Double HandedClub Certificate2025
the JokerNOR 14516
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°41.3°40.1°39.3°38.9°38.6°38.5°39.3°
Beat VMG2.473.454.244.795.115.265.355.435.40
52°3.855.256.296.997.347.527.617.717.72
60°4.105.536.557.217.557.737.837.947.97
75°4.325.836.867.387.747.968.128.318.41
90°4.586.157.197.707.958.118.288.638.87
110°4.496.077.197.838.228.518.789.239.53
120°4.225.837.057.778.228.628.999.6410.43
135°3.755.276.517.417.968.418.869.8711.75
150°3.104.435.626.637.397.898.289.0810.11
Run VMG2.683.844.875.746.416.897.308.008.75
Gybe Angles142.8°142.8°146.7°149.6°151.5°154.6°159.2°161.0°141.1°
APH ToD:535.8CDL: 10.051APH ToT: 1.1198CertNo:667090
BOAT
ClassJ/120DesignerJohnstoneBuilderJ-CompositeAge date01/2002Series date01/1995Offset filej120.offData file667090
HULL
Length Overall12.244 mMaximum Beam3.674 mDraft2.201 mDisplacement7,712 kgDLR5.6338IMS DivisionCruiser/RacerDynamic Allowance0.250%Age Allowance0.487%
PROPELLER
InstallationStrutTypeFolding 2 bladesDiameter0.460m
CREW
Maximum weight140 kg(declared)Minimum weight120 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail43.8844.69Headsail Luffed33.1233.12Headsail FlyingSymmetricAsymmetric112.17112.17 (1 asymmetric(s) with SHW/SFL < 85%)
STORM SAIL AREAS (m²)
Trysail13.48Storm Jib11.92Heavy Weather Jib32.18
SAIL LIMITS
Headsails6Spinnakers5
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
the JokerNOR 14516
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 VMG1458.01044.4849.4751.8704.4684.4673.2662.7667.2
52°934.0685.7571.9515.1490.2479.0473.2467.2466.3
60°877.5650.9549.3499.0476.6465.4459.6453.3451.5
75°832.6617.6524.8487.8465.0452.1443.3433.3427.9
90°785.3585.7500.4467.7452.9443.8435.0417.3406.0
110°801.8592.8500.5460.0438.0423.1410.2390.2377.8
120°852.5617.8510.7463.4437.7417.8400.6373.5345.2
135°959.2683.6552.6486.1452.1427.9406.3364.7306.3
150°1162.0812.0640.5543.3487.3456.4434.5396.4356.3
Run VMG1341.8937.6739.6627.4561.6522.3493.2450.2411.4
Selected Courses
Windward / Leeward1399.6991.0794.5689.6633.0603.4583.2556.5539.3
All purpose1053.3758.9621.1552.0516.2496.4481.9460.7444.0
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward663.60.9041
All purpose535.81.1198
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low690.00.8696
Triple Number Coastal/Long Distance Medium531.91.1280
Triple Number Coastal/Long Distance High477.61.2564
Triple Number Windward/Leeward Low892.70.6721
Triple Number Windward/Leeward Medium657.90.9120
Triple Number Windward/Leeward High578.21.0377
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance583.61.0282
Triple Number Coastal/Long Distance Low690.00.8696
Triple Number Coastal/Long Distance Medium531.91.1280
Triple Number Coastal/Long Distance High477.61.2564
Triple Number Windward/Leeward Low892.70.6721
Triple Number Windward/Leeward Medium657.90.9120
Triple Number Windward/Leeward High578.21.0377
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1479.6985.7745.6621.3551.1514.9486.4441.1423.9
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.7821
Downwind "popa"0.9695
70% up, 30% down "Ilhabela"0.8302
30% up, 70% down "Ilhabela-inverso"0.9045
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low690.00.8696
Triple Number Coastal/Long Distance Medium531.91.1280
Triple Number Coastal/Long Distance High477.61.2564
Triple Number Windward/Leeward Low892.70.6721
Triple Number Windward/Leeward Medium657.90.9120
Triple Number Windward/Leeward High578.21.0377
Predominantly Upwind583.21.0287
Predominantly Downwind539.41.1124
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low690.00.8696
Triple Number AP Medium532.01.1279
Triple Number AP High477.61.2564
Triple Number Windward/Leeward Low933.00.6431
Triple Number Windward/Leeward Medium657.90.9120
Triple Number Windward/Leeward High578.21.0377
Single Number Predominant Upwind608.20.9865
Single Number Predominant Reaching529.31.1336
Single Number Predominant Downwind562.91.0659
Predominant Upwind - Low846.70.7086
Predominant Upwind - Low/Med641.50.9353
Predominant Upwind - Medium564.01.0638
Predominant Upwind - Med/High527.41.1377
Predominant Upwind - High510.71.1749
Predominant Downwind Low820.40.7313
Predominant Downwind Low/Med607.50.9876
Predominant Downwind Medium520.51.1527
Predominant Downwind Med/High468.81.2800
Predominant Downwind High434.81.3799
Predominant Reaching Low731.50.8203
Predominant Reaching Low/Med559.51.0724
Predominant Reaching Medium494.81.2127
Predominant Reaching Med/High458.41.3088
Predominant Reaching High433.91.3829
SA/DSPL Upwind19.60SA/DSPL Downwind39.71
Scoring OptionTODTOT
5-Band Windward/Leeward Low1044.10.5747
5-Band Windward/Leeward Low/Med762.60.7868
5-Band Windward/Leeward Medium646.80.9277
5-Band Windward/Leeward Med/High586.31.0234
5-Band Windward/Leeward High558.11.0750
Windward/Leeward 60-40 Low1055.10.5687
Windward/Leeward 60-40 Low/Med774.60.7746
Windward/Leeward 60-40 Medium661.10.9076
Windward/Leeward 60-40 Med/High604.20.9930
Windward/Leeward 60-40 High579.61.0353
5-Band AP Low760.00.7895
5-Band AP Low/Med601.50.9975
5-Band AP Medium524.71.1435
5-Band AP Med/High483.61.2406
5-Band AP High461.51.3002
5-Band SF Bay Tour - Low900.70.6661
5-Band SF Bay Tour - Low/Med729.80.8221
5-Band SF Bay Tour - Medium623.60.9622
5-Band SF Bay Tour - Med/High568.81.0548
5-Band SF Bay Tour - High542.31.1063
Chicago-Mac Upwind0.9560
Chicago-Mac All Purpose0.9952
Chicago-Mac Downwind1.0284
Bayview-Mac Cove Island0.7247
Bayview-Mac Shore0.7299
Harvest Moon Regatta464.01.2931
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance583.61.0282
Triple Number Coastal/Long Distance Low690.00.8696
Triple Number Coastal/Long Distance Medium531.91.1280
Triple Number Coastal/Long Distance High477.61.2564
Triple Number Windward/Leeward Low892.70.6721
Triple Number Windward/Leeward Medium657.90.9120
Triple Number Windward/Leeward High578.21.0377
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1479.6985.7745.6621.3551.1514.9486.4441.1423.9
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance583.61.0282
Triple Number Coastal/Long Distance Low690.00.8696
Triple Number Coastal/Long Distance Medium531.91.1280
Triple Number Coastal/Long Distance High477.61.2564
Triple Number Windward/Leeward Low892.70.6721
Triple Number Windward/Leeward Medium657.90.9120
Triple Number Windward/Leeward High578.21.0377
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1479.6985.7745.6621.3551.1514.9486.4441.1423.9
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance583.6
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1479.6985.7745.6621.3551.1514.9486.4441.1423.9
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low690.00.8696
Triple Number Coastal/Long Distance Medium531.91.1280
Triple Number Coastal/Long Distance High477.61.2564
Triple Number Windward/Leeward Low892.70.6721
Triple Number Windward/Leeward Medium657.90.9120
Triple Number Windward/Leeward High578.21.0377
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating578.41.0373
FinRating, kevyt tuuli1022.60.9779
FinRating, kova tuuli464.11.0774
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low690.00.8696
Triple Number Coastal/Long Distance Medium531.91.1280
Triple Number Coastal/Long Distance High477.61.2564
Triple Number Windward/Leeward Low892.70.6721
Triple Number Windward/Leeward Medium657.90.9120
Triple Number Windward/Leeward High578.21.0377
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance1.0282
Triple Number Coastal/Long Distance Low0.8696
Triple Number Coastal/Long Distance Medium1.1280
Triple Number Coastal/Long Distance High1.2564
Triple Number Windward/Leeward Low0.6721
Triple Number Windward/Leeward Medium0.9120
Triple Number Windward/Leeward High1.0377
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1479.6985.7745.6621.3551.1514.9486.4441.1423.9
For information
General Purpose Handicap (GPH)601.7
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance583.61.0282
Triple Number Coastal/Long Distance Low690.00.8696
Triple Number Coastal/Long Distance Medium531.91.1280
Triple Number Coastal/Long Distance High477.61.2564
Triple Number Windward/Leeward Low892.70.6721
Triple Number Windward/Leeward Medium657.90.9120
Triple Number Windward/Leeward High578.21.0377
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1479.6985.7745.6621.3551.1514.9486.4441.1423.9
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low690.00.8696
Triple Number Coastal/Long Distance Medium531.91.1280
Triple Number Coastal/Long Distance High477.61.2564
Triple Number Windward/Leeward Low892.70.6721
Triple Number Windward/Leeward Medium657.90.9120
Triple Number Windward/Leeward High578.21.0377
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance583.61.0282
Triple Number Coastal/Long Distance Low690.00.8696
Triple Number Coastal/Long Distance Medium531.91.1280
Triple Number Coastal/Long Distance High477.61.2564
Triple Number Windward/Leeward Low892.70.6721
Triple Number Windward/Leeward Medium657.90.9120
Triple Number Windward/Leeward High578.21.0377
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1479.6985.7745.6621.3551.1514.9486.4441.1423.9
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance583.61.0282
Triple Number Coastal/Long Distance Low690.00.8696
Triple Number Coastal/Long Distance Medium531.91.1280
Triple Number Coastal/Long Distance High477.61.2564
Triple Number Windward/Leeward Low892.70.6721
Triple Number Windward/Leeward Medium657.90.9120
Triple Number Windward/Leeward High578.21.0377
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1479.6985.7745.6621.3551.1514.9486.4441.1423.9
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low690.0
Triple Number Coastal/Long Distance Medium531.9
Triple Number Coastal/Long Distance High477.6
Triple Number Windward/Leeward Low892.7
Triple Number Windward/Leeward Medium657.9
Triple Number Windward/Leeward High578.2
Predominantly Upwind583.2
Predominantly Downwind539.4
Predominantly Reaching517.0
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance583.61.0282
Triple Number Coastal/Long Distance Low690.00.8696
Triple Number Coastal/Long Distance Medium531.91.1280
Triple Number Coastal/Long Distance High477.61.2564
Triple Number Windward/Leeward Low892.70.6721
Triple Number Windward/Leeward Medium657.90.9120
Triple Number Windward/Leeward High578.21.0377
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1479.6985.7745.6621.3551.1514.9486.4441.1423.9
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8696
Triple Number Coastal/Long Distance Medium1.1280
Triple Number Coastal/Long Distance High1.2564
Triple Number Windward/Leeward Low0.6721
Triple Number Windward/Leeward Medium0.9120
Triple Number Windward/Leeward High1.0377
Coastal/Long Distance1.0282
Predominantly Upwind1.0287
Predominantly Downwind1.1124
For information
General Purpose Handicap (GPH)601.7
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)1.1198
Distanseseilas Trippeltall svak vind0.8696
Distanseseilas Trippeltall mellomvind1.1280
Distanseseilas Trippeltall sterk vind1.2564
Pølsebane Trippeltall svak vind0.6721
Pølsebane Trippeltall mellomvind0.9120
Pølsebane Trippeltall sterk vind1.0377
Motvind Singeltall1.0287
Medvind Singeltall1.1124
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low690.00.8696
Triple Number Coastal/Long Distance Medium531.91.1280
Triple Number Coastal/Long Distance High477.61.2564
Triple Number Windward/Leeward Low892.70.6721
Triple Number Windward/Leeward Medium657.90.9120
Triple Number Windward/Leeward High578.21.0377
Coastal/Long Distance583.61.0282
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind583.21.0287
Predominantly Downwind539.41.1124
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore544.41.1021
Cape Doctor Coastal449.01.3363
Triple Number Coastal/Long Distance Low690.00.8696
Triple Number Coastal/Long Distance Medium531.91.1280
Triple Number Coastal/Long Distance High477.61.2564
Triple Number Windward/Leeward Low892.70.6721
Triple Number Windward/Leeward Medium657.90.9120
Triple Number Windward/Leeward High578.21.0377
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8696
Triple Number Coastal/Long Distance Medium1.1280
Triple Number Coastal/Long Distance High1.2564
Triple Number Windward/Leeward Low0.6721
Triple Number Windward/Leeward Medium0.9120
Triple Number Windward/Leeward High1.0377
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8696
Triple Number Coastal/Long Distance Medium1.1280
Triple Number Coastal/Long Distance High1.2564
Triple Number Windward/Leeward Low0.6721
Triple Number Windward/Leeward Medium0.9120
Triple Number Windward/Leeward High1.0377
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance583.61.0282
Triple Number Coastal/Long Distance Low690.00.8696
Triple Number Coastal/Long Distance Medium531.91.1280
Triple Number Coastal/Long Distance High477.61.2564
Triple Number Windward/Leeward Low892.70.6721
Triple Number Windward/Leeward Medium657.90.9120
Triple Number Windward/Leeward High578.21.0377
Predominantly Upwind583.21.0287
Predominantly Downwind539.41.1124
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1479.6985.7745.6621.3551.1514.9486.4441.1423.9
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance583.61.0282
Triple Number Coastal/Long Distance Low690.00.8696
Triple Number Coastal/Long Distance Medium531.91.1280
Triple Number Coastal/Long Distance High477.61.2564
Triple Number Windward/Leeward Low892.70.6721
Triple Number Windward/Leeward Medium657.90.9120
Triple Number Windward/Leeward High578.21.0377
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1479.6985.7745.6621.3551.1514.9486.4441.1423.9
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low690.00.8696
Triple Number AP Medium532.01.1279
Triple Number AP High477.61.2564
Triple Number Windward/Leeward Low933.00.6431
Triple Number Windward/Leeward Medium657.90.9120
Triple Number Windward/Leeward High578.21.0377
Single Number Predominant Upwind608.20.9865
Single Number Predominant Reaching529.31.1336
Single Number Predominant Downwind562.91.0659
Predominant Upwind - Low846.70.7086
Predominant Upwind - Low/Med641.50.9353
Predominant Upwind - Medium564.01.0638
Predominant Upwind - Med/High527.41.1377
Predominant Upwind - High510.71.1749
Predominant Downwind Low820.40.7313
Predominant Downwind Low/Med607.50.9876
Predominant Downwind Medium520.51.1527
Predominant Downwind Med/High468.81.2800
Predominant Downwind High434.81.3799
Predominant Reaching Low731.50.8203
Predominant Reaching Low/Med559.51.0724
Predominant Reaching Medium494.81.2127
Predominant Reaching Med/High458.41.3088
Predominant Reaching High433.91.3829
SA/DSPL Upwind19.60SA/DSPL Downwind39.71
Scoring OptionTODTOT
5-Band Windward/Leeward Low1044.10.5747
5-Band Windward/Leeward Low/Med762.60.7868
5-Band Windward/Leeward Medium646.80.9277
5-Band Windward/Leeward Med/High586.31.0234
5-Band Windward/Leeward High558.11.0750
Windward/Leeward 60-40 Low1055.10.5687
Windward/Leeward 60-40 Low/Med774.60.7746
Windward/Leeward 60-40 Medium661.10.9076
Windward/Leeward 60-40 Med/High604.20.9930
Windward/Leeward 60-40 High579.61.0353
5-Band AP Low760.00.7895
5-Band AP Low/Med601.50.9975
5-Band AP Medium524.71.1435
5-Band AP Med/High483.61.2406
5-Band AP High461.51.3002
5-Band SF Bay Tour - Low900.70.6661
5-Band SF Bay Tour - Low/Med729.80.8221
5-Band SF Bay Tour - Medium623.60.9622
5-Band SF Bay Tour - Med/High568.81.0548
5-Band SF Bay Tour - High542.31.1063
Chicago-Mac Upwind0.9560
Chicago-Mac All Purpose0.9952
Chicago-Mac Downwind1.0284
Bayview-Mac Cove Island0.7247
Bayview-Mac Shore0.7299
Harvest Moon Regatta464.01.2931
Double HandedClub Certificate2025
the JokerNOR 14516
Norges Seilforbund
Sognsveien 73
0854 OSLO
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassJ/120MeasurementHINPlan reviewHull constructionCoredCarbon rudderNoLight stanchionsNoTrim tabNo
LOA12.244Max. Beam3.674Draft2.201Displacement7,712Wetted area31.62IMS L11.115LSM011.102Acc. length11.941Sink (kg/mm) 23.69
VCGD0.032VCGM-0.076RM Rated (kg·m) 187.0Limit of positive stability(°) N/AStability IndexN/ADefault crew weight170Declared crew weight140
PROPELLER
Propeller TypeFolding 2 blades
InstallationStrutTwin screwNoHydro generatorNo
PRD0.460PBWPIPA0.0032
EDL2.350ST10.048ST20.170
ST30.170ST40.098ST50.295
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerNoMainsail furlerArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0Checkstays1Spreaders2Rotating mastNo
P14.180IG15.350ISP16.100MDT10.125MDL10.215MDT20.114MDL20.176TL2.310MW0.185GO0.210
E5.430J4.430BAS1.690FSD0.000SFJ0.000SPL0.000WPLTPS6.500BD0.000MWT215.00MCG5.195
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodVCG entered directlyVCG entered0.032Flotation Date01/01/2015
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Double HandedClub Certificate2025
the JokerNOR 14516
Norges Seilforbund
Sognsveien 73
0854 OSLO
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment365-2021041211570.151.041.903.284.4043.8812/04/2021
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment365-2021041211590.070.641.202.293.344.3214.74YesNo 33.1212/04/2021645-2023041713460.150.631.152.123.144.2014.67YesNo 31.3817/04/20232023 HW-jib
ASYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLRatioAreaMeas.DateComment441-20190430155716.9516.0416.507.6710.1276%112.1730/04/2019
CRUISER/RACER REQUIREMENTS*
Accommodation length11.9 mTable area0.55 m²Headroom1.81 mMinimum number of berths5Personal gear stowage0.20 m³Fresh water capacity148 lMinimum number of seats in cockpit5Food stowage0.30 m³Fuel capacity88 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.