Club Certificate2025
Lentiggini AzzurreITA 17658
Hrvatski jedriličarski savez
Osječka 11
21000 Split
CROATIA
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 Angles44.3°44.3°42.1°40.7°39.7°38.9°38.5°37.9°38.0°
Beat VMG2.934.115.085.776.206.436.586.756.80
52°4.676.367.638.508.979.219.359.519.58
60°5.036.767.998.809.249.489.629.809.88
75°5.317.078.269.009.459.759.9810.2610.45
90°5.196.948.199.089.509.8210.1410.6711.04
110°5.016.928.409.339.8910.3410.6711.1911.62
120°4.846.758.269.239.8210.3310.8411.7012.36
135°4.316.087.568.699.429.9410.4611.5813.08
150°3.545.076.437.598.589.289.7610.6511.66
Run VMG3.064.395.576.587.448.088.569.3810.16
Gybe Angles141.1°141.1°144.2°147.8°150.7°152.9°156.3°162.2°159.2°
APH ToD:448.4CDL: 14.879APH ToT: 1.3381CertNo:147/25
BOAT
ClassSolaris 58DesignerJavier SotoBuilderSe.Re.GiAge date01/2015Series date01/2014Offset fileSolaris58.offData fileITA17658
HULL
Length Overall17.440 mMaximum Beam5.026 mDraft2.839 mDisplacement23,863 kgDLR5.3915IMS DivisionCruiser/RacerDynamic Allowance0.230%Age Allowance0.357%
PROPELLER
InstallationShaft exposedTypeFeathering 3 bladesDiameter0.620m
CREW
Maximum weight1,396 kg(default)Minimum weight1,187 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail105.61107.43Headsail Luffed83.7683.76Headsail FlyingSymmetricAsymmetric261.35261.35 (All asymmetric spinnakers with SHW/SFL > 85%)
STORM SAIL AREAS (m²)
Trysail31.40Storm Jib28.67Heavy Weather Jib77.40
SAIL LIMITS
Headsails8Spinnakers6
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
Lentiggini AzzurreITA 17658
Hrvatski jedriličarski savez
Osječka 11
21000 Split
CROATIA
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 VMG1227.6876.2709.3623.8580.9559.9547.3533.5529.8
52°771.4565.9471.5423.6401.3391.0385.2378.6375.7
60°715.4532.2450.4409.3389.6379.6374.2367.5364.2
75°677.7509.2436.1400.0380.9369.1360.8350.8344.5
90°693.5518.5439.6396.5379.0366.5355.1337.4326.0
110°718.4520.0428.5385.8364.0348.2337.5321.6309.9
120°743.1533.4435.7390.0366.7348.5332.1307.8291.4
135°834.5592.4476.0414.1382.1362.1344.3310.8275.2
150°1017.4710.3559.9474.0419.4387.8368.7338.0308.9
Run VMG1174.8820.1646.6547.3483.9445.5420.4383.7354.4
Selected Courses
Windward / Leeward1201.0848.2677.9585.6532.4502.7483.8458.6442.1
All purpose902.7648.4528.0464.8430.9411.3397.6378.3364.3
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward558.91.0736
All purpose448.41.3381
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low588.21.0201
Triple Number Coastal/Long Distance Medium445.41.3471
Triple Number Coastal/Long Distance High393.81.5236
Triple Number Windward/Leeward Low763.10.7863
Triple Number Windward/Leeward Medium554.81.0814
Triple Number Windward/Leeward High479.11.2524
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance490.01.2244
Triple Number Coastal/Long Distance Low588.21.0201
Triple Number Coastal/Long Distance Medium445.41.3471
Triple Number Coastal/Long Distance High393.81.5236
Triple Number Windward/Leeward Low763.10.7863
Triple Number Windward/Leeward Medium554.81.0814
Triple Number Windward/Leeward High479.11.2524
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1273.4845.4636.6525.9461.1427.1401.3361.8348.4
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.9479
Downwind "popa"1.1208
70% up, 30% down "Ilhabela"0.9939
30% up, 70% down "Ilhabela-inverso"1.0626
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low588.21.0201
Triple Number Coastal/Long Distance Medium445.41.3471
Triple Number Coastal/Long Distance High393.81.5236
Triple Number Windward/Leeward Low763.10.7863
Triple Number Windward/Leeward Medium554.81.0814
Triple Number Windward/Leeward High479.11.2524
Predominantly Upwind485.51.2357
Predominantly Downwind458.41.3090
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low588.21.0201
Triple Number AP Medium445.41.3470
Triple Number AP High393.81.5236
Triple Number Windward/Leeward Low797.60.7522
Triple Number Windward/Leeward Medium554.81.0814
Triple Number Windward/Leeward High479.11.2524
Single Number Predominant Upwind506.01.1857
Single Number Predominant Reaching446.01.3454
Single Number Predominant Downwind478.71.2534
Predominant Upwind - Low716.20.8377
Predominant Upwind - Low/Med538.31.1145
Predominant Upwind - Medium468.11.2818
Predominant Upwind - Med/High432.61.3870
Predominant Upwind - High415.91.4425
Predominant Downwind Low709.50.8457
Predominant Downwind Low/Med521.01.1517
Predominant Downwind Medium440.71.3616
Predominant Downwind Med/High392.71.5277
Predominant Downwind High364.01.6481
Predominant Reaching Low630.70.9513
Predominant Reaching Low/Med476.71.2587
Predominant Reaching Medium414.81.4465
Predominant Reaching Med/High379.31.5818
Predominant Reaching High357.41.6786
SA/DSPL Upwind22.61SA/DSPL Downwind43.81
Scoring OptionTODTOT
5-Band Windward/Leeward Low893.90.6712
5-Band Windward/Leeward Low/Med649.00.9246
5-Band Windward/Leeward Medium544.41.1022
5-Band Windward/Leeward Med/High486.81.2325
5-Band Windward/Leeward High460.11.3041
Windward/Leeward 60-40 Low899.60.6670
Windward/Leeward 60-40 Low/Med656.10.9145
Windward/Leeward 60-40 Medium554.01.0831
Windward/Leeward 60-40 Med/High499.41.2013
Windward/Leeward 60-40 High475.11.2628
5-Band AP Low649.60.9237
5-Band AP Low/Med509.11.1785
5-Band AP Medium438.61.3681
5-Band AP Med/High399.51.5020
5-Band AP High379.21.5822
5-Band SF Bay Tour - Low768.50.7807
5-Band SF Bay Tour - Low/Med619.00.9693
5-Band SF Bay Tour - Medium523.11.1469
5-Band SF Bay Tour - Med/High471.11.2736
5-Band SF Bay Tour - High446.31.3445
Chicago-Mac Upwind1.1456
Chicago-Mac All Purpose1.1792
Chicago-Mac Downwind1.2055
Bayview-Mac Cove Island0.8507
Bayview-Mac Shore0.8567
Harvest Moon Regatta387.11.5498
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance490.01.2244
Triple Number Coastal/Long Distance Low588.21.0201
Triple Number Coastal/Long Distance Medium445.41.3471
Triple Number Coastal/Long Distance High393.81.5236
Triple Number Windward/Leeward Low763.10.7863
Triple Number Windward/Leeward Medium554.81.0814
Triple Number Windward/Leeward High479.11.2524
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1273.4845.4636.6525.9461.1427.1401.3361.8348.4
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance490.01.2244
Triple Number Coastal/Long Distance Low588.21.0201
Triple Number Coastal/Long Distance Medium445.41.3471
Triple Number Coastal/Long Distance High393.81.5236
Triple Number Windward/Leeward Low763.10.7863
Triple Number Windward/Leeward Medium554.81.0814
Triple Number Windward/Leeward High479.11.2524
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1273.4845.4636.6525.9461.1427.1401.3361.8348.4
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance490.0
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1273.4845.4636.6525.9461.1427.1401.3361.8348.4
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low588.21.0201
Triple Number Coastal/Long Distance Medium445.41.3471
Triple Number Coastal/Long Distance High393.81.5236
Triple Number Windward/Leeward Low763.10.7863
Triple Number Windward/Leeward Medium554.81.0814
Triple Number Windward/Leeward High479.11.2524
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating490.01.2244
FinRating, kevyt tuuli876.41.1410
FinRating, kova tuuli381.31.3114
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low588.21.0201
Triple Number Coastal/Long Distance Medium445.41.3471
Triple Number Coastal/Long Distance High393.81.5236
Triple Number Windward/Leeward Low763.10.7863
Triple Number Windward/Leeward Medium554.81.0814
Triple Number Windward/Leeward High479.11.2524
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance1.2244
Triple Number Coastal/Long Distance Low1.0201
Triple Number Coastal/Long Distance Medium1.3471
Triple Number Coastal/Long Distance High1.5236
Triple Number Windward/Leeward Low0.7863
Triple Number Windward/Leeward Medium1.0814
Triple Number Windward/Leeward High1.2524
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1273.4845.4636.6525.9461.1427.1401.3361.8348.4
For information
General Purpose Handicap (GPH)505.8
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance490.01.2244
Triple Number Coastal/Long Distance Low588.21.0201
Triple Number Coastal/Long Distance Medium445.41.3471
Triple Number Coastal/Long Distance High393.81.5236
Triple Number Windward/Leeward Low763.10.7863
Triple Number Windward/Leeward Medium554.81.0814
Triple Number Windward/Leeward High479.11.2524
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1273.4845.4636.6525.9461.1427.1401.3361.8348.4
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low588.21.0201
Triple Number Coastal/Long Distance Medium445.41.3471
Triple Number Coastal/Long Distance High393.81.5236
Triple Number Windward/Leeward Low763.10.7863
Triple Number Windward/Leeward Medium554.81.0814
Triple Number Windward/Leeward High479.11.2524
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance490.01.2244
Triple Number Coastal/Long Distance Low588.21.0201
Triple Number Coastal/Long Distance Medium445.41.3471
Triple Number Coastal/Long Distance High393.81.5236
Triple Number Windward/Leeward Low763.10.7863
Triple Number Windward/Leeward Medium554.81.0814
Triple Number Windward/Leeward High479.11.2524
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1273.4845.4636.6525.9461.1427.1401.3361.8348.4
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance490.01.2244
Triple Number Coastal/Long Distance Low588.21.0201
Triple Number Coastal/Long Distance Medium445.41.3471
Triple Number Coastal/Long Distance High393.81.5236
Triple Number Windward/Leeward Low763.10.7863
Triple Number Windward/Leeward Medium554.81.0814
Triple Number Windward/Leeward High479.11.2524
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1273.4845.4636.6525.9461.1427.1401.3361.8348.4
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low588.2
Triple Number Coastal/Long Distance Medium445.4
Triple Number Coastal/Long Distance High393.8
Triple Number Windward/Leeward Low763.1
Triple Number Windward/Leeward Medium554.8
Triple Number Windward/Leeward High479.1
Predominantly Upwind485.5
Predominantly Downwind458.4
Predominantly Reaching437.2
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance490.01.2244
Triple Number Coastal/Long Distance Low588.21.0201
Triple Number Coastal/Long Distance Medium445.41.3471
Triple Number Coastal/Long Distance High393.81.5236
Triple Number Windward/Leeward Low763.10.7863
Triple Number Windward/Leeward Medium554.81.0814
Triple Number Windward/Leeward High479.11.2524
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1273.4845.4636.6525.9461.1427.1401.3361.8348.4
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low1.0201
Triple Number Coastal/Long Distance Medium1.3471
Triple Number Coastal/Long Distance High1.5236
Triple Number Windward/Leeward Low0.7863
Triple Number Windward/Leeward Medium1.0814
Triple Number Windward/Leeward High1.2524
Coastal/Long Distance1.2244
Predominantly Upwind1.2357
Predominantly Downwind1.3090
For information
General Purpose Handicap (GPH)505.8
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)1.3381
Distanseseilas Trippeltall svak vind1.0201
Distanseseilas Trippeltall mellomvind1.3471
Distanseseilas Trippeltall sterk vind1.5236
Pølsebane Trippeltall svak vind0.7863
Pølsebane Trippeltall mellomvind1.0814
Pølsebane Trippeltall sterk vind1.2524
Motvind Singeltall1.2357
Medvind Singeltall1.3090
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low588.21.0201
Triple Number Coastal/Long Distance Medium445.41.3471
Triple Number Coastal/Long Distance High393.81.5236
Triple Number Windward/Leeward Low763.10.7863
Triple Number Windward/Leeward Medium554.81.0814
Triple Number Windward/Leeward High479.11.2524
Coastal/Long Distance490.01.2244
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind485.51.2357
Predominantly Downwind458.41.3090
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore447.01.3421
Cape Doctor Coastal368.51.6283
Triple Number Coastal/Long Distance Low588.21.0201
Triple Number Coastal/Long Distance Medium445.41.3471
Triple Number Coastal/Long Distance High393.81.5236
Triple Number Windward/Leeward Low763.10.7863
Triple Number Windward/Leeward Medium554.81.0814
Triple Number Windward/Leeward High479.11.2524
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low1.0201
Triple Number Coastal/Long Distance Medium1.3471
Triple Number Coastal/Long Distance High1.5236
Triple Number Windward/Leeward Low0.7863
Triple Number Windward/Leeward Medium1.0814
Triple Number Windward/Leeward High1.2524
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low1.0201
Triple Number Coastal/Long Distance Medium1.3471
Triple Number Coastal/Long Distance High1.5236
Triple Number Windward/Leeward Low0.7863
Triple Number Windward/Leeward Medium1.0814
Triple Number Windward/Leeward High1.2524
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance490.01.2244
Triple Number Coastal/Long Distance Low588.21.0201
Triple Number Coastal/Long Distance Medium445.41.3471
Triple Number Coastal/Long Distance High393.81.5236
Triple Number Windward/Leeward Low763.10.7863
Triple Number Windward/Leeward Medium554.81.0814
Triple Number Windward/Leeward High479.11.2524
Predominantly Upwind485.51.2357
Predominantly Downwind458.41.3090
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1273.4845.4636.6525.9461.1427.1401.3361.8348.4
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance490.01.2244
Triple Number Coastal/Long Distance Low588.21.0201
Triple Number Coastal/Long Distance Medium445.41.3471
Triple Number Coastal/Long Distance High393.81.5236
Triple Number Windward/Leeward Low763.10.7863
Triple Number Windward/Leeward Medium554.81.0814
Triple Number Windward/Leeward High479.11.2524
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1273.4845.4636.6525.9461.1427.1401.3361.8348.4
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low588.21.0201
Triple Number AP Medium445.41.3470
Triple Number AP High393.81.5236
Triple Number Windward/Leeward Low797.60.7522
Triple Number Windward/Leeward Medium554.81.0814
Triple Number Windward/Leeward High479.11.2524
Single Number Predominant Upwind506.01.1857
Single Number Predominant Reaching446.01.3454
Single Number Predominant Downwind478.71.2534
Predominant Upwind - Low716.20.8377
Predominant Upwind - Low/Med538.31.1145
Predominant Upwind - Medium468.11.2818
Predominant Upwind - Med/High432.61.3870
Predominant Upwind - High415.91.4425
Predominant Downwind Low709.50.8457
Predominant Downwind Low/Med521.01.1517
Predominant Downwind Medium440.71.3616
Predominant Downwind Med/High392.71.5277
Predominant Downwind High364.01.6481
Predominant Reaching Low630.70.9513
Predominant Reaching Low/Med476.71.2587
Predominant Reaching Medium414.81.4465
Predominant Reaching Med/High379.31.5818
Predominant Reaching High357.41.6786
SA/DSPL Upwind22.61SA/DSPL Downwind43.81
Scoring OptionTODTOT
5-Band Windward/Leeward Low893.90.6712
5-Band Windward/Leeward Low/Med649.00.9246
5-Band Windward/Leeward Medium544.41.1022
5-Band Windward/Leeward Med/High486.81.2325
5-Band Windward/Leeward High460.11.3041
Windward/Leeward 60-40 Low899.60.6670
Windward/Leeward 60-40 Low/Med656.10.9145
Windward/Leeward 60-40 Medium554.01.0831
Windward/Leeward 60-40 Med/High499.41.2013
Windward/Leeward 60-40 High475.11.2628
5-Band AP Low649.60.9237
5-Band AP Low/Med509.11.1785
5-Band AP Medium438.61.3681
5-Band AP Med/High399.51.5020
5-Band AP High379.21.5822
5-Band SF Bay Tour - Low768.50.7807
5-Band SF Bay Tour - Low/Med619.00.9693
5-Band SF Bay Tour - Medium523.11.1469
5-Band SF Bay Tour - Med/High471.11.2736
5-Band SF Bay Tour - High446.31.3445
Chicago-Mac Upwind1.1456
Chicago-Mac All Purpose1.1792
Chicago-Mac Downwind1.2055
Bayview-Mac Cove Island0.8507
Bayview-Mac Shore0.8567
Harvest Moon Regatta387.11.5498
Club Certificate2025
Lentiggini AzzurreITA 17658
Hrvatski jedriličarski savez
Osječka 11
21000 Split
CROATIA
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassSolaris 58Measurement06/02/2020HINPlan reviewHull constructionSolidCarbon rudderNoLight stanchionsNoTrim tabNo
LOA17.440Max. Beam5.026Draft2.839Displacement23,863Wetted area65.68IMS L16.541LSM016.417Acc. length16.334Sink (kg/mm) 50.05
VCGD0.044VCGM-0.103RM Rated (kg·m) 798.3Limit of positive stability(°) N/AStability IndexN/ADefault crew weight1,396Declared crew weightN/A
PROPELLER
Propeller TypeFeathering 3 blades
InstallationShaft exposedTwin screwNoHydro generatorNo
PRD0.620PBW0.180PIPA0.0051
PSDPHDPHL
PSAESL
ST1ST2ST3
ST4ST5
RIG
Forestay tensionAftInner stayNone FittedMast materialCarbonSingle headsail furlerNoMainsail furlerNoArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders3Rotating mastNo
P23.000IG23.720ISP25.520MDT10.163MDL10.313MDT20.150MDL20.300TL1.050MW0.313GO0.375
E7.800J6.650BAS2.020FSD0.048SFJ0.500SPL0.000WPLTPS8.500BD0.420MWTMCG
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodRM estimatedFlotation Date03/06/2022
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Club Certificate2025
Lentiggini AzzurreITA 17658
Hrvatski jedriličarski savez
Osječka 11
21000 Split
CROATIA
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment11.692.824.78105.6123/02/2016IRC
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment10.110.971.843.637.0523.37NoNo 83.7623/02/2016IRC
ASYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLRatioAreaMeas.DateComment226.9522.0024.4813.0811.75111%261.35
CRUISER/RACER REQUIREMENTS*
Accommodation length16.3 mTable area0.77 m²Headroom1.90 mMinimum number of berths7Personal gear stowage0.28 m³Fresh water capacity361 lMinimum number of seats in cockpit7Food stowage0.42 m³Fuel capacity176 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.