Club Certificate2025
KAIESP-3045_C
RFEV
c/ Gamazo sn
39004 Santander – España
crucero@rfev.es
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 Angles43.6°43.6°41.7°40.1°38.6°37.9°37.5°37.5°38.4°
Beat VMG2.323.193.864.344.654.804.874.914.85
52°3.634.885.756.276.546.696.766.826.83
60°3.865.145.986.436.696.856.937.017.04
75°3.995.296.136.566.827.027.167.327.40
90°3.825.196.166.676.947.097.267.577.77
110°3.855.256.256.767.097.377.607.958.24
120°3.695.076.106.687.047.367.668.278.74
135°3.274.555.606.406.847.167.488.209.12
150°2.653.834.895.826.496.877.187.808.62
Run VMG2.293.314.245.055.786.316.717.307.87
Gybe Angles146.6°146.6°151.2°152.8°161.3°168.4°177.2°178.1°177.1°
APH ToD:603.7CDL: 8.033APH ToT: 0.9939CertNo:304501
BOAT
ClassDEHLER 34DesignerV. DE STADTBuilderDEHLERAge date05/1989Series date01/1982Offset fileG1005.BOFData fileE3045_C
HULL
Length Overall10.112 mMaximum Beam3.406 mDraft1.782 mDisplacement4,801 kgDLR8.0497IMS DivisionCruiser/RacerDynamic Allowance0.310%Age Allowance0.487%
PROPELLER
InstallationShaft exposedTypeFolding 2 bladesDiameter0.440m
CREW
Maximum weight540 kg(declared)Minimum weight410 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail30.1830.77Headsail Luffed29.1529.15Headsail FlyingSymmetric74.6674.66Asymmetric
STORM SAIL AREAS (m²)
Trysail8.84Storm Jib7.38Heavy Weather Jib19.90
SAIL LIMITS
Headsails5Spinnakers4
STABILITY
Righting MomentN/AStability IndexN/A
COMMENTS
PRUEBA DE ESCORA CADUCADA.1998
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
KAIESP-3045_C
RFEV
c/ Gamazo sn
39004 Santander – España
crucero@rfev.es
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 VMG1548.51128.3932.7829.3773.5749.6738.5733.5741.8
52°991.0738.0626.6574.5550.1537.8532.2527.5527.1
60°932.7700.8602.0559.6538.2525.9519.2513.4511.4
75°901.8680.4587.5548.6527.6513.1502.7491.9486.4
90°942.4694.1584.6539.7518.8508.1495.7475.5463.4
110°935.3685.8575.7532.2507.6488.6473.5452.6437.1
120°975.8710.0589.9538.7511.1489.3470.1435.5411.8
135°1102.5791.9642.9562.2526.6502.6481.2438.8394.9
150°1357.0941.1735.9618.7554.7523.7501.4461.6417.9
Run VMG1571.41086.7849.0712.8622.6570.2536.4493.5457.2
Selected Courses
Windward / Leeward1558.21107.5890.8771.0698.1659.9637.4613.5599.5
All purpose1177.9852.4700.6623.6581.0558.0542.6521.9506.9
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward734.50.8169
All purpose603.70.9939
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low776.50.7727
Triple Number Coastal/Long Distance Medium599.41.0010
Triple Number Coastal/Long Distance High538.71.1138
Triple Number Windward/Leeward Low999.20.6005
Triple Number Windward/Leeward Medium729.00.8231
Triple Number Windward/Leeward High634.00.9463
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance655.70.9150
Triple Number Coastal/Long Distance Low776.50.7727
Triple Number Coastal/Long Distance Medium599.41.0010
Triple Number Coastal/Long Distance High538.71.1138
Triple Number Windward/Leeward Low999.20.6005
Triple Number Windward/Leeward Medium729.00.8231
Triple Number Windward/Leeward High634.00.9463
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1654.41105.4838.3698.4617.9578.4548.7501.2485.2
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.7136
Downwind "popa"0.8622
70% up, 30% down "Ilhabela"0.7525
30% up, 70% down "Ilhabela-inverso"0.8115
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low776.50.7727
Triple Number Coastal/Long Distance Medium599.41.0010
Triple Number Coastal/Long Distance High538.71.1138
Triple Number Windward/Leeward Low999.20.6005
Triple Number Windward/Leeward Medium729.00.8231
Triple Number Windward/Leeward High634.00.9463
Predominantly Upwind651.90.9204
Predominantly Downwind612.30.9798
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low776.50.7727
Triple Number AP Medium599.51.0008
Triple Number AP High538.71.1138
Triple Number Windward/Leeward Low1043.30.5751
Triple Number Windward/Leeward Medium729.00.8231
Triple Number Windward/Leeward High634.00.9463
Single Number Predominant Upwind678.30.8846
Single Number Predominant Reaching603.80.9938
Single Number Predominant Downwind640.10.9374
Predominant Upwind - Low934.70.6419
Predominant Upwind - Low/Med715.60.8384
Predominant Upwind - Medium630.50.9516
Predominant Upwind - Med/High589.91.0172
Predominant Upwind - High574.41.0446
Predominant Downwind Low939.60.6386
Predominant Downwind Low/Med693.20.8655
Predominant Downwind Medium589.71.0175
Predominant Downwind Med/High529.71.1326
Predominant Downwind High495.91.2100
Predominant Reaching Low835.80.7178
Predominant Reaching Low/Med638.70.9395
Predominant Reaching Medium563.41.0650
Predominant Reaching Med/High522.31.1488
Predominant Reaching High497.51.2060
SA/DSPL Upwind20.74SA/DSPL Downwind36.65
Scoring OptionTODTOT
5-Band Windward/Leeward Low1166.50.5144
5-Band Windward/Leeward Low/Med852.10.7042
5-Band Windward/Leeward Medium714.90.8393
5-Band Windward/Leeward Med/High642.30.9342
5-Band Windward/Leeward High615.20.9753
Windward/Leeward 60-40 Low1170.10.5128
Windward/Leeward 60-40 Low/Med862.00.6961
Windward/Leeward 60-40 Medium729.80.8222
Windward/Leeward 60-40 Med/High662.30.9059
Windward/Leeward 60-40 High639.30.9385
5-Band AP Low857.60.6996
5-Band AP Low/Med678.10.8848
5-Band AP Medium591.01.0152
5-Band AP Med/High545.01.1010
5-Band AP High522.91.1475
5-Band SF Bay Tour - Low1005.10.5970
5-Band SF Bay Tour - Low/Med815.80.7355
5-Band SF Bay Tour - Medium693.20.8656
5-Band SF Bay Tour - Med/High630.00.9524
5-Band SF Bay Tour - High604.80.9920
Chicago-Mac Upwind0.8575
Chicago-Mac All Purpose0.8833
Chicago-Mac Downwind0.9041
Bayview-Mac Cove Island0.6463
Bayview-Mac Shore0.6511
Harvest Moon Regatta529.71.1328
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance655.70.9150
Triple Number Coastal/Long Distance Low776.50.7727
Triple Number Coastal/Long Distance Medium599.41.0010
Triple Number Coastal/Long Distance High538.71.1138
Triple Number Windward/Leeward Low999.20.6005
Triple Number Windward/Leeward Medium729.00.8231
Triple Number Windward/Leeward High634.00.9463
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1654.41105.4838.3698.4617.9578.4548.7501.2485.2
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance655.70.9150
Triple Number Coastal/Long Distance Low776.50.7727
Triple Number Coastal/Long Distance Medium599.41.0010
Triple Number Coastal/Long Distance High538.71.1138
Triple Number Windward/Leeward Low999.20.6005
Triple Number Windward/Leeward Medium729.00.8231
Triple Number Windward/Leeward High634.00.9463
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1654.41105.4838.3698.4617.9578.4548.7501.2485.2
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance655.7
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1654.41105.4838.3698.4617.9578.4548.7501.2485.2
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low776.50.7727
Triple Number Coastal/Long Distance Medium599.41.0010
Triple Number Coastal/Long Distance High538.71.1138
Triple Number Windward/Leeward Low999.20.6005
Triple Number Windward/Leeward Medium729.00.8231
Triple Number Windward/Leeward High634.00.9463
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating655.70.9150
FinRating, kevyt tuuli1145.90.8727
FinRating, kova tuuli526.20.9503
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low776.50.7727
Triple Number Coastal/Long Distance Medium599.41.0010
Triple Number Coastal/Long Distance High538.71.1138
Triple Number Windward/Leeward Low999.20.6005
Triple Number Windward/Leeward Medium729.00.8231
Triple Number Windward/Leeward High634.00.9463
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.9150
Triple Number Coastal/Long Distance Low0.7727
Triple Number Coastal/Long Distance Medium1.0010
Triple Number Coastal/Long Distance High1.1138
Triple Number Windward/Leeward Low0.6005
Triple Number Windward/Leeward Medium0.8231
Triple Number Windward/Leeward High0.9463
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1654.41105.4838.3698.4617.9578.4548.7501.2485.2
For information
General Purpose Handicap (GPH)677.7
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance655.70.9150
Triple Number Coastal/Long Distance Low776.50.7727
Triple Number Coastal/Long Distance Medium599.41.0010
Triple Number Coastal/Long Distance High538.71.1138
Triple Number Windward/Leeward Low999.20.6005
Triple Number Windward/Leeward Medium729.00.8231
Triple Number Windward/Leeward High634.00.9463
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1654.41105.4838.3698.4617.9578.4548.7501.2485.2
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low776.50.7727
Triple Number Coastal/Long Distance Medium599.41.0010
Triple Number Coastal/Long Distance High538.71.1138
Triple Number Windward/Leeward Low999.20.6005
Triple Number Windward/Leeward Medium729.00.8231
Triple Number Windward/Leeward High634.00.9463
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance655.70.9150
Triple Number Coastal/Long Distance Low776.50.7727
Triple Number Coastal/Long Distance Medium599.41.0010
Triple Number Coastal/Long Distance High538.71.1138
Triple Number Windward/Leeward Low999.20.6005
Triple Number Windward/Leeward Medium729.00.8231
Triple Number Windward/Leeward High634.00.9463
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1654.41105.4838.3698.4617.9578.4548.7501.2485.2
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance655.70.9150
Triple Number Coastal/Long Distance Low776.50.7727
Triple Number Coastal/Long Distance Medium599.41.0010
Triple Number Coastal/Long Distance High538.71.1138
Triple Number Windward/Leeward Low999.20.6005
Triple Number Windward/Leeward Medium729.00.8231
Triple Number Windward/Leeward High634.00.9463
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1654.41105.4838.3698.4617.9578.4548.7501.2485.2
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low776.5
Triple Number Coastal/Long Distance Medium599.4
Triple Number Coastal/Long Distance High538.7
Triple Number Windward/Leeward Low999.2
Triple Number Windward/Leeward Medium729.0
Triple Number Windward/Leeward High634.0
Predominantly Upwind651.9
Predominantly Downwind612.3
Predominantly Reaching589.5
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance655.70.9150
Triple Number Coastal/Long Distance Low776.50.7727
Triple Number Coastal/Long Distance Medium599.41.0010
Triple Number Coastal/Long Distance High538.71.1138
Triple Number Windward/Leeward Low999.20.6005
Triple Number Windward/Leeward Medium729.00.8231
Triple Number Windward/Leeward High634.00.9463
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1654.41105.4838.3698.4617.9578.4548.7501.2485.2
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7727
Triple Number Coastal/Long Distance Medium1.0010
Triple Number Coastal/Long Distance High1.1138
Triple Number Windward/Leeward Low0.6005
Triple Number Windward/Leeward Medium0.8231
Triple Number Windward/Leeward High0.9463
Coastal/Long Distance0.9150
Predominantly Upwind0.9204
Predominantly Downwind0.9798
For information
General Purpose Handicap (GPH)677.7
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)0.9939
Distanseseilas Trippeltall svak vind0.7727
Distanseseilas Trippeltall mellomvind1.0010
Distanseseilas Trippeltall sterk vind1.1138
Pølsebane Trippeltall svak vind0.6005
Pølsebane Trippeltall mellomvind0.8231
Pølsebane Trippeltall sterk vind0.9463
Motvind Singeltall0.9204
Medvind Singeltall0.9798
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low776.50.7727
Triple Number Coastal/Long Distance Medium599.41.0010
Triple Number Coastal/Long Distance High538.71.1138
Triple Number Windward/Leeward Low999.20.6005
Triple Number Windward/Leeward Medium729.00.8231
Triple Number Windward/Leeward High634.00.9463
Coastal/Long Distance655.70.9150
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind651.90.9204
Predominantly Downwind612.30.9798
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore603.70.9939
Cape Doctor Coastal511.41.1732
Triple Number Coastal/Long Distance Low776.50.7727
Triple Number Coastal/Long Distance Medium599.41.0010
Triple Number Coastal/Long Distance High538.71.1138
Triple Number Windward/Leeward Low999.20.6005
Triple Number Windward/Leeward Medium729.00.8231
Triple Number Windward/Leeward High634.00.9463
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7727
Triple Number Coastal/Long Distance Medium1.0010
Triple Number Coastal/Long Distance High1.1138
Triple Number Windward/Leeward Low0.6005
Triple Number Windward/Leeward Medium0.8231
Triple Number Windward/Leeward High0.9463
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7727
Triple Number Coastal/Long Distance Medium1.0010
Triple Number Coastal/Long Distance High1.1138
Triple Number Windward/Leeward Low0.6005
Triple Number Windward/Leeward Medium0.8231
Triple Number Windward/Leeward High0.9463
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance655.70.9150
Triple Number Coastal/Long Distance Low776.50.7727
Triple Number Coastal/Long Distance Medium599.41.0010
Triple Number Coastal/Long Distance High538.71.1138
Triple Number Windward/Leeward Low999.20.6005
Triple Number Windward/Leeward Medium729.00.8231
Triple Number Windward/Leeward High634.00.9463
Predominantly Upwind651.90.9204
Predominantly Downwind612.30.9798
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1654.41105.4838.3698.4617.9578.4548.7501.2485.2
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance655.70.9150
Triple Number Coastal/Long Distance Low776.50.7727
Triple Number Coastal/Long Distance Medium599.41.0010
Triple Number Coastal/Long Distance High538.71.1138
Triple Number Windward/Leeward Low999.20.6005
Triple Number Windward/Leeward Medium729.00.8231
Triple Number Windward/Leeward High634.00.9463
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1654.41105.4838.3698.4617.9578.4548.7501.2485.2
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low776.50.7727
Triple Number AP Medium599.51.0008
Triple Number AP High538.71.1138
Triple Number Windward/Leeward Low1043.30.5751
Triple Number Windward/Leeward Medium729.00.8231
Triple Number Windward/Leeward High634.00.9463
Single Number Predominant Upwind678.30.8846
Single Number Predominant Reaching603.80.9938
Single Number Predominant Downwind640.10.9374
Predominant Upwind - Low934.70.6419
Predominant Upwind - Low/Med715.60.8384
Predominant Upwind - Medium630.50.9516
Predominant Upwind - Med/High589.91.0172
Predominant Upwind - High574.41.0446
Predominant Downwind Low939.60.6386
Predominant Downwind Low/Med693.20.8655
Predominant Downwind Medium589.71.0175
Predominant Downwind Med/High529.71.1326
Predominant Downwind High495.91.2100
Predominant Reaching Low835.80.7178
Predominant Reaching Low/Med638.70.9395
Predominant Reaching Medium563.41.0650
Predominant Reaching Med/High522.31.1488
Predominant Reaching High497.51.2060
SA/DSPL Upwind20.74SA/DSPL Downwind36.65
Scoring OptionTODTOT
5-Band Windward/Leeward Low1166.50.5144
5-Band Windward/Leeward Low/Med852.10.7042
5-Band Windward/Leeward Medium714.90.8393
5-Band Windward/Leeward Med/High642.30.9342
5-Band Windward/Leeward High615.20.9753
Windward/Leeward 60-40 Low1170.10.5128
Windward/Leeward 60-40 Low/Med862.00.6961
Windward/Leeward 60-40 Medium729.80.8222
Windward/Leeward 60-40 Med/High662.30.9059
Windward/Leeward 60-40 High639.30.9385
5-Band AP Low857.60.6996
5-Band AP Low/Med678.10.8848
5-Band AP Medium591.01.0152
5-Band AP Med/High545.01.1010
5-Band AP High522.91.1475
5-Band SF Bay Tour - Low1005.10.5970
5-Band SF Bay Tour - Low/Med815.80.7355
5-Band SF Bay Tour - Medium693.20.8656
5-Band SF Bay Tour - Med/High630.00.9524
5-Band SF Bay Tour - High604.80.9920
Chicago-Mac Upwind0.8575
Chicago-Mac All Purpose0.8833
Chicago-Mac Downwind0.9041
Bayview-Mac Cove Island0.6463
Bayview-Mac Shore0.6511
Harvest Moon Regatta529.71.1328
Club Certificate2025
KAIESP-3045_C
RFEV
c/ Gamazo sn
39004 Santander – España
crucero@rfev.es
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassDEHLER 34Measurement04/02/2004HINPlan reviewHull constructionSolidCarbon rudderNoLight stanchionsNoTrim tabNo
LOA10.112Max. Beam3.406Draft1.782Displacement4,801Wetted area22.30IMS L8.613LSM08.417Acc. length9.904Sink (kg/mm) 16.18
VCGD0.078VCGM0.039RM Rated (kg·m) 98.3Limit of positive stability(°) N/AStability IndexN/ADefault crew weight538Declared crew weight540
PROPELLER
Propeller TypeFolding 2 blades
InstallationShaft exposedTwin screwNoHydro generatorNo
PRD0.440PBWPIPA0.0039
PSD0.025PHD0.054PHL0.126
PSA19.2°ESL0.905
ST10.029ST20.112ST30.112
ST40.050ST50.235
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerNoMainsail furlerNoArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0Checkstays0Spreaders1Rotating mastNo
P12.170IG12.141ISP12.141MDT10.090MDL10.180MDT20.090MDL20.180TLMW0.180GO0.180
E4.150J3.530BAS1.461FSD0.025SFJSPL3.590WPLTPSBD0.180MWTMCG
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodRM entered directlyRM entered100.0Flotation Date01/01/2010
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Club Certificate2025
KAIESP-3045_C
RFEV
c/ Gamazo sn
39004 Santander – España
crucero@rfev.es
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateCommentORC0.160.871.562.683.5230.18* Copied from legacy *
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment0020.060.631.232.513.865.2111.38NoNo 29.1516/12/2015
SYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLAreaMeas.DateCommentORC13.0613.0613.066.906.7074.66* Copied from legacy *
CRUISER/RACER REQUIREMENTS*
Accommodation length9.9 mTable area0.44 m²Headroom1.70 mMinimum number of berths4Personal gear stowage0.16 m³Fresh water capacity78 lMinimum number of seats in cockpit4Food stowage0.24 m³Fuel capacity48 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.