Club Certificate2025
CLASSYTUR
Turkiye
Sailing
Federation
www.tyf.org.tr/
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 Angles48.6°48.6°47.3°46.1°44.9°44.0°43.6°43.9°45.3°
Beat VMG1.872.713.454.044.504.865.095.175.03
52°3.034.345.486.316.957.417.697.887.79
60°3.374.755.896.717.337.758.038.268.26
75°3.564.996.157.017.638.058.338.708.85
90°3.885.436.717.648.208.488.658.919.28
110°4.015.657.007.948.498.909.279.7910.15
120°3.905.496.837.818.418.859.2810.0910.74
135°3.374.866.197.268.028.528.969.8310.82
150°2.794.085.286.347.227.888.349.069.79
Run VMG2.423.534.575.496.256.837.298.038.64
Gybe Angles142.9°142.9°146.0°147.1°148.7°150.7°154.9°161.5°160.8°
APH ToD:567.3CDL: 9.870APH ToT: 1.0576CertNo:
BOAT
ClassBAVARIA CR 46DesignerFarrBuilderBavariaAge date01/2022Series date01/2013Offset fileBAVARIA46C-SD.offData fileTUR CLASSY
HULL
Length Overall13.600 mMaximum Beam4.352 mDraft1.755 mDisplacement12,700 kgDLR6.2378IMS DivisionCruiser/RacerDynamic Allowance0.390%Age Allowance0.390%
PROPELLER
InstallationStrutTypeSolid 3 bladesDiameter0.500m
CREW
Maximum weight1,020 kg(declared)Minimum weight867 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail45.0944.85Headsail Luffed48.7148.71Headsail FlyingSymmetricAsymmetric160.68160.68 (All asymmetric spinnakers with SHW/SFL > 85%)
STORM SAIL AREAS (m²)
Trysail16.46Storm Jib16.03Heavy Weather Jib43.26
SAIL LIMITS
Headsails6Spinnakers5
STABILITY
Righting MomentN/AStability IndexN/A
COMMENTS
IRC STANDART 15Apr2024
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
CLASSYTUR
Turkiye
Sailing
Federation
www.tyf.org.tr/
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 VMG1922.31329.91042.7891.2799.4740.3707.7695.7715.7
52°1188.1829.1657.2570.4518.3486.1467.9457.1462.1
60°1069.8758.4610.8536.5491.4464.5448.3435.9436.0
75°1010.0721.9585.1513.5471.5447.2432.0413.7406.9
90°928.4662.8536.4471.1439.2424.8416.3404.2387.9
110°896.8637.4514.4453.6424.1404.4388.3367.8354.7
120°923.6655.2526.9461.1428.3406.7387.9356.7335.1
135°1067.9740.5581.2495.9448.8422.3401.9366.2332.7
150°1288.6882.2681.6567.7498.7456.7431.4397.2367.7
Run VMG1488.01018.6787.0655.5575.9527.0493.9448.3416.6
Selected Courses
Windward / Leeward1705.11174.3914.9773.4687.6633.7600.8572.0566.1
All purpose1267.0882.5696.2597.1539.8504.7482.6460.4451.4
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward726.60.8258
All purpose567.31.0576
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low789.40.7601
Triple Number Coastal/Long Distance Medium563.21.0654
Triple Number Coastal/Long Distance High479.81.2505
Triple Number Windward/Leeward Low1044.60.5744
Triple Number Windward/Leeward Medium721.70.8314
Triple Number Windward/Leeward High598.21.0030
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance625.20.9597
Triple Number Coastal/Long Distance Low789.40.7601
Triple Number Coastal/Long Distance Medium563.21.0654
Triple Number Coastal/Long Distance High479.81.2505
Triple Number Windward/Leeward Low1044.60.5744
Triple Number Windward/Leeward Medium721.70.8314
Triple Number Windward/Leeward High598.21.0030
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1795.31158.7849.7684.1582.9525.0485.3433.1420.4
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.6767
Downwind "popa"0.9320
70% up, 30% down "Ilhabela"0.7373
30% up, 70% down "Ilhabela-inverso"0.8372
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low789.40.7601
Triple Number Coastal/Long Distance Medium563.21.0654
Triple Number Coastal/Long Distance High479.81.2505
Triple Number Windward/Leeward Low1044.60.5744
Triple Number Windward/Leeward Medium721.70.8314
Triple Number Windward/Leeward High598.21.0030
Predominantly Upwind634.70.9454
Predominantly Downwind563.21.0653
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low789.40.7601
Triple Number AP Medium563.31.0652
Triple Number AP High479.81.2505
Triple Number Windward/Leeward Low1096.50.5472
Triple Number Windward/Leeward Medium721.70.8314
Triple Number Windward/Leeward High598.21.0030
Single Number Predominant Upwind670.00.8955
Single Number Predominant Reaching557.01.0773
Single Number Predominant Downwind592.81.0122
Predominant Upwind - Low1024.70.5855
Predominant Upwind - Low/Med731.50.8202
Predominant Upwind - Medium606.50.9893
Predominant Upwind - Med/High537.91.1154
Predominant Upwind - High517.61.1591
Predominant Downwind Low924.50.6490
Predominant Downwind Low/Med653.40.9182
Predominant Downwind Medium536.31.1187
Predominant Downwind Med/High468.91.2795
Predominant Downwind High436.11.3760
Predominant Reaching Low840.60.7138
Predominant Reaching Low/Med604.90.9919
Predominant Reaching Medium506.91.1837
Predominant Reaching Med/High454.21.3209
Predominant Reaching High430.91.3925
SA/DSPL Upwind17.09SA/DSPL Downwind37.48
Scoring OptionTODTOT
5-Band Windward/Leeward Low1242.10.4830
5-Band Windward/Leeward Low/Med869.60.6899
5-Band Windward/Leeward Medium704.50.8516
5-Band Windward/Leeward Med/High608.80.9855
5-Band Windward/Leeward High576.01.0418
Windward/Leeward 60-40 Low1274.90.4706
Windward/Leeward 60-40 Low/Med894.80.6705
Windward/Leeward 60-40 Medium727.10.8252
Windward/Leeward 60-40 Med/High630.80.9511
Windward/Leeward 60-40 High601.00.9983
5-Band AP Low869.50.6901
5-Band AP Low/Med665.60.9014
5-Band AP Medium551.71.0875
5-Band AP Med/High487.41.2310
5-Band AP High462.71.2968
5-Band SF Bay Tour - Low1065.20.5632
5-Band SF Bay Tour - Low/Med833.30.7200
5-Band SF Bay Tour - Medium678.60.8842
5-Band SF Bay Tour - Med/High589.71.0175
5-Band SF Bay Tour - High559.81.0718
Chicago-Mac Upwind0.8555
Chicago-Mac All Purpose0.9141
Chicago-Mac Downwind0.9688
Bayview-Mac Cove Island0.6261
Bayview-Mac Shore0.6296
Harvest Moon Regatta467.21.2843
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance625.20.9597
Triple Number Coastal/Long Distance Low789.40.7601
Triple Number Coastal/Long Distance Medium563.21.0654
Triple Number Coastal/Long Distance High479.81.2505
Triple Number Windward/Leeward Low1044.60.5744
Triple Number Windward/Leeward Medium721.70.8314
Triple Number Windward/Leeward High598.21.0030
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1795.31158.7849.7684.1582.9525.0485.3433.1420.4
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance625.20.9597
Triple Number Coastal/Long Distance Low789.40.7601
Triple Number Coastal/Long Distance Medium563.21.0654
Triple Number Coastal/Long Distance High479.81.2505
Triple Number Windward/Leeward Low1044.60.5744
Triple Number Windward/Leeward Medium721.70.8314
Triple Number Windward/Leeward High598.21.0030
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1795.31158.7849.7684.1582.9525.0485.3433.1420.4
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance625.2
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1795.31158.7849.7684.1582.9525.0485.3433.1420.4
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low789.40.7601
Triple Number Coastal/Long Distance Medium563.21.0654
Triple Number Coastal/Long Distance High479.81.2505
Triple Number Windward/Leeward Low1044.60.5744
Triple Number Windward/Leeward Medium721.70.8314
Triple Number Windward/Leeward High598.21.0030
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating625.20.9597
FinRating, kevyt tuuli1210.70.8260
FinRating, kova tuuli464.51.0765
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low789.40.7601
Triple Number Coastal/Long Distance Medium563.21.0654
Triple Number Coastal/Long Distance High479.81.2505
Triple Number Windward/Leeward Low1044.60.5744
Triple Number Windward/Leeward Medium721.70.8314
Triple Number Windward/Leeward High598.21.0030
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.9597
Triple Number Coastal/Long Distance Low0.7601
Triple Number Coastal/Long Distance Medium1.0654
Triple Number Coastal/Long Distance High1.2505
Triple Number Windward/Leeward Low0.5744
Triple Number Windward/Leeward Medium0.8314
Triple Number Windward/Leeward High1.0030
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1795.31158.7849.7684.1582.9525.0485.3433.1420.4
For information
General Purpose Handicap (GPH)648.6
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance625.20.9597
Triple Number Coastal/Long Distance Low789.40.7601
Triple Number Coastal/Long Distance Medium563.21.0654
Triple Number Coastal/Long Distance High479.81.2505
Triple Number Windward/Leeward Low1044.60.5744
Triple Number Windward/Leeward Medium721.70.8314
Triple Number Windward/Leeward High598.21.0030
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1795.31158.7849.7684.1582.9525.0485.3433.1420.4
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low789.40.7601
Triple Number Coastal/Long Distance Medium563.21.0654
Triple Number Coastal/Long Distance High479.81.2505
Triple Number Windward/Leeward Low1044.60.5744
Triple Number Windward/Leeward Medium721.70.8314
Triple Number Windward/Leeward High598.21.0030
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance625.20.9597
Triple Number Coastal/Long Distance Low789.40.7601
Triple Number Coastal/Long Distance Medium563.21.0654
Triple Number Coastal/Long Distance High479.81.2505
Triple Number Windward/Leeward Low1044.60.5744
Triple Number Windward/Leeward Medium721.70.8314
Triple Number Windward/Leeward High598.21.0030
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1795.31158.7849.7684.1582.9525.0485.3433.1420.4
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance625.20.9597
Triple Number Coastal/Long Distance Low789.40.7601
Triple Number Coastal/Long Distance Medium563.21.0654
Triple Number Coastal/Long Distance High479.81.2505
Triple Number Windward/Leeward Low1044.60.5744
Triple Number Windward/Leeward Medium721.70.8314
Triple Number Windward/Leeward High598.21.0030
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1795.31158.7849.7684.1582.9525.0485.3433.1420.4
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low789.4
Triple Number Coastal/Long Distance Medium563.2
Triple Number Coastal/Long Distance High479.8
Triple Number Windward/Leeward Low1044.6
Triple Number Windward/Leeward Medium721.7
Triple Number Windward/Leeward High598.2
Predominantly Upwind634.7
Predominantly Downwind563.2
Predominantly Reaching536.9
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance625.20.9597
Triple Number Coastal/Long Distance Low789.40.7601
Triple Number Coastal/Long Distance Medium563.21.0654
Triple Number Coastal/Long Distance High479.81.2505
Triple Number Windward/Leeward Low1044.60.5744
Triple Number Windward/Leeward Medium721.70.8314
Triple Number Windward/Leeward High598.21.0030
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1795.31158.7849.7684.1582.9525.0485.3433.1420.4
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7601
Triple Number Coastal/Long Distance Medium1.0654
Triple Number Coastal/Long Distance High1.2505
Triple Number Windward/Leeward Low0.5744
Triple Number Windward/Leeward Medium0.8314
Triple Number Windward/Leeward High1.0030
Coastal/Long Distance0.9597
Predominantly Upwind0.9454
Predominantly Downwind1.0653
For information
General Purpose Handicap (GPH)648.6
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)1.0576
Distanseseilas Trippeltall svak vind0.7601
Distanseseilas Trippeltall mellomvind1.0654
Distanseseilas Trippeltall sterk vind1.2505
Pølsebane Trippeltall svak vind0.5744
Pølsebane Trippeltall mellomvind0.8314
Pølsebane Trippeltall sterk vind1.0030
Motvind Singeltall0.9454
Medvind Singeltall1.0653
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low789.40.7601
Triple Number Coastal/Long Distance Medium563.21.0654
Triple Number Coastal/Long Distance High479.81.2505
Triple Number Windward/Leeward Low1044.60.5744
Triple Number Windward/Leeward Medium721.70.8314
Triple Number Windward/Leeward High598.21.0030
Coastal/Long Distance625.20.9597
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind634.70.9454
Predominantly Downwind563.21.0653
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore567.91.0565
Cape Doctor Coastal454.11.3213
Triple Number Coastal/Long Distance Low789.40.7601
Triple Number Coastal/Long Distance Medium563.21.0654
Triple Number Coastal/Long Distance High479.81.2505
Triple Number Windward/Leeward Low1044.60.5744
Triple Number Windward/Leeward Medium721.70.8314
Triple Number Windward/Leeward High598.21.0030
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7601
Triple Number Coastal/Long Distance Medium1.0654
Triple Number Coastal/Long Distance High1.2505
Triple Number Windward/Leeward Low0.5744
Triple Number Windward/Leeward Medium0.8314
Triple Number Windward/Leeward High1.0030
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7601
Triple Number Coastal/Long Distance Medium1.0654
Triple Number Coastal/Long Distance High1.2505
Triple Number Windward/Leeward Low0.5744
Triple Number Windward/Leeward Medium0.8314
Triple Number Windward/Leeward High1.0030
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance625.20.9597
Triple Number Coastal/Long Distance Low789.40.7601
Triple Number Coastal/Long Distance Medium563.21.0654
Triple Number Coastal/Long Distance High479.81.2505
Triple Number Windward/Leeward Low1044.60.5744
Triple Number Windward/Leeward Medium721.70.8314
Triple Number Windward/Leeward High598.21.0030
Predominantly Upwind634.70.9454
Predominantly Downwind563.21.0653
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1795.31158.7849.7684.1582.9525.0485.3433.1420.4
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance625.20.9597
Triple Number Coastal/Long Distance Low789.40.7601
Triple Number Coastal/Long Distance Medium563.21.0654
Triple Number Coastal/Long Distance High479.81.2505
Triple Number Windward/Leeward Low1044.60.5744
Triple Number Windward/Leeward Medium721.70.8314
Triple Number Windward/Leeward High598.21.0030
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1795.31158.7849.7684.1582.9525.0485.3433.1420.4
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low789.40.7601
Triple Number AP Medium563.31.0652
Triple Number AP High479.81.2505
Triple Number Windward/Leeward Low1096.50.5472
Triple Number Windward/Leeward Medium721.70.8314
Triple Number Windward/Leeward High598.21.0030
Single Number Predominant Upwind670.00.8955
Single Number Predominant Reaching557.01.0773
Single Number Predominant Downwind592.81.0122
Predominant Upwind - Low1024.70.5855
Predominant Upwind - Low/Med731.50.8202
Predominant Upwind - Medium606.50.9893
Predominant Upwind - Med/High537.91.1154
Predominant Upwind - High517.61.1591
Predominant Downwind Low924.50.6490
Predominant Downwind Low/Med653.40.9182
Predominant Downwind Medium536.31.1187
Predominant Downwind Med/High468.91.2795
Predominant Downwind High436.11.3760
Predominant Reaching Low840.60.7138
Predominant Reaching Low/Med604.90.9919
Predominant Reaching Medium506.91.1837
Predominant Reaching Med/High454.21.3209
Predominant Reaching High430.91.3925
SA/DSPL Upwind17.09SA/DSPL Downwind37.48
Scoring OptionTODTOT
5-Band Windward/Leeward Low1242.10.4830
5-Band Windward/Leeward Low/Med869.60.6899
5-Band Windward/Leeward Medium704.50.8516
5-Band Windward/Leeward Med/High608.80.9855
5-Band Windward/Leeward High576.01.0418
Windward/Leeward 60-40 Low1274.90.4706
Windward/Leeward 60-40 Low/Med894.80.6705
Windward/Leeward 60-40 Medium727.10.8252
Windward/Leeward 60-40 Med/High630.80.9511
Windward/Leeward 60-40 High601.00.9983
5-Band AP Low869.50.6901
5-Band AP Low/Med665.60.9014
5-Band AP Medium551.71.0875
5-Band AP Med/High487.41.2310
5-Band AP High462.71.2968
5-Band SF Bay Tour - Low1065.20.5632
5-Band SF Bay Tour - Low/Med833.30.7200
5-Band SF Bay Tour - Medium678.60.8842
5-Band SF Bay Tour - Med/High589.71.0175
5-Band SF Bay Tour - High559.81.0718
Chicago-Mac Upwind0.8555
Chicago-Mac All Purpose0.9141
Chicago-Mac Downwind0.9688
Bayview-Mac Cove Island0.6261
Bayview-Mac Shore0.6296
Harvest Moon Regatta467.21.2843
Club Certificate2025
CLASSYTUR
Turkiye
Sailing
Federation
www.tyf.org.tr/
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassBAVARIA CR 46MeasurementHINPlan reviewHull constructionSolidCarbon rudderNoLight stanchionsNoTrim tabNo
LOA13.600Max. Beam4.352Draft1.755Displacement12,700Wetted area46.38IMS L12.762LSM012.673Acc. length13.600Sink (kg/mm) 34.57
VCGD0.326VCGM0.319RM Rated (kg·m) 370.9Limit of positive stability(°) N/AStability IndexN/ADefault crew weight965Declared crew weight1,020
PROPELLER
Propeller TypeSolid 3 blades
InstallationStrutTwin screwNoHydro generatorNo
PRD0.500PBWPIPA0.0308
EDL2.100ST10.065ST20.180
ST30.180ST40.110ST50.265
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerNoMainsail furlerIn mastArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders2Rotating mastNo
P16.940IG17.900ISP18.820MDT10.146MDL10.289MDT20.000MDL20.000TL0.000MW0.000GO0.000
E5.550J5.510BAS1.768FSD0.042SFJ0.000SPL0.000WPLTPS5.850BD0.000MWT0.00MCG0.000
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodRM estimatedFlotation Date28/07/2025
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Club Certificate2025
CLASSYTUR
Turkiye
Sailing
Federation
www.tyf.org.tr/
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment00.621.232.574.0045.09IRC STANDART 15Apr24
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment00.611.212.605.9517.14NoNo 48.71IRC STANDART 15Apr24
ASYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLRatioAreaMeas.DateComment020.3016.9618.6310.4010.15102%160.68IRC STANDART 15Apr24
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.