Double HandedClub Certificate2025
MelodyNOR 12494
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 Angles45.6°45.6°43.4°42.4°41.9°41.8°41.8°42.6°44.5°
Beat VMG2.293.193.904.404.714.844.894.864.67
52°3.664.975.936.606.987.197.277.307.20
60°3.945.296.246.877.257.467.567.637.60
75°4.145.536.487.107.487.727.908.098.17
90°4.025.456.517.257.697.988.158.448.68
110°3.965.476.647.397.858.228.579.179.52
120°3.835.306.477.277.768.158.539.2810.11
135°3.344.725.906.827.447.878.269.049.97
150°2.743.975.096.046.827.377.768.439.12
Run VMG2.373.444.415.235.916.436.897.648.25
Gybe Angles143.5°143.5°147.4°148.9°150.5°154.7°160.3°177.3°177.5°
APH ToD:574.3CDL: 9.078APH ToT: 1.0448CertNo:9638
BOAT
ClassBavaria 38 Cr 02-0DesignerJAKOPIN&JAKOPINBuilderBavaria YachtbauAge date01/2004Series date01/2002Offset fileba38jjsd.offData file9638
HULL
Length Overall11.830 mMaximum Beam3.898 mDraft1.714 mDisplacement7,551 kgDLR6.5556IMS DivisionCruiser/RacerDynamic Allowance0.360%Age Allowance0.487%
PROPELLER
InstallationStrutTypeFolding 3 bladesDiameter0.400m
CREW
Maximum weight170 kg(default)Minimum weight120 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail38.4939.33Headsail Luffed35.8635.86Headsail FlyingSymmetricAsymmetric69.8170.66 (All asymmetric spinnakers with SHW/SFL > 85%)
STORM SAIL AREAS (m²)
Trysail11.27Storm Jib10.59Heavy Weather Jib28.58
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.
Double HandedClub Certificate2025
MelodyNOR 12494
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 VMG1570.81130.1923.1818.2765.1744.2735.8741.1770.4
52°983.6724.8606.7545.7515.6501.0495.2493.0500.2
60°913.4680.6576.8523.7496.7482.6476.0471.7473.9
75°869.5651.3555.4506.9481.3466.1455.7444.8440.6
90°894.8660.5553.2496.2468.2451.4441.8426.4414.7
110°909.8658.2541.9487.0458.8437.9420.1392.8378.1
120°940.9679.0556.4495.3464.0441.6421.9387.8356.2
135°1076.3762.2610.4527.9483.7457.4436.0398.4361.0
150°1313.5906.1706.7596.0528.2488.4463.9427.2394.6
Run VMG1516.61046.3816.0688.2609.6559.6522.7470.9436.3
Selected Courses
Windward / Leeward1542.71088.2869.5753.2687.4651.9629.3606.0603.3
All purpose1157.2830.3675.5594.6550.9526.6510.7492.3484.8
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward721.80.8312
All purpose574.31.0448
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low752.90.7969
Triple Number Coastal/Long Distance Medium569.81.0530
Triple Number Coastal/Long Distance High507.71.1817
Triple Number Windward/Leeward Low979.00.6129
Triple Number Windward/Leeward Medium715.60.8384
Triple Number Windward/Leeward High626.20.9581
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance628.10.9553
Triple Number Coastal/Long Distance Low752.90.7969
Triple Number Coastal/Long Distance Medium569.81.0530
Triple Number Coastal/Long Distance High507.71.1817
Triple Number Windward/Leeward Low979.00.6129
Triple Number Windward/Leeward Medium715.60.8384
Triple Number Windward/Leeward High626.20.9581
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1636.91084.0815.3674.3591.1547.4514.9464.1450.6
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.7170
Downwind "popa"0.8911
70% up, 30% down "Ilhabela"0.7616
30% up, 70% down "Ilhabela-inverso"0.8306
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low752.90.7969
Triple Number Coastal/Long Distance Medium569.81.0530
Triple Number Coastal/Long Distance High507.71.1817
Triple Number Windward/Leeward Low979.00.6129
Triple Number Windward/Leeward Medium715.60.8384
Triple Number Windward/Leeward High626.20.9581
Predominantly Upwind626.30.9581
Predominantly Downwind581.81.0313
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low752.90.7969
Triple Number AP Medium569.81.0529
Triple Number AP High507.81.1817
Triple Number Windward/Leeward Low1023.70.5861
Triple Number Windward/Leeward Medium715.60.8384
Triple Number Windward/Leeward High626.20.9581
Single Number Predominant Upwind654.20.9171
Single Number Predominant Reaching567.71.0568
Single Number Predominant Downwind609.40.9846
Predominant Upwind - Low919.40.6526
Predominant Upwind - Low/Med692.90.8659
Predominant Upwind - Medium603.60.9941
Predominant Upwind - Med/High562.91.0659
Predominant Upwind - High552.41.0861
Predominant Downwind Low909.50.6597
Predominant Downwind Low/Med663.40.9044
Predominant Downwind Medium558.81.0736
Predominant Downwind Med/High497.91.2050
Predominant Downwind High465.21.2898
Predominant Reaching Low808.20.7424
Predominant Reaching Low/Med607.10.9884
Predominant Reaching Medium525.31.1422
Predominant Reaching Med/High481.81.2454
Predominant Reaching High460.41.3032
SA/DSPL Upwind19.19SA/DSPL Downwind27.95
Scoring OptionTODTOT
5-Band Windward/Leeward Low1147.40.5229
5-Band Windward/Leeward Low/Med833.80.7196
5-Band Windward/Leeward Medium702.80.8538
5-Band Windward/Leeward Med/High634.10.9463
5-Band Windward/Leeward High609.60.9843
Windward/Leeward 60-40 Low1155.60.5192
Windward/Leeward 60-40 Low/Med845.70.7094
Windward/Leeward 60-40 Medium718.40.8351
Windward/Leeward 60-40 Med/High655.40.9155
Windward/Leeward 60-40 High636.70.9423
5-Band AP Low830.80.7222
5-Band AP Low/Med651.40.9211
5-Band AP Medium561.11.0693
5-Band AP Med/High513.71.1681
5-Band AP High494.11.2142
5-Band SF Bay Tour - Low986.90.6079
5-Band SF Bay Tour - Low/Med796.70.7531
5-Band SF Bay Tour - Medium676.50.8869
5-Band SF Bay Tour - Med/High615.80.9744
5-Band SF Bay Tour - High595.01.0084
Chicago-Mac Upwind0.8868
Chicago-Mac All Purpose0.9202
Chicago-Mac Downwind0.9471
Bayview-Mac Cove Island0.6620
Bayview-Mac Shore0.6669
Harvest Moon Regatta488.31.2287
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance628.10.9553
Triple Number Coastal/Long Distance Low752.90.7969
Triple Number Coastal/Long Distance Medium569.81.0530
Triple Number Coastal/Long Distance High507.71.1817
Triple Number Windward/Leeward Low979.00.6129
Triple Number Windward/Leeward Medium715.60.8384
Triple Number Windward/Leeward High626.20.9581
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1636.91084.0815.3674.3591.1547.4514.9464.1450.6
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance628.10.9553
Triple Number Coastal/Long Distance Low752.90.7969
Triple Number Coastal/Long Distance Medium569.81.0530
Triple Number Coastal/Long Distance High507.71.1817
Triple Number Windward/Leeward Low979.00.6129
Triple Number Windward/Leeward Medium715.60.8384
Triple Number Windward/Leeward High626.20.9581
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1636.91084.0815.3674.3591.1547.4514.9464.1450.6
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance628.1
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1636.91084.0815.3674.3591.1547.4514.9464.1450.6
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low752.90.7969
Triple Number Coastal/Long Distance Medium569.81.0530
Triple Number Coastal/Long Distance High507.71.1817
Triple Number Windward/Leeward Low979.00.6129
Triple Number Windward/Leeward Medium715.60.8384
Triple Number Windward/Leeward High626.20.9581
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating628.10.9553
FinRating, kevyt tuuli1124.40.8893
FinRating, kova tuuli496.41.0073
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low752.90.7969
Triple Number Coastal/Long Distance Medium569.81.0530
Triple Number Coastal/Long Distance High507.71.1817
Triple Number Windward/Leeward Low979.00.6129
Triple Number Windward/Leeward Medium715.60.8384
Triple Number Windward/Leeward High626.20.9581
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.9553
Triple Number Coastal/Long Distance Low0.7969
Triple Number Coastal/Long Distance Medium1.0530
Triple Number Coastal/Long Distance High1.1817
Triple Number Windward/Leeward Low0.6129
Triple Number Windward/Leeward Medium0.8384
Triple Number Windward/Leeward High0.9581
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1636.91084.0815.3674.3591.1547.4514.9464.1450.6
For information
General Purpose Handicap (GPH)647.6
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance628.10.9553
Triple Number Coastal/Long Distance Low752.90.7969
Triple Number Coastal/Long Distance Medium569.81.0530
Triple Number Coastal/Long Distance High507.71.1817
Triple Number Windward/Leeward Low979.00.6129
Triple Number Windward/Leeward Medium715.60.8384
Triple Number Windward/Leeward High626.20.9581
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1636.91084.0815.3674.3591.1547.4514.9464.1450.6
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low752.90.7969
Triple Number Coastal/Long Distance Medium569.81.0530
Triple Number Coastal/Long Distance High507.71.1817
Triple Number Windward/Leeward Low979.00.6129
Triple Number Windward/Leeward Medium715.60.8384
Triple Number Windward/Leeward High626.20.9581
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance628.10.9553
Triple Number Coastal/Long Distance Low752.90.7969
Triple Number Coastal/Long Distance Medium569.81.0530
Triple Number Coastal/Long Distance High507.71.1817
Triple Number Windward/Leeward Low979.00.6129
Triple Number Windward/Leeward Medium715.60.8384
Triple Number Windward/Leeward High626.20.9581
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1636.91084.0815.3674.3591.1547.4514.9464.1450.6
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance628.10.9553
Triple Number Coastal/Long Distance Low752.90.7969
Triple Number Coastal/Long Distance Medium569.81.0530
Triple Number Coastal/Long Distance High507.71.1817
Triple Number Windward/Leeward Low979.00.6129
Triple Number Windward/Leeward Medium715.60.8384
Triple Number Windward/Leeward High626.20.9581
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1636.91084.0815.3674.3591.1547.4514.9464.1450.6
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low752.9
Triple Number Coastal/Long Distance Medium569.8
Triple Number Coastal/Long Distance High507.7
Triple Number Windward/Leeward Low979.0
Triple Number Windward/Leeward Medium715.6
Triple Number Windward/Leeward High626.2
Predominantly Upwind626.3
Predominantly Downwind581.8
Predominantly Reaching554.2
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance628.10.9553
Triple Number Coastal/Long Distance Low752.90.7969
Triple Number Coastal/Long Distance Medium569.81.0530
Triple Number Coastal/Long Distance High507.71.1817
Triple Number Windward/Leeward Low979.00.6129
Triple Number Windward/Leeward Medium715.60.8384
Triple Number Windward/Leeward High626.20.9581
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1636.91084.0815.3674.3591.1547.4514.9464.1450.6
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7969
Triple Number Coastal/Long Distance Medium1.0530
Triple Number Coastal/Long Distance High1.1817
Triple Number Windward/Leeward Low0.6129
Triple Number Windward/Leeward Medium0.8384
Triple Number Windward/Leeward High0.9581
Coastal/Long Distance0.9553
Predominantly Upwind0.9581
Predominantly Downwind1.0313
For information
General Purpose Handicap (GPH)647.6
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)1.0448
Distanseseilas Trippeltall svak vind0.7969
Distanseseilas Trippeltall mellomvind1.0530
Distanseseilas Trippeltall sterk vind1.1817
Pølsebane Trippeltall svak vind0.6129
Pølsebane Trippeltall mellomvind0.8384
Pølsebane Trippeltall sterk vind0.9581
Motvind Singeltall0.9581
Medvind Singeltall1.0313
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low752.90.7969
Triple Number Coastal/Long Distance Medium569.81.0530
Triple Number Coastal/Long Distance High507.71.1817
Triple Number Windward/Leeward Low979.00.6129
Triple Number Windward/Leeward Medium715.60.8384
Triple Number Windward/Leeward High626.20.9581
Coastal/Long Distance628.10.9553
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind626.30.9581
Predominantly Downwind581.81.0313
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore604.10.9932
Cape Doctor Coastal487.01.2320
Triple Number Coastal/Long Distance Low752.90.7969
Triple Number Coastal/Long Distance Medium569.81.0530
Triple Number Coastal/Long Distance High507.71.1817
Triple Number Windward/Leeward Low979.00.6129
Triple Number Windward/Leeward Medium715.60.8384
Triple Number Windward/Leeward High626.20.9581
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7969
Triple Number Coastal/Long Distance Medium1.0530
Triple Number Coastal/Long Distance High1.1817
Triple Number Windward/Leeward Low0.6129
Triple Number Windward/Leeward Medium0.8384
Triple Number Windward/Leeward High0.9581
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7969
Triple Number Coastal/Long Distance Medium1.0530
Triple Number Coastal/Long Distance High1.1817
Triple Number Windward/Leeward Low0.6129
Triple Number Windward/Leeward Medium0.8384
Triple Number Windward/Leeward High0.9581
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance628.10.9553
Triple Number Coastal/Long Distance Low752.90.7969
Triple Number Coastal/Long Distance Medium569.81.0530
Triple Number Coastal/Long Distance High507.71.1817
Triple Number Windward/Leeward Low979.00.6129
Triple Number Windward/Leeward Medium715.60.8384
Triple Number Windward/Leeward High626.20.9581
Predominantly Upwind626.30.9581
Predominantly Downwind581.81.0313
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1636.91084.0815.3674.3591.1547.4514.9464.1450.6
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance628.10.9553
Triple Number Coastal/Long Distance Low752.90.7969
Triple Number Coastal/Long Distance Medium569.81.0530
Triple Number Coastal/Long Distance High507.71.1817
Triple Number Windward/Leeward Low979.00.6129
Triple Number Windward/Leeward Medium715.60.8384
Triple Number Windward/Leeward High626.20.9581
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1636.91084.0815.3674.3591.1547.4514.9464.1450.6
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low752.90.7969
Triple Number AP Medium569.81.0529
Triple Number AP High507.81.1817
Triple Number Windward/Leeward Low1023.70.5861
Triple Number Windward/Leeward Medium715.60.8384
Triple Number Windward/Leeward High626.20.9581
Single Number Predominant Upwind654.20.9171
Single Number Predominant Reaching567.71.0568
Single Number Predominant Downwind609.40.9846
Predominant Upwind - Low919.40.6526
Predominant Upwind - Low/Med692.90.8659
Predominant Upwind - Medium603.60.9941
Predominant Upwind - Med/High562.91.0659
Predominant Upwind - High552.41.0861
Predominant Downwind Low909.50.6597
Predominant Downwind Low/Med663.40.9044
Predominant Downwind Medium558.81.0736
Predominant Downwind Med/High497.91.2050
Predominant Downwind High465.21.2898
Predominant Reaching Low808.20.7424
Predominant Reaching Low/Med607.10.9884
Predominant Reaching Medium525.31.1422
Predominant Reaching Med/High481.81.2454
Predominant Reaching High460.41.3032
SA/DSPL Upwind19.19SA/DSPL Downwind27.95
Scoring OptionTODTOT
5-Band Windward/Leeward Low1147.40.5229
5-Band Windward/Leeward Low/Med833.80.7196
5-Band Windward/Leeward Medium702.80.8538
5-Band Windward/Leeward Med/High634.10.9463
5-Band Windward/Leeward High609.60.9843
Windward/Leeward 60-40 Low1155.60.5192
Windward/Leeward 60-40 Low/Med845.70.7094
Windward/Leeward 60-40 Medium718.40.8351
Windward/Leeward 60-40 Med/High655.40.9155
Windward/Leeward 60-40 High636.70.9423
5-Band AP Low830.80.7222
5-Band AP Low/Med651.40.9211
5-Band AP Medium561.11.0693
5-Band AP Med/High513.71.1681
5-Band AP High494.11.2142
5-Band SF Bay Tour - Low986.90.6079
5-Band SF Bay Tour - Low/Med796.70.7531
5-Band SF Bay Tour - Medium676.50.8869
5-Band SF Bay Tour - Med/High615.80.9744
5-Band SF Bay Tour - High595.01.0084
Chicago-Mac Upwind0.8868
Chicago-Mac All Purpose0.9202
Chicago-Mac Downwind0.9471
Bayview-Mac Cove Island0.6620
Bayview-Mac Shore0.6669
Harvest Moon Regatta488.31.2287
Double HandedClub Certificate2025
MelodyNOR 12494
Norges Seilforbund
Sognsveien 73
0854 OSLO
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassBavaria 38 Cr 02-0MeasurementHINPlan reviewHull constructionSolidCarbon rudderNoLight stanchionsNoTrim tabNo
LOA11.830Max. Beam3.898Draft1.714Displacement7,551Wetted area30.36IMS L10.539LSM010.481Acc. length11.990Sink (kg/mm) 23.42
VCGD0.000VCGM-0.013RM Rated (kg·m) 200.2Limit of positive stability(°) N/AStability IndexN/ADefault crew weight170Declared crew weightN/A
PROPELLER
Propeller TypeFolding 3 blades
InstallationStrutTwin screwNoHydro generatorNo
PRD0.400PBWPIPA0.0035
EDL2.050ST10.042ST20.180
ST30.180ST40.180ST50.245
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerNoMainsail furlerArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders2Rotating mastNo
P13.550IG14.550ISP14.550MDT10.150MDL10.200MDT20.000MDL20.000TLNo TaperMW0.000GO0.000
E4.750J4.100BAS1.800FSDFoilSFJ0.000SPL0.000WPLTPS4.600BD0.000MWT0.00MCG0.000
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodVCG entered directlyVCG entered0.000Flotation Date01/01/2015
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Double HandedClub Certificate2025
MelodyNOR 12494
Norges Seilforbund
Sognsveien 73
0854 OSLO
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment7071-2004012412000.160.001.823.043.9538.4901/01/1753
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment388-2011012620050.000.000.000.000.005.2013.55NoNo 35.8626/01/2011
ASYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLRatioAreaMeas.DateComment300-20040510110013.6611.9112.796.377.2888%69.8110/05/2004
CRUISER/RACER REQUIREMENTS*
Accommodation length12.0 mTable area0.55 m²Headroom1.81 mMinimum number of berths5Personal gear stowage0.20 m³Fresh water capacity150 lMinimum number of seats in cockpit5Food stowage0.30 m³Fuel capacity90 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.