Double HandedClub Certificate2025
ConcordiaFIN 12229
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 Angles43.9°43.9°41.6°41.4°41.9°41.8°41.9°42.7°44.2°
Beat VMG2.022.783.363.723.893.964.003.973.85
52°3.154.245.015.505.765.865.905.945.90
60°3.334.455.225.715.966.086.136.206.20
75°3.424.585.385.896.166.326.426.546.61
90°3.334.495.335.896.216.426.586.786.91
110°3.254.495.456.066.416.646.827.047.22
120°3.104.335.336.006.406.706.947.337.59
135°2.753.914.925.736.236.576.877.438.04
150°2.333.394.375.215.876.296.617.187.76
Run VMG2.022.943.794.535.195.726.126.717.22
Gybe Angles148.3°148.3°151.4°154.1°160.0°165.8°173.0°177.5°177.5°
APH ToD:687.5CDL: 6.146APH ToT: 0.8727CertNo:58
BOAT
ClassB-31DesignerBROSTRÖM & GRANDINBuilderAge date01/1971Series date01/1972Offset fileG1013.bofData fileFIN12229
HULL
Length Overall9.330 mMaximum Beam2.942 mDraft1.564 mDisplacement3,500 kgDLR10.6296IMS DivisionCruiser/RacerDynamic Allowance0.630%Age Allowance0.487%
PROPELLER
InstallationShaft exposedTypeSolid 3 bladesDiameter0.415m
CREW
Maximum weight200 kg(declared)Minimum weight120 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail16.6216.89Headsail Luffed29.8529.85Headsail FlyingSymmetric57.6957.69Asymmetric
STORM SAIL AREAS (m²)
Trysail4.76Storm Jib6.07Heavy Weather Jib16.37
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
ConcordiaFIN 12229
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 VMG1786.61296.31071.1968.2925.7908.2900.7907.2934.2
52°1142.7849.8719.0654.1625.3614.1609.7605.9610.7
60°1080.9809.2689.7630.7604.0592.0587.1580.9580.2
75°1051.9785.9668.9611.7584.4569.7560.8550.8544.7
90°1082.7802.2675.8611.6579.7560.4547.4531.0520.9
110°1108.0802.0660.6593.9561.8541.9528.0511.5498.6
120°1160.8831.0675.7599.6562.3537.7518.9491.0474.6
135°1310.3921.3731.6627.9577.6547.6523.7484.5447.7
150°1543.91061.8824.6691.5613.6572.4545.0501.6463.8
Run VMG1785.81226.0950.9794.9693.2629.7588.4536.7498.3
Selected Courses
Windward / Leeward1784.11261.21011.0881.6809.5768.9744.5721.9716.3
All purpose1362.0979.3799.1707.5660.5635.0619.1601.3593.0
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward847.60.7078
All purpose687.50.8727
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low889.20.6748
Triple Number Coastal/Long Distance Medium681.40.8806
Triple Number Coastal/Long Distance High616.40.9734
Triple Number Windward/Leeward Low1136.10.5281
Triple Number Windward/Leeward Medium840.10.7142
Triple Number Windward/Leeward High742.10.8085
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance747.40.8028
Triple Number Coastal/Long Distance Low889.20.6748
Triple Number Coastal/Long Distance Medium681.40.8806
Triple Number Coastal/Long Distance High616.40.9734
Triple Number Windward/Leeward Low1136.10.5281
Triple Number Windward/Leeward Medium840.10.7142
Triple Number Windward/Leeward High742.10.8085
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1887.71257.7952.1795.5706.6659.4624.0568.7557.5
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.6019
Downwind "popa"0.7749
70% up, 30% down "Ilhabela"0.6451
30% up, 70% down "Ilhabela-inverso"0.7134
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low889.20.6748
Triple Number Coastal/Long Distance Medium681.40.8806
Triple Number Coastal/Long Distance High616.40.9734
Triple Number Windward/Leeward Low1136.10.5281
Triple Number Windward/Leeward Medium840.10.7142
Triple Number Windward/Leeward High742.10.8085
Predominantly Upwind751.10.7988
Predominantly Downwind688.40.8716
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low889.20.6748
Triple Number AP Medium681.40.8805
Triple Number AP High616.40.9734
Triple Number Windward/Leeward Low1188.20.5050
Triple Number Windward/Leeward Medium840.10.7142
Triple Number Windward/Leeward High742.10.8085
Single Number Predominant Upwind783.00.7663
Single Number Predominant Reaching684.60.8764
Single Number Predominant Downwind722.40.8305
Predominant Upwind - Low1075.50.5579
Predominant Upwind - Low/Med820.90.7309
Predominant Upwind - Medium726.40.8260
Predominant Upwind - Med/High685.30.8755
Predominant Upwind - High674.20.8899
Predominant Downwind Low1078.40.5564
Predominant Downwind Low/Med785.10.7642
Predominant Downwind Medium661.30.9073
Predominant Downwind Med/High591.31.0147
Predominant Downwind High556.81.0775
Predominant Reaching Low964.40.6221
Predominant Reaching Low/Med727.80.8244
Predominant Reaching Medium634.50.9457
Predominant Reaching Med/High586.11.0238
Predominant Reaching High563.31.0652
SA/DSPL Upwind20.08SA/DSPL Downwind32.10
Scoring OptionTODTOT
5-Band Windward/Leeward Low1329.90.4512
5-Band Windward/Leeward Low/Med972.50.6170
5-Band Windward/Leeward Medium826.00.7264
5-Band Windward/Leeward Med/High750.30.7997
5-Band Windward/Leeward High724.80.8278
Windward/Leeward 60-40 Low1336.40.4490
Windward/Leeward 60-40 Low/Med987.30.6077
Windward/Leeward 60-40 Medium848.80.7069
Windward/Leeward 60-40 Med/High781.30.7680
Windward/Leeward 60-40 High762.00.7874
5-Band AP Low987.40.6077
5-Band AP Low/Med772.90.7763
5-Band AP Medium672.10.8927
5-Band AP Med/High622.30.9642
5-Band AP High602.90.9951
5-Band SF Bay Tour - Low1147.50.5229
5-Band SF Bay Tour - Low/Med932.80.6432
5-Band SF Bay Tour - Medium801.00.7490
5-Band SF Bay Tour - Med/High736.20.8150
5-Band SF Bay Tour - High714.60.8396
Chicago-Mac Upwind0.7437
Chicago-Mac All Purpose0.7737
Chicago-Mac Downwind0.8001
Bayview-Mac Cove Island0.5627
Bayview-Mac Shore0.5665
Harvest Moon Regatta589.71.0175
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance747.40.8028
Triple Number Coastal/Long Distance Low889.20.6748
Triple Number Coastal/Long Distance Medium681.40.8806
Triple Number Coastal/Long Distance High616.40.9734
Triple Number Windward/Leeward Low1136.10.5281
Triple Number Windward/Leeward Medium840.10.7142
Triple Number Windward/Leeward High742.10.8085
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1887.71257.7952.1795.5706.6659.4624.0568.7557.5
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance747.40.8028
Triple Number Coastal/Long Distance Low889.20.6748
Triple Number Coastal/Long Distance Medium681.40.8806
Triple Number Coastal/Long Distance High616.40.9734
Triple Number Windward/Leeward Low1136.10.5281
Triple Number Windward/Leeward Medium840.10.7142
Triple Number Windward/Leeward High742.10.8085
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1887.71257.7952.1795.5706.6659.4624.0568.7557.5
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance747.4
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1887.71257.7952.1795.5706.6659.4624.0568.7557.5
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low889.20.6748
Triple Number Coastal/Long Distance Medium681.40.8806
Triple Number Coastal/Long Distance High616.40.9734
Triple Number Windward/Leeward Low1136.10.5281
Triple Number Windward/Leeward Medium840.10.7142
Triple Number Windward/Leeward High742.10.8085
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating747.40.8028
FinRating, kevyt tuuli1309.30.7638
FinRating, kova tuuli605.90.8252
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low889.20.6748
Triple Number Coastal/Long Distance Medium681.40.8806
Triple Number Coastal/Long Distance High616.40.9734
Triple Number Windward/Leeward Low1136.10.5281
Triple Number Windward/Leeward Medium840.10.7142
Triple Number Windward/Leeward High742.10.8085
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.8028
Triple Number Coastal/Long Distance Low0.6748
Triple Number Coastal/Long Distance Medium0.8806
Triple Number Coastal/Long Distance High0.9734
Triple Number Windward/Leeward Low0.5281
Triple Number Windward/Leeward Medium0.7142
Triple Number Windward/Leeward High0.8085
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1887.71257.7952.1795.5706.6659.4624.0568.7557.5
For information
General Purpose Handicap (GPH)772.7
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance747.40.8028
Triple Number Coastal/Long Distance Low889.20.6748
Triple Number Coastal/Long Distance Medium681.40.8806
Triple Number Coastal/Long Distance High616.40.9734
Triple Number Windward/Leeward Low1136.10.5281
Triple Number Windward/Leeward Medium840.10.7142
Triple Number Windward/Leeward High742.10.8085
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1887.71257.7952.1795.5706.6659.4624.0568.7557.5
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low889.20.6748
Triple Number Coastal/Long Distance Medium681.40.8806
Triple Number Coastal/Long Distance High616.40.9734
Triple Number Windward/Leeward Low1136.10.5281
Triple Number Windward/Leeward Medium840.10.7142
Triple Number Windward/Leeward High742.10.8085
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance747.40.8028
Triple Number Coastal/Long Distance Low889.20.6748
Triple Number Coastal/Long Distance Medium681.40.8806
Triple Number Coastal/Long Distance High616.40.9734
Triple Number Windward/Leeward Low1136.10.5281
Triple Number Windward/Leeward Medium840.10.7142
Triple Number Windward/Leeward High742.10.8085
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1887.71257.7952.1795.5706.6659.4624.0568.7557.5
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance747.40.8028
Triple Number Coastal/Long Distance Low889.20.6748
Triple Number Coastal/Long Distance Medium681.40.8806
Triple Number Coastal/Long Distance High616.40.9734
Triple Number Windward/Leeward Low1136.10.5281
Triple Number Windward/Leeward Medium840.10.7142
Triple Number Windward/Leeward High742.10.8085
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1887.71257.7952.1795.5706.6659.4624.0568.7557.5
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low889.2
Triple Number Coastal/Long Distance Medium681.4
Triple Number Coastal/Long Distance High616.4
Triple Number Windward/Leeward Low1136.1
Triple Number Windward/Leeward Medium840.1
Triple Number Windward/Leeward High742.1
Predominantly Upwind751.1
Predominantly Downwind688.4
Predominantly Reaching664.4
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance747.40.8028
Triple Number Coastal/Long Distance Low889.20.6748
Triple Number Coastal/Long Distance Medium681.40.8806
Triple Number Coastal/Long Distance High616.40.9734
Triple Number Windward/Leeward Low1136.10.5281
Triple Number Windward/Leeward Medium840.10.7142
Triple Number Windward/Leeward High742.10.8085
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1887.71257.7952.1795.5706.6659.4624.0568.7557.5
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.6748
Triple Number Coastal/Long Distance Medium0.8806
Triple Number Coastal/Long Distance High0.9734
Triple Number Windward/Leeward Low0.5281
Triple Number Windward/Leeward Medium0.7142
Triple Number Windward/Leeward High0.8085
Coastal/Long Distance0.8028
Predominantly Upwind0.7988
Predominantly Downwind0.8716
For information
General Purpose Handicap (GPH)772.7
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)0.8727
Distanseseilas Trippeltall svak vind0.6748
Distanseseilas Trippeltall mellomvind0.8806
Distanseseilas Trippeltall sterk vind0.9734
Pølsebane Trippeltall svak vind0.5281
Pølsebane Trippeltall mellomvind0.7142
Pølsebane Trippeltall sterk vind0.8085
Motvind Singeltall0.7988
Medvind Singeltall0.8716
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low889.20.6748
Triple Number Coastal/Long Distance Medium681.40.8806
Triple Number Coastal/Long Distance High616.40.9734
Triple Number Windward/Leeward Low1136.10.5281
Triple Number Windward/Leeward Medium840.10.7142
Triple Number Windward/Leeward High742.10.8085
Coastal/Long Distance747.40.8028
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind751.10.7988
Predominantly Downwind688.40.8716
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore718.00.8357
Cape Doctor Coastal595.51.0076
Triple Number Coastal/Long Distance Low889.20.6748
Triple Number Coastal/Long Distance Medium681.40.8806
Triple Number Coastal/Long Distance High616.40.9734
Triple Number Windward/Leeward Low1136.10.5281
Triple Number Windward/Leeward Medium840.10.7142
Triple Number Windward/Leeward High742.10.8085
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.6748
Triple Number Coastal/Long Distance Medium0.8806
Triple Number Coastal/Long Distance High0.9734
Triple Number Windward/Leeward Low0.5281
Triple Number Windward/Leeward Medium0.7142
Triple Number Windward/Leeward High0.8085
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.6748
Triple Number Coastal/Long Distance Medium0.8806
Triple Number Coastal/Long Distance High0.9734
Triple Number Windward/Leeward Low0.5281
Triple Number Windward/Leeward Medium0.7142
Triple Number Windward/Leeward High0.8085
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance747.40.8028
Triple Number Coastal/Long Distance Low889.20.6748
Triple Number Coastal/Long Distance Medium681.40.8806
Triple Number Coastal/Long Distance High616.40.9734
Triple Number Windward/Leeward Low1136.10.5281
Triple Number Windward/Leeward Medium840.10.7142
Triple Number Windward/Leeward High742.10.8085
Predominantly Upwind751.10.7988
Predominantly Downwind688.40.8716
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1887.71257.7952.1795.5706.6659.4624.0568.7557.5
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance747.40.8028
Triple Number Coastal/Long Distance Low889.20.6748
Triple Number Coastal/Long Distance Medium681.40.8806
Triple Number Coastal/Long Distance High616.40.9734
Triple Number Windward/Leeward Low1136.10.5281
Triple Number Windward/Leeward Medium840.10.7142
Triple Number Windward/Leeward High742.10.8085
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1887.71257.7952.1795.5706.6659.4624.0568.7557.5
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low889.20.6748
Triple Number AP Medium681.40.8805
Triple Number AP High616.40.9734
Triple Number Windward/Leeward Low1188.20.5050
Triple Number Windward/Leeward Medium840.10.7142
Triple Number Windward/Leeward High742.10.8085
Single Number Predominant Upwind783.00.7663
Single Number Predominant Reaching684.60.8764
Single Number Predominant Downwind722.40.8305
Predominant Upwind - Low1075.50.5579
Predominant Upwind - Low/Med820.90.7309
Predominant Upwind - Medium726.40.8260
Predominant Upwind - Med/High685.30.8755
Predominant Upwind - High674.20.8899
Predominant Downwind Low1078.40.5564
Predominant Downwind Low/Med785.10.7642
Predominant Downwind Medium661.30.9073
Predominant Downwind Med/High591.31.0147
Predominant Downwind High556.81.0775
Predominant Reaching Low964.40.6221
Predominant Reaching Low/Med727.80.8244
Predominant Reaching Medium634.50.9457
Predominant Reaching Med/High586.11.0238
Predominant Reaching High563.31.0652
SA/DSPL Upwind20.08SA/DSPL Downwind32.10
Scoring OptionTODTOT
5-Band Windward/Leeward Low1329.90.4512
5-Band Windward/Leeward Low/Med972.50.6170
5-Band Windward/Leeward Medium826.00.7264
5-Band Windward/Leeward Med/High750.30.7997
5-Band Windward/Leeward High724.80.8278
Windward/Leeward 60-40 Low1336.40.4490
Windward/Leeward 60-40 Low/Med987.30.6077
Windward/Leeward 60-40 Medium848.80.7069
Windward/Leeward 60-40 Med/High781.30.7680
Windward/Leeward 60-40 High762.00.7874
5-Band AP Low987.40.6077
5-Band AP Low/Med772.90.7763
5-Band AP Medium672.10.8927
5-Band AP Med/High622.30.9642
5-Band AP High602.90.9951
5-Band SF Bay Tour - Low1147.50.5229
5-Band SF Bay Tour - Low/Med932.80.6432
5-Band SF Bay Tour - Medium801.00.7490
5-Band SF Bay Tour - Med/High736.20.8150
5-Band SF Bay Tour - High714.60.8396
Chicago-Mac Upwind0.7437
Chicago-Mac All Purpose0.7737
Chicago-Mac Downwind0.8001
Bayview-Mac Cove Island0.5627
Bayview-Mac Shore0.5665
Harvest Moon Regatta589.71.0175
Double HandedClub Certificate2025
ConcordiaFIN 12229
Avomeripurjehtijat ry
c/o Mainoskauppa Oy
Melkonkatu 16 B
00210 HELSINKI
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassB-31Measurement01/07/2014HINPlan reviewHull constructionCoredCarbon rudderNoLight stanchionsNoTrim tabNo
LOA9.330Max. Beam2.942Draft1.564Displacement3,500Wetted area17.23IMS L7.088LSM06.905Acc. length9.079Sink (kg/mm) 11.65
VCGD-0.105VCGM-0.017RM Rated (kg·m) 53.4Limit of positive stability(°) N/AStability IndexN/ADefault crew weight170Declared crew weight200
PROPELLER
Propeller TypeSolid 3 blades
InstallationShaft exposedTwin screwNoHydro generatorNo
PRD0.415PBWPIPA0.0215
PSDPHDPHL
PSAESL
ST1ST2ST3
ST4ST5
RIG
Forestay tensionAftInner stayMast materialAluminumSingle headsail furlerNoMainsail furlerNoArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders1Rotating mastNo
P9.700IG11.010ISP11.010MDT10.115MDL10.170MDT2MDL2TLNo TaperMWGO
E2.800J2.460BAS1.090FSDFoilSFJ0.360SPL3.460WPLTPSBD0.111MWTMCG
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodRM estimatedFlotation Date17/07/2025
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Double HandedClub Certificate2025
ConcordiaFIN 12229
Avomeripurjehtijat ry
c/o Mainoskauppa Oy
Melkonkatu 16 B
00210 HELSINKI
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment10.641.121.8816.62
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment11.302.605.1911.40NoNo 29.85
SYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLAreaMeas.DateComment111.1311.1311.136.226.2257.69
CRUISER/RACER REQUIREMENTS*
Accommodation length9.1 mTable area0.44 m²Headroom1.63 mMinimum number of berths4Personal gear stowage0.16 m³Fresh water capacity62 lMinimum number of seats in cockpit4Food stowage0.24 m³Fuel capacity32 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.