Club Certificate2025
ZACAPATUR 1059
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 Angles42.9°42.9°40.7°39.1°37.7°37.3°37.0°37.1°38.0°
Beat VMG2.523.494.274.845.165.295.375.445.40
52°3.915.296.286.917.237.377.457.547.55
60°4.155.566.527.087.407.577.677.787.81
75°4.305.726.677.207.537.807.998.208.30
90°4.395.926.977.437.667.848.128.588.87
110°4.486.057.137.698.128.438.689.149.55
120°4.345.917.037.628.108.589.049.7210.43
135°3.825.336.537.287.798.288.7910.2112.58
150°3.164.495.646.617.267.698.108.9911.17
Run VMG2.743.894.895.726.326.757.127.839.67
Gybe Angles143.0°143.0°147.1°150.2°152.8°157.4°160.8°158.3°141.2°
APH ToD:540.3CDL: 9.424APH ToT: 1.1104CertNo:
BOAT
ClassA-35DesignerBernard NiveltBuilderArchambaultAge date05/2007Series date01/2005Offset fileF234.OFFData fileTUR1059
HULL
Length Overall10.617 mMaximum Beam3.594 mDraft2.175 mDisplacement4,824 kgDLR5.8519IMS DivisionCruiser/RacerDynamic Allowance0.180%Age Allowance0.487%
PROPELLER
InstallationStrutTypeFolding 2 bladesDiameter0.405m
CREW
Maximum weight560 kg(declared)Minimum weight430 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail35.3535.94Headsail Luffed27.7527.75Headsail FlyingSymmetricAsymmetric107.41107.41 (All asymmetric spinnakers with SHW/SFL > 85%)
STORM SAIL AREAS (m²)
Trysail10.42Storm Jib10.12Heavy Weather Jib27.30
SAIL LIMITS
Headsails5Spinnakers4
STABILITY
Righting MomentN/AStability IndexN/A
COMMENTS
IRC Weighed 12Sep2024 - 4644kg
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
ZACAPATUR 1059
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 VMG1429.81031.9843.7744.2698.1679.9669.8661.4667.0
52°920.6680.6572.9521.1498.2488.3483.0477.7477.0
60°867.5647.8552.2508.6486.8475.6469.5463.0461.2
75°837.7629.0539.8500.1477.8461.7450.8439.0433.5
90°820.6608.1516.8484.4470.2459.1443.4419.8405.9
110°803.8595.4504.9468.0443.3427.1414.9393.8377.2
120°829.6609.5512.4472.3444.3419.5398.3370.4345.3
135°943.2675.8551.6494.3462.3434.9409.6352.7286.1
150°1137.6802.0637.9544.9496.0468.2444.7400.7322.3
Run VMG1313.9926.1736.5629.2569.9533.6505.4459.9372.2
Selected Courses
Windward / Leeward1371.6979.0790.1686.7634.0606.8587.6560.6519.6
All purpose1041.9755.6622.6556.5522.3502.3486.9463.2436.3
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward663.60.9041
All purpose540.31.1104
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low689.10.8707
Triple Number Coastal/Long Distance Medium537.11.1172
Triple Number Coastal/Long Distance High481.91.2452
Triple Number Windward/Leeward Low884.60.6783
Triple Number Windward/Leeward Medium657.80.9122
Triple Number Windward/Leeward High582.21.0305
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance586.61.0229
Triple Number Coastal/Long Distance Low689.10.8707
Triple Number Coastal/Long Distance Medium537.11.1172
Triple Number Coastal/Long Distance High481.91.2452
Triple Number Windward/Leeward Low884.60.6783
Triple Number Windward/Leeward Medium657.80.9122
Triple Number Windward/Leeward High582.21.0305
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1446.8973.7743.0622.4556.0520.9491.3444.5419.0
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.7881
Downwind "popa"0.9632
70% up, 30% down "Ilhabela"0.8336
30% up, 70% down "Ilhabela-inverso"0.9030
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low689.10.8707
Triple Number Coastal/Long Distance Medium537.11.1172
Triple Number Coastal/Long Distance High481.91.2452
Triple Number Windward/Leeward Low884.60.6783
Triple Number Windward/Leeward Medium657.80.9122
Triple Number Windward/Leeward High582.21.0305
Predominantly Upwind586.81.0225
Predominantly Downwind545.31.1002
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low689.10.8707
Triple Number AP Medium537.11.1171
Triple Number AP High481.91.2452
Triple Number Windward/Leeward Low922.90.6501
Triple Number Windward/Leeward Medium657.80.9122
Triple Number Windward/Leeward High582.21.0305
Single Number Predominant Upwind610.60.9826
Single Number Predominant Reaching536.41.1186
Single Number Predominant Downwind566.71.0588
Predominant Upwind - Low841.70.7128
Predominant Upwind - Low/Med642.90.9332
Predominant Upwind - Medium568.51.0555
Predominant Upwind - Med/High532.11.1277
Predominant Upwind - High513.11.1693
Predominant Downwind Low815.20.7360
Predominant Downwind Low/Med610.60.9827
Predominant Downwind Medium528.21.1360
Predominant Downwind Med/High475.21.2626
Predominant Downwind High433.11.3852
Predominant Reaching Low735.10.8162
Predominant Reaching Low/Med566.81.0586
Predominant Reaching Medium504.51.1893
Predominant Reaching Med/High464.91.2906
Predominant Reaching High433.91.3828
SA/DSPL Upwind21.99SA/DSPL Downwind49.74
Scoring OptionTODTOT
5-Band Windward/Leeward Low1030.00.5825
5-Band Windward/Leeward Low/Med758.40.7911
5-Band Windward/Leeward Medium647.30.9269
5-Band Windward/Leeward Med/High590.21.0167
5-Band Windward/Leeward High558.21.0749
Windward/Leeward 60-40 Low1040.80.5765
Windward/Leeward 60-40 Low/Med769.70.7795
Windward/Leeward 60-40 Medium660.40.9086
Windward/Leeward 60-40 Med/High606.60.9891
Windward/Leeward 60-40 High579.31.0357
5-Band AP Low757.10.7925
5-Band AP Low/Med604.10.9932
5-Band AP Medium530.01.1320
5-Band AP Med/High488.51.2283
5-Band AP High462.61.2969
5-Band SF Bay Tour - Low891.10.6733
5-Band SF Bay Tour - Low/Med726.20.8262
5-Band SF Bay Tour - Medium624.20.9612
5-Band SF Bay Tour - Med/High571.41.0500
5-Band SF Bay Tour - High541.21.1086
Chicago-Mac Upwind0.9534
Chicago-Mac All Purpose0.9899
Chicago-Mac Downwind1.0221
Bayview-Mac Cove Island0.7290
Bayview-Mac Shore0.7334
Harvest Moon Regatta471.01.2739
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance586.61.0229
Triple Number Coastal/Long Distance Low689.10.8707
Triple Number Coastal/Long Distance Medium537.11.1172
Triple Number Coastal/Long Distance High481.91.2452
Triple Number Windward/Leeward Low884.60.6783
Triple Number Windward/Leeward Medium657.80.9122
Triple Number Windward/Leeward High582.21.0305
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1446.8973.7743.0622.4556.0520.9491.3444.5419.0
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance586.61.0229
Triple Number Coastal/Long Distance Low689.10.8707
Triple Number Coastal/Long Distance Medium537.11.1172
Triple Number Coastal/Long Distance High481.91.2452
Triple Number Windward/Leeward Low884.60.6783
Triple Number Windward/Leeward Medium657.80.9122
Triple Number Windward/Leeward High582.21.0305
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1446.8973.7743.0622.4556.0520.9491.3444.5419.0
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance586.6
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1446.8973.7743.0622.4556.0520.9491.3444.5419.0
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low689.10.8707
Triple Number Coastal/Long Distance Medium537.11.1172
Triple Number Coastal/Long Distance High481.91.2452
Triple Number Windward/Leeward Low884.60.6783
Triple Number Windward/Leeward Medium657.80.9122
Triple Number Windward/Leeward High582.21.0305
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating586.61.0229
FinRating, kevyt tuuli1009.60.9905
FinRating, kova tuuli463.81.0782
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low689.10.8707
Triple Number Coastal/Long Distance Medium537.11.1172
Triple Number Coastal/Long Distance High481.91.2452
Triple Number Windward/Leeward Low884.60.6783
Triple Number Windward/Leeward Medium657.80.9122
Triple Number Windward/Leeward High582.21.0305
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance1.0229
Triple Number Coastal/Long Distance Low0.8707
Triple Number Coastal/Long Distance Medium1.1172
Triple Number Coastal/Long Distance High1.2452
Triple Number Windward/Leeward Low0.6783
Triple Number Windward/Leeward Medium0.9122
Triple Number Windward/Leeward High1.0305
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1446.8973.7743.0622.4556.0520.9491.3444.5419.0
For information
General Purpose Handicap (GPH)605.3
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance586.61.0229
Triple Number Coastal/Long Distance Low689.10.8707
Triple Number Coastal/Long Distance Medium537.11.1172
Triple Number Coastal/Long Distance High481.91.2452
Triple Number Windward/Leeward Low884.60.6783
Triple Number Windward/Leeward Medium657.80.9122
Triple Number Windward/Leeward High582.21.0305
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1446.8973.7743.0622.4556.0520.9491.3444.5419.0
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low689.10.8707
Triple Number Coastal/Long Distance Medium537.11.1172
Triple Number Coastal/Long Distance High481.91.2452
Triple Number Windward/Leeward Low884.60.6783
Triple Number Windward/Leeward Medium657.80.9122
Triple Number Windward/Leeward High582.21.0305
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance586.61.0229
Triple Number Coastal/Long Distance Low689.10.8707
Triple Number Coastal/Long Distance Medium537.11.1172
Triple Number Coastal/Long Distance High481.91.2452
Triple Number Windward/Leeward Low884.60.6783
Triple Number Windward/Leeward Medium657.80.9122
Triple Number Windward/Leeward High582.21.0305
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1446.8973.7743.0622.4556.0520.9491.3444.5419.0
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance586.61.0229
Triple Number Coastal/Long Distance Low689.10.8707
Triple Number Coastal/Long Distance Medium537.11.1172
Triple Number Coastal/Long Distance High481.91.2452
Triple Number Windward/Leeward Low884.60.6783
Triple Number Windward/Leeward Medium657.80.9122
Triple Number Windward/Leeward High582.21.0305
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1446.8973.7743.0622.4556.0520.9491.3444.5419.0
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low689.1
Triple Number Coastal/Long Distance Medium537.1
Triple Number Coastal/Long Distance High481.9
Triple Number Windward/Leeward Low884.6
Triple Number Windward/Leeward Medium657.8
Triple Number Windward/Leeward High582.2
Predominantly Upwind586.8
Predominantly Downwind545.3
Predominantly Reaching524.6
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance586.61.0229
Triple Number Coastal/Long Distance Low689.10.8707
Triple Number Coastal/Long Distance Medium537.11.1172
Triple Number Coastal/Long Distance High481.91.2452
Triple Number Windward/Leeward Low884.60.6783
Triple Number Windward/Leeward Medium657.80.9122
Triple Number Windward/Leeward High582.21.0305
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1446.8973.7743.0622.4556.0520.9491.3444.5419.0
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8707
Triple Number Coastal/Long Distance Medium1.1172
Triple Number Coastal/Long Distance High1.2452
Triple Number Windward/Leeward Low0.6783
Triple Number Windward/Leeward Medium0.9122
Triple Number Windward/Leeward High1.0305
Coastal/Long Distance1.0229
Predominantly Upwind1.0225
Predominantly Downwind1.1002
For information
General Purpose Handicap (GPH)605.3
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)1.1104
Distanseseilas Trippeltall svak vind0.8707
Distanseseilas Trippeltall mellomvind1.1172
Distanseseilas Trippeltall sterk vind1.2452
Pølsebane Trippeltall svak vind0.6783
Pølsebane Trippeltall mellomvind0.9122
Pølsebane Trippeltall sterk vind1.0305
Motvind Singeltall1.0225
Medvind Singeltall1.1002
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low689.10.8707
Triple Number Coastal/Long Distance Medium537.11.1172
Triple Number Coastal/Long Distance High481.91.2452
Triple Number Windward/Leeward Low884.60.6783
Triple Number Windward/Leeward Medium657.80.9122
Triple Number Windward/Leeward High582.21.0305
Coastal/Long Distance586.61.0229
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind586.81.0225
Predominantly Downwind545.31.1002
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore531.91.1280
Cape Doctor Coastal444.41.3502
Triple Number Coastal/Long Distance Low689.10.8707
Triple Number Coastal/Long Distance Medium537.11.1172
Triple Number Coastal/Long Distance High481.91.2452
Triple Number Windward/Leeward Low884.60.6783
Triple Number Windward/Leeward Medium657.80.9122
Triple Number Windward/Leeward High582.21.0305
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8707
Triple Number Coastal/Long Distance Medium1.1172
Triple Number Coastal/Long Distance High1.2452
Triple Number Windward/Leeward Low0.6783
Triple Number Windward/Leeward Medium0.9122
Triple Number Windward/Leeward High1.0305
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8707
Triple Number Coastal/Long Distance Medium1.1172
Triple Number Coastal/Long Distance High1.2452
Triple Number Windward/Leeward Low0.6783
Triple Number Windward/Leeward Medium0.9122
Triple Number Windward/Leeward High1.0305
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance586.61.0229
Triple Number Coastal/Long Distance Low689.10.8707
Triple Number Coastal/Long Distance Medium537.11.1172
Triple Number Coastal/Long Distance High481.91.2452
Triple Number Windward/Leeward Low884.60.6783
Triple Number Windward/Leeward Medium657.80.9122
Triple Number Windward/Leeward High582.21.0305
Predominantly Upwind586.81.0225
Predominantly Downwind545.31.1002
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1446.8973.7743.0622.4556.0520.9491.3444.5419.0
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance586.61.0229
Triple Number Coastal/Long Distance Low689.10.8707
Triple Number Coastal/Long Distance Medium537.11.1172
Triple Number Coastal/Long Distance High481.91.2452
Triple Number Windward/Leeward Low884.60.6783
Triple Number Windward/Leeward Medium657.80.9122
Triple Number Windward/Leeward High582.21.0305
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1446.8973.7743.0622.4556.0520.9491.3444.5419.0
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low689.10.8707
Triple Number AP Medium537.11.1171
Triple Number AP High481.91.2452
Triple Number Windward/Leeward Low922.90.6501
Triple Number Windward/Leeward Medium657.80.9122
Triple Number Windward/Leeward High582.21.0305
Single Number Predominant Upwind610.60.9826
Single Number Predominant Reaching536.41.1186
Single Number Predominant Downwind566.71.0588
Predominant Upwind - Low841.70.7128
Predominant Upwind - Low/Med642.90.9332
Predominant Upwind - Medium568.51.0555
Predominant Upwind - Med/High532.11.1277
Predominant Upwind - High513.11.1693
Predominant Downwind Low815.20.7360
Predominant Downwind Low/Med610.60.9827
Predominant Downwind Medium528.21.1360
Predominant Downwind Med/High475.21.2626
Predominant Downwind High433.11.3852
Predominant Reaching Low735.10.8162
Predominant Reaching Low/Med566.81.0586
Predominant Reaching Medium504.51.1893
Predominant Reaching Med/High464.91.2906
Predominant Reaching High433.91.3828
SA/DSPL Upwind21.99SA/DSPL Downwind49.74
Scoring OptionTODTOT
5-Band Windward/Leeward Low1030.00.5825
5-Band Windward/Leeward Low/Med758.40.7911
5-Band Windward/Leeward Medium647.30.9269
5-Band Windward/Leeward Med/High590.21.0167
5-Band Windward/Leeward High558.21.0749
Windward/Leeward 60-40 Low1040.80.5765
Windward/Leeward 60-40 Low/Med769.70.7795
Windward/Leeward 60-40 Medium660.40.9086
Windward/Leeward 60-40 Med/High606.60.9891
Windward/Leeward 60-40 High579.31.0357
5-Band AP Low757.10.7925
5-Band AP Low/Med604.10.9932
5-Band AP Medium530.01.1320
5-Band AP Med/High488.51.2283
5-Band AP High462.61.2969
5-Band SF Bay Tour - Low891.10.6733
5-Band SF Bay Tour - Low/Med726.20.8262
5-Band SF Bay Tour - Medium624.20.9612
5-Band SF Bay Tour - Med/High571.41.0500
5-Band SF Bay Tour - High541.21.1086
Chicago-Mac Upwind0.9534
Chicago-Mac All Purpose0.9899
Chicago-Mac Downwind1.0221
Bayview-Mac Cove Island0.7290
Bayview-Mac Shore0.7334
Harvest Moon Regatta471.01.2739
Club Certificate2025
ZACAPATUR 1059
Turkiye
Sailing
Federation
www.tyf.org.tr/
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassA-35Measurement28/01/2024HINPlan reviewHull constructionSolidCarbon rudderNoLight stanchionsNoTrim tabNo
LOA10.617Max. Beam3.594Draft2.175Displacement4,824Wetted area23.43IMS L9.696LSM09.376Acc. length10.617Sink (kg/mm) 17.86
VCGD-0.041VCGM-0.007RM Rated (kg·m) 109.6Limit of positive stability(°) N/AStability IndexN/ADefault crew weight628Declared crew weight560
PROPELLER
Propeller TypeFolding 2 blades
InstallationStrutTwin screwNoHydro generatorNo
PRD0.405PBWPIPA0.0034
EDL1.520ST10.065ST2
ST3ST40.098ST50.285
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerNoMainsail furlerNoArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders2Rotating mastNo
P13.650IG14.220ISP15.470MDT10.117MDL10.183MDT2MDL2TLTaperMW0.183GO0.183
E4.360J4.100BAS1.600FSD0.029SFJ-0.005SPLWPLTPS5.500BD0.157MWTMCG
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodRM estimatedFlotation Date04/09/2025
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Club Certificate2025
ZACAPATUR 1059
Turkiye
Sailing
Federation
www.tyf.org.tr/
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateCommentPENTEX0.150.911.652.813.6435.3528/01/2024BLACK
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateCommentDM0.100.611.142.173.174.1512.95NoNo 27.7506/01/2024BLACK mediumJ40.050.470.931.792.673.5211.84NoNo 21.1706/01/2024WHITE
ASYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLRatioAreaMeas.DateCommentQA316.6715.1415.917.948.7691%107.4128/01/2024BLACK
CRUISER/RACER REQUIREMENTS*
Accommodation length10.6 mTable area0.44 m²Headroom1.74 mMinimum number of berths4Personal gear stowage0.16 m³Fresh water capacity92 lMinimum number of seats in cockpit4Food stowage0.24 m³Fuel capacity62 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.