Club Certificate2025
X-LifeNED 8792
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 Angles43.8°43.8°41.6°40.1°38.9°38.2°37.9°38.2°39.1°
Beat VMG2.593.594.384.955.285.445.535.615.58
52°4.085.516.537.187.517.687.767.867.88
60°4.365.826.817.397.707.887.988.108.14
75°4.576.057.007.547.878.118.298.508.62
90°4.435.936.967.607.928.178.438.849.11
110°4.285.887.087.738.158.508.799.179.39
120°4.135.706.907.638.088.488.879.5910.08
135°3.625.086.307.217.798.218.639.5310.75
150°2.974.285.476.497.287.808.209.0210.01
Run VMG2.573.714.745.636.407.057.558.329.07
Gybe Angles144.1°144.1°148.7°152.5°157.4°164.8°171.4°177.2°175.9°
APH ToD:531.1CDL: 10.334APH ToT: 1.1297CertNo:24600
BOAT
ClassX-40DesignerN. JeppesonBuilderX-YachtsAge date01/2007Series date04/2004Offset fileX40STDK.OFFData fileNED8792
HULL
Length Overall12.225 mMaximum Beam3.764 mDraft2.106 mDisplacement8,041 kgDLR6.2592IMS DivisionCruiser/RacerDynamic Allowance0.210%Age Allowance0.487%
PROPELLER
InstallationStrutTypeFolding 2 bladesDiameter0.430m
CREW
Maximum weight775 kg(default)Minimum weight645 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail49.8650.62Headsail Luffed37.0637.06Headsail FlyingSymmetric105.81105.81Asymmetric
STORM SAIL AREAS (m²)
Trysail15.39Storm Jib13.19Heavy Weather Jib35.61
SAIL LIMITS
Headsails6Spinnakers5
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
X-LifeNED 8792
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 VMG1390.11003.9822.0727.3681.4662.0651.4642.2645.7
52°882.9653.9551.3501.6479.3468.9463.7457.9456.6
60°825.5618.4528.7487.4467.4456.7451.1444.5442.3
75°788.3595.4514.0477.3457.4444.0434.4423.6417.7
90°812.4607.3517.2474.0454.5440.4427.0407.1395.1
110°840.5611.7508.8465.5442.0423.6409.5392.5383.3
120°872.0631.9521.9471.9445.3424.3405.8375.5357.3
135°993.8708.0571.2499.0462.3438.4417.1377.6334.8
150°1213.0841.0658.2554.9494.5461.4438.8399.3359.6
Run VMG1400.5971.1760.0639.3562.3510.9476.6432.6396.8
Selected Courses
Windward / Leeward1394.4987.5791.0683.3621.9586.5564.0537.4521.3
All purpose1049.6757.3620.0549.4511.5489.4474.0453.0438.4
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward652.30.9199
All purpose531.11.1297
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low688.60.8713
Triple Number Coastal/Long Distance Medium527.71.1371
Triple Number Coastal/Long Distance High470.01.2766
Triple Number Windward/Leeward Low889.30.6747
Triple Number Windward/Leeward Medium647.60.9265
Triple Number Windward/Leeward High559.61.0721
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance578.51.0372
Triple Number Coastal/Long Distance Low688.60.8713
Triple Number Coastal/Long Distance Medium527.71.1371
Triple Number Coastal/Long Distance High470.01.2766
Triple Number Windward/Leeward Low889.30.6747
Triple Number Windward/Leeward Medium647.60.9265
Triple Number Windward/Leeward High559.61.0721
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1482.1985.8744.1617.3545.3507.8479.2433.8419.1
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.8092
Downwind "popa"0.9649
70% up, 30% down "Ilhabela"0.8504
30% up, 70% down "Ilhabela-inverso"0.9122
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low688.60.8713
Triple Number Coastal/Long Distance Medium527.71.1371
Triple Number Coastal/Long Distance High470.01.2766
Triple Number Windward/Leeward Low889.30.6747
Triple Number Windward/Leeward Medium647.60.9265
Triple Number Windward/Leeward High559.61.0721
Predominantly Upwind573.61.0460
Predominantly Downwind541.91.1072
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low688.60.8713
Triple Number AP Medium527.71.1370
Triple Number AP High470.01.2766
Triple Number Windward/Leeward Low929.10.6458
Triple Number Windward/Leeward Medium647.60.9265
Triple Number Windward/Leeward High559.61.0721
Single Number Predominant Upwind596.81.0053
Single Number Predominant Reaching530.21.1317
Single Number Predominant Downwind566.01.0601
Predominant Upwind - Low830.10.7228
Predominant Upwind - Low/Med631.20.9506
Predominant Upwind - Medium554.11.0829
Predominant Upwind - Med/High516.21.1624
Predominant Upwind - High499.61.2009
Predominant Downwind Low836.80.7170
Predominant Downwind Low/Med615.80.9743
Predominant Downwind Medium521.81.1500
Predominant Downwind Med/High464.11.2929
Predominant Downwind High430.41.3942
Predominant Reaching Low740.20.8106
Predominant Reaching Low/Med564.21.0634
Predominant Reaching Medium494.81.2127
Predominant Reaching Med/High454.31.3207
Predominant Reaching High429.61.3966
SA/DSPL Upwind21.51SA/DSPL Downwind38.52
Scoring OptionTODTOT
5-Band Windward/Leeward Low1040.30.5768
5-Band Windward/Leeward Low/Med757.00.7926
5-Band Windward/Leeward Medium635.40.9442
5-Band Windward/Leeward Med/High568.21.0561
5-Band Windward/Leeward High539.21.1128
Windward/Leeward 60-40 Low1043.20.5751
Windward/Leeward 60-40 Low/Med764.50.7848
Windward/Leeward 60-40 Medium647.40.9268
Windward/Leeward 60-40 Med/High585.41.0250
Windward/Leeward 60-40 High560.21.0710
5-Band AP Low761.40.7880
5-Band AP Low/Med599.31.0012
5-Band AP Medium520.01.1539
5-Band AP Med/High476.21.2599
5-Band AP High454.11.3212
5-Band SF Bay Tour - Low895.00.6704
5-Band SF Bay Tour - Low/Med723.60.8292
5-Band SF Bay Tour - Medium613.90.9773
5-Band SF Bay Tour - Med/High555.21.0807
5-Band SF Bay Tour - High528.71.1348
Chicago-Mac Upwind0.9736
Chicago-Mac All Purpose1.0003
Chicago-Mac Downwind1.0205
Bayview-Mac Cove Island0.7273
Bayview-Mac Shore0.7329
Harvest Moon Regatta462.31.2977
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance578.51.0372
Triple Number Coastal/Long Distance Low688.60.8713
Triple Number Coastal/Long Distance Medium527.71.1371
Triple Number Coastal/Long Distance High470.01.2766
Triple Number Windward/Leeward Low889.30.6747
Triple Number Windward/Leeward Medium647.60.9265
Triple Number Windward/Leeward High559.61.0721
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1482.1985.8744.1617.3545.3507.8479.2433.8419.1
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance578.51.0372
Triple Number Coastal/Long Distance Low688.60.8713
Triple Number Coastal/Long Distance Medium527.71.1371
Triple Number Coastal/Long Distance High470.01.2766
Triple Number Windward/Leeward Low889.30.6747
Triple Number Windward/Leeward Medium647.60.9265
Triple Number Windward/Leeward High559.61.0721
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1482.1985.8744.1617.3545.3507.8479.2433.8419.1
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance578.5
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1482.1985.8744.1617.3545.3507.8479.2433.8419.1
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low688.60.8713
Triple Number Coastal/Long Distance Medium527.71.1371
Triple Number Coastal/Long Distance High470.01.2766
Triple Number Windward/Leeward Low889.30.6747
Triple Number Windward/Leeward Medium647.60.9265
Triple Number Windward/Leeward High559.61.0721
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating (Coastal/Long Distance)578.51.0372
Triple Number Coastal/Long Distance Low688.60.8713
Triple Number Coastal/Long Distance Medium527.71.1371
Triple Number Coastal/Long Distance High470.01.2766
Triple Number Windward/Leeward Low889.30.6747
Triple Number Windward/Leeward Medium647.60.9265
Triple Number Windward/Leeward High559.61.0721
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1482.1985.8744.1617.3545.3507.8479.2433.8419.1
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low688.60.8713
Triple Number Coastal/Long Distance Medium527.71.1371
Triple Number Coastal/Long Distance High470.01.2766
Triple Number Windward/Leeward Low889.30.6747
Triple Number Windward/Leeward Medium647.60.9265
Triple Number Windward/Leeward High559.61.0721
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance1.0372
Triple Number Coastal/Long Distance Low0.8713
Triple Number Coastal/Long Distance Medium1.1371
Triple Number Coastal/Long Distance High1.2766
Triple Number Windward/Leeward Low0.6747
Triple Number Windward/Leeward Medium0.9265
Triple Number Windward/Leeward High1.0721
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1482.1985.8744.1617.3545.3507.8479.2433.8419.1
For information
General Purpose Handicap (GPH)597.4
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance578.51.0372
Triple Number Coastal/Long Distance Low688.60.8713
Triple Number Coastal/Long Distance Medium527.71.1371
Triple Number Coastal/Long Distance High470.01.2766
Triple Number Windward/Leeward Low889.30.6747
Triple Number Windward/Leeward Medium647.60.9265
Triple Number Windward/Leeward High559.61.0721
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1482.1985.8744.1617.3545.3507.8479.2433.8419.1
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low688.60.8713
Triple Number Coastal/Long Distance Medium527.71.1371
Triple Number Coastal/Long Distance High470.01.2766
Triple Number Windward/Leeward Low889.30.6747
Triple Number Windward/Leeward Medium647.60.9265
Triple Number Windward/Leeward High559.61.0721
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance578.51.0372
Triple Number Coastal/Long Distance Low688.60.8713
Triple Number Coastal/Long Distance Medium527.71.1371
Triple Number Coastal/Long Distance High470.01.2766
Triple Number Windward/Leeward Low889.30.6747
Triple Number Windward/Leeward Medium647.60.9265
Triple Number Windward/Leeward High559.61.0721
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1482.1985.8744.1617.3545.3507.8479.2433.8419.1
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance578.51.0372
Triple Number Coastal/Long Distance Low688.60.8713
Triple Number Coastal/Long Distance Medium527.71.1371
Triple Number Coastal/Long Distance High470.01.2766
Triple Number Windward/Leeward Low889.30.6747
Triple Number Windward/Leeward Medium647.60.9265
Triple Number Windward/Leeward High559.61.0721
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1482.1985.8744.1617.3545.3507.8479.2433.8419.1
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low688.6
Triple Number Coastal/Long Distance Medium527.7
Triple Number Coastal/Long Distance High470.0
Triple Number Windward/Leeward Low889.3
Triple Number Windward/Leeward Medium647.6
Triple Number Windward/Leeward High559.6
Predominantly Upwind573.6
Predominantly Downwind541.9
Predominantly Reaching519.4
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance578.51.0372
Triple Number Coastal/Long Distance Low688.60.8713
Triple Number Coastal/Long Distance Medium527.71.1371
Triple Number Coastal/Long Distance High470.01.2766
Triple Number Windward/Leeward Low889.30.6747
Triple Number Windward/Leeward Medium647.60.9265
Triple Number Windward/Leeward High559.61.0721
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1482.1985.8744.1617.3545.3507.8479.2433.8419.1
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8713
Triple Number Coastal/Long Distance Medium1.1371
Triple Number Coastal/Long Distance High1.2766
Triple Number Windward/Leeward Low0.6747
Triple Number Windward/Leeward Medium0.9265
Triple Number Windward/Leeward High1.0721
Coastal/Long Distance1.0372
Predominantly Upwind1.0460
Predominantly Downwind1.1072
For information
General Purpose Handicap (GPH)597.4
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)1.1297
Distanseseilas Trippeltall svak vind0.8713
Distanseseilas Trippeltall mellomvind1.1371
Distanseseilas Trippeltall sterk vind1.2766
Pølsebane Trippeltall svak vind0.6747
Pølsebane Trippeltall mellomvind0.9265
Pølsebane Trippeltall sterk vind1.0721
Motvind Singeltall1.0460
Medvind Singeltall1.1072
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low688.60.8713
Triple Number Coastal/Long Distance Medium527.71.1371
Triple Number Coastal/Long Distance High470.01.2766
Triple Number Windward/Leeward Low889.30.6747
Triple Number Windward/Leeward Medium647.60.9265
Triple Number Windward/Leeward High559.61.0721
Coastal/Long Distance578.51.0372
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind573.61.0460
Predominantly Downwind541.91.1072
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore526.11.1405
Cape Doctor Coastal442.81.3549
Triple Number Coastal/Long Distance Low688.60.8713
Triple Number Coastal/Long Distance Medium527.71.1371
Triple Number Coastal/Long Distance High470.01.2766
Triple Number Windward/Leeward Low889.30.6747
Triple Number Windward/Leeward Medium647.60.9265
Triple Number Windward/Leeward High559.61.0721
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8713
Triple Number Coastal/Long Distance Medium1.1371
Triple Number Coastal/Long Distance High1.2766
Triple Number Windward/Leeward Low0.6747
Triple Number Windward/Leeward Medium0.9265
Triple Number Windward/Leeward High1.0721
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8713
Triple Number Coastal/Long Distance Medium1.1371
Triple Number Coastal/Long Distance High1.2766
Triple Number Windward/Leeward Low0.6747
Triple Number Windward/Leeward Medium0.9265
Triple Number Windward/Leeward High1.0721
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance578.51.0372
Triple Number Coastal/Long Distance Low688.60.8713
Triple Number Coastal/Long Distance Medium527.71.1371
Triple Number Coastal/Long Distance High470.01.2766
Triple Number Windward/Leeward Low889.30.6747
Triple Number Windward/Leeward Medium647.60.9265
Triple Number Windward/Leeward High559.61.0721
Predominantly Upwind573.61.0460
Predominantly Downwind541.91.1072
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1482.1985.8744.1617.3545.3507.8479.2433.8419.1
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance578.51.0372
Triple Number Coastal/Long Distance Low688.60.8713
Triple Number Coastal/Long Distance Medium527.71.1371
Triple Number Coastal/Long Distance High470.01.2766
Triple Number Windward/Leeward Low889.30.6747
Triple Number Windward/Leeward Medium647.60.9265
Triple Number Windward/Leeward High559.61.0721
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1482.1985.8744.1617.3545.3507.8479.2433.8419.1
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low688.60.8713
Triple Number AP Medium527.71.1370
Triple Number AP High470.01.2766
Triple Number Windward/Leeward Low929.10.6458
Triple Number Windward/Leeward Medium647.60.9265
Triple Number Windward/Leeward High559.61.0721
Single Number Predominant Upwind596.81.0053
Single Number Predominant Reaching530.21.1317
Single Number Predominant Downwind566.01.0601
Predominant Upwind - Low830.10.7228
Predominant Upwind - Low/Med631.20.9506
Predominant Upwind - Medium554.11.0829
Predominant Upwind - Med/High516.21.1624
Predominant Upwind - High499.61.2009
Predominant Downwind Low836.80.7170
Predominant Downwind Low/Med615.80.9743
Predominant Downwind Medium521.81.1500
Predominant Downwind Med/High464.11.2929
Predominant Downwind High430.41.3942
Predominant Reaching Low740.20.8106
Predominant Reaching Low/Med564.21.0634
Predominant Reaching Medium494.81.2127
Predominant Reaching Med/High454.31.3207
Predominant Reaching High429.61.3966
SA/DSPL Upwind21.51SA/DSPL Downwind38.52
Scoring OptionTODTOT
5-Band Windward/Leeward Low1040.30.5768
5-Band Windward/Leeward Low/Med757.00.7926
5-Band Windward/Leeward Medium635.40.9442
5-Band Windward/Leeward Med/High568.21.0561
5-Band Windward/Leeward High539.21.1128
Windward/Leeward 60-40 Low1043.20.5751
Windward/Leeward 60-40 Low/Med764.50.7848
Windward/Leeward 60-40 Medium647.40.9268
Windward/Leeward 60-40 Med/High585.41.0250
Windward/Leeward 60-40 High560.21.0710
5-Band AP Low761.40.7880
5-Band AP Low/Med599.31.0012
5-Band AP Medium520.01.1539
5-Band AP Med/High476.21.2599
5-Band AP High454.11.3212
5-Band SF Bay Tour - Low895.00.6704
5-Band SF Bay Tour - Low/Med723.60.8292
5-Band SF Bay Tour - Medium613.90.9773
5-Band SF Bay Tour - Med/High555.21.0807
5-Band SF Bay Tour - High528.71.1348
Chicago-Mac Upwind0.9736
Chicago-Mac All Purpose1.0003
Chicago-Mac Downwind1.0205
Bayview-Mac Cove Island0.7273
Bayview-Mac Shore0.7329
Harvest Moon Regatta462.31.2977
Club Certificate2025
X-LifeNED 8792
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassX-40Measurement20/10/2007HINPlan reviewHull constructionCoredCarbon rudderNoLight stanchionsNoTrim tabNo
LOA12.225Max. Beam3.764Draft2.106Displacement8,041Wetted area30.97IMS L11.064LSM010.870Acc. length12.225Sink (kg/mm) 23.24
VCGD-0.075VCGM-0.094RM Rated (kg·m) 197.7Limit of positive stability(°) N/AStability IndexN/ADefault crew weight775Declared crew weightN/A
PROPELLER
Propeller TypeFolding 2 blades
InstallationStrutTwin screwNoHydro generatorNo
PRD0.430PBWPIPA0.0007
EDLST1ST2
ST3ST4ST5
RIG
Forestay tensionFixedInner stayNone FittedMast materialAluminumSingle headsail furlerNoMainsail furlerNoArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders3Rotating mastNo
P15.698IG16.239ISP16.379MDT10.127MDL10.226MDT2MDL2TLTaperMWGO
E5.600J4.390BAS1.789FSDFoilSFJ0.260SPL4.488WPLTPSBDMWTMCG
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodRM estimatedFlotation Date20/10/2007
SFFP0.280FFM1.403FF1.421LCFcl6.803SG1.0000
SAFP11.610FAM1.113FA1.125LCFsh7.045HBI1.222
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Club Certificate2025
X-LifeNED 8792
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment030.131.021.913.384.5549.86
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment030.080.641.202.333.464.6115.90NoNo 37.06
SYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLAreaMeas.DateComment0116.1716.1716.177.897.70105.81
CRUISER/RACER REQUIREMENTS*
Accommodation length12.2 mTable area0.55 m²Headroom1.82 mMinimum number of berths5Personal gear stowage0.20 m³Fresh water capacity155 lMinimum number of seats in cockpit5Food stowage0.30 m³Fuel capacity94 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.