Club Certificate2025
Amazing GraceCRO 2943
Hrvatski jedriličarski savez
Osječka 11
21000 Split
CROATIA
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 Angles47.1°47.1°45.6°44.0°42.8°41.9°41.3°41.2°42.3°
Beat VMG1.962.823.594.194.675.075.335.475.38
52°3.144.465.596.417.057.537.858.088.06
60°3.434.815.956.767.387.838.138.398.42
75°3.625.046.197.047.668.088.378.778.95
90°3.905.456.727.668.248.568.748.999.31
110°3.995.616.947.888.448.879.259.8310.19
120°3.885.456.757.738.348.799.2110.0310.78
135°3.384.846.127.167.948.458.889.7310.67
150°2.784.065.266.277.137.808.288.999.70
Run VMG2.413.524.555.436.186.767.237.998.59
Gybe Angles142.9°142.9°146.2°147.8°148.7°150.7°154.7°161.7°161.5°
APH ToD:560.5CDL: 10.092APH ToT: 1.0705CertNo:059/25
BOAT
ClassBavaria CR 46DesignerFarrBuilderBavariaAge date03/2022Series date02/2014Offset fileBAVARIACR45.offData fileCRO2943
HULL
Length Overall13.600 mMaximum Beam4.352 mDraft2.109 mDisplacement12,592 kgDLR6.4517IMS DivisionCruiser/RacerDynamic Allowance0.400%Age Allowance0.357%
PROPELLER
InstallationStrutTypeSolid 3 bladesDiameter0.432m
CREW
Maximum weight946 kg(default)Minimum weight804 kg ✱ when appliedNon Manual PowerCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail44.5544.31Headsail Luffed43.3843.38Headsail FlyingSymmetricAsymmetric143.32143.32 (1 asymmetric(s) with SHW/SFL < 85%)
STORM SAIL AREAS (m²)
Trysail16.36Storm Jib15.37Heavy Weather Jib41.49
SAIL LIMITS
Headsails6
✱ One set on the forestay
✱ Woven polyester sails
Spinnakers5
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
Amazing GraceCRO 2943
Hrvatski jedriličarski savez
Osječka 11
21000 Split
CROATIA
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 VMG1840.51276.61003.7859.9770.9710.5675.7658.0669.3
52°1147.9807.2644.5561.5510.6478.0458.4445.5446.5
60°1049.8748.0605.3532.2487.6460.0442.8428.9427.7
75°995.5714.3581.3511.5470.3445.8430.0410.4402.1
90°922.8660.4535.6470.3437.1420.4412.0400.5386.6
110°901.2642.0518.9457.0426.3406.0389.1366.3353.3
120°929.0661.1533.0466.0431.6409.7390.8359.0333.9
135°1064.8743.9587.8502.5453.6425.9405.6370.0337.3
150°1294.4885.7685.0573.8504.8461.3434.8400.3371.0
Run VMG1494.71022.7791.0662.5582.9532.4498.1450.8419.1
Selected Courses
Windward / Leeward1667.51149.6897.4761.2676.9621.5586.9554.4544.2
All purpose1244.0869.1687.7591.3534.2498.2475.3451.0439.7
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward713.20.8412
All purpose560.51.0705
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low778.40.7708
Triple Number Coastal/Long Distance Medium557.11.0771
Triple Number Coastal/Long Distance High471.91.2715
Triple Number Windward/Leeward Low1023.50.5862
Triple Number Windward/Leeward Medium709.50.8457
Triple Number Windward/Leeward High583.41.0285
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance616.60.9730
Triple Number Coastal/Long Distance Low778.40.7708
Triple Number Coastal/Long Distance Medium557.11.0771
Triple Number Coastal/Long Distance High471.91.2715
Triple Number Windward/Leeward Low1023.50.5862
Triple Number Windward/Leeward Medium709.50.8457
Triple Number Windward/Leeward High583.41.0285
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1758.31136.9835.8675.6576.0518.1478.7428.0413.7
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.7052
Downwind "popa"0.9250
70% up, 30% down "Ilhabela"0.7594
30% up, 70% down "Ilhabela-inverso"0.8459
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low778.40.7708
Triple Number Coastal/Long Distance Medium557.11.0771
Triple Number Coastal/Long Distance High471.91.2715
Triple Number Windward/Leeward Low1023.50.5862
Triple Number Windward/Leeward Medium709.50.8457
Triple Number Windward/Leeward High583.41.0285
Predominantly Upwind621.70.9651
Predominantly Downwind562.61.0664
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low778.40.7708
Triple Number AP Medium557.11.0769
Triple Number AP High471.91.2715
Triple Number Windward/Leeward Low1074.30.5585
Triple Number Windward/Leeward Medium709.50.8457
Triple Number Windward/Leeward High583.41.0285
Single Number Predominant Upwind654.80.9163
Single Number Predominant Reaching552.51.0859
Single Number Predominant Downwind591.41.0146
Predominant Upwind - Low998.60.6009
Predominant Upwind - Low/Med716.50.8374
Predominant Upwind - Medium594.61.0091
Predominant Upwind - Med/High524.51.1439
Predominant Upwind - High501.51.1964
Predominant Downwind Low919.30.6527
Predominant Downwind Low/Med652.70.9192
Predominant Downwind Medium536.31.1188
Predominant Downwind Med/High467.41.2838
Predominant Downwind High433.41.3843
Predominant Reaching Low831.70.7214
Predominant Reaching Low/Med601.40.9976
Predominant Reaching Medium503.91.1907
Predominant Reaching Med/High449.81.3339
Predominant Reaching High425.71.4094
SA/DSPL Upwind16.11SA/DSPL Downwind34.42
Scoring OptionTODTOT
5-Band Windward/Leeward Low1216.10.4934
5-Band Windward/Leeward Low/Med854.00.7026
5-Band Windward/Leeward Medium692.50.8665
5-Band Windward/Leeward Med/High594.91.0086
5-Band Windward/Leeward High558.31.0747
Windward/Leeward 60-40 Low1242.70.4828
Windward/Leeward 60-40 Low/Med874.90.6858
Windward/Leeward 60-40 Medium711.40.8434
Windward/Leeward 60-40 Med/High613.20.9784
Windward/Leeward 60-40 High579.21.0359
5-Band AP Low861.30.6967
5-Band AP Low/Med657.80.9121
5-Band AP Medium545.61.0998
5-Band AP Med/High480.01.2500
5-Band AP High453.21.3239
5-Band SF Bay Tour - Low1042.20.5757
5-Band SF Bay Tour - Low/Med817.60.7339
5-Band SF Bay Tour - Medium666.20.9006
5-Band SF Bay Tour - Med/High575.61.0424
5-Band SF Bay Tour - High542.21.1066
Chicago-Mac Upwind0.8752
Chicago-Mac All Purpose0.9259
Chicago-Mac Downwind0.9706
Bayview-Mac Cove Island0.6374
Bayview-Mac Shore0.6412
Harvest Moon Regatta466.11.2872
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance616.60.9730
Triple Number Coastal/Long Distance Low778.40.7708
Triple Number Coastal/Long Distance Medium557.11.0771
Triple Number Coastal/Long Distance High471.91.2715
Triple Number Windward/Leeward Low1023.50.5862
Triple Number Windward/Leeward Medium709.50.8457
Triple Number Windward/Leeward High583.41.0285
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1758.31136.9835.8675.6576.0518.1478.7428.0413.7
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance616.60.9730
Triple Number Coastal/Long Distance Low778.40.7708
Triple Number Coastal/Long Distance Medium557.11.0771
Triple Number Coastal/Long Distance High471.91.2715
Triple Number Windward/Leeward Low1023.50.5862
Triple Number Windward/Leeward Medium709.50.8457
Triple Number Windward/Leeward High583.41.0285
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1758.31136.9835.8675.6576.0518.1478.7428.0413.7
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance616.6
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1758.31136.9835.8675.6576.0518.1478.7428.0413.7
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low778.40.7708
Triple Number Coastal/Long Distance Medium557.11.0771
Triple Number Coastal/Long Distance High471.91.2715
Triple Number Windward/Leeward Low1023.50.5862
Triple Number Windward/Leeward Medium709.50.8457
Triple Number Windward/Leeward High583.41.0285
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating616.60.9730
FinRating, kevyt tuuli1188.20.8416
FinRating, kova tuuli455.71.0971
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low778.40.7708
Triple Number Coastal/Long Distance Medium557.11.0771
Triple Number Coastal/Long Distance High471.91.2715
Triple Number Windward/Leeward Low1023.50.5862
Triple Number Windward/Leeward Medium709.50.8457
Triple Number Windward/Leeward High583.41.0285
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.9730
Triple Number Coastal/Long Distance Low0.7708
Triple Number Coastal/Long Distance Medium1.0771
Triple Number Coastal/Long Distance High1.2715
Triple Number Windward/Leeward Low0.5862
Triple Number Windward/Leeward Medium0.8457
Triple Number Windward/Leeward High1.0285
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1758.31136.9835.8675.6576.0518.1478.7428.0413.7
For information
General Purpose Handicap (GPH)640.5
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance616.60.9730
Triple Number Coastal/Long Distance Low778.40.7708
Triple Number Coastal/Long Distance Medium557.11.0771
Triple Number Coastal/Long Distance High471.91.2715
Triple Number Windward/Leeward Low1023.50.5862
Triple Number Windward/Leeward Medium709.50.8457
Triple Number Windward/Leeward High583.41.0285
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1758.31136.9835.8675.6576.0518.1478.7428.0413.7
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low778.40.7708
Triple Number Coastal/Long Distance Medium557.11.0771
Triple Number Coastal/Long Distance High471.91.2715
Triple Number Windward/Leeward Low1023.50.5862
Triple Number Windward/Leeward Medium709.50.8457
Triple Number Windward/Leeward High583.41.0285
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance616.60.9730
Triple Number Coastal/Long Distance Low778.40.7708
Triple Number Coastal/Long Distance Medium557.11.0771
Triple Number Coastal/Long Distance High471.91.2715
Triple Number Windward/Leeward Low1023.50.5862
Triple Number Windward/Leeward Medium709.50.8457
Triple Number Windward/Leeward High583.41.0285
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1758.31136.9835.8675.6576.0518.1478.7428.0413.7
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance616.60.9730
Triple Number Coastal/Long Distance Low778.40.7708
Triple Number Coastal/Long Distance Medium557.11.0771
Triple Number Coastal/Long Distance High471.91.2715
Triple Number Windward/Leeward Low1023.50.5862
Triple Number Windward/Leeward Medium709.50.8457
Triple Number Windward/Leeward High583.41.0285
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1758.31136.9835.8675.6576.0518.1478.7428.0413.7
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low778.4
Triple Number Coastal/Long Distance Medium557.1
Triple Number Coastal/Long Distance High471.9
Triple Number Windward/Leeward Low1023.5
Triple Number Windward/Leeward Medium709.5
Triple Number Windward/Leeward High583.4
Predominantly Upwind621.7
Predominantly Downwind562.6
Predominantly Reaching534.9
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance616.60.9730
Triple Number Coastal/Long Distance Low778.40.7708
Triple Number Coastal/Long Distance Medium557.11.0771
Triple Number Coastal/Long Distance High471.91.2715
Triple Number Windward/Leeward Low1023.50.5862
Triple Number Windward/Leeward Medium709.50.8457
Triple Number Windward/Leeward High583.41.0285
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1758.31136.9835.8675.6576.0518.1478.7428.0413.7
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7708
Triple Number Coastal/Long Distance Medium1.0771
Triple Number Coastal/Long Distance High1.2715
Triple Number Windward/Leeward Low0.5862
Triple Number Windward/Leeward Medium0.8457
Triple Number Windward/Leeward High1.0285
Coastal/Long Distance0.9730
Predominantly Upwind0.9651
Predominantly Downwind1.0664
For information
General Purpose Handicap (GPH)640.5
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)1.0705
Distanseseilas Trippeltall svak vind0.7708
Distanseseilas Trippeltall mellomvind1.0771
Distanseseilas Trippeltall sterk vind1.2715
Pølsebane Trippeltall svak vind0.5862
Pølsebane Trippeltall mellomvind0.8457
Pølsebane Trippeltall sterk vind1.0285
Motvind Singeltall0.9651
Medvind Singeltall1.0664
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low778.40.7708
Triple Number Coastal/Long Distance Medium557.11.0771
Triple Number Coastal/Long Distance High471.91.2715
Triple Number Windward/Leeward Low1023.50.5862
Triple Number Windward/Leeward Medium709.50.8457
Triple Number Windward/Leeward High583.41.0285
Coastal/Long Distance616.60.9730
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind621.70.9651
Predominantly Downwind562.61.0664
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore547.31.0963
Cape Doctor Coastal443.01.3543
Triple Number Coastal/Long Distance Low778.40.7708
Triple Number Coastal/Long Distance Medium557.11.0771
Triple Number Coastal/Long Distance High471.91.2715
Triple Number Windward/Leeward Low1023.50.5862
Triple Number Windward/Leeward Medium709.50.8457
Triple Number Windward/Leeward High583.41.0285
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7708
Triple Number Coastal/Long Distance Medium1.0771
Triple Number Coastal/Long Distance High1.2715
Triple Number Windward/Leeward Low0.5862
Triple Number Windward/Leeward Medium0.8457
Triple Number Windward/Leeward High1.0285
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7708
Triple Number Coastal/Long Distance Medium1.0771
Triple Number Coastal/Long Distance High1.2715
Triple Number Windward/Leeward Low0.5862
Triple Number Windward/Leeward Medium0.8457
Triple Number Windward/Leeward High1.0285
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance616.60.9730
Triple Number Coastal/Long Distance Low778.40.7708
Triple Number Coastal/Long Distance Medium557.11.0771
Triple Number Coastal/Long Distance High471.91.2715
Triple Number Windward/Leeward Low1023.50.5862
Triple Number Windward/Leeward Medium709.50.8457
Triple Number Windward/Leeward High583.41.0285
Predominantly Upwind621.70.9651
Predominantly Downwind562.61.0664
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1758.31136.9835.8675.6576.0518.1478.7428.0413.7
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance616.60.9730
Triple Number Coastal/Long Distance Low778.40.7708
Triple Number Coastal/Long Distance Medium557.11.0771
Triple Number Coastal/Long Distance High471.91.2715
Triple Number Windward/Leeward Low1023.50.5862
Triple Number Windward/Leeward Medium709.50.8457
Triple Number Windward/Leeward High583.41.0285
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1758.31136.9835.8675.6576.0518.1478.7428.0413.7
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low778.40.7708
Triple Number AP Medium557.11.0769
Triple Number AP High471.91.2715
Triple Number Windward/Leeward Low1074.30.5585
Triple Number Windward/Leeward Medium709.50.8457
Triple Number Windward/Leeward High583.41.0285
Single Number Predominant Upwind654.80.9163
Single Number Predominant Reaching552.51.0859
Single Number Predominant Downwind591.41.0146
Predominant Upwind - Low998.60.6009
Predominant Upwind - Low/Med716.50.8374
Predominant Upwind - Medium594.61.0091
Predominant Upwind - Med/High524.51.1439
Predominant Upwind - High501.51.1964
Predominant Downwind Low919.30.6527
Predominant Downwind Low/Med652.70.9192
Predominant Downwind Medium536.31.1188
Predominant Downwind Med/High467.41.2838
Predominant Downwind High433.41.3843
Predominant Reaching Low831.70.7214
Predominant Reaching Low/Med601.40.9976
Predominant Reaching Medium503.91.1907
Predominant Reaching Med/High449.81.3339
Predominant Reaching High425.71.4094
SA/DSPL Upwind16.11SA/DSPL Downwind34.42
Scoring OptionTODTOT
5-Band Windward/Leeward Low1216.10.4934
5-Band Windward/Leeward Low/Med854.00.7026
5-Band Windward/Leeward Medium692.50.8665
5-Band Windward/Leeward Med/High594.91.0086
5-Band Windward/Leeward High558.31.0747
Windward/Leeward 60-40 Low1242.70.4828
Windward/Leeward 60-40 Low/Med874.90.6858
Windward/Leeward 60-40 Medium711.40.8434
Windward/Leeward 60-40 Med/High613.20.9784
Windward/Leeward 60-40 High579.21.0359
5-Band AP Low861.30.6967
5-Band AP Low/Med657.80.9121
5-Band AP Medium545.61.0998
5-Band AP Med/High480.01.2500
5-Band AP High453.21.3239
5-Band SF Bay Tour - Low1042.20.5757
5-Band SF Bay Tour - Low/Med817.60.7339
5-Band SF Bay Tour - Medium666.20.9006
5-Band SF Bay Tour - Med/High575.61.0424
5-Band SF Bay Tour - High542.21.1066
Chicago-Mac Upwind0.8752
Chicago-Mac All Purpose0.9259
Chicago-Mac Downwind0.9706
Bayview-Mac Cove Island0.6374
Bayview-Mac Shore0.6412
Harvest Moon Regatta466.11.2872
Club Certificate2025
Amazing GraceCRO 2943
Hrvatski jedriličarski savez
Osječka 11
21000 Split
CROATIA
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassBavaria CR 46Measurement31/03/2015HINPlan reviewHull constructionCoredCarbon rudderNoLight stanchionsNoTrim tabNo
LOA13.600Max. Beam4.352Draft2.109Displacement12,592Wetted area44.33IMS L12.680LSM012.496Acc. length13.600Sink (kg/mm) 33.91
VCGD0.274VCGM0.274RM Rated (kg·m) 360.2Limit of positive stability(°) N/AStability IndexN/ADefault crew weight946Declared crew weightN/A
PROPELLER
Propeller TypeSolid 3 blades
InstallationStrutTwin screwNoHydro generatorNo
PRD0.432PBWPIPA0.0226
EDLST1ST2
ST3ST4ST5
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerYesMainsail furlerIn mastArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders2Rotating mastNo
P16.900IG17.530ISP17.810MDT10.135MDL10.300MDT20.135MDL20.300TL0.000MW0.300GO0.300
E5.530J5.500BAS1.730FSD0.090SFJ0.000SPLWPLTPS6.000BD0.250MWTMCG
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodRM estimatedFlotation Date28/05/2014
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Club Certificate2025
Amazing GraceCRO 2943
Hrvatski jedriličarski savez
Osječka 11
21000 Split
CROATIA
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment10.060.631.242.553.9744.5503/07/2025
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment10.050.631.252.623.185.9217.00NoNo 43.3807/03/2025
ASYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLRatioAreaMeas.DateComment020.4118.5019.468.5010.2083%143.3220/04/2021
CRUISER/RACER REQUIREMENTS*
Accommodation length13.6 mTable area0.66 m²Headroom1.87 mMinimum number of berths6Personal gear stowage0.24 m³Fresh water capacity228 lMinimum number of seats in cockpit6Food stowage0.36 m³Fuel capacity122 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.