Double HandedClub Certificate2025
Joie de VieRSA-2350
ORC
Central Rating Office
Issuing certificates for
SOUTH AFRICA
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 Angles46.5°46.5°44.5°43.4°43.0°42.9°42.8°43.6°45.9°
Beat VMG2.032.833.473.914.224.414.484.444.23
52°3.264.445.335.946.346.576.696.726.56
60°3.544.765.636.226.596.816.947.016.95
75°3.714.975.866.456.807.037.197.387.41
90°3.634.905.826.466.847.097.277.577.79
110°3.134.385.416.216.737.067.307.728.13
120°2.914.145.196.016.606.977.247.688.14
135°2.493.644.685.536.236.727.047.507.92
150°2.143.103.984.815.516.116.577.177.60
Run VMG1.802.683.544.365.105.756.327.047.50
Gybe Angles143.9°143.9°176.6°178.4°179.3°179.3°179.8°180.0°180.0°
APH ToD:659.2CDL: 7.713APH ToT: 0.9102CertNo:ZAD293
BOAT
ClassFirst 35DesignerJean BerretBuilderBeneteauAge date01/1984Series date01/1981Offset fileFRS35-SD.offData fileRSA2350
HULL
Length Overall10.832 mMaximum Beam3.702 mDraft1.474 mDisplacement6,553 kgDLR8.4403IMS DivisionCruiser/RacerDynamic Allowance0.510%Age Allowance0.487%
PROPELLER
InstallationShaft exposedTypeFeathering 2 bladesDiameter0.390m
CREW
Maximum weight210 kg(declared)Minimum weight120 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail27.5127.85Headsail Luffed27.4127.41Headsail FlyingSymmetricAsymmetric
STORM SAIL AREAS (m²)
Trysail8.48Storm Jib9.68Heavy Weather Jib26.12
SAIL LIMITS
Headsails5
✱ One set on the forestay
Spinnakers0
✱ No 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.
Double HandedClub Certificate2025
Joie de VieRSA-2350
ORC
Central Rating Office
Issuing certificates for
SOUTH AFRICA
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 VMG1774.21273.11038.3921.1853.2816.6803.9809.9851.9
52°1103.2810.0675.8606.5567.5547.7538.2536.1548.9
60°1018.0756.8639.6578.6546.2528.7518.8513.5518.2
75°970.8724.2614.5558.0529.2512.3501.0487.8485.7
90°992.0734.8618.3557.3526.4508.1495.0475.3462.0
110°1151.9822.6664.9579.7534.6509.9493.1466.5442.8
120°1236.2870.4693.8598.8545.2516.1497.5469.0442.5
135°1443.4989.6768.7650.5577.9535.7511.1480.0454.3
150°1678.41162.4904.5748.1653.0588.9547.5502.2473.9
Run VMG1994.81342.31016.6824.9705.7625.6570.0511.2480.0
Selected Courses
Windward / Leeward1882.01307.71027.4873.0779.4721.1686.9660.6665.9
All purpose1392.0989.1795.6690.4629.3592.8571.7552.0549.0
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward822.50.7295
All purpose659.20.9102
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low892.30.6724
Triple Number Coastal/Long Distance Medium654.40.9169
Triple Number Coastal/Long Distance High569.61.0534
Triple Number Windward/Leeward Low1167.50.5139
Triple Number Windward/Leeward Medium816.80.7346
Triple Number Windward/Leeward High685.60.8751
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance723.60.8292
Triple Number Coastal/Long Distance Low892.30.6724
Triple Number Coastal/Long Distance Medium654.40.9169
Triple Number Coastal/Long Distance High569.61.0534
Triple Number Windward/Leeward Low1167.50.5139
Triple Number Windward/Leeward Medium816.80.7346
Triple Number Windward/Leeward High685.60.8751
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance2027.31311.2964.8783.6676.1617.1577.4523.0513.2
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.6446
Downwind "popa"0.7505
70% up, 30% down "Ilhabela"0.6731
30% up, 70% down "Ilhabela-inverso"0.7152
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low892.30.6724
Triple Number Coastal/Long Distance Medium654.40.9169
Triple Number Coastal/Long Distance High569.61.0534
Triple Number Windward/Leeward Low1167.50.5139
Triple Number Windward/Leeward Medium816.80.7346
Triple Number Windward/Leeward High685.60.8751
Predominantly Upwind706.10.8497
Predominantly Downwind679.10.8836
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low892.40.6724
Triple Number AP Medium654.50.9167
Triple Number AP High569.61.0534
Triple Number Windward/Leeward Low1223.80.4903
Triple Number Windward/Leeward Medium816.80.7346
Triple Number Windward/Leeward High685.60.8751
Single Number Predominant Upwind738.60.8124
Single Number Predominant Reaching654.50.9168
Single Number Predominant Downwind717.30.8365
Predominant Upwind - Low1062.30.5648
Predominant Upwind - Low/Med790.70.7588
Predominant Upwind - Medium678.00.8850
Predominant Upwind - Med/High621.50.9654
Predominant Upwind - High610.00.9837
Predominant Downwind Low1128.10.5319
Predominant Downwind Low/Med795.50.7543
Predominant Downwind Medium647.30.9269
Predominant Downwind Med/High560.21.0711
Predominant Downwind High524.61.1436
Predominant Reaching Low960.00.6250
Predominant Reaching Low/Med707.30.8483
Predominant Reaching Medium600.40.9993
Predominant Reaching Med/High541.91.1071
Predominant Reaching High519.21.1556
SA/DSPL Upwind15.59SA/DSPL Downwind15.59
Scoring OptionTODTOT
5-Band Windward/Leeward Low1381.80.4342
5-Band Windward/Leeward Low/Med977.70.6137
5-Band Windward/Leeward Medium798.20.7517
5-Band Windward/Leeward Med/High696.10.8620
5-Band Windward/Leeward High666.10.9008
Windward/Leeward 60-40 Low1373.40.4369
Windward/Leeward 60-40 Low/Med983.00.6104
Windward/Leeward 60-40 Medium812.50.7385
Windward/Leeward 60-40 Med/High719.10.8344
Windward/Leeward 60-40 High696.10.8620
5-Band AP Low1000.50.5997
5-Band AP Low/Med762.50.7869
5-Band AP Medium642.40.9340
5-Band AP Med/High576.81.0403
5-Band AP High554.91.0813
5-Band SF Bay Tour - Low1178.50.5091
5-Band SF Bay Tour - Low/Med934.90.6418
5-Band SF Bay Tour - Medium772.70.7765
5-Band SF Bay Tour - Med/High683.50.8779
5-Band SF Bay Tour - High659.10.9103
Chicago-Mac Upwind0.7822
Chicago-Mac All Purpose0.7960
Chicago-Mac Downwind0.7999
Bayview-Mac Cove Island0.5571
Bayview-Mac Shore0.5634
Harvest Moon Regatta561.21.0692
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance723.60.8292
Triple Number Coastal/Long Distance Low892.30.6724
Triple Number Coastal/Long Distance Medium654.40.9169
Triple Number Coastal/Long Distance High569.61.0534
Triple Number Windward/Leeward Low1167.50.5139
Triple Number Windward/Leeward Medium816.80.7346
Triple Number Windward/Leeward High685.60.8751
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance2027.31311.2964.8783.6676.1617.1577.4523.0513.2
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance723.60.8292
Triple Number Coastal/Long Distance Low892.30.6724
Triple Number Coastal/Long Distance Medium654.40.9169
Triple Number Coastal/Long Distance High569.61.0534
Triple Number Windward/Leeward Low1167.50.5139
Triple Number Windward/Leeward Medium816.80.7346
Triple Number Windward/Leeward High685.60.8751
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance2027.31311.2964.8783.6676.1617.1577.4523.0513.2
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance723.6
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance2027.31311.2964.8783.6676.1617.1577.4523.0513.2
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low892.30.6724
Triple Number Coastal/Long Distance Medium654.40.9169
Triple Number Coastal/Long Distance High569.61.0534
Triple Number Windward/Leeward Low1167.50.5139
Triple Number Windward/Leeward Medium816.80.7346
Triple Number Windward/Leeward High685.60.8751
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating723.60.8292
FinRating, kevyt tuuli1358.20.7363
FinRating, kova tuuli559.50.8936
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low892.30.6724
Triple Number Coastal/Long Distance Medium654.40.9169
Triple Number Coastal/Long Distance High569.61.0534
Triple Number Windward/Leeward Low1167.50.5139
Triple Number Windward/Leeward Medium816.80.7346
Triple Number Windward/Leeward High685.60.8751
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.8292
Triple Number Coastal/Long Distance Low0.6724
Triple Number Coastal/Long Distance Medium0.9169
Triple Number Coastal/Long Distance High1.0534
Triple Number Windward/Leeward Low0.5139
Triple Number Windward/Leeward Medium0.7346
Triple Number Windward/Leeward High0.8751
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance2027.31311.2964.8783.6676.1617.1577.4523.0513.2
For information
General Purpose Handicap (GPH)748.9
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance723.60.8292
Triple Number Coastal/Long Distance Low892.30.6724
Triple Number Coastal/Long Distance Medium654.40.9169
Triple Number Coastal/Long Distance High569.61.0534
Triple Number Windward/Leeward Low1167.50.5139
Triple Number Windward/Leeward Medium816.80.7346
Triple Number Windward/Leeward High685.60.8751
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance2027.31311.2964.8783.6676.1617.1577.4523.0513.2
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low892.30.6724
Triple Number Coastal/Long Distance Medium654.40.9169
Triple Number Coastal/Long Distance High569.61.0534
Triple Number Windward/Leeward Low1167.50.5139
Triple Number Windward/Leeward Medium816.80.7346
Triple Number Windward/Leeward High685.60.8751
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance723.60.8292
Triple Number Coastal/Long Distance Low892.30.6724
Triple Number Coastal/Long Distance Medium654.40.9169
Triple Number Coastal/Long Distance High569.61.0534
Triple Number Windward/Leeward Low1167.50.5139
Triple Number Windward/Leeward Medium816.80.7346
Triple Number Windward/Leeward High685.60.8751
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance2027.31311.2964.8783.6676.1617.1577.4523.0513.2
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance723.60.8292
Triple Number Coastal/Long Distance Low892.30.6724
Triple Number Coastal/Long Distance Medium654.40.9169
Triple Number Coastal/Long Distance High569.61.0534
Triple Number Windward/Leeward Low1167.50.5139
Triple Number Windward/Leeward Medium816.80.7346
Triple Number Windward/Leeward High685.60.8751
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance2027.31311.2964.8783.6676.1617.1577.4523.0513.2
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low892.3
Triple Number Coastal/Long Distance Medium654.4
Triple Number Coastal/Long Distance High569.6
Triple Number Windward/Leeward Low1167.5
Triple Number Windward/Leeward Medium816.8
Triple Number Windward/Leeward High685.6
Predominantly Upwind706.1
Predominantly Downwind679.1
Predominantly Reaching641.5
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance723.60.8292
Triple Number Coastal/Long Distance Low892.30.6724
Triple Number Coastal/Long Distance Medium654.40.9169
Triple Number Coastal/Long Distance High569.61.0534
Triple Number Windward/Leeward Low1167.50.5139
Triple Number Windward/Leeward Medium816.80.7346
Triple Number Windward/Leeward High685.60.8751
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance2027.31311.2964.8783.6676.1617.1577.4523.0513.2
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.6724
Triple Number Coastal/Long Distance Medium0.9169
Triple Number Coastal/Long Distance High1.0534
Triple Number Windward/Leeward Low0.5139
Triple Number Windward/Leeward Medium0.7346
Triple Number Windward/Leeward High0.8751
Coastal/Long Distance0.8292
Predominantly Upwind0.8497
Predominantly Downwind0.8836
For information
General Purpose Handicap (GPH)748.9
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)0.9102
Distanseseilas Trippeltall svak vind0.6724
Distanseseilas Trippeltall mellomvind0.9169
Distanseseilas Trippeltall sterk vind1.0534
Pølsebane Trippeltall svak vind0.5139
Pølsebane Trippeltall mellomvind0.7346
Pølsebane Trippeltall sterk vind0.8751
Motvind Singeltall0.8497
Medvind Singeltall0.8836
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low892.30.6724
Triple Number Coastal/Long Distance Medium654.40.9169
Triple Number Coastal/Long Distance High569.61.0534
Triple Number Windward/Leeward Low1167.50.5139
Triple Number Windward/Leeward Medium816.80.7346
Triple Number Windward/Leeward High685.60.8751
Coastal/Long Distance723.60.8292
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind706.10.8497
Predominantly Downwind679.10.8836
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore664.30.9032
Cape Doctor Coastal549.91.0911
Triple Number Coastal/Long Distance Low892.30.6724
Triple Number Coastal/Long Distance Medium654.40.9169
Triple Number Coastal/Long Distance High569.61.0534
Triple Number Windward/Leeward Low1167.50.5139
Triple Number Windward/Leeward Medium816.80.7346
Triple Number Windward/Leeward High685.60.8751
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.6724
Triple Number Coastal/Long Distance Medium0.9169
Triple Number Coastal/Long Distance High1.0534
Triple Number Windward/Leeward Low0.5139
Triple Number Windward/Leeward Medium0.7346
Triple Number Windward/Leeward High0.8751
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.6724
Triple Number Coastal/Long Distance Medium0.9169
Triple Number Coastal/Long Distance High1.0534
Triple Number Windward/Leeward Low0.5139
Triple Number Windward/Leeward Medium0.7346
Triple Number Windward/Leeward High0.8751
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance723.60.8292
Triple Number Coastal/Long Distance Low892.30.6724
Triple Number Coastal/Long Distance Medium654.40.9169
Triple Number Coastal/Long Distance High569.61.0534
Triple Number Windward/Leeward Low1167.50.5139
Triple Number Windward/Leeward Medium816.80.7346
Triple Number Windward/Leeward High685.60.8751
Predominantly Upwind706.10.8497
Predominantly Downwind679.10.8836
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance2027.31311.2964.8783.6676.1617.1577.4523.0513.2
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance723.60.8292
Triple Number Coastal/Long Distance Low892.30.6724
Triple Number Coastal/Long Distance Medium654.40.9169
Triple Number Coastal/Long Distance High569.61.0534
Triple Number Windward/Leeward Low1167.50.5139
Triple Number Windward/Leeward Medium816.80.7346
Triple Number Windward/Leeward High685.60.8751
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance2027.31311.2964.8783.6676.1617.1577.4523.0513.2
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low892.40.6724
Triple Number AP Medium654.50.9167
Triple Number AP High569.61.0534
Triple Number Windward/Leeward Low1223.80.4903
Triple Number Windward/Leeward Medium816.80.7346
Triple Number Windward/Leeward High685.60.8751
Single Number Predominant Upwind738.60.8124
Single Number Predominant Reaching654.50.9168
Single Number Predominant Downwind717.30.8365
Predominant Upwind - Low1062.30.5648
Predominant Upwind - Low/Med790.70.7588
Predominant Upwind - Medium678.00.8850
Predominant Upwind - Med/High621.50.9654
Predominant Upwind - High610.00.9837
Predominant Downwind Low1128.10.5319
Predominant Downwind Low/Med795.50.7543
Predominant Downwind Medium647.30.9269
Predominant Downwind Med/High560.21.0711
Predominant Downwind High524.61.1436
Predominant Reaching Low960.00.6250
Predominant Reaching Low/Med707.30.8483
Predominant Reaching Medium600.40.9993
Predominant Reaching Med/High541.91.1071
Predominant Reaching High519.21.1556
SA/DSPL Upwind15.59SA/DSPL Downwind15.59
Scoring OptionTODTOT
5-Band Windward/Leeward Low1381.80.4342
5-Band Windward/Leeward Low/Med977.70.6137
5-Band Windward/Leeward Medium798.20.7517
5-Band Windward/Leeward Med/High696.10.8620
5-Band Windward/Leeward High666.10.9008
Windward/Leeward 60-40 Low1373.40.4369
Windward/Leeward 60-40 Low/Med983.00.6104
Windward/Leeward 60-40 Medium812.50.7385
Windward/Leeward 60-40 Med/High719.10.8344
Windward/Leeward 60-40 High696.10.8620
5-Band AP Low1000.50.5997
5-Band AP Low/Med762.50.7869
5-Band AP Medium642.40.9340
5-Band AP Med/High576.81.0403
5-Band AP High554.91.0813
5-Band SF Bay Tour - Low1178.50.5091
5-Band SF Bay Tour - Low/Med934.90.6418
5-Band SF Bay Tour - Medium772.70.7765
5-Band SF Bay Tour - Med/High683.50.8779
5-Band SF Bay Tour - High659.10.9103
Chicago-Mac Upwind0.7822
Chicago-Mac All Purpose0.7960
Chicago-Mac Downwind0.7999
Bayview-Mac Cove Island0.5571
Bayview-Mac Shore0.5634
Harvest Moon Regatta561.21.0692
Double HandedClub Certificate2025
Joie de VieRSA-2350
ORC
Central Rating Office
Issuing certificates for
SOUTH AFRICA
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassFirst 35Measurement13/10/2025HINPlan reviewHull constructionSolidCarbon rudderNoLight stanchionsNoTrim tabNo
LOA10.832Max. Beam3.702Draft1.474Displacement6,553Wetted area25.76IMS L9.300LSM09.190Acc. length10.832Sink (kg/mm) 19.38
VCGD0.182VCGM0.142RM Rated (kg·m) 135.3Limit of positive stability(°) N/AStability IndexN/ADefault crew weight170Declared crew weight210
PROPELLER
Propeller TypeFeathering 2 blades
InstallationShaft exposedTwin screwNoHydro generatorNo
PRD0.390PBWPIPA0.0055
PSD0.025PHD0.070PHL0.105
PSA23.0°ESL0.920
ST10.015ST20.090ST30.095
ST40.050ST50.310
RIG
Forestay tensionAftInner stayAdjustableMast materialAluminumSingle headsail furlerYesMainsail furlerNoArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders2Rotating mastNo
P12.290IG13.737ISP13.737MDT10.135MDL10.205MDT2MDL2TLNo TaperMW0.205GO0.255
E3.940J4.050BAS1.397FSDFoilSFJ0.005SPLWPLTPS4.055BD0.130MWT172.00MCG4.415
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodRM estimatedFlotation Date19/11/2025
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Double HandedClub Certificate2025
Joie de VieRSA-2350
ORC
Central Rating Office
Issuing certificates for
SOUTH AFRICA
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateCommentM10.150.751.362.373.1827.5118/09/2025
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateCommentJRF-20.080.490.962.013.224.4712.90NoNo 27.4107/11/2025RFJST-10.060.260.470.951.542.215.94NoNo 6.1319/09/2025
CRUISER/RACER REQUIREMENTS*
Accommodation length10.8 mTable area0.55 m²Headroom1.75 mMinimum number of berths5Personal gear stowage0.20 m³Fresh water capacity120 lMinimum number of seats in cockpit5Food stowage0.30 m³Fuel capacity66 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.