Club Certificate2025
LA DIANAGER 4645
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 Angles43.4°43.4°40.8°39.7°39.2°38.9°38.5°38.3°38.9°
Beat VMG2.203.063.744.214.554.774.874.944.90
52°3.454.645.516.126.526.756.876.966.97
60°3.654.885.736.336.706.917.047.167.19
75°3.765.025.906.506.857.077.237.447.53
90°3.705.056.066.697.017.157.297.587.79
110°3.785.186.236.857.207.457.657.898.02
120°3.645.026.096.787.177.467.718.168.43
135°3.244.545.636.476.987.317.598.168.81
150°2.693.894.985.886.587.017.327.868.47
Run VMG2.333.374.325.115.816.376.807.407.89
Gybe Angles146.5°146.5°150.5°153.7°158.5°165.5°172.3°178.1°178.1°
APH ToD:605.2CDL: 8.274APH ToT: 0.9915CertNo:168774
BOAT
ClassSWAN 371DesignerRON HOLLANDBuilderNAUTORAge date01/1980Series date01/1979Offset fileSWN371.offData fileGER4645
HULL
Length Overall11.229 mMaximum Beam3.474 mDraft2.069 mDisplacement7,462 kgDLR9.2693IMS DivisionCruiser/RacerDynamic Allowance0.600%Age Allowance0.487%
PROPELLER
InstallationShaft exposedTypeFolding 2 bladesDiameter0.430m
CREW
Maximum weight400 kg(declared)Minimum weight270 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail25.7126.00Headsail Luffed31.2631.26Headsail FlyingSymmetric88.3188.31Asymmetric
STORM SAIL AREAS (m²)
Trysail7.82Storm Jib10.32Heavy Weather Jib27.84
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
LA DIANAGER 4645
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 VMG1632.81177.1963.7854.3790.8755.4738.8729.1735.1
52°1044.3775.2653.5587.8551.9533.7523.7517.1516.4
60°986.7738.5627.9568.3537.7521.0511.1502.9500.6
75°958.7717.7610.7554.0525.8509.0497.8484.0477.9
90°973.6713.0594.3538.0513.6503.7494.1475.1462.3
110°951.9694.3577.5525.4500.0483.3470.7456.5449.0
120°988.2717.0591.5531.0501.9482.6466.9441.3427.2
135°1112.1792.8639.1556.2516.0492.6474.1441.2408.6
150°1338.6924.7722.7612.4547.3513.3491.8458.2424.8
Run VMG1545.61067.7834.1704.2620.1564.8529.3486.8456.4
Selected Courses
Windward / Leeward1588.11122.4898.9779.3705.4660.1634.1607.9595.8
All purpose1209.3870.5710.9627.7581.2554.5538.1518.6507.0
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward739.30.8116
All purpose605.20.9915
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low790.70.7588
Triple Number Coastal/Long Distance Medium600.80.9986
Triple Number Coastal/Long Distance High534.91.1218
Triple Number Windward/Leeward Low1010.60.5937
Triple Number Windward/Leeward Medium734.80.8165
Triple Number Windward/Leeward High630.80.9512
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance657.40.9128
Triple Number Coastal/Long Distance Low790.70.7588
Triple Number Coastal/Long Distance Medium600.80.9986
Triple Number Coastal/Long Distance High534.91.1218
Triple Number Windward/Leeward Low1010.60.5937
Triple Number Windward/Leeward Medium734.80.8165
Triple Number Windward/Leeward High630.80.9512
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1674.61117.0846.0704.2619.6575.0544.2498.5486.0
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.6989
Downwind "popa"0.8737
70% up, 30% down "Ilhabela"0.7436
30% up, 70% down "Ilhabela-inverso"0.8127
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low790.70.7588
Triple Number Coastal/Long Distance Medium600.80.9986
Triple Number Coastal/Long Distance High534.91.1218
Triple Number Windward/Leeward Low1010.60.5937
Triple Number Windward/Leeward Medium734.80.8165
Triple Number Windward/Leeward High630.80.9512
Predominantly Upwind658.40.9113
Predominantly Downwind610.10.9834
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low790.70.7588
Triple Number AP Medium600.90.9985
Triple Number AP High534.91.1218
Triple Number Windward/Leeward Low1056.60.5679
Triple Number Windward/Leeward Medium734.80.8165
Triple Number Windward/Leeward High630.80.9512
Single Number Predominant Upwind686.50.8741
Single Number Predominant Reaching605.40.9911
Single Number Predominant Downwind638.40.9398
Predominant Upwind - Low966.50.6208
Predominant Upwind - Low/Med731.10.8207
Predominant Upwind - Medium635.30.9445
Predominant Upwind - Med/High586.51.0230
Predominant Upwind - High569.41.0537
Predominant Downwind Low945.50.6346
Predominant Downwind Low/Med693.20.8656
Predominant Downwind Medium586.21.0235
Predominant Downwind Med/High524.61.1437
Predominant Downwind High493.41.2160
Predominant Reaching Low853.50.7030
Predominant Reaching Low/Med644.20.9314
Predominant Reaching Medium561.41.0688
Predominant Reaching Med/High518.01.1582
Predominant Reaching High495.41.2111
SA/DSPL Upwind14.82SA/DSPL Downwind29.66
Scoring OptionTODTOT
5-Band Windward/Leeward Low1183.20.5071
5-Band Windward/Leeward Low/Med861.10.6968
5-Band Windward/Leeward Medium720.30.8330
5-Band Windward/Leeward Med/High640.00.9375
5-Band Windward/Leeward High610.40.9830
Windward/Leeward 60-40 Low1194.10.5025
Windward/Leeward 60-40 Low/Med875.10.6857
Windward/Leeward 60-40 Medium737.30.8137
Windward/Leeward 60-40 Med/High660.90.9079
Windward/Leeward 60-40 High634.70.9454
5-Band AP Low874.60.6860
5-Band AP Low/Med685.90.8747
5-Band AP Medium591.71.0141
5-Band AP Med/High541.21.1087
5-Band AP High519.91.1540
5-Band SF Bay Tour - Low1021.50.5874
5-Band SF Bay Tour - Low/Med826.10.7263
5-Band SF Bay Tour - Medium698.00.8596
5-Band SF Bay Tour - Med/High627.60.9560
5-Band SF Bay Tour - High601.30.9979
Chicago-Mac Upwind0.8443
Chicago-Mac All Purpose0.8770
Chicago-Mac Downwind0.9056
Bayview-Mac Cove Island0.6361
Bayview-Mac Shore0.6400
Harvest Moon Regatta527.41.1377
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance657.40.9128
Triple Number Coastal/Long Distance Low790.70.7588
Triple Number Coastal/Long Distance Medium600.80.9986
Triple Number Coastal/Long Distance High534.91.1218
Triple Number Windward/Leeward Low1010.60.5937
Triple Number Windward/Leeward Medium734.80.8165
Triple Number Windward/Leeward High630.80.9512
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1674.61117.0846.0704.2619.6575.0544.2498.5486.0
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance657.40.9128
Triple Number Coastal/Long Distance Low790.70.7588
Triple Number Coastal/Long Distance Medium600.80.9986
Triple Number Coastal/Long Distance High534.91.1218
Triple Number Windward/Leeward Low1010.60.5937
Triple Number Windward/Leeward Medium734.80.8165
Triple Number Windward/Leeward High630.80.9512
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1674.61117.0846.0704.2619.6575.0544.2498.5486.0
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance657.4
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1674.61117.0846.0704.2619.6575.0544.2498.5486.0
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low790.70.7588
Triple Number Coastal/Long Distance Medium600.80.9986
Triple Number Coastal/Long Distance High534.91.1218
Triple Number Windward/Leeward Low1010.60.5937
Triple Number Windward/Leeward Medium734.80.8165
Triple Number Windward/Leeward High630.80.9512
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating657.40.9128
FinRating, kevyt tuuli1163.30.8596
FinRating, kova tuuli524.00.9541
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low790.70.7588
Triple Number Coastal/Long Distance Medium600.80.9986
Triple Number Coastal/Long Distance High534.91.1218
Triple Number Windward/Leeward Low1010.60.5937
Triple Number Windward/Leeward Medium734.80.8165
Triple Number Windward/Leeward High630.80.9512
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.9128
Triple Number Coastal/Long Distance Low0.7588
Triple Number Coastal/Long Distance Medium0.9986
Triple Number Coastal/Long Distance High1.1218
Triple Number Windward/Leeward Low0.5937
Triple Number Windward/Leeward Medium0.8165
Triple Number Windward/Leeward High0.9512
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1674.61117.0846.0704.2619.6575.0544.2498.5486.0
For information
General Purpose Handicap (GPH)681.9
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance657.40.9128
Triple Number Coastal/Long Distance Low790.70.7588
Triple Number Coastal/Long Distance Medium600.80.9986
Triple Number Coastal/Long Distance High534.91.1218
Triple Number Windward/Leeward Low1010.60.5937
Triple Number Windward/Leeward Medium734.80.8165
Triple Number Windward/Leeward High630.80.9512
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1674.61117.0846.0704.2619.6575.0544.2498.5486.0
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low790.70.7588
Triple Number Coastal/Long Distance Medium600.80.9986
Triple Number Coastal/Long Distance High534.91.1218
Triple Number Windward/Leeward Low1010.60.5937
Triple Number Windward/Leeward Medium734.80.8165
Triple Number Windward/Leeward High630.80.9512
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance657.40.9128
Triple Number Coastal/Long Distance Low790.70.7588
Triple Number Coastal/Long Distance Medium600.80.9986
Triple Number Coastal/Long Distance High534.91.1218
Triple Number Windward/Leeward Low1010.60.5937
Triple Number Windward/Leeward Medium734.80.8165
Triple Number Windward/Leeward High630.80.9512
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1674.61117.0846.0704.2619.6575.0544.2498.5486.0
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance657.40.9128
Triple Number Coastal/Long Distance Low790.70.7588
Triple Number Coastal/Long Distance Medium600.80.9986
Triple Number Coastal/Long Distance High534.91.1218
Triple Number Windward/Leeward Low1010.60.5937
Triple Number Windward/Leeward Medium734.80.8165
Triple Number Windward/Leeward High630.80.9512
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1674.61117.0846.0704.2619.6575.0544.2498.5486.0
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low790.7
Triple Number Coastal/Long Distance Medium600.8
Triple Number Coastal/Long Distance High534.9
Triple Number Windward/Leeward Low1010.6
Triple Number Windward/Leeward Medium734.8
Triple Number Windward/Leeward High630.8
Predominantly Upwind658.4
Predominantly Downwind610.1
Predominantly Reaching588.6
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance657.40.9128
Triple Number Coastal/Long Distance Low790.70.7588
Triple Number Coastal/Long Distance Medium600.80.9986
Triple Number Coastal/Long Distance High534.91.1218
Triple Number Windward/Leeward Low1010.60.5937
Triple Number Windward/Leeward Medium734.80.8165
Triple Number Windward/Leeward High630.80.9512
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1674.61117.0846.0704.2619.6575.0544.2498.5486.0
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7588
Triple Number Coastal/Long Distance Medium0.9986
Triple Number Coastal/Long Distance High1.1218
Triple Number Windward/Leeward Low0.5937
Triple Number Windward/Leeward Medium0.8165
Triple Number Windward/Leeward High0.9512
Coastal/Long Distance0.9128
Predominantly Upwind0.9113
Predominantly Downwind0.9834
For information
General Purpose Handicap (GPH)681.9
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)0.9915
Distanseseilas Trippeltall svak vind0.7588
Distanseseilas Trippeltall mellomvind0.9986
Distanseseilas Trippeltall sterk vind1.1218
Pølsebane Trippeltall svak vind0.5937
Pølsebane Trippeltall mellomvind0.8165
Pølsebane Trippeltall sterk vind0.9512
Motvind Singeltall0.9113
Medvind Singeltall0.9834
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low790.70.7588
Triple Number Coastal/Long Distance Medium600.80.9986
Triple Number Coastal/Long Distance High534.91.1218
Triple Number Windward/Leeward Low1010.60.5937
Triple Number Windward/Leeward Medium734.80.8165
Triple Number Windward/Leeward High630.80.9512
Coastal/Long Distance657.40.9128
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind658.40.9113
Predominantly Downwind610.10.9834
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore599.41.0010
Cape Doctor Coastal510.51.1754
Triple Number Coastal/Long Distance Low790.70.7588
Triple Number Coastal/Long Distance Medium600.80.9986
Triple Number Coastal/Long Distance High534.91.1218
Triple Number Windward/Leeward Low1010.60.5937
Triple Number Windward/Leeward Medium734.80.8165
Triple Number Windward/Leeward High630.80.9512
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7588
Triple Number Coastal/Long Distance Medium0.9986
Triple Number Coastal/Long Distance High1.1218
Triple Number Windward/Leeward Low0.5937
Triple Number Windward/Leeward Medium0.8165
Triple Number Windward/Leeward High0.9512
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7588
Triple Number Coastal/Long Distance Medium0.9986
Triple Number Coastal/Long Distance High1.1218
Triple Number Windward/Leeward Low0.5937
Triple Number Windward/Leeward Medium0.8165
Triple Number Windward/Leeward High0.9512
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance657.40.9128
Triple Number Coastal/Long Distance Low790.70.7588
Triple Number Coastal/Long Distance Medium600.80.9986
Triple Number Coastal/Long Distance High534.91.1218
Triple Number Windward/Leeward Low1010.60.5937
Triple Number Windward/Leeward Medium734.80.8165
Triple Number Windward/Leeward High630.80.9512
Predominantly Upwind658.40.9113
Predominantly Downwind610.10.9834
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1674.61117.0846.0704.2619.6575.0544.2498.5486.0
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance657.40.9128
Triple Number Coastal/Long Distance Low790.70.7588
Triple Number Coastal/Long Distance Medium600.80.9986
Triple Number Coastal/Long Distance High534.91.1218
Triple Number Windward/Leeward Low1010.60.5937
Triple Number Windward/Leeward Medium734.80.8165
Triple Number Windward/Leeward High630.80.9512
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1674.61117.0846.0704.2619.6575.0544.2498.5486.0
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low790.70.7588
Triple Number AP Medium600.90.9985
Triple Number AP High534.91.1218
Triple Number Windward/Leeward Low1056.60.5679
Triple Number Windward/Leeward Medium734.80.8165
Triple Number Windward/Leeward High630.80.9512
Single Number Predominant Upwind686.50.8741
Single Number Predominant Reaching605.40.9911
Single Number Predominant Downwind638.40.9398
Predominant Upwind - Low966.50.6208
Predominant Upwind - Low/Med731.10.8207
Predominant Upwind - Medium635.30.9445
Predominant Upwind - Med/High586.51.0230
Predominant Upwind - High569.41.0537
Predominant Downwind Low945.50.6346
Predominant Downwind Low/Med693.20.8656
Predominant Downwind Medium586.21.0235
Predominant Downwind Med/High524.61.1437
Predominant Downwind High493.41.2160
Predominant Reaching Low853.50.7030
Predominant Reaching Low/Med644.20.9314
Predominant Reaching Medium561.41.0688
Predominant Reaching Med/High518.01.1582
Predominant Reaching High495.41.2111
SA/DSPL Upwind14.82SA/DSPL Downwind29.66
Scoring OptionTODTOT
5-Band Windward/Leeward Low1183.20.5071
5-Band Windward/Leeward Low/Med861.10.6968
5-Band Windward/Leeward Medium720.30.8330
5-Band Windward/Leeward Med/High640.00.9375
5-Band Windward/Leeward High610.40.9830
Windward/Leeward 60-40 Low1194.10.5025
Windward/Leeward 60-40 Low/Med875.10.6857
Windward/Leeward 60-40 Medium737.30.8137
Windward/Leeward 60-40 Med/High660.90.9079
Windward/Leeward 60-40 High634.70.9454
5-Band AP Low874.60.6860
5-Band AP Low/Med685.90.8747
5-Band AP Medium591.71.0141
5-Band AP Med/High541.21.1087
5-Band AP High519.91.1540
5-Band SF Bay Tour - Low1021.50.5874
5-Band SF Bay Tour - Low/Med826.10.7263
5-Band SF Bay Tour - Medium698.00.8596
5-Band SF Bay Tour - Med/High627.60.9560
5-Band SF Bay Tour - High601.30.9979
Chicago-Mac Upwind0.8443
Chicago-Mac All Purpose0.8770
Chicago-Mac Downwind0.9056
Bayview-Mac Cove Island0.6361
Bayview-Mac Shore0.6400
Harvest Moon Regatta527.41.1377
Club Certificate2025
LA DIANAGER 4645
Deutscher Segler Verband e.V.
Soling 16
24159 Kiel Schilksee
technik@dsv.org
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassSWAN 371Measurement22/04/2024HIN024Plan reviewHull constructionSolidCarbon rudderNoLight stanchionsNoTrim tabNo
LOA11.229Max. Beam3.474Draft2.069Displacement7,462Wetted area27.13IMS L9.416LSM09.302Acc. length11.229Sink (kg/mm) 19.00
VCGD0.019VCGM0.035RM Rated (kg·m) 125.8Limit of positive stability(°) N/AStability IndexN/ADefault crew weight621Declared crew weight400
PROPELLER
Propeller TypeFolding 2 blades
InstallationShaft exposedTwin screwNoHydro generatorNo
PRD0.430PBWPIPA0.0022
PSD0.020PHD0.050PHL0.050
PSA10.0°ESL1.020
ST1ST2ST3
ST4ST5
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerNoMainsail furlerNoArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0Checkstays1Spreaders2Rotating mastNo
P12.400IG14.360ISP14.510MDT10.115MDL10.187MDT2MDL2TLNo TaperMWGO
E3.600J4.500BAS1.580FSDNo FoilSFJ0.140SPL4.539WPLTPSBDMWTMCG
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodRM estimatedFlotation Date22/04/2024
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Club Certificate2025
LA DIANAGER 4645
Deutscher Segler Verband e.V.
Soling 16
24159 Kiel Schilksee
technik@dsv.org
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment1701750.110.701.252.212.9725.7105/04/2024
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment1701640.030.551.082.183.244.2514.50NoNo 31.2605/04/2024
SYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLAreaMeas.DateComment17017814.3214.3214.327.407.4088.3105/04/2024
CRUISER/RACER REQUIREMENTS*
Accommodation length11.2 mTable area0.55 m²Headroom1.77 mMinimum number of berths5Personal gear stowage0.20 m³Fresh water capacity130 lMinimum number of seats in cockpit5Food stowage0.30 m³Fuel capacity74 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.