Club Certificate2025
COCOTUR
Turkiye
Sailing
Federation
www.tyf.org.tr/
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 Angles48.9°48.9°47.5°46.3°45.1°44.1°43.6°43.9°45.4°
Beat VMG1.852.683.424.014.474.845.075.175.02
52°3.004.305.446.286.927.387.687.877.78
60°3.344.725.866.697.317.748.028.268.25
75°3.554.976.136.997.628.048.338.708.85
90°3.835.386.667.608.188.508.678.929.28
110°3.955.566.917.868.438.859.239.8010.16
120°3.835.406.727.718.348.789.2010.0210.76
135°3.334.796.097.157.938.458.879.7310.67
150°2.754.035.226.257.127.808.288.999.70
Run VMG2.383.494.525.416.166.767.237.998.59
Gybe Angles143.1°143.1°146.2°147.6°148.5°150.6°154.8°161.7°161.5°
APH ToD:571.6CDL: 9.825APH ToT: 1.0497CertNo:
BOAT
ClassBAVARIA CR 46DesignerFarrBuilderBavariaAge date01/2022Series date01/2013Offset fileBAVARIA46C-SD.offData fileTUR COCO
HULL
Length Overall13.600 mMaximum Beam4.352 mDraft1.755 mDisplacement12,700 kgDLR6.2378IMS DivisionCruiser/RacerDynamic Allowance0.400%Age Allowance0.390%
PROPELLER
InstallationStrutTypeSolid 3 bladesDiameter0.500m
CREW
Maximum weight1,020 kg(declared)Minimum weight867 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail45.0944.85Headsail Luffed47.9047.90Headsail FlyingSymmetricAsymmetric147.48147.48 (All asymmetric spinnakers with SHW/SFL > 85%)
STORM SAIL AREAS (m²)
Trysail16.46Storm Jib16.03Heavy Weather Jib43.26
SAIL LIMITS
Headsails6
✱ One set on the forestay
Spinnakers5
STABILITY
Righting MomentN/AStability IndexN/A
COMMENTS
IRC STANDART 28Apr2025
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
COCOTUR
Turkiye
Sailing
Federation
www.tyf.org.tr/
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 VMG1943.31342.71051.4897.7804.6744.3709.8696.6717.5
52°1200.5836.3661.6573.4520.5487.6468.8457.4462.7
60°1078.9763.5613.9538.5492.8465.3448.8436.0436.3
75°1015.3724.9586.9514.7472.3447.8432.4413.9407.0
90°939.3669.5540.7473.6440.0423.8415.3403.8388.1
110°911.7647.2521.2457.8427.0406.9390.1367.3354.2
120°940.1666.7535.5466.7431.9410.0391.2359.4334.6
135°1080.2751.3591.1503.8453.9426.0405.6370.0337.3
150°1311.4894.3689.5576.0505.7461.6434.9400.4371.0
Run VMG1514.41032.7796.2665.1584.0532.8498.1450.8419.2
Selected Courses
Windward / Leeward1728.71187.7923.8781.4694.3638.6603.9573.7568.3
All purpose1283.1892.3703.0602.5543.8507.6484.6461.6452.8
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward733.10.8184
All purpose571.61.0497
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low797.70.7522
Triple Number Coastal/Long Distance Medium567.61.0571
Triple Number Coastal/Long Distance High481.71.2455
Triple Number Windward/Leeward Low1055.80.5683
Triple Number Windward/Leeward Medium728.50.8236
Triple Number Windward/Leeward High601.30.9979
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance630.10.9522
Triple Number Coastal/Long Distance Low797.70.7522
Triple Number Coastal/Long Distance Medium567.61.0571
Triple Number Coastal/Long Distance High481.71.2455
Triple Number Windward/Leeward Low1055.80.5683
Triple Number Windward/Leeward Medium728.50.8236
Triple Number Windward/Leeward High601.30.9979
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1821.11172.2858.0690.7587.5528.1487.3434.4421.1
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.6723
Downwind "popa"0.9211
70% up, 30% down "Ilhabela"0.7316
30% up, 70% down "Ilhabela-inverso"0.8291
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low797.70.7522
Triple Number Coastal/Long Distance Medium567.61.0571
Triple Number Coastal/Long Distance High481.71.2455
Triple Number Windward/Leeward Low1055.80.5683
Triple Number Windward/Leeward Medium728.50.8236
Triple Number Windward/Leeward High601.30.9979
Predominantly Upwind638.90.9391
Predominantly Downwind568.81.0549
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low797.70.7522
Triple Number AP Medium567.71.0570
Triple Number AP High481.71.2455
Triple Number Windward/Leeward Low1108.80.5411
Triple Number Windward/Leeward Medium728.50.8236
Triple Number Windward/Leeward High601.30.9979
Single Number Predominant Upwind674.70.8893
Single Number Predominant Reaching561.11.0692
Single Number Predominant Downwind598.71.0021
Predominant Upwind - Low1035.40.5795
Predominant Upwind - Low/Med737.70.8134
Predominant Upwind - Medium610.30.9831
Predominant Upwind - Med/High539.71.1117
Predominant Upwind - High518.81.1565
Predominant Downwind Low936.40.6408
Predominant Downwind Low/Med661.10.9076
Predominant Downwind Medium541.51.1080
Predominant Downwind Med/High471.91.2715
Predominant Downwind High438.41.3686
Predominant Reaching Low850.10.7058
Predominant Reaching Low/Med610.80.9823
Predominant Reaching Medium510.31.1759
Predominant Reaching Med/High455.81.3165
Predominant Reaching High432.21.3881
SA/DSPL Upwind16.94SA/DSPL Downwind35.08
Scoring OptionTODTOT
5-Band Windward/Leeward Low1257.00.4773
5-Band Windward/Leeward Low/Med878.60.6829
5-Band Windward/Leeward Medium711.00.8439
5-Band Windward/Leeward Med/High612.30.9799
5-Band Windward/Leeward High578.01.0380
Windward/Leeward 60-40 Low1289.60.4653
Windward/Leeward 60-40 Low/Med903.60.6640
Windward/Leeward 60-40 Medium733.30.8182
Windward/Leeward 60-40 Med/High634.10.9462
Windward/Leeward 60-40 High602.90.9952
5-Band AP Low879.50.6822
5-Band AP Low/Med672.00.8929
5-Band AP Medium555.81.0795
5-Band AP Med/High489.61.2255
5-Band AP High464.11.2929
5-Band SF Bay Tour - Low1077.10.5570
5-Band SF Bay Tour - Low/Med841.90.7127
5-Band SF Bay Tour - Medium684.60.8764
5-Band SF Bay Tour - Med/High593.01.0118
5-Band SF Bay Tour - High561.91.0678
Chicago-Mac Upwind0.8491
Chicago-Mac All Purpose0.9061
Chicago-Mac Downwind0.9585
Bayview-Mac Cove Island0.6192
Bayview-Mac Shore0.6228
Harvest Moon Regatta469.91.2770
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance630.10.9522
Triple Number Coastal/Long Distance Low797.70.7522
Triple Number Coastal/Long Distance Medium567.61.0571
Triple Number Coastal/Long Distance High481.71.2455
Triple Number Windward/Leeward Low1055.80.5683
Triple Number Windward/Leeward Medium728.50.8236
Triple Number Windward/Leeward High601.30.9979
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1821.11172.2858.0690.7587.5528.1487.3434.4421.1
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance630.10.9522
Triple Number Coastal/Long Distance Low797.70.7522
Triple Number Coastal/Long Distance Medium567.61.0571
Triple Number Coastal/Long Distance High481.71.2455
Triple Number Windward/Leeward Low1055.80.5683
Triple Number Windward/Leeward Medium728.50.8236
Triple Number Windward/Leeward High601.30.9979
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1821.11172.2858.0690.7587.5528.1487.3434.4421.1
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance630.1
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1821.11172.2858.0690.7587.5528.1487.3434.4421.1
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low797.70.7522
Triple Number Coastal/Long Distance Medium567.61.0571
Triple Number Coastal/Long Distance High481.71.2455
Triple Number Windward/Leeward Low1055.80.5683
Triple Number Windward/Leeward Medium728.50.8236
Triple Number Windward/Leeward High601.30.9979
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating630.10.9522
FinRating, kevyt tuuli1225.70.8159
FinRating, kova tuuli465.91.0732
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low797.70.7522
Triple Number Coastal/Long Distance Medium567.61.0571
Triple Number Coastal/Long Distance High481.71.2455
Triple Number Windward/Leeward Low1055.80.5683
Triple Number Windward/Leeward Medium728.50.8236
Triple Number Windward/Leeward High601.30.9979
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.9522
Triple Number Coastal/Long Distance Low0.7522
Triple Number Coastal/Long Distance Medium1.0571
Triple Number Coastal/Long Distance High1.2455
Triple Number Windward/Leeward Low0.5683
Triple Number Windward/Leeward Medium0.8236
Triple Number Windward/Leeward High0.9979
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1821.11172.2858.0690.7587.5528.1487.3434.4421.1
For information
General Purpose Handicap (GPH)653.9
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance630.10.9522
Triple Number Coastal/Long Distance Low797.70.7522
Triple Number Coastal/Long Distance Medium567.61.0571
Triple Number Coastal/Long Distance High481.71.2455
Triple Number Windward/Leeward Low1055.80.5683
Triple Number Windward/Leeward Medium728.50.8236
Triple Number Windward/Leeward High601.30.9979
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1821.11172.2858.0690.7587.5528.1487.3434.4421.1
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low797.70.7522
Triple Number Coastal/Long Distance Medium567.61.0571
Triple Number Coastal/Long Distance High481.71.2455
Triple Number Windward/Leeward Low1055.80.5683
Triple Number Windward/Leeward Medium728.50.8236
Triple Number Windward/Leeward High601.30.9979
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance630.10.9522
Triple Number Coastal/Long Distance Low797.70.7522
Triple Number Coastal/Long Distance Medium567.61.0571
Triple Number Coastal/Long Distance High481.71.2455
Triple Number Windward/Leeward Low1055.80.5683
Triple Number Windward/Leeward Medium728.50.8236
Triple Number Windward/Leeward High601.30.9979
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1821.11172.2858.0690.7587.5528.1487.3434.4421.1
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance630.10.9522
Triple Number Coastal/Long Distance Low797.70.7522
Triple Number Coastal/Long Distance Medium567.61.0571
Triple Number Coastal/Long Distance High481.71.2455
Triple Number Windward/Leeward Low1055.80.5683
Triple Number Windward/Leeward Medium728.50.8236
Triple Number Windward/Leeward High601.30.9979
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1821.11172.2858.0690.7587.5528.1487.3434.4421.1
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low797.7
Triple Number Coastal/Long Distance Medium567.6
Triple Number Coastal/Long Distance High481.7
Triple Number Windward/Leeward Low1055.8
Triple Number Windward/Leeward Medium728.5
Triple Number Windward/Leeward High601.3
Predominantly Upwind638.9
Predominantly Downwind568.8
Predominantly Reaching541.4
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance630.10.9522
Triple Number Coastal/Long Distance Low797.70.7522
Triple Number Coastal/Long Distance Medium567.61.0571
Triple Number Coastal/Long Distance High481.71.2455
Triple Number Windward/Leeward Low1055.80.5683
Triple Number Windward/Leeward Medium728.50.8236
Triple Number Windward/Leeward High601.30.9979
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1821.11172.2858.0690.7587.5528.1487.3434.4421.1
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7522
Triple Number Coastal/Long Distance Medium1.0571
Triple Number Coastal/Long Distance High1.2455
Triple Number Windward/Leeward Low0.5683
Triple Number Windward/Leeward Medium0.8236
Triple Number Windward/Leeward High0.9979
Coastal/Long Distance0.9522
Predominantly Upwind0.9391
Predominantly Downwind1.0549
For information
General Purpose Handicap (GPH)653.9
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)1.0497
Distanseseilas Trippeltall svak vind0.7522
Distanseseilas Trippeltall mellomvind1.0571
Distanseseilas Trippeltall sterk vind1.2455
Pølsebane Trippeltall svak vind0.5683
Pølsebane Trippeltall mellomvind0.8236
Pølsebane Trippeltall sterk vind0.9979
Motvind Singeltall0.9391
Medvind Singeltall1.0549
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low797.70.7522
Triple Number Coastal/Long Distance Medium567.61.0571
Triple Number Coastal/Long Distance High481.71.2455
Triple Number Windward/Leeward Low1055.80.5683
Triple Number Windward/Leeward Medium728.50.8236
Triple Number Windward/Leeward High601.30.9979
Coastal/Long Distance630.10.9522
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind638.90.9391
Predominantly Downwind568.81.0549
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore570.01.0527
Cape Doctor Coastal455.51.3173
Triple Number Coastal/Long Distance Low797.70.7522
Triple Number Coastal/Long Distance Medium567.61.0571
Triple Number Coastal/Long Distance High481.71.2455
Triple Number Windward/Leeward Low1055.80.5683
Triple Number Windward/Leeward Medium728.50.8236
Triple Number Windward/Leeward High601.30.9979
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7522
Triple Number Coastal/Long Distance Medium1.0571
Triple Number Coastal/Long Distance High1.2455
Triple Number Windward/Leeward Low0.5683
Triple Number Windward/Leeward Medium0.8236
Triple Number Windward/Leeward High0.9979
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7522
Triple Number Coastal/Long Distance Medium1.0571
Triple Number Coastal/Long Distance High1.2455
Triple Number Windward/Leeward Low0.5683
Triple Number Windward/Leeward Medium0.8236
Triple Number Windward/Leeward High0.9979
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance630.10.9522
Triple Number Coastal/Long Distance Low797.70.7522
Triple Number Coastal/Long Distance Medium567.61.0571
Triple Number Coastal/Long Distance High481.71.2455
Triple Number Windward/Leeward Low1055.80.5683
Triple Number Windward/Leeward Medium728.50.8236
Triple Number Windward/Leeward High601.30.9979
Predominantly Upwind638.90.9391
Predominantly Downwind568.81.0549
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1821.11172.2858.0690.7587.5528.1487.3434.4421.1
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance630.10.9522
Triple Number Coastal/Long Distance Low797.70.7522
Triple Number Coastal/Long Distance Medium567.61.0571
Triple Number Coastal/Long Distance High481.71.2455
Triple Number Windward/Leeward Low1055.80.5683
Triple Number Windward/Leeward Medium728.50.8236
Triple Number Windward/Leeward High601.30.9979
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1821.11172.2858.0690.7587.5528.1487.3434.4421.1
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low797.70.7522
Triple Number AP Medium567.71.0570
Triple Number AP High481.71.2455
Triple Number Windward/Leeward Low1108.80.5411
Triple Number Windward/Leeward Medium728.50.8236
Triple Number Windward/Leeward High601.30.9979
Single Number Predominant Upwind674.70.8893
Single Number Predominant Reaching561.11.0692
Single Number Predominant Downwind598.71.0021
Predominant Upwind - Low1035.40.5795
Predominant Upwind - Low/Med737.70.8134
Predominant Upwind - Medium610.30.9831
Predominant Upwind - Med/High539.71.1117
Predominant Upwind - High518.81.1565
Predominant Downwind Low936.40.6408
Predominant Downwind Low/Med661.10.9076
Predominant Downwind Medium541.51.1080
Predominant Downwind Med/High471.91.2715
Predominant Downwind High438.41.3686
Predominant Reaching Low850.10.7058
Predominant Reaching Low/Med610.80.9823
Predominant Reaching Medium510.31.1759
Predominant Reaching Med/High455.81.3165
Predominant Reaching High432.21.3881
SA/DSPL Upwind16.94SA/DSPL Downwind35.08
Scoring OptionTODTOT
5-Band Windward/Leeward Low1257.00.4773
5-Band Windward/Leeward Low/Med878.60.6829
5-Band Windward/Leeward Medium711.00.8439
5-Band Windward/Leeward Med/High612.30.9799
5-Band Windward/Leeward High578.01.0380
Windward/Leeward 60-40 Low1289.60.4653
Windward/Leeward 60-40 Low/Med903.60.6640
Windward/Leeward 60-40 Medium733.30.8182
Windward/Leeward 60-40 Med/High634.10.9462
Windward/Leeward 60-40 High602.90.9952
5-Band AP Low879.50.6822
5-Band AP Low/Med672.00.8929
5-Band AP Medium555.81.0795
5-Band AP Med/High489.61.2255
5-Band AP High464.11.2929
5-Band SF Bay Tour - Low1077.10.5570
5-Band SF Bay Tour - Low/Med841.90.7127
5-Band SF Bay Tour - Medium684.60.8764
5-Band SF Bay Tour - Med/High593.01.0118
5-Band SF Bay Tour - High561.91.0678
Chicago-Mac Upwind0.8491
Chicago-Mac All Purpose0.9061
Chicago-Mac Downwind0.9585
Bayview-Mac Cove Island0.6192
Bayview-Mac Shore0.6228
Harvest Moon Regatta469.91.2770
Club Certificate2025
COCOTUR
Turkiye
Sailing
Federation
www.tyf.org.tr/
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassBAVARIA CR 46MeasurementHINPlan reviewHull constructionSolidCarbon rudderNoLight stanchionsNoTrim tabNo
LOA13.600Max. Beam4.352Draft1.755Displacement12,700Wetted area46.38IMS L12.762LSM012.673Acc. length13.600Sink (kg/mm) 34.57
VCGD0.327VCGM0.321RM Rated (kg·m) 370.5Limit of positive stability(°) N/AStability IndexN/ADefault crew weight965Declared crew weight1,020
PROPELLER
Propeller TypeSolid 3 blades
InstallationStrutTwin screwNoHydro generatorNo
PRD0.500PBWPIPA0.0308
EDL2.100ST10.065ST20.180
ST30.180ST40.110ST50.265
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerYesMainsail furlerIn mastArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders2Rotating mastNo
P16.940IG17.900ISP18.820MDT10.146MDL10.289MDT20.000MDL20.000TL0.000MW0.000GO0.000
E5.550J5.510BAS1.768FSD0.042SFJ0.000SPL0.000WPLTPS5.920BD0.000MWT0.00MCG0.000
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodRM estimatedFlotation Date04/08/2025
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Club Certificate2025
COCOTUR
Turkiye
Sailing
Federation
www.tyf.org.tr/
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment00.621.232.574.0045.09IRC STANDART 28Apr25
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment00.611.212.604.285.9517.14NoNo 47.90IRC STANDART 28Apr25
ASYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLRatioAreaMeas.DateComment019.7216.8618.299.649.8298%147.48IRC STANDART 28Apr25
CRUISER/RACER REQUIREMENTS*
Accommodation length13.6 mTable area0.66 m²Headroom1.87 mMinimum number of berths6Personal gear stowage0.24 m³Fresh water capacity228 lMinimum number of seats in cockpit6Food stowage0.36 m³Fuel capacity122 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.