Double HandedClub Certificate2025
MILLAFIN 1101
Avomeripurjehtijat ry
c/o Mainoskauppa Oy
Melkonkatu 16 B
00210 HELSINKI
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°40.5°39.4°39.0°39.1°39.3°40.4°43.4°
Beat VMG2.273.103.704.014.124.174.184.133.87
52°3.524.685.425.775.895.955.996.005.87
60°3.754.915.615.936.076.146.186.216.15
75°3.915.075.756.086.286.406.486.576.57
90°3.805.035.806.136.376.586.746.937.02
110°3.855.115.926.336.636.857.017.287.42
120°3.674.955.836.296.656.997.297.708.09
135°3.204.435.406.076.476.847.248.299.87
150°2.583.714.745.596.156.526.897.769.66
Run VMG2.233.224.114.875.546.016.377.058.36
Gybe Angles146.9°146.9°151.4°154.7°163.9°172.7°177.2°176.8°147.7°
APH ToD:651.5CDL: 6.362APH ToT: 0.9209CertNo:
BOAT
ClassALBIN EXPRESSDesignerPETER NORLINBuilderALBIN MARINAge date05/1988Series date05/1988Offset fileEXPRESS.OFFData fileL-1101
HULL
Length Overall7.798 mMaximum Beam2.524 mDraft1.436 mDisplacement1,842 kgDLR6.2140IMS DivisionSportboatDynamic Allowance0.180%Age Allowance0.487%
PROPELLER
InstallationNo PropellerTypeN/ADiameterN/A
CREW
Maximum weight200 kg(declared)Minimum weight120 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail19.0819.49Headsail Luffed15.4315.43Headsail FlyingSymmetric43.0943.09Asymmetric
STORM SAIL AREAS (m²)
Trysail5.57Storm Jib4.03Heavy Weather Jib10.87
SAIL LIMITS
Headsails5Spinnakers4
STABILITY
Righting MomentN/AStability IndexN/A
COMMENTS
EXPRESS STAND DATA SERIES 1979
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.
Double HandedClub Certificate2025
MILLAFIN 1101
Avomeripurjehtijat ry
c/o Mainoskauppa Oy
Melkonkatu 16 B
00210 HELSINKI
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 VMG1584.71162.1973.4896.7873.0863.8860.3871.5929.5
52°1022.5769.7663.9624.4611.1604.6601.0600.1613.8
60°960.7733.4642.1607.0593.2586.5582.2579.4585.8
75°921.4709.5626.6592.0573.4562.7555.8548.0547.9
90°947.6715.3620.3587.2565.3547.2534.5519.2512.5
110°934.4704.2608.1569.0543.0525.8513.6494.3485.5
120°980.3727.4617.9572.8541.7515.4494.2467.4445.1
135°1123.7812.6666.9593.5556.8526.0497.2434.2364.9
150°1395.4969.2759.8644.4585.8552.2522.7463.7372.7
Run VMG1615.61119.1876.4739.3649.7599.2565.1510.5430.4
Selected Courses
Windward / Leeward1598.21140.6924.9818.0761.3731.5712.7691.0680.0
All purpose1201.5879.2733.4666.6632.5612.4598.0577.5565.4
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward793.60.7560
All purpose651.50.9209
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low806.20.7442
Triple Number Coastal/Long Distance Medium647.20.9270
Triple Number Coastal/Long Distance High593.91.0102
Triple Number Windward/Leeward Low1032.70.5810
Triple Number Windward/Leeward Medium786.40.7630
Triple Number Windward/Leeward High709.30.8459
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance705.60.8504
Triple Number Coastal/Long Distance Low806.20.7442
Triple Number Coastal/Long Distance Medium647.20.9270
Triple Number Coastal/Long Distance High593.91.0102
Triple Number Windward/Leeward Low1032.70.5810
Triple Number Windward/Leeward Medium786.40.7630
Triple Number Windward/Leeward High709.30.8459
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1693.71138.5871.9743.6674.0634.9602.4550.1533.5
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.6461
Downwind "popa"0.8302
70% up, 30% down "Ilhabela"0.6921
30% up, 70% down "Ilhabela-inverso"0.7648
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low806.20.7442
Triple Number Coastal/Long Distance Medium647.20.9270
Triple Number Coastal/Long Distance High593.91.0102
Triple Number Windward/Leeward Low1032.70.5810
Triple Number Windward/Leeward Medium786.40.7630
Triple Number Windward/Leeward High709.30.8459
Predominantly Upwind709.70.8455
Predominantly Downwind648.10.9258
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low806.30.7442
Triple Number AP Medium647.30.9269
Triple Number AP High593.91.0102
Triple Number Windward/Leeward Low1078.80.5562
Triple Number Windward/Leeward Medium786.40.7630
Triple Number Windward/Leeward High709.30.8459
Single Number Predominant Upwind736.70.8144
Single Number Predominant Reaching644.20.9314
Single Number Predominant Downwind675.10.8887
Predominant Upwind - Low965.80.6213
Predominant Upwind - Low/Med760.30.7892
Predominant Upwind - Medium692.20.8668
Predominant Upwind - Med/High661.80.9066
Predominant Upwind - High652.60.9194
Predominant Downwind Low967.60.6201
Predominant Downwind Low/Med726.70.8257
Predominant Downwind Medium628.30.9549
Predominant Downwind Med/High566.61.0589
Predominant Downwind High524.01.1451
Predominant Reaching Low861.40.6966
Predominant Reaching Low/Med676.00.8876
Predominant Reaching Medium608.00.9869
Predominant Reaching Med/High565.91.0602
Predominant Reaching High538.51.1143
SA/DSPL Upwind22.92SA/DSPL Downwind41.29
Scoring OptionTODTOT
5-Band Windward/Leeward Low1201.60.4993
5-Band Windward/Leeward Low/Med894.80.6705
5-Band Windward/Leeward Medium775.30.7739
5-Band Windward/Leeward Med/High716.30.8376
5-Band Windward/Leeward High692.90.8660
Windward/Leeward 60-40 Low1205.40.4978
Windward/Leeward 60-40 Low/Med907.70.6610
Windward/Leeward 60-40 Medium796.80.7530
Windward/Leeward 60-40 Med/High745.80.8045
Windward/Leeward 60-40 High730.20.8217
5-Band AP Low884.80.6781
5-Band AP Low/Med716.40.8375
5-Band AP Medium640.30.9370
5-Band AP Med/High599.91.0002
5-Band AP High579.01.0363
5-Band SF Bay Tour - Low1036.90.5787
5-Band SF Bay Tour - Low/Med858.50.6989
5-Band SF Bay Tour - Medium753.90.7958
5-Band SF Bay Tour - Med/High702.70.8538
5-Band SF Bay Tour - High680.90.8811
Chicago-Mac Upwind0.7949
Chicago-Mac All Purpose0.8283
Chicago-Mac Downwind0.8587
Bayview-Mac Cove Island0.6199
Bayview-Mac Shore0.6245
Harvest Moon Regatta565.51.0610
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance705.60.8504
Triple Number Coastal/Long Distance Low806.20.7442
Triple Number Coastal/Long Distance Medium647.20.9270
Triple Number Coastal/Long Distance High593.91.0102
Triple Number Windward/Leeward Low1032.70.5810
Triple Number Windward/Leeward Medium786.40.7630
Triple Number Windward/Leeward High709.30.8459
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1693.71138.5871.9743.6674.0634.9602.4550.1533.5
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance705.60.8504
Triple Number Coastal/Long Distance Low806.20.7442
Triple Number Coastal/Long Distance Medium647.20.9270
Triple Number Coastal/Long Distance High593.91.0102
Triple Number Windward/Leeward Low1032.70.5810
Triple Number Windward/Leeward Medium786.40.7630
Triple Number Windward/Leeward High709.30.8459
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1693.71138.5871.9743.6674.0634.9602.4550.1533.5
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance705.6
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1693.71138.5871.9743.6674.0634.9602.4550.1533.5
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low806.20.7442
Triple Number Coastal/Long Distance Medium647.20.9270
Triple Number Coastal/Long Distance High593.91.0102
Triple Number Windward/Leeward Low1032.70.5810
Triple Number Windward/Leeward Medium786.40.7630
Triple Number Windward/Leeward High709.30.8459
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating705.60.8504
FinRating, kevyt tuuli1179.60.8478
FinRating, kova tuuli581.90.8593
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low806.20.7442
Triple Number Coastal/Long Distance Medium647.20.9270
Triple Number Coastal/Long Distance High593.91.0102
Triple Number Windward/Leeward Low1032.70.5810
Triple Number Windward/Leeward Medium786.40.7630
Triple Number Windward/Leeward High709.30.8459
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.8504
Triple Number Coastal/Long Distance Low0.7442
Triple Number Coastal/Long Distance Medium0.9270
Triple Number Coastal/Long Distance High1.0102
Triple Number Windward/Leeward Low0.5810
Triple Number Windward/Leeward Medium0.7630
Triple Number Windward/Leeward High0.8459
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1693.71138.5871.9743.6674.0634.9602.4550.1533.5
For information
General Purpose Handicap (GPH)724.3
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance705.60.8504
Triple Number Coastal/Long Distance Low806.20.7442
Triple Number Coastal/Long Distance Medium647.20.9270
Triple Number Coastal/Long Distance High593.91.0102
Triple Number Windward/Leeward Low1032.70.5810
Triple Number Windward/Leeward Medium786.40.7630
Triple Number Windward/Leeward High709.30.8459
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1693.71138.5871.9743.6674.0634.9602.4550.1533.5
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low806.20.7442
Triple Number Coastal/Long Distance Medium647.20.9270
Triple Number Coastal/Long Distance High593.91.0102
Triple Number Windward/Leeward Low1032.70.5810
Triple Number Windward/Leeward Medium786.40.7630
Triple Number Windward/Leeward High709.30.8459
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance705.60.8504
Triple Number Coastal/Long Distance Low806.20.7442
Triple Number Coastal/Long Distance Medium647.20.9270
Triple Number Coastal/Long Distance High593.91.0102
Triple Number Windward/Leeward Low1032.70.5810
Triple Number Windward/Leeward Medium786.40.7630
Triple Number Windward/Leeward High709.30.8459
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1693.71138.5871.9743.6674.0634.9602.4550.1533.5
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance705.60.8504
Triple Number Coastal/Long Distance Low806.20.7442
Triple Number Coastal/Long Distance Medium647.20.9270
Triple Number Coastal/Long Distance High593.91.0102
Triple Number Windward/Leeward Low1032.70.5810
Triple Number Windward/Leeward Medium786.40.7630
Triple Number Windward/Leeward High709.30.8459
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1693.71138.5871.9743.6674.0634.9602.4550.1533.5
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low806.2
Triple Number Coastal/Long Distance Medium647.2
Triple Number Coastal/Long Distance High593.9
Triple Number Windward/Leeward Low1032.7
Triple Number Windward/Leeward Medium786.4
Triple Number Windward/Leeward High709.3
Predominantly Upwind709.7
Predominantly Downwind648.1
Predominantly Reaching628.0
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance705.60.8504
Triple Number Coastal/Long Distance Low806.20.7442
Triple Number Coastal/Long Distance Medium647.20.9270
Triple Number Coastal/Long Distance High593.91.0102
Triple Number Windward/Leeward Low1032.70.5810
Triple Number Windward/Leeward Medium786.40.7630
Triple Number Windward/Leeward High709.30.8459
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1693.71138.5871.9743.6674.0634.9602.4550.1533.5
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7442
Triple Number Coastal/Long Distance Medium0.9270
Triple Number Coastal/Long Distance High1.0102
Triple Number Windward/Leeward Low0.5810
Triple Number Windward/Leeward Medium0.7630
Triple Number Windward/Leeward High0.8459
Coastal/Long Distance0.8504
Predominantly Upwind0.8455
Predominantly Downwind0.9258
For information
General Purpose Handicap (GPH)724.3
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)0.9209
Distanseseilas Trippeltall svak vind0.7442
Distanseseilas Trippeltall mellomvind0.9270
Distanseseilas Trippeltall sterk vind1.0102
Pølsebane Trippeltall svak vind0.5810
Pølsebane Trippeltall mellomvind0.7630
Pølsebane Trippeltall sterk vind0.8459
Motvind Singeltall0.8455
Medvind Singeltall0.9258
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low806.20.7442
Triple Number Coastal/Long Distance Medium647.20.9270
Triple Number Coastal/Long Distance High593.91.0102
Triple Number Windward/Leeward Low1032.70.5810
Triple Number Windward/Leeward Medium786.40.7630
Triple Number Windward/Leeward High709.30.8459
Coastal/Long Distance705.60.8504
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind709.70.8455
Predominantly Downwind648.10.9258
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore683.30.8781
Cape Doctor Coastal569.11.0544
Triple Number Coastal/Long Distance Low806.20.7442
Triple Number Coastal/Long Distance Medium647.20.9270
Triple Number Coastal/Long Distance High593.91.0102
Triple Number Windward/Leeward Low1032.70.5810
Triple Number Windward/Leeward Medium786.40.7630
Triple Number Windward/Leeward High709.30.8459
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7442
Triple Number Coastal/Long Distance Medium0.9270
Triple Number Coastal/Long Distance High1.0102
Triple Number Windward/Leeward Low0.5810
Triple Number Windward/Leeward Medium0.7630
Triple Number Windward/Leeward High0.8459
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7442
Triple Number Coastal/Long Distance Medium0.9270
Triple Number Coastal/Long Distance High1.0102
Triple Number Windward/Leeward Low0.5810
Triple Number Windward/Leeward Medium0.7630
Triple Number Windward/Leeward High0.8459
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance705.60.8504
Triple Number Coastal/Long Distance Low806.20.7442
Triple Number Coastal/Long Distance Medium647.20.9270
Triple Number Coastal/Long Distance High593.91.0102
Triple Number Windward/Leeward Low1032.70.5810
Triple Number Windward/Leeward Medium786.40.7630
Triple Number Windward/Leeward High709.30.8459
Predominantly Upwind709.70.8455
Predominantly Downwind648.10.9258
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1693.71138.5871.9743.6674.0634.9602.4550.1533.5
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance705.60.8504
Triple Number Coastal/Long Distance Low806.20.7442
Triple Number Coastal/Long Distance Medium647.20.9270
Triple Number Coastal/Long Distance High593.91.0102
Triple Number Windward/Leeward Low1032.70.5810
Triple Number Windward/Leeward Medium786.40.7630
Triple Number Windward/Leeward High709.30.8459
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1693.71138.5871.9743.6674.0634.9602.4550.1533.5
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low806.30.7442
Triple Number AP Medium647.30.9269
Triple Number AP High593.91.0102
Triple Number Windward/Leeward Low1078.80.5562
Triple Number Windward/Leeward Medium786.40.7630
Triple Number Windward/Leeward High709.30.8459
Single Number Predominant Upwind736.70.8144
Single Number Predominant Reaching644.20.9314
Single Number Predominant Downwind675.10.8887
Predominant Upwind - Low965.80.6213
Predominant Upwind - Low/Med760.30.7892
Predominant Upwind - Medium692.20.8668
Predominant Upwind - Med/High661.80.9066
Predominant Upwind - High652.60.9194
Predominant Downwind Low967.60.6201
Predominant Downwind Low/Med726.70.8257
Predominant Downwind Medium628.30.9549
Predominant Downwind Med/High566.61.0589
Predominant Downwind High524.01.1451
Predominant Reaching Low861.40.6966
Predominant Reaching Low/Med676.00.8876
Predominant Reaching Medium608.00.9869
Predominant Reaching Med/High565.91.0602
Predominant Reaching High538.51.1143
SA/DSPL Upwind22.92SA/DSPL Downwind41.29
Scoring OptionTODTOT
5-Band Windward/Leeward Low1201.60.4993
5-Band Windward/Leeward Low/Med894.80.6705
5-Band Windward/Leeward Medium775.30.7739
5-Band Windward/Leeward Med/High716.30.8376
5-Band Windward/Leeward High692.90.8660
Windward/Leeward 60-40 Low1205.40.4978
Windward/Leeward 60-40 Low/Med907.70.6610
Windward/Leeward 60-40 Medium796.80.7530
Windward/Leeward 60-40 Med/High745.80.8045
Windward/Leeward 60-40 High730.20.8217
5-Band AP Low884.80.6781
5-Band AP Low/Med716.40.8375
5-Band AP Medium640.30.9370
5-Band AP Med/High599.91.0002
5-Band AP High579.01.0363
5-Band SF Bay Tour - Low1036.90.5787
5-Band SF Bay Tour - Low/Med858.50.6989
5-Band SF Bay Tour - Medium753.90.7958
5-Band SF Bay Tour - Med/High702.70.8538
5-Band SF Bay Tour - High680.90.8811
Chicago-Mac Upwind0.7949
Chicago-Mac All Purpose0.8283
Chicago-Mac Downwind0.8587
Bayview-Mac Cove Island0.6199
Bayview-Mac Shore0.6245
Harvest Moon Regatta565.51.0610
Double HandedClub Certificate2025
MILLAFIN 1101
Avomeripurjehtijat ry
c/o Mainoskauppa Oy
Melkonkatu 16 B
00210 HELSINKI
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassALBIN EXPRESSMeasurement11/05/1994HINPlan reviewHull constructionSolidCarbon rudderNoLight stanchionsNoTrim tabNo
LOA7.798Max. Beam2.524Draft1.436Displacement1,842Wetted area12.72IMS L6.872LSM06.667Acc. length7.798Sink (kg/mm) 9.28
VCGD0.000VCGM0.030RM Rated (kg·m) 29.0Limit of positive stability(°) N/AStability IndexN/ADefault crew weight170Declared crew weight200
PROPELLER
Propeller TypeNo Propeller
Hydro generatorNo
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerNoMainsail furlerNoArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders1Rotating mastNo
P9.500IG8.970ISP8.970MDT10.090MDL10.130MDT20.090MDL20.130TL0.000MW0.130GO0.130
E3.350J3.050BAS1.170FSD0.000SFJ0.000SPL3.180WPLTPSBD0.092MWTMCG
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodRM entered directlyRM entered30.4Flotation Date22/04/1990
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Double HandedClub Certificate2025
MILLAFIN 1101
Avomeripurjehtijat ry
c/o Mainoskauppa Oy
Melkonkatu 16 B
00210 HELSINKI
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateCommentORC0.140.001.292.090.0019.08* Copied from legacy *
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateCommentORC3.200.00NoNo 15.43* Copied from legacy *
SYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLAreaMeas.DateCommentORC9.009.009.005.750.0043.09* Copied from legacy *
CRUISER/RACER REQUIREMENTS*
Accommodation length7.8 mTable area0.22 m²Headroom1.40 mMinimum number of berths2Personal gear stowage0.08 m³Fresh water capacity18 lMinimum number of seats in cockpit2Food stowage0.12 m³Fuel capacity20 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.