Double HandedClub Certificate2025
AndrikNOR 13348
Norges Seilforbund
Sognsveien 73
0854 OSLO
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 Angles44.0°44.0°42.0°41.0°40.3°40.1°40.2°40.8°42.6°
Beat VMG2.343.264.004.534.824.934.995.004.82
52°3.685.006.006.697.067.217.297.357.27
60°3.935.296.276.947.317.487.567.637.59
75°4.105.506.487.147.537.767.918.068.11
90°4.125.646.767.417.697.878.108.468.64
110°4.185.736.907.598.038.398.639.009.25
120°4.055.586.757.497.968.388.799.439.88
135°3.554.986.187.077.648.088.529.4310.70
150°2.914.195.336.297.057.567.958.709.54
Run VMG2.523.634.625.456.116.617.057.748.40
Gybe Angles143.0°143.0°147.2°149.2°151.0°155.2°160.6°163.7°161.9°
APH ToD:561.2CDL: 9.276APH ToT: 1.0691CertNo:20599
BOAT
ClassHanse 370DesignerJudel/VrolijkBuilderHanse YachtsAge date01/2008Series date01/2005Offset fileHANSE370.offData file20599
HULL
Length Overall11.298 mMaximum Beam3.742 mDraft2.006 mDisplacement7,445 kgDLR6.2947IMS DivisionCruiser/RacerDynamic Allowance0.280%Age Allowance0.487%
PROPELLER
InstallationStrutTypeFolding 3 bladesDiameter0.400m
CREW
Maximum weight170 kg(default)Minimum weight120 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail43.8344.72Headsail Luffed28.8528.85Headsail FlyingSymmetricAsymmetric98.4298.42 (All asymmetric spinnakers with SHW/SFL > 85%)
STORM SAIL AREAS (m²)
Trysail12.98Storm Jib11.33Heavy Weather Jib30.58
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
AndrikNOR 13348
Norges Seilforbund
Sognsveien 73
0854 OSLO
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 VMG1538.91104.5899.1794.4746.4729.5721.1720.6746.2
52°979.4719.6600.2538.2510.1499.5493.7489.9495.3
60°916.9680.4573.8518.7492.3481.4476.2471.5474.5
75°877.5654.4555.3504.5478.2463.8455.2446.6444.1
90°873.0638.9532.8485.7467.9457.7444.2425.4416.6
110°862.2627.9521.6474.2448.5429.1417.2400.0389.2
120°889.9645.6533.4480.9452.5429.4409.5381.9364.5
135°1014.7722.7583.0509.4471.0445.4422.7381.7336.5
150°1235.4859.6675.5572.2510.9476.1453.0413.8377.5
Run VMG1426.5992.5780.0660.7589.4544.5511.0465.3428.7
Selected Courses
Windward / Leeward1482.11048.5839.6727.5667.9637.0616.1592.9587.5
All purpose1118.4803.6654.9578.3539.2518.0503.1484.3476.0
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward700.90.8560
All purpose561.21.0691
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low729.30.8227
Triple Number Coastal/Long Distance Medium556.61.0780
Triple Number Coastal/Long Distance High499.81.2006
Triple Number Windward/Leeward Low944.00.6356
Triple Number Windward/Leeward Medium694.40.8641
Triple Number Windward/Leeward High612.60.9794
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance612.40.9798
Triple Number Coastal/Long Distance Low729.30.8227
Triple Number Coastal/Long Distance Medium556.61.0780
Triple Number Coastal/Long Distance High499.81.2006
Triple Number Windward/Leeward Low944.00.6356
Triple Number Windward/Leeward Medium694.40.8641
Triple Number Windward/Leeward High612.60.9794
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1567.31042.9787.4653.3577.5538.5507.0458.4448.3
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.7348
Downwind "popa"0.9244
70% up, 30% down "Ilhabela"0.7830
30% up, 70% down "Ilhabela-inverso"0.8580
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low729.30.8227
Triple Number Coastal/Long Distance Medium556.61.0780
Triple Number Coastal/Long Distance High499.81.2006
Triple Number Windward/Leeward Low944.00.6356
Triple Number Windward/Leeward Medium694.40.8641
Triple Number Windward/Leeward High612.60.9794
Predominantly Upwind613.50.9781
Predominantly Downwind565.31.0613
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low729.30.8227
Triple Number AP Medium556.71.0779
Triple Number AP High499.71.2006
Triple Number Windward/Leeward Low986.70.6081
Triple Number Windward/Leeward Medium694.40.8641
Triple Number Windward/Leeward High612.60.9794
Single Number Predominant Upwind641.00.9361
Single Number Predominant Reaching555.41.0802
Single Number Predominant Downwind591.21.0149
Predominant Upwind - Low896.50.6693
Predominant Upwind - Low/Med675.80.8878
Predominant Upwind - Medium592.21.0132
Predominant Upwind - Med/High555.01.0811
Predominant Upwind - High542.51.1060
Predominant Downwind Low870.60.6892
Predominant Downwind Low/Med639.90.9376
Predominant Downwind Medium544.61.1017
Predominant Downwind Med/High488.31.2288
Predominant Downwind High455.11.3185
Predominant Reaching Low780.60.7687
Predominant Reaching Low/Med589.31.0181
Predominant Reaching Medium516.21.1624
Predominant Reaching Med/High476.31.2598
Predominant Reaching High452.81.3251
SA/DSPL Upwind18.94SA/DSPL Downwind37.06
Scoring OptionTODTOT
5-Band Windward/Leeward Low1104.80.5431
5-Band Windward/Leeward Low/Med805.50.7449
5-Band Windward/Leeward Medium682.70.8789
5-Band Windward/Leeward Med/High620.10.9676
5-Band Windward/Leeward High596.01.0067
Windward/Leeward 60-40 Low1116.20.5375
Windward/Leeward 60-40 Low/Med818.40.7332
Windward/Leeward 60-40 Medium698.60.8589
Windward/Leeward 60-40 Med/High641.00.9361
Windward/Leeward 60-40 High621.80.9649
5-Band AP Low804.00.7462
5-Band AP Low/Med632.70.9483
5-Band AP Medium548.81.0933
5-Band AP Med/High505.51.1870
5-Band AP High486.11.2343
5-Band SF Bay Tour - Low952.40.6300
5-Band SF Bay Tour - Low/Med770.40.7788
5-Band SF Bay Tour - Medium657.80.9122
5-Band SF Bay Tour - Med/High601.90.9968
5-Band SF Bay Tour - High580.31.0339
Chicago-Mac Upwind0.9071
Chicago-Mac All Purpose0.9454
Chicago-Mac Downwind0.9783
Bayview-Mac Cove Island0.6845
Bayview-Mac Shore0.6891
Harvest Moon Regatta480.51.2487
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance612.40.9798
Triple Number Coastal/Long Distance Low729.30.8227
Triple Number Coastal/Long Distance Medium556.61.0780
Triple Number Coastal/Long Distance High499.81.2006
Triple Number Windward/Leeward Low944.00.6356
Triple Number Windward/Leeward Medium694.40.8641
Triple Number Windward/Leeward High612.60.9794
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1567.31042.9787.4653.3577.5538.5507.0458.4448.3
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance612.40.9798
Triple Number Coastal/Long Distance Low729.30.8227
Triple Number Coastal/Long Distance Medium556.61.0780
Triple Number Coastal/Long Distance High499.81.2006
Triple Number Windward/Leeward Low944.00.6356
Triple Number Windward/Leeward Medium694.40.8641
Triple Number Windward/Leeward High612.60.9794
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1567.31042.9787.4653.3577.5538.5507.0458.4448.3
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance612.4
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1567.31042.9787.4653.3577.5538.5507.0458.4448.3
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low729.30.8227
Triple Number Coastal/Long Distance Medium556.61.0780
Triple Number Coastal/Long Distance High499.81.2006
Triple Number Windward/Leeward Low944.00.6356
Triple Number Windward/Leeward Medium694.40.8641
Triple Number Windward/Leeward High612.60.9794
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating606.50.9893
FinRating, kevyt tuuli1082.60.9237
FinRating, kova tuuli489.11.0223
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low729.30.8227
Triple Number Coastal/Long Distance Medium556.61.0780
Triple Number Coastal/Long Distance High499.81.2006
Triple Number Windward/Leeward Low944.00.6356
Triple Number Windward/Leeward Medium694.40.8641
Triple Number Windward/Leeward High612.60.9794
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.9798
Triple Number Coastal/Long Distance Low0.8227
Triple Number Coastal/Long Distance Medium1.0780
Triple Number Coastal/Long Distance High1.2006
Triple Number Windward/Leeward Low0.6356
Triple Number Windward/Leeward Medium0.8641
Triple Number Windward/Leeward High0.9794
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1567.31042.9787.4653.3577.5538.5507.0458.4448.3
For information
General Purpose Handicap (GPH)631.5
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance612.40.9798
Triple Number Coastal/Long Distance Low729.30.8227
Triple Number Coastal/Long Distance Medium556.61.0780
Triple Number Coastal/Long Distance High499.81.2006
Triple Number Windward/Leeward Low944.00.6356
Triple Number Windward/Leeward Medium694.40.8641
Triple Number Windward/Leeward High612.60.9794
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1567.31042.9787.4653.3577.5538.5507.0458.4448.3
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low729.30.8227
Triple Number Coastal/Long Distance Medium556.61.0780
Triple Number Coastal/Long Distance High499.81.2006
Triple Number Windward/Leeward Low944.00.6356
Triple Number Windward/Leeward Medium694.40.8641
Triple Number Windward/Leeward High612.60.9794
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance612.40.9798
Triple Number Coastal/Long Distance Low729.30.8227
Triple Number Coastal/Long Distance Medium556.61.0780
Triple Number Coastal/Long Distance High499.81.2006
Triple Number Windward/Leeward Low944.00.6356
Triple Number Windward/Leeward Medium694.40.8641
Triple Number Windward/Leeward High612.60.9794
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1567.31042.9787.4653.3577.5538.5507.0458.4448.3
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance612.40.9798
Triple Number Coastal/Long Distance Low729.30.8227
Triple Number Coastal/Long Distance Medium556.61.0780
Triple Number Coastal/Long Distance High499.81.2006
Triple Number Windward/Leeward Low944.00.6356
Triple Number Windward/Leeward Medium694.40.8641
Triple Number Windward/Leeward High612.60.9794
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1567.31042.9787.4653.3577.5538.5507.0458.4448.3
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low729.3
Triple Number Coastal/Long Distance Medium556.6
Triple Number Coastal/Long Distance High499.8
Triple Number Windward/Leeward Low944.0
Triple Number Windward/Leeward Medium694.4
Triple Number Windward/Leeward High612.6
Predominantly Upwind613.5
Predominantly Downwind565.3
Predominantly Reaching541.0
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance612.40.9798
Triple Number Coastal/Long Distance Low729.30.8227
Triple Number Coastal/Long Distance Medium556.61.0780
Triple Number Coastal/Long Distance High499.81.2006
Triple Number Windward/Leeward Low944.00.6356
Triple Number Windward/Leeward Medium694.40.8641
Triple Number Windward/Leeward High612.60.9794
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1567.31042.9787.4653.3577.5538.5507.0458.4448.3
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8227
Triple Number Coastal/Long Distance Medium1.0780
Triple Number Coastal/Long Distance High1.2006
Triple Number Windward/Leeward Low0.6356
Triple Number Windward/Leeward Medium0.8641
Triple Number Windward/Leeward High0.9794
Coastal/Long Distance0.9798
Predominantly Upwind0.9781
Predominantly Downwind1.0613
For information
General Purpose Handicap (GPH)631.5
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)1.0691
Distanseseilas Trippeltall svak vind0.8227
Distanseseilas Trippeltall mellomvind1.0780
Distanseseilas Trippeltall sterk vind1.2006
Pølsebane Trippeltall svak vind0.6356
Pølsebane Trippeltall mellomvind0.8641
Pølsebane Trippeltall sterk vind0.9794
Motvind Singeltall0.9781
Medvind Singeltall1.0613
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low729.30.8227
Triple Number Coastal/Long Distance Medium556.61.0780
Triple Number Coastal/Long Distance High499.81.2006
Triple Number Windward/Leeward Low944.00.6356
Triple Number Windward/Leeward Medium694.40.8641
Triple Number Windward/Leeward High612.60.9794
Coastal/Long Distance612.40.9798
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind613.50.9781
Predominantly Downwind565.31.0613
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore589.11.0185
Cape Doctor Coastal478.51.2540
Triple Number Coastal/Long Distance Low729.30.8227
Triple Number Coastal/Long Distance Medium556.61.0780
Triple Number Coastal/Long Distance High499.81.2006
Triple Number Windward/Leeward Low944.00.6356
Triple Number Windward/Leeward Medium694.40.8641
Triple Number Windward/Leeward High612.60.9794
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8227
Triple Number Coastal/Long Distance Medium1.0780
Triple Number Coastal/Long Distance High1.2006
Triple Number Windward/Leeward Low0.6356
Triple Number Windward/Leeward Medium0.8641
Triple Number Windward/Leeward High0.9794
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8227
Triple Number Coastal/Long Distance Medium1.0780
Triple Number Coastal/Long Distance High1.2006
Triple Number Windward/Leeward Low0.6356
Triple Number Windward/Leeward Medium0.8641
Triple Number Windward/Leeward High0.9794
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance612.40.9798
Triple Number Coastal/Long Distance Low729.30.8227
Triple Number Coastal/Long Distance Medium556.61.0780
Triple Number Coastal/Long Distance High499.81.2006
Triple Number Windward/Leeward Low944.00.6356
Triple Number Windward/Leeward Medium694.40.8641
Triple Number Windward/Leeward High612.60.9794
Predominantly Upwind613.50.9781
Predominantly Downwind565.31.0613
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1567.31042.9787.4653.3577.5538.5507.0458.4448.3
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance612.40.9798
Triple Number Coastal/Long Distance Low729.30.8227
Triple Number Coastal/Long Distance Medium556.61.0780
Triple Number Coastal/Long Distance High499.81.2006
Triple Number Windward/Leeward Low944.00.6356
Triple Number Windward/Leeward Medium694.40.8641
Triple Number Windward/Leeward High612.60.9794
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1567.31042.9787.4653.3577.5538.5507.0458.4448.3
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low729.30.8227
Triple Number AP Medium556.71.0779
Triple Number AP High499.71.2006
Triple Number Windward/Leeward Low986.70.6081
Triple Number Windward/Leeward Medium694.40.8641
Triple Number Windward/Leeward High612.60.9794
Single Number Predominant Upwind641.00.9361
Single Number Predominant Reaching555.41.0802
Single Number Predominant Downwind591.21.0149
Predominant Upwind - Low896.50.6693
Predominant Upwind - Low/Med675.80.8878
Predominant Upwind - Medium592.21.0132
Predominant Upwind - Med/High555.01.0811
Predominant Upwind - High542.51.1060
Predominant Downwind Low870.60.6892
Predominant Downwind Low/Med639.90.9376
Predominant Downwind Medium544.61.1017
Predominant Downwind Med/High488.31.2288
Predominant Downwind High455.11.3185
Predominant Reaching Low780.60.7687
Predominant Reaching Low/Med589.31.0181
Predominant Reaching Medium516.21.1624
Predominant Reaching Med/High476.31.2598
Predominant Reaching High452.81.3251
SA/DSPL Upwind18.94SA/DSPL Downwind37.06
Scoring OptionTODTOT
5-Band Windward/Leeward Low1104.80.5431
5-Band Windward/Leeward Low/Med805.50.7449
5-Band Windward/Leeward Medium682.70.8789
5-Band Windward/Leeward Med/High620.10.9676
5-Band Windward/Leeward High596.01.0067
Windward/Leeward 60-40 Low1116.20.5375
Windward/Leeward 60-40 Low/Med818.40.7332
Windward/Leeward 60-40 Medium698.60.8589
Windward/Leeward 60-40 Med/High641.00.9361
Windward/Leeward 60-40 High621.80.9649
5-Band AP Low804.00.7462
5-Band AP Low/Med632.70.9483
5-Band AP Medium548.81.0933
5-Band AP Med/High505.51.1870
5-Band AP High486.11.2343
5-Band SF Bay Tour - Low952.40.6300
5-Band SF Bay Tour - Low/Med770.40.7788
5-Band SF Bay Tour - Medium657.80.9122
5-Band SF Bay Tour - Med/High601.90.9968
5-Band SF Bay Tour - High580.31.0339
Chicago-Mac Upwind0.9071
Chicago-Mac All Purpose0.9454
Chicago-Mac Downwind0.9783
Bayview-Mac Cove Island0.6845
Bayview-Mac Shore0.6891
Harvest Moon Regatta480.51.2487
Double HandedClub Certificate2025
AndrikNOR 13348
Norges Seilforbund
Sognsveien 73
0854 OSLO
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassHanse 370MeasurementHINPlan reviewHull constructionCoredCarbon rudderNoLight stanchionsNoTrim tabNo
LOA11.298Max. Beam3.742Draft2.006Displacement7,445Wetted area31.01IMS L10.547LSM010.574Acc. length11.298Sink (kg/mm) 24.15
VCGD0.180VCGM0.211RM Rated (kg·m) 189.9Limit of positive stability(°) N/AStability IndexN/ADefault crew weight170Declared crew weightN/A
PROPELLER
Propeller TypeFolding 3 blades
InstallationStrutTwin screwNoHydro generatorNo
PRD0.400PBWPIPA0.0034
EDL2.000ST10.050ST20.170
ST30.170ST40.100ST50.300
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerNoMainsail furlerArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders2Rotating mastNo
P14.400IG15.050ISP15.160MDT10.120MDL10.220MDT20.120MDL20.180TL1.000MW0.220GO0.220
E5.150J4.170BAS1.700FSDFoilSFJ0.000SPL0.000WPLTPS4.820BD0.000MWT180.00MCG5.960
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodVCG entered directlyVCG entered0.180Flotation Date01/01/2015
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Double HandedClub Certificate2025
AndrikNOR 13348
Norges Seilforbund
Sognsveien 73
0854 OSLO
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment1-2019052913070.171.051.913.294.3143.8329/05/2019
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment330-2020060209470.050.611.152.082.913.7014.50YesNo 28.8502/06/20201-2019052913080.000.000.000.000.003.6714.44NoNo 26.9729/05/2019
ASYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLRatioAreaMeas.DateComment1-20190529130815.9513.2914.628.456.59128%98.4229/05/2019
CRUISER/RACER REQUIREMENTS*
Accommodation length11.3 mTable area0.55 m²Headroom1.78 mMinimum number of berths5Personal gear stowage0.20 m³Fresh water capacity133 lMinimum number of seats in cockpit5Food stowage0.30 m³Fuel capacity76 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.