Club Certificate2025
ImaAUT
Austrian Sailing Federation
Seegelände 10
7100 Neusiedl am See
Austria
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 Angles44.2°44.2°42.0°40.4°39.1°38.1°37.5°37.1°37.4°
Beat VMG2.553.564.384.995.435.685.815.935.95
52°4.045.496.567.307.757.998.118.248.29
60°4.335.816.867.547.948.188.328.478.54
75°4.526.047.077.728.108.378.578.859.00
90°4.345.967.197.938.328.558.719.119.43
110°4.406.087.368.108.558.939.289.7510.12
120°4.285.937.217.998.478.899.3010.0910.72
135°3.805.326.597.558.148.578.999.8710.99
150°3.124.475.666.687.518.058.459.2110.06
Run VMG2.703.874.905.796.517.157.728.549.26
Gybe Angles142.4°142.4°146.5°149.0°150.8°160.6°172.7°178.1°178.1°
APH ToD:515.1CDL: 11.279APH ToT: 1.1649CertNo:041/25
BOAT
ClassDUFOUR 44 PERF.DesignerFELCIBuilderDUFOURAge date01/2007Series date01/2003Offset fileDUFOUR-44.offData fileIma
HULL
Length Overall13.330 mMaximum Beam4.226 mDraft2.357 mDisplacement11,640 kgDLR6.2028IMS DivisionCruiser/RacerDynamic Allowance0.270%Age Allowance0.487%
PROPELLER
InstallationStrutTypeFeathering 3 bladesDiameter0.440m
CREW
Maximum weight928 kg(default)Minimum weight789 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail54.2055.06Headsail Luffed47.7547.75Headsail FlyingSymmetricAsymmetric143.85143.85 (All asymmetric spinnakers with SHW/SFL > 85%)
STORM SAIL AREAS (m²)
Trysail16.27Storm Jib14.97Heavy Weather Jib40.41
SAIL LIMITS
Headsails7
✱ One set on the forestay
Spinnakers5
✱ Asymmetric may be tacked on the pole
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
ImaAUT
Austrian Sailing Federation
Seegelände 10
7100 Neusiedl am See
Austria
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 VMG1411.11012.1822.7721.1662.6633.8620.1607.3605.5
52°890.7656.2548.9492.9464.6450.6443.8437.0434.3
60°831.5619.2524.8477.2453.2440.2432.5425.1421.6
75°795.8596.3509.1466.5444.5430.3420.0407.0400.2
90°830.3603.7500.4454.0432.5421.3413.3395.0381.9
110°817.6592.1489.3444.5421.2403.0388.1369.3355.6
120°841.5607.4499.5450.4425.1405.1387.2356.7335.8
135°948.3676.7546.5477.0442.0419.9400.3364.6327.6
150°1154.2806.2635.8538.6479.6447.3426.0390.7358.0
Run VMG1332.1930.9734.2622.0553.4503.8466.3421.4388.9
Selected Courses
Windward / Leeward1371.3971.5778.4671.5608.0568.8543.2514.4497.2
All purpose1037.2745.4607.4535.3495.2471.1455.3433.9418.8
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward636.90.9420
All purpose515.11.1649
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low676.40.8871
Triple Number Coastal/Long Distance Medium511.91.1721
Triple Number Coastal/Long Distance High451.21.3297
Triple Number Windward/Leeward Low875.00.6857
Triple Number Windward/Leeward Medium633.60.9470
Triple Number Windward/Leeward High538.81.1136
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance562.21.0673
Triple Number Coastal/Long Distance Low676.40.8871
Triple Number Coastal/Long Distance Medium511.91.1721
Triple Number Coastal/Long Distance High451.21.3297
Triple Number Windward/Leeward Low875.00.6857
Triple Number Windward/Leeward Medium633.60.9470
Triple Number Windward/Leeward High538.81.1136
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1452.2967.5730.8604.1528.7489.1460.5416.4400.9
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.8268
Downwind "popa"0.9924
70% up, 30% down "Ilhabela"0.8704
30% up, 70% down "Ilhabela-inverso"0.9362
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low676.40.8871
Triple Number Coastal/Long Distance Medium511.91.1721
Triple Number Coastal/Long Distance High451.21.3297
Triple Number Windward/Leeward Low875.00.6857
Triple Number Windward/Leeward Medium633.60.9470
Triple Number Windward/Leeward High538.81.1136
Predominantly Upwind558.11.0752
Predominantly Downwind525.21.1424
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low676.40.8871
Triple Number AP Medium512.01.1719
Triple Number AP High451.21.3297
Triple Number Windward/Leeward Low913.90.6565
Triple Number Windward/Leeward Medium633.60.9470
Triple Number Windward/Leeward High538.81.1136
Single Number Predominant Upwind581.91.0312
Single Number Predominant Reaching513.61.1682
Single Number Predominant Downwind548.21.0944
Predominant Upwind - Low826.60.7259
Predominant Upwind - Low/Med621.20.9659
Predominant Upwind - Medium537.61.1161
Predominant Upwind - Med/High495.01.2122
Predominant Upwind - High477.11.2576
Predominant Downwind Low812.40.7386
Predominant Downwind Low/Med597.01.0050
Predominant Downwind Medium505.21.1877
Predominant Downwind Med/High448.41.3380
Predominant Downwind High415.71.4433
Predominant Reaching Low728.10.8241
Predominant Reaching Low/Med548.01.0949
Predominant Reaching Medium476.71.2588
Predominant Reaching Med/High437.21.3723
Predominant Reaching High413.91.4497
SA/DSPL Upwind19.69SA/DSPL Downwind38.25
Scoring OptionTODTOT
5-Band Windward/Leeward Low1023.30.5864
5-Band Windward/Leeward Low/Med744.00.8064
5-Band Windward/Leeward Medium620.80.9665
5-Band Windward/Leeward Med/High548.11.0947
5-Band Windward/Leeward High516.41.1620
Windward/Leeward 60-40 Low1031.50.5817
Windward/Leeward 60-40 Low/Med753.40.7963
Windward/Leeward 60-40 Medium632.10.9492
Windward/Leeward 60-40 Med/High563.21.0653
Windward/Leeward 60-40 High534.91.1216
5-Band AP Low746.60.8036
5-Band AP Low/Med585.81.0243
5-Band AP Medium503.91.1908
5-Band AP Med/High457.71.3109
5-Band AP High435.01.3793
5-Band SF Bay Tour - Low881.80.6805
5-Band SF Bay Tour - Low/Med710.80.8441
5-Band SF Bay Tour - Medium597.91.0035
5-Band SF Bay Tour - Med/High533.91.1237
5-Band SF Bay Tour - High505.51.1869
Chicago-Mac Upwind0.9952
Chicago-Mac All Purpose1.0272
Chicago-Mac Downwind1.0528
Bayview-Mac Cove Island0.7414
Bayview-Mac Shore0.7463
Harvest Moon Regatta446.71.3431
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance562.21.0673
Triple Number Coastal/Long Distance Low676.40.8871
Triple Number Coastal/Long Distance Medium511.91.1721
Triple Number Coastal/Long Distance High451.21.3297
Triple Number Windward/Leeward Low875.00.6857
Triple Number Windward/Leeward Medium633.60.9470
Triple Number Windward/Leeward High538.81.1136
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1452.2967.5730.8604.1528.7489.1460.5416.4400.9
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance562.21.0673
Triple Number Coastal/Long Distance Low676.40.8871
Triple Number Coastal/Long Distance Medium511.91.1721
Triple Number Coastal/Long Distance High451.21.3297
Triple Number Windward/Leeward Low875.00.6857
Triple Number Windward/Leeward Medium633.60.9470
Triple Number Windward/Leeward High538.81.1136
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1452.2967.5730.8604.1528.7489.1460.5416.4400.9
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance562.2
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1452.2967.5730.8604.1528.7489.1460.5416.4400.9
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low676.40.8871
Triple Number Coastal/Long Distance Medium511.91.1721
Triple Number Coastal/Long Distance High451.21.3297
Triple Number Windward/Leeward Low875.00.6857
Triple Number Windward/Leeward Medium633.60.9470
Triple Number Windward/Leeward High538.81.1136
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating562.21.0673
FinRating, kevyt tuuli1003.60.9964
FinRating, kova tuuli437.71.1423
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low676.40.8871
Triple Number Coastal/Long Distance Medium511.91.1721
Triple Number Coastal/Long Distance High451.21.3297
Triple Number Windward/Leeward Low875.00.6857
Triple Number Windward/Leeward Medium633.60.9470
Triple Number Windward/Leeward High538.81.1136
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance1.0673
Triple Number Coastal/Long Distance Low0.8871
Triple Number Coastal/Long Distance Medium1.1721
Triple Number Coastal/Long Distance High1.3297
Triple Number Windward/Leeward Low0.6857
Triple Number Windward/Leeward Medium0.9470
Triple Number Windward/Leeward High1.1136
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1452.2967.5730.8604.1528.7489.1460.5416.4400.9
For information
General Purpose Handicap (GPH)581.2
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance562.21.0673
Triple Number Coastal/Long Distance Low676.40.8871
Triple Number Coastal/Long Distance Medium511.91.1721
Triple Number Coastal/Long Distance High451.21.3297
Triple Number Windward/Leeward Low875.00.6857
Triple Number Windward/Leeward Medium633.60.9470
Triple Number Windward/Leeward High538.81.1136
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1452.2967.5730.8604.1528.7489.1460.5416.4400.9
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low676.40.8871
Triple Number Coastal/Long Distance Medium511.91.1721
Triple Number Coastal/Long Distance High451.21.3297
Triple Number Windward/Leeward Low875.00.6857
Triple Number Windward/Leeward Medium633.60.9470
Triple Number Windward/Leeward High538.81.1136
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance562.21.0673
Triple Number Coastal/Long Distance Low676.40.8871
Triple Number Coastal/Long Distance Medium511.91.1721
Triple Number Coastal/Long Distance High451.21.3297
Triple Number Windward/Leeward Low875.00.6857
Triple Number Windward/Leeward Medium633.60.9470
Triple Number Windward/Leeward High538.81.1136
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1452.2967.5730.8604.1528.7489.1460.5416.4400.9
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance562.21.0673
Triple Number Coastal/Long Distance Low676.40.8871
Triple Number Coastal/Long Distance Medium511.91.1721
Triple Number Coastal/Long Distance High451.21.3297
Triple Number Windward/Leeward Low875.00.6857
Triple Number Windward/Leeward Medium633.60.9470
Triple Number Windward/Leeward High538.81.1136
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1452.2967.5730.8604.1528.7489.1460.5416.4400.9
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low676.4
Triple Number Coastal/Long Distance Medium511.9
Triple Number Coastal/Long Distance High451.2
Triple Number Windward/Leeward Low875.0
Triple Number Windward/Leeward Medium633.6
Triple Number Windward/Leeward High538.8
Predominantly Upwind558.1
Predominantly Downwind525.2
Predominantly Reaching502.0
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance562.21.0673
Triple Number Coastal/Long Distance Low676.40.8871
Triple Number Coastal/Long Distance Medium511.91.1721
Triple Number Coastal/Long Distance High451.21.3297
Triple Number Windward/Leeward Low875.00.6857
Triple Number Windward/Leeward Medium633.60.9470
Triple Number Windward/Leeward High538.81.1136
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1452.2967.5730.8604.1528.7489.1460.5416.4400.9
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8871
Triple Number Coastal/Long Distance Medium1.1721
Triple Number Coastal/Long Distance High1.3297
Triple Number Windward/Leeward Low0.6857
Triple Number Windward/Leeward Medium0.9470
Triple Number Windward/Leeward High1.1136
Coastal/Long Distance1.0673
Predominantly Upwind1.0752
Predominantly Downwind1.1424
For information
General Purpose Handicap (GPH)581.2
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)1.1649
Distanseseilas Trippeltall svak vind0.8871
Distanseseilas Trippeltall mellomvind1.1721
Distanseseilas Trippeltall sterk vind1.3297
Pølsebane Trippeltall svak vind0.6857
Pølsebane Trippeltall mellomvind0.9470
Pølsebane Trippeltall sterk vind1.1136
Motvind Singeltall1.0752
Medvind Singeltall1.1424
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low676.40.8871
Triple Number Coastal/Long Distance Medium511.91.1721
Triple Number Coastal/Long Distance High451.21.3297
Triple Number Windward/Leeward Low875.00.6857
Triple Number Windward/Leeward Medium633.60.9470
Triple Number Windward/Leeward High538.81.1136
Coastal/Long Distance562.21.0673
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind558.11.0752
Predominantly Downwind525.21.1424
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore502.31.1944
Cape Doctor Coastal423.31.4174
Triple Number Coastal/Long Distance Low676.40.8871
Triple Number Coastal/Long Distance Medium511.91.1721
Triple Number Coastal/Long Distance High451.21.3297
Triple Number Windward/Leeward Low875.00.6857
Triple Number Windward/Leeward Medium633.60.9470
Triple Number Windward/Leeward High538.81.1136
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8871
Triple Number Coastal/Long Distance Medium1.1721
Triple Number Coastal/Long Distance High1.3297
Triple Number Windward/Leeward Low0.6857
Triple Number Windward/Leeward Medium0.9470
Triple Number Windward/Leeward High1.1136
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8871
Triple Number Coastal/Long Distance Medium1.1721
Triple Number Coastal/Long Distance High1.3297
Triple Number Windward/Leeward Low0.6857
Triple Number Windward/Leeward Medium0.9470
Triple Number Windward/Leeward High1.1136
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance562.21.0673
Triple Number Coastal/Long Distance Low676.40.8871
Triple Number Coastal/Long Distance Medium511.91.1721
Triple Number Coastal/Long Distance High451.21.3297
Triple Number Windward/Leeward Low875.00.6857
Triple Number Windward/Leeward Medium633.60.9470
Triple Number Windward/Leeward High538.81.1136
Predominantly Upwind558.11.0752
Predominantly Downwind525.21.1424
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1452.2967.5730.8604.1528.7489.1460.5416.4400.9
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance562.21.0673
Triple Number Coastal/Long Distance Low676.40.8871
Triple Number Coastal/Long Distance Medium511.91.1721
Triple Number Coastal/Long Distance High451.21.3297
Triple Number Windward/Leeward Low875.00.6857
Triple Number Windward/Leeward Medium633.60.9470
Triple Number Windward/Leeward High538.81.1136
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1452.2967.5730.8604.1528.7489.1460.5416.4400.9
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low676.40.8871
Triple Number AP Medium512.01.1719
Triple Number AP High451.21.3297
Triple Number Windward/Leeward Low913.90.6565
Triple Number Windward/Leeward Medium633.60.9470
Triple Number Windward/Leeward High538.81.1136
Single Number Predominant Upwind581.91.0312
Single Number Predominant Reaching513.61.1682
Single Number Predominant Downwind548.21.0944
Predominant Upwind - Low826.60.7259
Predominant Upwind - Low/Med621.20.9659
Predominant Upwind - Medium537.61.1161
Predominant Upwind - Med/High495.01.2122
Predominant Upwind - High477.11.2576
Predominant Downwind Low812.40.7386
Predominant Downwind Low/Med597.01.0050
Predominant Downwind Medium505.21.1877
Predominant Downwind Med/High448.41.3380
Predominant Downwind High415.71.4433
Predominant Reaching Low728.10.8241
Predominant Reaching Low/Med548.01.0949
Predominant Reaching Medium476.71.2588
Predominant Reaching Med/High437.21.3723
Predominant Reaching High413.91.4497
SA/DSPL Upwind19.69SA/DSPL Downwind38.25
Scoring OptionTODTOT
5-Band Windward/Leeward Low1023.30.5864
5-Band Windward/Leeward Low/Med744.00.8064
5-Band Windward/Leeward Medium620.80.9665
5-Band Windward/Leeward Med/High548.11.0947
5-Band Windward/Leeward High516.41.1620
Windward/Leeward 60-40 Low1031.50.5817
Windward/Leeward 60-40 Low/Med753.40.7963
Windward/Leeward 60-40 Medium632.10.9492
Windward/Leeward 60-40 Med/High563.21.0653
Windward/Leeward 60-40 High534.91.1216
5-Band AP Low746.60.8036
5-Band AP Low/Med585.81.0243
5-Band AP Medium503.91.1908
5-Band AP Med/High457.71.3109
5-Band AP High435.01.3793
5-Band SF Bay Tour - Low881.80.6805
5-Band SF Bay Tour - Low/Med710.80.8441
5-Band SF Bay Tour - Medium597.91.0035
5-Band SF Bay Tour - Med/High533.91.1237
5-Band SF Bay Tour - High505.51.1869
Chicago-Mac Upwind0.9952
Chicago-Mac All Purpose1.0272
Chicago-Mac Downwind1.0528
Bayview-Mac Cove Island0.7414
Bayview-Mac Shore0.7463
Harvest Moon Regatta446.71.3431
Club Certificate2025
ImaAUT
Austrian Sailing Federation
Seegelände 10
7100 Neusiedl am See
Austria
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassDUFOUR 44 PERF.Measurement01/09/2006HINFR-DUFE1823A707Plan reviewHull constructionSolidCarbon rudderNoLight stanchionsNoTrim tabNo
LOA13.330Max. Beam4.226Draft2.357Displacement11,640Wetted area39.15IMS L12.400LSM012.333Acc. length13.330Sink (kg/mm) 30.54
VCGD0.188VCGM0.070RM Rated (kg·m) 310.8Limit of positive stability(°) N/AStability IndexN/ADefault crew weight928Declared crew weightN/A
PROPELLER
Propeller TypeFeathering 3 blades
InstallationStrutTwin screwNoHydro generatorNo
PRD0.440PBWPIPA0.0039
EDL2.630ST10.040ST20.180
ST30.180ST40.180ST50.280
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerYesMainsail furlerNoArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0Checkstays0Spreaders3Rotating mastNo
P16.750IG17.300ISP17.300MDT10.130MDL10.230MDT20.120MDL20.100TL0.972MW0.230GO0.230
E5.550J5.220BAS1.610FSDFoilSFJ0.000SPL5.000WPLTPS6.260BD0.195MWT0.00MCG0.000
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodRM estimatedFlotation Date01/01/2013
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Club Certificate2025
ImaAUT
Austrian Sailing Federation
Seegelände 10
7100 Neusiedl am See
Austria
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateCommentorig0.171.081.983.494.6154.20
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateCommentorig0.060.791.512.884.165.3817.02NoNo 47.75
ASYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLRatioAreaMeas.DateCommentorig18.6016.6017.609.7610.0098%143.85
CRUISER/RACER REQUIREMENTS*
Accommodation length13.3 mTable area0.66 m²Headroom1.86 mMinimum number of berths6Personal gear stowage0.24 m³Fresh water capacity219 lMinimum number of seats in cockpit6Food stowage0.36 m³Fuel capacity116 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.