Double HandedClub Certificate2025
FramtiaNOR 15283
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 Angles43.4°43.4°41.7°40.7°40.3°40.1°40.1°40.7°42.6°
Beat VMG2.873.934.725.125.315.425.485.505.28
52°4.466.017.067.567.787.917.998.057.95
60°4.756.347.387.878.088.208.288.358.29
75°4.976.587.598.128.398.558.678.838.88
90°4.976.637.728.258.528.799.019.339.53
110°4.786.527.778.428.779.169.5110.0510.33
120°4.646.397.698.418.919.329.6310.5511.35
135°4.125.777.138.038.619.149.7111.1012.21
150°3.404.846.107.177.988.518.9810.0111.60
Run VMG2.954.195.286.216.937.447.878.6910.05
Gybe Angles142.0°142.0°145.3°149.2°152.0°154.7°158.5°156.1°144.2°
APH ToD:499.2CDL: 10.959APH ToT: 1.2019CertNo:666868
BOAT
ClassXP-44DesignerNielsJeppesenBuilderX-YachtsAge date01/2015Series date01/2011Offset fileXP-44-SD.offData file666868
HULL
Length Overall13.289 mMaximum Beam4.052 mDraft2.347 mDisplacement9,523 kgDLR5.3375IMS DivisionCruiser/RacerDynamic Allowance0.100%Age Allowance0.455%
PROPELLER
InstallationStrutTypeFolding 3 bladesDiameter0.440m
CREW
Maximum weight160 kg(declared)Minimum weight120 kg ✱ when appliedNon Manual PowerYesCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail60.8761.95Headsail Luffed49.1149.11Headsail FlyingSymmetricAsymmetric160.84160.84 (1 asymmetric(s) with SHW/SFL < 85%)
STORM SAIL AREAS (m²)
Trysail18.17Storm Jib16.51Heavy Weather Jib44.58
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.
Double HandedClub Certificate2025
FramtiaNOR 15283
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 VMG1256.2915.7763.4703.2677.9664.8657.3655.1682.0
52°806.8599.4509.9476.0462.6455.3450.8447.2452.9
60°757.4568.1488.1457.5445.6439.1434.9430.9434.1
75°723.8547.5474.0443.4428.9420.9415.2407.7405.3
90°724.5543.0466.1436.2422.6409.7399.4385.7377.8
110°752.9552.4463.4427.5410.3392.9378.4358.4348.5
120°776.6563.8468.1428.3404.0386.2373.8341.4317.2
135°874.4623.4505.2448.1418.1393.8370.8324.4294.9
150°1057.5744.1590.5501.8451.0422.9401.0359.7310.3
Run VMG1221.3859.2681.9579.5519.2484.1457.7414.3358.3
Selected Courses
Windward / Leeward1238.5887.5722.6641.3598.5574.4557.5534.7520.2
All purpose938.3682.1565.1511.8484.9467.7454.8435.3425.0
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward621.80.9649
All purpose499.21.2019
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low623.60.9621
Triple Number Coastal/Long Distance Medium496.21.2091
Triple Number Coastal/Long Distance High450.71.3313
Triple Number Windward/Leeward Low805.00.7453
Triple Number Windward/Leeward Medium617.10.9723
Triple Number Windward/Leeward High553.21.0846
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance543.71.1035
Triple Number Coastal/Long Distance Low623.60.9621
Triple Number Coastal/Long Distance Medium496.21.2091
Triple Number Coastal/Long Distance High450.71.3313
Triple Number Windward/Leeward Low805.00.7453
Triple Number Windward/Leeward Medium617.10.9723
Triple Number Windward/Leeward High553.21.0846
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1312.2884.6678.7576.9518.6485.8459.1413.1398.4
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.8338
Downwind "popa"1.0511
70% up, 30% down "Ilhabela"0.8889
30% up, 70% down "Ilhabela-inverso"0.9749
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low623.60.9621
Triple Number Coastal/Long Distance Medium496.21.2091
Triple Number Coastal/Long Distance High450.71.3313
Triple Number Windward/Leeward Low805.00.7453
Triple Number Windward/Leeward Medium617.10.9723
Triple Number Windward/Leeward High553.21.0846
Predominantly Upwind544.21.1026
Predominantly Downwind498.71.2031
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low623.60.9621
Triple Number AP Medium496.31.2090
Triple Number AP High450.71.3313
Triple Number Windward/Leeward Low840.30.7140
Triple Number Windward/Leeward Medium617.10.9723
Triple Number Windward/Leeward High553.21.0846
Single Number Predominant Upwind565.41.0613
Single Number Predominant Reaching489.61.2255
Single Number Predominant Downwind519.51.1549
Predominant Upwind - Low751.90.7980
Predominant Upwind - Low/Med586.81.0225
Predominant Upwind - Medium530.51.1310
Predominant Upwind - Med/High502.61.1939
Predominant Upwind - High490.81.2224
Predominant Downwind Low744.50.8059
Predominant Downwind Low/Med558.51.0744
Predominant Downwind Medium483.51.2409
Predominant Downwind Med/High435.91.3764
Predominant Downwind High403.41.4875
Predominant Reaching Low662.80.9053
Predominant Reaching Low/Med514.81.1655
Predominant Reaching Medium460.81.3021
Predominant Reaching Med/High427.11.4048
Predominant Reaching High405.21.4809
SA/DSPL Upwind24.30SA/DSPL Downwind48.98
Scoring OptionTODTOT
5-Band Windward/Leeward Low934.10.6423
5-Band Windward/Leeward Low/Med699.90.8573
5-Band Windward/Leeward Medium608.50.9860
5-Band Windward/Leeward Med/High560.01.0715
5-Band Windward/Leeward High536.11.1191
Windward/Leeward 60-40 Low939.80.6384
Windward/Leeward 60-40 Low/Med710.30.8447
Windward/Leeward 60-40 Medium623.80.9618
Windward/Leeward 60-40 Med/High580.01.0345
Windward/Leeward 60-40 High560.91.0696
5-Band AP Low684.90.8761
5-Band AP Low/Med551.71.0876
5-Band AP Medium490.61.2230
5-Band AP Med/High456.21.3152
5-Band AP High436.91.3734
5-Band SF Bay Tour - Low807.60.7429
5-Band SF Bay Tour - Low/Med669.40.8963
5-Band SF Bay Tour - Medium586.91.0223
5-Band SF Bay Tour - Med/High543.11.1047
5-Band SF Bay Tour - High521.21.1511
Chicago-Mac Upwind1.0331
Chicago-Mac All Purpose1.0769
Chicago-Mac Downwind1.1154
Bayview-Mac Cove Island0.8004
Bayview-Mac Shore0.8061
Harvest Moon Regatta428.71.3996
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance543.71.1035
Triple Number Coastal/Long Distance Low623.60.9621
Triple Number Coastal/Long Distance Medium496.21.2091
Triple Number Coastal/Long Distance High450.71.3313
Triple Number Windward/Leeward Low805.00.7453
Triple Number Windward/Leeward Medium617.10.9723
Triple Number Windward/Leeward High553.21.0846
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1312.2884.6678.7576.9518.6485.8459.1413.1398.4
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance543.71.1035
Triple Number Coastal/Long Distance Low623.60.9621
Triple Number Coastal/Long Distance Medium496.21.2091
Triple Number Coastal/Long Distance High450.71.3313
Triple Number Windward/Leeward Low805.00.7453
Triple Number Windward/Leeward Medium617.10.9723
Triple Number Windward/Leeward High553.21.0846
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1312.2884.6678.7576.9518.6485.8459.1413.1398.4
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance543.7
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1312.2884.6678.7576.9518.6485.8459.1413.1398.4
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low623.60.9621
Triple Number Coastal/Long Distance Medium496.21.2091
Triple Number Coastal/Long Distance High450.71.3313
Triple Number Windward/Leeward Low805.00.7453
Triple Number Windward/Leeward Medium617.10.9723
Triple Number Windward/Leeward High553.21.0846
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating543.71.1035
FinRating, kevyt tuuli915.11.0928
FinRating, kova tuuli438.91.1392
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low623.60.9621
Triple Number Coastal/Long Distance Medium496.21.2091
Triple Number Coastal/Long Distance High450.71.3313
Triple Number Windward/Leeward Low805.00.7453
Triple Number Windward/Leeward Medium617.10.9723
Triple Number Windward/Leeward High553.21.0846
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance1.1035
Triple Number Coastal/Long Distance Low0.9621
Triple Number Coastal/Long Distance Medium1.2091
Triple Number Coastal/Long Distance High1.3313
Triple Number Windward/Leeward Low0.7453
Triple Number Windward/Leeward Medium0.9723
Triple Number Windward/Leeward High1.0846
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1312.2884.6678.7576.9518.6485.8459.1413.1398.4
For information
General Purpose Handicap (GPH)556.4
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance543.71.1035
Triple Number Coastal/Long Distance Low623.60.9621
Triple Number Coastal/Long Distance Medium496.21.2091
Triple Number Coastal/Long Distance High450.71.3313
Triple Number Windward/Leeward Low805.00.7453
Triple Number Windward/Leeward Medium617.10.9723
Triple Number Windward/Leeward High553.21.0846
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1312.2884.6678.7576.9518.6485.8459.1413.1398.4
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low623.60.9621
Triple Number Coastal/Long Distance Medium496.21.2091
Triple Number Coastal/Long Distance High450.71.3313
Triple Number Windward/Leeward Low805.00.7453
Triple Number Windward/Leeward Medium617.10.9723
Triple Number Windward/Leeward High553.21.0846
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance543.71.1035
Triple Number Coastal/Long Distance Low623.60.9621
Triple Number Coastal/Long Distance Medium496.21.2091
Triple Number Coastal/Long Distance High450.71.3313
Triple Number Windward/Leeward Low805.00.7453
Triple Number Windward/Leeward Medium617.10.9723
Triple Number Windward/Leeward High553.21.0846
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1312.2884.6678.7576.9518.6485.8459.1413.1398.4
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance543.71.1035
Triple Number Coastal/Long Distance Low623.60.9621
Triple Number Coastal/Long Distance Medium496.21.2091
Triple Number Coastal/Long Distance High450.71.3313
Triple Number Windward/Leeward Low805.00.7453
Triple Number Windward/Leeward Medium617.10.9723
Triple Number Windward/Leeward High553.21.0846
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1312.2884.6678.7576.9518.6485.8459.1413.1398.4
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low623.6
Triple Number Coastal/Long Distance Medium496.2
Triple Number Coastal/Long Distance High450.7
Triple Number Windward/Leeward Low805.0
Triple Number Windward/Leeward Medium617.1
Triple Number Windward/Leeward High553.2
Predominantly Upwind544.2
Predominantly Downwind498.7
Predominantly Reaching478.4
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance543.71.1035
Triple Number Coastal/Long Distance Low623.60.9621
Triple Number Coastal/Long Distance Medium496.21.2091
Triple Number Coastal/Long Distance High450.71.3313
Triple Number Windward/Leeward Low805.00.7453
Triple Number Windward/Leeward Medium617.10.9723
Triple Number Windward/Leeward High553.21.0846
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1312.2884.6678.7576.9518.6485.8459.1413.1398.4
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.9621
Triple Number Coastal/Long Distance Medium1.2091
Triple Number Coastal/Long Distance High1.3313
Triple Number Windward/Leeward Low0.7453
Triple Number Windward/Leeward Medium0.9723
Triple Number Windward/Leeward High1.0846
Coastal/Long Distance1.1035
Predominantly Upwind1.1026
Predominantly Downwind1.2031
For information
General Purpose Handicap (GPH)556.4
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)1.2019
Distanseseilas Trippeltall svak vind0.9621
Distanseseilas Trippeltall mellomvind1.2091
Distanseseilas Trippeltall sterk vind1.3313
Pølsebane Trippeltall svak vind0.7453
Pølsebane Trippeltall mellomvind0.9723
Pølsebane Trippeltall sterk vind1.0846
Motvind Singeltall1.1026
Medvind Singeltall1.2031
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low623.60.9621
Triple Number Coastal/Long Distance Medium496.21.2091
Triple Number Coastal/Long Distance High450.71.3313
Triple Number Windward/Leeward Low805.00.7453
Triple Number Windward/Leeward Medium617.10.9723
Triple Number Windward/Leeward High553.21.0846
Coastal/Long Distance543.71.1035
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind544.21.1026
Predominantly Downwind498.71.2031
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore524.51.1439
Cape Doctor Coastal428.11.4016
Triple Number Coastal/Long Distance Low623.60.9621
Triple Number Coastal/Long Distance Medium496.21.2091
Triple Number Coastal/Long Distance High450.71.3313
Triple Number Windward/Leeward Low805.00.7453
Triple Number Windward/Leeward Medium617.10.9723
Triple Number Windward/Leeward High553.21.0846
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.9621
Triple Number Coastal/Long Distance Medium1.2091
Triple Number Coastal/Long Distance High1.3313
Triple Number Windward/Leeward Low0.7453
Triple Number Windward/Leeward Medium0.9723
Triple Number Windward/Leeward High1.0846
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.9621
Triple Number Coastal/Long Distance Medium1.2091
Triple Number Coastal/Long Distance High1.3313
Triple Number Windward/Leeward Low0.7453
Triple Number Windward/Leeward Medium0.9723
Triple Number Windward/Leeward High1.0846
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance543.71.1035
Triple Number Coastal/Long Distance Low623.60.9621
Triple Number Coastal/Long Distance Medium496.21.2091
Triple Number Coastal/Long Distance High450.71.3313
Triple Number Windward/Leeward Low805.00.7453
Triple Number Windward/Leeward Medium617.10.9723
Triple Number Windward/Leeward High553.21.0846
Predominantly Upwind544.21.1026
Predominantly Downwind498.71.2031
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1312.2884.6678.7576.9518.6485.8459.1413.1398.4
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance543.71.1035
Triple Number Coastal/Long Distance Low623.60.9621
Triple Number Coastal/Long Distance Medium496.21.2091
Triple Number Coastal/Long Distance High450.71.3313
Triple Number Windward/Leeward Low805.00.7453
Triple Number Windward/Leeward Medium617.10.9723
Triple Number Windward/Leeward High553.21.0846
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1312.2884.6678.7576.9518.6485.8459.1413.1398.4
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low623.60.9621
Triple Number AP Medium496.31.2090
Triple Number AP High450.71.3313
Triple Number Windward/Leeward Low840.30.7140
Triple Number Windward/Leeward Medium617.10.9723
Triple Number Windward/Leeward High553.21.0846
Single Number Predominant Upwind565.41.0613
Single Number Predominant Reaching489.61.2255
Single Number Predominant Downwind519.51.1549
Predominant Upwind - Low751.90.7980
Predominant Upwind - Low/Med586.81.0225
Predominant Upwind - Medium530.51.1310
Predominant Upwind - Med/High502.61.1939
Predominant Upwind - High490.81.2224
Predominant Downwind Low744.50.8059
Predominant Downwind Low/Med558.51.0744
Predominant Downwind Medium483.51.2409
Predominant Downwind Med/High435.91.3764
Predominant Downwind High403.41.4875
Predominant Reaching Low662.80.9053
Predominant Reaching Low/Med514.81.1655
Predominant Reaching Medium460.81.3021
Predominant Reaching Med/High427.11.4048
Predominant Reaching High405.21.4809
SA/DSPL Upwind24.30SA/DSPL Downwind48.98
Scoring OptionTODTOT
5-Band Windward/Leeward Low934.10.6423
5-Band Windward/Leeward Low/Med699.90.8573
5-Band Windward/Leeward Medium608.50.9860
5-Band Windward/Leeward Med/High560.01.0715
5-Band Windward/Leeward High536.11.1191
Windward/Leeward 60-40 Low939.80.6384
Windward/Leeward 60-40 Low/Med710.30.8447
Windward/Leeward 60-40 Medium623.80.9618
Windward/Leeward 60-40 Med/High580.01.0345
Windward/Leeward 60-40 High560.91.0696
5-Band AP Low684.90.8761
5-Band AP Low/Med551.71.0876
5-Band AP Medium490.61.2230
5-Band AP Med/High456.21.3152
5-Band AP High436.91.3734
5-Band SF Bay Tour - Low807.60.7429
5-Band SF Bay Tour - Low/Med669.40.8963
5-Band SF Bay Tour - Medium586.91.0223
5-Band SF Bay Tour - Med/High543.11.1047
5-Band SF Bay Tour - High521.21.1511
Chicago-Mac Upwind1.0331
Chicago-Mac All Purpose1.0769
Chicago-Mac Downwind1.1154
Bayview-Mac Cove Island0.8004
Bayview-Mac Shore0.8061
Harvest Moon Regatta428.71.3996
Double HandedClub Certificate2025
FramtiaNOR 15283
Norges Seilforbund
Sognsveien 73
0854 OSLO
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassXP-44MeasurementHINPlan reviewHull constructionCoredCarbon rudderNoLight stanchionsNoTrim tabNo
LOA13.289Max. Beam4.052Draft2.347Displacement9,523Wetted area36.80IMS L12.211LSM012.127Acc. length13.169Sink (kg/mm) 27.32
VCGD-0.070VCGM-0.054RM Rated (kg·m) 248.5Limit of positive stability(°) N/AStability IndexN/ADefault crew weight170Declared crew weight160
PROPELLER
Propeller TypeFolding 3 blades
InstallationStrutTwin screwNoHydro generatorNo
PRD0.440PBWPIPA0.0039
EDL2.750ST10.050ST20.180
ST30.180ST40.110ST50.270
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerNoMainsail furlerArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders2Rotating mastNo
P17.420IG18.170ISP19.260MDT10.130MDL10.250MDT20.130MDL20.180TL1.400MW0.000GO0.000
E5.960J4.960BAS1.750FSDFoilSFJ0.000SPL0.000WPLTPS6.100BD0.000MWT356.00MCG5.960
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodVCG entered directlyVCG entered-0.070Flotation Date01/01/2015
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Double HandedClub Certificate2025
FramtiaNOR 15283
Norges Seilforbund
Sognsveien 73
0854 OSLO
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment388-2024042415290.251.232.203.774.9060.8724/04/2024
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment388-2022050409350.070.751.442.774.045.2318.10YesNo 49.1104/05/2022
ASYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLRatioAreaMeas.DateComment437-20150522160421.0618.0119.549.8510.0099%160.8422/05/2015437-20150522161118.5017.0117.766.658.8076%104.7522/05/2015
CRUISER/RACER REQUIREMENTS*
Accommodation length13.2 mTable area0.66 m²Headroom1.86 mMinimum number of berths6Personal gear stowage0.24 m³Fresh water capacity216 lMinimum number of seats in cockpit6Food stowage0.36 m³Fuel capacity114 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.