Club Certificate2025
KOBI SLIMAKESP-11319_C
RFEV
c/ Gamazo sn
39004 Santander – España
crucero@rfev.es
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 Angles45.0°45.0°43.1°41.4°40.8°41.2°41.3°41.6°42.2°
Beat VMG1.882.633.223.633.924.084.184.264.28
52°2.994.074.875.395.766.016.166.286.34
60°3.204.305.095.615.986.236.386.516.58
75°3.294.435.255.826.196.436.606.806.90
90°3.174.365.285.926.326.526.676.957.14
110°3.244.465.416.096.506.766.977.237.39
120°3.104.305.276.016.476.766.997.397.63
135°2.733.884.885.686.256.616.877.337.75
150°2.323.374.345.155.826.316.637.097.52
Run VMG2.012.923.764.495.135.686.126.727.14
Gybe Angles148.3°148.3°151.9°155.0°160.0°164.2°170.0°178.6°178.6°
APH ToD:686.8CDL: 6.862APH ToT: 0.8736CertNo:1131901
BOAT
ClassSUN LIGHT 30DesignerD. ANDRIEUBuilderJEANNEAUAge date04/1989Series date01/1987Offset fileSUNLIT30.OFFData fileE11319_C
HULL
Length Overall8.872 mMaximum Beam3.186 mDraft1.806 mDisplacement8,662 kgDLR13.0823IMS DivisionCruiser/RacerDynamic Allowance0.720%Age Allowance0.487%
PROPELLER
InstallationShaft exposedTypeSolid 2 bladesDiameter0.300m
CREW
Maximum weight566 kg(default)Minimum weight436 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail21.0021.33Headsail Luffed36.1136.11Headsail FlyingSymmetric74.5574.55Asymmetric
STORM SAIL AREAS (m²)
Trysail5.99Storm Jib7.66Heavy Weather Jib20.66
SAIL LIMITS
Headsails5
✱ One set on the forestay
✱ Woven polyester sails
Spinnakers4
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
KOBI SLIMAKESP-11319_C
RFEV
c/ Gamazo sn
39004 Santander – España
crucero@rfev.es
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 VMG1910.11370.51117.3990.7919.5882.3861.6844.3840.9
52°1205.0884.6739.4668.2624.7598.5584.2573.2567.8
60°1126.3836.8707.6641.5601.7578.2563.9553.1546.9
75°1094.0812.9686.3618.7581.3559.6545.6529.5521.7
90°1137.2826.2681.6607.7569.8552.0539.3518.2504.1
110°1111.1807.6665.5590.7553.6532.2516.4498.0487.2
120°1160.5837.1683.2599.0556.3532.6515.0487.0471.5
135°1317.6927.5738.2634.3576.0544.5523.9491.3464.6
150°1552.21067.6830.1698.6618.2570.6543.0507.6479.0
Run VMG1794.01232.7957.1801.9701.2633.4587.9535.8504.5
Selected Courses
Windward / Leeward1850.91301.61037.2896.3810.4757.9724.8690.0672.7
All purpose1408.81007.3816.6715.9657.9624.5603.7580.0566.1
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward849.70.7061
All purpose686.80.8736
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low912.00.6579
Triple Number Coastal/Long Distance Medium682.10.8797
Triple Number Coastal/Long Distance High600.01.0000
Triple Number Windward/Leeward Low1169.40.5131
Triple Number Windward/Leeward Medium844.80.7102
Triple Number Windward/Leeward High720.00.8333
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance748.30.8019
Triple Number Coastal/Long Distance Low912.00.6579
Triple Number Coastal/Long Distance Medium682.10.8797
Triple Number Coastal/Long Distance High600.01.0000
Triple Number Windward/Leeward Low1169.40.5131
Triple Number Windward/Leeward Medium844.80.7102
Triple Number Windward/Leeward High720.00.8333
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1952.91294.7974.9806.7704.5648.7609.3552.4537.9
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.6012
Downwind "popa"0.7706
70% up, 30% down "Ilhabela"0.6436
30% up, 70% down "Ilhabela-inverso"0.7106
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low912.00.6579
Triple Number Coastal/Long Distance Medium682.10.8797
Triple Number Coastal/Long Distance High600.01.0000
Triple Number Windward/Leeward Low1169.40.5131
Triple Number Windward/Leeward Medium844.80.7102
Triple Number Windward/Leeward High720.00.8333
Predominantly Upwind751.80.7981
Predominantly Downwind691.00.8684
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low912.00.6579
Triple Number AP Medium682.20.8795
Triple Number AP High600.01.0000
Triple Number Windward/Leeward Low1223.60.4904
Triple Number Windward/Leeward Medium844.80.7102
Triple Number Windward/Leeward High720.00.8333
Single Number Predominant Upwind784.80.7645
Single Number Predominant Reaching685.70.8750
Single Number Predominant Downwind725.20.8274
Predominant Upwind - Low1119.20.5361
Predominant Upwind - Low/Med839.30.7149
Predominant Upwind - Medium724.60.8281
Predominant Upwind - Med/High664.10.9035
Predominant Upwind - High641.40.9355
Predominant Downwind Low1097.40.5468
Predominant Downwind Low/Med794.10.7556
Predominant Downwind Medium662.00.9063
Predominant Downwind Med/High584.91.0259
Predominant Downwind High548.81.0933
Predominant Reaching Low990.30.6059
Predominant Reaching Low/Med736.70.8144
Predominant Reaching Medium631.90.9494
Predominant Reaching Med/High575.61.0423
Predominant Reaching High549.41.0920
SA/DSPL Upwind13.44SA/DSPL Downwind22.49
Scoring OptionTODTOT
5-Band Windward/Leeward Low1373.10.4370
5-Band Windward/Leeward Low/Med993.00.6042
5-Band Windward/Leeward Medium827.70.7249
5-Band Windward/Leeward Med/High731.70.8200
5-Band Windward/Leeward High693.00.8658
Windward/Leeward 60-40 Low1386.90.4326
Windward/Leeward 60-40 Low/Med1010.50.5937
Windward/Leeward 60-40 Medium849.50.7063
Windward/Leeward 60-40 Med/High758.80.7908
Windward/Leeward 60-40 High723.70.8290
5-Band AP Low1010.60.5937
5-Band AP Low/Med785.70.7636
5-Band AP Medium670.60.8947
5-Band AP Med/High607.80.9872
5-Band AP High581.71.0315
5-Band SF Bay Tour - Low1184.60.5065
5-Band SF Bay Tour - Low/Med953.00.6296
5-Band SF Bay Tour - Medium801.50.7486
5-Band SF Bay Tour - Med/High717.00.8368
5-Band SF Bay Tour - High683.50.8779
Chicago-Mac Upwind0.7368
Chicago-Mac All Purpose0.7677
Chicago-Mac Downwind0.7949
Bayview-Mac Cove Island0.5495
Bayview-Mac Shore0.5529
Harvest Moon Regatta587.11.0219
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance748.30.8019
Triple Number Coastal/Long Distance Low912.00.6579
Triple Number Coastal/Long Distance Medium682.10.8797
Triple Number Coastal/Long Distance High600.01.0000
Triple Number Windward/Leeward Low1169.40.5131
Triple Number Windward/Leeward Medium844.80.7102
Triple Number Windward/Leeward High720.00.8333
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1952.91294.7974.9806.7704.5648.7609.3552.4537.9
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance748.30.8019
Triple Number Coastal/Long Distance Low912.00.6579
Triple Number Coastal/Long Distance Medium682.10.8797
Triple Number Coastal/Long Distance High600.01.0000
Triple Number Windward/Leeward Low1169.40.5131
Triple Number Windward/Leeward Medium844.80.7102
Triple Number Windward/Leeward High720.00.8333
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1952.91294.7974.9806.7704.5648.7609.3552.4537.9
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance748.3
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1952.91294.7974.9806.7704.5648.7609.3552.4537.9
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low912.00.6579
Triple Number Coastal/Long Distance Medium682.10.8797
Triple Number Coastal/Long Distance High600.01.0000
Triple Number Windward/Leeward Low1169.40.5131
Triple Number Windward/Leeward Medium844.80.7102
Triple Number Windward/Leeward High720.00.8333
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating748.30.8019
FinRating, kevyt tuuli1350.00.7407
FinRating, kova tuuli585.10.8546
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low912.00.6579
Triple Number Coastal/Long Distance Medium682.10.8797
Triple Number Coastal/Long Distance High600.01.0000
Triple Number Windward/Leeward Low1169.40.5131
Triple Number Windward/Leeward Medium844.80.7102
Triple Number Windward/Leeward High720.00.8333
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.8019
Triple Number Coastal/Long Distance Low0.6579
Triple Number Coastal/Long Distance Medium0.8797
Triple Number Coastal/Long Distance High1.0000
Triple Number Windward/Leeward Low0.5131
Triple Number Windward/Leeward Medium0.7102
Triple Number Windward/Leeward High0.8333
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1952.91294.7974.9806.7704.5648.7609.3552.4537.9
For information
General Purpose Handicap (GPH)777.0
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance748.30.8019
Triple Number Coastal/Long Distance Low912.00.6579
Triple Number Coastal/Long Distance Medium682.10.8797
Triple Number Coastal/Long Distance High600.01.0000
Triple Number Windward/Leeward Low1169.40.5131
Triple Number Windward/Leeward Medium844.80.7102
Triple Number Windward/Leeward High720.00.8333
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1952.91294.7974.9806.7704.5648.7609.3552.4537.9
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low912.00.6579
Triple Number Coastal/Long Distance Medium682.10.8797
Triple Number Coastal/Long Distance High600.01.0000
Triple Number Windward/Leeward Low1169.40.5131
Triple Number Windward/Leeward Medium844.80.7102
Triple Number Windward/Leeward High720.00.8333
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance748.30.8019
Triple Number Coastal/Long Distance Low912.00.6579
Triple Number Coastal/Long Distance Medium682.10.8797
Triple Number Coastal/Long Distance High600.01.0000
Triple Number Windward/Leeward Low1169.40.5131
Triple Number Windward/Leeward Medium844.80.7102
Triple Number Windward/Leeward High720.00.8333
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1952.91294.7974.9806.7704.5648.7609.3552.4537.9
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance748.30.8019
Triple Number Coastal/Long Distance Low912.00.6579
Triple Number Coastal/Long Distance Medium682.10.8797
Triple Number Coastal/Long Distance High600.01.0000
Triple Number Windward/Leeward Low1169.40.5131
Triple Number Windward/Leeward Medium844.80.7102
Triple Number Windward/Leeward High720.00.8333
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1952.91294.7974.9806.7704.5648.7609.3552.4537.9
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low912.0
Triple Number Coastal/Long Distance Medium682.1
Triple Number Coastal/Long Distance High600.0
Triple Number Windward/Leeward Low1169.4
Triple Number Windward/Leeward Medium844.8
Triple Number Windward/Leeward High720.0
Predominantly Upwind751.8
Predominantly Downwind691.0
Predominantly Reaching665.0
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance748.30.8019
Triple Number Coastal/Long Distance Low912.00.6579
Triple Number Coastal/Long Distance Medium682.10.8797
Triple Number Coastal/Long Distance High600.01.0000
Triple Number Windward/Leeward Low1169.40.5131
Triple Number Windward/Leeward Medium844.80.7102
Triple Number Windward/Leeward High720.00.8333
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1952.91294.7974.9806.7704.5648.7609.3552.4537.9
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.6579
Triple Number Coastal/Long Distance Medium0.8797
Triple Number Coastal/Long Distance High1.0000
Triple Number Windward/Leeward Low0.5131
Triple Number Windward/Leeward Medium0.7102
Triple Number Windward/Leeward High0.8333
Coastal/Long Distance0.8019
Predominantly Upwind0.7981
Predominantly Downwind0.8684
For information
General Purpose Handicap (GPH)777.0
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)0.8736
Distanseseilas Trippeltall svak vind0.6579
Distanseseilas Trippeltall mellomvind0.8797
Distanseseilas Trippeltall sterk vind1.0000
Pølsebane Trippeltall svak vind0.5131
Pølsebane Trippeltall mellomvind0.7102
Pølsebane Trippeltall sterk vind0.8333
Motvind Singeltall0.7981
Medvind Singeltall0.8684
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low912.00.6579
Triple Number Coastal/Long Distance Medium682.10.8797
Triple Number Coastal/Long Distance High600.01.0000
Triple Number Windward/Leeward Low1169.40.5131
Triple Number Windward/Leeward Medium844.80.7102
Triple Number Windward/Leeward High720.00.8333
Coastal/Long Distance748.30.8019
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind751.80.7981
Predominantly Downwind691.00.8684
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore677.90.8851
Cape Doctor Coastal570.31.0521
Triple Number Coastal/Long Distance Low912.00.6579
Triple Number Coastal/Long Distance Medium682.10.8797
Triple Number Coastal/Long Distance High600.01.0000
Triple Number Windward/Leeward Low1169.40.5131
Triple Number Windward/Leeward Medium844.80.7102
Triple Number Windward/Leeward High720.00.8333
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.6579
Triple Number Coastal/Long Distance Medium0.8797
Triple Number Coastal/Long Distance High1.0000
Triple Number Windward/Leeward Low0.5131
Triple Number Windward/Leeward Medium0.7102
Triple Number Windward/Leeward High0.8333
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.6579
Triple Number Coastal/Long Distance Medium0.8797
Triple Number Coastal/Long Distance High1.0000
Triple Number Windward/Leeward Low0.5131
Triple Number Windward/Leeward Medium0.7102
Triple Number Windward/Leeward High0.8333
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance748.30.8019
Triple Number Coastal/Long Distance Low912.00.6579
Triple Number Coastal/Long Distance Medium682.10.8797
Triple Number Coastal/Long Distance High600.01.0000
Triple Number Windward/Leeward Low1169.40.5131
Triple Number Windward/Leeward Medium844.80.7102
Triple Number Windward/Leeward High720.00.8333
Predominantly Upwind751.80.7981
Predominantly Downwind691.00.8684
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1952.91294.7974.9806.7704.5648.7609.3552.4537.9
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance748.30.8019
Triple Number Coastal/Long Distance Low912.00.6579
Triple Number Coastal/Long Distance Medium682.10.8797
Triple Number Coastal/Long Distance High600.01.0000
Triple Number Windward/Leeward Low1169.40.5131
Triple Number Windward/Leeward Medium844.80.7102
Triple Number Windward/Leeward High720.00.8333
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1952.91294.7974.9806.7704.5648.7609.3552.4537.9
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low912.00.6579
Triple Number AP Medium682.20.8795
Triple Number AP High600.01.0000
Triple Number Windward/Leeward Low1223.60.4904
Triple Number Windward/Leeward Medium844.80.7102
Triple Number Windward/Leeward High720.00.8333
Single Number Predominant Upwind784.80.7645
Single Number Predominant Reaching685.70.8750
Single Number Predominant Downwind725.20.8274
Predominant Upwind - Low1119.20.5361
Predominant Upwind - Low/Med839.30.7149
Predominant Upwind - Medium724.60.8281
Predominant Upwind - Med/High664.10.9035
Predominant Upwind - High641.40.9355
Predominant Downwind Low1097.40.5468
Predominant Downwind Low/Med794.10.7556
Predominant Downwind Medium662.00.9063
Predominant Downwind Med/High584.91.0259
Predominant Downwind High548.81.0933
Predominant Reaching Low990.30.6059
Predominant Reaching Low/Med736.70.8144
Predominant Reaching Medium631.90.9494
Predominant Reaching Med/High575.61.0423
Predominant Reaching High549.41.0920
SA/DSPL Upwind13.44SA/DSPL Downwind22.49
Scoring OptionTODTOT
5-Band Windward/Leeward Low1373.10.4370
5-Band Windward/Leeward Low/Med993.00.6042
5-Band Windward/Leeward Medium827.70.7249
5-Band Windward/Leeward Med/High731.70.8200
5-Band Windward/Leeward High693.00.8658
Windward/Leeward 60-40 Low1386.90.4326
Windward/Leeward 60-40 Low/Med1010.50.5937
Windward/Leeward 60-40 Medium849.50.7063
Windward/Leeward 60-40 Med/High758.80.7908
Windward/Leeward 60-40 High723.70.8290
5-Band AP Low1010.60.5937
5-Band AP Low/Med785.70.7636
5-Band AP Medium670.60.8947
5-Band AP Med/High607.80.9872
5-Band AP High581.71.0315
5-Band SF Bay Tour - Low1184.60.5065
5-Band SF Bay Tour - Low/Med953.00.6296
5-Band SF Bay Tour - Medium801.50.7486
5-Band SF Bay Tour - Med/High717.00.8368
5-Band SF Bay Tour - High683.50.8779
Chicago-Mac Upwind0.7368
Chicago-Mac All Purpose0.7677
Chicago-Mac Downwind0.7949
Bayview-Mac Cove Island0.5495
Bayview-Mac Shore0.5529
Harvest Moon Regatta587.11.0219
Club Certificate2025
KOBI SLIMAKESP-11319_C
RFEV
c/ Gamazo sn
39004 Santander – España
crucero@rfev.es
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassSUN LIGHT 30MeasurementHINPlan reviewHull constructionSolidCarbon rudderNoLight stanchionsNoTrim tabNo
LOA8.872Max. Beam3.186Draft1.806Displacement8,662Wetted area26.12IMS L8.450LSM08.715Acc. length8.880Sink (kg/mm) 17.38
VCGD0.468VCGM0.152RM Rated (kg·m) 74.3Limit of positive stability(°) N/AStability IndexN/ADefault crew weight566Declared crew weightN/A
PROPELLER
Propeller TypeSolid 2 blades
InstallationShaft exposedTwin screwNoHydro generatorNo
PRD0.300PBWPIPA0.0118
PSD0.025PHD0.050PHL0.110
PSA23.0°ESL0.860
ST10.023ST20.072ST30.089
ST40.052ST50.250
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerYesMainsail furlerNoArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0Checkstays0Spreaders2Rotating mastNo
P11.000IG12.370ISP12.560MDT10.100MDL10.110MDT2MDL2TLMWGO
E3.110J3.650BAS1.270FSD0.050SFJ0.000SPL4.000WPLTPSBDMWTMCG
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodRM entered directlyRM entered75.0Flotation Date01/01/2010
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Club Certificate2025
KOBI SLIMAKESP-11319_C
RFEV
c/ Gamazo sn
39004 Santander – España
crucero@rfev.es
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment121.00
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateCommentORC5.50NoNo 36.11
SYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLAreaMeas.DateCommentORC0.0074.55RI
CRUISER/RACER REQUIREMENTS*
Accommodation length8.9 mTable area0.33 m²Headroom1.60 mMinimum number of berths3Personal gear stowage0.12 m³Fresh water capacity44 lMinimum number of seats in cockpit3Food stowage0.18 m³Fuel capacity28 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.