Club Certificate2025
KARMAGER 8566
Deutscher Segler Verband e.V.
Soling 16
24159 Kiel Schilksee
technik@dsv.org
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 Angles42.8°42.8°40.6°39.5°38.6°38.3°38.2°38.3°39.5°
Beat VMG2.493.424.144.634.894.995.055.095.00
52°3.865.186.106.686.967.077.147.217.19
60°4.095.446.346.877.157.277.347.427.42
75°4.245.626.517.027.327.517.647.787.84
90°4.095.546.577.117.357.617.838.138.29
110°4.135.636.717.287.647.918.098.398.63
120°3.975.456.567.207.617.978.308.759.08
135°3.494.886.046.887.377.768.158.959.93
150°2.854.115.256.226.957.407.778.519.42
Run VMG2.473.564.545.406.156.747.197.898.57
Gybe Angles145.3°145.3°149.8°152.3°159.2°166.4°173.6°177.2°176.3°
APH ToD:566.6CDL: 8.952APH ToT: 1.0590CertNo:142675
BOAT
ClassFIRST 36.7DesignerFARRBuilderBENETEAUAge date09/2001Series date01/2001Offset fileFIRST367.offData fileGER8566
HULL
Length Overall10.640 mMaximum Beam3.458 mDraft2.255 mDisplacement6,140 kgDLR7.0645IMS DivisionCruiser/RacerDynamic Allowance0.220%Age Allowance0.487%
PROPELLER
InstallationStrutTypeFolding 2 bladesDiameter0.382m
CREW
Maximum weight500 kg(declared)Minimum weight370 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail38.6439.37Headsail Luffed29.7629.76Headsail FlyingSymmetric93.7293.72Asymmetric
STORM SAIL AREAS (m²)
Trysail11.37Storm Jib10.13Heavy Weather Jib27.34
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
KARMAGER 8566
Deutscher Segler Verband e.V.
Soling 16
24159 Kiel Schilksee
technik@dsv.org
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 VMG1445.21052.5870.1777.7736.7720.9712.3707.1719.7
52°932.2695.4590.5538.9517.3508.9504.2499.6500.5
60°880.5662.1568.0523.9503.8494.9490.2484.9485.5
75°848.8640.9552.9513.0492.0479.2471.3462.5459.0
90°879.6649.4547.8506.3489.7473.2460.0442.9434.1
110°872.7639.9536.7494.5471.3454.9444.8428.9417.3
120°906.5660.5549.2500.0473.2451.7433.6411.6396.4
135°1032.9737.4596.5523.6488.2463.7441.9402.5362.6
150°1262.1876.0686.1578.6517.9486.5463.5422.9382.3
Run VMG1458.41011.5792.2666.7585.5534.4500.9456.6420.1
Selected Courses
Windward / Leeward1450.31032.0831.1722.2661.1627.7606.6581.8569.9
All purpose1099.5796.1654.6583.3546.2525.3511.1492.0480.2
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward692.80.8661
All purpose566.61.0590
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low725.30.8272
Triple Number Coastal/Long Distance Medium562.41.0669
Triple Number Coastal/Long Distance High507.51.1823
Triple Number Windward/Leeward Low931.50.6441
Triple Number Windward/Leeward Medium687.30.8730
Triple Number Windward/Leeward High602.60.9957
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance615.60.9747
Triple Number Coastal/Long Distance Low725.30.8272
Triple Number Coastal/Long Distance Medium562.41.0669
Triple Number Coastal/Long Distance High507.51.1823
Triple Number Windward/Leeward Low931.50.6441
Triple Number Windward/Leeward Medium687.30.8730
Triple Number Windward/Leeward High602.60.9957
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1538.31029.9782.5653.8582.0544.8515.8471.3459.5
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.7531
Downwind "popa"0.9235
70% up, 30% down "Ilhabela"0.7972
30% up, 70% down "Ilhabela-inverso"0.8648
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low725.30.8272
Triple Number Coastal/Long Distance Medium562.41.0669
Triple Number Coastal/Long Distance High507.51.1823
Triple Number Windward/Leeward Low931.50.6441
Triple Number Windward/Leeward Medium687.30.8730
Triple Number Windward/Leeward High602.60.9957
Predominantly Upwind614.20.9769
Predominantly Downwind572.51.0481
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low725.30.8272
Triple Number AP Medium562.41.0668
Triple Number AP High507.51.1823
Triple Number Windward/Leeward Low972.70.6168
Triple Number Windward/Leeward Medium687.30.8730
Triple Number Windward/Leeward High602.60.9957
Single Number Predominant Upwind638.80.9393
Single Number Predominant Reaching565.11.0617
Single Number Predominant Downwind598.21.0030
Predominant Upwind - Low874.30.6862
Predominant Upwind - Low/Med670.70.8946
Predominant Upwind - Medium594.61.0091
Predominant Upwind - Med/High559.11.0732
Predominant Upwind - High545.01.1010
Predominant Downwind Low876.50.6845
Predominant Downwind Low/Med647.60.9265
Predominant Downwind Medium552.01.0869
Predominant Downwind Med/High494.61.2131
Predominant Downwind High461.91.2991
Predominant Reaching Low781.30.7680
Predominant Reaching Low/Med597.61.0040
Predominant Reaching Medium528.01.1364
Predominant Reaching Med/High488.11.2292
Predominant Reaching High465.01.2902
SA/DSPL Upwind20.28SA/DSPL Downwind39.23
Scoring OptionTODTOT
5-Band Windward/Leeward Low1086.70.5521
5-Band Windward/Leeward Low/Med797.20.7526
5-Band Windward/Leeward Medium675.30.8885
5-Band Windward/Leeward Med/High610.60.9827
5-Band Windward/Leeward High584.01.0273
Windward/Leeward 60-40 Low1090.40.5503
Windward/Leeward 60-40 Low/Med806.70.7438
Windward/Leeward 60-40 Medium690.20.8693
Windward/Leeward 60-40 Med/High631.40.9502
Windward/Leeward 60-40 High609.30.9848
5-Band AP Low801.50.7486
5-Band AP Low/Med634.30.9459
5-Band AP Medium555.01.0811
5-Band AP Med/High513.21.1690
5-Band AP High493.31.2164
5-Band SF Bay Tour - Low936.90.6404
5-Band SF Bay Tour - Low/Med763.00.7864
5-Band SF Bay Tour - Medium654.00.9175
5-Band SF Bay Tour - Med/High598.01.0033
5-Band SF Bay Tour - High574.11.0451
Chicago-Mac Upwind0.9120
Chicago-Mac All Purpose0.9420
Chicago-Mac Downwind0.9673
Bayview-Mac Cove Island0.6910
Bayview-Mac Shore0.6960
Harvest Moon Regatta493.81.2151
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance615.60.9747
Triple Number Coastal/Long Distance Low725.30.8272
Triple Number Coastal/Long Distance Medium562.41.0669
Triple Number Coastal/Long Distance High507.51.1823
Triple Number Windward/Leeward Low931.50.6441
Triple Number Windward/Leeward Medium687.30.8730
Triple Number Windward/Leeward High602.60.9957
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1538.31029.9782.5653.8582.0544.8515.8471.3459.5
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance615.60.9747
Triple Number Coastal/Long Distance Low725.30.8272
Triple Number Coastal/Long Distance Medium562.41.0669
Triple Number Coastal/Long Distance High507.51.1823
Triple Number Windward/Leeward Low931.50.6441
Triple Number Windward/Leeward Medium687.30.8730
Triple Number Windward/Leeward High602.60.9957
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1538.31029.9782.5653.8582.0544.8515.8471.3459.5
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance615.6
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1538.31029.9782.5653.8582.0544.8515.8471.3459.5
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low725.30.8272
Triple Number Coastal/Long Distance Medium562.41.0669
Triple Number Coastal/Long Distance High507.51.1823
Triple Number Windward/Leeward Low931.50.6441
Triple Number Windward/Leeward Medium687.30.8730
Triple Number Windward/Leeward High602.60.9957
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating615.60.9747
FinRating, kevyt tuuli1067.80.9365
FinRating, kova tuuli496.81.0064
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low725.30.8272
Triple Number Coastal/Long Distance Medium562.41.0669
Triple Number Coastal/Long Distance High507.51.1823
Triple Number Windward/Leeward Low931.50.6441
Triple Number Windward/Leeward Medium687.30.8730
Triple Number Windward/Leeward High602.60.9957
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.9747
Triple Number Coastal/Long Distance Low0.8272
Triple Number Coastal/Long Distance Medium1.0669
Triple Number Coastal/Long Distance High1.1823
Triple Number Windward/Leeward Low0.6441
Triple Number Windward/Leeward Medium0.8730
Triple Number Windward/Leeward High0.9957
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1538.31029.9782.5653.8582.0544.8515.8471.3459.5
For information
General Purpose Handicap (GPH)635.2
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance615.60.9747
Triple Number Coastal/Long Distance Low725.30.8272
Triple Number Coastal/Long Distance Medium562.41.0669
Triple Number Coastal/Long Distance High507.51.1823
Triple Number Windward/Leeward Low931.50.6441
Triple Number Windward/Leeward Medium687.30.8730
Triple Number Windward/Leeward High602.60.9957
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1538.31029.9782.5653.8582.0544.8515.8471.3459.5
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low725.30.8272
Triple Number Coastal/Long Distance Medium562.41.0669
Triple Number Coastal/Long Distance High507.51.1823
Triple Number Windward/Leeward Low931.50.6441
Triple Number Windward/Leeward Medium687.30.8730
Triple Number Windward/Leeward High602.60.9957
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance615.60.9747
Triple Number Coastal/Long Distance Low725.30.8272
Triple Number Coastal/Long Distance Medium562.41.0669
Triple Number Coastal/Long Distance High507.51.1823
Triple Number Windward/Leeward Low931.50.6441
Triple Number Windward/Leeward Medium687.30.8730
Triple Number Windward/Leeward High602.60.9957
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1538.31029.9782.5653.8582.0544.8515.8471.3459.5
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance615.60.9747
Triple Number Coastal/Long Distance Low725.30.8272
Triple Number Coastal/Long Distance Medium562.41.0669
Triple Number Coastal/Long Distance High507.51.1823
Triple Number Windward/Leeward Low931.50.6441
Triple Number Windward/Leeward Medium687.30.8730
Triple Number Windward/Leeward High602.60.9957
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1538.31029.9782.5653.8582.0544.8515.8471.3459.5
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low725.3
Triple Number Coastal/Long Distance Medium562.4
Triple Number Coastal/Long Distance High507.5
Triple Number Windward/Leeward Low931.5
Triple Number Windward/Leeward Medium687.3
Triple Number Windward/Leeward High602.6
Predominantly Upwind614.2
Predominantly Downwind572.5
Predominantly Reaching551.3
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance615.60.9747
Triple Number Coastal/Long Distance Low725.30.8272
Triple Number Coastal/Long Distance Medium562.41.0669
Triple Number Coastal/Long Distance High507.51.1823
Triple Number Windward/Leeward Low931.50.6441
Triple Number Windward/Leeward Medium687.30.8730
Triple Number Windward/Leeward High602.60.9957
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1538.31029.9782.5653.8582.0544.8515.8471.3459.5
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8272
Triple Number Coastal/Long Distance Medium1.0669
Triple Number Coastal/Long Distance High1.1823
Triple Number Windward/Leeward Low0.6441
Triple Number Windward/Leeward Medium0.8730
Triple Number Windward/Leeward High0.9957
Coastal/Long Distance0.9747
Predominantly Upwind0.9769
Predominantly Downwind1.0481
For information
General Purpose Handicap (GPH)635.2
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)1.0590
Distanseseilas Trippeltall svak vind0.8272
Distanseseilas Trippeltall mellomvind1.0669
Distanseseilas Trippeltall sterk vind1.1823
Pølsebane Trippeltall svak vind0.6441
Pølsebane Trippeltall mellomvind0.8730
Pølsebane Trippeltall sterk vind0.9957
Motvind Singeltall0.9769
Medvind Singeltall1.0481
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low725.30.8272
Triple Number Coastal/Long Distance Medium562.41.0669
Triple Number Coastal/Long Distance High507.51.1823
Triple Number Windward/Leeward Low931.50.6441
Triple Number Windward/Leeward Medium687.30.8730
Triple Number Windward/Leeward High602.60.9957
Coastal/Long Distance615.60.9747
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind614.20.9769
Predominantly Downwind572.51.0481
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore573.41.0463
Cape Doctor Coastal483.71.2403
Triple Number Coastal/Long Distance Low725.30.8272
Triple Number Coastal/Long Distance Medium562.41.0669
Triple Number Coastal/Long Distance High507.51.1823
Triple Number Windward/Leeward Low931.50.6441
Triple Number Windward/Leeward Medium687.30.8730
Triple Number Windward/Leeward High602.60.9957
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8272
Triple Number Coastal/Long Distance Medium1.0669
Triple Number Coastal/Long Distance High1.1823
Triple Number Windward/Leeward Low0.6441
Triple Number Windward/Leeward Medium0.8730
Triple Number Windward/Leeward High0.9957
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8272
Triple Number Coastal/Long Distance Medium1.0669
Triple Number Coastal/Long Distance High1.1823
Triple Number Windward/Leeward Low0.6441
Triple Number Windward/Leeward Medium0.8730
Triple Number Windward/Leeward High0.9957
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance615.60.9747
Triple Number Coastal/Long Distance Low725.30.8272
Triple Number Coastal/Long Distance Medium562.41.0669
Triple Number Coastal/Long Distance High507.51.1823
Triple Number Windward/Leeward Low931.50.6441
Triple Number Windward/Leeward Medium687.30.8730
Triple Number Windward/Leeward High602.60.9957
Predominantly Upwind614.20.9769
Predominantly Downwind572.51.0481
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1538.31029.9782.5653.8582.0544.8515.8471.3459.5
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance615.60.9747
Triple Number Coastal/Long Distance Low725.30.8272
Triple Number Coastal/Long Distance Medium562.41.0669
Triple Number Coastal/Long Distance High507.51.1823
Triple Number Windward/Leeward Low931.50.6441
Triple Number Windward/Leeward Medium687.30.8730
Triple Number Windward/Leeward High602.60.9957
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1538.31029.9782.5653.8582.0544.8515.8471.3459.5
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low725.30.8272
Triple Number AP Medium562.41.0668
Triple Number AP High507.51.1823
Triple Number Windward/Leeward Low972.70.6168
Triple Number Windward/Leeward Medium687.30.8730
Triple Number Windward/Leeward High602.60.9957
Single Number Predominant Upwind638.80.9393
Single Number Predominant Reaching565.11.0617
Single Number Predominant Downwind598.21.0030
Predominant Upwind - Low874.30.6862
Predominant Upwind - Low/Med670.70.8946
Predominant Upwind - Medium594.61.0091
Predominant Upwind - Med/High559.11.0732
Predominant Upwind - High545.01.1010
Predominant Downwind Low876.50.6845
Predominant Downwind Low/Med647.60.9265
Predominant Downwind Medium552.01.0869
Predominant Downwind Med/High494.61.2131
Predominant Downwind High461.91.2991
Predominant Reaching Low781.30.7680
Predominant Reaching Low/Med597.61.0040
Predominant Reaching Medium528.01.1364
Predominant Reaching Med/High488.11.2292
Predominant Reaching High465.01.2902
SA/DSPL Upwind20.28SA/DSPL Downwind39.23
Scoring OptionTODTOT
5-Band Windward/Leeward Low1086.70.5521
5-Band Windward/Leeward Low/Med797.20.7526
5-Band Windward/Leeward Medium675.30.8885
5-Band Windward/Leeward Med/High610.60.9827
5-Band Windward/Leeward High584.01.0273
Windward/Leeward 60-40 Low1090.40.5503
Windward/Leeward 60-40 Low/Med806.70.7438
Windward/Leeward 60-40 Medium690.20.8693
Windward/Leeward 60-40 Med/High631.40.9502
Windward/Leeward 60-40 High609.30.9848
5-Band AP Low801.50.7486
5-Band AP Low/Med634.30.9459
5-Band AP Medium555.01.0811
5-Band AP Med/High513.21.1690
5-Band AP High493.31.2164
5-Band SF Bay Tour - Low936.90.6404
5-Band SF Bay Tour - Low/Med763.00.7864
5-Band SF Bay Tour - Medium654.00.9175
5-Band SF Bay Tour - Med/High598.01.0033
5-Band SF Bay Tour - High574.11.0451
Chicago-Mac Upwind0.9120
Chicago-Mac All Purpose0.9420
Chicago-Mac Downwind0.9673
Bayview-Mac Cove Island0.6910
Bayview-Mac Shore0.6960
Harvest Moon Regatta493.81.2151
Club Certificate2025
KARMAGER 8566
Deutscher Segler Verband e.V.
Soling 16
24159 Kiel Schilksee
technik@dsv.org
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassFIRST 36.7Measurement29/06/2017HIN102Plan reviewHull constructionSolidCarbon rudderNoLight stanchionsNoTrim tabNo
LOA10.640Max. Beam3.458Draft2.255Displacement6,140Wetted area26.19IMS L9.687LSM09.543Acc. length10.640Sink (kg/mm) 20.11
VCGD0.270VCGM0.231RM Rated (kg·m) 129.0Limit of positive stability(°) N/AStability IndexN/ADefault crew weight644Declared crew weight500
PROPELLER
Propeller TypeFolding 2 blades
InstallationStrutTwin screwNoHydro generatorNo
PRD0.382PBW0.112PIPA0.0036
EDL2.520ST10.065ST20.180
ST30.180ST40.110ST50.260
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerNoMainsail furlerNoArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0Checkstays0Spreaders3Rotating mastNo
P13.815IG14.165ISP14.205MDT10.111MDL10.189MDT20.105MDL20.151TL0.720MW0.189GO0.207
E4.700J3.980BAS1.580FSD0.033SFJ0.000SPL4.050WPLTPSBD0.160MWT164.00MCG5.400
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodRM entered directlyRM entered129.0Flotation Date10/06/2024
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Club Certificate2025
KARMAGER 8566
Deutscher Segler Verband e.V.
Soling 16
24159 Kiel Schilksee
technik@dsv.org
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment1742680.150.971.743.053.9638.6404/12/2023
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment1766910.080.641.202.223.154.0913.83YesNo 29.7621/05/2024
SYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLAreaMeas.DateComment17426314.1414.1414.147.987.8593.7207/12/202317427214.0114.0114.016.017.9474.6707/12/2023S 3
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.