Club Certificate2025
FraganciaNOR 9727
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°41.2°40.4°40.1°39.9°39.9°40.4°42.1°
Beat VMG2.403.273.914.284.454.534.554.544.40
52°3.744.975.796.246.456.536.576.606.55
60°3.985.236.026.446.646.746.786.846.83
75°4.145.426.196.606.846.997.097.207.25
90°4.045.346.176.636.907.127.297.527.67
110°3.885.266.246.767.097.367.577.838.04
120°3.705.076.106.697.067.377.668.148.44
135°3.264.555.606.386.857.207.538.219.02
150°2.683.864.935.826.486.897.227.878.64
Run VMG2.323.354.275.075.776.326.737.367.97
Gybe Angles146.2°146.2°151.2°154.3°161.5°168.7°177.2°178.1°177.7°
APH ToD:610.0CDL: 7.635APH ToT: 0.9836CertNo:667054
BOAT
ClassLINJETT 33DesignerGUSTAVSSONMATSBuilderRosättravarvetAge date01/2002Series date01/1994Offset fileLINJETT33.offData file667054
HULL
Length Overall10.040 mMaximum Beam3.232 mDraft1.590 mDisplacement4,462 kgDLR7.7931IMS DivisionCruiser/RacerDynamic Allowance0.270%Age Allowance0.487%
PROPELLER
InstallationStrutTypeFolding 2 bladesDiameter0.380m
CREW
Maximum weight350 kg(declared)Minimum weight220 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail29.8030.34Headsail Luffed28.5828.58Headsail FlyingSymmetric63.7363.73Asymmetric
STORM SAIL AREAS (m²)
Trysail8.61Storm Jib7.30Heavy Weather Jib19.70
SAIL LIMITS
Headsails5Spinnakers4
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.
Club Certificate2025
FraganciaNOR 9727
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 VMG1501.31101.9921.5840.3808.4795.3791.2793.5818.2
52°961.9723.7621.8576.6558.6551.4548.1545.4549.6
60°905.3687.9597.9559.1542.0534.5530.6526.3527.4
75°869.8664.6581.5545.3526.6515.1508.0500.0496.4
90°891.0674.5583.8543.2521.4505.9494.1478.5469.6
110°928.3684.3576.8532.3507.6489.3475.9460.0447.8
120°972.5709.4590.4537.9509.8488.3470.1442.1426.3
135°1104.7791.8642.6564.0525.8500.2478.0438.6399.2
150°1344.1931.9730.0618.5555.9522.6498.7457.4416.5
Run VMG1553.41076.0842.2710.1624.5570.0534.6489.1451.8
Selected Courses
Windward / Leeward1525.41088.9881.9775.2716.4682.6662.9641.3635.0
All purpose1151.1839.1695.8626.0589.9569.1555.7538.1529.3
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward747.50.8027
All purpose610.00.9836
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low767.50.7818
Triple Number Coastal/Long Distance Medium605.50.9909
Triple Number Coastal/Long Distance High552.51.0860
Triple Number Windward/Leeward Low985.40.6089
Triple Number Windward/Leeward Medium741.40.8093
Triple Number Windward/Leeward High659.80.9094
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance662.60.9056
Triple Number Coastal/Long Distance Low767.50.7818
Triple Number Coastal/Long Distance Medium605.50.9909
Triple Number Coastal/Long Distance High552.51.0860
Triple Number Windward/Leeward Low985.40.6089
Triple Number Windward/Leeward Medium741.40.8093
Triple Number Windward/Leeward High659.80.9094
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1619.51087.6830.6701.7629.5590.7560.8511.8501.0
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.6940
Downwind "popa"0.8666
70% up, 30% down "Ilhabela"0.7381
30% up, 70% down "Ilhabela-inverso"0.8064
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low767.50.7818
Triple Number Coastal/Long Distance Medium605.50.9909
Triple Number Coastal/Long Distance High552.51.0860
Triple Number Windward/Leeward Low985.40.6089
Triple Number Windward/Leeward Medium741.40.8093
Triple Number Windward/Leeward High659.80.9094
Predominantly Upwind661.70.9067
Predominantly Downwind613.60.9778
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low767.50.7818
Triple Number AP Medium605.60.9908
Triple Number AP High552.51.0860
Triple Number Windward/Leeward Low1028.90.5831
Triple Number Windward/Leeward Medium741.40.8093
Triple Number Windward/Leeward High659.80.9094
Single Number Predominant Upwind687.00.8734
Single Number Predominant Reaching605.10.9916
Single Number Predominant Downwind641.00.9361
Predominant Upwind - Low916.20.6549
Predominant Upwind - Low/Med714.80.8394
Predominant Upwind - Medium642.90.9332
Predominant Upwind - Med/High611.00.9820
Predominant Upwind - High600.40.9993
Predominant Downwind Low928.70.6461
Predominant Downwind Low/Med691.50.8676
Predominant Downwind Medium592.81.0122
Predominant Downwind Med/High534.11.1234
Predominant Downwind High502.01.1953
Predominant Reaching Low821.30.7305
Predominant Reaching Low/Med637.60.9410
Predominant Reaching Medium567.41.0574
Predominant Reaching Med/High528.11.1361
Predominant Reaching High506.51.1846
SA/DSPL Upwind21.44SA/DSPL Downwind34.34
Scoring OptionTODTOT
5-Band Windward/Leeward Low1146.80.5232
5-Band Windward/Leeward Low/Med850.30.7056
5-Band Windward/Leeward Medium729.80.8221
5-Band Windward/Leeward Med/High667.10.8994
5-Band Windward/Leeward High644.00.9317
Windward/Leeward 60-40 Low1148.70.5223
Windward/Leeward 60-40 Low/Med860.80.6970
Windward/Leeward 60-40 Medium747.70.8024
Windward/Leeward 60-40 Med/High692.40.8665
Windward/Leeward 60-40 High674.60.8894
5-Band AP Low845.30.7098
5-Band AP Low/Med676.60.8867
5-Band AP Medium598.31.0028
5-Band AP Med/High557.91.0755
5-Band AP High539.61.1118
5-Band SF Bay Tour - Low990.00.6061
5-Band SF Bay Tour - Low/Med814.80.7364
5-Band SF Bay Tour - Medium708.00.8475
5-Band SF Bay Tour - Med/High654.70.9164
5-Band SF Bay Tour - High634.40.9458
Chicago-Mac Upwind0.8501
Chicago-Mac All Purpose0.8795
Chicago-Mac Downwind0.9040
Bayview-Mac Cove Island0.6523
Bayview-Mac Shore0.6575
Harvest Moon Regatta530.21.1317
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance662.60.9056
Triple Number Coastal/Long Distance Low767.50.7818
Triple Number Coastal/Long Distance Medium605.50.9909
Triple Number Coastal/Long Distance High552.51.0860
Triple Number Windward/Leeward Low985.40.6089
Triple Number Windward/Leeward Medium741.40.8093
Triple Number Windward/Leeward High659.80.9094
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1619.51087.6830.6701.7629.5590.7560.8511.8501.0
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance662.60.9056
Triple Number Coastal/Long Distance Low767.50.7818
Triple Number Coastal/Long Distance Medium605.50.9909
Triple Number Coastal/Long Distance High552.51.0860
Triple Number Windward/Leeward Low985.40.6089
Triple Number Windward/Leeward Medium741.40.8093
Triple Number Windward/Leeward High659.80.9094
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1619.51087.6830.6701.7629.5590.7560.8511.8501.0
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance662.6
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1619.51087.6830.6701.7629.5590.7560.8511.8501.0
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low767.50.7818
Triple Number Coastal/Long Distance Medium605.50.9909
Triple Number Coastal/Long Distance High552.51.0860
Triple Number Windward/Leeward Low985.40.6089
Triple Number Windward/Leeward Medium741.40.8093
Triple Number Windward/Leeward High659.80.9094
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating662.60.9056
FinRating, kevyt tuuli1126.00.8881
FinRating, kova tuuli543.00.9208
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low767.50.7818
Triple Number Coastal/Long Distance Medium605.50.9909
Triple Number Coastal/Long Distance High552.51.0860
Triple Number Windward/Leeward Low985.40.6089
Triple Number Windward/Leeward Medium741.40.8093
Triple Number Windward/Leeward High659.80.9094
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.9056
Triple Number Coastal/Long Distance Low0.7818
Triple Number Coastal/Long Distance Medium0.9909
Triple Number Coastal/Long Distance High1.0860
Triple Number Windward/Leeward Low0.6089
Triple Number Windward/Leeward Medium0.8093
Triple Number Windward/Leeward High0.9094
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1619.51087.6830.6701.7629.5590.7560.8511.8501.0
For information
General Purpose Handicap (GPH)680.9
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance662.60.9056
Triple Number Coastal/Long Distance Low767.50.7818
Triple Number Coastal/Long Distance Medium605.50.9909
Triple Number Coastal/Long Distance High552.51.0860
Triple Number Windward/Leeward Low985.40.6089
Triple Number Windward/Leeward Medium741.40.8093
Triple Number Windward/Leeward High659.80.9094
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1619.51087.6830.6701.7629.5590.7560.8511.8501.0
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low767.50.7818
Triple Number Coastal/Long Distance Medium605.50.9909
Triple Number Coastal/Long Distance High552.51.0860
Triple Number Windward/Leeward Low985.40.6089
Triple Number Windward/Leeward Medium741.40.8093
Triple Number Windward/Leeward High659.80.9094
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance662.60.9056
Triple Number Coastal/Long Distance Low767.50.7818
Triple Number Coastal/Long Distance Medium605.50.9909
Triple Number Coastal/Long Distance High552.51.0860
Triple Number Windward/Leeward Low985.40.6089
Triple Number Windward/Leeward Medium741.40.8093
Triple Number Windward/Leeward High659.80.9094
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1619.51087.6830.6701.7629.5590.7560.8511.8501.0
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance662.60.9056
Triple Number Coastal/Long Distance Low767.50.7818
Triple Number Coastal/Long Distance Medium605.50.9909
Triple Number Coastal/Long Distance High552.51.0860
Triple Number Windward/Leeward Low985.40.6089
Triple Number Windward/Leeward Medium741.40.8093
Triple Number Windward/Leeward High659.80.9094
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1619.51087.6830.6701.7629.5590.7560.8511.8501.0
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low767.5
Triple Number Coastal/Long Distance Medium605.5
Triple Number Coastal/Long Distance High552.5
Triple Number Windward/Leeward Low985.4
Triple Number Windward/Leeward Medium741.4
Triple Number Windward/Leeward High659.8
Predominantly Upwind661.7
Predominantly Downwind613.6
Predominantly Reaching591.2
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance662.60.9056
Triple Number Coastal/Long Distance Low767.50.7818
Triple Number Coastal/Long Distance Medium605.50.9909
Triple Number Coastal/Long Distance High552.51.0860
Triple Number Windward/Leeward Low985.40.6089
Triple Number Windward/Leeward Medium741.40.8093
Triple Number Windward/Leeward High659.80.9094
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1619.51087.6830.6701.7629.5590.7560.8511.8501.0
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7818
Triple Number Coastal/Long Distance Medium0.9909
Triple Number Coastal/Long Distance High1.0860
Triple Number Windward/Leeward Low0.6089
Triple Number Windward/Leeward Medium0.8093
Triple Number Windward/Leeward High0.9094
Coastal/Long Distance0.9056
Predominantly Upwind0.9067
Predominantly Downwind0.9778
For information
General Purpose Handicap (GPH)680.9
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)0.9836
Distanseseilas Trippeltall svak vind0.7818
Distanseseilas Trippeltall mellomvind0.9909
Distanseseilas Trippeltall sterk vind1.0860
Pølsebane Trippeltall svak vind0.6089
Pølsebane Trippeltall mellomvind0.8093
Pølsebane Trippeltall sterk vind0.9094
Motvind Singeltall0.9067
Medvind Singeltall0.9778
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low767.50.7818
Triple Number Coastal/Long Distance Medium605.50.9909
Triple Number Coastal/Long Distance High552.51.0860
Triple Number Windward/Leeward Low985.40.6089
Triple Number Windward/Leeward Medium741.40.8093
Triple Number Windward/Leeward High659.80.9094
Coastal/Long Distance662.60.9056
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind661.70.9067
Predominantly Downwind613.60.9778
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore636.90.9421
Cape Doctor Coastal531.91.1280
Triple Number Coastal/Long Distance Low767.50.7818
Triple Number Coastal/Long Distance Medium605.50.9909
Triple Number Coastal/Long Distance High552.51.0860
Triple Number Windward/Leeward Low985.40.6089
Triple Number Windward/Leeward Medium741.40.8093
Triple Number Windward/Leeward High659.80.9094
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7818
Triple Number Coastal/Long Distance Medium0.9909
Triple Number Coastal/Long Distance High1.0860
Triple Number Windward/Leeward Low0.6089
Triple Number Windward/Leeward Medium0.8093
Triple Number Windward/Leeward High0.9094
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7818
Triple Number Coastal/Long Distance Medium0.9909
Triple Number Coastal/Long Distance High1.0860
Triple Number Windward/Leeward Low0.6089
Triple Number Windward/Leeward Medium0.8093
Triple Number Windward/Leeward High0.9094
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance662.60.9056
Triple Number Coastal/Long Distance Low767.50.7818
Triple Number Coastal/Long Distance Medium605.50.9909
Triple Number Coastal/Long Distance High552.51.0860
Triple Number Windward/Leeward Low985.40.6089
Triple Number Windward/Leeward Medium741.40.8093
Triple Number Windward/Leeward High659.80.9094
Predominantly Upwind661.70.9067
Predominantly Downwind613.60.9778
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1619.51087.6830.6701.7629.5590.7560.8511.8501.0
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance662.60.9056
Triple Number Coastal/Long Distance Low767.50.7818
Triple Number Coastal/Long Distance Medium605.50.9909
Triple Number Coastal/Long Distance High552.51.0860
Triple Number Windward/Leeward Low985.40.6089
Triple Number Windward/Leeward Medium741.40.8093
Triple Number Windward/Leeward High659.80.9094
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1619.51087.6830.6701.7629.5590.7560.8511.8501.0
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low767.50.7818
Triple Number AP Medium605.60.9908
Triple Number AP High552.51.0860
Triple Number Windward/Leeward Low1028.90.5831
Triple Number Windward/Leeward Medium741.40.8093
Triple Number Windward/Leeward High659.80.9094
Single Number Predominant Upwind687.00.8734
Single Number Predominant Reaching605.10.9916
Single Number Predominant Downwind641.00.9361
Predominant Upwind - Low916.20.6549
Predominant Upwind - Low/Med714.80.8394
Predominant Upwind - Medium642.90.9332
Predominant Upwind - Med/High611.00.9820
Predominant Upwind - High600.40.9993
Predominant Downwind Low928.70.6461
Predominant Downwind Low/Med691.50.8676
Predominant Downwind Medium592.81.0122
Predominant Downwind Med/High534.11.1234
Predominant Downwind High502.01.1953
Predominant Reaching Low821.30.7305
Predominant Reaching Low/Med637.60.9410
Predominant Reaching Medium567.41.0574
Predominant Reaching Med/High528.11.1361
Predominant Reaching High506.51.1846
SA/DSPL Upwind21.44SA/DSPL Downwind34.34
Scoring OptionTODTOT
5-Band Windward/Leeward Low1146.80.5232
5-Band Windward/Leeward Low/Med850.30.7056
5-Band Windward/Leeward Medium729.80.8221
5-Band Windward/Leeward Med/High667.10.8994
5-Band Windward/Leeward High644.00.9317
Windward/Leeward 60-40 Low1148.70.5223
Windward/Leeward 60-40 Low/Med860.80.6970
Windward/Leeward 60-40 Medium747.70.8024
Windward/Leeward 60-40 Med/High692.40.8665
Windward/Leeward 60-40 High674.60.8894
5-Band AP Low845.30.7098
5-Band AP Low/Med676.60.8867
5-Band AP Medium598.31.0028
5-Band AP Med/High557.91.0755
5-Band AP High539.61.1118
5-Band SF Bay Tour - Low990.00.6061
5-Band SF Bay Tour - Low/Med814.80.7364
5-Band SF Bay Tour - Medium708.00.8475
5-Band SF Bay Tour - Med/High654.70.9164
5-Band SF Bay Tour - High634.40.9458
Chicago-Mac Upwind0.8501
Chicago-Mac All Purpose0.8795
Chicago-Mac Downwind0.9040
Bayview-Mac Cove Island0.6523
Bayview-Mac Shore0.6575
Harvest Moon Regatta530.21.1317
Club Certificate2025
FraganciaNOR 9727
Norges Seilforbund
Sognsveien 73
0854 OSLO
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassLINJETT 33MeasurementHINPlan reviewHull constructionSolidCarbon rudderNoLight stanchionsNoTrim tabNo
LOA10.040Max. Beam3.232Draft1.590Displacement4,462Wetted area20.64IMS L8.447LSM08.303Acc. length10.040Sink (kg/mm) 14.80
VCGD-0.050VCGM0.009RM Rated (kg·m) 74.2Limit of positive stability(°) N/AStability IndexN/ADefault crew weight528Declared crew weight350
PROPELLER
Propeller TypeFolding 2 blades
InstallationStrutTwin screwNoHydro generatorNo
PRD0.380PBWPIPA0.0033
EDL1.460ST10.050ST20.170
ST30.170ST40.100ST50.300
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerNoMainsail furlerArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders2Rotating mastNo
P12.450IG12.080ISP12.120MDT10.100MDL10.160MDT20.090MDL20.110TL2.320MW0.000GO0.000
E3.950J3.220BAS1.490FSD0.030SFJ0.000SPL3.730WPLTPS3.500BD0.000MWT0.00MCG0.000
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodVCG entered directlyVCG entered-0.050Flotation Date01/01/2015
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Club Certificate2025
FraganciaNOR 9727
Norges Seilforbund
Sognsveien 73
0854 OSLO
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment1-2016090116380.150.851.532.603.3929.8001/09/2016
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment626-2022041315330.040.591.162.393.715.0911.60NoNo 28.5813/04/2022626-2020060415580.040.460.861.702.533.3511.67YesNo 19.7804/06/2020336-2023031413490.100.440.771.532.353.259.50NoNo 15.0714/03/2023
SYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLAreaMeas.DateComment306-20180515091212.1012.1012.106.406.0063.7315/05/2018
CRUISER/RACER REQUIREMENTS*
Accommodation length10.0 mTable area0.44 m²Headroom1.70 mMinimum number of berths4Personal gear stowage0.16 m³Fresh water capacity80 lMinimum number of seats in cockpit4Food stowage0.24 m³Fuel capacity50 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.