Non Spin/HSFClub Certificate2025
Vesle SimlaNOR 10224
Norges Seilforbund
Sognsveien 73
0854 OSLO
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 Angles42.5°42.5°40.3°39.1°38.7°38.6°38.6°39.1°40.8°
Beat VMG2.263.113.774.234.444.534.574.584.43
52°3.494.695.546.116.386.486.546.596.55
60°3.684.925.766.316.586.706.776.846.81
75°3.775.055.936.476.797.017.147.307.36
90°3.644.945.886.486.857.187.467.817.99
110°3.184.435.456.246.747.147.558.328.84
120°2.964.175.206.026.597.007.428.299.23
135°2.543.664.675.516.206.687.067.908.86
150°2.143.154.114.955.686.286.727.488.32
Run VMG1.852.733.584.375.095.746.297.077.84
Gybe Angles151.4°151.4°156.4°173.5°174.8°175.7°177.5°178.2°178.0°
APH ToD:644.5CDL: 7.571APH ToT: 0.9309CertNo:8104
BOAT
ClassFIRST 27.7DesignerFinotBuilderBeneteauAge date01/2003Series date01/2002Offset fileFIRST277.offData file8104
HULL
Length Overall8.300 mMaximum Beam3.022 mDraft2.131 mDisplacement2,848 kgDLR4.4222IMS DivisionCruiser/RacerDynamic Allowance0.260%Age Allowance0.487%
PROPELLER
InstallationStrutTypeFolding 2 bladesDiameter0.380m
CREW
Maximum weight450 kg(declared)Minimum weight320 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail28.1428.95Headsail Luffed20.4620.46Headsail FlyingSymmetricAsymmetric
STORM SAIL AREAS (m²)
Trysail8.06Storm Jib6.81Heavy Weather Jib18.38
SAIL LIMITS
Headsails5
✱ Zero set flying
Spinnakers0
✱ Spinnaker pole aboard
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.
Non Spin/HSFClub Certificate2025
Vesle SimlaNOR 10224
Norges Seilforbund
Sognsveien 73
0854 OSLO
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 VMG1591.31157.2954.7851.8810.1795.1787.5786.4812.4
52°1030.7767.8650.0589.3564.4555.6550.5546.4549.9
60°977.7732.3624.6571.0546.8537.6532.1526.5528.5
75°956.1713.1606.6556.5529.9513.6504.5493.2489.3
90°989.7729.3611.9555.4525.2501.6482.8461.1450.7
110°1131.6812.5660.0577.1534.1504.0476.6432.4407.4
120°1214.8862.6692.4598.2546.6514.4485.3434.5390.0
135°1419.5983.5770.7653.2581.0539.3509.7455.8406.2
150°1682.51141.6875.4726.9633.8573.0535.9481.1432.8
Run VMG1947.91317.11004.4823.9706.8626.8572.0509.1459.3
Selected Courses
Windward / Leeward1765.81237.1979.6837.8758.5711.0679.8647.8635.8
All purpose1332.6950.7768.0670.4617.8586.7565.4537.7523.0
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward797.50.7524
All purpose644.50.9309
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low859.40.6982
Triple Number Coastal/Long Distance Medium640.10.9374
Triple Number Coastal/Long Distance High560.31.0708
Triple Number Windward/Leeward Low1108.40.5413
Triple Number Windward/Leeward Medium791.50.7581
Triple Number Windward/Leeward High675.60.8881
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance704.00.8522
Triple Number Coastal/Long Distance Low859.40.6982
Triple Number Coastal/Long Distance Medium640.10.9374
Triple Number Coastal/Long Distance High560.31.0708
Triple Number Windward/Leeward Low1108.40.5413
Triple Number Windward/Leeward Medium791.50.7581
Triple Number Windward/Leeward High675.60.8881
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1906.61245.1923.9755.9660.7609.9571.0510.1490.2
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.6837
Downwind "popa"0.7554
70% up, 30% down "Ilhabela"0.7038
30% up, 70% down "Ilhabela-inverso"0.7324
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low859.40.6982
Triple Number Coastal/Long Distance Medium640.10.9374
Triple Number Coastal/Long Distance High560.31.0708
Triple Number Windward/Leeward Low1108.40.5413
Triple Number Windward/Leeward Medium791.50.7581
Triple Number Windward/Leeward High675.60.8881
Predominantly Upwind687.40.8729
Predominantly Downwind672.60.8921
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low859.30.6982
Triple Number AP Medium640.10.9373
Triple Number AP High560.31.0708
Triple Number Windward/Leeward Low1160.30.5171
Triple Number Windward/Leeward Medium791.50.7581
Triple Number Windward/Leeward High675.60.8881
Single Number Predominant Upwind715.50.8385
Single Number Predominant Reaching644.70.9306
Single Number Predominant Downwind707.90.8476
Predominant Upwind - Low1003.00.5982
Predominant Upwind - Low/Med757.40.7922
Predominant Upwind - Medium661.90.9065
Predominant Upwind - Med/High616.30.9735
Predominant Upwind - High600.01.0001
Predominant Downwind Low1100.70.5451
Predominant Downwind Low/Med784.10.7652
Predominant Downwind Medium643.60.9323
Predominant Downwind Med/High557.01.0772
Predominant Downwind High511.91.1722
Predominant Reaching Low935.40.6414
Predominant Reaching Low/Med695.40.8628
Predominant Reaching Medium595.51.0076
Predominant Reaching Med/High537.01.1173
Predominant Reaching High506.61.1844
SA/DSPL Upwind24.11SA/DSPL Downwind24.11
Scoring OptionTODTOT
5-Band Windward/Leeward Low1305.90.4595
5-Band Windward/Leeward Low/Med934.90.6418
5-Band Windward/Leeward Medium775.50.7737
5-Band Windward/Leeward Med/High686.30.8743
5-Band Windward/Leeward High651.20.9213
Windward/Leeward 60-40 Low1287.70.4659
Windward/Leeward 60-40 Low/Med933.30.6429
Windward/Leeward 60-40 Medium785.40.7640
Windward/Leeward 60-40 Med/High707.10.8485
Windward/Leeward 60-40 High679.20.8834
5-Band AP Low970.70.6181
5-Band AP Low/Med738.30.8127
5-Band AP Medium629.40.9532
5-Band AP Med/High568.71.0550
5-Band AP High539.91.1112
5-Band SF Bay Tour - Low1115.30.5380
5-Band SF Bay Tour - Low/Med891.90.6727
5-Band SF Bay Tour - Medium748.80.8013
5-Band SF Bay Tour - Med/High671.60.8934
5-Band SF Bay Tour - High640.30.9370
Chicago-Mac Upwind0.8120
Chicago-Mac All Purpose0.8166
Chicago-Mac Downwind0.8111
Bayview-Mac Cove Island0.5805
Bayview-Mac Shore0.5873
Harvest Moon Regatta550.71.0895
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance704.00.8522
Triple Number Coastal/Long Distance Low859.40.6982
Triple Number Coastal/Long Distance Medium640.10.9374
Triple Number Coastal/Long Distance High560.31.0708
Triple Number Windward/Leeward Low1108.40.5413
Triple Number Windward/Leeward Medium791.50.7581
Triple Number Windward/Leeward High675.60.8881
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1906.61245.1923.9755.9660.7609.9571.0510.1490.2
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance704.00.8522
Triple Number Coastal/Long Distance Low859.40.6982
Triple Number Coastal/Long Distance Medium640.10.9374
Triple Number Coastal/Long Distance High560.31.0708
Triple Number Windward/Leeward Low1108.40.5413
Triple Number Windward/Leeward Medium791.50.7581
Triple Number Windward/Leeward High675.60.8881
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1906.61245.1923.9755.9660.7609.9571.0510.1490.2
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance704.0
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1906.61245.1923.9755.9660.7609.9571.0510.1490.2
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low859.40.6982
Triple Number Coastal/Long Distance Medium640.10.9374
Triple Number Coastal/Long Distance High560.31.0708
Triple Number Windward/Leeward Low1108.40.5413
Triple Number Windward/Leeward Medium791.50.7581
Triple Number Windward/Leeward High675.60.8881
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating704.00.8522
FinRating, kevyt tuuli1289.20.7757
FinRating, kova tuuli542.60.9214
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low859.40.6982
Triple Number Coastal/Long Distance Medium640.10.9374
Triple Number Coastal/Long Distance High560.31.0708
Triple Number Windward/Leeward Low1108.40.5413
Triple Number Windward/Leeward Medium791.50.7581
Triple Number Windward/Leeward High675.60.8881
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.8522
Triple Number Coastal/Long Distance Low0.6982
Triple Number Coastal/Long Distance Medium0.9374
Triple Number Coastal/Long Distance High1.0708
Triple Number Windward/Leeward Low0.5413
Triple Number Windward/Leeward Medium0.7581
Triple Number Windward/Leeward High0.8881
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1906.61245.1923.9755.9660.7609.9571.0510.1490.2
For information
General Purpose Handicap (GPH)729.7
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance704.00.8522
Triple Number Coastal/Long Distance Low859.40.6982
Triple Number Coastal/Long Distance Medium640.10.9374
Triple Number Coastal/Long Distance High560.31.0708
Triple Number Windward/Leeward Low1108.40.5413
Triple Number Windward/Leeward Medium791.50.7581
Triple Number Windward/Leeward High675.60.8881
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1906.61245.1923.9755.9660.7609.9571.0510.1490.2
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low859.40.6982
Triple Number Coastal/Long Distance Medium640.10.9374
Triple Number Coastal/Long Distance High560.31.0708
Triple Number Windward/Leeward Low1108.40.5413
Triple Number Windward/Leeward Medium791.50.7581
Triple Number Windward/Leeward High675.60.8881
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance704.00.8522
Triple Number Coastal/Long Distance Low859.40.6982
Triple Number Coastal/Long Distance Medium640.10.9374
Triple Number Coastal/Long Distance High560.31.0708
Triple Number Windward/Leeward Low1108.40.5413
Triple Number Windward/Leeward Medium791.50.7581
Triple Number Windward/Leeward High675.60.8881
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1906.61245.1923.9755.9660.7609.9571.0510.1490.2
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance704.00.8522
Triple Number Coastal/Long Distance Low859.40.6982
Triple Number Coastal/Long Distance Medium640.10.9374
Triple Number Coastal/Long Distance High560.31.0708
Triple Number Windward/Leeward Low1108.40.5413
Triple Number Windward/Leeward Medium791.50.7581
Triple Number Windward/Leeward High675.60.8881
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1906.61245.1923.9755.9660.7609.9571.0510.1490.2
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low859.4
Triple Number Coastal/Long Distance Medium640.1
Triple Number Coastal/Long Distance High560.3
Triple Number Windward/Leeward Low1108.4
Triple Number Windward/Leeward Medium791.5
Triple Number Windward/Leeward High675.6
Predominantly Upwind687.4
Predominantly Downwind672.6
Predominantly Reaching634.3
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance704.00.8522
Triple Number Coastal/Long Distance Low859.40.6982
Triple Number Coastal/Long Distance Medium640.10.9374
Triple Number Coastal/Long Distance High560.31.0708
Triple Number Windward/Leeward Low1108.40.5413
Triple Number Windward/Leeward Medium791.50.7581
Triple Number Windward/Leeward High675.60.8881
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1906.61245.1923.9755.9660.7609.9571.0510.1490.2
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.6982
Triple Number Coastal/Long Distance Medium0.9374
Triple Number Coastal/Long Distance High1.0708
Triple Number Windward/Leeward Low0.5413
Triple Number Windward/Leeward Medium0.7581
Triple Number Windward/Leeward High0.8881
Coastal/Long Distance0.8522
Predominantly Upwind0.8729
Predominantly Downwind0.8921
For information
General Purpose Handicap (GPH)729.7
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)0.9309
Distanseseilas Trippeltall svak vind0.6982
Distanseseilas Trippeltall mellomvind0.9374
Distanseseilas Trippeltall sterk vind1.0708
Pølsebane Trippeltall svak vind0.5413
Pølsebane Trippeltall mellomvind0.7581
Pølsebane Trippeltall sterk vind0.8881
Motvind Singeltall0.8729
Medvind Singeltall0.8921
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low859.40.6982
Triple Number Coastal/Long Distance Medium640.10.9374
Triple Number Coastal/Long Distance High560.31.0708
Triple Number Windward/Leeward Low1108.40.5413
Triple Number Windward/Leeward Medium791.50.7581
Triple Number Windward/Leeward High675.60.8881
Coastal/Long Distance704.00.8522
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind687.40.8729
Predominantly Downwind672.60.8921
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore639.40.9384
Cape Doctor Coastal527.41.1376
Triple Number Coastal/Long Distance Low859.40.6982
Triple Number Coastal/Long Distance Medium640.10.9374
Triple Number Coastal/Long Distance High560.31.0708
Triple Number Windward/Leeward Low1108.40.5413
Triple Number Windward/Leeward Medium791.50.7581
Triple Number Windward/Leeward High675.60.8881
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.6982
Triple Number Coastal/Long Distance Medium0.9374
Triple Number Coastal/Long Distance High1.0708
Triple Number Windward/Leeward Low0.5413
Triple Number Windward/Leeward Medium0.7581
Triple Number Windward/Leeward High0.8881
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.6982
Triple Number Coastal/Long Distance Medium0.9374
Triple Number Coastal/Long Distance High1.0708
Triple Number Windward/Leeward Low0.5413
Triple Number Windward/Leeward Medium0.7581
Triple Number Windward/Leeward High0.8881
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance704.00.8522
Triple Number Coastal/Long Distance Low859.40.6982
Triple Number Coastal/Long Distance Medium640.10.9374
Triple Number Coastal/Long Distance High560.31.0708
Triple Number Windward/Leeward Low1108.40.5413
Triple Number Windward/Leeward Medium791.50.7581
Triple Number Windward/Leeward High675.60.8881
Predominantly Upwind687.40.8729
Predominantly Downwind672.60.8921
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1906.61245.1923.9755.9660.7609.9571.0510.1490.2
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance704.00.8522
Triple Number Coastal/Long Distance Low859.40.6982
Triple Number Coastal/Long Distance Medium640.10.9374
Triple Number Coastal/Long Distance High560.31.0708
Triple Number Windward/Leeward Low1108.40.5413
Triple Number Windward/Leeward Medium791.50.7581
Triple Number Windward/Leeward High675.60.8881
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1906.61245.1923.9755.9660.7609.9571.0510.1490.2
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low859.30.6982
Triple Number AP Medium640.10.9373
Triple Number AP High560.31.0708
Triple Number Windward/Leeward Low1160.30.5171
Triple Number Windward/Leeward Medium791.50.7581
Triple Number Windward/Leeward High675.60.8881
Single Number Predominant Upwind715.50.8385
Single Number Predominant Reaching644.70.9306
Single Number Predominant Downwind707.90.8476
Predominant Upwind - Low1003.00.5982
Predominant Upwind - Low/Med757.40.7922
Predominant Upwind - Medium661.90.9065
Predominant Upwind - Med/High616.30.9735
Predominant Upwind - High600.01.0001
Predominant Downwind Low1100.70.5451
Predominant Downwind Low/Med784.10.7652
Predominant Downwind Medium643.60.9323
Predominant Downwind Med/High557.01.0772
Predominant Downwind High511.91.1722
Predominant Reaching Low935.40.6414
Predominant Reaching Low/Med695.40.8628
Predominant Reaching Medium595.51.0076
Predominant Reaching Med/High537.01.1173
Predominant Reaching High506.61.1844
SA/DSPL Upwind24.11SA/DSPL Downwind24.11
Scoring OptionTODTOT
5-Band Windward/Leeward Low1305.90.4595
5-Band Windward/Leeward Low/Med934.90.6418
5-Band Windward/Leeward Medium775.50.7737
5-Band Windward/Leeward Med/High686.30.8743
5-Band Windward/Leeward High651.20.9213
Windward/Leeward 60-40 Low1287.70.4659
Windward/Leeward 60-40 Low/Med933.30.6429
Windward/Leeward 60-40 Medium785.40.7640
Windward/Leeward 60-40 Med/High707.10.8485
Windward/Leeward 60-40 High679.20.8834
5-Band AP Low970.70.6181
5-Band AP Low/Med738.30.8127
5-Band AP Medium629.40.9532
5-Band AP Med/High568.71.0550
5-Band AP High539.91.1112
5-Band SF Bay Tour - Low1115.30.5380
5-Band SF Bay Tour - Low/Med891.90.6727
5-Band SF Bay Tour - Medium748.80.8013
5-Band SF Bay Tour - Med/High671.60.8934
5-Band SF Bay Tour - High640.30.9370
Chicago-Mac Upwind0.8120
Chicago-Mac All Purpose0.8166
Chicago-Mac Downwind0.8111
Bayview-Mac Cove Island0.5805
Bayview-Mac Shore0.5873
Harvest Moon Regatta550.71.0895
Non Spin/HSFClub Certificate2025
Vesle SimlaNOR 10224
Norges Seilforbund
Sognsveien 73
0854 OSLO
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassFIRST 27.7MeasurementHINPlan reviewHull constructionSolidCarbon rudderNoLight stanchionsNoTrim tabNo
LOA8.300Max. Beam3.022Draft2.131Displacement2,848Wetted area18.70IMS L8.347LSM08.635Acc. length8.300Sink (kg/mm) 14.15
VCGD0.170VCGM0.213RM Rated (kg·m) 59.7Limit of positive stability(°) N/AStability IndexN/ADefault crew weight558Declared crew weight450
PROPELLER
Propeller TypeFolding 2 blades
InstallationStrutTwin screwNoHydro generatorNo
PRD0.380PBWPIPA0.0031
EDL2.200ST10.042ST20.180
ST30.180ST40.112ST50.227
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerNoMainsail furlerArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders1Rotating mastNo
P10.960IG11.630ISP11.830MDT10.110MDL10.160MDT20.110MDL20.160TLNo TaperMW0.160GO0.170
E4.200J3.190BAS1.410FSDFoilSFJ0.000SPL3.480WPLTPS4.100BD0.000MWT72.00MCG4.560
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodVCG entered directlyVCG entered0.170Flotation Date01/01/2015
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Non Spin/HSFClub Certificate2025
Vesle SimlaNOR 10224
Norges Seilforbund
Sognsveien 73
0854 OSLO
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment306-2017060217070.160.001.662.793.5728.1402/06/2017seilet var feil målt, nederste breddemål rettet i dag
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment306-2017060216520.060.490.911.782.673.5711.41YesNo 20.4602/06/2017625-2024040506160.030.410.811.682.643.6010.85NoNo 18.9005/04/2024
CRUISER/RACER REQUIREMENTS*
Accommodation length8.3 mTable area0.33 m²Headroom1.40 mMinimum number of berths3Personal gear stowage0.12 m³Fresh water capacity35 lMinimum number of seats in cockpit3Food stowage0.18 m³Fuel capacity20 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.