Non Spin/HSFClub Certificate2025
Fast BornNOR 11142
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 Angles43.5°43.5°41.5°39.7°38.3°37.8°37.5°37.5°38.1°
Beat VMG2.463.424.204.785.155.315.405.465.42
52°3.875.246.246.907.297.487.577.677.69
60°4.125.526.507.117.487.707.817.958.00
75°4.265.696.667.267.647.958.208.468.62
90°4.125.556.567.237.658.018.368.929.24
110°3.484.866.006.877.457.898.349.2110.03
120°3.244.585.726.627.277.738.189.1110.13
135°2.764.005.126.046.807.357.788.659.64
150°2.293.394.435.366.166.837.358.169.02
Run VMG1.992.933.844.675.446.146.767.658.41
Gybe Angles146.7°146.7°151.0°156.4°165.8°171.4°175.4°178.8°178.6°
APH ToD:577.3CDL: 9.822APH ToT: 1.0394CertNo:9085
BOAT
ClassPerformance 35DesignerKennethAlbinssonBuilderSkrovabAge date01/2005Series date01/1998Offset fileFastBornCL.offData file9085
HULL
Length Overall10.700 mMaximum Beam3.754 mDraft2.071 mDisplacement4,783 kgDLR3.7667IMS DivisionCruiser/RacerDynamic Allowance0.280%Age Allowance0.487%
PROPELLER
InstallationStrutTypeFolding 2 bladesDiameter0.400m
CREW
Maximum weight771 kg(default)Minimum weight641 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail36.4237.11Headsail Luffed37.8637.86Headsail FlyingSymmetricAsymmetric
STORM SAIL AREAS (m²)
Trysail10.64Storm Jib10.20Heavy Weather Jib27.53
SAIL LIMITS
Headsails6
✱ 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
Fast BornNOR 11142
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 VMG1463.31052.4857.5753.3699.1677.9667.2659.3663.8
52°931.2687.3576.9521.4493.8481.4475.6469.4468.2
60°873.9651.9554.0506.5481.6467.7460.8452.8449.9
75°845.9633.1540.3496.0471.2452.7439.2425.4417.5
90°873.9649.0548.5497.9470.5449.4430.4403.8389.6
110°1034.8740.7600.2524.4483.0456.1431.7390.8359.0
120°1110.9786.0629.3543.9495.1465.5440.2395.1355.2
135°1302.4899.9703.4595.8529.7489.5462.9416.0373.4
150°1570.71062.4811.7671.5584.6526.8489.8441.4399.3
Run VMG1813.01226.7936.7770.5662.2586.7532.8470.7427.9
Selected Courses
Windward / Leeward1635.81139.6897.1761.9680.7632.3600.0565.0545.9
All purpose1219.8866.5696.8605.1552.2520.7499.0470.7451.6
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward718.00.8357
All purpose577.31.0394
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low781.70.7676
Triple Number Coastal/Long Distance Medium574.01.0453
Triple Number Coastal/Long Distance High493.81.2151
Triple Number Windward/Leeward Low1018.30.5892
Triple Number Windward/Leeward Medium713.70.8407
Triple Number Windward/Leeward High594.91.0085
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance632.60.9485
Triple Number Coastal/Long Distance Low781.70.7676
Triple Number Coastal/Long Distance Medium574.01.0453
Triple Number Coastal/Long Distance High493.81.2151
Triple Number Windward/Leeward Low1018.30.5892
Triple Number Windward/Leeward Medium713.70.8407
Triple Number Windward/Leeward High594.91.0085
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1775.01148.3844.9685.1590.3541.3504.9449.9428.3
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.7826
Downwind "popa"0.8098
70% up, 30% down "Ilhabela"0.7906
30% up, 70% down "Ilhabela-inverso"0.8015
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low781.70.7676
Triple Number Coastal/Long Distance Medium574.01.0453
Triple Number Coastal/Long Distance High493.81.2151
Triple Number Windward/Leeward Low1018.30.5892
Triple Number Windward/Leeward Medium713.70.8407
Triple Number Windward/Leeward High594.91.0085
Predominantly Upwind609.00.9853
Predominantly Downwind612.70.9793
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low781.70.7676
Triple Number AP Medium574.11.0451
Triple Number AP High493.81.2151
Triple Number Windward/Leeward Low1066.80.5624
Triple Number Windward/Leeward Medium713.70.8407
Triple Number Windward/Leeward High594.91.0085
Single Number Predominant Upwind634.50.9457
Single Number Predominant Reaching578.71.0368
Single Number Predominant Downwind644.60.9308
Predominant Upwind - Low909.80.6595
Predominant Upwind - Low/Med679.30.8833
Predominant Upwind - Medium584.71.0261
Predominant Upwind - Med/High536.11.1191
Predominant Upwind - High516.21.1623
Predominant Downwind Low1009.50.5943
Predominant Downwind Low/Med717.00.8368
Predominant Downwind Medium585.71.0245
Predominant Downwind Med/High502.71.1937
Predominant Downwind High458.91.3074
Predominant Reaching Low847.10.7083
Predominant Reaching Low/Med627.70.9559
Predominant Reaching Medium534.31.1230
Predominant Reaching Med/High477.51.2566
Predominant Reaching High446.41.3440
SA/DSPL Upwind26.03SA/DSPL Downwind26.03
Scoring OptionTODTOT
5-Band Windward/Leeward Low1203.60.4985
5-Band Windward/Leeward Low/Med853.20.7032
5-Band Windward/Leeward Medium697.40.8603
5-Band Windward/Leeward Med/High606.40.9895
5-Band Windward/Leeward High567.71.0568
Windward/Leeward 60-40 Low1184.20.5067
Windward/Leeward 60-40 Low/Med847.80.7077
Windward/Leeward 60-40 Medium701.00.8560
Windward/Leeward 60-40 Med/High619.20.9690
Windward/Leeward 60-40 High586.51.0231
5-Band AP Low883.90.6788
5-Band AP Low/Med668.10.8980
5-Band AP Medium563.31.0651
5-Band AP Med/High502.31.1944
5-Band AP High472.31.2703
5-Band SF Bay Tour - Low1023.10.5864
5-Band SF Bay Tour - Low/Med810.50.7403
5-Band SF Bay Tour - Medium669.60.8961
5-Band SF Bay Tour - Med/High590.31.0164
5-Band SF Bay Tour - High556.21.0788
Chicago-Mac Upwind0.9122
Chicago-Mac All Purpose0.9062
Chicago-Mac Downwind0.8889
Bayview-Mac Cove Island0.6374
Bayview-Mac Shore0.6455
Harvest Moon Regatta496.61.2082
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance632.60.9485
Triple Number Coastal/Long Distance Low781.70.7676
Triple Number Coastal/Long Distance Medium574.01.0453
Triple Number Coastal/Long Distance High493.81.2151
Triple Number Windward/Leeward Low1018.30.5892
Triple Number Windward/Leeward Medium713.70.8407
Triple Number Windward/Leeward High594.91.0085
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1775.01148.3844.9685.1590.3541.3504.9449.9428.3
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance632.60.9485
Triple Number Coastal/Long Distance Low781.70.7676
Triple Number Coastal/Long Distance Medium574.01.0453
Triple Number Coastal/Long Distance High493.81.2151
Triple Number Windward/Leeward Low1018.30.5892
Triple Number Windward/Leeward Medium713.70.8407
Triple Number Windward/Leeward High594.91.0085
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1775.01148.3844.9685.1590.3541.3504.9449.9428.3
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance632.6
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1775.01148.3844.9685.1590.3541.3504.9449.9428.3
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low781.70.7676
Triple Number Coastal/Long Distance Medium574.01.0453
Triple Number Coastal/Long Distance High493.81.2151
Triple Number Windward/Leeward Low1018.30.5892
Triple Number Windward/Leeward Medium713.70.8407
Triple Number Windward/Leeward High594.91.0085
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating632.60.9485
FinRating, kevyt tuuli1186.60.8427
FinRating, kova tuuli475.11.0525
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low781.70.7676
Triple Number Coastal/Long Distance Medium574.01.0453
Triple Number Coastal/Long Distance High493.81.2151
Triple Number Windward/Leeward Low1018.30.5892
Triple Number Windward/Leeward Medium713.70.8407
Triple Number Windward/Leeward High594.91.0085
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.9485
Triple Number Coastal/Long Distance Low0.7676
Triple Number Coastal/Long Distance Medium1.0453
Triple Number Coastal/Long Distance High1.2151
Triple Number Windward/Leeward Low0.5892
Triple Number Windward/Leeward Medium0.8407
Triple Number Windward/Leeward High1.0085
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1775.01148.3844.9685.1590.3541.3504.9449.9428.3
For information
General Purpose Handicap (GPH)656.0
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance632.60.9485
Triple Number Coastal/Long Distance Low781.70.7676
Triple Number Coastal/Long Distance Medium574.01.0453
Triple Number Coastal/Long Distance High493.81.2151
Triple Number Windward/Leeward Low1018.30.5892
Triple Number Windward/Leeward Medium713.70.8407
Triple Number Windward/Leeward High594.91.0085
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1775.01148.3844.9685.1590.3541.3504.9449.9428.3
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low781.70.7676
Triple Number Coastal/Long Distance Medium574.01.0453
Triple Number Coastal/Long Distance High493.81.2151
Triple Number Windward/Leeward Low1018.30.5892
Triple Number Windward/Leeward Medium713.70.8407
Triple Number Windward/Leeward High594.91.0085
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance632.60.9485
Triple Number Coastal/Long Distance Low781.70.7676
Triple Number Coastal/Long Distance Medium574.01.0453
Triple Number Coastal/Long Distance High493.81.2151
Triple Number Windward/Leeward Low1018.30.5892
Triple Number Windward/Leeward Medium713.70.8407
Triple Number Windward/Leeward High594.91.0085
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1775.01148.3844.9685.1590.3541.3504.9449.9428.3
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance632.60.9485
Triple Number Coastal/Long Distance Low781.70.7676
Triple Number Coastal/Long Distance Medium574.01.0453
Triple Number Coastal/Long Distance High493.81.2151
Triple Number Windward/Leeward Low1018.30.5892
Triple Number Windward/Leeward Medium713.70.8407
Triple Number Windward/Leeward High594.91.0085
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1775.01148.3844.9685.1590.3541.3504.9449.9428.3
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low781.7
Triple Number Coastal/Long Distance Medium574.0
Triple Number Coastal/Long Distance High493.8
Triple Number Windward/Leeward Low1018.3
Triple Number Windward/Leeward Medium713.7
Triple Number Windward/Leeward High594.9
Predominantly Upwind609.0
Predominantly Downwind612.7
Predominantly Reaching573.2
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance632.60.9485
Triple Number Coastal/Long Distance Low781.70.7676
Triple Number Coastal/Long Distance Medium574.01.0453
Triple Number Coastal/Long Distance High493.81.2151
Triple Number Windward/Leeward Low1018.30.5892
Triple Number Windward/Leeward Medium713.70.8407
Triple Number Windward/Leeward High594.91.0085
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1775.01148.3844.9685.1590.3541.3504.9449.9428.3
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7676
Triple Number Coastal/Long Distance Medium1.0453
Triple Number Coastal/Long Distance High1.2151
Triple Number Windward/Leeward Low0.5892
Triple Number Windward/Leeward Medium0.8407
Triple Number Windward/Leeward High1.0085
Coastal/Long Distance0.9485
Predominantly Upwind0.9853
Predominantly Downwind0.9793
For information
General Purpose Handicap (GPH)656.0
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)1.0394
Distanseseilas Trippeltall svak vind0.7676
Distanseseilas Trippeltall mellomvind1.0453
Distanseseilas Trippeltall sterk vind1.2151
Pølsebane Trippeltall svak vind0.5892
Pølsebane Trippeltall mellomvind0.8407
Pølsebane Trippeltall sterk vind1.0085
Motvind Singeltall0.9853
Medvind Singeltall0.9793
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low781.70.7676
Triple Number Coastal/Long Distance Medium574.01.0453
Triple Number Coastal/Long Distance High493.81.2151
Triple Number Windward/Leeward Low1018.30.5892
Triple Number Windward/Leeward Medium713.70.8407
Triple Number Windward/Leeward High594.91.0085
Coastal/Long Distance632.60.9485
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind609.00.9853
Predominantly Downwind612.70.9793
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore551.61.0878
Cape Doctor Coastal457.31.3119
Triple Number Coastal/Long Distance Low781.70.7676
Triple Number Coastal/Long Distance Medium574.01.0453
Triple Number Coastal/Long Distance High493.81.2151
Triple Number Windward/Leeward Low1018.30.5892
Triple Number Windward/Leeward Medium713.70.8407
Triple Number Windward/Leeward High594.91.0085
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7676
Triple Number Coastal/Long Distance Medium1.0453
Triple Number Coastal/Long Distance High1.2151
Triple Number Windward/Leeward Low0.5892
Triple Number Windward/Leeward Medium0.8407
Triple Number Windward/Leeward High1.0085
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7676
Triple Number Coastal/Long Distance Medium1.0453
Triple Number Coastal/Long Distance High1.2151
Triple Number Windward/Leeward Low0.5892
Triple Number Windward/Leeward Medium0.8407
Triple Number Windward/Leeward High1.0085
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance632.60.9485
Triple Number Coastal/Long Distance Low781.70.7676
Triple Number Coastal/Long Distance Medium574.01.0453
Triple Number Coastal/Long Distance High493.81.2151
Triple Number Windward/Leeward Low1018.30.5892
Triple Number Windward/Leeward Medium713.70.8407
Triple Number Windward/Leeward High594.91.0085
Predominantly Upwind609.00.9853
Predominantly Downwind612.70.9793
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1775.01148.3844.9685.1590.3541.3504.9449.9428.3
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance632.60.9485
Triple Number Coastal/Long Distance Low781.70.7676
Triple Number Coastal/Long Distance Medium574.01.0453
Triple Number Coastal/Long Distance High493.81.2151
Triple Number Windward/Leeward Low1018.30.5892
Triple Number Windward/Leeward Medium713.70.8407
Triple Number Windward/Leeward High594.91.0085
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1775.01148.3844.9685.1590.3541.3504.9449.9428.3
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low781.70.7676
Triple Number AP Medium574.11.0451
Triple Number AP High493.81.2151
Triple Number Windward/Leeward Low1066.80.5624
Triple Number Windward/Leeward Medium713.70.8407
Triple Number Windward/Leeward High594.91.0085
Single Number Predominant Upwind634.50.9457
Single Number Predominant Reaching578.71.0368
Single Number Predominant Downwind644.60.9308
Predominant Upwind - Low909.80.6595
Predominant Upwind - Low/Med679.30.8833
Predominant Upwind - Medium584.71.0261
Predominant Upwind - Med/High536.11.1191
Predominant Upwind - High516.21.1623
Predominant Downwind Low1009.50.5943
Predominant Downwind Low/Med717.00.8368
Predominant Downwind Medium585.71.0245
Predominant Downwind Med/High502.71.1937
Predominant Downwind High458.91.3074
Predominant Reaching Low847.10.7083
Predominant Reaching Low/Med627.70.9559
Predominant Reaching Medium534.31.1230
Predominant Reaching Med/High477.51.2566
Predominant Reaching High446.41.3440
SA/DSPL Upwind26.03SA/DSPL Downwind26.03
Scoring OptionTODTOT
5-Band Windward/Leeward Low1203.60.4985
5-Band Windward/Leeward Low/Med853.20.7032
5-Band Windward/Leeward Medium697.40.8603
5-Band Windward/Leeward Med/High606.40.9895
5-Band Windward/Leeward High567.71.0568
Windward/Leeward 60-40 Low1184.20.5067
Windward/Leeward 60-40 Low/Med847.80.7077
Windward/Leeward 60-40 Medium701.00.8560
Windward/Leeward 60-40 Med/High619.20.9690
Windward/Leeward 60-40 High586.51.0231
5-Band AP Low883.90.6788
5-Band AP Low/Med668.10.8980
5-Band AP Medium563.31.0651
5-Band AP Med/High502.31.1944
5-Band AP High472.31.2703
5-Band SF Bay Tour - Low1023.10.5864
5-Band SF Bay Tour - Low/Med810.50.7403
5-Band SF Bay Tour - Medium669.60.8961
5-Band SF Bay Tour - Med/High590.31.0164
5-Band SF Bay Tour - High556.21.0788
Chicago-Mac Upwind0.9122
Chicago-Mac All Purpose0.9062
Chicago-Mac Downwind0.8889
Bayview-Mac Cove Island0.6374
Bayview-Mac Shore0.6455
Harvest Moon Regatta496.61.2082
Non Spin/HSFClub Certificate2025
Fast BornNOR 11142
Norges Seilforbund
Sognsveien 73
0854 OSLO
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassPerformance 35MeasurementHINPlan reviewHull constructionSolidCarbon rudderNoLight stanchionsNoTrim tabNo
LOA10.700Max. Beam3.754Draft2.071Displacement4,783Wetted area26.45IMS L10.521LSM010.828Acc. length10.700Sink (kg/mm) 20.67
VCGD0.020VCGM-0.045RM Rated (kg·m) 136.8Limit of positive stability(°) N/AStability IndexN/ADefault crew weight771Declared crew weightN/A
PROPELLER
Propeller TypeFolding 2 blades
InstallationStrutTwin screwNoHydro generatorNo
PRD0.400PBWPIPA0.0037
EDL2.000ST10.065ST20.180
ST30.180ST40.110ST50.250
RIG
Forestay tensionAftInner stayNone FittedMast materialSingle headsail furlerNoMainsail furlerArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders3Rotating mastNo
P13.500IG14.280ISP15.200MDT10.120MDL10.230MDT20.000MDL20.000TL0.000MW0.000GO0.000
E4.500J3.800BAS1.800FSD0.030SFJ0.000SPL4.182WPLTPS4.740BD0.000MWT0.00MCG0.000
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodVCG entered directlyVCG entered0.020Flotation Date01/01/2015
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Non Spin/HSFClub Certificate2025
Fast BornNOR 11142
Norges Seilforbund
Sognsveien 73
0854 OSLO
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment437-2020042710570.180.931.722.943.8036.4227/04/2020
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment625-2023041307590.070.681.312.684.095.5213.91NoNo 37.8613/04/2023625-2025042812200.050.601.152.092.993.8513.95YesNo 28.3628/04/2025371-2014021710020.050.460.861.672.673.7714.18NoNo 25.3717/02/2014
CRUISER/RACER REQUIREMENTS*
Accommodation length10.7 mTable area0.55 m²Headroom1.75 mMinimum number of berths5Personal gear stowage0.20 m³Fresh water capacity117 lMinimum number of seats in cockpit5Food stowage0.30 m³Fuel capacity64 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.