Non Spin/HSFClub Certificate2025
NyabinghiESP-11381_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 Angles45.1°45.1°43.4°41.7°40.3°39.4°39.5°39.2°39.6°
Beat VMG2.803.914.825.515.956.176.306.436.43
52°4.456.097.338.168.638.878.999.129.18
60°4.836.517.698.448.879.129.259.429.53
75°5.136.827.948.639.059.369.619.9010.12
90°5.006.697.858.609.079.429.7510.2910.67
110°4.365.947.148.068.759.239.6410.4511.27
120°3.785.366.727.788.569.089.5010.3311.27
135°3.214.675.997.097.988.659.129.9210.76
150°2.643.905.106.147.037.728.339.159.86
Run VMG2.293.384.425.326.096.877.608.729.46
Gybe Angles143.3°143.3°145.3°146.2°146.7°168.1°169.2°172.3°173.2°
APH ToD:496.8CDL: 13.365APH ToT: 1.2078CertNo:1138101
BOAT
ClassSUN ODYSSEY 54 DSDesignerFAUROUX/GARRONIBuilderJEANNEAUAge date01/2008Series date01/2007Offset fileSO54DSCL.OFFData fileE11381_C
HULL
Length Overall16.380 mMaximum Beam4.896 mDraft2.269 mDisplacement16,780 kgDLR5.7014IMS DivisionCruiser/RacerDynamic Allowance0.250%Age Allowance0.487%
PROPELLER
InstallationShaft exposedTypeFolding 3 bladesDiameter0.400m
CREW
Maximum weight750 kg(declared)Minimum weight620 kg ✱ when appliedNon Manual PowerYesCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail65.5666.89Headsail Luffed96.1496.14Headsail FlyingSymmetricAsymmetric
STORM SAIL AREAS (m²)
Trysail18.70Storm Jib20.29Heavy Weather Jib54.76
SAIL LIMITS
Headsails1
✱ One set on the forestay
✱ Zero set flying
✱ Woven polyester sails
Spinnakers0
✱ No spinnaker pole aboard
STABILITY
Righting MomentN/AStability IndexN/A
COMMENTS
medidas estimadaS. CASCO ESTIMADO
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.
Non Spin/HSFClub Certificate2025
NyabinghiESP-11381_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 VMG1286.2921.6747.6653.8605.1583.4571.3560.2559.6
52°808.9591.2491.1441.4417.1405.8400.3394.5392.0
60°744.8553.3468.0426.6405.9394.7389.0382.1377.9
75°701.8528.2453.5417.3397.7384.6374.8363.5355.7
90°719.3538.2458.6418.6397.0382.0369.4349.7337.5
110°826.4606.2504.0446.9411.2390.1373.6344.6319.4
120°952.2671.7536.1462.5420.6396.5379.0348.4319.4
135°1120.5771.7601.3508.1451.0416.4394.9363.0334.5
150°1363.0922.4705.9586.0512.1466.1432.0393.3365.0
Run VMG1572.61065.1815.1676.6591.3524.0473.4412.9380.4
Selected Courses
Windward / Leeward1427.6993.4781.4665.2598.2553.7522.3486.5470.0
All purpose1047.5744.1598.6520.3475.6448.5429.8405.9390.8
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward627.60.9560
All purpose496.81.2078
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low671.40.8937
Triple Number Coastal/Long Distance Medium494.01.2146
Triple Number Coastal/Long Distance High425.51.4101
Triple Number Windward/Leeward Low887.30.6762
Triple Number Windward/Leeward Medium624.70.9605
Triple Number Windward/Leeward High516.81.1611
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance547.61.0957
Triple Number Coastal/Long Distance Low671.40.8937
Triple Number Coastal/Long Distance Medium494.01.2146
Triple Number Coastal/Long Distance High425.51.4101
Triple Number Windward/Leeward Low887.30.6762
Triple Number Windward/Leeward Medium624.70.9605
Triple Number Windward/Leeward High516.81.1611
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1553.71000.5733.5593.8510.7467.5435.4389.2372.3
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.9046
Downwind "popa"0.9214
70% up, 30% down "Ilhabela"0.9096
30% up, 70% down "Ilhabela-inverso"0.9163
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low671.40.8937
Triple Number Coastal/Long Distance Medium494.01.2146
Triple Number Coastal/Long Distance High425.51.4101
Triple Number Windward/Leeward Low887.30.6762
Triple Number Windward/Leeward Medium624.70.9605
Triple Number Windward/Leeward High516.81.1611
Predominantly Upwind522.41.1486
Predominantly Downwind529.31.1335
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low671.30.8937
Triple Number AP Medium494.01.2145
Triple Number AP High425.51.4101
Triple Number Windward/Leeward Low930.00.6452
Triple Number Windward/Leeward Medium624.70.9605
Triple Number Windward/Leeward High516.81.1611
Single Number Predominant Upwind544.71.1016
Single Number Predominant Reaching494.31.2139
Single Number Predominant Downwind556.91.0775
Predominant Upwind - Low785.90.7635
Predominant Upwind - Low/Med584.01.0275
Predominant Upwind - Medium501.41.1967
Predominant Upwind - Med/High458.21.3094
Predominant Upwind - High440.21.3629
Predominant Downwind Low869.30.6902
Predominant Downwind Low/Med617.80.9712
Predominant Downwind Medium506.51.1846
Predominant Downwind Med/High435.11.3790
Predominant Downwind High398.41.5061
Predominant Reaching Low722.30.8306
Predominant Reaching Low/Med535.01.1216
Predominant Reaching Medium455.91.3160
Predominant Reaching Med/High409.01.4671
Predominant Reaching High384.71.5597
SA/DSPL Upwind24.44SA/DSPL Downwind24.44
Scoring OptionTODTOT
5-Band Windward/Leeward Low1049.40.5718
5-Band Windward/Leeward Low/Med744.60.8058
5-Band Windward/Leeward Medium610.80.9824
5-Band Windward/Leeward Med/High528.01.1364
5-Band Windward/Leeward High489.91.2248
Windward/Leeward 60-40 Low1033.40.5806
Windward/Leeward 60-40 Low/Med739.50.8113
Windward/Leeward 60-40 Medium612.30.9798
Windward/Leeward 60-40 Med/High537.31.1168
Windward/Leeward 60-40 High504.31.1898
5-Band AP Low755.40.7943
5-Band AP Low/Med574.31.0448
5-Band AP Medium484.91.2373
5-Band AP Med/High432.81.3864
5-Band AP High407.41.4727
5-Band SF Bay Tour - Low890.30.6739
5-Band SF Bay Tour - Low/Med705.10.8510
5-Band SF Bay Tour - Medium583.11.0290
5-Band SF Bay Tour - Med/High511.71.1727
5-Band SF Bay Tour - High479.61.2509
Chicago-Mac Upwind1.0613
Chicago-Mac All Purpose1.0521
Chicago-Mac Downwind1.0289
Bayview-Mac Cove Island0.7370
Bayview-Mac Shore0.7468
Harvest Moon Regatta427.91.4021
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance547.61.0957
Triple Number Coastal/Long Distance Low671.40.8937
Triple Number Coastal/Long Distance Medium494.01.2146
Triple Number Coastal/Long Distance High425.51.4101
Triple Number Windward/Leeward Low887.30.6762
Triple Number Windward/Leeward Medium624.70.9605
Triple Number Windward/Leeward High516.81.1611
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1553.71000.5733.5593.8510.7467.5435.4389.2372.3
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance547.61.0957
Triple Number Coastal/Long Distance Low671.40.8937
Triple Number Coastal/Long Distance Medium494.01.2146
Triple Number Coastal/Long Distance High425.51.4101
Triple Number Windward/Leeward Low887.30.6762
Triple Number Windward/Leeward Medium624.70.9605
Triple Number Windward/Leeward High516.81.1611
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1553.71000.5733.5593.8510.7467.5435.4389.2372.3
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance547.6
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1553.71000.5733.5593.8510.7467.5435.4389.2372.3
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low671.40.8937
Triple Number Coastal/Long Distance Medium494.01.2146
Triple Number Coastal/Long Distance High425.51.4101
Triple Number Windward/Leeward Low887.30.6762
Triple Number Windward/Leeward Medium624.70.9605
Triple Number Windward/Leeward High516.81.1611
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating547.61.0957
FinRating, kevyt tuuli1031.40.9696
FinRating, kova tuuli411.01.2166
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low671.40.8937
Triple Number Coastal/Long Distance Medium494.01.2146
Triple Number Coastal/Long Distance High425.51.4101
Triple Number Windward/Leeward Low887.30.6762
Triple Number Windward/Leeward Medium624.70.9605
Triple Number Windward/Leeward High516.81.1611
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance1.0957
Triple Number Coastal/Long Distance Low0.8937
Triple Number Coastal/Long Distance Medium1.2146
Triple Number Coastal/Long Distance High1.4101
Triple Number Windward/Leeward Low0.6762
Triple Number Windward/Leeward Medium0.9605
Triple Number Windward/Leeward High1.1611
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1553.71000.5733.5593.8510.7467.5435.4389.2372.3
For information
General Purpose Handicap (GPH)564.3
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance547.61.0957
Triple Number Coastal/Long Distance Low671.40.8937
Triple Number Coastal/Long Distance Medium494.01.2146
Triple Number Coastal/Long Distance High425.51.4101
Triple Number Windward/Leeward Low887.30.6762
Triple Number Windward/Leeward Medium624.70.9605
Triple Number Windward/Leeward High516.81.1611
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1553.71000.5733.5593.8510.7467.5435.4389.2372.3
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low671.40.8937
Triple Number Coastal/Long Distance Medium494.01.2146
Triple Number Coastal/Long Distance High425.51.4101
Triple Number Windward/Leeward Low887.30.6762
Triple Number Windward/Leeward Medium624.70.9605
Triple Number Windward/Leeward High516.81.1611
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance547.61.0957
Triple Number Coastal/Long Distance Low671.40.8937
Triple Number Coastal/Long Distance Medium494.01.2146
Triple Number Coastal/Long Distance High425.51.4101
Triple Number Windward/Leeward Low887.30.6762
Triple Number Windward/Leeward Medium624.70.9605
Triple Number Windward/Leeward High516.81.1611
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1553.71000.5733.5593.8510.7467.5435.4389.2372.3
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance547.61.0957
Triple Number Coastal/Long Distance Low671.40.8937
Triple Number Coastal/Long Distance Medium494.01.2146
Triple Number Coastal/Long Distance High425.51.4101
Triple Number Windward/Leeward Low887.30.6762
Triple Number Windward/Leeward Medium624.70.9605
Triple Number Windward/Leeward High516.81.1611
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1553.71000.5733.5593.8510.7467.5435.4389.2372.3
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low671.4
Triple Number Coastal/Long Distance Medium494.0
Triple Number Coastal/Long Distance High425.5
Triple Number Windward/Leeward Low887.3
Triple Number Windward/Leeward Medium624.7
Triple Number Windward/Leeward High516.8
Predominantly Upwind522.4
Predominantly Downwind529.3
Predominantly Reaching491.3
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance547.61.0957
Triple Number Coastal/Long Distance Low671.40.8937
Triple Number Coastal/Long Distance Medium494.01.2146
Triple Number Coastal/Long Distance High425.51.4101
Triple Number Windward/Leeward Low887.30.6762
Triple Number Windward/Leeward Medium624.70.9605
Triple Number Windward/Leeward High516.81.1611
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1553.71000.5733.5593.8510.7467.5435.4389.2372.3
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8937
Triple Number Coastal/Long Distance Medium1.2146
Triple Number Coastal/Long Distance High1.4101
Triple Number Windward/Leeward Low0.6762
Triple Number Windward/Leeward Medium0.9605
Triple Number Windward/Leeward High1.1611
Coastal/Long Distance1.0957
Predominantly Upwind1.1486
Predominantly Downwind1.1335
For information
General Purpose Handicap (GPH)564.3
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)1.2078
Distanseseilas Trippeltall svak vind0.8937
Distanseseilas Trippeltall mellomvind1.2146
Distanseseilas Trippeltall sterk vind1.4101
Pølsebane Trippeltall svak vind0.6762
Pølsebane Trippeltall mellomvind0.9605
Pølsebane Trippeltall sterk vind1.1611
Motvind Singeltall1.1486
Medvind Singeltall1.1335
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low671.40.8937
Triple Number Coastal/Long Distance Medium494.01.2146
Triple Number Coastal/Long Distance High425.51.4101
Triple Number Windward/Leeward Low887.30.6762
Triple Number Windward/Leeward Medium624.70.9605
Triple Number Windward/Leeward High516.81.1611
Coastal/Long Distance547.61.0957
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind522.41.1486
Predominantly Downwind529.31.1335
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore475.01.2632
Cape Doctor Coastal395.31.5178
Triple Number Coastal/Long Distance Low671.40.8937
Triple Number Coastal/Long Distance Medium494.01.2146
Triple Number Coastal/Long Distance High425.51.4101
Triple Number Windward/Leeward Low887.30.6762
Triple Number Windward/Leeward Medium624.70.9605
Triple Number Windward/Leeward High516.81.1611
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8937
Triple Number Coastal/Long Distance Medium1.2146
Triple Number Coastal/Long Distance High1.4101
Triple Number Windward/Leeward Low0.6762
Triple Number Windward/Leeward Medium0.9605
Triple Number Windward/Leeward High1.1611
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8937
Triple Number Coastal/Long Distance Medium1.2146
Triple Number Coastal/Long Distance High1.4101
Triple Number Windward/Leeward Low0.6762
Triple Number Windward/Leeward Medium0.9605
Triple Number Windward/Leeward High1.1611
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance547.61.0957
Triple Number Coastal/Long Distance Low671.40.8937
Triple Number Coastal/Long Distance Medium494.01.2146
Triple Number Coastal/Long Distance High425.51.4101
Triple Number Windward/Leeward Low887.30.6762
Triple Number Windward/Leeward Medium624.70.9605
Triple Number Windward/Leeward High516.81.1611
Predominantly Upwind522.41.1486
Predominantly Downwind529.31.1335
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1553.71000.5733.5593.8510.7467.5435.4389.2372.3
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance547.61.0957
Triple Number Coastal/Long Distance Low671.40.8937
Triple Number Coastal/Long Distance Medium494.01.2146
Triple Number Coastal/Long Distance High425.51.4101
Triple Number Windward/Leeward Low887.30.6762
Triple Number Windward/Leeward Medium624.70.9605
Triple Number Windward/Leeward High516.81.1611
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1553.71000.5733.5593.8510.7467.5435.4389.2372.3
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low671.30.8937
Triple Number AP Medium494.01.2145
Triple Number AP High425.51.4101
Triple Number Windward/Leeward Low930.00.6452
Triple Number Windward/Leeward Medium624.70.9605
Triple Number Windward/Leeward High516.81.1611
Single Number Predominant Upwind544.71.1016
Single Number Predominant Reaching494.31.2139
Single Number Predominant Downwind556.91.0775
Predominant Upwind - Low785.90.7635
Predominant Upwind - Low/Med584.01.0275
Predominant Upwind - Medium501.41.1967
Predominant Upwind - Med/High458.21.3094
Predominant Upwind - High440.21.3629
Predominant Downwind Low869.30.6902
Predominant Downwind Low/Med617.80.9712
Predominant Downwind Medium506.51.1846
Predominant Downwind Med/High435.11.3790
Predominant Downwind High398.41.5061
Predominant Reaching Low722.30.8306
Predominant Reaching Low/Med535.01.1216
Predominant Reaching Medium455.91.3160
Predominant Reaching Med/High409.01.4671
Predominant Reaching High384.71.5597
SA/DSPL Upwind24.44SA/DSPL Downwind24.44
Scoring OptionTODTOT
5-Band Windward/Leeward Low1049.40.5718
5-Band Windward/Leeward Low/Med744.60.8058
5-Band Windward/Leeward Medium610.80.9824
5-Band Windward/Leeward Med/High528.01.1364
5-Band Windward/Leeward High489.91.2248
Windward/Leeward 60-40 Low1033.40.5806
Windward/Leeward 60-40 Low/Med739.50.8113
Windward/Leeward 60-40 Medium612.30.9798
Windward/Leeward 60-40 Med/High537.31.1168
Windward/Leeward 60-40 High504.31.1898
5-Band AP Low755.40.7943
5-Band AP Low/Med574.31.0448
5-Band AP Medium484.91.2373
5-Band AP Med/High432.81.3864
5-Band AP High407.41.4727
5-Band SF Bay Tour - Low890.30.6739
5-Band SF Bay Tour - Low/Med705.10.8510
5-Band SF Bay Tour - Medium583.11.0290
5-Band SF Bay Tour - Med/High511.71.1727
5-Band SF Bay Tour - High479.61.2509
Chicago-Mac Upwind1.0613
Chicago-Mac All Purpose1.0521
Chicago-Mac Downwind1.0289
Bayview-Mac Cove Island0.7370
Bayview-Mac Shore0.7468
Harvest Moon Regatta427.91.4021
Non Spin/HSFClub Certificate2025
NyabinghiESP-11381_C
RFEV
c/ Gamazo sn
39004 Santander – España
crucero@rfev.es
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassSUN ODYSSEY 54 DSMeasurementHINPlan reviewHull constructionSolidCarbon rudderNoLight stanchionsNoTrim tabNo
LOA16.380Max. Beam4.896Draft2.269Displacement16,780Wetted area51.96IMS L14.548LSM014.329Acc. length15.912Sink (kg/mm) 42.03
VCGD-0.105VCGM-0.140RM Rated (kg·m) 698.3Limit of positive stability(°) N/AStability IndexN/ADefault crew weight1,150Declared crew weight750
PROPELLER
Propeller TypeFolding 3 blades
InstallationShaft exposedTwin screwNoHydro generatorNo
PRD0.400PBWPIPA0.0055
PSD0.030PHD0.068PHL0.120
PSA15.0°ESL1.400
ST10.025ST20.120ST30.150
ST40.055ST50.250
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerYesMainsail furlerIn mastArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders3Rotating mastNo
P18.260IG20.140ISP21.000MDT10.100MDL10.110MDT2MDL2TLMWGO
E5.850J5.900BAS1.900FSD0.050SFJ0.400SPLWPLTPSBDMWTMCG
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodRM entered directlyRM entered700.0Flotation Date01/01/2010
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Non Spin/HSFClub Certificate2025
NyabinghiESP-11381_C
RFEV
c/ Gamazo sn
39004 Santander – España
crucero@rfev.es
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateCommentORC65.56
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateCommentA9.00NoNo 96.14
CRUISER/RACER REQUIREMENTS*
Accommodation length15.9 mTable area0.77 m²Headroom1.90 mMinimum number of berths7Personal gear stowage0.28 m³Fresh water capacity347 lMinimum number of seats in cockpit7Food stowage0.42 m³Fuel capacity168 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.