Double HandedClub Certificate2025
Mickan IIINOR 15366
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 Angles48.0°48.0°48.0°48.0°48.0°48.0°48.0°48.0°48.0°
Beat VMG2.893.694.104.334.534.694.7713.5817.57
52°4.325.516.136.476.777.017.1320.3126.26
60°3.134.395.426.186.697.037.337.948.56
75°3.665.066.126.797.217.618.018.9511.00
90°3.895.326.376.977.417.848.299.5914.48
110°3.695.136.256.957.437.938.4510.0414.97
120°3.554.976.126.867.357.838.339.7414.12
135°3.194.525.676.537.087.548.019.1511.58
150°2.673.905.035.976.687.167.598.529.85
Run VMG2.313.374.365.215.956.547.017.828.72
Gybe Angles148.0°148.0°151.6°155.2°161.5°168.2°176.3°177.2°166.7°
APH ToD:580.1CDL: 8.003APH ToT: 1.0343CertNo:667138
BOAT
ClassFirst 31.7 HRDesignerGroupeFinotBuilderBeneteauAge dateSeries date01/1998Offset fileFIRST317.offData file667138
HULL
Length Overall9.610 mMaximum Beam3.212 mDraft1.921 mDisplacement3,740 kgDLR5.1208IMS DivisionCruiser/RacerDynamic Allowance0.310%Age Allowance0.487%
PROPELLER
InstallationStrutTypeFolding 2 bladesDiameter0.380m
CREW
Maximum weight170 kg(default)Minimum weight120 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail26.5127.10Headsail Luffed19.4719.47Headsail Flying41.8941.89Symmetric62.1862.18Asymmetric
STORM SAIL AREAS (m²)
Trysail7.65Storm Jib7.62Heavy Weather Jib20.56
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.
Double HandedClub Certificate2025
Mickan IIINOR 15366
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 VMG1245.6976.2877.9831.9794.7768.0754.9265.0204.8
52°833.7653.2587.2556.4531.4513.6504.8177.3137.1
60°1150.2820.6663.9582.7538.3511.9491.1453.2420.4
75°982.7712.2587.9530.5499.2473.0449.4402.3327.4
90°924.4676.3565.1516.2486.0459.2434.3375.5248.6
110°975.2701.8575.6518.0484.2454.2425.9358.5240.5
120°1013.4723.8588.4524.9489.8460.0432.3369.6254.9
135°1128.8795.7635.1551.1508.5477.7449.7393.5311.0
150°1347.6924.1716.4602.8538.6502.7474.1422.4365.4
Run VMG1557.41067.0826.2691.2605.5550.2513.8460.6412.8
Selected Courses
Windward / Leeward1391.11021.6852.0761.6700.1659.1634.4362.8308.8
All purpose1119.4819.6682.3613.1570.2539.9517.2350.7278.5
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward712.00.8427
All purpose580.11.0343
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low750.90.7990
Triple Number Coastal/Long Distance Medium586.21.0235
Triple Number Coastal/Long Distance High460.41.3031
Triple Number Windward/Leeward Low936.80.6405
Triple Number Windward/Leeward Medium723.00.8299
Triple Number Windward/Leeward High538.71.1137
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance639.30.9385
Triple Number Coastal/Long Distance Low750.90.7990
Triple Number Coastal/Long Distance Medium586.21.0235
Triple Number Coastal/Long Distance High460.41.3031
Triple Number Windward/Leeward Low936.80.6405
Triple Number Windward/Leeward Medium723.00.8299
Triple Number Windward/Leeward High538.71.1137
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1476.61026.1808.3691.0612.8563.7523.3395.6316.9
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.7972
Downwind "popa"0.8909
70% up, 30% down "Ilhabela"0.8231
30% up, 70% down "Ilhabela-inverso"0.8605
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low750.90.7990
Triple Number Coastal/Long Distance Medium586.21.0235
Triple Number Coastal/Long Distance High460.41.3031
Triple Number Windward/Leeward Low936.80.6405
Triple Number Windward/Leeward Medium723.00.8299
Triple Number Windward/Leeward High538.71.1137
Predominantly Upwind633.00.9479
Predominantly Downwind590.81.0156
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low750.90.7990
Triple Number AP Medium586.31.0234
Triple Number AP High460.41.3031
Triple Number Windward/Leeward Low974.20.6159
Triple Number Windward/Leeward Medium723.00.8299
Triple Number Windward/Leeward High538.71.1137
Single Number Predominant Upwind618.80.9696
Single Number Predominant Reaching560.81.0698
Single Number Predominant Downwind606.10.9899
Predominant Upwind - Low847.10.7083
Predominant Upwind - Low/Med685.50.8753
Predominant Upwind - Medium617.70.9713
Predominant Upwind - Med/High525.81.1411
Predominant Upwind - High320.01.8748
Predominant Downwind Low909.70.6596
Predominant Downwind Low/Med673.20.8913
Predominant Downwind Medium570.41.0519
Predominant Downwind Med/High487.61.2305
Predominant Downwind High386.61.5520
Predominant Reaching Low799.50.7505
Predominant Reaching Low/Med616.50.9732
Predominant Reaching Medium540.21.1107
Predominant Reaching Med/High467.31.2839
Predominant Reaching High352.01.7044
SA/DSPL Upwind19.00SA/DSPL Downwind36.65
Scoring OptionTODTOT
5-Band Windward/Leeward Low1074.20.5586
5-Band Windward/Leeward Low/Med822.70.7293
5-Band Windward/Leeward Medium710.70.8443
5-Band Windward/Leeward Med/High597.21.0047
5-Band Windward/Leeward High400.41.4983
Windward/Leeward 60-40 Low1063.10.5644
Windward/Leeward 60-40 Low/Med830.90.7221
Windward/Leeward 60-40 Medium728.60.8236
Windward/Leeward 60-40 Med/High612.90.9789
Windward/Leeward 60-40 High388.21.5455
5-Band AP Low847.10.7083
5-Band AP Low/Med661.60.9070
5-Band AP Medium577.21.0396
5-Band AP Med/High496.81.2076
5-Band AP High367.01.6347
5-Band SF Bay Tour - Low932.80.6432
5-Band SF Bay Tour - Low/Med788.20.7612
5-Band SF Bay Tour - Medium688.80.8711
5-Band SF Bay Tour - Med/High582.51.0301
5-Band SF Bay Tour - High384.11.5621
Chicago-Mac Upwind0.9211
Chicago-Mac All Purpose0.9367
Chicago-Mac Downwind0.9457
Bayview-Mac Cove Island0.6857
Bayview-Mac Shore0.6917
Harvest Moon Regatta498.71.2031
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance639.30.9385
Triple Number Coastal/Long Distance Low750.90.7990
Triple Number Coastal/Long Distance Medium586.21.0235
Triple Number Coastal/Long Distance High460.41.3031
Triple Number Windward/Leeward Low936.80.6405
Triple Number Windward/Leeward Medium723.00.8299
Triple Number Windward/Leeward High538.71.1137
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1476.61026.1808.3691.0612.8563.7523.3395.6316.9
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance639.30.9385
Triple Number Coastal/Long Distance Low750.90.7990
Triple Number Coastal/Long Distance Medium586.21.0235
Triple Number Coastal/Long Distance High460.41.3031
Triple Number Windward/Leeward Low936.80.6405
Triple Number Windward/Leeward Medium723.00.8299
Triple Number Windward/Leeward High538.71.1137
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1476.61026.1808.3691.0612.8563.7523.3395.6316.9
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance639.3
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1476.61026.1808.3691.0612.8563.7523.3395.6316.9
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low750.90.7990
Triple Number Coastal/Long Distance Medium586.21.0235
Triple Number Coastal/Long Distance High460.41.3031
Triple Number Windward/Leeward Low936.80.6405
Triple Number Windward/Leeward Medium723.00.8299
Triple Number Windward/Leeward High538.71.1137
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating639.30.9385
FinRating, kevyt tuuli1071.20.9336
FinRating, kova tuuli390.61.2801
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low750.90.7990
Triple Number Coastal/Long Distance Medium586.21.0235
Triple Number Coastal/Long Distance High460.41.3031
Triple Number Windward/Leeward Low936.80.6405
Triple Number Windward/Leeward Medium723.00.8299
Triple Number Windward/Leeward High538.71.1137
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.9385
Triple Number Coastal/Long Distance Low0.7990
Triple Number Coastal/Long Distance Medium1.0235
Triple Number Coastal/Long Distance High1.3031
Triple Number Windward/Leeward Low0.6405
Triple Number Windward/Leeward Medium0.8299
Triple Number Windward/Leeward High1.1137
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1476.61026.1808.3691.0612.8563.7523.3395.6316.9
For information
General Purpose Handicap (GPH)653.3
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance639.30.9385
Triple Number Coastal/Long Distance Low750.90.7990
Triple Number Coastal/Long Distance Medium586.21.0235
Triple Number Coastal/Long Distance High460.41.3031
Triple Number Windward/Leeward Low936.80.6405
Triple Number Windward/Leeward Medium723.00.8299
Triple Number Windward/Leeward High538.71.1137
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1476.61026.1808.3691.0612.8563.7523.3395.6316.9
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low750.90.7990
Triple Number Coastal/Long Distance Medium586.21.0235
Triple Number Coastal/Long Distance High460.41.3031
Triple Number Windward/Leeward Low936.80.6405
Triple Number Windward/Leeward Medium723.00.8299
Triple Number Windward/Leeward High538.71.1137
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance639.30.9385
Triple Number Coastal/Long Distance Low750.90.7990
Triple Number Coastal/Long Distance Medium586.21.0235
Triple Number Coastal/Long Distance High460.41.3031
Triple Number Windward/Leeward Low936.80.6405
Triple Number Windward/Leeward Medium723.00.8299
Triple Number Windward/Leeward High538.71.1137
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1476.61026.1808.3691.0612.8563.7523.3395.6316.9
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance639.30.9385
Triple Number Coastal/Long Distance Low750.90.7990
Triple Number Coastal/Long Distance Medium586.21.0235
Triple Number Coastal/Long Distance High460.41.3031
Triple Number Windward/Leeward Low936.80.6405
Triple Number Windward/Leeward Medium723.00.8299
Triple Number Windward/Leeward High538.71.1137
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1476.61026.1808.3691.0612.8563.7523.3395.6316.9
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low750.9
Triple Number Coastal/Long Distance Medium586.2
Triple Number Coastal/Long Distance High460.4
Triple Number Windward/Leeward Low936.8
Triple Number Windward/Leeward Medium723.0
Triple Number Windward/Leeward High538.7
Predominantly Upwind633.0
Predominantly Downwind590.8
Predominantly Reaching564.7
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance639.30.9385
Triple Number Coastal/Long Distance Low750.90.7990
Triple Number Coastal/Long Distance Medium586.21.0235
Triple Number Coastal/Long Distance High460.41.3031
Triple Number Windward/Leeward Low936.80.6405
Triple Number Windward/Leeward Medium723.00.8299
Triple Number Windward/Leeward High538.71.1137
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1476.61026.1808.3691.0612.8563.7523.3395.6316.9
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7990
Triple Number Coastal/Long Distance Medium1.0235
Triple Number Coastal/Long Distance High1.3031
Triple Number Windward/Leeward Low0.6405
Triple Number Windward/Leeward Medium0.8299
Triple Number Windward/Leeward High1.1137
Coastal/Long Distance0.9385
Predominantly Upwind0.9479
Predominantly Downwind1.0156
For information
General Purpose Handicap (GPH)653.3
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)1.0343
Distanseseilas Trippeltall svak vind0.7990
Distanseseilas Trippeltall mellomvind1.0235
Distanseseilas Trippeltall sterk vind1.3031
Pølsebane Trippeltall svak vind0.6405
Pølsebane Trippeltall mellomvind0.8299
Pølsebane Trippeltall sterk vind1.1137
Motvind Singeltall0.9479
Medvind Singeltall1.0156
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low750.90.7990
Triple Number Coastal/Long Distance Medium586.21.0235
Triple Number Coastal/Long Distance High460.41.3031
Triple Number Windward/Leeward Low936.80.6405
Triple Number Windward/Leeward Medium723.00.8299
Triple Number Windward/Leeward High538.71.1137
Coastal/Long Distance639.30.9385
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind633.00.9479
Predominantly Downwind590.81.0156
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore325.01.8460
Cape Doctor Coastal300.21.9987
Triple Number Coastal/Long Distance Low750.90.7990
Triple Number Coastal/Long Distance Medium586.21.0235
Triple Number Coastal/Long Distance High460.41.3031
Triple Number Windward/Leeward Low936.80.6405
Triple Number Windward/Leeward Medium723.00.8299
Triple Number Windward/Leeward High538.71.1137
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7990
Triple Number Coastal/Long Distance Medium1.0235
Triple Number Coastal/Long Distance High1.3031
Triple Number Windward/Leeward Low0.6405
Triple Number Windward/Leeward Medium0.8299
Triple Number Windward/Leeward High1.1137
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7990
Triple Number Coastal/Long Distance Medium1.0235
Triple Number Coastal/Long Distance High1.3031
Triple Number Windward/Leeward Low0.6405
Triple Number Windward/Leeward Medium0.8299
Triple Number Windward/Leeward High1.1137
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance639.30.9385
Triple Number Coastal/Long Distance Low750.90.7990
Triple Number Coastal/Long Distance Medium586.21.0235
Triple Number Coastal/Long Distance High460.41.3031
Triple Number Windward/Leeward Low936.80.6405
Triple Number Windward/Leeward Medium723.00.8299
Triple Number Windward/Leeward High538.71.1137
Predominantly Upwind633.00.9479
Predominantly Downwind590.81.0156
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1476.61026.1808.3691.0612.8563.7523.3395.6316.9
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance639.30.9385
Triple Number Coastal/Long Distance Low750.90.7990
Triple Number Coastal/Long Distance Medium586.21.0235
Triple Number Coastal/Long Distance High460.41.3031
Triple Number Windward/Leeward Low936.80.6405
Triple Number Windward/Leeward Medium723.00.8299
Triple Number Windward/Leeward High538.71.1137
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1476.61026.1808.3691.0612.8563.7523.3395.6316.9
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low750.90.7990
Triple Number AP Medium586.31.0234
Triple Number AP High460.41.3031
Triple Number Windward/Leeward Low974.20.6159
Triple Number Windward/Leeward Medium723.00.8299
Triple Number Windward/Leeward High538.71.1137
Single Number Predominant Upwind618.80.9696
Single Number Predominant Reaching560.81.0698
Single Number Predominant Downwind606.10.9899
Predominant Upwind - Low847.10.7083
Predominant Upwind - Low/Med685.50.8753
Predominant Upwind - Medium617.70.9713
Predominant Upwind - Med/High525.81.1411
Predominant Upwind - High320.01.8748
Predominant Downwind Low909.70.6596
Predominant Downwind Low/Med673.20.8913
Predominant Downwind Medium570.41.0519
Predominant Downwind Med/High487.61.2305
Predominant Downwind High386.61.5520
Predominant Reaching Low799.50.7505
Predominant Reaching Low/Med616.50.9732
Predominant Reaching Medium540.21.1107
Predominant Reaching Med/High467.31.2839
Predominant Reaching High352.01.7044
SA/DSPL Upwind19.00SA/DSPL Downwind36.65
Scoring OptionTODTOT
5-Band Windward/Leeward Low1074.20.5586
5-Band Windward/Leeward Low/Med822.70.7293
5-Band Windward/Leeward Medium710.70.8443
5-Band Windward/Leeward Med/High597.21.0047
5-Band Windward/Leeward High400.41.4983
Windward/Leeward 60-40 Low1063.10.5644
Windward/Leeward 60-40 Low/Med830.90.7221
Windward/Leeward 60-40 Medium728.60.8236
Windward/Leeward 60-40 Med/High612.90.9789
Windward/Leeward 60-40 High388.21.5455
5-Band AP Low847.10.7083
5-Band AP Low/Med661.60.9070
5-Band AP Medium577.21.0396
5-Band AP Med/High496.81.2076
5-Band AP High367.01.6347
5-Band SF Bay Tour - Low932.80.6432
5-Band SF Bay Tour - Low/Med788.20.7612
5-Band SF Bay Tour - Medium688.80.8711
5-Band SF Bay Tour - Med/High582.51.0301
5-Band SF Bay Tour - High384.11.5621
Chicago-Mac Upwind0.9211
Chicago-Mac All Purpose0.9367
Chicago-Mac Downwind0.9457
Bayview-Mac Cove Island0.6857
Bayview-Mac Shore0.6917
Harvest Moon Regatta498.71.2031
Double HandedClub Certificate2025
Mickan IIINOR 15366
Norges Seilforbund
Sognsveien 73
0854 OSLO
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassFirst 31.7 HRMeasurementHINPlan reviewHull constructionSolidCarbon rudderNoLight stanchionsNoTrim tabNo
LOA9.610Max. Beam3.212Draft1.921Displacement3,740Wetted area20.61IMS L8.945LSM09.005Acc. length9.610Sink (kg/mm) 16.04
VCGD-999.000VCGM-999.039RM Rated (kg·m) 65293.2Limit of positive stability(°) N/AStability IndexN/ADefault crew weight170Declared crew weightN/A
PROPELLER
Propeller TypeFolding 2 blades
InstallationStrutTwin screwNoHydro generatorNo
PRD0.380PBWPIPA0.0033
EDL2.380ST10.050ST20.170
ST30.170ST40.100ST50.310
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerNoMainsail furlerArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders1Rotating mastNo
P11.200IG12.270ISP12.370MDT10.100MDL10.160MDT20.100MDL20.160TL0.000MW0.160GO0.180
E3.900J3.500BAS1.530FSDFoilSFJ0.000SPL3.580WPLTPS4.210BD0.000MWT0.00MCG0.000
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodVCG entered directlyVCG entered-999.000Flotation Date01/01/2015
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Double HandedClub Certificate2025
Mickan IIINOR 15366
Norges Seilforbund
Sognsveien 73
0854 OSLO
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment365-2020052710090.140.831.532.593.3326.5127/05/2020
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment626-2018042515360.031.052.003.634.955.8312.56NoYes041.8925/04/2018625-2025080712590.090.460.871.712.593.5011.19YesNo 19.4707/08/2025
SYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLAreaMeas.DateComment445-20170524214511.7511.7511.756.356.3562.1824/05/2017
CRUISER/RACER REQUIREMENTS*
Accommodation length9.6 mTable area0.44 m²Headroom1.67 mMinimum number of berths4Personal gear stowage0.16 m³Fresh water capacity72 lMinimum number of seats in cockpit4Food stowage0.24 m³Fuel capacity42 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.