Double HandedClub Certificate2025
PiikaFIN-9815
Avomeripurjehtijat ry
c/o Mainoskauppa Oy
Melkonkatu 16 B
00210 HELSINKI
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 Angles43.4°43.4°41.5°40.7°40.2°40.0°39.9°40.3°41.7°
Beat VMG2.443.354.034.454.664.754.794.794.66
52°3.805.106.006.526.776.876.936.976.92
60°4.035.376.256.736.987.097.157.227.20
75°4.205.556.426.907.177.357.477.617.68
90°4.095.456.386.917.237.477.677.978.15
110°3.875.326.417.037.407.707.918.218.38
120°3.725.156.266.957.377.738.068.578.93
135°3.274.615.756.617.147.537.928.719.73
150°2.693.915.035.986.717.187.568.329.23
Run VMG2.333.394.365.195.926.516.977.688.39
Gybe Angles145.7°145.7°150.1°153.2°158.8°165.5°172.3°177.2°175.9°
APH ToD:586.4CDL: 8.380APH ToT: 1.0232CertNo:
BOAT
ClassEF 34DesignerSTRÅHLMANNBuilderEF MARINEAge date06/2004Series date12/2000Offset fileEF34.OFFData fileFIN9815
HULL
Length Overall10.430 mMaximum Beam3.244 mDraft1.796 mDisplacement5,100 kgDLR6.3843IMS DivisionCruiser/RacerDynamic Allowance0.320%Age Allowance0.487%
PROPELLER
InstallationStrutTypeFolding 2 bladesDiameter0.410m
CREW
Maximum weight180 kg(declared)Minimum weight120 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail29.6630.06Headsail Luffed33.8133.81Headsail FlyingSymmetric71.8571.85Asymmetric
STORM SAIL AREAS (m²)
Trysail9.17Storm Jib8.76Heavy Weather Jib23.63
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.
Double HandedClub Certificate2025
PiikaFIN-9815
Avomeripurjehtijat ry
c/o Mainoskauppa Oy
Melkonkatu 16 B
00210 HELSINKI
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 VMG1476.01076.0893.0808.3773.1757.9751.4751.1771.8
52°948.3706.0599.8552.2531.9523.8519.7516.7520.3
60°892.5670.9576.2534.6516.0507.5503.2498.7500.3
75°856.7648.1560.6521.6501.9489.6481.8473.1468.8
90°880.6660.0564.7521.1498.1482.0469.2451.7441.7
110°931.4677.1562.0512.5486.6467.4455.4438.5429.6
120°968.6699.6575.4517.9488.3466.0446.6420.0403.3
135°1101.1780.6626.4544.9504.2477.9454.8413.3369.9
150°1337.0920.4715.9602.4536.8501.4476.4432.9390.1
Run VMG1543.81062.8826.5693.3608.6553.1516.7468.9429.3
Selected Courses
Windward / Leeward1508.01069.4859.7750.8690.8655.5634.0610.0600.6
All purpose1139.9823.6676.3603.5565.7543.6529.2510.1499.6
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward721.90.8312
All purpose586.41.0232
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low749.90.8001
Triple Number Coastal/Long Distance Medium582.01.0309
Triple Number Coastal/Long Distance High525.61.1415
Triple Number Windward/Leeward Low964.60.6220
Triple Number Windward/Leeward Medium716.10.8379
Triple Number Windward/Leeward High630.40.9518
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance637.90.9406
Triple Number Coastal/Long Distance Low749.90.8001
Triple Number Coastal/Long Distance Medium582.01.0309
Triple Number Coastal/Long Distance High525.61.1415
Triple Number Windward/Leeward Low964.60.6220
Triple Number Windward/Leeward Medium716.10.8379
Triple Number Windward/Leeward High630.40.9518
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1604.61068.7809.4678.1604.2564.4533.8485.3473.4
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.7228
Downwind "popa"0.8880
70% up, 30% down "Ilhabela"0.7655
30% up, 70% down "Ilhabela-inverso"0.8310
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low749.90.8001
Triple Number Coastal/Long Distance Medium582.01.0309
Triple Number Coastal/Long Distance High525.61.1415
Triple Number Windward/Leeward Low964.60.6220
Triple Number Windward/Leeward Medium716.10.8379
Triple Number Windward/Leeward High630.40.9518
Predominantly Upwind635.20.9445
Predominantly Downwind592.71.0123
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low749.90.8001
Triple Number AP Medium582.11.0308
Triple Number AP High525.61.1415
Triple Number Windward/Leeward Low1008.20.5951
Triple Number Windward/Leeward Medium716.10.8379
Triple Number Windward/Leeward High630.40.9518
Single Number Predominant Upwind660.70.9082
Single Number Predominant Reaching582.61.0299
Single Number Predominant Downwind620.20.9674
Predominant Upwind - Low897.30.6686
Predominant Upwind - Low/Med691.20.8681
Predominant Upwind - Medium615.80.9744
Predominant Upwind - Med/High581.11.0326
Predominant Upwind - High568.61.0553
Predominant Downwind Low914.70.6559
Predominant Downwind Low/Med672.70.8920
Predominant Downwind Medium571.31.0503
Predominant Downwind Med/High510.51.1754
Predominant Downwind High476.21.2600
Predominant Reaching Low806.50.7440
Predominant Reaching Low/Med617.30.9720
Predominant Reaching Medium544.01.1029
Predominant Reaching Med/High502.51.1941
Predominant Reaching High479.01.2527
SA/DSPL Upwind21.31SA/DSPL Downwind34.08
Scoring OptionTODTOT
5-Band Windward/Leeward Low1127.10.5323
5-Band Windward/Leeward Low/Med827.30.7253
5-Band Windward/Leeward Medium704.20.8520
5-Band Windward/Leeward Med/High638.40.9399
5-Band Windward/Leeward High612.50.9796
Windward/Leeward 60-40 Low1127.70.5320
Windward/Leeward 60-40 Low/Med836.30.7175
Windward/Leeward 60-40 Medium720.30.8330
Windward/Leeward 60-40 Med/High661.50.9070
Windward/Leeward 60-40 High641.00.9361
5-Band AP Low831.00.7220
5-Band AP Low/Med656.00.9146
5-Band AP Medium574.41.0445
5-Band AP Med/High531.51.1290
5-Band AP High511.51.1729
5-Band SF Bay Tour - Low970.30.6184
5-Band SF Bay Tour - Low/Med791.60.7580
5-Band SF Bay Tour - Medium681.60.8803
5-Band SF Bay Tour - Med/High625.00.9600
5-Band SF Bay Tour - High602.00.9966
Chicago-Mac Upwind0.8823
Chicago-Mac All Purpose0.9101
Chicago-Mac Downwind0.9323
Bayview-Mac Cove Island0.6665
Bayview-Mac Shore0.6719
Harvest Moon Regatta507.11.1833
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance637.90.9406
Triple Number Coastal/Long Distance Low749.90.8001
Triple Number Coastal/Long Distance Medium582.01.0309
Triple Number Coastal/Long Distance High525.61.1415
Triple Number Windward/Leeward Low964.60.6220
Triple Number Windward/Leeward Medium716.10.8379
Triple Number Windward/Leeward High630.40.9518
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1604.61068.7809.4678.1604.2564.4533.8485.3473.4
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance637.90.9406
Triple Number Coastal/Long Distance Low749.90.8001
Triple Number Coastal/Long Distance Medium582.01.0309
Triple Number Coastal/Long Distance High525.61.1415
Triple Number Windward/Leeward Low964.60.6220
Triple Number Windward/Leeward Medium716.10.8379
Triple Number Windward/Leeward High630.40.9518
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1604.61068.7809.4678.1604.2564.4533.8485.3473.4
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance637.9
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1604.61068.7809.4678.1604.2564.4533.8485.3473.4
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low749.90.8001
Triple Number Coastal/Long Distance Medium582.01.0309
Triple Number Coastal/Long Distance High525.61.1415
Triple Number Windward/Leeward Low964.60.6220
Triple Number Windward/Leeward Medium716.10.8379
Triple Number Windward/Leeward High630.40.9518
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating637.90.9406
FinRating, kevyt tuuli1107.90.9026
FinRating, kova tuuli514.60.9717
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low749.90.8001
Triple Number Coastal/Long Distance Medium582.01.0309
Triple Number Coastal/Long Distance High525.61.1415
Triple Number Windward/Leeward Low964.60.6220
Triple Number Windward/Leeward Medium716.10.8379
Triple Number Windward/Leeward High630.40.9518
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.9406
Triple Number Coastal/Long Distance Low0.8001
Triple Number Coastal/Long Distance Medium1.0309
Triple Number Coastal/Long Distance High1.1415
Triple Number Windward/Leeward Low0.6220
Triple Number Windward/Leeward Medium0.8379
Triple Number Windward/Leeward High0.9518
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1604.61068.7809.4678.1604.2564.4533.8485.3473.4
For information
General Purpose Handicap (GPH)657.3
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance637.90.9406
Triple Number Coastal/Long Distance Low749.90.8001
Triple Number Coastal/Long Distance Medium582.01.0309
Triple Number Coastal/Long Distance High525.61.1415
Triple Number Windward/Leeward Low964.60.6220
Triple Number Windward/Leeward Medium716.10.8379
Triple Number Windward/Leeward High630.40.9518
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1604.61068.7809.4678.1604.2564.4533.8485.3473.4
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low749.90.8001
Triple Number Coastal/Long Distance Medium582.01.0309
Triple Number Coastal/Long Distance High525.61.1415
Triple Number Windward/Leeward Low964.60.6220
Triple Number Windward/Leeward Medium716.10.8379
Triple Number Windward/Leeward High630.40.9518
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance637.90.9406
Triple Number Coastal/Long Distance Low749.90.8001
Triple Number Coastal/Long Distance Medium582.01.0309
Triple Number Coastal/Long Distance High525.61.1415
Triple Number Windward/Leeward Low964.60.6220
Triple Number Windward/Leeward Medium716.10.8379
Triple Number Windward/Leeward High630.40.9518
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1604.61068.7809.4678.1604.2564.4533.8485.3473.4
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance637.90.9406
Triple Number Coastal/Long Distance Low749.90.8001
Triple Number Coastal/Long Distance Medium582.01.0309
Triple Number Coastal/Long Distance High525.61.1415
Triple Number Windward/Leeward Low964.60.6220
Triple Number Windward/Leeward Medium716.10.8379
Triple Number Windward/Leeward High630.40.9518
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1604.61068.7809.4678.1604.2564.4533.8485.3473.4
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low749.9
Triple Number Coastal/Long Distance Medium582.0
Triple Number Coastal/Long Distance High525.6
Triple Number Windward/Leeward Low964.6
Triple Number Windward/Leeward Medium716.1
Triple Number Windward/Leeward High630.4
Predominantly Upwind635.2
Predominantly Downwind592.7
Predominantly Reaching569.2
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance637.90.9406
Triple Number Coastal/Long Distance Low749.90.8001
Triple Number Coastal/Long Distance Medium582.01.0309
Triple Number Coastal/Long Distance High525.61.1415
Triple Number Windward/Leeward Low964.60.6220
Triple Number Windward/Leeward Medium716.10.8379
Triple Number Windward/Leeward High630.40.9518
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1604.61068.7809.4678.1604.2564.4533.8485.3473.4
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8001
Triple Number Coastal/Long Distance Medium1.0309
Triple Number Coastal/Long Distance High1.1415
Triple Number Windward/Leeward Low0.6220
Triple Number Windward/Leeward Medium0.8379
Triple Number Windward/Leeward High0.9518
Coastal/Long Distance0.9406
Predominantly Upwind0.9445
Predominantly Downwind1.0123
For information
General Purpose Handicap (GPH)657.3
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)1.0232
Distanseseilas Trippeltall svak vind0.8001
Distanseseilas Trippeltall mellomvind1.0309
Distanseseilas Trippeltall sterk vind1.1415
Pølsebane Trippeltall svak vind0.6220
Pølsebane Trippeltall mellomvind0.8379
Pølsebane Trippeltall sterk vind0.9518
Motvind Singeltall0.9445
Medvind Singeltall1.0123
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low749.90.8001
Triple Number Coastal/Long Distance Medium582.01.0309
Triple Number Coastal/Long Distance High525.61.1415
Triple Number Windward/Leeward Low964.60.6220
Triple Number Windward/Leeward Medium716.10.8379
Triple Number Windward/Leeward High630.40.9518
Coastal/Long Distance637.90.9406
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind635.20.9445
Predominantly Downwind592.71.0123
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore603.40.9944
Cape Doctor Coastal502.71.1935
Triple Number Coastal/Long Distance Low749.90.8001
Triple Number Coastal/Long Distance Medium582.01.0309
Triple Number Coastal/Long Distance High525.61.1415
Triple Number Windward/Leeward Low964.60.6220
Triple Number Windward/Leeward Medium716.10.8379
Triple Number Windward/Leeward High630.40.9518
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8001
Triple Number Coastal/Long Distance Medium1.0309
Triple Number Coastal/Long Distance High1.1415
Triple Number Windward/Leeward Low0.6220
Triple Number Windward/Leeward Medium0.8379
Triple Number Windward/Leeward High0.9518
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8001
Triple Number Coastal/Long Distance Medium1.0309
Triple Number Coastal/Long Distance High1.1415
Triple Number Windward/Leeward Low0.6220
Triple Number Windward/Leeward Medium0.8379
Triple Number Windward/Leeward High0.9518
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance637.90.9406
Triple Number Coastal/Long Distance Low749.90.8001
Triple Number Coastal/Long Distance Medium582.01.0309
Triple Number Coastal/Long Distance High525.61.1415
Triple Number Windward/Leeward Low964.60.6220
Triple Number Windward/Leeward Medium716.10.8379
Triple Number Windward/Leeward High630.40.9518
Predominantly Upwind635.20.9445
Predominantly Downwind592.71.0123
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1604.61068.7809.4678.1604.2564.4533.8485.3473.4
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance637.90.9406
Triple Number Coastal/Long Distance Low749.90.8001
Triple Number Coastal/Long Distance Medium582.01.0309
Triple Number Coastal/Long Distance High525.61.1415
Triple Number Windward/Leeward Low964.60.6220
Triple Number Windward/Leeward Medium716.10.8379
Triple Number Windward/Leeward High630.40.9518
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1604.61068.7809.4678.1604.2564.4533.8485.3473.4
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low749.90.8001
Triple Number AP Medium582.11.0308
Triple Number AP High525.61.1415
Triple Number Windward/Leeward Low1008.20.5951
Triple Number Windward/Leeward Medium716.10.8379
Triple Number Windward/Leeward High630.40.9518
Single Number Predominant Upwind660.70.9082
Single Number Predominant Reaching582.61.0299
Single Number Predominant Downwind620.20.9674
Predominant Upwind - Low897.30.6686
Predominant Upwind - Low/Med691.20.8681
Predominant Upwind - Medium615.80.9744
Predominant Upwind - Med/High581.11.0326
Predominant Upwind - High568.61.0553
Predominant Downwind Low914.70.6559
Predominant Downwind Low/Med672.70.8920
Predominant Downwind Medium571.31.0503
Predominant Downwind Med/High510.51.1754
Predominant Downwind High476.21.2600
Predominant Reaching Low806.50.7440
Predominant Reaching Low/Med617.30.9720
Predominant Reaching Medium544.01.1029
Predominant Reaching Med/High502.51.1941
Predominant Reaching High479.01.2527
SA/DSPL Upwind21.31SA/DSPL Downwind34.08
Scoring OptionTODTOT
5-Band Windward/Leeward Low1127.10.5323
5-Band Windward/Leeward Low/Med827.30.7253
5-Band Windward/Leeward Medium704.20.8520
5-Band Windward/Leeward Med/High638.40.9399
5-Band Windward/Leeward High612.50.9796
Windward/Leeward 60-40 Low1127.70.5320
Windward/Leeward 60-40 Low/Med836.30.7175
Windward/Leeward 60-40 Medium720.30.8330
Windward/Leeward 60-40 Med/High661.50.9070
Windward/Leeward 60-40 High641.00.9361
5-Band AP Low831.00.7220
5-Band AP Low/Med656.00.9146
5-Band AP Medium574.41.0445
5-Band AP Med/High531.51.1290
5-Band AP High511.51.1729
5-Band SF Bay Tour - Low970.30.6184
5-Band SF Bay Tour - Low/Med791.60.7580
5-Band SF Bay Tour - Medium681.60.8803
5-Band SF Bay Tour - Med/High625.00.9600
5-Band SF Bay Tour - High602.00.9966
Chicago-Mac Upwind0.8823
Chicago-Mac All Purpose0.9101
Chicago-Mac Downwind0.9323
Bayview-Mac Cove Island0.6665
Bayview-Mac Shore0.6719
Harvest Moon Regatta507.11.1833
Double HandedClub Certificate2025
PiikaFIN-9815
Avomeripurjehtijat ry
c/o Mainoskauppa Oy
Melkonkatu 16 B
00210 HELSINKI
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassEF 34Measurement13/06/2021HINPlan reviewHull constructionCoredCarbon rudderNoLight stanchionsNoTrim tabNo
LOA10.430Max. Beam3.244Draft1.796Displacement5,100Wetted area23.03IMS L9.298LSM09.278Acc. length10.430Sink (kg/mm) 17.12
VCGD-0.095VCGM-0.049RM Rated (kg·m) 100.5Limit of positive stability(°) N/AStability IndexN/ADefault crew weight170Declared crew weight180
PROPELLER
Propeller TypeFolding 2 blades
InstallationStrutTwin screwNoHydro generatorNo
PRD0.410PBW0.112PIPA0.0038
EDL1.790ST10.065ST20.180
ST30.180ST40.110ST50.335
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerNoMainsail furlerNoArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders2Rotating mastNo
P12.320IG13.230ISP13.230MDT10.095MDL10.175MDT20.095MDL20.150TL2.000MW0.150GO0.150
E4.250J3.810BAS1.550FSD0.034SFJ0.300SPL3.710WPLTPSBD0.143MWT142.10MCG4.300
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodRM estimatedFlotation Date01/01/2022
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Double HandedClub Certificate2025
PiikaFIN-9815
Avomeripurjehtijat ry
c/o Mainoskauppa Oy
Melkonkatu 16 B
00210 HELSINKI
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment10.781.432.543.4529.66
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment15.1912.80NoNo 33.8124.1012.80NoNo 26.7107/06/2025
SYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLAreaMeas.DateComment112.9312.9312.936.686.6271.85
CRUISER/RACER REQUIREMENTS*
Accommodation length10.4 mTable area0.44 m²Headroom1.73 mMinimum number of berths4Personal gear stowage0.16 m³Fresh water capacity88 lMinimum number of seats in cockpit4Food stowage0.24 m³Fuel capacity58 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.