Club Certificate2025
LUCIFERTUR
Turkiye
Sailing
Federation
www.tyf.org.tr/
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 Angles47.1°47.1°45.5°43.9°42.9°42.0°41.8°41.9°43.5°
Beat VMG1.942.763.463.984.394.694.844.884.74
52°3.134.375.386.096.616.957.157.257.20
60°3.424.715.716.416.897.217.407.557.56
75°3.594.925.946.667.137.447.667.948.05
90°3.765.236.387.137.517.707.858.148.44
110°4.005.556.757.477.898.248.518.879.17
120°3.875.436.687.437.898.298.669.299.73
135°3.334.816.137.107.658.088.499.3410.47
150°2.844.085.216.277.097.567.918.589.30
Run VMG2.463.534.515.436.146.586.947.558.12
Gybe Angles144.0°144.0°147.1°146.5°150.5°153.2°157.5°160.2°158.6°
APH ToD:589.7CDL: 8.551APH ToT: 1.0175CertNo:
BOAT
ClassBAVARIA 38 CRDesignerBuilderBavariaAge date09/2003Series date08/2003Offset filembav38.offData fileTUR LUCIFER
HULL
Length Overall11.767 mMaximum Beam3.900 mDraft1.700 mDisplacement7,500 kgDLR6.6834IMS DivisionCruiser/RacerDynamic Allowance0.350%Age Allowance0.487%
PROPELLER
InstallationStrutTypeSolid 3 bladesDiameter0.350m
CREW
Maximum weight560 kg(declared)Minimum weight430 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail28.2228.00Headsail Luffed37.8037.80Headsail FlyingSymmetricAsymmetric139.18139.18 (All asymmetric spinnakers with SHW/SFL > 85%)
STORM SAIL AREAS (m²)
Trysail10.43Storm Jib9.05Heavy Weather Jib24.42
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
LUCIFERTUR
Turkiye
Sailing
Federation
www.tyf.org.tr/
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 VMG1854.61304.11040.3903.6821.0768.4743.9737.5759.0
52°1150.5823.3669.4591.6545.0518.1503.4496.2499.9
60°1051.8764.2630.5561.8522.5499.6486.3477.1476.4
75°1001.6731.5606.4540.7504.7483.9470.1453.3447.0
90°957.1689.0564.0504.9479.4467.5458.6442.3426.6
110°901.1649.1533.2482.0456.0437.1423.1405.9392.5
120°929.6662.6538.7484.3456.1434.1415.5387.5370.0
135°1079.9748.0587.4506.7470.3445.7423.9385.3344.0
150°1269.2883.4691.0574.4508.0476.3455.2419.7387.3
Run VMG1465.51020.1797.9663.2586.3547.0518.4476.8443.3
Selected Courses
Windward / Leeward1660.21162.1919.1783.4703.6657.7631.1607.2601.2
All purpose1247.2882.4707.3614.9563.6533.2514.1494.1484.4
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward742.80.8078
All purpose589.71.0175
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low794.80.7549
Triple Number Coastal/Long Distance Medium585.11.0255
Triple Number Coastal/Long Distance High511.41.1733
Triple Number Windward/Leeward Low1040.60.5766
Triple Number Windward/Leeward Medium736.70.8144
Triple Number Windward/Leeward High628.80.9542
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance646.20.9285
Triple Number Coastal/Long Distance Low794.80.7549
Triple Number Coastal/Long Distance Medium585.11.0255
Triple Number Coastal/Long Distance High511.41.1733
Triple Number Windward/Leeward Low1040.60.5766
Triple Number Windward/Leeward Medium736.70.8144
Triple Number Windward/Leeward High628.80.9542
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1743.31147.9856.5698.6605.2553.8518.0468.0455.9
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.6647
Downwind "popa"0.9111
70% up, 30% down "Ilhabela"0.7234
30% up, 70% down "Ilhabela-inverso"0.8199
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low794.80.7549
Triple Number Coastal/Long Distance Medium585.11.0255
Triple Number Coastal/Long Distance High511.41.1733
Triple Number Windward/Leeward Low1040.60.5766
Triple Number Windward/Leeward Medium736.70.8144
Triple Number Windward/Leeward High628.80.9542
Predominantly Upwind656.80.9135
Predominantly Downwind582.61.0299
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low794.80.7549
Triple Number AP Medium585.21.0254
Triple Number AP High511.41.1733
Triple Number Windward/Leeward Low1089.00.5510
Triple Number Windward/Leeward Medium736.70.8144
Triple Number Windward/Leeward High628.80.9542
Single Number Predominant Upwind690.20.8693
Single Number Predominant Reaching581.51.0318
Single Number Predominant Downwind611.40.9814
Predominant Upwind - Low1016.70.5902
Predominant Upwind - Low/Med744.00.8065
Predominant Upwind - Medium630.80.9512
Predominant Upwind - Med/High571.21.0503
Predominant Upwind - High553.81.0833
Predominant Downwind Low927.30.6471
Predominant Downwind Low/Med666.20.9007
Predominant Downwind Medium557.11.0770
Predominant Downwind Med/High496.61.2083
Predominant Downwind High464.41.2920
Predominant Reaching Low849.00.7067
Predominant Reaching Low/Med623.30.9626
Predominant Reaching Medium534.21.1232
Predominant Reaching Med/High487.01.2321
Predominant Reaching High463.21.2954
SA/DSPL Upwind17.12SA/DSPL Downwind43.40
Scoring OptionTODTOT
5-Band Windward/Leeward Low1225.80.4895
5-Band Windward/Leeward Low/Med875.20.6855
5-Band Windward/Leeward Medium721.10.8320
5-Band Windward/Leeward Med/High637.70.9409
5-Band Windward/Leeward High610.30.9832
Windward/Leeward 60-40 Low1255.80.4778
Windward/Leeward 60-40 Low/Med899.90.6667
Windward/Leeward 60-40 Medium744.40.8060
Windward/Leeward 60-40 Med/High660.80.9080
Windward/Leeward 60-40 High636.70.9424
5-Band AP Low871.80.6883
5-Band AP Low/Med679.30.8833
5-Band AP Medium574.91.0437
5-Band AP Med/High518.11.1580
5-Band AP High495.91.2100
5-Band SF Bay Tour - Low1057.30.5675
5-Band SF Bay Tour - Low/Med839.60.7147
5-Band SF Bay Tour - Medium696.30.8617
5-Band SF Bay Tour - Med/High618.70.9698
5-Band SF Bay Tour - High593.21.0115
Chicago-Mac Upwind0.8347
Chicago-Mac All Purpose0.8899
Chicago-Mac Downwind0.9437
Bayview-Mac Cove Island0.6259
Bayview-Mac Shore0.6287
Harvest Moon Regatta495.91.2099
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance646.20.9285
Triple Number Coastal/Long Distance Low794.80.7549
Triple Number Coastal/Long Distance Medium585.11.0255
Triple Number Coastal/Long Distance High511.41.1733
Triple Number Windward/Leeward Low1040.60.5766
Triple Number Windward/Leeward Medium736.70.8144
Triple Number Windward/Leeward High628.80.9542
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1743.31147.9856.5698.6605.2553.8518.0468.0455.9
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance646.20.9285
Triple Number Coastal/Long Distance Low794.80.7549
Triple Number Coastal/Long Distance Medium585.11.0255
Triple Number Coastal/Long Distance High511.41.1733
Triple Number Windward/Leeward Low1040.60.5766
Triple Number Windward/Leeward Medium736.70.8144
Triple Number Windward/Leeward High628.80.9542
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1743.31147.9856.5698.6605.2553.8518.0468.0455.9
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance646.2
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1743.31147.9856.5698.6605.2553.8518.0468.0455.9
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low794.80.7549
Triple Number Coastal/Long Distance Medium585.11.0255
Triple Number Coastal/Long Distance High511.41.1733
Triple Number Windward/Leeward Low1040.60.5766
Triple Number Windward/Leeward Medium736.70.8144
Triple Number Windward/Leeward High628.80.9542
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating646.20.9285
FinRating, kevyt tuuli1195.90.8362
FinRating, kova tuuli498.91.0023
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low794.80.7549
Triple Number Coastal/Long Distance Medium585.11.0255
Triple Number Coastal/Long Distance High511.41.1733
Triple Number Windward/Leeward Low1040.60.5766
Triple Number Windward/Leeward Medium736.70.8144
Triple Number Windward/Leeward High628.80.9542
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.9285
Triple Number Coastal/Long Distance Low0.7549
Triple Number Coastal/Long Distance Medium1.0255
Triple Number Coastal/Long Distance High1.1733
Triple Number Windward/Leeward Low0.5766
Triple Number Windward/Leeward Medium0.8144
Triple Number Windward/Leeward High0.9542
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1743.31147.9856.5698.6605.2553.8518.0468.0455.9
For information
General Purpose Handicap (GPH)669.3
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance646.20.9285
Triple Number Coastal/Long Distance Low794.80.7549
Triple Number Coastal/Long Distance Medium585.11.0255
Triple Number Coastal/Long Distance High511.41.1733
Triple Number Windward/Leeward Low1040.60.5766
Triple Number Windward/Leeward Medium736.70.8144
Triple Number Windward/Leeward High628.80.9542
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1743.31147.9856.5698.6605.2553.8518.0468.0455.9
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low794.80.7549
Triple Number Coastal/Long Distance Medium585.11.0255
Triple Number Coastal/Long Distance High511.41.1733
Triple Number Windward/Leeward Low1040.60.5766
Triple Number Windward/Leeward Medium736.70.8144
Triple Number Windward/Leeward High628.80.9542
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance646.20.9285
Triple Number Coastal/Long Distance Low794.80.7549
Triple Number Coastal/Long Distance Medium585.11.0255
Triple Number Coastal/Long Distance High511.41.1733
Triple Number Windward/Leeward Low1040.60.5766
Triple Number Windward/Leeward Medium736.70.8144
Triple Number Windward/Leeward High628.80.9542
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1743.31147.9856.5698.6605.2553.8518.0468.0455.9
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance646.20.9285
Triple Number Coastal/Long Distance Low794.80.7549
Triple Number Coastal/Long Distance Medium585.11.0255
Triple Number Coastal/Long Distance High511.41.1733
Triple Number Windward/Leeward Low1040.60.5766
Triple Number Windward/Leeward Medium736.70.8144
Triple Number Windward/Leeward High628.80.9542
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1743.31147.9856.5698.6605.2553.8518.0468.0455.9
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low794.8
Triple Number Coastal/Long Distance Medium585.1
Triple Number Coastal/Long Distance High511.4
Triple Number Windward/Leeward Low1040.6
Triple Number Windward/Leeward Medium736.7
Triple Number Windward/Leeward High628.8
Predominantly Upwind656.8
Predominantly Downwind582.6
Predominantly Reaching560.6
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance646.20.9285
Triple Number Coastal/Long Distance Low794.80.7549
Triple Number Coastal/Long Distance Medium585.11.0255
Triple Number Coastal/Long Distance High511.41.1733
Triple Number Windward/Leeward Low1040.60.5766
Triple Number Windward/Leeward Medium736.70.8144
Triple Number Windward/Leeward High628.80.9542
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1743.31147.9856.5698.6605.2553.8518.0468.0455.9
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7549
Triple Number Coastal/Long Distance Medium1.0255
Triple Number Coastal/Long Distance High1.1733
Triple Number Windward/Leeward Low0.5766
Triple Number Windward/Leeward Medium0.8144
Triple Number Windward/Leeward High0.9542
Coastal/Long Distance0.9285
Predominantly Upwind0.9135
Predominantly Downwind1.0299
For information
General Purpose Handicap (GPH)669.3
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)1.0175
Distanseseilas Trippeltall svak vind0.7549
Distanseseilas Trippeltall mellomvind1.0255
Distanseseilas Trippeltall sterk vind1.1733
Pølsebane Trippeltall svak vind0.5766
Pølsebane Trippeltall mellomvind0.8144
Pølsebane Trippeltall sterk vind0.9542
Motvind Singeltall0.9135
Medvind Singeltall1.0299
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low794.80.7549
Triple Number Coastal/Long Distance Medium585.11.0255
Triple Number Coastal/Long Distance High511.41.1733
Triple Number Windward/Leeward Low1040.60.5766
Triple Number Windward/Leeward Medium736.70.8144
Triple Number Windward/Leeward High628.80.9542
Coastal/Long Distance646.20.9285
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind656.80.9135
Predominantly Downwind582.61.0299
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore603.00.9951
Cape Doctor Coastal487.31.2313
Triple Number Coastal/Long Distance Low794.80.7549
Triple Number Coastal/Long Distance Medium585.11.0255
Triple Number Coastal/Long Distance High511.41.1733
Triple Number Windward/Leeward Low1040.60.5766
Triple Number Windward/Leeward Medium736.70.8144
Triple Number Windward/Leeward High628.80.9542
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7549
Triple Number Coastal/Long Distance Medium1.0255
Triple Number Coastal/Long Distance High1.1733
Triple Number Windward/Leeward Low0.5766
Triple Number Windward/Leeward Medium0.8144
Triple Number Windward/Leeward High0.9542
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7549
Triple Number Coastal/Long Distance Medium1.0255
Triple Number Coastal/Long Distance High1.1733
Triple Number Windward/Leeward Low0.5766
Triple Number Windward/Leeward Medium0.8144
Triple Number Windward/Leeward High0.9542
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance646.20.9285
Triple Number Coastal/Long Distance Low794.80.7549
Triple Number Coastal/Long Distance Medium585.11.0255
Triple Number Coastal/Long Distance High511.41.1733
Triple Number Windward/Leeward Low1040.60.5766
Triple Number Windward/Leeward Medium736.70.8144
Triple Number Windward/Leeward High628.80.9542
Predominantly Upwind656.80.9135
Predominantly Downwind582.61.0299
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1743.31147.9856.5698.6605.2553.8518.0468.0455.9
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance646.20.9285
Triple Number Coastal/Long Distance Low794.80.7549
Triple Number Coastal/Long Distance Medium585.11.0255
Triple Number Coastal/Long Distance High511.41.1733
Triple Number Windward/Leeward Low1040.60.5766
Triple Number Windward/Leeward Medium736.70.8144
Triple Number Windward/Leeward High628.80.9542
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1743.31147.9856.5698.6605.2553.8518.0468.0455.9
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low794.80.7549
Triple Number AP Medium585.21.0254
Triple Number AP High511.41.1733
Triple Number Windward/Leeward Low1089.00.5510
Triple Number Windward/Leeward Medium736.70.8144
Triple Number Windward/Leeward High628.80.9542
Single Number Predominant Upwind690.20.8693
Single Number Predominant Reaching581.51.0318
Single Number Predominant Downwind611.40.9814
Predominant Upwind - Low1016.70.5902
Predominant Upwind - Low/Med744.00.8065
Predominant Upwind - Medium630.80.9512
Predominant Upwind - Med/High571.21.0503
Predominant Upwind - High553.81.0833
Predominant Downwind Low927.30.6471
Predominant Downwind Low/Med666.20.9007
Predominant Downwind Medium557.11.0770
Predominant Downwind Med/High496.61.2083
Predominant Downwind High464.41.2920
Predominant Reaching Low849.00.7067
Predominant Reaching Low/Med623.30.9626
Predominant Reaching Medium534.21.1232
Predominant Reaching Med/High487.01.2321
Predominant Reaching High463.21.2954
SA/DSPL Upwind17.12SA/DSPL Downwind43.40
Scoring OptionTODTOT
5-Band Windward/Leeward Low1225.80.4895
5-Band Windward/Leeward Low/Med875.20.6855
5-Band Windward/Leeward Medium721.10.8320
5-Band Windward/Leeward Med/High637.70.9409
5-Band Windward/Leeward High610.30.9832
Windward/Leeward 60-40 Low1255.80.4778
Windward/Leeward 60-40 Low/Med899.90.6667
Windward/Leeward 60-40 Medium744.40.8060
Windward/Leeward 60-40 Med/High660.80.9080
Windward/Leeward 60-40 High636.70.9424
5-Band AP Low871.80.6883
5-Band AP Low/Med679.30.8833
5-Band AP Medium574.91.0437
5-Band AP Med/High518.11.1580
5-Band AP High495.91.2100
5-Band SF Bay Tour - Low1057.30.5675
5-Band SF Bay Tour - Low/Med839.60.7147
5-Band SF Bay Tour - Medium696.30.8617
5-Band SF Bay Tour - Med/High618.70.9698
5-Band SF Bay Tour - High593.21.0115
Chicago-Mac Upwind0.8347
Chicago-Mac All Purpose0.8899
Chicago-Mac Downwind0.9437
Bayview-Mac Cove Island0.6259
Bayview-Mac Shore0.6287
Harvest Moon Regatta495.91.2099
Club Certificate2025
LUCIFERTUR
Turkiye
Sailing
Federation
www.tyf.org.tr/
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassBAVARIA 38 CRMeasurement06/01/2026HINPlan reviewHull constructionSolidCarbon rudderNoLight stanchionsNoTrim tabNo
LOA11.767Max. Beam3.900Draft1.700Displacement7,500Wetted area29.87IMS L10.485LSM010.391Acc. length11.767Sink (kg/mm) 23.19
VCGD0.224VCGM0.216RM Rated (kg·m) 167.2Limit of positive stability(°) N/AStability IndexN/ADefault crew weight727Declared crew weight560
PROPELLER
Propeller TypeSolid 3 blades
InstallationStrutTwin screwNoHydro generatorNo
PRD0.350PBWPIPA0.0153
EDL2.500ST10.042ST20.180
ST30.180ST40.112ST50.300
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerYesMainsail furlerIn mastArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0Checkstays0Spreaders2Rotating mastNo
P12.600IG13.414ISP13.650MDT10.115MDL10.210MDT20.115MDL20.210TL0.000MW0.210GO0.220
E4.730J4.100BAS1.660FSD0.032SFJ0.000SPLWPLTPS4.200BD0.170MWT100.00MCG6.000
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodRM estimatedFlotation Date06/01/2026
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Club Certificate2025
LUCIFERTUR
Turkiye
Sailing
Federation
www.tyf.org.tr/
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment10.020.531.062.193.3428.2206/01/2026measured by CAGATAY ONUR
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment10.040.681.342.754.235.7313.47NoNo 37.8006/01/2025measured by CAGATAY ONUR
ASYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLRatioAreaMeas.DateComment019.5516.6018.089.408.60109%139.1806/01/2026measured by CAGATAY ONUR
CRUISER/RACER REQUIREMENTS*
Accommodation length11.8 mTable area0.55 m²Headroom1.80 mMinimum number of berths5Personal gear stowage0.20 m³Fresh water capacity145 lMinimum number of seats in cockpit5Food stowage0.30 m³Fuel capacity86 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.