Club Certificate2025
illuminatiNOR 11051
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 Angles42.6°42.6°40.7°39.9°39.5°39.3°39.3°39.5°41.0°
Beat VMG2.803.774.424.744.894.985.035.064.93
52°4.325.686.526.907.057.157.227.287.24
60°4.575.956.757.137.287.377.457.537.52
75°4.746.146.927.317.537.667.777.937.99
90°4.636.056.907.357.647.878.058.328.51
110°4.195.726.827.407.778.028.228.558.87
120°4.055.566.687.347.778.148.508.949.32
135°3.544.976.167.027.547.968.399.2810.40
150°2.914.205.356.347.087.567.978.849.96
Run VMG2.523.634.645.516.256.867.338.108.90
Gybe Angles144.6°144.6°149.2°152.5°158.5°166.0°172.3°176.3°169.8°
APH ToD:553.7CDL: 9.133APH ToT: 1.0835CertNo:8536
BOAT
ClassBavaria 35 MatchDesignerJakopin&JakopinBuilderBavaria YachtbauAge date01/2004Series date01/2004Offset fileBA35MDK3.OFFData file8536
HULL
Length Overall10.840 mMaximum Beam3.276 mDraft2.015 mDisplacement5,825 kgDLR5.7542IMS DivisionCruiser/RacerDynamic Allowance0.020%Age Allowance0.487%
PROPELLER
InstallationStrutTypeFolding 2 bladesDiameter0.400m
CREW
Maximum weight400 kg(declared)Minimum weight270 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail40.8441.74Headsail Luffed42.6542.65Headsail FlyingSymmetric91.0491.04Asymmetric
STORM SAIL AREAS (m²)
Trysail11.94Storm Jib10.40Heavy Weather Jib28.08
SAIL LIMITS
Headsails5Spinnakers4
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
illuminatiNOR 11051
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 VMG1283.7955.5814.3759.9736.4723.0715.5712.1730.9
52°833.7633.8552.5521.9510.4503.4498.8494.5497.1
60°787.9605.1533.0504.9494.6488.2483.5478.3478.7
75°758.7586.4520.0492.4478.0470.1463.5454.0450.4
90°778.2595.5521.9489.5471.0457.4447.3432.8422.9
110°858.2629.4528.0486.5463.5448.6438.0421.2405.9
120°889.3648.0538.8490.4463.5442.0423.5402.7386.3
135°1015.8723.9584.7513.1477.6452.0428.9387.7346.1
150°1235.2858.0672.5567.5508.1476.1451.6407.3361.4
Run VMG1426.7990.7776.5653.8575.7525.1491.4444.7404.6
Selected Courses
Windward / Leeward1352.9973.1795.4706.9656.1624.0603.4578.4567.7
All purpose1022.8750.0626.7569.0537.9518.4504.6485.2473.4
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward680.50.8818
All purpose553.71.0835
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low688.40.8716
Triple Number Coastal/Long Distance Medium550.81.0893
Triple Number Coastal/Long Distance High500.81.1981
Triple Number Windward/Leeward Low884.20.6786
Triple Number Windward/Leeward Medium676.60.8868
Triple Number Windward/Leeward High599.21.0013
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance601.70.9972
Triple Number Coastal/Long Distance Low688.40.8716
Triple Number Coastal/Long Distance Medium550.81.0893
Triple Number Coastal/Long Distance High500.81.1981
Triple Number Windward/Leeward Low884.20.6786
Triple Number Windward/Leeward Medium676.60.8868
Triple Number Windward/Leeward High599.21.0013
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1443.1974.8749.6638.8574.3537.7508.5463.2450.5
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.7754
Downwind "popa"0.9421
70% up, 30% down "Ilhabela"0.8189
30% up, 70% down "Ilhabela-inverso"0.8850
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low688.40.8716
Triple Number Coastal/Long Distance Medium550.81.0893
Triple Number Coastal/Long Distance High500.81.1981
Triple Number Windward/Leeward Low884.20.6786
Triple Number Windward/Leeward Medium676.60.8868
Triple Number Windward/Leeward High599.21.0013
Predominantly Upwind598.21.0030
Predominantly Downwind558.21.0748
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low688.40.8716
Triple Number AP Medium550.81.0893
Triple Number AP High500.81.1981
Triple Number Windward/Leeward Low922.50.6504
Triple Number Windward/Leeward Medium676.60.8868
Triple Number Windward/Leeward High599.21.0013
Single Number Predominant Upwind618.60.9700
Single Number Predominant Reaching546.11.0988
Single Number Predominant Downwind582.21.0306
Predominant Upwind - Low807.20.7433
Predominant Upwind - Low/Med641.50.9353
Predominant Upwind - Medium583.81.0277
Predominant Upwind - Med/High554.01.0831
Predominant Upwind - High541.01.1091
Predominant Downwind Low840.40.7139
Predominant Downwind Low/Med628.70.9543
Predominant Downwind Medium540.41.1103
Predominant Downwind Med/High484.71.2378
Predominant Downwind High451.31.3294
Predominant Reaching Low733.30.8182
Predominant Reaching Low/Med574.91.0436
Predominant Reaching Medium514.71.1657
Predominant Reaching Med/High478.01.2553
Predominant Reaching High455.51.3173
SA/DSPL Upwind25.64SA/DSPL Downwind40.50
Scoring OptionTODTOT
5-Band Windward/Leeward Low1024.20.5858
5-Band Windward/Leeward Low/Med769.80.7794
5-Band Windward/Leeward Medium666.30.9004
5-Band Windward/Leeward Med/High607.10.9883
5-Band Windward/Leeward High580.91.0329
Windward/Leeward 60-40 Low1019.80.5884
Windward/Leeward 60-40 Low/Med776.70.7725
Windward/Leeward 60-40 Medium681.60.8803
Windward/Leeward 60-40 Med/High629.30.9535
Windward/Leeward 60-40 High607.90.9870
5-Band AP Low759.10.7904
5-Band AP Low/Med611.40.9813
5-Band AP Medium544.41.1021
5-Band AP Med/High506.51.1847
5-Band AP High486.51.2332
5-Band SF Bay Tour - Low884.10.6786
5-Band SF Bay Tour - Low/Med736.10.8151
5-Band SF Bay Tour - Medium645.00.9302
5-Band SF Bay Tour - Med/High594.21.0098
5-Band SF Bay Tour - High570.51.0516
Chicago-Mac Upwind0.9451
Chicago-Mac All Purpose0.9731
Chicago-Mac Downwind0.9946
Bayview-Mac Cove Island0.7279
Bayview-Mac Shore0.7346
Harvest Moon Regatta480.11.2497
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance601.70.9972
Triple Number Coastal/Long Distance Low688.40.8716
Triple Number Coastal/Long Distance Medium550.81.0893
Triple Number Coastal/Long Distance High500.81.1981
Triple Number Windward/Leeward Low884.20.6786
Triple Number Windward/Leeward Medium676.60.8868
Triple Number Windward/Leeward High599.21.0013
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1443.1974.8749.6638.8574.3537.7508.5463.2450.5
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance601.70.9972
Triple Number Coastal/Long Distance Low688.40.8716
Triple Number Coastal/Long Distance Medium550.81.0893
Triple Number Coastal/Long Distance High500.81.1981
Triple Number Windward/Leeward Low884.20.6786
Triple Number Windward/Leeward Medium676.60.8868
Triple Number Windward/Leeward High599.21.0013
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1443.1974.8749.6638.8574.3537.7508.5463.2450.5
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance601.7
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1443.1974.8749.6638.8574.3537.7508.5463.2450.5
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low688.40.8716
Triple Number Coastal/Long Distance Medium550.81.0893
Triple Number Coastal/Long Distance High500.81.1981
Triple Number Windward/Leeward Low884.20.6786
Triple Number Windward/Leeward Medium676.60.8868
Triple Number Windward/Leeward High599.21.0013
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating601.70.9972
FinRating, kevyt tuuli1005.80.9942
FinRating, kova tuuli489.51.0214
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low688.40.8716
Triple Number Coastal/Long Distance Medium550.81.0893
Triple Number Coastal/Long Distance High500.81.1981
Triple Number Windward/Leeward Low884.20.6786
Triple Number Windward/Leeward Medium676.60.8868
Triple Number Windward/Leeward High599.21.0013
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.9972
Triple Number Coastal/Long Distance Low0.8716
Triple Number Coastal/Long Distance Medium1.0893
Triple Number Coastal/Long Distance High1.1981
Triple Number Windward/Leeward Low0.6786
Triple Number Windward/Leeward Medium0.8868
Triple Number Windward/Leeward High1.0013
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1443.1974.8749.6638.8574.3537.7508.5463.2450.5
For information
General Purpose Handicap (GPH)616.3
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance601.70.9972
Triple Number Coastal/Long Distance Low688.40.8716
Triple Number Coastal/Long Distance Medium550.81.0893
Triple Number Coastal/Long Distance High500.81.1981
Triple Number Windward/Leeward Low884.20.6786
Triple Number Windward/Leeward Medium676.60.8868
Triple Number Windward/Leeward High599.21.0013
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1443.1974.8749.6638.8574.3537.7508.5463.2450.5
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low688.40.8716
Triple Number Coastal/Long Distance Medium550.81.0893
Triple Number Coastal/Long Distance High500.81.1981
Triple Number Windward/Leeward Low884.20.6786
Triple Number Windward/Leeward Medium676.60.8868
Triple Number Windward/Leeward High599.21.0013
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance601.70.9972
Triple Number Coastal/Long Distance Low688.40.8716
Triple Number Coastal/Long Distance Medium550.81.0893
Triple Number Coastal/Long Distance High500.81.1981
Triple Number Windward/Leeward Low884.20.6786
Triple Number Windward/Leeward Medium676.60.8868
Triple Number Windward/Leeward High599.21.0013
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1443.1974.8749.6638.8574.3537.7508.5463.2450.5
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance601.70.9972
Triple Number Coastal/Long Distance Low688.40.8716
Triple Number Coastal/Long Distance Medium550.81.0893
Triple Number Coastal/Long Distance High500.81.1981
Triple Number Windward/Leeward Low884.20.6786
Triple Number Windward/Leeward Medium676.60.8868
Triple Number Windward/Leeward High599.21.0013
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1443.1974.8749.6638.8574.3537.7508.5463.2450.5
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low688.4
Triple Number Coastal/Long Distance Medium550.8
Triple Number Coastal/Long Distance High500.8
Triple Number Windward/Leeward Low884.2
Triple Number Windward/Leeward Medium676.6
Triple Number Windward/Leeward High599.2
Predominantly Upwind598.2
Predominantly Downwind558.2
Predominantly Reaching535.7
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance601.70.9972
Triple Number Coastal/Long Distance Low688.40.8716
Triple Number Coastal/Long Distance Medium550.81.0893
Triple Number Coastal/Long Distance High500.81.1981
Triple Number Windward/Leeward Low884.20.6786
Triple Number Windward/Leeward Medium676.60.8868
Triple Number Windward/Leeward High599.21.0013
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1443.1974.8749.6638.8574.3537.7508.5463.2450.5
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8716
Triple Number Coastal/Long Distance Medium1.0893
Triple Number Coastal/Long Distance High1.1981
Triple Number Windward/Leeward Low0.6786
Triple Number Windward/Leeward Medium0.8868
Triple Number Windward/Leeward High1.0013
Coastal/Long Distance0.9972
Predominantly Upwind1.0030
Predominantly Downwind1.0748
For information
General Purpose Handicap (GPH)616.3
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)1.0835
Distanseseilas Trippeltall svak vind0.8716
Distanseseilas Trippeltall mellomvind1.0893
Distanseseilas Trippeltall sterk vind1.1981
Pølsebane Trippeltall svak vind0.6786
Pølsebane Trippeltall mellomvind0.8868
Pølsebane Trippeltall sterk vind1.0013
Motvind Singeltall1.0030
Medvind Singeltall1.0748
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low688.40.8716
Triple Number Coastal/Long Distance Medium550.81.0893
Triple Number Coastal/Long Distance High500.81.1981
Triple Number Windward/Leeward Low884.20.6786
Triple Number Windward/Leeward Medium676.60.8868
Triple Number Windward/Leeward High599.21.0013
Coastal/Long Distance601.70.9972
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind598.21.0030
Predominantly Downwind558.21.0748
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore570.91.0509
Cape Doctor Coastal477.01.2579
Triple Number Coastal/Long Distance Low688.40.8716
Triple Number Coastal/Long Distance Medium550.81.0893
Triple Number Coastal/Long Distance High500.81.1981
Triple Number Windward/Leeward Low884.20.6786
Triple Number Windward/Leeward Medium676.60.8868
Triple Number Windward/Leeward High599.21.0013
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8716
Triple Number Coastal/Long Distance Medium1.0893
Triple Number Coastal/Long Distance High1.1981
Triple Number Windward/Leeward Low0.6786
Triple Number Windward/Leeward Medium0.8868
Triple Number Windward/Leeward High1.0013
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8716
Triple Number Coastal/Long Distance Medium1.0893
Triple Number Coastal/Long Distance High1.1981
Triple Number Windward/Leeward Low0.6786
Triple Number Windward/Leeward Medium0.8868
Triple Number Windward/Leeward High1.0013
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance601.70.9972
Triple Number Coastal/Long Distance Low688.40.8716
Triple Number Coastal/Long Distance Medium550.81.0893
Triple Number Coastal/Long Distance High500.81.1981
Triple Number Windward/Leeward Low884.20.6786
Triple Number Windward/Leeward Medium676.60.8868
Triple Number Windward/Leeward High599.21.0013
Predominantly Upwind598.21.0030
Predominantly Downwind558.21.0748
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1443.1974.8749.6638.8574.3537.7508.5463.2450.5
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance601.70.9972
Triple Number Coastal/Long Distance Low688.40.8716
Triple Number Coastal/Long Distance Medium550.81.0893
Triple Number Coastal/Long Distance High500.81.1981
Triple Number Windward/Leeward Low884.20.6786
Triple Number Windward/Leeward Medium676.60.8868
Triple Number Windward/Leeward High599.21.0013
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1443.1974.8749.6638.8574.3537.7508.5463.2450.5
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low688.40.8716
Triple Number AP Medium550.81.0893
Triple Number AP High500.81.1981
Triple Number Windward/Leeward Low922.50.6504
Triple Number Windward/Leeward Medium676.60.8868
Triple Number Windward/Leeward High599.21.0013
Single Number Predominant Upwind618.60.9700
Single Number Predominant Reaching546.11.0988
Single Number Predominant Downwind582.21.0306
Predominant Upwind - Low807.20.7433
Predominant Upwind - Low/Med641.50.9353
Predominant Upwind - Medium583.81.0277
Predominant Upwind - Med/High554.01.0831
Predominant Upwind - High541.01.1091
Predominant Downwind Low840.40.7139
Predominant Downwind Low/Med628.70.9543
Predominant Downwind Medium540.41.1103
Predominant Downwind Med/High484.71.2378
Predominant Downwind High451.31.3294
Predominant Reaching Low733.30.8182
Predominant Reaching Low/Med574.91.0436
Predominant Reaching Medium514.71.1657
Predominant Reaching Med/High478.01.2553
Predominant Reaching High455.51.3173
SA/DSPL Upwind25.64SA/DSPL Downwind40.50
Scoring OptionTODTOT
5-Band Windward/Leeward Low1024.20.5858
5-Band Windward/Leeward Low/Med769.80.7794
5-Band Windward/Leeward Medium666.30.9004
5-Band Windward/Leeward Med/High607.10.9883
5-Band Windward/Leeward High580.91.0329
Windward/Leeward 60-40 Low1019.80.5884
Windward/Leeward 60-40 Low/Med776.70.7725
Windward/Leeward 60-40 Medium681.60.8803
Windward/Leeward 60-40 Med/High629.30.9535
Windward/Leeward 60-40 High607.90.9870
5-Band AP Low759.10.7904
5-Band AP Low/Med611.40.9813
5-Band AP Medium544.41.1021
5-Band AP Med/High506.51.1847
5-Band AP High486.51.2332
5-Band SF Bay Tour - Low884.10.6786
5-Band SF Bay Tour - Low/Med736.10.8151
5-Band SF Bay Tour - Medium645.00.9302
5-Band SF Bay Tour - Med/High594.21.0098
5-Band SF Bay Tour - High570.51.0516
Chicago-Mac Upwind0.9451
Chicago-Mac All Purpose0.9731
Chicago-Mac Downwind0.9946
Bayview-Mac Cove Island0.7279
Bayview-Mac Shore0.7346
Harvest Moon Regatta480.11.2497
Club Certificate2025
illuminatiNOR 11051
Norges Seilforbund
Sognsveien 73
0854 OSLO
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassBavaria 35 MatchMeasurementHINPlan reviewHull constructionCoredCarbon rudderNoLight stanchionsNoTrim tabNo
LOA10.840Max. Beam3.276Draft2.015Displacement5,825Wetted area25.30IMS L10.042LSM010.040Acc. length10.647Sink (kg/mm) 19.11
VCGD-0.004VCGM0.015RM Rated (kg·m) 116.6Limit of positive stability(°) N/AStability IndexN/ADefault crew weight692Declared crew weight400
PROPELLER
Propeller TypeFolding 2 blades
InstallationStrutTwin screwNoHydro generatorNo
PRD0.400PBWPIPA0.0037
EDL2.200ST10.048ST20.170
ST30.170ST40.170ST50.345
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerNoMainsail furlerArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders2Rotating mastNo
P13.800IG14.355ISP14.565MDT10.112MDL10.210MDT20.112MDL20.146TL0.000MW0.171GO0.189
E4.940J4.000BAS1.608FSDFoilSFJ0.000SPL4.030WPLTPS0.000BD0.000MWT160.00MCG5.430
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodVCG entered directlyVCG entered-0.004Flotation Date01/01/2015
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Club Certificate2025
illuminatiNOR 11051
Norges Seilforbund
Sognsveien 73
0854 OSLO
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment398-2013082314200.151.041.883.234.1740.8423/08/2013
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment234-2004082311000.000.004.303.231.895.8314.58NoNo 42.6523/08/2004398-2013101112510.030.701.402.804.385.8913.88NoNo 40.1011/10/2013
SYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLAreaMeas.DateComment235-20240427074014.2714.2714.277.717.4491.0426/04/2024234-20040823120014.6414.6414.640.000.0088.5023/08/2004
CRUISER/RACER REQUIREMENTS*
Accommodation length10.6 mTable area0.44 m²Headroom1.74 mMinimum number of berths4Personal gear stowage0.16 m³Fresh water capacity92 lMinimum number of seats in cockpit4Food stowage0.24 m³Fuel capacity62 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.