Club Certificate2025
Acid DropBUL 124
ORC Bulgaria
Varna
Mosrka Gara 1
orcratingbulgaria@gmail.com
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 Angles42.2°42.2°40.1°38.3°37.2°36.7°36.9°37.0°38.4°
Beat VMG2.653.664.464.975.195.305.375.425.31
52°4.115.536.517.057.277.377.457.537.47
60°4.365.796.727.227.477.607.697.807.78
75°4.535.966.867.347.707.968.108.318.40
90°4.415.956.997.417.728.118.448.869.09
110°4.536.097.177.798.288.618.939.529.99
120°4.385.967.087.738.348.929.3910.2111.04
135°3.835.366.587.347.948.579.2811.1713.39
150°3.184.515.666.637.307.818.339.6312.83
Run VMG2.753.904.905.746.356.797.228.3411.11
Gybe Angles142.6°142.6°146.7°149.8°152.8°154.3°151.9°144.3°143.4°
APH ToD:532.1CDL: 9.454APH ToT: 1.1277CertNo:013/25
BOAT
ClassFiumanka 33DesignerJustinBuilderAge date04/2008Series date01/2000Offset fileFIUMA33N.offData fileBUL124
HULL
Length Overall9.900 mMaximum Beam3.370 mDraft2.241 mDisplacement3,624 kgDLR4.1755IMS DivisionCruiser/RacerDynamic Allowance0.110%Age Allowance0.487%
PROPELLER
InstallationStrutTypeFolding 2 bladesDiameter0.380m
CREW
Maximum weight500 kg(declared)Minimum weight370 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail33.8334.22Headsail Luffed29.8029.80Headsail FlyingSymmetricAsymmetric104.87104.87 (All asymmetric spinnakers with SHW/SFL > 85%)
STORM SAIL AREAS (m²)
Trysail10.54Storm Jib10.47Heavy Weather Jib28.26
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
Acid DropBUL 124
ORC Bulgaria
Varna
Mosrka Gara 1
orcratingbulgaria@gmail.com
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 VMG1360.4983.0807.2723.7693.3679.1670.8663.9677.6
52°876.3651.1552.6511.0495.4488.1483.4478.2481.9
60°824.8621.4535.4498.9481.8473.7468.1461.5462.6
75°794.7603.7525.0490.2467.5452.5444.2433.3428.6
90°816.3605.0515.3485.8466.2443.9426.7406.5395.8
110°794.8590.7501.9462.3435.0418.0403.3378.3360.5
120°821.3604.3508.3465.6431.5403.6383.4352.6326.0
135°939.6671.4547.2490.3453.3420.0387.8322.4268.9
150°1131.6798.6635.7542.8492.9461.1432.3373.8280.5
Run VMG1307.3922.1734.0626.8566.6530.4498.6431.6323.9
Selected Courses
Windward / Leeward1333.6952.6770.6675.3630.0604.8584.7547.7500.8
All purpose1013.9736.8609.3548.3516.6495.9479.3451.2424.1
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward655.50.9153
All purpose532.11.1277
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low673.10.8914
Triple Number Coastal/Long Distance Medium529.71.1327
Triple Number Coastal/Long Distance High472.91.2688
Triple Number Windward/Leeward Low861.60.6964
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High575.91.0419
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance577.61.0388
Triple Number Coastal/Long Distance Low673.10.8914
Triple Number Coastal/Long Distance Medium529.71.1327
Triple Number Coastal/Long Distance High472.91.2688
Triple Number Windward/Leeward Low861.60.6964
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High575.91.0419
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1410.2949.5726.2612.8550.5514.3483.2431.8404.5
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.8044
Downwind "popa"0.9744
70% up, 30% down "Ilhabela"0.8489
30% up, 70% down "Ilhabela-inverso"0.9163
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low673.10.8914
Triple Number Coastal/Long Distance Medium529.71.1327
Triple Number Coastal/Long Distance High472.91.2688
Triple Number Windward/Leeward Low861.60.6964
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High575.91.0419
Predominantly Upwind577.91.0382
Predominantly Downwind537.31.1167
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low673.10.8914
Triple Number AP Medium529.81.1326
Triple Number AP High472.91.2688
Triple Number Windward/Leeward Low899.30.6672
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High575.91.0419
Single Number Predominant Upwind600.01.0000
Single Number Predominant Reaching527.31.1380
Single Number Predominant Downwind557.41.0764
Predominant Upwind - Low813.70.7374
Predominant Upwind - Low/Med627.80.9558
Predominant Upwind - Medium561.71.0681
Predominant Upwind - Med/High527.01.1386
Predominant Upwind - High507.61.1821
Predominant Downwind Low804.40.7459
Predominant Downwind Low/Med603.90.9936
Predominant Downwind Medium521.61.1502
Predominant Downwind Med/High462.81.2963
Predominant Downwind High413.61.4508
Predominant Reaching Low722.80.8301
Predominant Reaching Low/Med559.81.0719
Predominant Reaching Medium497.61.2057
Predominant Reaching Med/High452.71.3254
Predominant Reaching High419.71.4297
SA/DSPL Upwind26.85SA/DSPL Downwind58.53
Scoring OptionTODTOT
5-Band Windward/Leeward Low1002.40.5986
5-Band Windward/Leeward Low/Med743.00.8075
5-Band Windward/Leeward Medium641.20.9358
5-Band Windward/Leeward Med/High585.61.0245
5-Band Windward/Leeward High546.01.0989
Windward/Leeward 60-40 Low1008.60.5949
Windward/Leeward 60-40 Low/Med751.80.7981
Windward/Leeward 60-40 Medium653.60.9180
Windward/Leeward 60-40 Med/High603.10.9948
Windward/Leeward 60-40 High570.31.0521
5-Band AP Low740.80.8099
5-Band AP Low/Med592.91.0120
5-Band AP Medium523.01.1473
5-Band AP Med/High480.51.2488
5-Band AP High451.31.3294
5-Band SF Bay Tour - Low866.10.6928
5-Band SF Bay Tour - Low/Med710.50.8444
5-Band SF Bay Tour - Medium617.20.9722
5-Band SF Bay Tour - Med/High565.61.0609
5-Band SF Bay Tour - High529.91.1322
Chicago-Mac Upwind0.9721
Chicago-Mac All Purpose1.0063
Chicago-Mac Downwind1.0367
Bayview-Mac Cove Island0.7449
Bayview-Mac Shore0.7495
Harvest Moon Regatta459.21.3065
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance577.61.0388
Triple Number Coastal/Long Distance Low673.10.8914
Triple Number Coastal/Long Distance Medium529.71.1327
Triple Number Coastal/Long Distance High472.91.2688
Triple Number Windward/Leeward Low861.60.6964
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High575.91.0419
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1410.2949.5726.2612.8550.5514.3483.2431.8404.5
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance577.61.0388
Triple Number Coastal/Long Distance Low673.10.8914
Triple Number Coastal/Long Distance Medium529.71.1327
Triple Number Coastal/Long Distance High472.91.2688
Triple Number Windward/Leeward Low861.60.6964
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High575.91.0419
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1410.2949.5726.2612.8550.5514.3483.2431.8404.5
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance577.6
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1410.2949.5726.2612.8550.5514.3483.2431.8404.5
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low673.10.8914
Triple Number Coastal/Long Distance Medium529.71.1327
Triple Number Coastal/Long Distance High472.91.2688
Triple Number Windward/Leeward Low861.60.6964
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High575.91.0419
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating572.51.0480
FinRating, kevyt tuuli984.21.0161
FinRating, kova tuuli451.91.1065
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low673.10.8914
Triple Number Coastal/Long Distance Medium529.71.1327
Triple Number Coastal/Long Distance High472.91.2688
Triple Number Windward/Leeward Low861.60.6964
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High575.91.0419
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance1.0388
Triple Number Coastal/Long Distance Low0.8914
Triple Number Coastal/Long Distance Medium1.1327
Triple Number Coastal/Long Distance High1.2688
Triple Number Windward/Leeward Low0.6964
Triple Number Windward/Leeward Medium0.9224
Triple Number Windward/Leeward High1.0419
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1410.2949.5726.2612.8550.5514.3483.2431.8404.5
For information
General Purpose Handicap (GPH)595.0
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance577.61.0388
Triple Number Coastal/Long Distance Low673.10.8914
Triple Number Coastal/Long Distance Medium529.71.1327
Triple Number Coastal/Long Distance High472.91.2688
Triple Number Windward/Leeward Low861.60.6964
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High575.91.0419
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1410.2949.5726.2612.8550.5514.3483.2431.8404.5
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low673.10.8914
Triple Number Coastal/Long Distance Medium529.71.1327
Triple Number Coastal/Long Distance High472.91.2688
Triple Number Windward/Leeward Low861.60.6964
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High575.91.0419
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance577.61.0388
Triple Number Coastal/Long Distance Low673.10.8914
Triple Number Coastal/Long Distance Medium529.71.1327
Triple Number Coastal/Long Distance High472.91.2688
Triple Number Windward/Leeward Low861.60.6964
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High575.91.0419
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1410.2949.5726.2612.8550.5514.3483.2431.8404.5
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance577.61.0388
Triple Number Coastal/Long Distance Low673.10.8914
Triple Number Coastal/Long Distance Medium529.71.1327
Triple Number Coastal/Long Distance High472.91.2688
Triple Number Windward/Leeward Low861.60.6964
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High575.91.0419
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1410.2949.5726.2612.8550.5514.3483.2431.8404.5
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low673.1
Triple Number Coastal/Long Distance Medium529.7
Triple Number Coastal/Long Distance High472.9
Triple Number Windward/Leeward Low861.6
Triple Number Windward/Leeward Medium650.5
Triple Number Windward/Leeward High575.9
Predominantly Upwind577.9
Predominantly Downwind537.3
Predominantly Reaching516.2
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance577.61.0388
Triple Number Coastal/Long Distance Low673.10.8914
Triple Number Coastal/Long Distance Medium529.71.1327
Triple Number Coastal/Long Distance High472.91.2688
Triple Number Windward/Leeward Low861.60.6964
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High575.91.0419
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1410.2949.5726.2612.8550.5514.3483.2431.8404.5
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8914
Triple Number Coastal/Long Distance Medium1.1327
Triple Number Coastal/Long Distance High1.2688
Triple Number Windward/Leeward Low0.6964
Triple Number Windward/Leeward Medium0.9224
Triple Number Windward/Leeward High1.0419
Coastal/Long Distance1.0388
Predominantly Upwind1.0382
Predominantly Downwind1.1167
For information
General Purpose Handicap (GPH)595.0
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)1.1277
Distanseseilas Trippeltall svak vind0.8914
Distanseseilas Trippeltall mellomvind1.1327
Distanseseilas Trippeltall sterk vind1.2688
Pølsebane Trippeltall svak vind0.6964
Pølsebane Trippeltall mellomvind0.9224
Pølsebane Trippeltall sterk vind1.0419
Motvind Singeltall1.0382
Medvind Singeltall1.1167
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low673.10.8914
Triple Number Coastal/Long Distance Medium529.71.1327
Triple Number Coastal/Long Distance High472.91.2688
Triple Number Windward/Leeward Low861.60.6964
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High575.91.0419
Coastal/Long Distance577.61.0388
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind577.91.0382
Predominantly Downwind537.31.1167
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore514.91.1654
Cape Doctor Coastal432.21.3882
Triple Number Coastal/Long Distance Low673.10.8914
Triple Number Coastal/Long Distance Medium529.71.1327
Triple Number Coastal/Long Distance High472.91.2688
Triple Number Windward/Leeward Low861.60.6964
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High575.91.0419
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8914
Triple Number Coastal/Long Distance Medium1.1327
Triple Number Coastal/Long Distance High1.2688
Triple Number Windward/Leeward Low0.6964
Triple Number Windward/Leeward Medium0.9224
Triple Number Windward/Leeward High1.0419
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8914
Triple Number Coastal/Long Distance Medium1.1327
Triple Number Coastal/Long Distance High1.2688
Triple Number Windward/Leeward Low0.6964
Triple Number Windward/Leeward Medium0.9224
Triple Number Windward/Leeward High1.0419
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance577.61.0388
Triple Number Coastal/Long Distance Low673.10.8914
Triple Number Coastal/Long Distance Medium529.71.1327
Triple Number Coastal/Long Distance High472.91.2688
Triple Number Windward/Leeward Low861.60.6964
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High575.91.0419
Predominantly Upwind577.91.0382
Predominantly Downwind537.31.1167
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1410.2949.5726.2612.8550.5514.3483.2431.8404.5
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance577.61.0388
Triple Number Coastal/Long Distance Low673.10.8914
Triple Number Coastal/Long Distance Medium529.71.1327
Triple Number Coastal/Long Distance High472.91.2688
Triple Number Windward/Leeward Low861.60.6964
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High575.91.0419
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1410.2949.5726.2612.8550.5514.3483.2431.8404.5
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low673.10.8914
Triple Number AP Medium529.81.1326
Triple Number AP High472.91.2688
Triple Number Windward/Leeward Low899.30.6672
Triple Number Windward/Leeward Medium650.50.9224
Triple Number Windward/Leeward High575.91.0419
Single Number Predominant Upwind600.01.0000
Single Number Predominant Reaching527.31.1380
Single Number Predominant Downwind557.41.0764
Predominant Upwind - Low813.70.7374
Predominant Upwind - Low/Med627.80.9558
Predominant Upwind - Medium561.71.0681
Predominant Upwind - Med/High527.01.1386
Predominant Upwind - High507.61.1821
Predominant Downwind Low804.40.7459
Predominant Downwind Low/Med603.90.9936
Predominant Downwind Medium521.61.1502
Predominant Downwind Med/High462.81.2963
Predominant Downwind High413.61.4508
Predominant Reaching Low722.80.8301
Predominant Reaching Low/Med559.81.0719
Predominant Reaching Medium497.61.2057
Predominant Reaching Med/High452.71.3254
Predominant Reaching High419.71.4297
SA/DSPL Upwind26.85SA/DSPL Downwind58.53
Scoring OptionTODTOT
5-Band Windward/Leeward Low1002.40.5986
5-Band Windward/Leeward Low/Med743.00.8075
5-Band Windward/Leeward Medium641.20.9358
5-Band Windward/Leeward Med/High585.61.0245
5-Band Windward/Leeward High546.01.0989
Windward/Leeward 60-40 Low1008.60.5949
Windward/Leeward 60-40 Low/Med751.80.7981
Windward/Leeward 60-40 Medium653.60.9180
Windward/Leeward 60-40 Med/High603.10.9948
Windward/Leeward 60-40 High570.31.0521
5-Band AP Low740.80.8099
5-Band AP Low/Med592.91.0120
5-Band AP Medium523.01.1473
5-Band AP Med/High480.51.2488
5-Band AP High451.31.3294
5-Band SF Bay Tour - Low866.10.6928
5-Band SF Bay Tour - Low/Med710.50.8444
5-Band SF Bay Tour - Medium617.20.9722
5-Band SF Bay Tour - Med/High565.61.0609
5-Band SF Bay Tour - High529.91.1322
Chicago-Mac Upwind0.9721
Chicago-Mac All Purpose1.0063
Chicago-Mac Downwind1.0367
Bayview-Mac Cove Island0.7449
Bayview-Mac Shore0.7495
Harvest Moon Regatta459.21.3065
Club Certificate2025
Acid DropBUL 124
ORC Bulgaria
Varna
Mosrka Gara 1
orcratingbulgaria@gmail.com
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassFiumanka 33Measurement01/04/2011HINPlan reviewHull constructionCoredCarbon rudderNoLight stanchionsNoTrim tabNo
LOA9.900Max. Beam3.370Draft2.241Displacement3,624Wetted area21.54IMS L9.630LSM09.538Acc. length9.900Sink (kg/mm) 17.50
VCGD0.114VCGM0.050RM Rated (kg·m) 100.8Limit of positive stability(°) N/AStability IndexN/ADefault crew weight643Declared crew weight500
PROPELLER
Propeller TypeFolding 2 blades
InstallationStrutTwin screwNoHydro generatorNo
PRD0.380PBW0.112PIPA0.0035
EDL1.199ST10.065ST20.180
ST30.180ST40.110ST50.250
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerNoMainsail furlerNoArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders2Rotating mastNo
P13.610IG14.467ISP14.567MDT10.105MDL10.185MDT20.105MDL20.155TL0.800MW0.185GO0.185
E4.425J4.115BAS1.382FSD0.035SFJSPLWPLTPS4.920BD0.130MWTMCG
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodRM estimatedFlotation Date01/04/2011
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Club Certificate2025
Acid DropBUL 124
ORC Bulgaria
Varna
Mosrka Gara 1
orcratingbulgaria@gmail.com
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment10.140.811.442.623.5933.8321/04/2018
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment10.070.581.152.223.214.1113.84YesNo 29.8021/04/201820.060.390.731.371.982.5514.17YesNo 18.9701/04/2011
ASYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLRatioAreaMeas.DateComment115.6612.8514.268.699.3893%104.8701/04/2011
CRUISER/RACER REQUIREMENTS*
Accommodation length9.9 mTable area0.44 m²Headroom1.70 mMinimum number of berths4Personal gear stowage0.16 m³Fresh water capacity78 lMinimum number of seats in cockpit4Food stowage0.24 m³Fuel capacity48 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.