Club Certificate2025
CAMINOESP-11392_C
RFEV
c/ Gamazo sn
39004 Santander – España
crucero@rfev.es
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 Angles45.6°45.6°43.9°42.6°41.4°40.1°39.5°39.4°40.5°
Beat VMG2.163.043.794.364.835.225.475.635.56
52°3.444.765.806.577.137.527.788.018.02
60°3.725.086.126.877.387.727.988.288.35
75°3.895.296.337.087.577.908.178.628.90
90°3.905.416.627.467.978.348.648.979.19
110°3.955.496.737.568.068.488.889.7010.41
120°3.825.326.537.407.948.378.789.6410.81
135°3.334.735.946.907.588.048.449.2410.24
150°2.733.985.126.096.897.497.918.589.26
Run VMG2.373.444.435.275.976.516.967.688.28
Gybe Angles143.5°143.5°146.9°148.5°149.6°152.6°157.9°163.7°179.3°
APH ToD:562.5CDL: 9.571APH ToT: 1.0666CertNo:1139201
BOAT
ClassDUFOUR 410 GLDesignerFELCIBuilderDUFOURAge date01/2015Series date01/2014Offset fileD410PRG.offData fileE11392_C
HULL
Length Overall11.980 mMaximum Beam4.214 mDraft2.070 mDisplacement8,761 kgDLR6.7503IMS DivisionCruiser/RacerDynamic Allowance0.380%Age Allowance0.357%
PROPELLER
InstallationStrutTypeFolding 3 bladesDiameter0.400m
CREW
Maximum weight600 kg(declared)Minimum weight470 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail38.4438.82Headsail Luffed34.6634.66Headsail FlyingSymmetricAsymmetric89.6389.63 (All asymmetric spinnakers with SHW/SFL > 85%)
STORM SAIL AREAS (m²)
Trysail12.14Storm Jib12.49Heavy Weather Jib33.71
SAIL LIMITS
Headsails5
✱ One set on the forestay
Spinnakers4
STABILITY
Righting MomentN/AStability IndexN/A
COMMENTS
CASCO DISEÑADOR.
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
CAMINOESP-11392_C
RFEV
c/ Gamazo sn
39004 Santander – España
crucero@rfev.es
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 VMG1669.61182.8949.8825.3745.0690.3658.7639.9647.2
52°1047.1757.0620.7548.3505.0478.7462.6449.4448.7
60°969.0708.9588.4524.3487.9466.0451.3434.7431.4
75°925.4680.7568.3508.3475.4455.5440.7417.4404.6
90°922.4665.0544.0482.6451.6431.5416.6401.2391.9
110°912.2655.2534.8476.1446.4424.6405.3371.2345.7
120°943.4677.0551.0486.4453.2430.3410.1373.3332.9
135°1082.2761.8606.5521.9475.0447.8426.7389.4351.7
150°1317.0905.2703.4591.5522.7480.8455.4419.6388.6
Run VMG1520.71045.3812.3683.0603.5553.2517.1469.0435.0
Selected Courses
Windward / Leeward1594.61114.1881.0754.2674.3621.7587.9554.5541.1
All purpose1196.2848.2681.3592.0539.0504.9481.8455.1439.8
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward707.80.8477
All purpose562.51.0666
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low764.70.7846
Triple Number Coastal/Long Distance Medium560.01.0714
Triple Number Coastal/Long Distance High477.51.2565
Triple Number Windward/Leeward Low997.50.6015
Triple Number Windward/Leeward Medium705.00.8511
Triple Number Windward/Leeward High583.81.0277
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance617.10.9724
Triple Number Coastal/Long Distance Low764.70.7846
Triple Number Coastal/Long Distance Medium560.01.0714
Triple Number Coastal/Long Distance High477.51.2565
Triple Number Windward/Leeward Low997.50.6015
Triple Number Windward/Leeward Medium705.00.8511
Triple Number Windward/Leeward High583.81.0277
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1689.21107.2824.2673.1578.8524.6486.5435.1416.5
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.7379
Downwind "popa"0.8968
70% up, 30% down "Ilhabela"0.7793
30% up, 70% down "Ilhabela-inverso"0.8424
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low764.70.7846
Triple Number Coastal/Long Distance Medium560.01.0714
Triple Number Coastal/Long Distance High477.51.2565
Triple Number Windward/Leeward Low997.50.6015
Triple Number Windward/Leeward Medium705.00.8511
Triple Number Windward/Leeward High583.81.0277
Predominantly Upwind613.80.9775
Predominantly Downwind573.81.0457
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low764.80.7846
Triple Number AP Medium560.11.0713
Triple Number AP High477.51.2565
Triple Number Windward/Leeward Low1044.60.5744
Triple Number Windward/Leeward Medium705.00.8511
Triple Number Windward/Leeward High583.81.0277
Single Number Predominant Upwind642.30.9341
Single Number Predominant Reaching557.51.0763
Single Number Predominant Downwind601.30.9978
Predominant Upwind - Low950.90.6310
Predominant Upwind - Low/Med699.00.8584
Predominant Upwind - Medium589.21.0184
Predominant Upwind - Med/High524.31.1444
Predominant Upwind - High500.61.1985
Predominant Downwind Low919.00.6529
Predominant Downwind Low/Med661.30.9073
Predominant Downwind Medium548.91.0932
Predominant Downwind Med/High480.41.2490
Predominant Downwind High444.81.3489
Predominant Reaching Low821.90.7300
Predominant Reaching Low/Med604.60.9924
Predominant Reaching Medium512.61.1704
Predominant Reaching Med/High458.51.3087
Predominant Reaching High432.41.3875
SA/DSPL Upwind17.08SA/DSPL Downwind29.92
Scoring OptionTODTOT
5-Band Windward/Leeward Low1176.10.5102
5-Band Windward/Leeward Low/Med840.10.7142
5-Band Windward/Leeward Medium688.80.8711
5-Band Windward/Leeward Med/High595.31.0079
5-Band Windward/Leeward High557.91.0754
Windward/Leeward 60-40 Low1190.10.5041
Windward/Leeward 60-40 Low/Med854.10.7025
Windward/Leeward 60-40 Medium702.80.8537
Windward/Leeward 60-40 Med/High609.90.9838
Windward/Leeward 60-40 High575.21.0431
5-Band AP Low846.70.7087
5-Band AP Low/Med653.40.9183
5-Band AP Medium549.21.0925
5-Band AP Med/High486.01.2346
5-Band AP High457.01.3128
5-Band SF Bay Tour - Low1009.70.5942
5-Band SF Bay Tour - Low/Med803.00.7472
5-Band SF Bay Tour - Medium662.20.9061
5-Band SF Bay Tour - Med/High576.11.0415
5-Band SF Bay Tour - High541.71.1076
Chicago-Mac Upwind0.8948
Chicago-Mac All Purpose0.9294
Chicago-Mac Downwind0.9562
Bayview-Mac Cove Island0.6528
Bayview-Mac Shore0.6574
Harvest Moon Regatta476.71.2585
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance617.10.9724
Triple Number Coastal/Long Distance Low764.70.7846
Triple Number Coastal/Long Distance Medium560.01.0714
Triple Number Coastal/Long Distance High477.51.2565
Triple Number Windward/Leeward Low997.50.6015
Triple Number Windward/Leeward Medium705.00.8511
Triple Number Windward/Leeward High583.81.0277
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1689.21107.2824.2673.1578.8524.6486.5435.1416.5
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance617.10.9724
Triple Number Coastal/Long Distance Low764.70.7846
Triple Number Coastal/Long Distance Medium560.01.0714
Triple Number Coastal/Long Distance High477.51.2565
Triple Number Windward/Leeward Low997.50.6015
Triple Number Windward/Leeward Medium705.00.8511
Triple Number Windward/Leeward High583.81.0277
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1689.21107.2824.2673.1578.8524.6486.5435.1416.5
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance617.1
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1689.21107.2824.2673.1578.8524.6486.5435.1416.5
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low764.70.7846
Triple Number Coastal/Long Distance Medium560.01.0714
Triple Number Coastal/Long Distance High477.51.2565
Triple Number Windward/Leeward Low997.50.6015
Triple Number Windward/Leeward Medium705.00.8511
Triple Number Windward/Leeward High583.81.0277
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating617.10.9724
FinRating, kevyt tuuli1152.10.8680
FinRating, kova tuuli460.11.0868
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low764.70.7846
Triple Number Coastal/Long Distance Medium560.01.0714
Triple Number Coastal/Long Distance High477.51.2565
Triple Number Windward/Leeward Low997.50.6015
Triple Number Windward/Leeward Medium705.00.8511
Triple Number Windward/Leeward High583.81.0277
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.9724
Triple Number Coastal/Long Distance Low0.7846
Triple Number Coastal/Long Distance Medium1.0714
Triple Number Coastal/Long Distance High1.2565
Triple Number Windward/Leeward Low0.6015
Triple Number Windward/Leeward Medium0.8511
Triple Number Windward/Leeward High1.0277
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1689.21107.2824.2673.1578.8524.6486.5435.1416.5
For information
General Purpose Handicap (GPH)639.9
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance617.10.9724
Triple Number Coastal/Long Distance Low764.70.7846
Triple Number Coastal/Long Distance Medium560.01.0714
Triple Number Coastal/Long Distance High477.51.2565
Triple Number Windward/Leeward Low997.50.6015
Triple Number Windward/Leeward Medium705.00.8511
Triple Number Windward/Leeward High583.81.0277
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1689.21107.2824.2673.1578.8524.6486.5435.1416.5
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low764.70.7846
Triple Number Coastal/Long Distance Medium560.01.0714
Triple Number Coastal/Long Distance High477.51.2565
Triple Number Windward/Leeward Low997.50.6015
Triple Number Windward/Leeward Medium705.00.8511
Triple Number Windward/Leeward High583.81.0277
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance617.10.9724
Triple Number Coastal/Long Distance Low764.70.7846
Triple Number Coastal/Long Distance Medium560.01.0714
Triple Number Coastal/Long Distance High477.51.2565
Triple Number Windward/Leeward Low997.50.6015
Triple Number Windward/Leeward Medium705.00.8511
Triple Number Windward/Leeward High583.81.0277
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1689.21107.2824.2673.1578.8524.6486.5435.1416.5
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance617.10.9724
Triple Number Coastal/Long Distance Low764.70.7846
Triple Number Coastal/Long Distance Medium560.01.0714
Triple Number Coastal/Long Distance High477.51.2565
Triple Number Windward/Leeward Low997.50.6015
Triple Number Windward/Leeward Medium705.00.8511
Triple Number Windward/Leeward High583.81.0277
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1689.21107.2824.2673.1578.8524.6486.5435.1416.5
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low764.7
Triple Number Coastal/Long Distance Medium560.0
Triple Number Coastal/Long Distance High477.5
Triple Number Windward/Leeward Low997.5
Triple Number Windward/Leeward Medium705.0
Triple Number Windward/Leeward High583.8
Predominantly Upwind613.8
Predominantly Downwind573.8
Predominantly Reaching544.0
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance617.10.9724
Triple Number Coastal/Long Distance Low764.70.7846
Triple Number Coastal/Long Distance Medium560.01.0714
Triple Number Coastal/Long Distance High477.51.2565
Triple Number Windward/Leeward Low997.50.6015
Triple Number Windward/Leeward Medium705.00.8511
Triple Number Windward/Leeward High583.81.0277
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1689.21107.2824.2673.1578.8524.6486.5435.1416.5
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7846
Triple Number Coastal/Long Distance Medium1.0714
Triple Number Coastal/Long Distance High1.2565
Triple Number Windward/Leeward Low0.6015
Triple Number Windward/Leeward Medium0.8511
Triple Number Windward/Leeward High1.0277
Coastal/Long Distance0.9724
Predominantly Upwind0.9775
Predominantly Downwind1.0457
For information
General Purpose Handicap (GPH)639.9
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)1.0666
Distanseseilas Trippeltall svak vind0.7846
Distanseseilas Trippeltall mellomvind1.0714
Distanseseilas Trippeltall sterk vind1.2565
Pølsebane Trippeltall svak vind0.6015
Pølsebane Trippeltall mellomvind0.8511
Pølsebane Trippeltall sterk vind1.0277
Motvind Singeltall0.9775
Medvind Singeltall1.0457
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low764.70.7846
Triple Number Coastal/Long Distance Medium560.01.0714
Triple Number Coastal/Long Distance High477.51.2565
Triple Number Windward/Leeward Low997.50.6015
Triple Number Windward/Leeward Medium705.00.8511
Triple Number Windward/Leeward High583.81.0277
Coastal/Long Distance617.10.9724
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind613.80.9775
Predominantly Downwind573.81.0457
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore545.11.1007
Cape Doctor Coastal444.31.3503
Triple Number Coastal/Long Distance Low764.70.7846
Triple Number Coastal/Long Distance Medium560.01.0714
Triple Number Coastal/Long Distance High477.51.2565
Triple Number Windward/Leeward Low997.50.6015
Triple Number Windward/Leeward Medium705.00.8511
Triple Number Windward/Leeward High583.81.0277
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7846
Triple Number Coastal/Long Distance Medium1.0714
Triple Number Coastal/Long Distance High1.2565
Triple Number Windward/Leeward Low0.6015
Triple Number Windward/Leeward Medium0.8511
Triple Number Windward/Leeward High1.0277
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7846
Triple Number Coastal/Long Distance Medium1.0714
Triple Number Coastal/Long Distance High1.2565
Triple Number Windward/Leeward Low0.6015
Triple Number Windward/Leeward Medium0.8511
Triple Number Windward/Leeward High1.0277
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance617.10.9724
Triple Number Coastal/Long Distance Low764.70.7846
Triple Number Coastal/Long Distance Medium560.01.0714
Triple Number Coastal/Long Distance High477.51.2565
Triple Number Windward/Leeward Low997.50.6015
Triple Number Windward/Leeward Medium705.00.8511
Triple Number Windward/Leeward High583.81.0277
Predominantly Upwind613.80.9775
Predominantly Downwind573.81.0457
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1689.21107.2824.2673.1578.8524.6486.5435.1416.5
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance617.10.9724
Triple Number Coastal/Long Distance Low764.70.7846
Triple Number Coastal/Long Distance Medium560.01.0714
Triple Number Coastal/Long Distance High477.51.2565
Triple Number Windward/Leeward Low997.50.6015
Triple Number Windward/Leeward Medium705.00.8511
Triple Number Windward/Leeward High583.81.0277
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1689.21107.2824.2673.1578.8524.6486.5435.1416.5
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low764.80.7846
Triple Number AP Medium560.11.0713
Triple Number AP High477.51.2565
Triple Number Windward/Leeward Low1044.60.5744
Triple Number Windward/Leeward Medium705.00.8511
Triple Number Windward/Leeward High583.81.0277
Single Number Predominant Upwind642.30.9341
Single Number Predominant Reaching557.51.0763
Single Number Predominant Downwind601.30.9978
Predominant Upwind - Low950.90.6310
Predominant Upwind - Low/Med699.00.8584
Predominant Upwind - Medium589.21.0184
Predominant Upwind - Med/High524.31.1444
Predominant Upwind - High500.61.1985
Predominant Downwind Low919.00.6529
Predominant Downwind Low/Med661.30.9073
Predominant Downwind Medium548.91.0932
Predominant Downwind Med/High480.41.2490
Predominant Downwind High444.81.3489
Predominant Reaching Low821.90.7300
Predominant Reaching Low/Med604.60.9924
Predominant Reaching Medium512.61.1704
Predominant Reaching Med/High458.51.3087
Predominant Reaching High432.41.3875
SA/DSPL Upwind17.08SA/DSPL Downwind29.92
Scoring OptionTODTOT
5-Band Windward/Leeward Low1176.10.5102
5-Band Windward/Leeward Low/Med840.10.7142
5-Band Windward/Leeward Medium688.80.8711
5-Band Windward/Leeward Med/High595.31.0079
5-Band Windward/Leeward High557.91.0754
Windward/Leeward 60-40 Low1190.10.5041
Windward/Leeward 60-40 Low/Med854.10.7025
Windward/Leeward 60-40 Medium702.80.8537
Windward/Leeward 60-40 Med/High609.90.9838
Windward/Leeward 60-40 High575.21.0431
5-Band AP Low846.70.7087
5-Band AP Low/Med653.40.9183
5-Band AP Medium549.21.0925
5-Band AP Med/High486.01.2346
5-Band AP High457.01.3128
5-Band SF Bay Tour - Low1009.70.5942
5-Band SF Bay Tour - Low/Med803.00.7472
5-Band SF Bay Tour - Medium662.20.9061
5-Band SF Bay Tour - Med/High576.11.0415
5-Band SF Bay Tour - High541.71.1076
Chicago-Mac Upwind0.8948
Chicago-Mac All Purpose0.9294
Chicago-Mac Downwind0.9562
Bayview-Mac Cove Island0.6528
Bayview-Mac Shore0.6574
Harvest Moon Regatta476.71.2585
Club Certificate2025
CAMINOESP-11392_C
RFEV
c/ Gamazo sn
39004 Santander – España
crucero@rfev.es
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassDUFOUR 410 GLMeasurement04/08/2025HINPlan reviewHull constructionCoredCarbon rudderNoLight stanchionsNoTrim tabNo
LOA11.980Max. Beam4.214Draft2.070Displacement8,761Wetted area35.30IMS L11.108LSM010.907Acc. length11.980Sink (kg/mm) 27.44
VCGD-0.050VCGM-0.019RM Rated (kg·m) 308.8Limit of positive stability(°) N/AStability IndexN/ADefault crew weight779Declared crew weight600
PROPELLER
Propeller TypeFolding 3 blades
InstallationStrutTwin screwNoHydro generatorNo
PRD0.400PBWPIPA0.0030
EDL3.080ST10.055ST20.175
ST30.190ST40.090ST50.285
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerYesMainsail furlerNoArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders2Rotating mastNo
P14.750IG15.800ISP15.900MDT10.100MDL10.110MDT2MDL2TLMWGO
E4.700J4.300BAS1.310FSD0.040SFJ0.100SPLWPLTPS5.100BDMWTMCG
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodRM entered directlyRM entered310.0Flotation Date01/01/2010
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Club Certificate2025
CAMINOESP-11392_C
RFEV
c/ Gamazo sn
39004 Santander – España
crucero@rfev.es
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment10.080.781.462.773.8038.4430/07/2025
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment10.070.591.162.393.685.0114.17NoNo 34.6630/07/2025
ASYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLRatioAreaMeas.DateComment114.5313.4814.017.438.6886%89.6330/07/2025
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.