Non Spin/HSFClub Certificate2025
Felicia NOR 10528
Norges Seilforbund
Sognsveien 73
0854 OSLO
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 Angles42.3°42.3°40.3°38.6°37.8°37.4°37.4°38.0°39.3°
Beat VMG2.733.724.454.915.095.185.225.265.17
52°4.225.606.506.967.157.237.287.347.34
60°4.485.866.697.127.327.417.487.567.56
75°4.646.026.827.237.497.677.777.938.01
90°4.515.916.777.247.547.808.028.298.48
110°3.915.276.276.987.407.748.078.659.02
120°3.524.906.006.807.287.637.978.649.36
135°3.014.295.406.306.937.347.688.349.09
150°2.463.614.685.606.386.957.347.988.64
Run VMG2.133.124.064.885.636.326.877.598.19
Gybe Angles144.4°144.4°150.1°155.9°163.7°172.7°178.1°179.5°179.0°
APH ToD:571.6CDL: 9.264APH ToT: 1.0496CertNo:7883
BOAT
ClassFIRST 36.7DesignerBruceFarrBuilderBeneteauAge date01/2002Series date01/2001Offset fileFIRST367.offData file7883
HULL
Length Overall11.000 mMaximum Beam3.458 mDraft2.229 mDisplacement5,679 kgDLR6.9667IMS DivisionCruiser/RacerDynamic Allowance0.100%Age Allowance0.487%
PROPELLER
InstallationStrutTypeFolding 2 bladesDiameter0.400m
CREW
Maximum weight625 kg(default)Minimum weight495 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail39.7940.65Headsail Luffed41.3141.31Headsail FlyingSymmetricAsymmetric
STORM SAIL AREAS (m²)
Trysail11.52Storm Jib10.32Heavy Weather Jib27.86
SAIL LIMITS
Headsails5
✱ Zero set flying
Spinnakers0
✱ Spinnaker pole aboard
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.
Non Spin/HSFClub Certificate2025
Felicia NOR 10528
Norges Seilforbund
Sognsveien 73
0854 OSLO
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 VMG1319.1967.8808.1733.9707.3695.5689.0684.7695.9
52°853.6643.1554.3517.6503.8498.0494.3490.4490.8
60°804.4614.8538.1505.9491.7485.6481.6476.4476.4
75°775.0597.7528.2497.8480.4469.4463.1454.0449.4
90°798.2608.8531.6497.5477.1461.3449.1434.2424.6
110°921.1682.7574.1515.6486.2464.9446.3416.0399.2
120°1022.5735.4599.7529.6494.6471.7451.8416.8384.8
135°1197.6840.1666.4571.8519.4490.2469.0431.6396.1
150°1465.5998.2768.9642.5564.3517.7490.2451.1416.9
Run VMG1690.01152.6887.8737.3639.0569.5523.7474.5439.3
Selected Courses
Windward / Leeward1501.41060.2847.9735.6673.1632.5606.3579.6567.6
All purpose1115.6807.7663.8590.5551.6527.8511.9491.0478.3
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward703.00.8535
All purpose571.61.0496
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low735.70.8155
Triple Number Coastal/Long Distance Medium568.01.0564
Triple Number Coastal/Long Distance High508.01.1811
Triple Number Windward/Leeward Low954.00.6289
Triple Number Windward/Leeward Medium698.30.8592
Triple Number Windward/Leeward High602.80.9953
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance623.70.9620
Triple Number Coastal/Long Distance Low735.70.8155
Triple Number Coastal/Long Distance Medium568.01.0564
Triple Number Coastal/Long Distance High508.01.1811
Triple Number Windward/Leeward Low954.00.6289
Triple Number Windward/Leeward Medium698.30.8592
Triple Number Windward/Leeward High602.80.9953
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1627.31069.5800.3664.7588.3547.9517.7471.2455.4
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.7945
Downwind "popa"0.8426
70% up, 30% down "Ilhabela"0.8084
30% up, 70% down "Ilhabela-inverso"0.8276
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low735.70.8155
Triple Number Coastal/Long Distance Medium568.01.0564
Triple Number Coastal/Long Distance High508.01.1811
Triple Number Windward/Leeward Low954.00.6289
Triple Number Windward/Leeward Medium698.30.8592
Triple Number Windward/Leeward High602.80.9953
Predominantly Upwind603.50.9942
Predominantly Downwind598.21.0031
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low735.80.8155
Triple Number AP Medium568.01.0563
Triple Number AP High508.01.1811
Triple Number Windward/Leeward Low997.90.6013
Triple Number Windward/Leeward Medium698.30.8592
Triple Number Windward/Leeward High602.80.9953
Single Number Predominant Upwind625.80.9588
Single Number Predominant Reaching570.21.0522
Single Number Predominant Downwind627.70.9559
Predominant Upwind - Low844.70.7103
Predominant Upwind - Low/Med654.40.9169
Predominant Upwind - Medium585.01.0257
Predominant Upwind - Med/High551.41.0880
Predominant Upwind - High537.91.1155
Predominant Downwind Low942.80.6364
Predominant Downwind Low/Med686.30.8743
Predominant Downwind Medium575.41.0427
Predominant Downwind Med/High507.91.1814
Predominant Downwind High473.81.2665
Predominant Reaching Low790.30.7592
Predominant Reaching Low/Med605.70.9906
Predominant Reaching Medium532.41.1270
Predominant Reaching Med/High490.11.2242
Predominant Reaching High467.81.2825
SA/DSPL Upwind25.33SA/DSPL Downwind25.33
Scoring OptionTODTOT
5-Band Windward/Leeward Low1118.20.5366
5-Band Windward/Leeward Low/Med813.80.7373
5-Band Windward/Leeward Medium685.60.8751
5-Band Windward/Leeward Med/High611.90.9806
5-Band Windward/Leeward High582.11.0307
Windward/Leeward 60-40 Low1097.70.5466
Windward/Leeward 60-40 Low/Med809.20.7415
Windward/Leeward 60-40 Medium691.80.8673
Windward/Leeward 60-40 Med/High627.70.9559
Windward/Leeward 60-40 High603.20.9947
5-Band AP Low824.60.7276
5-Band AP Low/Med642.60.9337
5-Band AP Medium560.11.0713
5-Band AP Med/High514.41.1665
5-Band AP High492.41.2185
5-Band SF Bay Tour - Low953.90.6290
5-Band SF Bay Tour - Low/Med773.70.7755
5-Band SF Bay Tour - Medium660.50.9084
5-Band SF Bay Tour - Med/High598.81.0019
5-Band SF Bay Tour - High573.11.0470
Chicago-Mac Upwind0.9324
Chicago-Mac All Purpose0.9307
Chicago-Mac Downwind0.9185
Bayview-Mac Cove Island0.6774
Bayview-Mac Shore0.6861
Harvest Moon Regatta500.31.1994
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance623.70.9620
Triple Number Coastal/Long Distance Low735.70.8155
Triple Number Coastal/Long Distance Medium568.01.0564
Triple Number Coastal/Long Distance High508.01.1811
Triple Number Windward/Leeward Low954.00.6289
Triple Number Windward/Leeward Medium698.30.8592
Triple Number Windward/Leeward High602.80.9953
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1627.31069.5800.3664.7588.3547.9517.7471.2455.4
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance623.70.9620
Triple Number Coastal/Long Distance Low735.70.8155
Triple Number Coastal/Long Distance Medium568.01.0564
Triple Number Coastal/Long Distance High508.01.1811
Triple Number Windward/Leeward Low954.00.6289
Triple Number Windward/Leeward Medium698.30.8592
Triple Number Windward/Leeward High602.80.9953
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1627.31069.5800.3664.7588.3547.9517.7471.2455.4
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance623.7
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1627.31069.5800.3664.7588.3547.9517.7471.2455.4
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low735.70.8155
Triple Number Coastal/Long Distance Medium568.01.0564
Triple Number Coastal/Long Distance High508.01.1811
Triple Number Windward/Leeward Low954.00.6289
Triple Number Windward/Leeward Medium698.30.8592
Triple Number Windward/Leeward High602.80.9953
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating623.70.9620
FinRating, kevyt tuuli1101.60.9078
FinRating, kova tuuli495.91.0082
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low735.70.8155
Triple Number Coastal/Long Distance Medium568.01.0564
Triple Number Coastal/Long Distance High508.01.1811
Triple Number Windward/Leeward Low954.00.6289
Triple Number Windward/Leeward Medium698.30.8592
Triple Number Windward/Leeward High602.80.9953
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.9620
Triple Number Coastal/Long Distance Low0.8155
Triple Number Coastal/Long Distance Medium1.0564
Triple Number Coastal/Long Distance High1.1811
Triple Number Windward/Leeward Low0.6289
Triple Number Windward/Leeward Medium0.8592
Triple Number Windward/Leeward High0.9953
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1627.31069.5800.3664.7588.3547.9517.7471.2455.4
For information
General Purpose Handicap (GPH)641.8
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance623.70.9620
Triple Number Coastal/Long Distance Low735.70.8155
Triple Number Coastal/Long Distance Medium568.01.0564
Triple Number Coastal/Long Distance High508.01.1811
Triple Number Windward/Leeward Low954.00.6289
Triple Number Windward/Leeward Medium698.30.8592
Triple Number Windward/Leeward High602.80.9953
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1627.31069.5800.3664.7588.3547.9517.7471.2455.4
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low735.70.8155
Triple Number Coastal/Long Distance Medium568.01.0564
Triple Number Coastal/Long Distance High508.01.1811
Triple Number Windward/Leeward Low954.00.6289
Triple Number Windward/Leeward Medium698.30.8592
Triple Number Windward/Leeward High602.80.9953
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance623.70.9620
Triple Number Coastal/Long Distance Low735.70.8155
Triple Number Coastal/Long Distance Medium568.01.0564
Triple Number Coastal/Long Distance High508.01.1811
Triple Number Windward/Leeward Low954.00.6289
Triple Number Windward/Leeward Medium698.30.8592
Triple Number Windward/Leeward High602.80.9953
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1627.31069.5800.3664.7588.3547.9517.7471.2455.4
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance623.70.9620
Triple Number Coastal/Long Distance Low735.70.8155
Triple Number Coastal/Long Distance Medium568.01.0564
Triple Number Coastal/Long Distance High508.01.1811
Triple Number Windward/Leeward Low954.00.6289
Triple Number Windward/Leeward Medium698.30.8592
Triple Number Windward/Leeward High602.80.9953
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1627.31069.5800.3664.7588.3547.9517.7471.2455.4
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low735.7
Triple Number Coastal/Long Distance Medium568.0
Triple Number Coastal/Long Distance High508.0
Triple Number Windward/Leeward Low954.0
Triple Number Windward/Leeward Medium698.3
Triple Number Windward/Leeward High602.8
Predominantly Upwind603.5
Predominantly Downwind598.2
Predominantly Reaching564.0
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance623.70.9620
Triple Number Coastal/Long Distance Low735.70.8155
Triple Number Coastal/Long Distance Medium568.01.0564
Triple Number Coastal/Long Distance High508.01.1811
Triple Number Windward/Leeward Low954.00.6289
Triple Number Windward/Leeward Medium698.30.8592
Triple Number Windward/Leeward High602.80.9953
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1627.31069.5800.3664.7588.3547.9517.7471.2455.4
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8155
Triple Number Coastal/Long Distance Medium1.0564
Triple Number Coastal/Long Distance High1.1811
Triple Number Windward/Leeward Low0.6289
Triple Number Windward/Leeward Medium0.8592
Triple Number Windward/Leeward High0.9953
Coastal/Long Distance0.9620
Predominantly Upwind0.9942
Predominantly Downwind1.0031
For information
General Purpose Handicap (GPH)641.8
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)1.0496
Distanseseilas Trippeltall svak vind0.8155
Distanseseilas Trippeltall mellomvind1.0564
Distanseseilas Trippeltall sterk vind1.1811
Pølsebane Trippeltall svak vind0.6289
Pølsebane Trippeltall mellomvind0.8592
Pølsebane Trippeltall sterk vind0.9953
Motvind Singeltall0.9942
Medvind Singeltall1.0031
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low735.70.8155
Triple Number Coastal/Long Distance Medium568.01.0564
Triple Number Coastal/Long Distance High508.01.1811
Triple Number Windward/Leeward Low954.00.6289
Triple Number Windward/Leeward Medium698.30.8592
Triple Number Windward/Leeward High602.80.9953
Coastal/Long Distance623.70.9620
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind603.50.9942
Predominantly Downwind598.21.0031
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore571.21.0504
Cape Doctor Coastal482.11.2445
Triple Number Coastal/Long Distance Low735.70.8155
Triple Number Coastal/Long Distance Medium568.01.0564
Triple Number Coastal/Long Distance High508.01.1811
Triple Number Windward/Leeward Low954.00.6289
Triple Number Windward/Leeward Medium698.30.8592
Triple Number Windward/Leeward High602.80.9953
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8155
Triple Number Coastal/Long Distance Medium1.0564
Triple Number Coastal/Long Distance High1.1811
Triple Number Windward/Leeward Low0.6289
Triple Number Windward/Leeward Medium0.8592
Triple Number Windward/Leeward High0.9953
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8155
Triple Number Coastal/Long Distance Medium1.0564
Triple Number Coastal/Long Distance High1.1811
Triple Number Windward/Leeward Low0.6289
Triple Number Windward/Leeward Medium0.8592
Triple Number Windward/Leeward High0.9953
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance623.70.9620
Triple Number Coastal/Long Distance Low735.70.8155
Triple Number Coastal/Long Distance Medium568.01.0564
Triple Number Coastal/Long Distance High508.01.1811
Triple Number Windward/Leeward Low954.00.6289
Triple Number Windward/Leeward Medium698.30.8592
Triple Number Windward/Leeward High602.80.9953
Predominantly Upwind603.50.9942
Predominantly Downwind598.21.0031
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1627.31069.5800.3664.7588.3547.9517.7471.2455.4
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance623.70.9620
Triple Number Coastal/Long Distance Low735.70.8155
Triple Number Coastal/Long Distance Medium568.01.0564
Triple Number Coastal/Long Distance High508.01.1811
Triple Number Windward/Leeward Low954.00.6289
Triple Number Windward/Leeward Medium698.30.8592
Triple Number Windward/Leeward High602.80.9953
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1627.31069.5800.3664.7588.3547.9517.7471.2455.4
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low735.80.8155
Triple Number AP Medium568.01.0563
Triple Number AP High508.01.1811
Triple Number Windward/Leeward Low997.90.6013
Triple Number Windward/Leeward Medium698.30.8592
Triple Number Windward/Leeward High602.80.9953
Single Number Predominant Upwind625.80.9588
Single Number Predominant Reaching570.21.0522
Single Number Predominant Downwind627.70.9559
Predominant Upwind - Low844.70.7103
Predominant Upwind - Low/Med654.40.9169
Predominant Upwind - Medium585.01.0257
Predominant Upwind - Med/High551.41.0880
Predominant Upwind - High537.91.1155
Predominant Downwind Low942.80.6364
Predominant Downwind Low/Med686.30.8743
Predominant Downwind Medium575.41.0427
Predominant Downwind Med/High507.91.1814
Predominant Downwind High473.81.2665
Predominant Reaching Low790.30.7592
Predominant Reaching Low/Med605.70.9906
Predominant Reaching Medium532.41.1270
Predominant Reaching Med/High490.11.2242
Predominant Reaching High467.81.2825
SA/DSPL Upwind25.33SA/DSPL Downwind25.33
Scoring OptionTODTOT
5-Band Windward/Leeward Low1118.20.5366
5-Band Windward/Leeward Low/Med813.80.7373
5-Band Windward/Leeward Medium685.60.8751
5-Band Windward/Leeward Med/High611.90.9806
5-Band Windward/Leeward High582.11.0307
Windward/Leeward 60-40 Low1097.70.5466
Windward/Leeward 60-40 Low/Med809.20.7415
Windward/Leeward 60-40 Medium691.80.8673
Windward/Leeward 60-40 Med/High627.70.9559
Windward/Leeward 60-40 High603.20.9947
5-Band AP Low824.60.7276
5-Band AP Low/Med642.60.9337
5-Band AP Medium560.11.0713
5-Band AP Med/High514.41.1665
5-Band AP High492.41.2185
5-Band SF Bay Tour - Low953.90.6290
5-Band SF Bay Tour - Low/Med773.70.7755
5-Band SF Bay Tour - Medium660.50.9084
5-Band SF Bay Tour - Med/High598.81.0019
5-Band SF Bay Tour - High573.11.0470
Chicago-Mac Upwind0.9324
Chicago-Mac All Purpose0.9307
Chicago-Mac Downwind0.9185
Bayview-Mac Cove Island0.6774
Bayview-Mac Shore0.6861
Harvest Moon Regatta500.31.1994
Non Spin/HSFClub Certificate2025
Felicia NOR 10528
Norges Seilforbund
Sognsveien 73
0854 OSLO
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassFIRST 36.7MeasurementHINPlan reviewHull constructionSolidCarbon rudderNoLight stanchionsNoTrim tabNo
LOA11.000Max. Beam3.458Draft2.229Displacement5,679Wetted area25.30IMS L9.613LSM09.341Acc. length10.746Sink (kg/mm) 19.41
VCGD0.140VCGM0.125RM Rated (kg·m) 132.9Limit of positive stability(°) N/AStability IndexN/ADefault crew weight625Declared crew weightN/A
PROPELLER
Propeller TypeFolding 2 blades
InstallationStrutTwin screwNoHydro generatorNo
PRD0.400PBWPIPA0.0033
EDL2.480ST10.040ST20.180
ST30.180ST40.110ST50.260
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerNoMainsail furlerArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders3Rotating mastNo
P13.850IG14.150ISP14.250MDT10.110MDL10.180MDT20.110MDL20.180TL0.760MW0.180GO0.240
E4.750J4.000BAS1.570FSDFoilSFJ0.000SPL4.060WPLTPS0.000BD0.000MWT175.00MCG4.960
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodVCG entered directlyVCG entered0.140Flotation Date01/01/2015
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Non Spin/HSFClub Certificate2025
Felicia NOR 10528
Norges Seilforbund
Sognsveien 73
0854 OSLO
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment7883-2004012412000.190.001.823.084.0339.7901/01/1753152-2014051619200.161.071.853.133.9739.6016/05/2014
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment7883-2004012412010.000.000.000.000.005.7614.09NoNo 41.3101/01/1753329-2006033113490.000.000.000.000.005.7414.10NoNo 41.2031/03/2006152-2014051620000.070.531.021.962.933.8013.70NoNo 26.7616/05/2014
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.