Non Spin/HSFClub Certificate2025
FarMedRSA-1335
ORC
Central Rating Office
Issuing certificates for
SOUTH AFRICA
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 Angles44.1°44.1°42.3°41.0°40.3°39.8°39.7°39.4°40.4°
Beat VMG1.902.653.263.704.044.294.414.474.37
52°2.984.074.895.465.886.166.316.396.35
60°3.174.285.105.686.076.336.486.596.59
75°3.254.405.245.856.246.496.676.896.94
90°3.164.295.155.806.236.516.727.047.25
110°2.763.884.845.596.156.516.777.207.56
120°2.603.704.665.426.016.416.707.177.60
135°2.263.304.245.015.656.146.486.987.43
150°1.922.853.744.525.175.746.186.747.18
Run VMG1.662.473.263.984.625.205.716.436.89
Gybe Angles150.5°150.5°154.6°162.2°169.9°173.5°175.9°179.0°179.2°
APH ToD:709.5CDL: 6.755APH ToT: 0.8456CertNo:ZAN047
BOAT
ClassMiuraDesignerBerckermeyerBuilderNebeAge date01/1990Series date01/1970Offset fileSA92033.OFFData fileRSA1335
HULL
Length Overall9.330 mMaximum Beam3.148 mDraft1.774 mDisplacement4,784 kgDLR9.8763IMS DivisionCruiser/RacerDynamic Allowance0.640%Age Allowance0.487%
PROPELLER
InstallationShaft exposedTypeSolid 2 bladesDiameter0.320m
CREW
Maximum weight420 kg(declared)Minimum weight290 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail17.7017.91Headsail Luffed28.1728.18Headsail FlyingSymmetricAsymmetric
STORM SAIL AREAS (m²)
Trysail5.44Storm Jib7.12Heavy Weather Jib19.22
SAIL LIMITS
Headsails5
✱ Zero set flying
Spinnakers0
✱ Spinnaker pole aboard
STABILITY
Righting MomentN/AStability IndexN/A
COMMENTS
vemedina@telkomsa.net
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.
Non Spin/HSFClub Certificate2025
FarMedRSA-1335
ORC
Central Rating Office
Issuing certificates for
SOUTH AFRICA
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 VMG1895.01357.31103.7972.4890.3840.0816.3805.6824.5
52°1207.7885.0736.7658.8611.9584.8570.5563.1566.8
60°1136.0840.7706.4634.2593.0569.1555.5546.0546.6
75°1107.4818.5686.5615.3576.9554.7539.8522.5518.4
90°1140.9839.3699.2620.5577.7552.9536.0511.7496.8
110°1305.9927.0744.5644.2585.7553.3532.0499.7475.9
120°1386.2972.8773.0664.7598.8561.3537.7502.4473.9
135°1592.31092.2849.1719.1637.4586.1555.3516.1484.5
150°1872.41261.6961.4796.8696.0627.3582.7534.4501.5
Run VMG2166.21456.31105.1905.4778.8692.6630.5559.5522.3
Selected Courses
Windward / Leeward2027.71406.81104.4938.9834.6766.3723.4682.5673.4
All purpose1532.91082.8866.0748.5677.1632.7605.6577.6566.5
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward878.70.6829
All purpose709.50.8456
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low974.30.6158
Triple Number Coastal/Long Distance Medium705.60.8504
Triple Number Coastal/Long Distance High601.90.9969
Triple Number Windward/Leeward Low1255.50.4779
Triple Number Windward/Leeward Medium874.80.6859
Triple Number Windward/Leeward High718.80.8347
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance775.70.7735
Triple Number Coastal/Long Distance Low974.30.6158
Triple Number Coastal/Long Distance Medium705.60.8504
Triple Number Coastal/Long Distance High601.90.9969
Triple Number Windward/Leeward Low1255.50.4779
Triple Number Windward/Leeward Medium874.80.6859
Triple Number Windward/Leeward High718.80.8347
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance2179.51411.71040.5845.4724.8657.6612.7554.4539.3
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.6190
Downwind "popa"0.6854
70% up, 30% down "Ilhabela"0.6375
30% up, 70% down "Ilhabela-inverso"0.6640
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low974.30.6158
Triple Number Coastal/Long Distance Medium705.60.8504
Triple Number Coastal/Long Distance High601.90.9969
Triple Number Windward/Leeward Low1255.50.4779
Triple Number Windward/Leeward Medium874.80.6859
Triple Number Windward/Leeward High718.80.8347
Predominantly Upwind756.90.7927
Predominantly Downwind741.80.8089
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low974.40.6158
Triple Number AP Medium705.60.8503
Triple Number AP High601.90.9969
Triple Number Windward/Leeward Low1316.50.4557
Triple Number Windward/Leeward Medium874.80.6859
Triple Number Windward/Leeward High718.80.8347
Single Number Predominant Upwind790.60.7590
Single Number Predominant Reaching714.40.8399
Single Number Predominant Downwind782.50.7668
Predominant Upwind - Low1155.60.5192
Predominant Upwind - Low/Med855.60.7013
Predominant Upwind - Medium725.80.8267
Predominant Upwind - Med/High653.20.9186
Predominant Upwind - High630.70.9514
Predominant Downwind Low1236.30.4853
Predominant Downwind Low/Med871.50.6885
Predominant Downwind Medium707.30.8483
Predominant Downwind Med/High605.90.9902
Predominant Downwind High560.81.0698
Predominant Reaching Low1063.20.5643
Predominant Reaching Low/Med778.80.7704
Predominant Reaching Medium654.60.9165
Predominant Reaching Med/High582.41.0303
Predominant Reaching High551.71.0875
SA/DSPL Upwind16.08SA/DSPL Downwind16.08
Scoring OptionTODTOT
5-Band Windward/Leeward Low1487.10.4035
5-Band Windward/Leeward Low/Med1050.80.5710
5-Band Windward/Leeward Medium853.70.7028
5-Band Windward/Leeward Med/High733.10.8184
5-Band Windward/Leeward High688.00.8721
Windward/Leeward 60-40 Low1475.40.4067
Windward/Leeward 60-40 Low/Med1053.30.5697
Windward/Leeward 60-40 Medium864.40.6941
Windward/Leeward 60-40 Med/High751.40.7985
Windward/Leeward 60-40 High712.60.8420
5-Band AP Low1101.90.5445
5-Band AP Low/Med828.60.7241
5-Band AP Medium691.30.8679
5-Band AP Med/High611.50.9813
5-Band AP High580.51.0335
5-Band SF Bay Tour - Low1269.20.4727
5-Band SF Bay Tour - Low/Med1003.70.5978
5-Band SF Bay Tour - Medium823.50.7286
5-Band SF Bay Tour - Med/High716.20.8378
5-Band SF Bay Tour - High677.80.8852
Chicago-Mac Upwind0.7287
Chicago-Mac All Purpose0.7346
Chicago-Mac Downwind0.7322
Bayview-Mac Cove Island0.5136
Bayview-Mac Shore0.5189
Harvest Moon Regatta608.00.9868
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance775.70.7735
Triple Number Coastal/Long Distance Low974.30.6158
Triple Number Coastal/Long Distance Medium705.60.8504
Triple Number Coastal/Long Distance High601.90.9969
Triple Number Windward/Leeward Low1255.50.4779
Triple Number Windward/Leeward Medium874.80.6859
Triple Number Windward/Leeward High718.80.8347
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance2179.51411.71040.5845.4724.8657.6612.7554.4539.3
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance775.70.7735
Triple Number Coastal/Long Distance Low974.30.6158
Triple Number Coastal/Long Distance Medium705.60.8504
Triple Number Coastal/Long Distance High601.90.9969
Triple Number Windward/Leeward Low1255.50.4779
Triple Number Windward/Leeward Medium874.80.6859
Triple Number Windward/Leeward High718.80.8347
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance2179.51411.71040.5845.4724.8657.6612.7554.4539.3
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance775.7
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance2179.51411.71040.5845.4724.8657.6612.7554.4539.3
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low974.30.6158
Triple Number Coastal/Long Distance Medium705.60.8504
Triple Number Coastal/Long Distance High601.90.9969
Triple Number Windward/Leeward Low1255.50.4779
Triple Number Windward/Leeward Medium874.80.6859
Triple Number Windward/Leeward High718.80.8347
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating775.70.7735
FinRating, kevyt tuuli1468.50.6810
FinRating, kova tuuli586.20.8530
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low974.30.6158
Triple Number Coastal/Long Distance Medium705.60.8504
Triple Number Coastal/Long Distance High601.90.9969
Triple Number Windward/Leeward Low1255.50.4779
Triple Number Windward/Leeward Medium874.80.6859
Triple Number Windward/Leeward High718.80.8347
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.7735
Triple Number Coastal/Long Distance Low0.6158
Triple Number Coastal/Long Distance Medium0.8504
Triple Number Coastal/Long Distance High0.9969
Triple Number Windward/Leeward Low0.4779
Triple Number Windward/Leeward Medium0.6859
Triple Number Windward/Leeward High0.8347
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance2179.51411.71040.5845.4724.8657.6612.7554.4539.3
For information
General Purpose Handicap (GPH)808.8
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance775.70.7735
Triple Number Coastal/Long Distance Low974.30.6158
Triple Number Coastal/Long Distance Medium705.60.8504
Triple Number Coastal/Long Distance High601.90.9969
Triple Number Windward/Leeward Low1255.50.4779
Triple Number Windward/Leeward Medium874.80.6859
Triple Number Windward/Leeward High718.80.8347
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance2179.51411.71040.5845.4724.8657.6612.7554.4539.3
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low974.30.6158
Triple Number Coastal/Long Distance Medium705.60.8504
Triple Number Coastal/Long Distance High601.90.9969
Triple Number Windward/Leeward Low1255.50.4779
Triple Number Windward/Leeward Medium874.80.6859
Triple Number Windward/Leeward High718.80.8347
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance775.70.7735
Triple Number Coastal/Long Distance Low974.30.6158
Triple Number Coastal/Long Distance Medium705.60.8504
Triple Number Coastal/Long Distance High601.90.9969
Triple Number Windward/Leeward Low1255.50.4779
Triple Number Windward/Leeward Medium874.80.6859
Triple Number Windward/Leeward High718.80.8347
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance2179.51411.71040.5845.4724.8657.6612.7554.4539.3
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance775.70.7735
Triple Number Coastal/Long Distance Low974.30.6158
Triple Number Coastal/Long Distance Medium705.60.8504
Triple Number Coastal/Long Distance High601.90.9969
Triple Number Windward/Leeward Low1255.50.4779
Triple Number Windward/Leeward Medium874.80.6859
Triple Number Windward/Leeward High718.80.8347
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance2179.51411.71040.5845.4724.8657.6612.7554.4539.3
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low974.3
Triple Number Coastal/Long Distance Medium705.6
Triple Number Coastal/Long Distance High601.9
Triple Number Windward/Leeward Low1255.5
Triple Number Windward/Leeward Medium874.8
Triple Number Windward/Leeward High718.8
Predominantly Upwind756.9
Predominantly Downwind741.8
Predominantly Reaching701.2
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance775.70.7735
Triple Number Coastal/Long Distance Low974.30.6158
Triple Number Coastal/Long Distance Medium705.60.8504
Triple Number Coastal/Long Distance High601.90.9969
Triple Number Windward/Leeward Low1255.50.4779
Triple Number Windward/Leeward Medium874.80.6859
Triple Number Windward/Leeward High718.80.8347
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance2179.51411.71040.5845.4724.8657.6612.7554.4539.3
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.6158
Triple Number Coastal/Long Distance Medium0.8504
Triple Number Coastal/Long Distance High0.9969
Triple Number Windward/Leeward Low0.4779
Triple Number Windward/Leeward Medium0.6859
Triple Number Windward/Leeward High0.8347
Coastal/Long Distance0.7735
Predominantly Upwind0.7927
Predominantly Downwind0.8089
For information
General Purpose Handicap (GPH)808.8
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)0.8456
Distanseseilas Trippeltall svak vind0.6158
Distanseseilas Trippeltall mellomvind0.8504
Distanseseilas Trippeltall sterk vind0.9969
Pølsebane Trippeltall svak vind0.4779
Pølsebane Trippeltall mellomvind0.6859
Pølsebane Trippeltall sterk vind0.8347
Motvind Singeltall0.7927
Medvind Singeltall0.8089
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low974.30.6158
Triple Number Coastal/Long Distance Medium705.60.8504
Triple Number Coastal/Long Distance High601.90.9969
Triple Number Windward/Leeward Low1255.50.4779
Triple Number Windward/Leeward Medium874.80.6859
Triple Number Windward/Leeward High718.80.8347
Coastal/Long Distance775.70.7735
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind756.90.7927
Predominantly Downwind741.80.8089
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore676.20.8874
Cape Doctor Coastal569.81.0529
Triple Number Coastal/Long Distance Low974.30.6158
Triple Number Coastal/Long Distance Medium705.60.8504
Triple Number Coastal/Long Distance High601.90.9969
Triple Number Windward/Leeward Low1255.50.4779
Triple Number Windward/Leeward Medium874.80.6859
Triple Number Windward/Leeward High718.80.8347
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.6158
Triple Number Coastal/Long Distance Medium0.8504
Triple Number Coastal/Long Distance High0.9969
Triple Number Windward/Leeward Low0.4779
Triple Number Windward/Leeward Medium0.6859
Triple Number Windward/Leeward High0.8347
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.6158
Triple Number Coastal/Long Distance Medium0.8504
Triple Number Coastal/Long Distance High0.9969
Triple Number Windward/Leeward Low0.4779
Triple Number Windward/Leeward Medium0.6859
Triple Number Windward/Leeward High0.8347
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance775.70.7735
Triple Number Coastal/Long Distance Low974.30.6158
Triple Number Coastal/Long Distance Medium705.60.8504
Triple Number Coastal/Long Distance High601.90.9969
Triple Number Windward/Leeward Low1255.50.4779
Triple Number Windward/Leeward Medium874.80.6859
Triple Number Windward/Leeward High718.80.8347
Predominantly Upwind756.90.7927
Predominantly Downwind741.80.8089
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance2179.51411.71040.5845.4724.8657.6612.7554.4539.3
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance775.70.7735
Triple Number Coastal/Long Distance Low974.30.6158
Triple Number Coastal/Long Distance Medium705.60.8504
Triple Number Coastal/Long Distance High601.90.9969
Triple Number Windward/Leeward Low1255.50.4779
Triple Number Windward/Leeward Medium874.80.6859
Triple Number Windward/Leeward High718.80.8347
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance2179.51411.71040.5845.4724.8657.6612.7554.4539.3
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low974.40.6158
Triple Number AP Medium705.60.8503
Triple Number AP High601.90.9969
Triple Number Windward/Leeward Low1316.50.4557
Triple Number Windward/Leeward Medium874.80.6859
Triple Number Windward/Leeward High718.80.8347
Single Number Predominant Upwind790.60.7590
Single Number Predominant Reaching714.40.8399
Single Number Predominant Downwind782.50.7668
Predominant Upwind - Low1155.60.5192
Predominant Upwind - Low/Med855.60.7013
Predominant Upwind - Medium725.80.8267
Predominant Upwind - Med/High653.20.9186
Predominant Upwind - High630.70.9514
Predominant Downwind Low1236.30.4853
Predominant Downwind Low/Med871.50.6885
Predominant Downwind Medium707.30.8483
Predominant Downwind Med/High605.90.9902
Predominant Downwind High560.81.0698
Predominant Reaching Low1063.20.5643
Predominant Reaching Low/Med778.80.7704
Predominant Reaching Medium654.60.9165
Predominant Reaching Med/High582.41.0303
Predominant Reaching High551.71.0875
SA/DSPL Upwind16.08SA/DSPL Downwind16.08
Scoring OptionTODTOT
5-Band Windward/Leeward Low1487.10.4035
5-Band Windward/Leeward Low/Med1050.80.5710
5-Band Windward/Leeward Medium853.70.7028
5-Band Windward/Leeward Med/High733.10.8184
5-Band Windward/Leeward High688.00.8721
Windward/Leeward 60-40 Low1475.40.4067
Windward/Leeward 60-40 Low/Med1053.30.5697
Windward/Leeward 60-40 Medium864.40.6941
Windward/Leeward 60-40 Med/High751.40.7985
Windward/Leeward 60-40 High712.60.8420
5-Band AP Low1101.90.5445
5-Band AP Low/Med828.60.7241
5-Band AP Medium691.30.8679
5-Band AP Med/High611.50.9813
5-Band AP High580.51.0335
5-Band SF Bay Tour - Low1269.20.4727
5-Band SF Bay Tour - Low/Med1003.70.5978
5-Band SF Bay Tour - Medium823.50.7286
5-Band SF Bay Tour - Med/High716.20.8378
5-Band SF Bay Tour - High677.80.8852
Chicago-Mac Upwind0.7287
Chicago-Mac All Purpose0.7346
Chicago-Mac Downwind0.7322
Bayview-Mac Cove Island0.5136
Bayview-Mac Shore0.5189
Harvest Moon Regatta608.00.9868
Non Spin/HSFClub Certificate2025
FarMedRSA-1335
ORC
Central Rating Office
Issuing certificates for
SOUTH AFRICA
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassMiuraMeasurement23/12/2013HINPlan reviewHull constructionSolidCarbon rudderNoLight stanchionsNoTrim tabNo
LOA9.330Max. Beam3.148Draft1.774Displacement4,784Wetted area21.48IMS L7.883LSM07.853Acc. length9.330Sink (kg/mm) 15.04
VCGD0.148VCGM0.149RM Rated (kg·m) 78.6Limit of positive stability(°) N/AStability IndexN/ADefault crew weight488Declared crew weight420
PROPELLER
Propeller TypeSolid 2 blades
InstallationShaft exposedTwin screwNoHydro generatorNo
PRD0.320PBW0.105PIPA0.0119
PSD0.028PHD0.049PHL0.120
PSA18.0°ESL0.635
ST10.015ST20.115ST30.162
ST40.052ST50.105
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerNoMainsail furlerNoArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0Checkstays0Spreaders1Rotating mastNo
P9.900IG11.855ISP11.805MDT10.120MDL10.170MDT2MDL2TLNo TaperMW0.185GO0.210
E3.140J3.890BAS1.485FSD0.013SFJ0.000SPL3.900WPLTPSBD0.132MWTMCG
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodRM estimatedFlotation Date03/12/2015
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Non Spin/HSFClub Certificate2025
FarMedRSA-1335
ORC
Central Rating Office
Issuing certificates for
SOUTH AFRICA
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateCommentM1-10.130.601.091.892.5417.7030/11/2025
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateCommentJ2-10.060.591.162.383.665.0811.50NoNo 28.1730/10/2025
CRUISER/RACER REQUIREMENTS*
Accommodation length9.3 mTable area0.44 m²Headroom1.65 mMinimum number of berths4Personal gear stowage0.16 m³Fresh water capacity66 lMinimum number of seats in cockpit4Food stowage0.24 m³Fuel capacity36 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.