Club Certificate2025
LunaNOR 10766
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 Angles42.4°42.4°40.4°38.9°38.2°37.8°37.7°37.9°39.1°
Beat VMG2.213.063.744.224.524.634.694.724.63
52°3.404.615.496.076.416.546.616.676.66
60°3.584.835.716.266.596.746.826.916.89
75°3.674.955.876.426.767.007.177.347.42
90°3.775.146.136.696.987.177.417.818.00
110°3.765.176.236.837.307.728.058.498.88
120°3.625.006.056.727.217.718.199.039.64
135°3.194.465.536.346.867.347.848.9810.62
150°2.633.784.815.666.336.797.188.049.06
Run VMG2.283.284.164.905.495.966.367.077.85
Gybe Angles144.9°144.9°147.7°148.7°151.4°157.4°161.9°160.6°142.9°
APH ToD:613.9CDL: 7.689APH ToT: 0.9774CertNo:8296
BOAT
ClassFirst 27.7DesignerFinotBuilderBeneteauAge date01/2003Series date01/2002Offset fileFIRST277.offData file8296
HULL
Length Overall8.300 mMaximum Beam3.022 mDraft2.140 mDisplacement2,915 kgDLR4.5334IMS DivisionCruiser/RacerDynamic Allowance0.180%Age Allowance0.487%
PROPELLER
InstallationStrutTypeFolding 2 bladesDiameter0.340m
CREW
Maximum weight558 kg(default)Minimum weight428 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail27.9628.78Headsail Luffed19.7219.72Headsail FlyingSymmetricAsymmetric60.7360.73 (All asymmetric spinnakers with SHW/SFL > 85%)
STORM SAIL AREAS (m²)
Trysail7.99Storm Jib6.66Heavy Weather Jib17.98
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
LunaNOR 10766
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 VMG1632.51177.1963.3853.3797.2777.7768.2763.3777.8
52°1059.7781.4655.4592.7561.8550.3544.7539.5540.9
60°1006.5746.0630.1574.7546.7533.9527.9521.3522.3
75°982.1726.8613.3560.5532.8514.1502.2490.3485.4
90°955.4700.8586.8537.8515.5502.3486.0461.2449.9
110°957.7695.9577.9527.1493.2466.4447.4424.0405.2
120°994.3720.6594.9536.0499.3466.9439.5398.6373.6
135°1130.0806.6651.4568.0524.6490.4459.0400.9339.1
150°1367.2951.8749.0636.3568.8530.5501.1447.8397.2
Run VMG1578.41099.1864.9734.7655.9604.2566.1509.4458.6
Selected Courses
Windward / Leeward1604.71138.1914.1794.0726.6690.9667.2636.4618.2
All purpose1221.1878.5717.6635.8591.1565.3546.6520.4503.2
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward761.80.7876
All purpose613.90.9774
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low798.10.7518
Triple Number Coastal/Long Distance Medium610.10.9835
Triple Number Coastal/Long Distance High541.51.1081
Triple Number Windward/Leeward Low1026.20.5847
Triple Number Windward/Leeward Medium755.80.7939
Triple Number Windward/Leeward High661.60.9069
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance668.40.8976
Triple Number Coastal/Long Distance Low798.10.7518
Triple Number Coastal/Long Distance Medium610.10.9835
Triple Number Coastal/Long Distance High541.51.1081
Triple Number Windward/Leeward Low1026.20.5847
Triple Number Windward/Leeward Medium755.80.7939
Triple Number Windward/Leeward High661.60.9069
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1699.81134.2859.3715.7631.3587.4551.8494.3477.3
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.6885
Downwind "popa"0.8343
70% up, 30% down "Ilhabela"0.7266
30% up, 70% down "Ilhabela-inverso"0.7845
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low798.10.7518
Triple Number Coastal/Long Distance Medium610.10.9835
Triple Number Coastal/Long Distance High541.51.1081
Triple Number Windward/Leeward Low1026.20.5847
Triple Number Windward/Leeward Medium755.80.7939
Triple Number Windward/Leeward High661.60.9069
Predominantly Upwind667.80.8984
Predominantly Downwind623.30.9626
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low798.00.7518
Triple Number AP Medium610.10.9834
Triple Number AP High541.51.1081
Triple Number Windward/Leeward Low1072.00.5597
Triple Number Windward/Leeward Medium755.80.7939
Triple Number Windward/Leeward High661.60.9069
Single Number Predominant Upwind696.20.8618
Single Number Predominant Reaching609.30.9848
Single Number Predominant Downwind650.40.9226
Predominant Upwind - Low971.20.6178
Predominant Upwind - Low/Med736.10.8152
Predominant Upwind - Medium645.10.9300
Predominant Upwind - Med/High601.90.9969
Predominant Upwind - High583.51.0282
Predominant Downwind Low959.40.6254
Predominant Downwind Low/Med707.20.8484
Predominant Downwind Medium601.20.9981
Predominant Downwind Med/High533.81.1239
Predominant Downwind High489.81.2251
Predominant Reaching Low856.60.7004
Predominant Reaching Low/Med649.30.9241
Predominant Reaching Medium568.21.0561
Predominant Reaching Med/High519.61.1548
Predominant Reaching High487.71.2303
SA/DSPL Upwind23.28SA/DSPL Downwind43.30
Scoring OptionTODTOT
5-Band Windward/Leeward Low1198.90.5004
5-Band Windward/Leeward Low/Med877.10.6841
5-Band Windward/Leeward Medium742.50.8080
5-Band Windward/Leeward Med/High671.00.8942
5-Band Windward/Leeward High638.60.9396
Windward/Leeward 60-40 Low1206.60.4972
Windward/Leeward 60-40 Low/Med887.90.6757
Windward/Leeward 60-40 Medium757.00.7926
Windward/Leeward 60-40 Med/High691.10.8682
Windward/Leeward 60-40 High664.20.9034
5-Band AP Low884.10.6787
5-Band AP Low/Med693.80.8648
5-Band AP Medium601.00.9983
5-Band AP Med/High549.11.0927
5-Band AP High522.01.1495
5-Band SF Bay Tour - Low1034.00.5803
5-Band SF Bay Tour - Low/Med838.50.7155
5-Band SF Bay Tour - Medium714.80.8394
5-Band SF Bay Tour - Med/High649.70.9234
5-Band SF Bay Tour - High619.30.9689
Chicago-Mac Upwind0.8349
Chicago-Mac All Purpose0.8643
Chicago-Mac Downwind0.8878
Bayview-Mac Cove Island0.6280
Bayview-Mac Shore0.6325
Harvest Moon Regatta526.41.1397
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance668.40.8976
Triple Number Coastal/Long Distance Low798.10.7518
Triple Number Coastal/Long Distance Medium610.10.9835
Triple Number Coastal/Long Distance High541.51.1081
Triple Number Windward/Leeward Low1026.20.5847
Triple Number Windward/Leeward Medium755.80.7939
Triple Number Windward/Leeward High661.60.9069
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1699.81134.2859.3715.7631.3587.4551.8494.3477.3
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance668.40.8976
Triple Number Coastal/Long Distance Low798.10.7518
Triple Number Coastal/Long Distance Medium610.10.9835
Triple Number Coastal/Long Distance High541.51.1081
Triple Number Windward/Leeward Low1026.20.5847
Triple Number Windward/Leeward Medium755.80.7939
Triple Number Windward/Leeward High661.60.9069
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1699.81134.2859.3715.7631.3587.4551.8494.3477.3
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance668.4
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1699.81134.2859.3715.7631.3587.4551.8494.3477.3
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low798.10.7518
Triple Number Coastal/Long Distance Medium610.10.9835
Triple Number Coastal/Long Distance High541.51.1081
Triple Number Windward/Leeward Low1026.20.5847
Triple Number Windward/Leeward Medium755.80.7939
Triple Number Windward/Leeward High661.60.9069
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating668.40.8976
FinRating, kevyt tuuli1177.40.8493
FinRating, kova tuuli524.80.9527
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low798.10.7518
Triple Number Coastal/Long Distance Medium610.10.9835
Triple Number Coastal/Long Distance High541.51.1081
Triple Number Windward/Leeward Low1026.20.5847
Triple Number Windward/Leeward Medium755.80.7939
Triple Number Windward/Leeward High661.60.9069
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.8976
Triple Number Coastal/Long Distance Low0.7518
Triple Number Coastal/Long Distance Medium0.9835
Triple Number Coastal/Long Distance High1.1081
Triple Number Windward/Leeward Low0.5847
Triple Number Windward/Leeward Medium0.7939
Triple Number Windward/Leeward High0.9069
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1699.81134.2859.3715.7631.3587.4551.8494.3477.3
For information
General Purpose Handicap (GPH)691.0
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance668.40.8976
Triple Number Coastal/Long Distance Low798.10.7518
Triple Number Coastal/Long Distance Medium610.10.9835
Triple Number Coastal/Long Distance High541.51.1081
Triple Number Windward/Leeward Low1026.20.5847
Triple Number Windward/Leeward Medium755.80.7939
Triple Number Windward/Leeward High661.60.9069
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1699.81134.2859.3715.7631.3587.4551.8494.3477.3
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low798.10.7518
Triple Number Coastal/Long Distance Medium610.10.9835
Triple Number Coastal/Long Distance High541.51.1081
Triple Number Windward/Leeward Low1026.20.5847
Triple Number Windward/Leeward Medium755.80.7939
Triple Number Windward/Leeward High661.60.9069
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance668.40.8976
Triple Number Coastal/Long Distance Low798.10.7518
Triple Number Coastal/Long Distance Medium610.10.9835
Triple Number Coastal/Long Distance High541.51.1081
Triple Number Windward/Leeward Low1026.20.5847
Triple Number Windward/Leeward Medium755.80.7939
Triple Number Windward/Leeward High661.60.9069
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1699.81134.2859.3715.7631.3587.4551.8494.3477.3
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance668.40.8976
Triple Number Coastal/Long Distance Low798.10.7518
Triple Number Coastal/Long Distance Medium610.10.9835
Triple Number Coastal/Long Distance High541.51.1081
Triple Number Windward/Leeward Low1026.20.5847
Triple Number Windward/Leeward Medium755.80.7939
Triple Number Windward/Leeward High661.60.9069
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1699.81134.2859.3715.7631.3587.4551.8494.3477.3
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low798.1
Triple Number Coastal/Long Distance Medium610.1
Triple Number Coastal/Long Distance High541.5
Triple Number Windward/Leeward Low1026.2
Triple Number Windward/Leeward Medium755.8
Triple Number Windward/Leeward High661.6
Predominantly Upwind667.8
Predominantly Downwind623.3
Predominantly Reaching595.5
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance668.40.8976
Triple Number Coastal/Long Distance Low798.10.7518
Triple Number Coastal/Long Distance Medium610.10.9835
Triple Number Coastal/Long Distance High541.51.1081
Triple Number Windward/Leeward Low1026.20.5847
Triple Number Windward/Leeward Medium755.80.7939
Triple Number Windward/Leeward High661.60.9069
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1699.81134.2859.3715.7631.3587.4551.8494.3477.3
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7518
Triple Number Coastal/Long Distance Medium0.9835
Triple Number Coastal/Long Distance High1.1081
Triple Number Windward/Leeward Low0.5847
Triple Number Windward/Leeward Medium0.7939
Triple Number Windward/Leeward High0.9069
Coastal/Long Distance0.8976
Predominantly Upwind0.8984
Predominantly Downwind0.9626
For information
General Purpose Handicap (GPH)691.0
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)0.9774
Distanseseilas Trippeltall svak vind0.7518
Distanseseilas Trippeltall mellomvind0.9835
Distanseseilas Trippeltall sterk vind1.1081
Pølsebane Trippeltall svak vind0.5847
Pølsebane Trippeltall mellomvind0.7939
Pølsebane Trippeltall sterk vind0.9069
Motvind Singeltall0.8984
Medvind Singeltall0.9626
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low798.10.7518
Triple Number Coastal/Long Distance Medium610.10.9835
Triple Number Coastal/Long Distance High541.51.1081
Triple Number Windward/Leeward Low1026.20.5847
Triple Number Windward/Leeward Medium755.80.7939
Triple Number Windward/Leeward High661.60.9069
Coastal/Long Distance668.40.8976
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind667.80.8984
Predominantly Downwind623.30.9626
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore623.60.9621
Cape Doctor Coastal508.31.1803
Triple Number Coastal/Long Distance Low798.10.7518
Triple Number Coastal/Long Distance Medium610.10.9835
Triple Number Coastal/Long Distance High541.51.1081
Triple Number Windward/Leeward Low1026.20.5847
Triple Number Windward/Leeward Medium755.80.7939
Triple Number Windward/Leeward High661.60.9069
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7518
Triple Number Coastal/Long Distance Medium0.9835
Triple Number Coastal/Long Distance High1.1081
Triple Number Windward/Leeward Low0.5847
Triple Number Windward/Leeward Medium0.7939
Triple Number Windward/Leeward High0.9069
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7518
Triple Number Coastal/Long Distance Medium0.9835
Triple Number Coastal/Long Distance High1.1081
Triple Number Windward/Leeward Low0.5847
Triple Number Windward/Leeward Medium0.7939
Triple Number Windward/Leeward High0.9069
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance668.40.8976
Triple Number Coastal/Long Distance Low798.10.7518
Triple Number Coastal/Long Distance Medium610.10.9835
Triple Number Coastal/Long Distance High541.51.1081
Triple Number Windward/Leeward Low1026.20.5847
Triple Number Windward/Leeward Medium755.80.7939
Triple Number Windward/Leeward High661.60.9069
Predominantly Upwind667.80.8984
Predominantly Downwind623.30.9626
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1699.81134.2859.3715.7631.3587.4551.8494.3477.3
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance668.40.8976
Triple Number Coastal/Long Distance Low798.10.7518
Triple Number Coastal/Long Distance Medium610.10.9835
Triple Number Coastal/Long Distance High541.51.1081
Triple Number Windward/Leeward Low1026.20.5847
Triple Number Windward/Leeward Medium755.80.7939
Triple Number Windward/Leeward High661.60.9069
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1699.81134.2859.3715.7631.3587.4551.8494.3477.3
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low798.00.7518
Triple Number AP Medium610.10.9834
Triple Number AP High541.51.1081
Triple Number Windward/Leeward Low1072.00.5597
Triple Number Windward/Leeward Medium755.80.7939
Triple Number Windward/Leeward High661.60.9069
Single Number Predominant Upwind696.20.8618
Single Number Predominant Reaching609.30.9848
Single Number Predominant Downwind650.40.9226
Predominant Upwind - Low971.20.6178
Predominant Upwind - Low/Med736.10.8152
Predominant Upwind - Medium645.10.9300
Predominant Upwind - Med/High601.90.9969
Predominant Upwind - High583.51.0282
Predominant Downwind Low959.40.6254
Predominant Downwind Low/Med707.20.8484
Predominant Downwind Medium601.20.9981
Predominant Downwind Med/High533.81.1239
Predominant Downwind High489.81.2251
Predominant Reaching Low856.60.7004
Predominant Reaching Low/Med649.30.9241
Predominant Reaching Medium568.21.0561
Predominant Reaching Med/High519.61.1548
Predominant Reaching High487.71.2303
SA/DSPL Upwind23.28SA/DSPL Downwind43.30
Scoring OptionTODTOT
5-Band Windward/Leeward Low1198.90.5004
5-Band Windward/Leeward Low/Med877.10.6841
5-Band Windward/Leeward Medium742.50.8080
5-Band Windward/Leeward Med/High671.00.8942
5-Band Windward/Leeward High638.60.9396
Windward/Leeward 60-40 Low1206.60.4972
Windward/Leeward 60-40 Low/Med887.90.6757
Windward/Leeward 60-40 Medium757.00.7926
Windward/Leeward 60-40 Med/High691.10.8682
Windward/Leeward 60-40 High664.20.9034
5-Band AP Low884.10.6787
5-Band AP Low/Med693.80.8648
5-Band AP Medium601.00.9983
5-Band AP Med/High549.11.0927
5-Band AP High522.01.1495
5-Band SF Bay Tour - Low1034.00.5803
5-Band SF Bay Tour - Low/Med838.50.7155
5-Band SF Bay Tour - Medium714.80.8394
5-Band SF Bay Tour - Med/High649.70.9234
5-Band SF Bay Tour - High619.30.9689
Chicago-Mac Upwind0.8349
Chicago-Mac All Purpose0.8643
Chicago-Mac Downwind0.8878
Bayview-Mac Cove Island0.6280
Bayview-Mac Shore0.6325
Harvest Moon Regatta526.41.1397
Club Certificate2025
LunaNOR 10766
Norges Seilforbund
Sognsveien 73
0854 OSLO
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassFirst 27.7MeasurementHINPlan reviewHull constructionSolidCarbon rudderNoLight stanchionsNoTrim tabNo
LOA8.300Max. Beam3.022Draft2.140Displacement2,915Wetted area18.81IMS L8.361LSM08.631Acc. length8.300Sink (kg/mm) 14.18
VCGD0.202VCGM0.240RM Rated (kg·m) 57.8Limit of positive stability(°) N/AStability IndexN/ADefault crew weight558Declared crew weightN/A
PROPELLER
Propeller TypeFolding 2 blades
InstallationStrutTwin screwNoHydro generatorNo
PRD0.340PBWPIPA0.0031
EDL2.000ST10.042ST20.180
ST30.180ST40.180ST50.250
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerNoMainsail furlerArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders1Rotating mastNo
P10.870IG11.495ISP11.765MDT10.105MDL10.160MDT20.105MDL20.160TL0.000MW0.160GO0.172
E4.200J3.180BAS1.410FSDFoilSFJ0.000SPL0.000WPLTPS3.640BD0.000MWT0.00MCG4.555
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodVCG entered directlyVCG entered0.202Flotation Date01/01/2015
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Club Certificate2025
LunaNOR 10766
Norges Seilforbund
Sognsveien 73
0854 OSLO
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment315-2004040212000.150.001.662.783.6027.9602/04/2004
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment315-2004040212010.000.000.000.000.003.5810.82NoNo 19.7202/04/2004398-2007051409440.000.000.000.000.003.4510.90NoNo 19.1414/05/2007
ASYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLRatioAreaMeas.DateComment398-20070514094212.1710.4011.296.466.45100%60.7314/05/2007
CRUISER/RACER REQUIREMENTS*
Accommodation length8.3 mTable area0.33 m²Headroom1.40 mMinimum number of berths3Personal gear stowage0.12 m³Fresh water capacity35 lMinimum number of seats in cockpit3Food stowage0.18 m³Fuel capacity20 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.