Club Certificate2025
FridolinaFIN 12120
Avomeripurjehtijat ry
c/o Mainoskauppa Oy
Melkonkatu 16 B
00210 HELSINKI
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 Angles44.1°44.1°41.6°39.9°38.9°38.3°38.1°38.2°39.3°
Beat VMG2.563.564.374.945.235.375.445.505.41
52°4.035.476.517.167.467.597.677.767.75
60°4.325.786.797.367.667.817.908.008.00
75°4.526.016.987.527.858.098.258.448.53
90°4.365.957.107.698.008.198.478.869.09
110°4.416.037.227.868.328.739.069.549.94
120°4.255.867.087.768.258.729.2010.1310.87
135°3.725.236.497.377.918.388.8610.0511.99
150°3.064.385.576.587.347.828.229.0710.24
Run VMG2.653.804.825.706.376.867.298.008.87
Gybe Angles142.2°142.2°146.2°149.4°151.9°156.5°161.7°162.4°143.2°
APH ToD:530.0CDL: 10.130APH ToT: 1.1321CertNo:12120C
BOAT
ClassArcona 400DesignerStefan QvibergBuilderArcona YachtsAge dateSeries date05/1997Offset fileARC40.OFFData fileL12120C
HULL
Length Overall11.995 mMaximum Beam3.794 mDraft2.081 mDisplacement7,000 kgDLR5.7233IMS DivisionCruiser/RacerDynamic Allowance0.190%Age Allowance0.487%
PROPELLER
InstallationStrutTypeFolding 2 bladesDiameter0.400m
CREW
Maximum weight600 kg(declared)Minimum weight470 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail48.8149.65Headsail Luffed34.5534.55Headsail FlyingSymmetricAsymmetric104.51104.51 (All asymmetric spinnakers with SHW/SFL > 85%)
STORM SAIL AREAS (m²)
Trysail14.84Storm Jib12.44Heavy Weather Jib33.58
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.
Club Certificate2025
FridolinaFIN 12120
Avomeripurjehtijat ry
c/o Mainoskauppa Oy
Melkonkatu 16 B
00210 HELSINKI
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 VMG1408.41011.0823.3729.0687.8671.0661.8654.9665.5
52°892.4658.2552.8503.1482.5474.2469.3464.1464.4
60°833.6622.5530.5488.8469.8460.8455.8449.8450.0
75°795.6599.2515.8478.7458.4445.1436.4426.5422.2
90°824.9605.0507.3468.0450.1439.5425.2406.1396.0
110°817.1596.7498.5458.1432.6412.3397.4377.2362.0
120°847.1613.8508.4463.9436.6412.8391.4355.5331.2
135°968.0688.0554.9488.6455.4429.8406.2358.3300.2
150°1177.9821.5646.5547.2490.7460.3437.9397.1351.4
Run VMG1360.2948.6746.6631.9565.2524.7494.1449.9405.8
Selected Courses
Windward / Leeward1383.9979.8785.0680.4626.5597.8578.0552.4535.6
All purpose1043.6751.0613.9545.8511.2491.1476.0454.1438.0
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward656.50.9139
All purpose530.01.1321
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low682.40.8792
Triple Number Coastal/Long Distance Medium526.31.1401
Triple Number Coastal/Long Distance High471.51.2724
Triple Number Windward/Leeward Low882.40.6800
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High573.31.0465
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance577.41.0391
Triple Number Coastal/Long Distance Low682.40.8792
Triple Number Coastal/Long Distance Medium526.31.1401
Triple Number Coastal/Long Distance High471.51.2724
Triple Number Windward/Leeward Low882.40.6800
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High573.31.0465
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1468.5976.7737.6614.0545.7510.2480.7432.7416.8
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.8017
Downwind "popa"0.9631
70% up, 30% down "Ilhabela"0.8441
30% up, 70% down "Ilhabela-inverso"0.9083
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low682.40.8792
Triple Number Coastal/Long Distance Medium526.31.1401
Triple Number Coastal/Long Distance High471.51.2724
Triple Number Windward/Leeward Low882.40.6800
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High573.31.0465
Predominantly Upwind574.41.0446
Predominantly Downwind538.51.1143
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low682.40.8792
Triple Number AP Medium526.31.1400
Triple Number AP High471.61.2724
Triple Number Windward/Leeward Low922.10.6507
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High573.31.0465
Single Number Predominant Upwind598.81.0020
Single Number Predominant Reaching526.81.1390
Single Number Predominant Downwind562.21.0673
Predominant Upwind - Low830.20.7227
Predominant Upwind - Low/Med629.60.9529
Predominant Upwind - Medium555.71.0797
Predominant Upwind - Med/High521.01.1516
Predominant Upwind - High505.01.1881
Predominant Downwind Low823.10.7290
Predominant Downwind Low/Med607.50.9877
Predominant Downwind Medium519.81.1542
Predominant Downwind Med/High466.31.2868
Predominant Downwind High430.11.3949
Predominant Reaching Low733.90.8176
Predominant Reaching Low/Med557.81.0757
Predominant Reaching Medium492.01.2196
Predominant Reaching Med/High453.51.3231
Predominant Reaching High427.11.4049
SA/DSPL Upwind22.63SA/DSPL Downwind41.63
Scoring OptionTODTOT
5-Band Windward/Leeward Low1032.20.5813
5-Band Windward/Leeward Low/Med753.40.7964
5-Band Windward/Leeward Medium639.80.9378
5-Band Windward/Leeward Med/High581.11.0326
5-Band Windward/Leeward High553.91.0832
Windward/Leeward 60-40 Low1038.50.5778
Windward/Leeward 60-40 Low/Med762.30.7871
Windward/Leeward 60-40 Medium652.00.9202
Windward/Leeward 60-40 Med/High597.71.0038
Windward/Leeward 60-40 High574.71.0440
5-Band AP Low753.50.7963
5-Band AP Low/Med594.91.0085
5-Band AP Medium519.21.1557
5-Band AP Med/High477.81.2557
5-Band AP High455.11.3183
5-Band SF Bay Tour - Low888.50.6753
5-Band SF Bay Tour - Low/Med719.80.8336
5-Band SF Bay Tour - Medium616.20.9737
5-Band SF Bay Tour - Med/High563.21.0653
5-Band SF Bay Tour - High537.41.1165
Chicago-Mac Upwind0.9722
Chicago-Mac All Purpose1.0037
Chicago-Mac Downwind1.0293
Bayview-Mac Cove Island0.7312
Bayview-Mac Shore0.7362
Harvest Moon Regatta458.81.3076
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance577.41.0391
Triple Number Coastal/Long Distance Low682.40.8792
Triple Number Coastal/Long Distance Medium526.31.1401
Triple Number Coastal/Long Distance High471.51.2724
Triple Number Windward/Leeward Low882.40.6800
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High573.31.0465
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1468.5976.7737.6614.0545.7510.2480.7432.7416.8
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance577.41.0391
Triple Number Coastal/Long Distance Low682.40.8792
Triple Number Coastal/Long Distance Medium526.31.1401
Triple Number Coastal/Long Distance High471.51.2724
Triple Number Windward/Leeward Low882.40.6800
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High573.31.0465
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1468.5976.7737.6614.0545.7510.2480.7432.7416.8
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance577.4
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1468.5976.7737.6614.0545.7510.2480.7432.7416.8
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low682.40.8792
Triple Number Coastal/Long Distance Medium526.31.1401
Triple Number Coastal/Long Distance High471.51.2724
Triple Number Windward/Leeward Low882.40.6800
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High573.31.0465
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating577.41.0391
FinRating, kevyt tuuli1012.60.9875
FinRating, kova tuuli457.51.0929
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low682.40.8792
Triple Number Coastal/Long Distance Medium526.31.1401
Triple Number Coastal/Long Distance High471.51.2724
Triple Number Windward/Leeward Low882.40.6800
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High573.31.0465
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance1.0391
Triple Number Coastal/Long Distance Low0.8792
Triple Number Coastal/Long Distance Medium1.1401
Triple Number Coastal/Long Distance High1.2724
Triple Number Windward/Leeward Low0.6800
Triple Number Windward/Leeward Medium0.9224
Triple Number Windward/Leeward High1.0465
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1468.5976.7737.6614.0545.7510.2480.7432.7416.8
For information
General Purpose Handicap (GPH)595.1
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance577.41.0391
Triple Number Coastal/Long Distance Low682.40.8792
Triple Number Coastal/Long Distance Medium526.31.1401
Triple Number Coastal/Long Distance High471.51.2724
Triple Number Windward/Leeward Low882.40.6800
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High573.31.0465
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1468.5976.7737.6614.0545.7510.2480.7432.7416.8
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low682.40.8792
Triple Number Coastal/Long Distance Medium526.31.1401
Triple Number Coastal/Long Distance High471.51.2724
Triple Number Windward/Leeward Low882.40.6800
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High573.31.0465
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance577.41.0391
Triple Number Coastal/Long Distance Low682.40.8792
Triple Number Coastal/Long Distance Medium526.31.1401
Triple Number Coastal/Long Distance High471.51.2724
Triple Number Windward/Leeward Low882.40.6800
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High573.31.0465
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1468.5976.7737.6614.0545.7510.2480.7432.7416.8
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance577.41.0391
Triple Number Coastal/Long Distance Low682.40.8792
Triple Number Coastal/Long Distance Medium526.31.1401
Triple Number Coastal/Long Distance High471.51.2724
Triple Number Windward/Leeward Low882.40.6800
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High573.31.0465
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1468.5976.7737.6614.0545.7510.2480.7432.7416.8
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low682.4
Triple Number Coastal/Long Distance Medium526.3
Triple Number Coastal/Long Distance High471.5
Triple Number Windward/Leeward Low882.4
Triple Number Windward/Leeward Medium650.5
Triple Number Windward/Leeward High573.3
Predominantly Upwind574.4
Predominantly Downwind538.5
Predominantly Reaching514.9
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance577.41.0391
Triple Number Coastal/Long Distance Low682.40.8792
Triple Number Coastal/Long Distance Medium526.31.1401
Triple Number Coastal/Long Distance High471.51.2724
Triple Number Windward/Leeward Low882.40.6800
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High573.31.0465
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1468.5976.7737.6614.0545.7510.2480.7432.7416.8
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8792
Triple Number Coastal/Long Distance Medium1.1401
Triple Number Coastal/Long Distance High1.2724
Triple Number Windward/Leeward Low0.6800
Triple Number Windward/Leeward Medium0.9224
Triple Number Windward/Leeward High1.0465
Coastal/Long Distance1.0391
Predominantly Upwind1.0446
Predominantly Downwind1.1143
For information
General Purpose Handicap (GPH)595.1
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)1.1321
Distanseseilas Trippeltall svak vind0.8792
Distanseseilas Trippeltall mellomvind1.1401
Distanseseilas Trippeltall sterk vind1.2724
Pølsebane Trippeltall svak vind0.6800
Pølsebane Trippeltall mellomvind0.9224
Pølsebane Trippeltall sterk vind1.0465
Motvind Singeltall1.0446
Medvind Singeltall1.1143
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low682.40.8792
Triple Number Coastal/Long Distance Medium526.31.1401
Triple Number Coastal/Long Distance High471.51.2724
Triple Number Windward/Leeward Low882.40.6800
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High573.31.0465
Coastal/Long Distance577.41.0391
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind574.41.0446
Predominantly Downwind538.51.1143
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore540.71.1097
Cape Doctor Coastal442.81.3549
Triple Number Coastal/Long Distance Low682.40.8792
Triple Number Coastal/Long Distance Medium526.31.1401
Triple Number Coastal/Long Distance High471.51.2724
Triple Number Windward/Leeward Low882.40.6800
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High573.31.0465
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8792
Triple Number Coastal/Long Distance Medium1.1401
Triple Number Coastal/Long Distance High1.2724
Triple Number Windward/Leeward Low0.6800
Triple Number Windward/Leeward Medium0.9224
Triple Number Windward/Leeward High1.0465
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8792
Triple Number Coastal/Long Distance Medium1.1401
Triple Number Coastal/Long Distance High1.2724
Triple Number Windward/Leeward Low0.6800
Triple Number Windward/Leeward Medium0.9224
Triple Number Windward/Leeward High1.0465
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance577.41.0391
Triple Number Coastal/Long Distance Low682.40.8792
Triple Number Coastal/Long Distance Medium526.31.1401
Triple Number Coastal/Long Distance High471.51.2724
Triple Number Windward/Leeward Low882.40.6800
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High573.31.0465
Predominantly Upwind574.41.0446
Predominantly Downwind538.51.1143
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1468.5976.7737.6614.0545.7510.2480.7432.7416.8
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance577.41.0391
Triple Number Coastal/Long Distance Low682.40.8792
Triple Number Coastal/Long Distance Medium526.31.1401
Triple Number Coastal/Long Distance High471.51.2724
Triple Number Windward/Leeward Low882.40.6800
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High573.31.0465
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1468.5976.7737.6614.0545.7510.2480.7432.7416.8
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low682.40.8792
Triple Number AP Medium526.31.1400
Triple Number AP High471.61.2724
Triple Number Windward/Leeward Low922.10.6507
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High573.31.0465
Single Number Predominant Upwind598.81.0020
Single Number Predominant Reaching526.81.1390
Single Number Predominant Downwind562.21.0673
Predominant Upwind - Low830.20.7227
Predominant Upwind - Low/Med629.60.9529
Predominant Upwind - Medium555.71.0797
Predominant Upwind - Med/High521.01.1516
Predominant Upwind - High505.01.1881
Predominant Downwind Low823.10.7290
Predominant Downwind Low/Med607.50.9877
Predominant Downwind Medium519.81.1542
Predominant Downwind Med/High466.31.2868
Predominant Downwind High430.11.3949
Predominant Reaching Low733.90.8176
Predominant Reaching Low/Med557.81.0757
Predominant Reaching Medium492.01.2196
Predominant Reaching Med/High453.51.3231
Predominant Reaching High427.11.4049
SA/DSPL Upwind22.63SA/DSPL Downwind41.63
Scoring OptionTODTOT
5-Band Windward/Leeward Low1032.20.5813
5-Band Windward/Leeward Low/Med753.40.7964
5-Band Windward/Leeward Medium639.80.9378
5-Band Windward/Leeward Med/High581.11.0326
5-Band Windward/Leeward High553.91.0832
Windward/Leeward 60-40 Low1038.50.5778
Windward/Leeward 60-40 Low/Med762.30.7871
Windward/Leeward 60-40 Medium652.00.9202
Windward/Leeward 60-40 Med/High597.71.0038
Windward/Leeward 60-40 High574.71.0440
5-Band AP Low753.50.7963
5-Band AP Low/Med594.91.0085
5-Band AP Medium519.21.1557
5-Band AP Med/High477.81.2557
5-Band AP High455.11.3183
5-Band SF Bay Tour - Low888.50.6753
5-Band SF Bay Tour - Low/Med719.80.8336
5-Band SF Bay Tour - Medium616.20.9737
5-Band SF Bay Tour - Med/High563.21.0653
5-Band SF Bay Tour - High537.41.1165
Chicago-Mac Upwind0.9722
Chicago-Mac All Purpose1.0037
Chicago-Mac Downwind1.0293
Bayview-Mac Cove Island0.7312
Bayview-Mac Shore0.7362
Harvest Moon Regatta458.81.3076
Club Certificate2025
FridolinaFIN 12120
Avomeripurjehtijat ry
c/o Mainoskauppa Oy
Melkonkatu 16 B
00210 HELSINKI
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassArcona 400Measurement26/04/2022HINPlan reviewHull constructionCoredCarbon rudderNoLight stanchionsNoTrim tabNo
LOA11.995Max. Beam3.794Draft2.081Displacement7,000Wetted area30.29IMS L10.834LSM010.693Acc. length11.995Sink (kg/mm) 23.74
VCGD-0.140VCGM0.046RM Rated (kg·m) 197.0Limit of positive stability(°) N/AStability IndexN/ADefault crew weight757Declared crew weight600
PROPELLER
Propeller TypeFolding 2 blades
InstallationStrutTwin screwNoHydro generatorNo
PRD0.400PBWPIPA0.0039
EDL2.800ST10.065ST20.180
ST30.180ST40.110ST50.300
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerNoMainsail furlerNoArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders3Rotating mastNo
P15.357IG15.770ISP16.085MDT10.119MDL10.227MDT2MDL2TLTaperMWGO
E5.520J4.260BAS1.655FSDFoilSFJSPLWPLTPS5.210BDMWTMCG
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodVCG entered directlyVCG entered-0.140Flotation Date26/04/2022
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Club Certificate2025
FridolinaFIN 12120
Avomeripurjehtijat ry
c/o Mainoskauppa Oy
Melkonkatu 16 B
00210 HELSINKI
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment20.181.091.953.404.5048.8117/05/2025
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment10.050.611.202.223.274.3415.60NoNo 34.55
ASYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLRatioAreaMeas.DateComment116.8714.8015.848.007.60105%104.51
CRUISER/RACER REQUIREMENTS*
Accommodation length12.0 mTable area0.55 m²Headroom1.81 mMinimum number of berths5Personal gear stowage0.20 m³Fresh water capacity150 lMinimum number of seats in cockpit5Food stowage0.30 m³Fuel capacity90 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.