Club Certificate2025
StormvogelNED 8087
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 Angles40.1°40.1°38.5°37.7°37.1°36.7°36.4°36.3°37.3°
Beat VMG2.973.964.635.045.255.375.465.555.51
52°4.425.806.657.107.327.447.527.617.64
60°4.636.026.847.277.497.627.707.817.85
75°4.766.176.987.417.667.827.948.108.20
90°4.626.117.047.477.727.948.128.368.57
110°4.856.377.307.778.088.298.458.688.78
120°4.706.247.227.738.108.418.679.029.28
135°4.195.696.797.467.888.258.609.2710.00
150°3.504.845.936.847.437.848.198.879.58
Run VMG3.034.195.145.936.597.167.628.318.95
Gybe Angles144.1°144.1°148.3°151.3°159.4°172.3°178.1°179.0°179.0°
APH ToD:526.7CDL: 9.955APH ToT: 1.1391CertNo:26654
BOAT
ClassBestevaer 50DesignerDijkstraBuilderKM MakkumAge date01/2009Series date09/1998Offset fileH5992E-NED8087.offData fileNED8087
HULL
Length Overall14.990 mMaximum Beam4.100 mDraft3.287 mDisplacement10,724 kgDLR10.3277IMS DivisionCruiser/RacerDynamic Allowance0.260%Age Allowance0.487%
PROPELLER
InstallationShaft exposedTypeFeathering 3 bladesDiameterm
CREW
Maximum weight701 kg(default)Minimum weight571 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail66.3467.21Headsail Luffed47.5847.58Headsail FlyingSymmetricAsymmetric157.24157.24 (All asymmetric spinnakers with SHW/SFL > 85%)
STORM SAIL AREAS (m²)
Trysail20.72Storm Jib18.32Heavy Weather Jib49.46
SAIL LIMITS
Headsails6Spinnakers5
✱ Asymmetric may be tacked on the pole
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
StormvogelNED 8087
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 VMG1212.1908.7776.8714.2685.7669.9659.7649.1653.7
52°813.6620.4541.4507.1491.5484.0478.7472.8471.2
60°777.7597.6526.0495.2480.4472.5467.5461.1458.8
75°755.9583.5516.1486.1470.1460.1453.3444.2439.0
90°780.0589.7511.2481.8466.3453.1443.4430.4420.3
110°743.0565.4493.0463.3445.4434.2425.9414.9409.9
120°766.1577.4498.3465.5444.6428.1415.1398.9388.1
135°860.2632.5530.1482.5456.6436.2418.5388.5359.9
150°1028.2744.1607.1526.1484.2459.2439.6406.1375.6
Run VMG1188.5859.2701.1606.7546.6502.5472.2433.1402.1
Selected Courses
Windward / Leeward1199.7884.0738.9660.4616.2586.2565.9541.1527.9
All purpose928.8694.0591.0540.6513.4495.8483.2466.0455.3
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward635.90.9435
All purpose526.71.1391
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low642.50.9338
Triple Number Coastal/Long Distance Medium524.51.1439
Triple Number Coastal/Long Distance High479.91.2502
Triple Number Windward/Leeward Low811.50.7394
Triple Number Windward/Leeward Medium633.60.9469
Triple Number Windward/Leeward High561.71.0682
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance569.51.0536
Triple Number Coastal/Long Distance Low642.50.9338
Triple Number Coastal/Long Distance Medium524.51.1439
Triple Number Coastal/Long Distance High479.91.2502
Triple Number Windward/Leeward Low811.50.7394
Triple Number Windward/Leeward Medium633.60.9469
Triple Number Windward/Leeward High561.71.0682
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1261.1881.5698.3601.6545.7513.4488.1449.9438.9
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.8294
Downwind "popa"1.0191
70% up, 30% down "Ilhabela"0.8784
30% up, 70% down "Ilhabela-inverso"0.9536
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low642.50.9338
Triple Number Coastal/Long Distance Medium524.51.1439
Triple Number Coastal/Long Distance High479.91.2502
Triple Number Windward/Leeward Low811.50.7394
Triple Number Windward/Leeward Medium633.60.9469
Triple Number Windward/Leeward High561.71.0682
Predominantly Upwind569.21.0541
Predominantly Downwind529.01.1343
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low642.50.9338
Triple Number AP Medium524.61.1438
Triple Number AP High479.91.2502
Triple Number Windward/Leeward Low842.50.7122
Triple Number Windward/Leeward Medium633.60.9469
Triple Number Windward/Leeward High561.71.0682
Single Number Predominant Upwind587.41.0215
Single Number Predominant Reaching523.21.1467
Single Number Predominant Downwind547.51.0959
Predominant Upwind - Low763.00.7864
Predominant Upwind - Low/Med611.10.9818
Predominant Upwind - Medium555.81.0795
Predominant Upwind - Med/High525.91.1409
Predominant Upwind - High511.71.1726
Predominant Downwind Low754.50.7952
Predominant Downwind Low/Med585.21.0252
Predominant Downwind Medium514.71.1658
Predominant Downwind Med/High467.71.2827
Predominant Downwind High440.11.3634
Predominant Reaching Low685.70.8750
Predominant Reaching Low/Med547.51.0959
Predominant Reaching Medium496.11.2094
Predominant Reaching Med/High464.01.2932
Predominant Reaching High444.71.3491
SA/DSPL Upwind23.24SA/DSPL Downwind45.61
Scoring OptionTODTOT
5-Band Windward/Leeward Low926.80.6474
5-Band Windward/Leeward Low/Med714.50.8398
5-Band Windward/Leeward Medium624.50.9608
5-Band Windward/Leeward Med/High569.41.0537
5-Band Windward/Leeward High543.11.1047
Windward/Leeward 60-40 Low931.70.6439
Windward/Leeward 60-40 Low/Med723.70.8290
Windward/Leeward 60-40 Medium638.20.9401
Windward/Leeward 60-40 Med/High587.91.0206
Windward/Leeward 60-40 High564.81.0623
5-Band AP Low699.60.8576
5-Band AP Low/Med576.91.0400
5-Band AP Medium518.91.1563
5-Band AP Med/High485.01.2371
5-Band AP High467.21.2843
5-Band SF Bay Tour - Low810.10.7406
5-Band SF Bay Tour - Low/Med685.10.8757
5-Band SF Bay Tour - Medium605.40.9910
5-Band SF Bay Tour - Med/High558.41.0745
5-Band SF Bay Tour - High535.21.1212
Chicago-Mac Upwind0.9955
Chicago-Mac All Purpose1.0300
Chicago-Mac Downwind1.0617
Bayview-Mac Cove Island0.7910
Bayview-Mac Shore0.7955
Harvest Moon Regatta467.11.2844
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance569.51.0536
Triple Number Coastal/Long Distance Low642.50.9338
Triple Number Coastal/Long Distance Medium524.51.1439
Triple Number Coastal/Long Distance High479.91.2502
Triple Number Windward/Leeward Low811.50.7394
Triple Number Windward/Leeward Medium633.60.9469
Triple Number Windward/Leeward High561.71.0682
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1261.1881.5698.3601.6545.7513.4488.1449.9438.9
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance569.51.0536
Triple Number Coastal/Long Distance Low642.50.9338
Triple Number Coastal/Long Distance Medium524.51.1439
Triple Number Coastal/Long Distance High479.91.2502
Triple Number Windward/Leeward Low811.50.7394
Triple Number Windward/Leeward Medium633.60.9469
Triple Number Windward/Leeward High561.71.0682
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1261.1881.5698.3601.6545.7513.4488.1449.9438.9
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance569.5
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1261.1881.5698.3601.6545.7513.4488.1449.9438.9
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low642.50.9338
Triple Number Coastal/Long Distance Medium524.51.1439
Triple Number Coastal/Long Distance High479.91.2502
Triple Number Windward/Leeward Low811.50.7394
Triple Number Windward/Leeward Medium633.60.9469
Triple Number Windward/Leeward High561.71.0682
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating (Coastal/Long Distance)569.51.0536
Triple Number Coastal/Long Distance Low642.50.9338
Triple Number Coastal/Long Distance Medium524.51.1439
Triple Number Coastal/Long Distance High479.91.2502
Triple Number Windward/Leeward Low811.50.7394
Triple Number Windward/Leeward Medium633.60.9469
Triple Number Windward/Leeward High561.71.0682
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1261.1881.5698.3601.6545.7513.4488.1449.9438.9
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low642.50.9338
Triple Number Coastal/Long Distance Medium524.51.1439
Triple Number Coastal/Long Distance High479.91.2502
Triple Number Windward/Leeward Low811.50.7394
Triple Number Windward/Leeward Medium633.60.9469
Triple Number Windward/Leeward High561.71.0682
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance1.0536
Triple Number Coastal/Long Distance Low0.9338
Triple Number Coastal/Long Distance Medium1.1439
Triple Number Coastal/Long Distance High1.2502
Triple Number Windward/Leeward Low0.7394
Triple Number Windward/Leeward Medium0.9469
Triple Number Windward/Leeward High1.0682
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1261.1881.5698.3601.6545.7513.4488.1449.9438.9
For information
General Purpose Handicap (GPH)583.1
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance569.51.0536
Triple Number Coastal/Long Distance Low642.50.9338
Triple Number Coastal/Long Distance Medium524.51.1439
Triple Number Coastal/Long Distance High479.91.2502
Triple Number Windward/Leeward Low811.50.7394
Triple Number Windward/Leeward Medium633.60.9469
Triple Number Windward/Leeward High561.71.0682
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1261.1881.5698.3601.6545.7513.4488.1449.9438.9
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low642.50.9338
Triple Number Coastal/Long Distance Medium524.51.1439
Triple Number Coastal/Long Distance High479.91.2502
Triple Number Windward/Leeward Low811.50.7394
Triple Number Windward/Leeward Medium633.60.9469
Triple Number Windward/Leeward High561.71.0682
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance569.51.0536
Triple Number Coastal/Long Distance Low642.50.9338
Triple Number Coastal/Long Distance Medium524.51.1439
Triple Number Coastal/Long Distance High479.91.2502
Triple Number Windward/Leeward Low811.50.7394
Triple Number Windward/Leeward Medium633.60.9469
Triple Number Windward/Leeward High561.71.0682
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1261.1881.5698.3601.6545.7513.4488.1449.9438.9
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance569.51.0536
Triple Number Coastal/Long Distance Low642.50.9338
Triple Number Coastal/Long Distance Medium524.51.1439
Triple Number Coastal/Long Distance High479.91.2502
Triple Number Windward/Leeward Low811.50.7394
Triple Number Windward/Leeward Medium633.60.9469
Triple Number Windward/Leeward High561.71.0682
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1261.1881.5698.3601.6545.7513.4488.1449.9438.9
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low642.5
Triple Number Coastal/Long Distance Medium524.5
Triple Number Coastal/Long Distance High479.9
Triple Number Windward/Leeward Low811.5
Triple Number Windward/Leeward Medium633.6
Triple Number Windward/Leeward High561.7
Predominantly Upwind569.2
Predominantly Downwind529.0
Predominantly Reaching512.4
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance569.51.0536
Triple Number Coastal/Long Distance Low642.50.9338
Triple Number Coastal/Long Distance Medium524.51.1439
Triple Number Coastal/Long Distance High479.91.2502
Triple Number Windward/Leeward Low811.50.7394
Triple Number Windward/Leeward Medium633.60.9469
Triple Number Windward/Leeward High561.71.0682
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1261.1881.5698.3601.6545.7513.4488.1449.9438.9
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.9338
Triple Number Coastal/Long Distance Medium1.1439
Triple Number Coastal/Long Distance High1.2502
Triple Number Windward/Leeward Low0.7394
Triple Number Windward/Leeward Medium0.9469
Triple Number Windward/Leeward High1.0682
Coastal/Long Distance1.0536
Predominantly Upwind1.0541
Predominantly Downwind1.1343
For information
General Purpose Handicap (GPH)583.1
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)1.1391
Distanseseilas Trippeltall svak vind0.9338
Distanseseilas Trippeltall mellomvind1.1439
Distanseseilas Trippeltall sterk vind1.2502
Pølsebane Trippeltall svak vind0.7394
Pølsebane Trippeltall mellomvind0.9469
Pølsebane Trippeltall sterk vind1.0682
Motvind Singeltall1.0541
Medvind Singeltall1.1343
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low642.50.9338
Triple Number Coastal/Long Distance Medium524.51.1439
Triple Number Coastal/Long Distance High479.91.2502
Triple Number Windward/Leeward Low811.50.7394
Triple Number Windward/Leeward Medium633.60.9469
Triple Number Windward/Leeward High561.71.0682
Coastal/Long Distance569.51.0536
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind569.21.0541
Predominantly Downwind529.01.1343
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore531.91.1281
Cape Doctor Coastal458.51.3085
Triple Number Coastal/Long Distance Low642.50.9338
Triple Number Coastal/Long Distance Medium524.51.1439
Triple Number Coastal/Long Distance High479.91.2502
Triple Number Windward/Leeward Low811.50.7394
Triple Number Windward/Leeward Medium633.60.9469
Triple Number Windward/Leeward High561.71.0682
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.9338
Triple Number Coastal/Long Distance Medium1.1439
Triple Number Coastal/Long Distance High1.2502
Triple Number Windward/Leeward Low0.7394
Triple Number Windward/Leeward Medium0.9469
Triple Number Windward/Leeward High1.0682
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.9338
Triple Number Coastal/Long Distance Medium1.1439
Triple Number Coastal/Long Distance High1.2502
Triple Number Windward/Leeward Low0.7394
Triple Number Windward/Leeward Medium0.9469
Triple Number Windward/Leeward High1.0682
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance569.51.0536
Triple Number Coastal/Long Distance Low642.50.9338
Triple Number Coastal/Long Distance Medium524.51.1439
Triple Number Coastal/Long Distance High479.91.2502
Triple Number Windward/Leeward Low811.50.7394
Triple Number Windward/Leeward Medium633.60.9469
Triple Number Windward/Leeward High561.71.0682
Predominantly Upwind569.21.0541
Predominantly Downwind529.01.1343
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1261.1881.5698.3601.6545.7513.4488.1449.9438.9
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance569.51.0536
Triple Number Coastal/Long Distance Low642.50.9338
Triple Number Coastal/Long Distance Medium524.51.1439
Triple Number Coastal/Long Distance High479.91.2502
Triple Number Windward/Leeward Low811.50.7394
Triple Number Windward/Leeward Medium633.60.9469
Triple Number Windward/Leeward High561.71.0682
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1261.1881.5698.3601.6545.7513.4488.1449.9438.9
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low642.50.9338
Triple Number AP Medium524.61.1438
Triple Number AP High479.91.2502
Triple Number Windward/Leeward Low842.50.7122
Triple Number Windward/Leeward Medium633.60.9469
Triple Number Windward/Leeward High561.71.0682
Single Number Predominant Upwind587.41.0215
Single Number Predominant Reaching523.21.1467
Single Number Predominant Downwind547.51.0959
Predominant Upwind - Low763.00.7864
Predominant Upwind - Low/Med611.10.9818
Predominant Upwind - Medium555.81.0795
Predominant Upwind - Med/High525.91.1409
Predominant Upwind - High511.71.1726
Predominant Downwind Low754.50.7952
Predominant Downwind Low/Med585.21.0252
Predominant Downwind Medium514.71.1658
Predominant Downwind Med/High467.71.2827
Predominant Downwind High440.11.3634
Predominant Reaching Low685.70.8750
Predominant Reaching Low/Med547.51.0959
Predominant Reaching Medium496.11.2094
Predominant Reaching Med/High464.01.2932
Predominant Reaching High444.71.3491
SA/DSPL Upwind23.24SA/DSPL Downwind45.61
Scoring OptionTODTOT
5-Band Windward/Leeward Low926.80.6474
5-Band Windward/Leeward Low/Med714.50.8398
5-Band Windward/Leeward Medium624.50.9608
5-Band Windward/Leeward Med/High569.41.0537
5-Band Windward/Leeward High543.11.1047
Windward/Leeward 60-40 Low931.70.6439
Windward/Leeward 60-40 Low/Med723.70.8290
Windward/Leeward 60-40 Medium638.20.9401
Windward/Leeward 60-40 Med/High587.91.0206
Windward/Leeward 60-40 High564.81.0623
5-Band AP Low699.60.8576
5-Band AP Low/Med576.91.0400
5-Band AP Medium518.91.1563
5-Band AP Med/High485.01.2371
5-Band AP High467.21.2843
5-Band SF Bay Tour - Low810.10.7406
5-Band SF Bay Tour - Low/Med685.10.8757
5-Band SF Bay Tour - Medium605.40.9910
5-Band SF Bay Tour - Med/High558.41.0745
5-Band SF Bay Tour - High535.21.1212
Chicago-Mac Upwind0.9955
Chicago-Mac All Purpose1.0300
Chicago-Mac Downwind1.0617
Bayview-Mac Cove Island0.7910
Bayview-Mac Shore0.7955
Harvest Moon Regatta467.11.2844
Club Certificate2025
StormvogelNED 8087
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassBestevaer 50Measurement04/11/2009HINPlan reviewHull constructionSolidCarbon rudderNoLight stanchionsNoTrim tabNo
LOA14.990Max. Beam4.100Draft3.287Displacement10,724Wetted area31.82IMS L10.427LSM010.125Acc. length13.325Sink (kg/mm) 23.85
VCGD-0.322VCGM-0.072RM Rated (kg·m) 219.4Limit of positive stability(°) N/AStability IndexN/ACenterboard weight400.0Default crew weight701Declared crew weightN/A
PROPELLER
Propeller TypeFeathering 3 blades
InstallationShaft exposedTwin screwNoHydro generatorNo
PRDPBW
PSDPHDPHL
PSAESL
ST1ST2ST3
ST4ST5
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerNoMainsail furlerNoArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays1CheckstaysSpreaders2Rotating mastNo
P18.350IG19.140ISP19.640MDT10.155MDL10.265MDT2MDL2TLTaperMWGO
E6.450J5.650BAS1.490FSDSFJ0.340SPL5.375WPLTPSBDMWTMCG
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodRM estimatedFlotation Date20/07/2009
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Club Certificate2025
StormvogelNED 8087
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment010.201.142.103.835.2166.34
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment010.090.731.402.643.875.0418.25NoNo 47.58
ASYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLRatioAreaMeas.DateComment0119.3618.1918.789.9910.2997%157.24
CRUISER/RACER REQUIREMENTS*
Accommodation length13.3 mTable area0.66 m²Headroom1.86 mMinimum number of berths6Personal gear stowage0.24 m³Fresh water capacity219 lMinimum number of seats in cockpit6Food stowage0.36 m³Fuel capacity116 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.