Club Certificate2025
KrakenNOR 16222
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 Angles44.7°44.7°43.0°41.5°40.4°39.7°39.3°39.0°39.4°
Beat VMG2.813.914.815.495.926.136.246.346.31
52°4.466.087.298.138.608.848.959.069.08
60°4.826.477.648.418.859.109.229.349.39
75°5.096.767.888.609.049.349.559.799.92
90°4.956.627.788.559.109.429.6610.1410.43
110°4.556.337.758.729.299.7410.1610.7711.20
120°4.416.167.578.569.179.6410.0911.0011.86
135°3.875.486.867.968.749.269.7110.6311.71
150°3.174.585.856.967.908.619.109.8610.64
Run VMG2.743.965.076.036.847.477.978.789.49
Gybe Angles141.7°141.7°145.6°148.5°149.8°151.9°155.8°162.8°175.0°
APH ToD:476.7CDL: 13.421APH ToT: 1.2586CertNo:676258
BOAT
ClassHanse 548DesignerJUDELFRIEDRICH/VROELIJKROLFBuilderHanse YachtsAge date01/2022Series date01/2022Offset fileHANSE548TK.offData file676258
HULL
Length Overall15.750 mMaximum Beam5.050 mDraft2.579 mDisplacement19,601 kgDLR6.3380IMS DivisionCruiser/RacerDynamic Allowance0.330%Age Allowance0.098%
PROPELLER
InstallationShaft non exposedTypeFolding 3 bladesDiameter0.500m
CREW
Maximum weight1,177 kg(default)Minimum weight1,001 kg ✱ when appliedNon Manual PowerYesCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail72.6973.15Headsail Luffed97.8897.88Headsail FlyingSymmetricAsymmetric184.04184.04 (All asymmetric spinnakers with SHW/SFL > 85%)
STORM SAIL AREAS (m²)
Trysail23.72Storm Jib23.12Heavy Weather Jib62.41
SAIL LIMITS
Headsails7Spinnakers5
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.
Club Certificate2025
KrakenNOR 16222
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 VMG1283.1920.9748.4655.7608.4587.7576.8568.2570.5
52°806.7592.4493.9443.1418.4407.3402.1397.4396.5
60°746.4556.0471.3428.2406.6395.6390.4385.3383.4
75°707.6532.5456.7418.7398.3385.6376.8367.8362.7
90°727.3543.8462.9421.1395.6382.0372.7355.0345.0
110°791.1568.6464.3412.9387.5369.6354.4334.1321.5
120°815.6584.8475.7420.4392.5373.5356.7327.2303.5
135°929.9657.0524.9452.4411.9388.7370.8338.6307.3
150°1136.2786.6614.9517.4455.9418.3395.8365.2338.3
Run VMG1311.9908.3710.1597.4526.4481.9451.9410.1379.5
Selected Courses
Windward / Leeward1296.8914.6729.3626.6567.4534.8514.3489.1475.0
All purpose970.6696.2565.7495.6456.7435.1420.7401.6389.5
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward597.01.0050
All purpose476.71.2586
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low630.90.9510
Triple Number Coastal/Long Distance Medium473.41.2675
Triple Number Coastal/Long Distance High417.21.4383
Triple Number Windward/Leeward Low821.90.7300
Triple Number Windward/Leeward Medium592.51.0127
Triple Number Windward/Leeward High510.01.1765
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance522.11.1492
Triple Number Coastal/Long Distance Low630.90.9510
Triple Number Coastal/Long Distance Medium473.41.2675
Triple Number Coastal/Long Distance High417.21.4383
Triple Number Windward/Leeward Low821.90.7300
Triple Number Windward/Leeward Medium592.51.0127
Triple Number Windward/Leeward High510.01.1765
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1384.1914.0684.6562.0489.3452.3425.2383.5369.6
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.9001
Downwind "popa"1.0279
70% up, 30% down "Ilhabela"0.9350
30% up, 70% down "Ilhabela-inverso"0.9859
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low630.90.9510
Triple Number Coastal/Long Distance Medium473.41.2675
Triple Number Coastal/Long Distance High417.21.4383
Triple Number Windward/Leeward Low821.90.7300
Triple Number Windward/Leeward Medium592.51.0127
Triple Number Windward/Leeward High510.01.1765
Predominantly Upwind512.71.1702
Predominantly Downwind492.51.2182
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low630.90.9510
Triple Number AP Medium473.41.2673
Triple Number AP High417.21.4383
Triple Number Windward/Leeward Low859.20.6983
Triple Number Windward/Leeward Medium592.51.0127
Triple Number Windward/Leeward High510.01.1765
Single Number Predominant Upwind534.71.1221
Single Number Predominant Reaching474.61.2641
Single Number Predominant Downwind515.71.1635
Predominant Upwind - Low759.50.7900
Predominant Upwind - Low/Med570.11.0525
Predominant Upwind - Medium493.41.2162
Predominant Upwind - Med/High456.11.3155
Predominant Upwind - High441.41.3592
Predominant Downwind Low773.70.7755
Predominant Downwind Low/Med563.81.0642
Predominant Downwind Medium472.61.2696
Predominant Downwind Med/High419.11.4315
Predominant Downwind High389.91.5390
Predominant Reaching Low676.30.8872
Predominant Reaching Low/Med509.41.1780
Predominant Reaching Medium439.91.3641
Predominant Reaching Med/High401.41.4946
Predominant Reaching High380.51.5770
SA/DSPL Upwind23.23SA/DSPL Downwind34.97
Scoring OptionTODTOT
5-Band Windward/Leeward Low964.00.6224
5-Band Windward/Leeward Low/Med696.50.8615
5-Band Windward/Leeward Medium580.91.0329
5-Band Windward/Leeward Med/High518.01.1583
5-Band Windward/Leeward High491.01.2219
Windward/Leeward 60-40 Low964.90.6218
Windward/Leeward 60-40 Low/Med701.30.8556
Windward/Leeward 60-40 Medium589.11.0186
Windward/Leeward 60-40 Med/High530.41.1313
Windward/Leeward 60-40 High506.81.1838
5-Band AP Low699.50.8577
5-Band AP Low/Med544.11.1027
5-Band AP Medium465.71.2885
5-Band AP Med/High423.01.4186
5-Band AP High402.81.4894
5-Band SF Bay Tour - Low826.90.7256
5-Band SF Bay Tour - Low/Med663.30.9046
5-Band SF Bay Tour - Medium557.21.0768
5-Band SF Bay Tour - Med/High500.91.1979
5-Band SF Bay Tour - High476.81.2584
Chicago-Mac Upwind1.0832
Chicago-Mac All Purpose1.1048
Chicago-Mac Downwind1.1172
Bayview-Mac Cove Island0.7923
Bayview-Mac Shore0.7991
Harvest Moon Regatta411.31.4589
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance522.11.1492
Triple Number Coastal/Long Distance Low630.90.9510
Triple Number Coastal/Long Distance Medium473.41.2675
Triple Number Coastal/Long Distance High417.21.4383
Triple Number Windward/Leeward Low821.90.7300
Triple Number Windward/Leeward Medium592.51.0127
Triple Number Windward/Leeward High510.01.1765
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1384.1914.0684.6562.0489.3452.3425.2383.5369.6
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance522.11.1492
Triple Number Coastal/Long Distance Low630.90.9510
Triple Number Coastal/Long Distance Medium473.41.2675
Triple Number Coastal/Long Distance High417.21.4383
Triple Number Windward/Leeward Low821.90.7300
Triple Number Windward/Leeward Medium592.51.0127
Triple Number Windward/Leeward High510.01.1765
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1384.1914.0684.6562.0489.3452.3425.2383.5369.6
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance522.1
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1384.1914.0684.6562.0489.3452.3425.2383.5369.6
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low630.90.9510
Triple Number Coastal/Long Distance Medium473.41.2675
Triple Number Coastal/Long Distance High417.21.4383
Triple Number Windward/Leeward Low821.90.7300
Triple Number Windward/Leeward Medium592.51.0127
Triple Number Windward/Leeward High510.01.1765
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating522.11.1492
FinRating, kevyt tuuli945.41.0578
FinRating, kova tuuli405.21.2339
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low630.90.9510
Triple Number Coastal/Long Distance Medium473.41.2675
Triple Number Coastal/Long Distance High417.21.4383
Triple Number Windward/Leeward Low821.90.7300
Triple Number Windward/Leeward Medium592.51.0127
Triple Number Windward/Leeward High510.01.1765
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance1.1492
Triple Number Coastal/Long Distance Low0.9510
Triple Number Coastal/Long Distance Medium1.2675
Triple Number Coastal/Long Distance High1.4383
Triple Number Windward/Leeward Low0.7300
Triple Number Windward/Leeward Medium1.0127
Triple Number Windward/Leeward High1.1765
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1384.1914.0684.6562.0489.3452.3425.2383.5369.6
For information
General Purpose Handicap (GPH)538.8
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance522.11.1492
Triple Number Coastal/Long Distance Low630.90.9510
Triple Number Coastal/Long Distance Medium473.41.2675
Triple Number Coastal/Long Distance High417.21.4383
Triple Number Windward/Leeward Low821.90.7300
Triple Number Windward/Leeward Medium592.51.0127
Triple Number Windward/Leeward High510.01.1765
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1384.1914.0684.6562.0489.3452.3425.2383.5369.6
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low630.90.9510
Triple Number Coastal/Long Distance Medium473.41.2675
Triple Number Coastal/Long Distance High417.21.4383
Triple Number Windward/Leeward Low821.90.7300
Triple Number Windward/Leeward Medium592.51.0127
Triple Number Windward/Leeward High510.01.1765
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance522.11.1492
Triple Number Coastal/Long Distance Low630.90.9510
Triple Number Coastal/Long Distance Medium473.41.2675
Triple Number Coastal/Long Distance High417.21.4383
Triple Number Windward/Leeward Low821.90.7300
Triple Number Windward/Leeward Medium592.51.0127
Triple Number Windward/Leeward High510.01.1765
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1384.1914.0684.6562.0489.3452.3425.2383.5369.6
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance522.11.1492
Triple Number Coastal/Long Distance Low630.90.9510
Triple Number Coastal/Long Distance Medium473.41.2675
Triple Number Coastal/Long Distance High417.21.4383
Triple Number Windward/Leeward Low821.90.7300
Triple Number Windward/Leeward Medium592.51.0127
Triple Number Windward/Leeward High510.01.1765
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1384.1914.0684.6562.0489.3452.3425.2383.5369.6
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low630.9
Triple Number Coastal/Long Distance Medium473.4
Triple Number Coastal/Long Distance High417.2
Triple Number Windward/Leeward Low821.9
Triple Number Windward/Leeward Medium592.5
Triple Number Windward/Leeward High510.0
Predominantly Upwind512.7
Predominantly Downwind492.5
Predominantly Reaching466.6
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance522.11.1492
Triple Number Coastal/Long Distance Low630.90.9510
Triple Number Coastal/Long Distance Medium473.41.2675
Triple Number Coastal/Long Distance High417.21.4383
Triple Number Windward/Leeward Low821.90.7300
Triple Number Windward/Leeward Medium592.51.0127
Triple Number Windward/Leeward High510.01.1765
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1384.1914.0684.6562.0489.3452.3425.2383.5369.6
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.9510
Triple Number Coastal/Long Distance Medium1.2675
Triple Number Coastal/Long Distance High1.4383
Triple Number Windward/Leeward Low0.7300
Triple Number Windward/Leeward Medium1.0127
Triple Number Windward/Leeward High1.1765
Coastal/Long Distance1.1492
Predominantly Upwind1.1702
Predominantly Downwind1.2182
For information
General Purpose Handicap (GPH)538.8
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)1.2586
Distanseseilas Trippeltall svak vind0.9510
Distanseseilas Trippeltall mellomvind1.2675
Distanseseilas Trippeltall sterk vind1.4383
Pølsebane Trippeltall svak vind0.7300
Pølsebane Trippeltall mellomvind1.0127
Pølsebane Trippeltall sterk vind1.1765
Motvind Singeltall1.1702
Medvind Singeltall1.2182
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low630.90.9510
Triple Number Coastal/Long Distance Medium473.41.2675
Triple Number Coastal/Long Distance High417.21.4383
Triple Number Windward/Leeward Low821.90.7300
Triple Number Windward/Leeward Medium592.51.0127
Triple Number Windward/Leeward High510.01.1765
Coastal/Long Distance522.11.1492
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind512.71.1702
Predominantly Downwind492.51.2182
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore479.21.2520
Cape Doctor Coastal393.11.5262
Triple Number Coastal/Long Distance Low630.90.9510
Triple Number Coastal/Long Distance Medium473.41.2675
Triple Number Coastal/Long Distance High417.21.4383
Triple Number Windward/Leeward Low821.90.7300
Triple Number Windward/Leeward Medium592.51.0127
Triple Number Windward/Leeward High510.01.1765
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.9510
Triple Number Coastal/Long Distance Medium1.2675
Triple Number Coastal/Long Distance High1.4383
Triple Number Windward/Leeward Low0.7300
Triple Number Windward/Leeward Medium1.0127
Triple Number Windward/Leeward High1.1765
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.9510
Triple Number Coastal/Long Distance Medium1.2675
Triple Number Coastal/Long Distance High1.4383
Triple Number Windward/Leeward Low0.7300
Triple Number Windward/Leeward Medium1.0127
Triple Number Windward/Leeward High1.1765
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance522.11.1492
Triple Number Coastal/Long Distance Low630.90.9510
Triple Number Coastal/Long Distance Medium473.41.2675
Triple Number Coastal/Long Distance High417.21.4383
Triple Number Windward/Leeward Low821.90.7300
Triple Number Windward/Leeward Medium592.51.0127
Triple Number Windward/Leeward High510.01.1765
Predominantly Upwind512.71.1702
Predominantly Downwind492.51.2182
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1384.1914.0684.6562.0489.3452.3425.2383.5369.6
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance522.11.1492
Triple Number Coastal/Long Distance Low630.90.9510
Triple Number Coastal/Long Distance Medium473.41.2675
Triple Number Coastal/Long Distance High417.21.4383
Triple Number Windward/Leeward Low821.90.7300
Triple Number Windward/Leeward Medium592.51.0127
Triple Number Windward/Leeward High510.01.1765
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1384.1914.0684.6562.0489.3452.3425.2383.5369.6
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low630.90.9510
Triple Number AP Medium473.41.2673
Triple Number AP High417.21.4383
Triple Number Windward/Leeward Low859.20.6983
Triple Number Windward/Leeward Medium592.51.0127
Triple Number Windward/Leeward High510.01.1765
Single Number Predominant Upwind534.71.1221
Single Number Predominant Reaching474.61.2641
Single Number Predominant Downwind515.71.1635
Predominant Upwind - Low759.50.7900
Predominant Upwind - Low/Med570.11.0525
Predominant Upwind - Medium493.41.2162
Predominant Upwind - Med/High456.11.3155
Predominant Upwind - High441.41.3592
Predominant Downwind Low773.70.7755
Predominant Downwind Low/Med563.81.0642
Predominant Downwind Medium472.61.2696
Predominant Downwind Med/High419.11.4315
Predominant Downwind High389.91.5390
Predominant Reaching Low676.30.8872
Predominant Reaching Low/Med509.41.1780
Predominant Reaching Medium439.91.3641
Predominant Reaching Med/High401.41.4946
Predominant Reaching High380.51.5770
SA/DSPL Upwind23.23SA/DSPL Downwind34.97
Scoring OptionTODTOT
5-Band Windward/Leeward Low964.00.6224
5-Band Windward/Leeward Low/Med696.50.8615
5-Band Windward/Leeward Medium580.91.0329
5-Band Windward/Leeward Med/High518.01.1583
5-Band Windward/Leeward High491.01.2219
Windward/Leeward 60-40 Low964.90.6218
Windward/Leeward 60-40 Low/Med701.30.8556
Windward/Leeward 60-40 Medium589.11.0186
Windward/Leeward 60-40 Med/High530.41.1313
Windward/Leeward 60-40 High506.81.1838
5-Band AP Low699.50.8577
5-Band AP Low/Med544.11.1027
5-Band AP Medium465.71.2885
5-Band AP Med/High423.01.4186
5-Band AP High402.81.4894
5-Band SF Bay Tour - Low826.90.7256
5-Band SF Bay Tour - Low/Med663.30.9046
5-Band SF Bay Tour - Medium557.21.0768
5-Band SF Bay Tour - Med/High500.91.1979
5-Band SF Bay Tour - High476.81.2584
Chicago-Mac Upwind1.0832
Chicago-Mac All Purpose1.1048
Chicago-Mac Downwind1.1172
Bayview-Mac Cove Island0.7923
Bayview-Mac Shore0.7991
Harvest Moon Regatta411.31.4589
Club Certificate2025
KrakenNOR 16222
Norges Seilforbund
Sognsveien 73
0854 OSLO
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassHanse 548MeasurementHINPlan reviewHull constructionCoredCarbon rudderNoLight stanchionsNoTrim tabNo
LOA15.750Max. Beam5.050Draft2.579Displacement19,601Wetted area58.05IMS L14.793LSM014.568Acc. length15.782Sink (kg/mm) 44.02
VCGD0.081VCGM0.094RM Rated (kg·m) 659.1Limit of positive stability(°) N/AStability IndexN/ADefault crew weight1,177Declared crew weightN/A
PROPELLER
Propeller TypeFolding 3 blades
InstallationShaft non exposedTwin screwNoHydro generatorNo
PRD0.500PBWPIPA0.0008
PSDPHDPHL
PSAESL
RIG
Forestay tensionAftInner stayFixedMast materialAluminumSingle headsail furlerNoMainsail furlerIn mastArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders3Rotating mastNo
P21.040IG21.500ISP22.240MDT10.140MDL10.280MDT20.140MDL20.280TL0.000MW0.000GO0.000
E6.440J6.500BAS2.110FSD0.040SFJ0.000SPL0.000WPLTPS6.990BD0.000MWT0.00MCG0.000
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodVCG entered directlyVCG entered0.081Flotation Date01/01/2015
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Club Certificate2025
KrakenNOR 16222
Norges Seilforbund
Sognsveien 73
0854 OSLO
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment455-2023051522030.080.991.903.585.0872.6915/05/2023
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment455-2023051522060.071.102.204.486.869.5621.26NoNo 97.8815/05/2023455-2023051522150.050.751.462.804.115.3420.17YesNo 55.5915/05/2023
ASYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLRatioAreaMeas.DateComment625-20240712055022.4518.6620.5610.5311.6091%184.0412/07/2024
CRUISER/RACER REQUIREMENTS*
Accommodation length15.8 mTable area0.77 m²Headroom1.90 mMinimum number of berths7Personal gear stowage0.28 m³Fresh water capacity343 lMinimum number of seats in cockpit7Food stowage0.42 m³Fuel capacity166 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.