Club Certificate2025
LIBECCIOGER 8724
Deutscher Segler Verband e.V.
Soling 16
24159 Kiel Schilksee
technik@dsv.org
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 Angles43.8°43.8°41.8°40.3°38.9°37.8°37.9°38.1°39.1°
Beat VMG2.303.213.964.514.935.165.255.325.26
52°3.594.925.926.597.017.247.357.447.44
60°3.835.206.196.817.187.417.557.677.68
75°3.985.386.376.977.337.597.808.058.15
90°4.155.636.707.257.497.647.878.328.61
110°4.195.736.847.427.818.118.328.668.96
120°4.045.566.697.347.778.178.549.089.52
135°3.554.996.177.017.517.938.369.2910.75
150°2.954.245.406.387.087.547.938.759.85
Run VMG2.553.674.685.546.276.857.318.058.79
Gybe Angles145.1°145.1°149.4°153.0°159.0°166.2°173.2°176.3°170.5°
APH ToD:560.7CDL: 9.075APH ToT: 1.0701CertNo:171695
BOAT
ClassFIRST 35DesignerBRUCE FARRBuilderBENETEAUAge date06/2013Series date02/2009Offset fileFIRST35.offData fileGER8724
HULL
Length Overall10.660 mMaximum Beam3.636 mDraft2.201 mDisplacement5,691 kgDLR6.8087IMS DivisionCruiser/RacerDynamic Allowance0.220%Age Allowance0.487%
PROPELLER
InstallationStrutTypeFolding 3 bladesDiameter0.410m
CREW
Maximum weight750 kg(declared)Minimum weight620 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail37.2137.63Headsail Luffed23.6323.63Headsail FlyingSymmetric103.00103.00Asymmetric
STORM SAIL AREAS (m²)
Trysail11.76Storm Jib10.48Heavy Weather Jib28.28
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.
Club Certificate2025
LIBECCIOGER 8724
Deutscher Segler Verband e.V.
Soling 16
24159 Kiel Schilksee
technik@dsv.org
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 VMG1568.01121.4909.6797.4730.0698.1686.0677.3684.6
52°1001.5731.9608.0546.1513.6497.4489.8483.9483.6
60°939.8692.6581.4528.5501.3485.6476.7469.6468.5
75°904.9669.5564.7516.3491.4474.5461.6447.1442.0
90°868.1639.0537.6496.5480.8471.0457.3432.7418.1
110°859.5628.5525.9485.0461.2443.7432.9415.7401.9
120°890.6647.9538.2490.4463.1440.6421.7396.6378.1
135°1014.4722.0583.2513.7479.1453.7430.7387.4334.9
150°1222.2849.6666.6564.3508.1477.3453.7411.3365.5
Run VMG1411.3981.0769.8649.5574.5525.2492.5447.4409.5
Selected Courses
Windward / Leeward1489.31051.2839.7723.5652.2611.6589.3562.4547.0
All purpose1126.7808.1658.2582.2539.0513.9497.9475.6459.6
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward686.30.8743
All purpose560.71.0701
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low733.10.8184
Triple Number Coastal/Long Distance Medium557.11.0771
Triple Number Coastal/Long Distance High493.51.2157
Triple Number Windward/Leeward Low945.50.6346
Triple Number Windward/Leeward Medium681.40.8805
Triple Number Windward/Leeward High584.71.0261
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance609.70.9840
Triple Number Coastal/Long Distance Low733.10.8184
Triple Number Coastal/Long Distance Medium557.11.0771
Triple Number Coastal/Long Distance High493.51.2157
Triple Number Windward/Leeward Low945.50.6346
Triple Number Windward/Leeward Medium681.40.8805
Triple Number Windward/Leeward High584.71.0261
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1570.81044.2787.9653.3574.1532.7502.8456.7441.2
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.7474
Downwind "popa"0.9460
70% up, 30% down "Ilhabela"0.7976
30% up, 70% down "Ilhabela-inverso"0.8761
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low733.10.8184
Triple Number Coastal/Long Distance Medium557.11.0771
Triple Number Coastal/Long Distance High493.51.2157
Triple Number Windward/Leeward Low945.50.6346
Triple Number Windward/Leeward Medium681.40.8805
Triple Number Windward/Leeward High584.71.0261
Predominantly Upwind611.60.9811
Predominantly Downwind564.01.0639
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low733.20.8184
Triple Number AP Medium557.11.0770
Triple Number AP High493.51.2157
Triple Number Windward/Leeward Low988.20.6071
Triple Number Windward/Leeward Medium681.40.8805
Triple Number Windward/Leeward High584.71.0261
Single Number Predominant Upwind638.60.9396
Single Number Predominant Reaching558.71.0740
Single Number Predominant Downwind588.81.0190
Predominant Upwind - Low906.00.6622
Predominant Upwind - Low/Med680.50.8817
Predominant Upwind - Medium589.81.0174
Predominant Upwind - Med/High544.01.1029
Predominant Upwind - High526.01.1408
Predominant Downwind Low869.50.6900
Predominant Downwind Low/Med639.60.9382
Predominant Downwind Medium543.11.1049
Predominant Downwind Med/High483.81.2403
Predominant Downwind High447.71.3403
Predominant Reaching Low783.40.7659
Predominant Reaching Low/Med593.81.0105
Predominant Reaching Medium520.81.1521
Predominant Reaching Med/High478.21.2547
Predominant Reaching High450.71.3313
SA/DSPL Upwind18.98SA/DSPL Downwind43.73
Scoring OptionTODTOT
5-Band Windward/Leeward Low1107.90.5415
5-Band Windward/Leeward Low/Med802.20.7479
5-Band Windward/Leeward Medium667.70.8986
5-Band Windward/Leeward Med/High593.71.0105
5-Band Windward/Leeward High564.41.0632
Windward/Leeward 60-40 Low1122.40.5346
Windward/Leeward 60-40 Low/Med816.70.7347
Windward/Leeward 60-40 Medium683.60.8777
Windward/Leeward 60-40 Med/High613.00.9787
Windward/Leeward 60-40 High587.51.0213
5-Band AP Low808.30.7423
5-Band AP Low/Med635.90.9436
5-Band AP Medium548.51.0940
5-Band AP Med/High500.31.1994
5-Band AP High476.71.2587
5-Band SF Bay Tour - Low956.20.6275
5-Band SF Bay Tour - Low/Med769.50.7797
5-Band SF Bay Tour - Medium646.90.9276
5-Band SF Bay Tour - Med/High580.81.0330
5-Band SF Bay Tour - High553.41.0842
Chicago-Mac Upwind0.9073
Chicago-Mac All Purpose0.9467
Chicago-Mac Downwind0.9815
Bayview-Mac Cove Island0.6840
Bayview-Mac Shore0.6883
Harvest Moon Regatta486.91.2322
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance609.70.9840
Triple Number Coastal/Long Distance Low733.10.8184
Triple Number Coastal/Long Distance Medium557.11.0771
Triple Number Coastal/Long Distance High493.51.2157
Triple Number Windward/Leeward Low945.50.6346
Triple Number Windward/Leeward Medium681.40.8805
Triple Number Windward/Leeward High584.71.0261
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1570.81044.2787.9653.3574.1532.7502.8456.7441.2
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance609.70.9840
Triple Number Coastal/Long Distance Low733.10.8184
Triple Number Coastal/Long Distance Medium557.11.0771
Triple Number Coastal/Long Distance High493.51.2157
Triple Number Windward/Leeward Low945.50.6346
Triple Number Windward/Leeward Medium681.40.8805
Triple Number Windward/Leeward High584.71.0261
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1570.81044.2787.9653.3574.1532.7502.8456.7441.2
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance609.7
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1570.81044.2787.9653.3574.1532.7502.8456.7441.2
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low733.10.8184
Triple Number Coastal/Long Distance Medium557.11.0771
Triple Number Coastal/Long Distance High493.51.2157
Triple Number Windward/Leeward Low945.50.6346
Triple Number Windward/Leeward Medium681.40.8805
Triple Number Windward/Leeward High584.71.0261
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating609.70.9840
FinRating, kevyt tuuli1085.80.9210
FinRating, kova tuuli480.01.0417
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low733.10.8184
Triple Number Coastal/Long Distance Medium557.11.0771
Triple Number Coastal/Long Distance High493.51.2157
Triple Number Windward/Leeward Low945.50.6346
Triple Number Windward/Leeward Medium681.40.8805
Triple Number Windward/Leeward High584.71.0261
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.9840
Triple Number Coastal/Long Distance Low0.8184
Triple Number Coastal/Long Distance Medium1.0771
Triple Number Coastal/Long Distance High1.2157
Triple Number Windward/Leeward Low0.6346
Triple Number Windward/Leeward Medium0.8805
Triple Number Windward/Leeward High1.0261
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1570.81044.2787.9653.3574.1532.7502.8456.7441.2
For information
General Purpose Handicap (GPH)632.1
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance609.70.9840
Triple Number Coastal/Long Distance Low733.10.8184
Triple Number Coastal/Long Distance Medium557.11.0771
Triple Number Coastal/Long Distance High493.51.2157
Triple Number Windward/Leeward Low945.50.6346
Triple Number Windward/Leeward Medium681.40.8805
Triple Number Windward/Leeward High584.71.0261
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1570.81044.2787.9653.3574.1532.7502.8456.7441.2
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low733.10.8184
Triple Number Coastal/Long Distance Medium557.11.0771
Triple Number Coastal/Long Distance High493.51.2157
Triple Number Windward/Leeward Low945.50.6346
Triple Number Windward/Leeward Medium681.40.8805
Triple Number Windward/Leeward High584.71.0261
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance609.70.9840
Triple Number Coastal/Long Distance Low733.10.8184
Triple Number Coastal/Long Distance Medium557.11.0771
Triple Number Coastal/Long Distance High493.51.2157
Triple Number Windward/Leeward Low945.50.6346
Triple Number Windward/Leeward Medium681.40.8805
Triple Number Windward/Leeward High584.71.0261
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1570.81044.2787.9653.3574.1532.7502.8456.7441.2
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance609.70.9840
Triple Number Coastal/Long Distance Low733.10.8184
Triple Number Coastal/Long Distance Medium557.11.0771
Triple Number Coastal/Long Distance High493.51.2157
Triple Number Windward/Leeward Low945.50.6346
Triple Number Windward/Leeward Medium681.40.8805
Triple Number Windward/Leeward High584.71.0261
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1570.81044.2787.9653.3574.1532.7502.8456.7441.2
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low733.1
Triple Number Coastal/Long Distance Medium557.1
Triple Number Coastal/Long Distance High493.5
Triple Number Windward/Leeward Low945.5
Triple Number Windward/Leeward Medium681.4
Triple Number Windward/Leeward High584.7
Predominantly Upwind611.6
Predominantly Downwind564.0
Predominantly Reaching544.0
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance609.70.9840
Triple Number Coastal/Long Distance Low733.10.8184
Triple Number Coastal/Long Distance Medium557.11.0771
Triple Number Coastal/Long Distance High493.51.2157
Triple Number Windward/Leeward Low945.50.6346
Triple Number Windward/Leeward Medium681.40.8805
Triple Number Windward/Leeward High584.71.0261
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1570.81044.2787.9653.3574.1532.7502.8456.7441.2
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8184
Triple Number Coastal/Long Distance Medium1.0771
Triple Number Coastal/Long Distance High1.2157
Triple Number Windward/Leeward Low0.6346
Triple Number Windward/Leeward Medium0.8805
Triple Number Windward/Leeward High1.0261
Coastal/Long Distance0.9840
Predominantly Upwind0.9811
Predominantly Downwind1.0639
For information
General Purpose Handicap (GPH)632.1
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)1.0701
Distanseseilas Trippeltall svak vind0.8184
Distanseseilas Trippeltall mellomvind1.0771
Distanseseilas Trippeltall sterk vind1.2157
Pølsebane Trippeltall svak vind0.6346
Pølsebane Trippeltall mellomvind0.8805
Pølsebane Trippeltall sterk vind1.0261
Motvind Singeltall0.9811
Medvind Singeltall1.0639
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low733.10.8184
Triple Number Coastal/Long Distance Medium557.11.0771
Triple Number Coastal/Long Distance High493.51.2157
Triple Number Windward/Leeward Low945.50.6346
Triple Number Windward/Leeward Medium681.40.8805
Triple Number Windward/Leeward High584.71.0261
Coastal/Long Distance609.70.9840
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind611.60.9811
Predominantly Downwind564.01.0639
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore551.61.0877
Cape Doctor Coastal464.41.2920
Triple Number Coastal/Long Distance Low733.10.8184
Triple Number Coastal/Long Distance Medium557.11.0771
Triple Number Coastal/Long Distance High493.51.2157
Triple Number Windward/Leeward Low945.50.6346
Triple Number Windward/Leeward Medium681.40.8805
Triple Number Windward/Leeward High584.71.0261
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8184
Triple Number Coastal/Long Distance Medium1.0771
Triple Number Coastal/Long Distance High1.2157
Triple Number Windward/Leeward Low0.6346
Triple Number Windward/Leeward Medium0.8805
Triple Number Windward/Leeward High1.0261
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8184
Triple Number Coastal/Long Distance Medium1.0771
Triple Number Coastal/Long Distance High1.2157
Triple Number Windward/Leeward Low0.6346
Triple Number Windward/Leeward Medium0.8805
Triple Number Windward/Leeward High1.0261
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance609.70.9840
Triple Number Coastal/Long Distance Low733.10.8184
Triple Number Coastal/Long Distance Medium557.11.0771
Triple Number Coastal/Long Distance High493.51.2157
Triple Number Windward/Leeward Low945.50.6346
Triple Number Windward/Leeward Medium681.40.8805
Triple Number Windward/Leeward High584.71.0261
Predominantly Upwind611.60.9811
Predominantly Downwind564.01.0639
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1570.81044.2787.9653.3574.1532.7502.8456.7441.2
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance609.70.9840
Triple Number Coastal/Long Distance Low733.10.8184
Triple Number Coastal/Long Distance Medium557.11.0771
Triple Number Coastal/Long Distance High493.51.2157
Triple Number Windward/Leeward Low945.50.6346
Triple Number Windward/Leeward Medium681.40.8805
Triple Number Windward/Leeward High584.71.0261
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1570.81044.2787.9653.3574.1532.7502.8456.7441.2
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low733.20.8184
Triple Number AP Medium557.11.0770
Triple Number AP High493.51.2157
Triple Number Windward/Leeward Low988.20.6071
Triple Number Windward/Leeward Medium681.40.8805
Triple Number Windward/Leeward High584.71.0261
Single Number Predominant Upwind638.60.9396
Single Number Predominant Reaching558.71.0740
Single Number Predominant Downwind588.81.0190
Predominant Upwind - Low906.00.6622
Predominant Upwind - Low/Med680.50.8817
Predominant Upwind - Medium589.81.0174
Predominant Upwind - Med/High544.01.1029
Predominant Upwind - High526.01.1408
Predominant Downwind Low869.50.6900
Predominant Downwind Low/Med639.60.9382
Predominant Downwind Medium543.11.1049
Predominant Downwind Med/High483.81.2403
Predominant Downwind High447.71.3403
Predominant Reaching Low783.40.7659
Predominant Reaching Low/Med593.81.0105
Predominant Reaching Medium520.81.1521
Predominant Reaching Med/High478.21.2547
Predominant Reaching High450.71.3313
SA/DSPL Upwind18.98SA/DSPL Downwind43.73
Scoring OptionTODTOT
5-Band Windward/Leeward Low1107.90.5415
5-Band Windward/Leeward Low/Med802.20.7479
5-Band Windward/Leeward Medium667.70.8986
5-Band Windward/Leeward Med/High593.71.0105
5-Band Windward/Leeward High564.41.0632
Windward/Leeward 60-40 Low1122.40.5346
Windward/Leeward 60-40 Low/Med816.70.7347
Windward/Leeward 60-40 Medium683.60.8777
Windward/Leeward 60-40 Med/High613.00.9787
Windward/Leeward 60-40 High587.51.0213
5-Band AP Low808.30.7423
5-Band AP Low/Med635.90.9436
5-Band AP Medium548.51.0940
5-Band AP Med/High500.31.1994
5-Band AP High476.71.2587
5-Band SF Bay Tour - Low956.20.6275
5-Band SF Bay Tour - Low/Med769.50.7797
5-Band SF Bay Tour - Medium646.90.9276
5-Band SF Bay Tour - Med/High580.81.0330
5-Band SF Bay Tour - High553.41.0842
Chicago-Mac Upwind0.9073
Chicago-Mac All Purpose0.9467
Chicago-Mac Downwind0.9815
Bayview-Mac Cove Island0.6840
Bayview-Mac Shore0.6883
Harvest Moon Regatta486.91.2322
Club Certificate2025
LIBECCIOGER 8724
Deutscher Segler Verband e.V.
Soling 16
24159 Kiel Schilksee
technik@dsv.org
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassFIRST 35Measurement10/09/2025HIN170Plan reviewHull constructionSolidCarbon rudderNoLight stanchionsNoTrim tabNo
LOA10.660Max. Beam3.636Draft2.201Displacement5,691Wetted area26.20IMS L9.781LSM09.419Acc. length10.660Sink (kg/mm) 19.36
VCGD0.052VCGM0.048RM Rated (kg·m) 127.5Limit of positive stability(°) N/AStability IndexN/ADefault crew weight632Declared crew weight750
PROPELLER
Propeller TypeFolding 3 blades
InstallationStrutTwin screwNoHydro generatorNo
PRD0.410PBW0.124PIPA0.0033
EDL2.120ST10.040ST20.180
ST30.180ST40.111ST50.220
RIG
Forestay tensionAftInner stayNone FittedMast materialCarbonSingle headsail furlerYesMainsail furlerNoArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0Checkstays0Spreaders2Rotating mastNo
P14.000IG14.400ISP15.730MDT10.091MDL10.170MDT20.088MDL20.129TL1.150MW0.170GO0.190
E4.800J3.960BAS1.593FSD0.030SFJ0.000SPL4.406WPLTPSBD0.230MWT124.00MCG4.990
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodRM entered directlyRM entered127.0Flotation Date10/09/2025
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Club Certificate2025
LIBECCIOGER 8724
Deutscher Segler Verband e.V.
Soling 16
24159 Kiel Schilksee
technik@dsv.org
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment1787690.150.861.542.783.8337.2104/03/2025
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment1787700.090.430.811.682.633.7313.38NoNo 23.6304/03/2025
SYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLAreaMeas.DateComment17876815.0015.0015.008.308.00103.0004/03/2025
CRUISER/RACER REQUIREMENTS*
Accommodation length10.7 mTable area0.55 m²Headroom1.75 mMinimum number of berths5Personal gear stowage0.20 m³Fresh water capacity117 lMinimum number of seats in cockpit5Food stowage0.30 m³Fuel capacity64 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.