Non Spin/HSFClub Certificate2025
SAARE DAAMEST 754
Estonian Yachting Union
Purje 8, maja 3
11911 Tallinn
Estonia
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 Angles45.3°45.3°42.9°41.8°41.4°41.2°40.9°40.9°41.8°
Beat VMG2.283.193.934.464.825.035.135.205.13
52°3.654.965.956.677.137.387.507.617.59
60°3.935.296.266.967.397.627.767.877.89
75°4.125.526.517.197.597.858.038.258.34
90°4.035.436.457.187.617.908.138.508.75
110°3.464.835.966.847.447.838.128.639.11
120°3.194.535.676.587.277.718.028.569.08
135°2.693.935.076.006.787.377.768.338.85
150°2.283.344.335.256.036.717.257.948.48
Run VMG1.952.893.814.715.516.236.887.768.32
Gybe Angles144.7°144.7°173.9°176.6°179.3°179.8°179.9°179.9°180.0°
APH ToD:592.3CDL: 9.607APH ToT: 1.0130CertNo:
BOAT
ClassSAARE 41DesignerSTRAHLMANNBuilderSAARE PAATAge date01/2021Series date08/2008Offset fileCLSA41.OFFData fileEST754
HULL
Length Overall12.500 mMaximum Beam3.892 mDraft1.996 mDisplacement10,605 kgDLR7.5628IMS DivisionCruiser/RacerDynamic Allowance0.450%Age Allowance0.487%
PROPELLER
InstallationStrutTypeFolding 3 bladesDiameter0.456m
CREW
Maximum weight400 kg(declared)Minimum weight270 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail46.7647.50Headsail Luffed32.4832.48Headsail FlyingSymmetricAsymmetric
STORM SAIL AREAS (m²)
Trysail14.11Storm Jib13.54Heavy Weather Jib36.54
SAIL LIMITS
Headsails1
✱ One set on the forestay
✱ Zero set flying
Spinnakers0
✱ No spinnaker pole aboard
STABILITY
Righting MomentN/AStability IndexN/A
COMMENTS
Rig, propeller data from GER6670 according to owner declaration
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
SAARE DAAMEST 754
Estonian Yachting Union
Purje 8, maja 3
11911 Tallinn
Estonia
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 VMG1576.31128.2916.2807.0746.9715.8701.7692.0701.9
52°986.6725.4605.0540.0504.9487.8480.0473.3474.0
60°916.1681.1575.0517.4487.5472.2464.1457.3456.3
75°873.6652.1553.3501.0474.1458.6448.4436.5431.4
90°893.0662.5557.9501.7472.9455.6442.8423.7411.6
110°1041.8746.1604.4526.3483.6459.9443.6417.1395.3
120°1127.3795.1634.6546.9495.5467.2449.0420.7396.3
135°1336.3915.4710.5600.4531.1488.7463.9432.4406.7
150°1578.41078.9830.5685.8597.4536.9496.7453.1424.8
Run VMG1849.21245.8944.1765.1653.1577.5523.4464.0432.9
Selected Courses
Windward / Leeward1710.71187.0930.2786.1700.0646.6612.6578.0567.4
All purpose1264.6896.8719.3621.6565.1531.4510.6487.2476.0
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward739.10.8118
All purpose592.31.0130
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low808.00.7426
Triple Number Coastal/Long Distance Medium588.41.0198
Triple Number Coastal/Long Distance High507.01.1835
Triple Number Windward/Leeward Low1058.60.5668
Triple Number Windward/Leeward Medium734.60.8168
Triple Number Windward/Leeward High608.10.9866
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance650.80.9220
Triple Number Coastal/Long Distance Low808.00.7426
Triple Number Coastal/Long Distance Medium588.41.0198
Triple Number Coastal/Long Distance High507.01.1835
Triple Number Windward/Leeward Low1058.60.5668
Triple Number Windward/Leeward Medium734.60.8168
Triple Number Windward/Leeward High608.10.9866
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1851.01192.9874.0705.5606.4553.0516.2465.2451.4
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.7358
Downwind "popa"0.8119
70% up, 30% down "Ilhabela"0.7571
30% up, 70% down "Ilhabela-inverso"0.7875
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low808.00.7426
Triple Number Coastal/Long Distance Medium588.41.0198
Triple Number Coastal/Long Distance High507.01.1835
Triple Number Windward/Leeward Low1058.60.5668
Triple Number Windward/Leeward Medium734.60.8168
Triple Number Windward/Leeward High608.10.9866
Predominantly Upwind630.40.9517
Predominantly Downwind619.20.9690
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low808.00.7426
Triple Number AP Medium588.41.0197
Triple Number AP High507.01.1835
Triple Number Windward/Leeward Low1109.60.5407
Triple Number Windward/Leeward Medium734.60.8168
Triple Number Windward/Leeward High608.10.9866
Single Number Predominant Upwind658.20.9116
Single Number Predominant Reaching590.81.0155
Single Number Predominant Downwind653.60.9180
Predominant Upwind - Low955.00.6283
Predominant Upwind - Low/Med707.80.8477
Predominant Upwind - Medium604.30.9929
Predominant Upwind - Med/High550.81.0893
Predominant Upwind - High532.81.1261
Predominant Downwind Low1035.10.5796
Predominant Downwind Low/Med728.20.8239
Predominant Downwind Medium589.91.0171
Predominant Downwind Med/High506.21.1854
Predominant Downwind High469.01.2793
Predominant Reaching Low872.70.6875
Predominant Reaching Low/Med641.30.9356
Predominant Reaching Medium542.01.1069
Predominant Reaching Med/High486.01.2346
Predominant Reaching High461.41.3004
SA/DSPL Upwind16.29SA/DSPL Downwind16.29
Scoring OptionTODTOT
5-Band Windward/Leeward Low1254.20.4784
5-Band Windward/Leeward Low/Med883.20.6793
5-Band Windward/Leeward Medium717.30.8365
5-Band Windward/Leeward Med/High619.90.9680
5-Band Windward/Leeward High582.11.0307
Windward/Leeward 60-40 Low1240.80.4835
Windward/Leeward 60-40 Low/Med883.40.6792
Windward/Leeward 60-40 Medium726.20.8262
Windward/Leeward 60-40 Med/High637.10.9417
Windward/Leeward 60-40 High604.80.9921
5-Band AP Low909.90.6594
5-Band AP Low/Med688.20.8718
5-Band AP Medium577.11.0396
5-Band AP Med/High514.71.1657
5-Band AP High489.31.2263
5-Band SF Bay Tour - Low1066.80.5624
5-Band SF Bay Tour - Low/Med842.20.7125
5-Band SF Bay Tour - Medium692.30.8667
5-Band SF Bay Tour - Med/High607.00.9884
5-Band SF Bay Tour - High575.01.0434
Chicago-Mac Upwind0.8770
Chicago-Mac All Purpose0.8825
Chicago-Mac Downwind0.8764
Bayview-Mac Cove Island0.6149
Bayview-Mac Shore0.6224
Harvest Moon Regatta506.11.1856
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance650.80.9220
Triple Number Coastal/Long Distance Low808.00.7426
Triple Number Coastal/Long Distance Medium588.41.0198
Triple Number Coastal/Long Distance High507.01.1835
Triple Number Windward/Leeward Low1058.60.5668
Triple Number Windward/Leeward Medium734.60.8168
Triple Number Windward/Leeward High608.10.9866
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1851.01192.9874.0705.5606.4553.0516.2465.2451.4
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance650.80.9220
Triple Number Coastal/Long Distance Low808.00.7426
Triple Number Coastal/Long Distance Medium588.41.0198
Triple Number Coastal/Long Distance High507.01.1835
Triple Number Windward/Leeward Low1058.60.5668
Triple Number Windward/Leeward Medium734.60.8168
Triple Number Windward/Leeward High608.10.9866
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1851.01192.9874.0705.5606.4553.0516.2465.2451.4
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance650.8
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1851.01192.9874.0705.5606.4553.0516.2465.2451.4
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low808.00.7426
Triple Number Coastal/Long Distance Medium588.41.0198
Triple Number Coastal/Long Distance High507.01.1835
Triple Number Windward/Leeward Low1058.60.5668
Triple Number Windward/Leeward Medium734.60.8168
Triple Number Windward/Leeward High608.10.9866
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating650.80.9220
FinRating, kevyt tuuli1233.80.8105
FinRating, kova tuuli493.41.0134
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low808.00.7426
Triple Number Coastal/Long Distance Medium588.41.0198
Triple Number Coastal/Long Distance High507.01.1835
Triple Number Windward/Leeward Low1058.60.5668
Triple Number Windward/Leeward Medium734.60.8168
Triple Number Windward/Leeward High608.10.9866
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.9220
Triple Number Coastal/Long Distance Low0.7426
Triple Number Coastal/Long Distance Medium1.0198
Triple Number Coastal/Long Distance High1.1835
Triple Number Windward/Leeward Low0.5668
Triple Number Windward/Leeward Medium0.8168
Triple Number Windward/Leeward High0.9866
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1851.01192.9874.0705.5606.4553.0516.2465.2451.4
For information
General Purpose Handicap (GPH)674.1
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance650.80.9220
Triple Number Coastal/Long Distance Low808.00.7426
Triple Number Coastal/Long Distance Medium588.41.0198
Triple Number Coastal/Long Distance High507.01.1835
Triple Number Windward/Leeward Low1058.60.5668
Triple Number Windward/Leeward Medium734.60.8168
Triple Number Windward/Leeward High608.10.9866
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1851.01192.9874.0705.5606.4553.0516.2465.2451.4
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low808.00.7426
Triple Number Coastal/Long Distance Medium588.41.0198
Triple Number Coastal/Long Distance High507.01.1835
Triple Number Windward/Leeward Low1058.60.5668
Triple Number Windward/Leeward Medium734.60.8168
Triple Number Windward/Leeward High608.10.9866
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance650.80.9220
Triple Number Coastal/Long Distance Low808.00.7426
Triple Number Coastal/Long Distance Medium588.41.0198
Triple Number Coastal/Long Distance High507.01.1835
Triple Number Windward/Leeward Low1058.60.5668
Triple Number Windward/Leeward Medium734.60.8168
Triple Number Windward/Leeward High608.10.9866
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1851.01192.9874.0705.5606.4553.0516.2465.2451.4
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance650.80.9220
Triple Number Coastal/Long Distance Low808.00.7426
Triple Number Coastal/Long Distance Medium588.41.0198
Triple Number Coastal/Long Distance High507.01.1835
Triple Number Windward/Leeward Low1058.60.5668
Triple Number Windward/Leeward Medium734.60.8168
Triple Number Windward/Leeward High608.10.9866
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1851.01192.9874.0705.5606.4553.0516.2465.2451.4
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low808.0
Triple Number Coastal/Long Distance Medium588.4
Triple Number Coastal/Long Distance High507.0
Triple Number Windward/Leeward Low1058.6
Triple Number Windward/Leeward Medium734.6
Triple Number Windward/Leeward High608.1
Predominantly Upwind630.4
Predominantly Downwind619.2
Predominantly Reaching581.8
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance650.80.9220
Triple Number Coastal/Long Distance Low808.00.7426
Triple Number Coastal/Long Distance Medium588.41.0198
Triple Number Coastal/Long Distance High507.01.1835
Triple Number Windward/Leeward Low1058.60.5668
Triple Number Windward/Leeward Medium734.60.8168
Triple Number Windward/Leeward High608.10.9866
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1851.01192.9874.0705.5606.4553.0516.2465.2451.4
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7426
Triple Number Coastal/Long Distance Medium1.0198
Triple Number Coastal/Long Distance High1.1835
Triple Number Windward/Leeward Low0.5668
Triple Number Windward/Leeward Medium0.8168
Triple Number Windward/Leeward High0.9866
Coastal/Long Distance0.9220
Predominantly Upwind0.9517
Predominantly Downwind0.9690
For information
General Purpose Handicap (GPH)674.1
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)1.0130
Distanseseilas Trippeltall svak vind0.7426
Distanseseilas Trippeltall mellomvind1.0198
Distanseseilas Trippeltall sterk vind1.1835
Pølsebane Trippeltall svak vind0.5668
Pølsebane Trippeltall mellomvind0.8168
Pølsebane Trippeltall sterk vind0.9866
Motvind Singeltall0.9517
Medvind Singeltall0.9690
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low808.00.7426
Triple Number Coastal/Long Distance Medium588.41.0198
Triple Number Coastal/Long Distance High507.01.1835
Triple Number Windward/Leeward Low1058.60.5668
Triple Number Windward/Leeward Medium734.60.8168
Triple Number Windward/Leeward High608.10.9866
Coastal/Long Distance650.80.9220
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind630.40.9517
Predominantly Downwind619.20.9690
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore570.61.0516
Cape Doctor Coastal479.31.2518
Triple Number Coastal/Long Distance Low808.00.7426
Triple Number Coastal/Long Distance Medium588.41.0198
Triple Number Coastal/Long Distance High507.01.1835
Triple Number Windward/Leeward Low1058.60.5668
Triple Number Windward/Leeward Medium734.60.8168
Triple Number Windward/Leeward High608.10.9866
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7426
Triple Number Coastal/Long Distance Medium1.0198
Triple Number Coastal/Long Distance High1.1835
Triple Number Windward/Leeward Low0.5668
Triple Number Windward/Leeward Medium0.8168
Triple Number Windward/Leeward High0.9866
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7426
Triple Number Coastal/Long Distance Medium1.0198
Triple Number Coastal/Long Distance High1.1835
Triple Number Windward/Leeward Low0.5668
Triple Number Windward/Leeward Medium0.8168
Triple Number Windward/Leeward High0.9866
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance650.80.9220
Triple Number Coastal/Long Distance Low808.00.7426
Triple Number Coastal/Long Distance Medium588.41.0198
Triple Number Coastal/Long Distance High507.01.1835
Triple Number Windward/Leeward Low1058.60.5668
Triple Number Windward/Leeward Medium734.60.8168
Triple Number Windward/Leeward High608.10.9866
Predominantly Upwind630.40.9517
Predominantly Downwind619.20.9690
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1851.01192.9874.0705.5606.4553.0516.2465.2451.4
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance650.80.9220
Triple Number Coastal/Long Distance Low808.00.7426
Triple Number Coastal/Long Distance Medium588.41.0198
Triple Number Coastal/Long Distance High507.01.1835
Triple Number Windward/Leeward Low1058.60.5668
Triple Number Windward/Leeward Medium734.60.8168
Triple Number Windward/Leeward High608.10.9866
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1851.01192.9874.0705.5606.4553.0516.2465.2451.4
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low808.00.7426
Triple Number AP Medium588.41.0197
Triple Number AP High507.01.1835
Triple Number Windward/Leeward Low1109.60.5407
Triple Number Windward/Leeward Medium734.60.8168
Triple Number Windward/Leeward High608.10.9866
Single Number Predominant Upwind658.20.9116
Single Number Predominant Reaching590.81.0155
Single Number Predominant Downwind653.60.9180
Predominant Upwind - Low955.00.6283
Predominant Upwind - Low/Med707.80.8477
Predominant Upwind - Medium604.30.9929
Predominant Upwind - Med/High550.81.0893
Predominant Upwind - High532.81.1261
Predominant Downwind Low1035.10.5796
Predominant Downwind Low/Med728.20.8239
Predominant Downwind Medium589.91.0171
Predominant Downwind Med/High506.21.1854
Predominant Downwind High469.01.2793
Predominant Reaching Low872.70.6875
Predominant Reaching Low/Med641.30.9356
Predominant Reaching Medium542.01.1069
Predominant Reaching Med/High486.01.2346
Predominant Reaching High461.41.3004
SA/DSPL Upwind16.29SA/DSPL Downwind16.29
Scoring OptionTODTOT
5-Band Windward/Leeward Low1254.20.4784
5-Band Windward/Leeward Low/Med883.20.6793
5-Band Windward/Leeward Medium717.30.8365
5-Band Windward/Leeward Med/High619.90.9680
5-Band Windward/Leeward High582.11.0307
Windward/Leeward 60-40 Low1240.80.4835
Windward/Leeward 60-40 Low/Med883.40.6792
Windward/Leeward 60-40 Medium726.20.8262
Windward/Leeward 60-40 Med/High637.10.9417
Windward/Leeward 60-40 High604.80.9921
5-Band AP Low909.90.6594
5-Band AP Low/Med688.20.8718
5-Band AP Medium577.11.0396
5-Band AP Med/High514.71.1657
5-Band AP High489.31.2263
5-Band SF Bay Tour - Low1066.80.5624
5-Band SF Bay Tour - Low/Med842.20.7125
5-Band SF Bay Tour - Medium692.30.8667
5-Band SF Bay Tour - Med/High607.00.9884
5-Band SF Bay Tour - High575.01.0434
Chicago-Mac Upwind0.8770
Chicago-Mac All Purpose0.8825
Chicago-Mac Downwind0.8764
Bayview-Mac Cove Island0.6149
Bayview-Mac Shore0.6224
Harvest Moon Regatta506.11.1856
Non Spin/HSFClub Certificate2025
SAARE DAAMEST 754
Estonian Yachting Union
Purje 8, maja 3
11911 Tallinn
Estonia
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassSAARE 41Measurement16/04/2024HINEE-SAY41C10D021Plan reviewHull constructionCoredCarbon rudderNoLight stanchionsNoTrim tabNo
LOA12.500Max. Beam3.892Draft1.996Displacement10,605Wetted area35.02IMS L11.220LSM011.192Acc. length12.500Sink (kg/mm) 25.86
VCGD-0.021VCGM-0.022RM Rated (kg·m) 227.1Limit of positive stability(°) N/AStability IndexN/ADefault crew weight808Declared crew weight400
PROPELLER
Propeller TypeFolding 3 blades
InstallationStrutTwin screwNoHydro generatorNo
PRD0.456PBW0.120PIPA0.0041
EDL1.600ST10.065ST20.180
ST30.180ST40.110ST50.298
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerYesMainsail furlerIn mastArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders2Rotating mastNo
P15.500IG16.450ISPMDT10.120MDL10.255MDT2MDL2TLTaperMW0.255GO0.255
E5.200J4.670BAS1.780FSD0.039SFJ0.270SPL0.000WPLTPS0.000BD0.171MWTMCG
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodRM estimatedFlotation Date01/10/2025
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Non Spin/HSFClub Certificate2025
SAARE DAAMEST 754
Estonian Yachting Union
Purje 8, maja 3
11911 Tallinn
Estonia
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment10.241.091.873.194.2746.7619/04/2024
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment10.080.621.132.042.933.9416.05NoNo 32.4819/04/2024
CRUISER/RACER REQUIREMENTS*
Accommodation length12.5 mTable area0.55 m²Headroom1.83 mMinimum number of berths5Personal gear stowage0.20 m³Fresh water capacity162 lMinimum number of seats in cockpit5Food stowage0.30 m³Fuel capacity100 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.