Club Certificate2025
LA BRUJA TUFAESP-6296_C
RFEV
c/ Gamazo sn
39004 Santander – España
crucero@rfev.es
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 Angles44.1°44.1°42.3°40.4°38.7°38.1°37.9°38.6°40.2°
Beat VMG2.343.203.854.314.594.694.734.704.57
52°3.674.915.756.206.436.556.606.636.60
60°3.945.195.966.356.576.706.766.836.84
75°4.135.376.106.476.706.887.027.177.26
90°3.985.296.166.616.907.117.267.487.71
110°3.945.306.226.677.007.337.678.368.81
120°3.755.126.096.586.927.267.638.559.58
135°3.304.585.616.306.697.007.348.239.52
150°2.703.864.885.726.326.686.977.648.59
Run VMG2.333.344.234.965.656.196.577.157.82
Gybe Angles144.2°144.2°148.1°152.3°163.3°176.3°179.0°179.0°178.0°
APH ToD:611.7CDL: 7.634APH ToT: 0.9808CertNo:629601
BOAT
ClassDEHLER 31DesignerV. DE STADTBuilderDEHLERAge date07/1991Series date01/1982Offset fileG1101.BOFData fileE6296_C
HULL
Length Overall9.430 mMaximum Beam3.102 mDraft1.492 mDisplacement3,613 kgDLR7.9107IMS DivisionCruiser/RacerDynamic Allowance0.080%Age Allowance0.487%
PROPELLER
InstallationShaft exposedTypeFeathering 2 bladesDiameter0.300m
CREW
Maximum weight474 kg(default)Minimum weight344 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail27.8428.56Headsail Luffed28.4628.46Headsail FlyingSymmetricAsymmetric59.4459.44 (All asymmetric spinnakers with SHW/SFL > 85%)
STORM SAIL AREAS (m²)
Trysail7.94Storm Jib5.73Heavy Weather Jib15.46
SAIL LIMITS
Headsails5
✱ One set on the forestay
✱ Woven polyester sails
Spinnakers4
✱ 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
LA BRUJA TUFAESP-6296_C
RFEV
c/ Gamazo sn
39004 Santander – España
crucero@rfev.es
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 VMG1537.01125.7935.6835.4784.9767.2760.5765.8788.3
52°980.5733.1626.4580.5559.5549.6545.6542.6545.1
60°913.4693.7603.6566.8547.9537.1532.3526.9526.5
75°872.3669.8589.9556.6537.0523.1513.1502.3496.0
90°905.6680.1584.5544.4521.7506.0496.0481.1467.0
110°913.5679.2578.8539.7514.1491.2469.2430.5408.8
120°959.1703.7591.3547.3520.3496.1471.6421.3375.7
135°1092.5785.8641.9571.4538.5514.1490.4437.6378.0
150°1333.0933.0737.8629.5569.3539.0516.2471.1419.2
Run VMG1542.41077.3852.0726.2637.5581.2547.6503.6460.1
Selected Courses
Windward / Leeward1538.21101.5893.8780.8711.2674.2654.0634.7624.2
All purpose1157.9845.4702.3631.5591.1568.5553.4531.4514.9
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward746.00.8043
All purpose611.70.9808
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low773.90.7753
Triple Number Coastal/Long Distance Medium608.10.9866
Triple Number Coastal/Long Distance High548.91.0930
Triple Number Windward/Leeward Low997.70.6014
Triple Number Windward/Leeward Medium740.40.8104
Triple Number Windward/Leeward High651.80.9205
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance664.50.9029
Triple Number Coastal/Long Distance Low773.90.7753
Triple Number Coastal/Long Distance Medium608.10.9866
Triple Number Coastal/Long Distance High548.91.0930
Triple Number Windward/Leeward Low997.70.6014
Triple Number Windward/Leeward Medium740.40.8104
Triple Number Windward/Leeward High651.80.9205
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1631.41099.1840.9707.3628.9589.4559.5507.3485.7
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.7029
Downwind "popa"0.8527
70% up, 30% down "Ilhabela"0.7420
30% up, 70% down "Ilhabela-inverso"0.8015
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low773.90.7753
Triple Number Coastal/Long Distance Medium608.10.9866
Triple Number Coastal/Long Distance High548.91.0930
Triple Number Windward/Leeward Low997.70.6014
Triple Number Windward/Leeward Medium740.40.8104
Triple Number Windward/Leeward High651.80.9205
Predominantly Upwind659.80.9094
Predominantly Downwind619.90.9679
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low773.90.7753
Triple Number AP Medium608.20.9865
Triple Number AP High549.01.0930
Triple Number Windward/Leeward Low1040.60.5766
Triple Number Windward/Leeward Medium740.40.8104
Triple Number Windward/Leeward High651.80.9205
Single Number Predominant Upwind685.70.8750
Single Number Predominant Reaching607.70.9874
Single Number Predominant Downwind645.90.9289
Predominant Upwind - Low927.90.6466
Predominant Upwind - Low/Med718.90.8346
Predominant Upwind - Medium639.70.9380
Predominant Upwind - Med/High603.30.9945
Predominant Upwind - High591.31.0147
Predominant Downwind Low930.80.6446
Predominant Downwind Low/Med697.30.8605
Predominant Downwind Medium599.31.0011
Predominant Downwind Med/High539.41.1123
Predominant Downwind High503.01.1927
Predominant Reaching Low826.00.7264
Predominant Reaching Low/Med641.10.9359
Predominant Reaching Medium570.41.0518
Predominant Reaching Med/High529.91.1322
Predominant Reaching High504.71.1888
SA/DSPL Upwind23.81SA/DSPL Downwind36.91
Scoring OptionTODTOT
5-Band Windward/Leeward Low1159.10.5176
5-Band Windward/Leeward Low/Med857.60.6996
5-Band Windward/Leeward Medium727.10.8252
5-Band Windward/Leeward Med/High659.00.9105
5-Band Windward/Leeward High636.20.9431
Windward/Leeward 60-40 Low1163.50.5157
Windward/Leeward 60-40 Low/Med867.30.6918
Windward/Leeward 60-40 Medium741.90.8088
Windward/Leeward 60-40 Med/High680.10.8822
Windward/Leeward 60-40 High662.70.9053
5-Band AP Low848.90.7068
5-Band AP Low/Med682.00.8798
5-Band AP Medium600.20.9997
5-Band AP Med/High555.41.0802
5-Band AP High532.41.1270
5-Band SF Bay Tour - Low1001.40.5991
5-Band SF Bay Tour - Low/Med820.90.7309
5-Band SF Bay Tour - Medium704.90.8512
5-Band SF Bay Tour - Med/High646.10.9286
5-Band SF Bay Tour - High623.90.9616
Chicago-Mac Upwind0.8499
Chicago-Mac All Purpose0.8760
Chicago-Mac Downwind0.8966
Bayview-Mac Cove Island0.6487
Bayview-Mac Shore0.6536
Harvest Moon Regatta535.31.1208
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance664.50.9029
Triple Number Coastal/Long Distance Low773.90.7753
Triple Number Coastal/Long Distance Medium608.10.9866
Triple Number Coastal/Long Distance High548.91.0930
Triple Number Windward/Leeward Low997.70.6014
Triple Number Windward/Leeward Medium740.40.8104
Triple Number Windward/Leeward High651.80.9205
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1631.41099.1840.9707.3628.9589.4559.5507.3485.7
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance664.50.9029
Triple Number Coastal/Long Distance Low773.90.7753
Triple Number Coastal/Long Distance Medium608.10.9866
Triple Number Coastal/Long Distance High548.91.0930
Triple Number Windward/Leeward Low997.70.6014
Triple Number Windward/Leeward Medium740.40.8104
Triple Number Windward/Leeward High651.80.9205
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1631.41099.1840.9707.3628.9589.4559.5507.3485.7
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance664.5
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1631.41099.1840.9707.3628.9589.4559.5507.3485.7
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low773.90.7753
Triple Number Coastal/Long Distance Medium608.10.9866
Triple Number Coastal/Long Distance High548.91.0930
Triple Number Windward/Leeward Low997.70.6014
Triple Number Windward/Leeward Medium740.40.8104
Triple Number Windward/Leeward High651.80.9205
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating664.50.9029
FinRating, kevyt tuuli1136.20.8801
FinRating, kova tuuli534.70.9350
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low773.90.7753
Triple Number Coastal/Long Distance Medium608.10.9866
Triple Number Coastal/Long Distance High548.91.0930
Triple Number Windward/Leeward Low997.70.6014
Triple Number Windward/Leeward Medium740.40.8104
Triple Number Windward/Leeward High651.80.9205
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.9029
Triple Number Coastal/Long Distance Low0.7753
Triple Number Coastal/Long Distance Medium0.9866
Triple Number Coastal/Long Distance High1.0930
Triple Number Windward/Leeward Low0.6014
Triple Number Windward/Leeward Medium0.8104
Triple Number Windward/Leeward High0.9205
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1631.41099.1840.9707.3628.9589.4559.5507.3485.7
For information
General Purpose Handicap (GPH)684.0
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance664.50.9029
Triple Number Coastal/Long Distance Low773.90.7753
Triple Number Coastal/Long Distance Medium608.10.9866
Triple Number Coastal/Long Distance High548.91.0930
Triple Number Windward/Leeward Low997.70.6014
Triple Number Windward/Leeward Medium740.40.8104
Triple Number Windward/Leeward High651.80.9205
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1631.41099.1840.9707.3628.9589.4559.5507.3485.7
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low773.90.7753
Triple Number Coastal/Long Distance Medium608.10.9866
Triple Number Coastal/Long Distance High548.91.0930
Triple Number Windward/Leeward Low997.70.6014
Triple Number Windward/Leeward Medium740.40.8104
Triple Number Windward/Leeward High651.80.9205
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance664.50.9029
Triple Number Coastal/Long Distance Low773.90.7753
Triple Number Coastal/Long Distance Medium608.10.9866
Triple Number Coastal/Long Distance High548.91.0930
Triple Number Windward/Leeward Low997.70.6014
Triple Number Windward/Leeward Medium740.40.8104
Triple Number Windward/Leeward High651.80.9205
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1631.41099.1840.9707.3628.9589.4559.5507.3485.7
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance664.50.9029
Triple Number Coastal/Long Distance Low773.90.7753
Triple Number Coastal/Long Distance Medium608.10.9866
Triple Number Coastal/Long Distance High548.91.0930
Triple Number Windward/Leeward Low997.70.6014
Triple Number Windward/Leeward Medium740.40.8104
Triple Number Windward/Leeward High651.80.9205
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1631.41099.1840.9707.3628.9589.4559.5507.3485.7
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low773.9
Triple Number Coastal/Long Distance Medium608.1
Triple Number Coastal/Long Distance High548.9
Triple Number Windward/Leeward Low997.7
Triple Number Windward/Leeward Medium740.4
Triple Number Windward/Leeward High651.8
Predominantly Upwind659.8
Predominantly Downwind619.9
Predominantly Reaching595.3
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance664.50.9029
Triple Number Coastal/Long Distance Low773.90.7753
Triple Number Coastal/Long Distance Medium608.10.9866
Triple Number Coastal/Long Distance High548.91.0930
Triple Number Windward/Leeward Low997.70.6014
Triple Number Windward/Leeward Medium740.40.8104
Triple Number Windward/Leeward High651.80.9205
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1631.41099.1840.9707.3628.9589.4559.5507.3485.7
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7753
Triple Number Coastal/Long Distance Medium0.9866
Triple Number Coastal/Long Distance High1.0930
Triple Number Windward/Leeward Low0.6014
Triple Number Windward/Leeward Medium0.8104
Triple Number Windward/Leeward High0.9205
Coastal/Long Distance0.9029
Predominantly Upwind0.9094
Predominantly Downwind0.9679
For information
General Purpose Handicap (GPH)684.0
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)0.9808
Distanseseilas Trippeltall svak vind0.7753
Distanseseilas Trippeltall mellomvind0.9866
Distanseseilas Trippeltall sterk vind1.0930
Pølsebane Trippeltall svak vind0.6014
Pølsebane Trippeltall mellomvind0.8104
Pølsebane Trippeltall sterk vind0.9205
Motvind Singeltall0.9094
Medvind Singeltall0.9679
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low773.90.7753
Triple Number Coastal/Long Distance Medium608.10.9866
Triple Number Coastal/Long Distance High548.91.0930
Triple Number Windward/Leeward Low997.70.6014
Triple Number Windward/Leeward Medium740.40.8104
Triple Number Windward/Leeward High651.80.9205
Coastal/Long Distance664.50.9029
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind659.80.9094
Predominantly Downwind619.90.9679
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore627.30.9564
Cape Doctor Coastal519.81.1542
Triple Number Coastal/Long Distance Low773.90.7753
Triple Number Coastal/Long Distance Medium608.10.9866
Triple Number Coastal/Long Distance High548.91.0930
Triple Number Windward/Leeward Low997.70.6014
Triple Number Windward/Leeward Medium740.40.8104
Triple Number Windward/Leeward High651.80.9205
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7753
Triple Number Coastal/Long Distance Medium0.9866
Triple Number Coastal/Long Distance High1.0930
Triple Number Windward/Leeward Low0.6014
Triple Number Windward/Leeward Medium0.8104
Triple Number Windward/Leeward High0.9205
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7753
Triple Number Coastal/Long Distance Medium0.9866
Triple Number Coastal/Long Distance High1.0930
Triple Number Windward/Leeward Low0.6014
Triple Number Windward/Leeward Medium0.8104
Triple Number Windward/Leeward High0.9205
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance664.50.9029
Triple Number Coastal/Long Distance Low773.90.7753
Triple Number Coastal/Long Distance Medium608.10.9866
Triple Number Coastal/Long Distance High548.91.0930
Triple Number Windward/Leeward Low997.70.6014
Triple Number Windward/Leeward Medium740.40.8104
Triple Number Windward/Leeward High651.80.9205
Predominantly Upwind659.80.9094
Predominantly Downwind619.90.9679
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1631.41099.1840.9707.3628.9589.4559.5507.3485.7
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance664.50.9029
Triple Number Coastal/Long Distance Low773.90.7753
Triple Number Coastal/Long Distance Medium608.10.9866
Triple Number Coastal/Long Distance High548.91.0930
Triple Number Windward/Leeward Low997.70.6014
Triple Number Windward/Leeward Medium740.40.8104
Triple Number Windward/Leeward High651.80.9205
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1631.41099.1840.9707.3628.9589.4559.5507.3485.7
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low773.90.7753
Triple Number AP Medium608.20.9865
Triple Number AP High549.01.0930
Triple Number Windward/Leeward Low1040.60.5766
Triple Number Windward/Leeward Medium740.40.8104
Triple Number Windward/Leeward High651.80.9205
Single Number Predominant Upwind685.70.8750
Single Number Predominant Reaching607.70.9874
Single Number Predominant Downwind645.90.9289
Predominant Upwind - Low927.90.6466
Predominant Upwind - Low/Med718.90.8346
Predominant Upwind - Medium639.70.9380
Predominant Upwind - Med/High603.30.9945
Predominant Upwind - High591.31.0147
Predominant Downwind Low930.80.6446
Predominant Downwind Low/Med697.30.8605
Predominant Downwind Medium599.31.0011
Predominant Downwind Med/High539.41.1123
Predominant Downwind High503.01.1927
Predominant Reaching Low826.00.7264
Predominant Reaching Low/Med641.10.9359
Predominant Reaching Medium570.41.0518
Predominant Reaching Med/High529.91.1322
Predominant Reaching High504.71.1888
SA/DSPL Upwind23.81SA/DSPL Downwind36.91
Scoring OptionTODTOT
5-Band Windward/Leeward Low1159.10.5176
5-Band Windward/Leeward Low/Med857.60.6996
5-Band Windward/Leeward Medium727.10.8252
5-Band Windward/Leeward Med/High659.00.9105
5-Band Windward/Leeward High636.20.9431
Windward/Leeward 60-40 Low1163.50.5157
Windward/Leeward 60-40 Low/Med867.30.6918
Windward/Leeward 60-40 Medium741.90.8088
Windward/Leeward 60-40 Med/High680.10.8822
Windward/Leeward 60-40 High662.70.9053
5-Band AP Low848.90.7068
5-Band AP Low/Med682.00.8798
5-Band AP Medium600.20.9997
5-Band AP Med/High555.41.0802
5-Band AP High532.41.1270
5-Band SF Bay Tour - Low1001.40.5991
5-Band SF Bay Tour - Low/Med820.90.7309
5-Band SF Bay Tour - Medium704.90.8512
5-Band SF Bay Tour - Med/High646.10.9286
5-Band SF Bay Tour - High623.90.9616
Chicago-Mac Upwind0.8499
Chicago-Mac All Purpose0.8760
Chicago-Mac Downwind0.8966
Bayview-Mac Cove Island0.6487
Bayview-Mac Shore0.6536
Harvest Moon Regatta535.31.1208
Club Certificate2025
LA BRUJA TUFAESP-6296_C
RFEV
c/ Gamazo sn
39004 Santander – España
crucero@rfev.es
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassDEHLER 31MeasurementHINPlan reviewHull constructionSolidCarbon rudderNoLight stanchionsNoTrim tabNo
LOA9.430Max. Beam3.102Draft1.492Displacement3,613Wetted area18.81IMS L8.029LSM07.700Acc. length9.430Sink (kg/mm) 14.06
VCGD-0.193VCGM-0.170RM Rated (kg·m) 88.7Limit of positive stability(°) N/AStability IndexN/ADefault crew weight474Declared crew weightN/A
PROPELLER
Propeller TypeFeathering 2 blades
InstallationShaft exposedTwin screwNoHydro generatorNo
PRD0.300PBW0.005PIPA0.0012
PSDPHDPHL
PSAESL
ST1ST2ST3
ST4ST5
RIG
Forestay tensionAftInner stayNone FittedMast materialSingle headsail furlerYesMainsail furlerArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders1Rotating mastNo
P11.200IG10.700ISP10.700MDT10.121MDL10.165MDT20.121MDL20.165TLMW0.165GO0.165
E4.050J3.250BAS1.370FSD0.030SFJ0.000SPL3.730WPLTPSBD0.152MWTMCG
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodRM entered directlyRM entered90.0Flotation Date01/01/2010
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Club Certificate2025
LA BRUJA TUFAESP-6296_C
RFEV
c/ Gamazo sn
39004 Santander – España
crucero@rfev.es
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment127.84
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateCommentORC5.000.00NoNo 28.46* Copied from legacy *
ASYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLRatioAreaMeas.DateComment010.63NaN59.44
CRUISER/RACER REQUIREMENTS*
Accommodation length9.4 mTable area0.44 m²Headroom1.66 mMinimum number of berths4Personal gear stowage0.16 m³Fresh water capacity68 lMinimum number of seats in cockpit4Food stowage0.24 m³Fuel capacity38 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.