Double HandedClub Certificate2025
BefanaNED 8253
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 Angles44.0°44.0°41.9°40.8°40.0°39.7°39.8°40.7°43.0°
Beat VMG2.313.203.894.374.614.704.734.694.48
52°3.634.905.826.416.686.796.846.876.77
60°3.885.196.086.626.897.017.077.127.07
75°4.075.406.276.787.087.277.397.517.54
90°3.985.396.396.907.127.387.607.898.03
110°4.035.486.517.077.437.717.888.188.36
120°3.885.316.376.997.407.778.108.568.93
135°3.414.775.896.687.177.567.958.8210.11
150°2.814.055.176.106.777.217.598.379.41
Run VMG2.443.514.485.316.016.587.017.728.45
Gybe Angles145.7°145.7°150.3°153.9°160.6°167.3°175.4°177.2°173.6°
APH ToD:588.9CDL: 8.103APH ToT: 1.0189CertNo:27796
BOAT
ClassWinner 10.20Designerv/d stadtBuilderWinnerAge date03/2011Series date01/2011Offset fileWINNER1010.offData fileNED8253
HULL
Length Overall10.129 mMaximum Beam3.320 mDraft1.788 mDisplacement4,717 kgDLR6.9982IMS DivisionCruiser/RacerDynamic Allowance0.220%Age Allowance0.455%
PROPELLER
InstallationStrutTypeFolding 2 bladesDiameter0.400m
CREW
Maximum weight200 kg(declared)Minimum weight120 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail33.4434.02Headsail Luffed24.1424.14Headsail FlyingSymmetric75.4775.47Asymmetric
STORM SAIL AREAS (m²)
Trysail9.96Storm Jib8.29Heavy Weather Jib22.37
SAIL LIMITS
Headsails5
✱ One set on the forestay
Spinnakers4
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
BefanaNED 8253
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 VMG1555.81126.6925.6823.6780.7766.6761.3767.0803.4
52°991.6734.2618.3561.7538.7530.4526.3524.2531.7
60°927.7694.1591.9543.6522.5513.9509.5505.9509.2
75°884.5666.7573.7530.7508.3495.1487.3479.2477.6
90°905.6668.4563.8521.6505.6487.7473.6456.5448.3
110°893.1657.0552.7509.3484.4467.1456.6440.1430.7
120°926.8677.5565.0514.9486.3463.4444.2420.5403.3
135°1055.2754.1611.3538.8502.3476.0452.6408.3356.0
150°1279.8888.3696.4590.4531.9499.5474.6430.3382.6
Run VMG1477.81025.7804.0678.3598.9547.4513.3466.1426.0
Selected Courses
Windward / Leeward1515.71076.2864.8750.9689.8657.0637.3616.5614.7
All purpose1145.5828.0679.6605.1567.5546.3532.4514.7507.1
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward723.40.8295
All purpose588.91.0189
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low753.80.7960
Triple Number Coastal/Long Distance Medium584.11.0273
Triple Number Coastal/Long Distance High529.21.1337
Triple Number Windward/Leeward Low970.40.6183
Triple Number Windward/Leeward Medium716.60.8373
Triple Number Windward/Leeward High634.50.9457
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance640.20.9373
Triple Number Coastal/Long Distance Low753.80.7960
Triple Number Coastal/Long Distance Medium584.11.0273
Triple Number Coastal/Long Distance High529.21.1337
Triple Number Windward/Leeward Low970.40.6183
Triple Number Windward/Leeward Medium716.60.8373
Triple Number Windward/Leeward High634.50.9457
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1602.01071.1812.7678.8605.7567.0536.5489.2479.0
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.7057
Downwind "popa"0.9064
70% up, 30% down "Ilhabela"0.7559
30% up, 70% down "Ilhabela-inverso"0.8352
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low753.80.7960
Triple Number Coastal/Long Distance Medium584.11.0273
Triple Number Coastal/Long Distance High529.21.1337
Triple Number Windward/Leeward Low970.40.6183
Triple Number Windward/Leeward Medium716.60.8373
Triple Number Windward/Leeward High634.50.9457
Predominantly Upwind642.60.9338
Predominantly Downwind590.01.0170
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low753.80.7960
Triple Number AP Medium584.11.0272
Triple Number AP High529.21.1337
Triple Number Windward/Leeward Low1013.70.5919
Triple Number Windward/Leeward Medium716.60.8373
Triple Number Windward/Leeward High634.50.9457
Single Number Predominant Upwind669.90.8956
Single Number Predominant Reaching584.91.0259
Single Number Predominant Downwind616.30.9736
Predominant Upwind - Low919.60.6524
Predominant Upwind - Low/Med701.80.8549
Predominant Upwind - Medium621.70.9651
Predominant Upwind - Med/High586.81.0224
Predominant Upwind - High576.81.0403
Predominant Downwind Low901.10.6659
Predominant Downwind Low/Med666.30.9005
Predominant Downwind Medium569.21.0541
Predominant Downwind Med/High510.51.1752
Predominant Downwind High476.21.2599
Predominant Reaching Low808.70.7419
Predominant Reaching Low/Med618.00.9709
Predominant Reaching Medium546.41.0982
Predominant Reaching Med/High505.31.1873
Predominant Reaching High481.81.2453
SA/DSPL Upwind20.37SA/DSPL Downwind38.52
Scoring OptionTODTOT
5-Band Windward/Leeward Low1133.50.5293
5-Band Windward/Leeward Low/Med829.90.7229
5-Band Windward/Leeward Medium704.70.8515
5-Band Windward/Leeward Med/High641.50.9352
5-Band Windward/Leeward High619.80.9680
Windward/Leeward 60-40 Low1143.50.5247
Windward/Leeward 60-40 Low/Med843.50.7113
Windward/Leeward 60-40 Medium722.90.8300
Windward/Leeward 60-40 Med/High666.20.9006
Windward/Leeward 60-40 High650.30.9226
5-Band AP Low829.60.7232
5-Band AP Low/Med658.60.9110
5-Band AP Medium576.61.0407
5-Band AP Med/High534.71.1222
5-Band AP High516.51.1618
5-Band SF Bay Tour - Low978.90.6130
5-Band SF Bay Tour - Low/Med796.00.7538
5-Band SF Bay Tour - Medium683.40.8780
5-Band SF Bay Tour - Med/High628.70.9544
5-Band SF Bay Tour - High609.20.9848
Chicago-Mac Upwind0.8697
Chicago-Mac All Purpose0.9065
Chicago-Mac Downwind0.9394
Bayview-Mac Cove Island0.6635
Bayview-Mac Shore0.6679
Harvest Moon Regatta508.91.1790
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance640.20.9373
Triple Number Coastal/Long Distance Low753.80.7960
Triple Number Coastal/Long Distance Medium584.11.0273
Triple Number Coastal/Long Distance High529.21.1337
Triple Number Windward/Leeward Low970.40.6183
Triple Number Windward/Leeward Medium716.60.8373
Triple Number Windward/Leeward High634.50.9457
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1602.01071.1812.7678.8605.7567.0536.5489.2479.0
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance640.20.9373
Triple Number Coastal/Long Distance Low753.80.7960
Triple Number Coastal/Long Distance Medium584.11.0273
Triple Number Coastal/Long Distance High529.21.1337
Triple Number Windward/Leeward Low970.40.6183
Triple Number Windward/Leeward Medium716.60.8373
Triple Number Windward/Leeward High634.50.9457
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1602.01071.1812.7678.8605.7567.0536.5489.2479.0
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance640.2
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1602.01071.1812.7678.8605.7567.0536.5489.2479.0
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low753.80.7960
Triple Number Coastal/Long Distance Medium584.11.0273
Triple Number Coastal/Long Distance High529.21.1337
Triple Number Windward/Leeward Low970.40.6183
Triple Number Windward/Leeward Medium716.60.8373
Triple Number Windward/Leeward High634.50.9457
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating (Coastal/Long Distance)640.20.9373
Triple Number Coastal/Long Distance Low753.80.7960
Triple Number Coastal/Long Distance Medium584.11.0273
Triple Number Coastal/Long Distance High529.21.1337
Triple Number Windward/Leeward Low970.40.6183
Triple Number Windward/Leeward Medium716.60.8373
Triple Number Windward/Leeward High634.50.9457
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1602.01071.1812.7678.8605.7567.0536.5489.2479.0
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low753.80.7960
Triple Number Coastal/Long Distance Medium584.11.0273
Triple Number Coastal/Long Distance High529.21.1337
Triple Number Windward/Leeward Low970.40.6183
Triple Number Windward/Leeward Medium716.60.8373
Triple Number Windward/Leeward High634.50.9457
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.9373
Triple Number Coastal/Long Distance Low0.7960
Triple Number Coastal/Long Distance Medium1.0273
Triple Number Coastal/Long Distance High1.1337
Triple Number Windward/Leeward Low0.6183
Triple Number Windward/Leeward Medium0.8373
Triple Number Windward/Leeward High0.9457
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1602.01071.1812.7678.8605.7567.0536.5489.2479.0
For information
General Purpose Handicap (GPH)660.1
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance640.20.9373
Triple Number Coastal/Long Distance Low753.80.7960
Triple Number Coastal/Long Distance Medium584.11.0273
Triple Number Coastal/Long Distance High529.21.1337
Triple Number Windward/Leeward Low970.40.6183
Triple Number Windward/Leeward Medium716.60.8373
Triple Number Windward/Leeward High634.50.9457
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1602.01071.1812.7678.8605.7567.0536.5489.2479.0
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low753.80.7960
Triple Number Coastal/Long Distance Medium584.11.0273
Triple Number Coastal/Long Distance High529.21.1337
Triple Number Windward/Leeward Low970.40.6183
Triple Number Windward/Leeward Medium716.60.8373
Triple Number Windward/Leeward High634.50.9457
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance640.20.9373
Triple Number Coastal/Long Distance Low753.80.7960
Triple Number Coastal/Long Distance Medium584.11.0273
Triple Number Coastal/Long Distance High529.21.1337
Triple Number Windward/Leeward Low970.40.6183
Triple Number Windward/Leeward Medium716.60.8373
Triple Number Windward/Leeward High634.50.9457
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1602.01071.1812.7678.8605.7567.0536.5489.2479.0
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance640.20.9373
Triple Number Coastal/Long Distance Low753.80.7960
Triple Number Coastal/Long Distance Medium584.11.0273
Triple Number Coastal/Long Distance High529.21.1337
Triple Number Windward/Leeward Low970.40.6183
Triple Number Windward/Leeward Medium716.60.8373
Triple Number Windward/Leeward High634.50.9457
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1602.01071.1812.7678.8605.7567.0536.5489.2479.0
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low753.8
Triple Number Coastal/Long Distance Medium584.1
Triple Number Coastal/Long Distance High529.2
Triple Number Windward/Leeward Low970.4
Triple Number Windward/Leeward Medium716.6
Triple Number Windward/Leeward High634.5
Predominantly Upwind642.6
Predominantly Downwind590.0
Predominantly Reaching569.3
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance640.20.9373
Triple Number Coastal/Long Distance Low753.80.7960
Triple Number Coastal/Long Distance Medium584.11.0273
Triple Number Coastal/Long Distance High529.21.1337
Triple Number Windward/Leeward Low970.40.6183
Triple Number Windward/Leeward Medium716.60.8373
Triple Number Windward/Leeward High634.50.9457
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1602.01071.1812.7678.8605.7567.0536.5489.2479.0
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7960
Triple Number Coastal/Long Distance Medium1.0273
Triple Number Coastal/Long Distance High1.1337
Triple Number Windward/Leeward Low0.6183
Triple Number Windward/Leeward Medium0.8373
Triple Number Windward/Leeward High0.9457
Coastal/Long Distance0.9373
Predominantly Upwind0.9338
Predominantly Downwind1.0170
For information
General Purpose Handicap (GPH)660.1
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)1.0189
Distanseseilas Trippeltall svak vind0.7960
Distanseseilas Trippeltall mellomvind1.0273
Distanseseilas Trippeltall sterk vind1.1337
Pølsebane Trippeltall svak vind0.6183
Pølsebane Trippeltall mellomvind0.8373
Pølsebane Trippeltall sterk vind0.9457
Motvind Singeltall0.9338
Medvind Singeltall1.0170
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low753.80.7960
Triple Number Coastal/Long Distance Medium584.11.0273
Triple Number Coastal/Long Distance High529.21.1337
Triple Number Windward/Leeward Low970.40.6183
Triple Number Windward/Leeward Medium716.60.8373
Triple Number Windward/Leeward High634.50.9457
Coastal/Long Distance640.20.9373
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind642.60.9338
Predominantly Downwind590.01.0170
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore615.20.9752
Cape Doctor Coastal509.41.1778
Triple Number Coastal/Long Distance Low753.80.7960
Triple Number Coastal/Long Distance Medium584.11.0273
Triple Number Coastal/Long Distance High529.21.1337
Triple Number Windward/Leeward Low970.40.6183
Triple Number Windward/Leeward Medium716.60.8373
Triple Number Windward/Leeward High634.50.9457
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7960
Triple Number Coastal/Long Distance Medium1.0273
Triple Number Coastal/Long Distance High1.1337
Triple Number Windward/Leeward Low0.6183
Triple Number Windward/Leeward Medium0.8373
Triple Number Windward/Leeward High0.9457
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7960
Triple Number Coastal/Long Distance Medium1.0273
Triple Number Coastal/Long Distance High1.1337
Triple Number Windward/Leeward Low0.6183
Triple Number Windward/Leeward Medium0.8373
Triple Number Windward/Leeward High0.9457
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance640.20.9373
Triple Number Coastal/Long Distance Low753.80.7960
Triple Number Coastal/Long Distance Medium584.11.0273
Triple Number Coastal/Long Distance High529.21.1337
Triple Number Windward/Leeward Low970.40.6183
Triple Number Windward/Leeward Medium716.60.8373
Triple Number Windward/Leeward High634.50.9457
Predominantly Upwind642.60.9338
Predominantly Downwind590.01.0170
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1602.01071.1812.7678.8605.7567.0536.5489.2479.0
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance640.20.9373
Triple Number Coastal/Long Distance Low753.80.7960
Triple Number Coastal/Long Distance Medium584.11.0273
Triple Number Coastal/Long Distance High529.21.1337
Triple Number Windward/Leeward Low970.40.6183
Triple Number Windward/Leeward Medium716.60.8373
Triple Number Windward/Leeward High634.50.9457
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1602.01071.1812.7678.8605.7567.0536.5489.2479.0
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low753.80.7960
Triple Number AP Medium584.11.0272
Triple Number AP High529.21.1337
Triple Number Windward/Leeward Low1013.70.5919
Triple Number Windward/Leeward Medium716.60.8373
Triple Number Windward/Leeward High634.50.9457
Single Number Predominant Upwind669.90.8956
Single Number Predominant Reaching584.91.0259
Single Number Predominant Downwind616.30.9736
Predominant Upwind - Low919.60.6524
Predominant Upwind - Low/Med701.80.8549
Predominant Upwind - Medium621.70.9651
Predominant Upwind - Med/High586.81.0224
Predominant Upwind - High576.81.0403
Predominant Downwind Low901.10.6659
Predominant Downwind Low/Med666.30.9005
Predominant Downwind Medium569.21.0541
Predominant Downwind Med/High510.51.1752
Predominant Downwind High476.21.2599
Predominant Reaching Low808.70.7419
Predominant Reaching Low/Med618.00.9709
Predominant Reaching Medium546.41.0982
Predominant Reaching Med/High505.31.1873
Predominant Reaching High481.81.2453
SA/DSPL Upwind20.37SA/DSPL Downwind38.52
Scoring OptionTODTOT
5-Band Windward/Leeward Low1133.50.5293
5-Band Windward/Leeward Low/Med829.90.7229
5-Band Windward/Leeward Medium704.70.8515
5-Band Windward/Leeward Med/High641.50.9352
5-Band Windward/Leeward High619.80.9680
Windward/Leeward 60-40 Low1143.50.5247
Windward/Leeward 60-40 Low/Med843.50.7113
Windward/Leeward 60-40 Medium722.90.8300
Windward/Leeward 60-40 Med/High666.20.9006
Windward/Leeward 60-40 High650.30.9226
5-Band AP Low829.60.7232
5-Band AP Low/Med658.60.9110
5-Band AP Medium576.61.0407
5-Band AP Med/High534.71.1222
5-Band AP High516.51.1618
5-Band SF Bay Tour - Low978.90.6130
5-Band SF Bay Tour - Low/Med796.00.7538
5-Band SF Bay Tour - Medium683.40.8780
5-Band SF Bay Tour - Med/High628.70.9544
5-Band SF Bay Tour - High609.20.9848
Chicago-Mac Upwind0.8697
Chicago-Mac All Purpose0.9065
Chicago-Mac Downwind0.9394
Bayview-Mac Cove Island0.6635
Bayview-Mac Shore0.6679
Harvest Moon Regatta508.91.1790
Double HandedClub Certificate2025
BefanaNED 8253
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassWinner 10.20Measurement14/04/2011HINPlan reviewHull constructionSolidCarbon rudderNoLight stanchionsNoTrim tabNo
LOA10.129Max. Beam3.320Draft1.788Displacement4,717Wetted area22.95IMS L8.890LSM08.767Acc. length10.129Sink (kg/mm) 17.54
VCGD-0.014VCGM0.047RM Rated (kg·m) 114.6Limit of positive stability(°) N/AStability IndexN/ADefault crew weight170Declared crew weight200
PROPELLER
Propeller TypeFolding 2 blades
InstallationStrutTwin screwNoHydro generatorNo
PRD0.400PBWPIPA0.0006
EDLST1ST2
ST3ST4ST5
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerYesMainsail furlerNoArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders2Rotating mastNo
P13.000IG12.870ISP13.440MDT10.126MDL10.190MDT2MDL2TLTaperMWGO
E4.375J3.700BAS1.350FSDFoilSFJ0.270SPL3.780WPLTPSBDMWTMCG
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodRM estimatedFlotation Date14/04/2011
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Double HandedClub Certificate2025
BefanaNED 8253
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment20220.160.911.612.763.6433.44
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment20.080.510.981.912.843.7412.68YesNo 24.1416/05/201420220.030.490.921.812.833.7312.65YesNo 23.56
SYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLAreaMeas.DateComment112.8512.8512.857.106.8475.4705/01/2017
CRUISER/RACER REQUIREMENTS*
Accommodation length10.1 mTable area0.44 m²Headroom1.71 mMinimum number of berths4Personal gear stowage0.16 m³Fresh water capacity82 lMinimum number of seats in cockpit4Food stowage0.24 m³Fuel capacity52 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.