Club Certificate2025
Mistral GagnantBEL 161
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 Angles43.7°43.7°41.5°39.7°37.9°37.1°36.7°36.7°37.3°
Beat VMG2.363.304.094.675.055.225.325.415.40
52°3.705.066.096.747.097.267.357.467.49
60°3.945.346.356.937.267.457.567.697.74
75°4.125.616.657.117.427.687.888.108.22
90°4.445.946.947.427.697.888.048.498.75
110°4.325.897.017.598.038.388.689.249.74
120°4.195.756.907.538.058.538.999.8311.03
135°3.705.196.407.187.728.268.8210.3413.00
150°3.064.375.536.507.167.628.069.0311.62
Run VMG2.653.794.795.636.236.667.047.8210.06
Gybe Angles143.1°143.1°147.0°149.9°152.5°156.3°158.8°148.3°141.7°
APH ToD:549.3CDL: 9.253APH ToT: 1.0922CertNo:
BOAT
ClassJ 105DesignerJOHNSTONEBuilderJ-COMPOSITEAge date01/2000Series date01/1992Offset filej105.offData fileBEL161
HULL
Length Overall10.570 mMaximum Beam3.344 mDraft2.016 mDisplacement4,091 kgDLR4.7466IMS DivisionCruiser/RacerDynamic Allowance0.180%Age Allowance0.487%
PROPELLER
InstallationShaft exposedTypeFolding 3 bladesDiameter0.380m
CREW
Maximum weight641 kg(default)Minimum weight511 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail33.6934.39Headsail Luffed24.3924.39Headsail FlyingSymmetricAsymmetric94.9094.90 (1 asymmetric(s) with SHW/SFL < 85%)
STORM SAIL AREAS (m²)
Trysail9.86Storm Jib7.74Heavy Weather Jib20.90
SAIL LIMITS
Headsails5
✱ One set on the forestay
Spinnakers4
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
Mistral GagnantBEL 161
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 VMG1527.81089.3880.4770.8713.2689.7677.2666.0666.6
52°974.1711.6591.5534.1507.8495.8489.6482.7480.4
60°913.7674.0567.2519.2495.9483.1476.1468.1464.8
75°874.0641.8541.1506.5485.3468.7456.8444.3437.9
90°810.9606.0518.8485.1468.0456.8447.9424.2411.6
110°833.9611.7513.7474.3448.2429.6414.9389.4369.4
120°860.1626.3521.7478.0447.3422.0400.5366.1326.5
135°974.1694.1562.9501.2466.5436.0408.2348.1276.9
150°1175.5823.5651.0554.1502.5472.5446.4398.6309.8
Run VMG1357.7950.9751.7639.8577.8540.5511.1460.3357.7
Selected Courses
Windward / Leeward1442.61020.1816.1705.3645.5615.1594.1563.2512.1
All purpose1087.2781.8638.8568.0529.8507.5491.2464.6432.3
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward677.90.8851
All purpose549.31.0922
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low710.30.8447
Triple Number Coastal/Long Distance Medium546.01.0989
Triple Number Coastal/Long Distance High485.31.2363
Triple Number Windward/Leeward Low918.10.6535
Triple Number Windward/Leeward Medium672.00.8928
Triple Number Windward/Leeward High587.71.0209
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance597.61.0040
Triple Number Coastal/Long Distance Low710.30.8447
Triple Number Coastal/Long Distance Medium546.01.0989
Triple Number Coastal/Long Distance High485.31.2363
Triple Number Windward/Leeward Low918.10.6535
Triple Number Windward/Leeward Medium672.00.8928
Triple Number Windward/Leeward High587.71.0209
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1522.11013.2765.8637.2564.3526.4496.0445.9413.5
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.7655
Downwind "popa"0.9476
70% up, 30% down "Ilhabela"0.8123
30% up, 70% down "Ilhabela-inverso"0.8845
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low710.30.8447
Triple Number Coastal/Long Distance Medium546.01.0989
Triple Number Coastal/Long Distance High485.31.2363
Triple Number Windward/Leeward Low918.10.6535
Triple Number Windward/Leeward Medium672.00.8928
Triple Number Windward/Leeward High587.71.0209
Predominantly Upwind598.71.0021
Predominantly Downwind553.31.0844
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low710.30.8447
Triple Number AP Medium546.11.0987
Triple Number AP High485.31.2363
Triple Number Windward/Leeward Low959.50.6253
Triple Number Windward/Leeward Medium672.00.8928
Triple Number Windward/Leeward High587.71.0209
Single Number Predominant Upwind624.30.9610
Single Number Predominant Reaching543.11.1048
Single Number Predominant Downwind575.41.0428
Predominant Upwind - Low877.00.6842
Predominant Upwind - Low/Med661.50.9070
Predominant Upwind - Medium578.61.0370
Predominant Upwind - Med/High537.61.1160
Predominant Upwind - High516.31.1622
Predominant Downwind Low838.80.7153
Predominant Downwind Low/Med622.90.9632
Predominant Downwind Medium534.81.1220
Predominant Downwind Med/High478.31.2545
Predominant Downwind High432.71.3868
Predominant Reaching Low752.70.7972
Predominant Reaching Low/Med576.51.0408
Predominant Reaching Medium509.31.1781
Predominant Reaching Med/High467.91.2824
Predominant Reaching High435.41.3779
SA/DSPL Upwind22.60SA/DSPL Downwind50.03
Scoring OptionTODTOT
5-Band Windward/Leeward Low1074.80.5583
5-Band Windward/Leeward Low/Med781.90.7674
5-Band Windward/Leeward Medium660.30.9087
5-Band Windward/Leeward Med/High596.71.0055
5-Band Windward/Leeward High559.71.0720
Windward/Leeward 60-40 Low1089.10.5509
Windward/Leeward 60-40 Low/Med795.10.7546
Windward/Leeward 60-40 Medium674.20.8899
Windward/Leeward 60-40 Med/High613.50.9780
Windward/Leeward 60-40 High581.41.0321
5-Band AP Low781.50.7677
5-Band AP Low/Med618.80.9696
5-Band AP Medium538.31.1147
5-Band AP Med/High492.71.2178
5-Band AP High463.61.2941
5-Band SF Bay Tour - Low927.70.6468
5-Band SF Bay Tour - Low/Med748.90.8011
5-Band SF Bay Tour - Medium636.50.9427
5-Band SF Bay Tour - Med/High577.11.0398
5-Band SF Bay Tour - High542.21.1067
Chicago-Mac Upwind0.9301
Chicago-Mac All Purpose0.9700
Chicago-Mac Downwind1.0048
Bayview-Mac Cove Island0.7051
Bayview-Mac Shore0.7097
Harvest Moon Regatta475.31.2622
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance597.61.0040
Triple Number Coastal/Long Distance Low710.30.8447
Triple Number Coastal/Long Distance Medium546.01.0989
Triple Number Coastal/Long Distance High485.31.2363
Triple Number Windward/Leeward Low918.10.6535
Triple Number Windward/Leeward Medium672.00.8928
Triple Number Windward/Leeward High587.71.0209
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1522.11013.2765.8637.2564.3526.4496.0445.9413.5
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance597.61.0040
Triple Number Coastal/Long Distance Low710.30.8447
Triple Number Coastal/Long Distance Medium546.01.0989
Triple Number Coastal/Long Distance High485.31.2363
Triple Number Windward/Leeward Low918.10.6535
Triple Number Windward/Leeward Medium672.00.8928
Triple Number Windward/Leeward High587.71.0209
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1522.11013.2765.8637.2564.3526.4496.0445.9413.5
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance597.6
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1522.11013.2765.8637.2564.3526.4496.0445.9413.5
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low710.30.8447
Triple Number Coastal/Long Distance Medium546.01.0989
Triple Number Coastal/Long Distance High485.31.2363
Triple Number Windward/Leeward Low918.10.6535
Triple Number Windward/Leeward Medium672.00.8928
Triple Number Windward/Leeward High587.71.0209
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating597.61.0040
FinRating, kevyt tuuli1052.00.9506
FinRating, kova tuuli463.41.0790
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low710.30.8447
Triple Number Coastal/Long Distance Medium546.01.0989
Triple Number Coastal/Long Distance High485.31.2363
Triple Number Windward/Leeward Low918.10.6535
Triple Number Windward/Leeward Medium672.00.8928
Triple Number Windward/Leeward High587.71.0209
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance1.0040
Triple Number Coastal/Long Distance Low0.8447
Triple Number Coastal/Long Distance Medium1.0989
Triple Number Coastal/Long Distance High1.2363
Triple Number Windward/Leeward Low0.6535
Triple Number Windward/Leeward Medium0.8928
Triple Number Windward/Leeward High1.0209
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1522.11013.2765.8637.2564.3526.4496.0445.9413.5
For information
General Purpose Handicap (GPH)617.7
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance597.61.0040
Triple Number Coastal/Long Distance Low710.30.8447
Triple Number Coastal/Long Distance Medium546.01.0989
Triple Number Coastal/Long Distance High485.31.2363
Triple Number Windward/Leeward Low918.10.6535
Triple Number Windward/Leeward Medium672.00.8928
Triple Number Windward/Leeward High587.71.0209
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1522.11013.2765.8637.2564.3526.4496.0445.9413.5
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low710.30.8447
Triple Number Coastal/Long Distance Medium546.01.0989
Triple Number Coastal/Long Distance High485.31.2363
Triple Number Windward/Leeward Low918.10.6535
Triple Number Windward/Leeward Medium672.00.8928
Triple Number Windward/Leeward High587.71.0209
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance597.61.0040
Triple Number Coastal/Long Distance Low710.30.8447
Triple Number Coastal/Long Distance Medium546.01.0989
Triple Number Coastal/Long Distance High485.31.2363
Triple Number Windward/Leeward Low918.10.6535
Triple Number Windward/Leeward Medium672.00.8928
Triple Number Windward/Leeward High587.71.0209
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1522.11013.2765.8637.2564.3526.4496.0445.9413.5
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance597.61.0040
Triple Number Coastal/Long Distance Low710.30.8447
Triple Number Coastal/Long Distance Medium546.01.0989
Triple Number Coastal/Long Distance High485.31.2363
Triple Number Windward/Leeward Low918.10.6535
Triple Number Windward/Leeward Medium672.00.8928
Triple Number Windward/Leeward High587.71.0209
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1522.11013.2765.8637.2564.3526.4496.0445.9413.5
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low710.3
Triple Number Coastal/Long Distance Medium546.0
Triple Number Coastal/Long Distance High485.3
Triple Number Windward/Leeward Low918.1
Triple Number Windward/Leeward Medium672.0
Triple Number Windward/Leeward High587.7
Predominantly Upwind598.7
Predominantly Downwind553.3
Predominantly Reaching531.1
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance597.61.0040
Triple Number Coastal/Long Distance Low710.30.8447
Triple Number Coastal/Long Distance Medium546.01.0989
Triple Number Coastal/Long Distance High485.31.2363
Triple Number Windward/Leeward Low918.10.6535
Triple Number Windward/Leeward Medium672.00.8928
Triple Number Windward/Leeward High587.71.0209
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1522.11013.2765.8637.2564.3526.4496.0445.9413.5
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8447
Triple Number Coastal/Long Distance Medium1.0989
Triple Number Coastal/Long Distance High1.2363
Triple Number Windward/Leeward Low0.6535
Triple Number Windward/Leeward Medium0.8928
Triple Number Windward/Leeward High1.0209
Coastal/Long Distance1.0040
Predominantly Upwind1.0021
Predominantly Downwind1.0844
For information
General Purpose Handicap (GPH)617.7
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)1.0922
Distanseseilas Trippeltall svak vind0.8447
Distanseseilas Trippeltall mellomvind1.0989
Distanseseilas Trippeltall sterk vind1.2363
Pølsebane Trippeltall svak vind0.6535
Pølsebane Trippeltall mellomvind0.8928
Pølsebane Trippeltall sterk vind1.0209
Motvind Singeltall1.0021
Medvind Singeltall1.0844
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low710.30.8447
Triple Number Coastal/Long Distance Medium546.01.0989
Triple Number Coastal/Long Distance High485.31.2363
Triple Number Windward/Leeward Low918.10.6535
Triple Number Windward/Leeward Medium672.00.8928
Triple Number Windward/Leeward High587.71.0209
Coastal/Long Distance597.61.0040
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind598.71.0021
Predominantly Downwind553.31.0844
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore527.41.1376
Cape Doctor Coastal442.01.3574
Triple Number Coastal/Long Distance Low710.30.8447
Triple Number Coastal/Long Distance Medium546.01.0989
Triple Number Coastal/Long Distance High485.31.2363
Triple Number Windward/Leeward Low918.10.6535
Triple Number Windward/Leeward Medium672.00.8928
Triple Number Windward/Leeward High587.71.0209
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8447
Triple Number Coastal/Long Distance Medium1.0989
Triple Number Coastal/Long Distance High1.2363
Triple Number Windward/Leeward Low0.6535
Triple Number Windward/Leeward Medium0.8928
Triple Number Windward/Leeward High1.0209
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8447
Triple Number Coastal/Long Distance Medium1.0989
Triple Number Coastal/Long Distance High1.2363
Triple Number Windward/Leeward Low0.6535
Triple Number Windward/Leeward Medium0.8928
Triple Number Windward/Leeward High1.0209
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance597.61.0040
Triple Number Coastal/Long Distance Low710.30.8447
Triple Number Coastal/Long Distance Medium546.01.0989
Triple Number Coastal/Long Distance High485.31.2363
Triple Number Windward/Leeward Low918.10.6535
Triple Number Windward/Leeward Medium672.00.8928
Triple Number Windward/Leeward High587.71.0209
Predominantly Upwind598.71.0021
Predominantly Downwind553.31.0844
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1522.11013.2765.8637.2564.3526.4496.0445.9413.5
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance597.61.0040
Triple Number Coastal/Long Distance Low710.30.8447
Triple Number Coastal/Long Distance Medium546.01.0989
Triple Number Coastal/Long Distance High485.31.2363
Triple Number Windward/Leeward Low918.10.6535
Triple Number Windward/Leeward Medium672.00.8928
Triple Number Windward/Leeward High587.71.0209
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1522.11013.2765.8637.2564.3526.4496.0445.9413.5
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low710.30.8447
Triple Number AP Medium546.11.0987
Triple Number AP High485.31.2363
Triple Number Windward/Leeward Low959.50.6253
Triple Number Windward/Leeward Medium672.00.8928
Triple Number Windward/Leeward High587.71.0209
Single Number Predominant Upwind624.30.9610
Single Number Predominant Reaching543.11.1048
Single Number Predominant Downwind575.41.0428
Predominant Upwind - Low877.00.6842
Predominant Upwind - Low/Med661.50.9070
Predominant Upwind - Medium578.61.0370
Predominant Upwind - Med/High537.61.1160
Predominant Upwind - High516.31.1622
Predominant Downwind Low838.80.7153
Predominant Downwind Low/Med622.90.9632
Predominant Downwind Medium534.81.1220
Predominant Downwind Med/High478.31.2545
Predominant Downwind High432.71.3868
Predominant Reaching Low752.70.7972
Predominant Reaching Low/Med576.51.0408
Predominant Reaching Medium509.31.1781
Predominant Reaching Med/High467.91.2824
Predominant Reaching High435.41.3779
SA/DSPL Upwind22.60SA/DSPL Downwind50.03
Scoring OptionTODTOT
5-Band Windward/Leeward Low1074.80.5583
5-Band Windward/Leeward Low/Med781.90.7674
5-Band Windward/Leeward Medium660.30.9087
5-Band Windward/Leeward Med/High596.71.0055
5-Band Windward/Leeward High559.71.0720
Windward/Leeward 60-40 Low1089.10.5509
Windward/Leeward 60-40 Low/Med795.10.7546
Windward/Leeward 60-40 Medium674.20.8899
Windward/Leeward 60-40 Med/High613.50.9780
Windward/Leeward 60-40 High581.41.0321
5-Band AP Low781.50.7677
5-Band AP Low/Med618.80.9696
5-Band AP Medium538.31.1147
5-Band AP Med/High492.71.2178
5-Band AP High463.61.2941
5-Band SF Bay Tour - Low927.70.6468
5-Band SF Bay Tour - Low/Med748.90.8011
5-Band SF Bay Tour - Medium636.50.9427
5-Band SF Bay Tour - Med/High577.11.0398
5-Band SF Bay Tour - High542.21.1067
Chicago-Mac Upwind0.9301
Chicago-Mac All Purpose0.9700
Chicago-Mac Downwind1.0048
Bayview-Mac Cove Island0.7051
Bayview-Mac Shore0.7097
Harvest Moon Regatta475.31.2622
Club Certificate2025
Mistral GagnantBEL 161
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassJ 105Measurement28/11/2025HINPlan reviewHull constructionCoredCarbon rudderNoLight stanchionsNoTrim tabNo
LOA10.570Max. Beam3.344Draft2.016Displacement4,091Wetted area23.11IMS L9.738LSM09.516Acc. length10.570Sink (kg/mm) 17.35
VCGD0.090VCGM0.062RM Rated (kg·m) 90.6Limit of positive stability(°) N/AStability IndexN/ADefault crew weight641Declared crew weightN/A
PROPELLER
Propeller TypeFolding 3 blades
InstallationShaft exposedTwin screwNoHydro generatorNo
PRD0.380PBW0.098PIPA0.0044
PSD0.024PHD0.068PHL0.137
PSA16.5°ESL0.914
ST10.018ST20.091ST30.091
ST40.046ST50.186
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerYesMainsail furlerNoArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders2Rotating mastNo
P12.650IG12.380ISP14.270MDT10.105MDL10.185MDT20.105MDL20.110TL1.850MW0.185GO0.205
E4.450J4.120BAS1.530FSD0.030SFJSPLWPLTPS5.880BD0.130MWTMCG
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodRM estimatedFlotation Date02/12/2025
BALLAST
TANKS
INVENTORY
IdDescriptionWeight SailingLCGVCGGAIdDescriptionWeight SailingLCGVCGGASaSSailor Services5.000.50   
INVENTORY
Fixed Ballast Total0
Total deductible
OTHER ITEMSIdKindDescriptionWeightLCGVCGSaSDeductibleSailor Services185.000.50Total deductible185.000.50
Club Certificate2025
Mistral GagnantBEL 161
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateCommentM10.180.921.672.883.7933.6915/12/2017
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateCommentJ10.080.490.961.973.054.1212.07NoNo 24.3914/12/2017
ASYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLRatioAreaMeas.DateCommentA216.2213.2914.767.737.67101%94.9002/12/2025A514.5511.4112.986.498.2978%74.0902/12/2025
CRUISER/RACER REQUIREMENTS*
Accommodation length10.6 mTable area0.44 m²Headroom1.74 mMinimum number of berths4Personal gear stowage0.16 m³Fresh water capacity92 lMinimum number of seats in cockpit4Food stowage0.24 m³Fuel capacity62 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.