Non Spin/HSFClub Certificate2025
MardollNOR 11029
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 Angles43.3°43.3°41.8°40.1°38.9°38.3°38.2°38.9°40.2°
Beat VMG2.453.374.094.614.915.045.105.125.03
52°3.855.176.096.666.977.117.177.237.23
60°4.115.466.346.847.137.297.377.467.48
75°4.275.636.506.987.287.507.667.847.95
90°4.135.516.456.987.317.577.818.178.39
110°3.564.905.956.727.187.527.838.438.96
120°3.294.605.706.537.057.417.738.379.05
135°2.814.045.146.026.697.137.468.088.76
150°2.323.424.475.376.136.737.147.758.36
Run VMG2.012.963.874.695.426.106.667.387.95
Gybe Angles146.0°146.0°151.0°156.8°164.9°172.7°177.7°179.5°179.5°
APH ToD:594.8CDL: 8.861APH ToT: 1.0088CertNo:9292
BOAT
ClassDufour 34 StandardDesignerUmbertoFeliciBuilderDufour YachtsAge date01/2004Series date07/2003Offset fileDUF34PERF.offData file9292
HULL
Length Overall10.280 mMaximum Beam3.482 mDraft1.927 mDisplacement5,231 kgDLR6.7353IMS DivisionCruiser/RacerDynamic Allowance0.280%Age Allowance0.487%
PROPELLER
InstallationStrutTypeFolding 2 bladesDiameter0.380m
CREW
Maximum weight610 kg(default)Minimum weight480 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail32.5933.52Headsail Luffed34.0734.07Headsail FlyingSymmetricAsymmetric
STORM SAIL AREAS (m²)
Trysail9.31Storm Jib8.49Heavy Weather Jib22.92
SAIL LIMITS
Headsails5
✱ Zero set flying
Spinnakers0
✱ Spinnaker pole aboard
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.
Non Spin/HSFClub Certificate2025
MardollNOR 11029
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 VMG1466.81066.7879.7781.1732.6714.8706.5703.1715.0
52°934.4696.0590.7540.3516.9506.6502.0497.6498.2
60°875.9659.9567.9526.0505.0493.8488.6482.6481.5
75°843.9639.1553.4515.4494.4480.1469.8459.0452.9
90°872.6652.8557.9515.5492.5475.5461.0440.5429.0
110°1011.2734.9605.1535.6501.4479.0459.8427.3401.6
120°1095.0781.9631.9551.6510.6486.1465.9430.1397.9
135°1279.8890.4700.9598.0538.0504.9482.8445.5411.0
150°1553.91051.6805.2670.4586.9534.9504.3464.5430.5
Run VMG1792.41214.2929.2768.2663.9590.6540.7487.9452.6
Selected Courses
Windward / Leeward1626.31140.5904.5774.6698.2652.7623.6595.5583.8
All purpose1211.2867.6704.5618.4570.4542.8524.8502.7489.2
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward734.60.8168
All purpose594.81.0088
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low786.10.7633
Triple Number Coastal/Long Distance Medium590.71.0158
Triple Number Coastal/Long Distance High521.01.1516
Triple Number Windward/Leeward Low1022.50.5868
Triple Number Windward/Leeward Medium729.50.8225
Triple Number Windward/Leeward High620.30.9672
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance650.20.9228
Triple Number Coastal/Long Distance Low786.10.7633
Triple Number Coastal/Long Distance Medium590.71.0158
Triple Number Coastal/Long Distance High521.01.1516
Triple Number Windward/Leeward Low1022.50.5868
Triple Number Windward/Leeward Medium729.50.8225
Triple Number Windward/Leeward High620.30.9672
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1759.71147.9851.7698.1609.0563.7531.1481.8465.5
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.7521
Downwind "popa"0.8085
70% up, 30% down "Ilhabela"0.7682
30% up, 70% down "Ilhabela-inverso"0.7907
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low786.10.7633
Triple Number Coastal/Long Distance Medium590.71.0158
Triple Number Coastal/Long Distance High521.01.1516
Triple Number Windward/Leeward Low1022.50.5868
Triple Number Windward/Leeward Medium729.50.8225
Triple Number Windward/Leeward High620.30.9672
Predominantly Upwind629.70.9528
Predominantly Downwind623.10.9630
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low786.10.7633
Triple Number AP Medium590.71.0157
Triple Number AP High521.01.1516
Triple Number Windward/Leeward Low1070.20.5606
Triple Number Windward/Leeward Medium729.50.8225
Triple Number Windward/Leeward High620.30.9672
Single Number Predominant Upwind655.40.9155
Single Number Predominant Reaching595.11.0083
Single Number Predominant Downwind655.40.9154
Predominant Upwind - Low915.40.6554
Predominant Upwind - Low/Med694.30.8642
Predominant Upwind - Medium607.00.9884
Predominant Upwind - Med/High565.01.0620
Predominant Upwind - High550.01.0910
Predominant Downwind Low1004.20.5975
Predominant Downwind Low/Med721.00.8321
Predominant Downwind Medium597.21.0046
Predominant Downwind Med/High522.61.1481
Predominant Downwind High486.31.2338
Predominant Reaching Low847.10.7083
Predominant Reaching Low/Med637.20.9417
Predominant Reaching Medium551.61.0878
Predominant Reaching Med/High503.01.1929
Predominant Reaching High478.31.2544
SA/DSPL Upwind22.00SA/DSPL Downwind22.00
Scoring OptionTODTOT
5-Band Windward/Leeward Low1203.80.4984
5-Band Windward/Leeward Low/Med863.00.6952
5-Band Windward/Leeward Medium714.30.8400
5-Band Windward/Leeward Med/High630.10.9522
5-Band Windward/Leeward High598.31.0028
Windward/Leeward 60-40 Low1187.00.5055
Windward/Leeward 60-40 Low/Med860.60.6972
Windward/Leeward 60-40 Medium721.00.8322
Windward/Leeward 60-40 Med/High646.00.9288
Windward/Leeward 60-40 High619.80.9681
5-Band AP Low883.00.6795
5-Band AP Low/Med678.40.8845
5-Band AP Medium581.11.0325
5-Band AP Med/High527.91.1365
5-Band AP High504.21.1901
5-Band SF Bay Tour - Low1026.40.5845
5-Band SF Bay Tour - Low/Med821.30.7305
5-Band SF Bay Tour - Medium687.90.8722
5-Band SF Bay Tour - Med/High616.20.9736
5-Band SF Bay Tour - High589.01.0187
Chicago-Mac Upwind0.8862
Chicago-Mac All Purpose0.8871
Chicago-Mac Downwind0.8777
Bayview-Mac Cove Island0.6341
Bayview-Mac Shore0.6418
Harvest Moon Regatta517.31.1599
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance650.20.9228
Triple Number Coastal/Long Distance Low786.10.7633
Triple Number Coastal/Long Distance Medium590.71.0158
Triple Number Coastal/Long Distance High521.01.1516
Triple Number Windward/Leeward Low1022.50.5868
Triple Number Windward/Leeward Medium729.50.8225
Triple Number Windward/Leeward High620.30.9672
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1759.71147.9851.7698.1609.0563.7531.1481.8465.5
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance650.20.9228
Triple Number Coastal/Long Distance Low786.10.7633
Triple Number Coastal/Long Distance Medium590.71.0158
Triple Number Coastal/Long Distance High521.01.1516
Triple Number Windward/Leeward Low1022.50.5868
Triple Number Windward/Leeward Medium729.50.8225
Triple Number Windward/Leeward High620.30.9672
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1759.71147.9851.7698.1609.0563.7531.1481.8465.5
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance650.2
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1759.71147.9851.7698.1609.0563.7531.1481.8465.5
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low786.10.7633
Triple Number Coastal/Long Distance Medium590.71.0158
Triple Number Coastal/Long Distance High521.01.1516
Triple Number Windward/Leeward Low1022.50.5868
Triple Number Windward/Leeward Medium729.50.8225
Triple Number Windward/Leeward High620.30.9672
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating650.20.9228
FinRating, kevyt tuuli1185.40.8436
FinRating, kova tuuli508.10.9841
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low786.10.7633
Triple Number Coastal/Long Distance Medium590.71.0158
Triple Number Coastal/Long Distance High521.01.1516
Triple Number Windward/Leeward Low1022.50.5868
Triple Number Windward/Leeward Medium729.50.8225
Triple Number Windward/Leeward High620.30.9672
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.9228
Triple Number Coastal/Long Distance Low0.7633
Triple Number Coastal/Long Distance Medium1.0158
Triple Number Coastal/Long Distance High1.1516
Triple Number Windward/Leeward Low0.5868
Triple Number Windward/Leeward Medium0.8225
Triple Number Windward/Leeward High0.9672
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1759.71147.9851.7698.1609.0563.7531.1481.8465.5
For information
General Purpose Handicap (GPH)672.1
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance650.20.9228
Triple Number Coastal/Long Distance Low786.10.7633
Triple Number Coastal/Long Distance Medium590.71.0158
Triple Number Coastal/Long Distance High521.01.1516
Triple Number Windward/Leeward Low1022.50.5868
Triple Number Windward/Leeward Medium729.50.8225
Triple Number Windward/Leeward High620.30.9672
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1759.71147.9851.7698.1609.0563.7531.1481.8465.5
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low786.10.7633
Triple Number Coastal/Long Distance Medium590.71.0158
Triple Number Coastal/Long Distance High521.01.1516
Triple Number Windward/Leeward Low1022.50.5868
Triple Number Windward/Leeward Medium729.50.8225
Triple Number Windward/Leeward High620.30.9672
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance650.20.9228
Triple Number Coastal/Long Distance Low786.10.7633
Triple Number Coastal/Long Distance Medium590.71.0158
Triple Number Coastal/Long Distance High521.01.1516
Triple Number Windward/Leeward Low1022.50.5868
Triple Number Windward/Leeward Medium729.50.8225
Triple Number Windward/Leeward High620.30.9672
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1759.71147.9851.7698.1609.0563.7531.1481.8465.5
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance650.20.9228
Triple Number Coastal/Long Distance Low786.10.7633
Triple Number Coastal/Long Distance Medium590.71.0158
Triple Number Coastal/Long Distance High521.01.1516
Triple Number Windward/Leeward Low1022.50.5868
Triple Number Windward/Leeward Medium729.50.8225
Triple Number Windward/Leeward High620.30.9672
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1759.71147.9851.7698.1609.0563.7531.1481.8465.5
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low786.1
Triple Number Coastal/Long Distance Medium590.7
Triple Number Coastal/Long Distance High521.0
Triple Number Windward/Leeward Low1022.5
Triple Number Windward/Leeward Medium729.5
Triple Number Windward/Leeward High620.3
Predominantly Upwind629.7
Predominantly Downwind623.1
Predominantly Reaching587.2
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance650.20.9228
Triple Number Coastal/Long Distance Low786.10.7633
Triple Number Coastal/Long Distance Medium590.71.0158
Triple Number Coastal/Long Distance High521.01.1516
Triple Number Windward/Leeward Low1022.50.5868
Triple Number Windward/Leeward Medium729.50.8225
Triple Number Windward/Leeward High620.30.9672
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1759.71147.9851.7698.1609.0563.7531.1481.8465.5
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7633
Triple Number Coastal/Long Distance Medium1.0158
Triple Number Coastal/Long Distance High1.1516
Triple Number Windward/Leeward Low0.5868
Triple Number Windward/Leeward Medium0.8225
Triple Number Windward/Leeward High0.9672
Coastal/Long Distance0.9228
Predominantly Upwind0.9528
Predominantly Downwind0.9630
For information
General Purpose Handicap (GPH)672.1
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)1.0088
Distanseseilas Trippeltall svak vind0.7633
Distanseseilas Trippeltall mellomvind1.0158
Distanseseilas Trippeltall sterk vind1.1516
Pølsebane Trippeltall svak vind0.5868
Pølsebane Trippeltall mellomvind0.8225
Pølsebane Trippeltall sterk vind0.9672
Motvind Singeltall0.9528
Medvind Singeltall0.9630
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low786.10.7633
Triple Number Coastal/Long Distance Medium590.71.0158
Triple Number Coastal/Long Distance High521.01.1516
Triple Number Windward/Leeward Low1022.50.5868
Triple Number Windward/Leeward Medium729.50.8225
Triple Number Windward/Leeward High620.30.9672
Coastal/Long Distance650.20.9228
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind629.70.9528
Predominantly Downwind623.10.9630
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore587.31.0216
Cape Doctor Coastal493.21.2165
Triple Number Coastal/Long Distance Low786.10.7633
Triple Number Coastal/Long Distance Medium590.71.0158
Triple Number Coastal/Long Distance High521.01.1516
Triple Number Windward/Leeward Low1022.50.5868
Triple Number Windward/Leeward Medium729.50.8225
Triple Number Windward/Leeward High620.30.9672
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7633
Triple Number Coastal/Long Distance Medium1.0158
Triple Number Coastal/Long Distance High1.1516
Triple Number Windward/Leeward Low0.5868
Triple Number Windward/Leeward Medium0.8225
Triple Number Windward/Leeward High0.9672
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7633
Triple Number Coastal/Long Distance Medium1.0158
Triple Number Coastal/Long Distance High1.1516
Triple Number Windward/Leeward Low0.5868
Triple Number Windward/Leeward Medium0.8225
Triple Number Windward/Leeward High0.9672
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance650.20.9228
Triple Number Coastal/Long Distance Low786.10.7633
Triple Number Coastal/Long Distance Medium590.71.0158
Triple Number Coastal/Long Distance High521.01.1516
Triple Number Windward/Leeward Low1022.50.5868
Triple Number Windward/Leeward Medium729.50.8225
Triple Number Windward/Leeward High620.30.9672
Predominantly Upwind629.70.9528
Predominantly Downwind623.10.9630
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1759.71147.9851.7698.1609.0563.7531.1481.8465.5
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance650.20.9228
Triple Number Coastal/Long Distance Low786.10.7633
Triple Number Coastal/Long Distance Medium590.71.0158
Triple Number Coastal/Long Distance High521.01.1516
Triple Number Windward/Leeward Low1022.50.5868
Triple Number Windward/Leeward Medium729.50.8225
Triple Number Windward/Leeward High620.30.9672
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1759.71147.9851.7698.1609.0563.7531.1481.8465.5
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low786.10.7633
Triple Number AP Medium590.71.0157
Triple Number AP High521.01.1516
Triple Number Windward/Leeward Low1070.20.5606
Triple Number Windward/Leeward Medium729.50.8225
Triple Number Windward/Leeward High620.30.9672
Single Number Predominant Upwind655.40.9155
Single Number Predominant Reaching595.11.0083
Single Number Predominant Downwind655.40.9154
Predominant Upwind - Low915.40.6554
Predominant Upwind - Low/Med694.30.8642
Predominant Upwind - Medium607.00.9884
Predominant Upwind - Med/High565.01.0620
Predominant Upwind - High550.01.0910
Predominant Downwind Low1004.20.5975
Predominant Downwind Low/Med721.00.8321
Predominant Downwind Medium597.21.0046
Predominant Downwind Med/High522.61.1481
Predominant Downwind High486.31.2338
Predominant Reaching Low847.10.7083
Predominant Reaching Low/Med637.20.9417
Predominant Reaching Medium551.61.0878
Predominant Reaching Med/High503.01.1929
Predominant Reaching High478.31.2544
SA/DSPL Upwind22.00SA/DSPL Downwind22.00
Scoring OptionTODTOT
5-Band Windward/Leeward Low1203.80.4984
5-Band Windward/Leeward Low/Med863.00.6952
5-Band Windward/Leeward Medium714.30.8400
5-Band Windward/Leeward Med/High630.10.9522
5-Band Windward/Leeward High598.31.0028
Windward/Leeward 60-40 Low1187.00.5055
Windward/Leeward 60-40 Low/Med860.60.6972
Windward/Leeward 60-40 Medium721.00.8322
Windward/Leeward 60-40 Med/High646.00.9288
Windward/Leeward 60-40 High619.80.9681
5-Band AP Low883.00.6795
5-Band AP Low/Med678.40.8845
5-Band AP Medium581.11.0325
5-Band AP Med/High527.91.1365
5-Band AP High504.21.1901
5-Band SF Bay Tour - Low1026.40.5845
5-Band SF Bay Tour - Low/Med821.30.7305
5-Band SF Bay Tour - Medium687.90.8722
5-Band SF Bay Tour - Med/High616.20.9736
5-Band SF Bay Tour - High589.01.0187
Chicago-Mac Upwind0.8862
Chicago-Mac All Purpose0.8871
Chicago-Mac Downwind0.8777
Bayview-Mac Cove Island0.6341
Bayview-Mac Shore0.6418
Harvest Moon Regatta517.31.1599
Non Spin/HSFClub Certificate2025
MardollNOR 11029
Norges Seilforbund
Sognsveien 73
0854 OSLO
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassDufour 34 StandardMeasurementHINPlan reviewHull constructionCoredCarbon rudderNoLight stanchionsNoTrim tabNo
LOA10.280Max. Beam3.482Draft1.927Displacement5,231Wetted area23.67IMS L9.414LSM09.191Acc. length10.300Sink (kg/mm) 18.35
VCGD0.030VCGM0.061RM Rated (kg·m) 118.7Limit of positive stability(°) N/AStability IndexN/ADefault crew weight610Declared crew weightN/A
PROPELLER
Propeller TypeFolding 2 blades
InstallationStrutTwin screwNoHydro generatorNo
PRD0.380PBWPIPA0.0032
EDL2.170ST10.048ST20.170
ST30.170ST40.098ST50.290
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerNoMainsail furlerArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders2Rotating mastNo
P11.820IG12.960ISP12.980MDT10.120MDL10.180MDT20.120MDL20.180TL0.720MW0.180GO0.200
E4.500J3.750BAS1.680FSDFoilSFJ0.000SPL3.830WPLTPS0.000BD0.000MWT118.50MCG5.030
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodVCG entered directlyVCG entered0.030Flotation Date01/01/2015
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Non Spin/HSFClub Certificate2025
MardollNOR 11029
Norges Seilforbund
Sognsveien 73
0854 OSLO
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment441-2011070815150.150.001.772.983.8732.5908/07/2011
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment441-2011070815050.000.000.000.000.005.2312.80NoNo 34.0708/07/2011990-2024040415200.070.591.212.533.935.3712.23NoNo 31.8129/01/2013441-2011071114020.050.001.001.872.733.5612.71NoNo 23.3911/07/2011
CRUISER/RACER REQUIREMENTS*
Accommodation length10.3 mTable area0.44 m²Headroom1.72 mMinimum number of berths4Personal gear stowage0.16 m³Fresh water capacity86 lMinimum number of seats in cockpit4Food stowage0.24 m³Fuel capacity56 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.