Non Spin/HSFClub Certificate2025
Tante MagdaNOR 13410
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 Angles46.0°46.0°44.0°43.0°41.8°40.5°39.8°40.0°41.6°
Beat VMG2.042.843.483.964.334.614.774.804.65
52°3.244.445.355.986.396.666.826.936.88
60°3.494.735.646.246.606.847.007.167.16
75°3.664.925.836.436.787.027.217.507.63
90°3.584.835.756.416.807.067.297.687.96
110°3.134.365.386.176.697.037.307.818.29
120°2.934.135.165.976.566.937.217.738.25
135°2.523.654.675.506.186.666.997.518.02
150°2.123.144.114.955.676.276.707.267.75
Run VMG1.832.723.584.355.055.686.236.967.44
Gybe Angles149.8°149.8°154.1°161.3°168.5°173.2°177.2°179.5°179.5°
APH ToD:652.7CDL: 7.695APH ToT: 0.9193CertNo:9900
BOAT
ClassBavaria 32 AC 01-05DesignerBuilderBavaria YachtbauAge date01/2003Series date01/2001Offset fileBAVA32CL.OFFData file9900
HULL
Length Overall9.900 mMaximum Beam3.350 mDraft1.558 mDisplacement4,855 kgDLR7.0896IMS DivisionCruiser/RacerDynamic Allowance0.400%Age Allowance0.487%
PROPELLER
InstallationStrutTypeFolding 2 bladesDiameter0.380m
CREW
Maximum weight575 kg(default)Minimum weight445 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail24.4824.73Headsail Luffed25.0125.01Headsail FlyingSymmetricAsymmetric
STORM SAIL AREAS (m²)
Trysail7.91Storm Jib6.68Heavy Weather Jib18.01
SAIL LIMITS
Headsails1
✱ One set on the forestay
✱ Zero set flying
Spinnakers0
✱ Spinnaker pole aboard
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.
Non Spin/HSFClub Certificate2025
Tante MagdaNOR 13410
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 VMG1767.51269.41034.2909.8831.5780.8755.3749.8773.7
52°1110.1811.2673.3602.4563.1540.8527.8519.7523.1
60°1031.3760.5637.9576.9545.1526.3514.0502.7502.8
75°983.7731.3618.0559.7530.9513.1499.5480.2471.9
90°1005.8744.9626.0561.9529.6510.1494.0468.9452.5
110°1150.0825.0669.4583.5537.7511.9493.0461.0434.1
120°1229.6870.9697.9603.1549.1519.5499.3465.8436.4
135°1431.4986.5770.4654.6582.4540.2515.0479.5449.0
150°1701.71147.1875.1726.7635.3574.3537.2495.7464.5
Run VMG1968.61324.51006.5826.7712.4633.7577.8517.6483.8
Selected Courses
Windward / Leeward1865.01296.91020.3868.3772.0707.2666.5633.7628.7
All purpose1392.6986.9792.0686.8624.0584.4559.6534.7524.4
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward811.90.7390
All purpose652.70.9193
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low889.40.6746
Triple Number Coastal/Long Distance Medium649.00.9245
Triple Number Coastal/Long Distance High556.51.0782
Triple Number Windward/Leeward Low1158.70.5178
Triple Number Windward/Leeward Medium808.60.7420
Triple Number Windward/Leeward High664.40.9031
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance715.40.8387
Triple Number Coastal/Long Distance Low889.40.6746
Triple Number Coastal/Long Distance Medium649.00.9245
Triple Number Coastal/Long Distance High556.51.0782
Triple Number Windward/Leeward Low1158.70.5178
Triple Number Windward/Leeward Medium808.60.7420
Triple Number Windward/Leeward High664.40.9031
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance2005.91299.7958.1778.6668.7607.3566.2512.2497.5
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.6634
Downwind "popa"0.7501
70% up, 30% down "Ilhabela"0.6873
30% up, 70% down "Ilhabela-inverso"0.7218
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low889.40.6746
Triple Number Coastal/Long Distance Medium649.00.9245
Triple Number Coastal/Long Distance High556.51.0782
Triple Number Windward/Leeward Low1158.70.5178
Triple Number Windward/Leeward Medium808.60.7420
Triple Number Windward/Leeward High664.40.9031
Predominantly Upwind698.20.8594
Predominantly Downwind679.40.8832
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low889.50.6746
Triple Number AP Medium649.10.9244
Triple Number AP High556.51.0782
Triple Number Windward/Leeward Low1214.40.4941
Triple Number Windward/Leeward Medium808.60.7420
Triple Number Windward/Leeward High664.40.9031
Single Number Predominant Upwind729.10.8229
Single Number Predominant Reaching653.20.9185
Single Number Predominant Downwind716.00.8380
Predominant Upwind - Low1061.10.5655
Predominant Upwind - Low/Med787.60.7618
Predominant Upwind - Medium670.20.8953
Predominant Upwind - Med/High604.10.9933
Predominant Upwind - High584.11.0272
Predominant Downwind Low1122.30.5346
Predominant Downwind Low/Med794.70.7550
Predominant Downwind Medium648.40.9254
Predominant Downwind Med/High558.71.0738
Predominant Downwind High518.71.1566
Predominant Reaching Low961.30.6241
Predominant Reaching Low/Med708.70.8466
Predominant Reaching Medium600.50.9992
Predominant Reaching Med/High537.61.1162
Predominant Reaching High509.31.1780
SA/DSPL Upwind17.17SA/DSPL Downwind17.17
Scoring OptionTODTOT
5-Band Windward/Leeward Low1370.60.4378
5-Band Windward/Leeward Low/Med970.80.6180
5-Band Windward/Leeward Medium789.00.7604
5-Band Windward/Leeward Med/High676.80.8865
5-Band Windward/Leeward High638.50.9397
Windward/Leeward 60-40 Low1363.50.4400
Windward/Leeward 60-40 Low/Med975.60.6150
Windward/Leeward 60-40 Medium800.50.7495
Windward/Leeward 60-40 Med/High694.40.8640
Windward/Leeward 60-40 High661.80.9066
5-Band AP Low998.30.6010
5-Band AP Low/Med758.80.7907
5-Band AP Medium636.40.9428
5-Band AP Med/High565.01.0619
5-Band AP High537.21.1168
5-Band SF Bay Tour - Low1170.30.5127
5-Band SF Bay Tour - Low/Med927.30.6470
5-Band SF Bay Tour - Medium761.40.7880
5-Band SF Bay Tour - Med/High662.00.9064
5-Band SF Bay Tour - High629.40.9532
Chicago-Mac Upwind0.7903
Chicago-Mac All Purpose0.8005
Chicago-Mac Downwind0.8011
Bayview-Mac Cove Island0.5605
Bayview-Mac Shore0.5666
Harvest Moon Regatta559.21.0729
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance715.40.8387
Triple Number Coastal/Long Distance Low889.40.6746
Triple Number Coastal/Long Distance Medium649.00.9245
Triple Number Coastal/Long Distance High556.51.0782
Triple Number Windward/Leeward Low1158.70.5178
Triple Number Windward/Leeward Medium808.60.7420
Triple Number Windward/Leeward High664.40.9031
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance2005.91299.7958.1778.6668.7607.3566.2512.2497.5
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance715.40.8387
Triple Number Coastal/Long Distance Low889.40.6746
Triple Number Coastal/Long Distance Medium649.00.9245
Triple Number Coastal/Long Distance High556.51.0782
Triple Number Windward/Leeward Low1158.70.5178
Triple Number Windward/Leeward Medium808.60.7420
Triple Number Windward/Leeward High664.40.9031
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance2005.91299.7958.1778.6668.7607.3566.2512.2497.5
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance715.4
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance2005.91299.7958.1778.6668.7607.3566.2512.2497.5
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low889.40.6746
Triple Number Coastal/Long Distance Medium649.00.9245
Triple Number Coastal/Long Distance High556.51.0782
Triple Number Windward/Leeward Low1158.70.5178
Triple Number Windward/Leeward Medium808.60.7420
Triple Number Windward/Leeward High664.40.9031
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating715.40.8387
FinRating, kevyt tuuli1348.30.7417
FinRating, kova tuuli542.30.9220
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low889.40.6746
Triple Number Coastal/Long Distance Medium649.00.9245
Triple Number Coastal/Long Distance High556.51.0782
Triple Number Windward/Leeward Low1158.70.5178
Triple Number Windward/Leeward Medium808.60.7420
Triple Number Windward/Leeward High664.40.9031
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.8387
Triple Number Coastal/Long Distance Low0.6746
Triple Number Coastal/Long Distance Medium0.9245
Triple Number Coastal/Long Distance High1.0782
Triple Number Windward/Leeward Low0.5178
Triple Number Windward/Leeward Medium0.7420
Triple Number Windward/Leeward High0.9031
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance2005.91299.7958.1778.6668.7607.3566.2512.2497.5
For information
General Purpose Handicap (GPH)742.7
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance715.40.8387
Triple Number Coastal/Long Distance Low889.40.6746
Triple Number Coastal/Long Distance Medium649.00.9245
Triple Number Coastal/Long Distance High556.51.0782
Triple Number Windward/Leeward Low1158.70.5178
Triple Number Windward/Leeward Medium808.60.7420
Triple Number Windward/Leeward High664.40.9031
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance2005.91299.7958.1778.6668.7607.3566.2512.2497.5
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low889.40.6746
Triple Number Coastal/Long Distance Medium649.00.9245
Triple Number Coastal/Long Distance High556.51.0782
Triple Number Windward/Leeward Low1158.70.5178
Triple Number Windward/Leeward Medium808.60.7420
Triple Number Windward/Leeward High664.40.9031
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance715.40.8387
Triple Number Coastal/Long Distance Low889.40.6746
Triple Number Coastal/Long Distance Medium649.00.9245
Triple Number Coastal/Long Distance High556.51.0782
Triple Number Windward/Leeward Low1158.70.5178
Triple Number Windward/Leeward Medium808.60.7420
Triple Number Windward/Leeward High664.40.9031
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance2005.91299.7958.1778.6668.7607.3566.2512.2497.5
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance715.40.8387
Triple Number Coastal/Long Distance Low889.40.6746
Triple Number Coastal/Long Distance Medium649.00.9245
Triple Number Coastal/Long Distance High556.51.0782
Triple Number Windward/Leeward Low1158.70.5178
Triple Number Windward/Leeward Medium808.60.7420
Triple Number Windward/Leeward High664.40.9031
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance2005.91299.7958.1778.6668.7607.3566.2512.2497.5
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low889.4
Triple Number Coastal/Long Distance Medium649.0
Triple Number Coastal/Long Distance High556.5
Triple Number Windward/Leeward Low1158.7
Triple Number Windward/Leeward Medium808.6
Triple Number Windward/Leeward High664.4
Predominantly Upwind698.2
Predominantly Downwind679.4
Predominantly Reaching641.9
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance715.40.8387
Triple Number Coastal/Long Distance Low889.40.6746
Triple Number Coastal/Long Distance Medium649.00.9245
Triple Number Coastal/Long Distance High556.51.0782
Triple Number Windward/Leeward Low1158.70.5178
Triple Number Windward/Leeward Medium808.60.7420
Triple Number Windward/Leeward High664.40.9031
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance2005.91299.7958.1778.6668.7607.3566.2512.2497.5
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.6746
Triple Number Coastal/Long Distance Medium0.9245
Triple Number Coastal/Long Distance High1.0782
Triple Number Windward/Leeward Low0.5178
Triple Number Windward/Leeward Medium0.7420
Triple Number Windward/Leeward High0.9031
Coastal/Long Distance0.8387
Predominantly Upwind0.8594
Predominantly Downwind0.8832
For information
General Purpose Handicap (GPH)742.7
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)0.9193
Distanseseilas Trippeltall svak vind0.6746
Distanseseilas Trippeltall mellomvind0.9245
Distanseseilas Trippeltall sterk vind1.0782
Pølsebane Trippeltall svak vind0.5178
Pølsebane Trippeltall mellomvind0.7420
Pølsebane Trippeltall sterk vind0.9031
Motvind Singeltall0.8594
Medvind Singeltall0.8832
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low889.40.6746
Triple Number Coastal/Long Distance Medium649.00.9245
Triple Number Coastal/Long Distance High556.51.0782
Triple Number Windward/Leeward Low1158.70.5178
Triple Number Windward/Leeward Medium808.60.7420
Triple Number Windward/Leeward High664.40.9031
Coastal/Long Distance715.40.8387
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind698.20.8594
Predominantly Downwind679.40.8832
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore630.20.9521
Cape Doctor Coastal527.51.1375
Triple Number Coastal/Long Distance Low889.40.6746
Triple Number Coastal/Long Distance Medium649.00.9245
Triple Number Coastal/Long Distance High556.51.0782
Triple Number Windward/Leeward Low1158.70.5178
Triple Number Windward/Leeward Medium808.60.7420
Triple Number Windward/Leeward High664.40.9031
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.6746
Triple Number Coastal/Long Distance Medium0.9245
Triple Number Coastal/Long Distance High1.0782
Triple Number Windward/Leeward Low0.5178
Triple Number Windward/Leeward Medium0.7420
Triple Number Windward/Leeward High0.9031
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.6746
Triple Number Coastal/Long Distance Medium0.9245
Triple Number Coastal/Long Distance High1.0782
Triple Number Windward/Leeward Low0.5178
Triple Number Windward/Leeward Medium0.7420
Triple Number Windward/Leeward High0.9031
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance715.40.8387
Triple Number Coastal/Long Distance Low889.40.6746
Triple Number Coastal/Long Distance Medium649.00.9245
Triple Number Coastal/Long Distance High556.51.0782
Triple Number Windward/Leeward Low1158.70.5178
Triple Number Windward/Leeward Medium808.60.7420
Triple Number Windward/Leeward High664.40.9031
Predominantly Upwind698.20.8594
Predominantly Downwind679.40.8832
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance2005.91299.7958.1778.6668.7607.3566.2512.2497.5
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance715.40.8387
Triple Number Coastal/Long Distance Low889.40.6746
Triple Number Coastal/Long Distance Medium649.00.9245
Triple Number Coastal/Long Distance High556.51.0782
Triple Number Windward/Leeward Low1158.70.5178
Triple Number Windward/Leeward Medium808.60.7420
Triple Number Windward/Leeward High664.40.9031
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance2005.91299.7958.1778.6668.7607.3566.2512.2497.5
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low889.50.6746
Triple Number AP Medium649.10.9244
Triple Number AP High556.51.0782
Triple Number Windward/Leeward Low1214.40.4941
Triple Number Windward/Leeward Medium808.60.7420
Triple Number Windward/Leeward High664.40.9031
Single Number Predominant Upwind729.10.8229
Single Number Predominant Reaching653.20.9185
Single Number Predominant Downwind716.00.8380
Predominant Upwind - Low1061.10.5655
Predominant Upwind - Low/Med787.60.7618
Predominant Upwind - Medium670.20.8953
Predominant Upwind - Med/High604.10.9933
Predominant Upwind - High584.11.0272
Predominant Downwind Low1122.30.5346
Predominant Downwind Low/Med794.70.7550
Predominant Downwind Medium648.40.9254
Predominant Downwind Med/High558.71.0738
Predominant Downwind High518.71.1566
Predominant Reaching Low961.30.6241
Predominant Reaching Low/Med708.70.8466
Predominant Reaching Medium600.50.9992
Predominant Reaching Med/High537.61.1162
Predominant Reaching High509.31.1780
SA/DSPL Upwind17.17SA/DSPL Downwind17.17
Scoring OptionTODTOT
5-Band Windward/Leeward Low1370.60.4378
5-Band Windward/Leeward Low/Med970.80.6180
5-Band Windward/Leeward Medium789.00.7604
5-Band Windward/Leeward Med/High676.80.8865
5-Band Windward/Leeward High638.50.9397
Windward/Leeward 60-40 Low1363.50.4400
Windward/Leeward 60-40 Low/Med975.60.6150
Windward/Leeward 60-40 Medium800.50.7495
Windward/Leeward 60-40 Med/High694.40.8640
Windward/Leeward 60-40 High661.80.9066
5-Band AP Low998.30.6010
5-Band AP Low/Med758.80.7907
5-Band AP Medium636.40.9428
5-Band AP Med/High565.01.0619
5-Band AP High537.21.1168
5-Band SF Bay Tour - Low1170.30.5127
5-Band SF Bay Tour - Low/Med927.30.6470
5-Band SF Bay Tour - Medium761.40.7880
5-Band SF Bay Tour - Med/High662.00.9064
5-Band SF Bay Tour - High629.40.9532
Chicago-Mac Upwind0.7903
Chicago-Mac All Purpose0.8005
Chicago-Mac Downwind0.8011
Bayview-Mac Cove Island0.5605
Bayview-Mac Shore0.5666
Harvest Moon Regatta559.21.0729
Non Spin/HSFClub Certificate2025
Tante MagdaNOR 13410
Norges Seilforbund
Sognsveien 73
0854 OSLO
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassBavaria 32 AC 01-05MeasurementHINPlan reviewHull constructionSolidCarbon rudderNoLight stanchionsNoTrim tabNo
LOA9.900Max. Beam3.350Draft1.558Displacement4,855Wetted area21.22IMS L8.939LSM08.814Acc. length9.880Sink (kg/mm) 16.46
VCGD0.000VCGM-0.057RM Rated (kg·m) 104.1Limit of positive stability(°) N/AStability IndexN/ADefault crew weight575Declared crew weightN/A
PROPELLER
Propeller TypeFolding 2 blades
InstallationStrutTwin screwNoHydro generatorNo
PRD0.380PBWPIPA0.0034
EDL1.780ST10.050ST20.170
ST30.170ST40.170ST50.290
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerYesMainsail furlerArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders2Rotating mastNo
P11.150IG11.550ISP11.710MDT10.100MDL10.160MDT20.000MDL20.000TL0.000MW0.000GO0.000
E4.050J3.460BAS1.510FSDFoilSFJ0.000SPL3.600WPLTPS0.000BD0.000MWT0.00MCG0.000
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodVCG entered directlyVCG entered0.000Flotation Date01/01/2015
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Non Spin/HSFClub Certificate2025
Tante MagdaNOR 13410
Norges Seilforbund
Sognsveien 73
0854 OSLO
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment394-2018120109150.060.641.232.283.2224.4801/12/2018
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment394-2018120109000.030.501.092.273.574.9310.61NoNo 25.0101/12/2018625-2023062015470.070.541.011.862.763.7210.74YesNo 20.1820/06/2023
CRUISER/RACER REQUIREMENTS*
Accommodation length9.9 mTable area0.44 m²Headroom1.70 mMinimum number of berths4Personal gear stowage0.16 m³Fresh water capacity78 lMinimum number of seats in cockpit4Food stowage0.24 m³Fuel capacity48 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.