0518
Predominant Reaching Med/High532.91.1260
Predominant Reaching High509.91.1766
SA/DSPL Upwind25.07SA/DSPL Downwind39.48
Scoring OptionTODTOT
5-Band Windward/Leeward Low1127.80.5320
5-Band Windward/Leeward Low/Med843.70.7112
5-Band Windward/Leeward Medium728.40.8238
5-Band Windward/Leeward Med/High664.00.9037
5-Band Windward/Leeward High634.70.9453
Windward/Leeward 60-40 Low1119.60.5359
Windward/Leeward 60-40 Low/Med850.50.7054
Windward/Leeward 60-40 Medium745.30.8050
Windward/Leeward 60-40 Med/High688.10.8720
Windward/Leeward 60-40 High663.60.9042
5-Band AP Low836.40.7174
5-Band AP Low/Med672.90.8917
5-Band AP Medium601.20.9981
5-Band AP Med/High561.81.0680
5-Band AP High540.81.1095
5-Band SF Bay Tour - Low970.40.6183
5-Band SF Bay Tour - Low/Med806.60.7438
5-Band SF Bay Tour - Medium706.40.8493
5-Band SF Bay Tour - Med/High651.40.9211
5-Band SF Bay Tour - High624.80.9603
Chicago-Mac Upwind0.8585
Chicago-Mac All Purpose0.8828
Chicago-Mac Downwind0.9016
Bayview-Mac Cove Island0.6609
Bayview-Mac Shore0.6671
Harvest Moon Regatta535.01.1215
Club Certificate2025
HegrenNOR 16365
Norges Seilforbund
Sognsveien 73
0854 OSLO
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassAphrodite 101MeasurementHINPlan reviewHull constructionSolidCarbon rudderNoLight stanchionsNoTrim tabNo
LOA9.904Max. Beam2.444Draft1.737Displacement3,105Wetted area15.78IMS L8.105LSM07.952Acc. length7.943Sink (kg/mm) 10.56
VCGD-0.180VCGM-0.196RM Rated (kg·m) 36.9Limit of positive stability(°) N/AStability IndexN/ADefault crew weight496Declared crew weight330
PROPELLER
Propeller TypeFolding 2 blades
InstallationShaft exposedTwin screwNoHydro generatorNo
PRD0.380PBWPIPA0.0131
PSD0.030PHD0.080PHL0.150
PSA22.0°ESL3.140
ST10.030ST20.000ST30.100
ST40.100ST50.100
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerNoMainsail furlerArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays1CheckstaysSpreaders1Rotating mastNo
P12.000IG10.910ISP10.910MDT10.085MDL10.145MDT20.000MDL20.000TL1.700MW0.000GO0.000
E3.430J3.600BAS0.870FSDFoilSFJ0.750SPL3.700WPLTPS0.000BD0.000MWT0.00MCG0.000
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodVCG entered directlyVCG entered-0.180Flotation Date01/01/2015
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Club Certificate2025
HegrenNOR 16365
Norges Seilforbund
Sognsveien 73
0854 OSLO
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment152-2025071108250.150.701.232.182.9324.4111/07/2025
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment152-2025071108220.080.631.252.583.985.3811.05YesNo 29.1311/07/2025152-2025071108240.070.481.051.682.393.0910.78YesNo 17.8211/07/2025
SYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLAreaMeas.DateComment152-20250711082610.7310.7310.736.776.4459.9411/07/2025
CRUISER/RACER REQUIREMENTS*
Accommodation length7.9 mTable area0.22 m²Headroom1.40 mMinimum number of berths2Personal gear stowage0.08 m³Fresh water capacity19 lMinimum number of seats in cockpit2Food stowage0.12 m³Fuel capacity20 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.