Club Certificate2025
IsbjørnNOR 15046
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°41.3°40.1°39.8°39.2°38.8°38.2°38.3°
Beat VMG2.633.594.324.835.155.325.445.565.59
52°4.105.466.407.037.387.577.687.797.84
60°4.345.736.657.237.567.757.878.008.07
75°4.485.906.817.387.727.938.088.308.43
90°4.375.796.727.367.747.998.198.488.70
110°4.095.596.737.487.918.208.428.728.93
120°3.975.446.577.397.878.208.478.959.28
135°3.544.926.066.977.608.008.328.929.52
150°2.904.195.346.287.087.648.018.609.20
Run VMG2.513.634.625.466.206.857.368.088.62
Gybe Angles146.0°146.0°150.5°153.4°156.5°162.8°168.7°178.1°178.1°
APH ToD:544.7CDL: 10.299APH ToT: 1.1014CertNo:676323
BOAT
ClassS&S Swan 48DesignerSparkman&StephensBuilderNautorAge date01/1972Series date01/1971Offset fileSWN48S&S.offData file676323
HULL
Length Overall14.606 mMaximum Beam4.152 mDraft2.366 mDisplacement16,066 kgDLR10.7531IMS DivisionCruiser/RacerDynamic Allowance0.510%Age Allowance0.487%
PROPELLER
InstallationShaft exposedTypeFeathering 3 bladesDiameter0.450m
CREW
Maximum weight833 kg(default)Minimum weight703 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail53.1853.83Headsail Luffed73.4173.41Headsail FlyingSymmetric145.92145.92Asymmetric
STORM SAIL AREAS (m²)
Trysail16.27Storm Jib17.55Heavy Weather Jib47.36
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
IsbjørnNOR 15046
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 VMG1366.51002.3834.0744.8699.6676.3662.1647.6643.5
52°877.4659.0562.9512.3487.7475.3468.9462.1459.3
60°829.0627.9541.7497.6476.0464.3457.5449.9446.1
75°802.8610.3529.0487.7466.6454.0445.5433.7426.8
90°823.1622.3535.4489.0465.2450.6439.8424.8413.7
110°880.4643.7534.9481.0455.2439.2427.3412.7402.9
120°906.2662.1548.2487.3457.5439.1425.0402.2387.8
135°1018.2731.7594.3516.6473.5449.8432.5403.5378.1
150°1240.3859.6674.4573.0508.5471.4449.6418.4391.2
Run VMG1431.5992.6778.4659.1580.2525.8489.0445.8417.7
Selected Courses
Windward / Leeward1397.1997.5806.2702.0639.9601.0575.6546.7530.6
All purpose1059.4771.4636.9564.8524.7501.1485.8466.5453.8
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward668.00.8982
All purpose544.71.1014
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low704.10.8521
Triple Number Coastal/Long Distance Medium541.51.1080
Triple Number Coastal/Long Distance High482.41.2438
Triple Number Windward/Leeward Low901.80.6653
Triple Number Windward/Leeward Medium664.70.9026
Triple Number Windward/Leeward High571.11.0506
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance592.71.0124
Triple Number Coastal/Long Distance Low704.10.8521
Triple Number Coastal/Long Distance Medium541.51.1080
Triple Number Coastal/Long Distance High482.41.2438
Triple Number Windward/Leeward Low901.80.6653
Triple Number Windward/Leeward Medium664.70.9026
Triple Number Windward/Leeward High571.11.0506
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1483.3997.0760.0634.4559.8519.9491.2449.1436.4
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.7974
Downwind "popa"0.9394
70% up, 30% down "Ilhabela"0.8353
30% up, 70% down "Ilhabela-inverso"0.8918
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low704.10.8521
Triple Number Coastal/Long Distance Medium541.51.1080
Triple Number Coastal/Long Distance High482.41.2438
Triple Number Windward/Leeward Low901.80.6653
Triple Number Windward/Leeward Medium664.70.9026
Triple Number Windward/Leeward High571.11.0506
Predominantly Upwind586.41.0231
Predominantly Downwind556.91.0773
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low704.20.8521
Triple Number AP Medium541.61.1079
Triple Number AP High482.41.2438
Triple Number Windward/Leeward Low941.10.6375
Triple Number Windward/Leeward Medium664.70.9026
Triple Number Windward/Leeward High571.11.0506
Single Number Predominant Upwind608.10.9867
Single Number Predominant Reaching543.81.1033
Single Number Predominant Downwind581.41.0320
Predominant Upwind - Low837.00.7169
Predominant Upwind - Low/Med644.70.9306
Predominant Upwind - Medium566.91.0584
Predominant Upwind - Med/High526.41.1399
Predominant Upwind - High509.31.1780
Predominant Downwind Low854.60.7021
Predominant Downwind Low/Med633.10.9478
Predominant Downwind Medium536.01.1194
Predominant Downwind Med/High477.31.2571
Predominant Downwind High447.61.3405
Predominant Reaching Low754.70.7950
Predominant Reaching Low/Med579.91.0346
Predominant Reaching Medium507.51.1824
Predominant Reaching Med/High466.71.2855
Predominant Reaching High446.01.3454
SA/DSPL Upwind19.70SA/DSPL Downwind30.98
Scoring OptionTODTOT
5-Band Windward/Leeward Low1050.00.5714
5-Band Windward/Leeward Low/Med773.10.7761
5-Band Windward/Leeward Medium652.20.9199
5-Band Windward/Leeward Med/High580.41.0337
5-Band Windward/Leeward High548.91.0930
Windward/Leeward 60-40 Low1050.30.5713
Windward/Leeward 60-40 Low/Med780.00.7692
Windward/Leeward 60-40 Medium664.00.9036
Windward/Leeward 60-40 Med/High597.41.0044
Windward/Leeward 60-40 High569.01.0544
5-Band AP Low778.30.7709
5-Band AP Low/Med614.70.9761
5-Band AP Medium533.51.1247
5-Band AP Med/High488.41.2285
5-Band AP High467.61.2831
5-Band SF Bay Tour - Low906.40.6619
5-Band SF Bay Tour - Low/Med739.40.8115
5-Band SF Bay Tour - Medium629.90.9525
5-Band SF Bay Tour - Med/High567.71.0570
5-Band SF Bay Tour - High540.21.1107
Chicago-Mac Upwind0.9549
Chicago-Mac All Purpose0.9774
Chicago-Mac Downwind0.9934
Bayview-Mac Cove Island0.7168
Bayview-Mac Shore0.7226
Harvest Moon Regatta476.21.2601
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance592.71.0124
Triple Number Coastal/Long Distance Low704.10.8521
Triple Number Coastal/Long Distance Medium541.51.1080
Triple Number Coastal/Long Distance High482.41.2438
Triple Number Windward/Leeward Low901.80.6653
Triple Number Windward/Leeward Medium664.70.9026
Triple Number Windward/Leeward High571.11.0506
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1483.3997.0760.0634.4559.8519.9491.2449.1436.4
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance592.71.0124
Triple Number Coastal/Long Distance Low704.10.8521
Triple Number Coastal/Long Distance Medium541.51.1080
Triple Number Coastal/Long Distance High482.41.2438
Triple Number Windward/Leeward Low901.80.6653
Triple Number Windward/Leeward Medium664.70.9026
Triple Number Windward/Leeward High571.11.0506
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1483.3997.0760.0634.4559.8519.9491.2449.1436.4
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance592.7
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1483.3997.0760.0634.4559.8519.9491.2449.1436.4
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low704.10.8521
Triple Number Coastal/Long Distance Medium541.51.1080
Triple Number Coastal/Long Distance High482.41.2438
Triple Number Windward/Leeward Low901.80.6653
Triple Number Windward/Leeward Medium664.70.9026
Triple Number Windward/Leeward High571.11.0506
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating592.71.0124
FinRating, kevyt tuuli1032.10.9689
FinRating, kova tuuli471.21.0612
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low704.10.8521
Triple Number Coastal/Long Distance Medium541.51.1080
Triple Number Coastal/Long Distance High482.41.2438
Triple Number Windward/Leeward Low901.80.6653
Triple Number Windward/Leeward Medium664.70.9026
Triple Number Windward/Leeward High571.11.0506
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance1.0124
Triple Number Coastal/Long Distance Low0.8521
Triple Number Coastal/Long Distance Medium1.1080
Triple Number Coastal/Long Distance High1.2438
Triple Number Windward/Leeward Low0.6653
Triple Number Windward/Leeward Medium0.9026
Triple Number Windward/Leeward High1.0506
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1483.3997.0760.0634.4559.8519.9491.2449.1436.4
For information
General Purpose Handicap (GPH)612.1
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance592.71.0124
Triple Number Coastal/Long Distance Low704.10.8521
Triple Number Coastal/Long Distance Medium541.51.1080
Triple Number Coastal/Long Distance High482.41.2438
Triple Number Windward/Leeward Low901.80.6653
Triple Number Windward/Leeward Medium664.70.9026
Triple Number Windward/Leeward High571.11.0506
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1483.3997.0760.0634.4559.8519.9491.2449.1436.4
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low704.10.8521
Triple Number Coastal/Long Distance Medium541.51.1080
Triple Number Coastal/Long Distance High482.41.2438
Triple Number Windward/Leeward Low901.80.6653
Triple Number Windward/Leeward Medium664.70.9026
Triple Number Windward/Leeward High571.11.0506
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance592.71.0124
Triple Number Coastal/Long Distance Low704.10.8521
Triple Number Coastal/Long Distance Medium541.51.1080
Triple Number Coastal/Long Distance High482.41.2438
Triple Number Windward/Leeward Low901.80.6653
Triple Number Windward/Leeward Medium664.70.9026
Triple Number Windward/Leeward High571.11.0506
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1483.3997.0760.0634.4559.8519.9491.2449.1436.4
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance592.71.0124
Triple Number Coastal/Long Distance Low704.10.8521
Triple Number Coastal/Long Distance Medium541.51.1080
Triple Number Coastal/Long Distance High482.41.2438
Triple Number Windward/Leeward Low901.80.6653
Triple Number Windward/Leeward Medium664.70.9026
Triple Number Windward/Leeward High571.11.0506
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1483.3997.0760.0634.4559.8519.9491.2449.1436.4
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low704.1
Triple Number Coastal/Long Distance Medium541.5
Triple Number Coastal/Long Distance High482.4
Triple Number Windward/Leeward Low901.8
Triple Number Windward/Leeward Medium664.7
Triple Number Windward/Leeward High571.1
Predominantly Upwind586.4
Predominantly Downwind556.9
Predominantly Reaching533.7
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance592.71.0124
Triple Number Coastal/Long Distance Low704.10.8521
Triple Number Coastal/Long Distance Medium541.51.1080
Triple Number Coastal/Long Distance High482.41.2438
Triple Number Windward/Leeward Low901.80.6653
Triple Number Windward/Leeward Medium664.70.9026
Triple Number Windward/Leeward High571.11.0506
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1483.3997.0760.0634.4559.8519.9491.2449.1436.4
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8521
Triple Number Coastal/Long Distance Medium1.1080
Triple Number Coastal/Long Distance High1.2438
Triple Number Windward/Leeward Low0.6653
Triple Number Windward/Leeward Medium0.9026
Triple Number Windward/Leeward High1.0506
Coastal/Long Distance1.0124
Predominantly Upwind1.0231
Predominantly Downwind1.0773
For information
General Purpose Handicap (GPH)612.1
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)1.1014
Distanseseilas Trippeltall svak vind0.8521
Distanseseilas Trippeltall mellomvind1.1080
Distanseseilas Trippeltall sterk vind1.2438
Pølsebane Trippeltall svak vind0.6653
Pølsebane Trippeltall mellomvind0.9026
Pølsebane Trippeltall sterk vind1.0506
Motvind Singeltall1.0231
Medvind Singeltall1.0773
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low704.10.8521
Triple Number Coastal/Long Distance Medium541.51.1080
Triple Number Coastal/Long Distance High482.41.2438
Triple Number Windward/Leeward Low901.80.6653
Triple Number Windward/Leeward Medium664.70.9026
Triple Number Windward/Leeward High571.11.0506
Coastal/Long Distance592.71.0124
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind586.41.0231
Predominantly Downwind556.91.0773
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore535.41.1206
Cape Doctor Coastal457.61.3112
Triple Number Coastal/Long Distance Low704.10.8521
Triple Number Coastal/Long Distance Medium541.51.1080
Triple Number Coastal/Long Distance High482.41.2438
Triple Number Windward/Leeward Low901.80.6653
Triple Number Windward/Leeward Medium664.70.9026
Triple Number Windward/Leeward High571.11.0506
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8521
Triple Number Coastal/Long Distance Medium1.1080
Triple Number Coastal/Long Distance High1.2438
Triple Number Windward/Leeward Low0.6653
Triple Number Windward/Leeward Medium0.9026
Triple Number Windward/Leeward High1.0506
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8521
Triple Number Coastal/Long Distance Medium1.1080
Triple Number Coastal/Long Distance High1.2438
Triple Number Windward/Leeward Low0.6653
Triple Number Windward/Leeward Medium0.9026
Triple Number Windward/Leeward High1.0506
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance592.71.0124
Triple Number Coastal/Long Distance Low704.10.8521
Triple Number Coastal/Long Distance Medium541.51.1080
Triple Number Coastal/Long Distance High482.41.2438
Triple Number Windward/Leeward Low901.80.6653
Triple Number Windward/Leeward Medium664.70.9026
Triple Number Windward/Leeward High571.11.0506
Predominantly Upwind586.41.0231
Predominantly Downwind556.91.0773
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1483.3997.0760.0634.4559.8519.9491.2449.1436.4
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance592.71.0124
Triple Number Coastal/Long Distance Low704.10.8521
Triple Number Coastal/Long Distance Medium541.51.1080
Triple Number Coastal/Long Distance High482.41.2438
Triple Number Windward/Leeward Low901.80.6653
Triple Number Windward/Leeward Medium664.70.9026
Triple Number Windward/Leeward High571.11.0506
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1483.3997.0760.0634.4559.8519.9491.2449.1436.4
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low704.20.8521
Triple Number AP Medium541.61.1079
Triple Number AP High482.41.2438
Triple Number Windward/Leeward Low941.10.6375
Triple Number Windward/Leeward Medium664.70.9026
Triple Number Windward/Leeward High571.11.0506
Single Number Predominant Upwind608.10.9867
Single Number Predominant Reaching543.81.1033
Single Number Predominant Downwind581.41.0320
Predominant Upwind - Low837.00.7169
Predominant Upwind - Low/Med644.70.9306
Predominant Upwind - Medium566.91.0584
Predominant Upwind - Med/High526.41.1399
Predominant Upwind - High509.31.1780
Predominant Downwind Low854.60.7021
Predominant Downwind Low/Med633.10.9478
Predominant Downwind Medium536.01.1194
Predominant Downwind Med/High477.31.2571
Predominant Downwind High447.61.3405
Predominant Reaching Low754.70.7950
Predominant Reaching Low/Med579.91.0346
Predominant Reaching Medium507.51.1824
Predominant Reaching Med/High466.71.2855
Predominant Reaching High446.01.3454
SA/DSPL Upwind19.70SA/DSPL Downwind30.98
Scoring OptionTODTOT
5-Band Windward/Leeward Low1050.00.5714
5-Band Windward/Leeward Low/Med773.10.7761
5-Band Windward/Leeward Medium652.20.9199
5-Band Windward/Leeward Med/High580.41.0337
5-Band Windward/Leeward High548.91.0930
Windward/Leeward 60-40 Low1050.30.5713
Windward/Leeward 60-40 Low/Med780.00.7692
Windward/Leeward 60-40 Medium664.00.9036
Windward/Leeward 60-40 Med/High597.41.0044
Windward/Leeward 60-40 High569.01.0544
5-Band AP Low778.30.7709
5-Band AP Low/Med614.70.9761
5-Band AP Medium533.51.1247
5-Band AP Med/High488.41.2285
5-Band AP High467.61.2831
5-Band SF Bay Tour - Low906.40.6619
5-Band SF Bay Tour - Low/Med739.40.8115
5-Band SF Bay Tour - Medium629.90.9525
5-Band SF Bay Tour - Med/High567.71.0570
5-Band SF Bay Tour - High540.21.1107
Chicago-Mac Upwind0.9549
Chicago-Mac All Purpose0.9774
Chicago-Mac Downwind0.9934
Bayview-Mac Cove Island0.7168
Bayview-Mac Shore0.7226
Harvest Moon Regatta476.21.2601
Club Certificate2025
IsbjørnNOR 15046
Norges Seilforbund
Sognsveien 73
0854 OSLO
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassS&S Swan 48MeasurementHINPlan reviewHull constructionSolidCarbon rudderNoLight stanchionsNoTrim tabNo
LOA14.606Max. Beam4.152Draft2.366Displacement16,066Wetted area42.15IMS L11.487LSM011.431Acc. length13.494Sink (kg/mm) 28.09
VCGD-0.250VCGM-0.273RM Rated (kg·m) 316.4Limit of positive stability(°) N/AStability IndexN/ADefault crew weight833Declared crew weightN/A
PROPELLER
Propeller TypeFeathering 3 blades
InstallationShaft exposedTwin screwNoHydro generatorNo
PRD0.450PBWPIPA0.0079
PSD0.040PHD0.090PHL0.162
PSA18.0°ESL0.890
ST10.057ST20.138ST30.187
ST40.071ST50.160
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerNoMainsail furlerArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays2CheckstaysSpreaders2Rotating mastNo
P17.340IG18.730ISP18.740MDT10.150MDL10.290MDT20.000MDL20.000TLTaperMW0.000GO0.000
E5.360J6.110BAS1.590FSDFoilSFJ0.120SPL6.253WPLTPS0.000BD0.000MWT0.00MCG0.000
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodVCG entered directlyVCG entered-0.250Flotation Date01/01/2015
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Club Certificate2025
IsbjørnNOR 15046
Norges Seilforbund
Sognsveien 73
0854 OSLO
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment400-2023061212160.171.061.863.284.3453.1809/06/2023
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment400-2023061212180.090.991.963.996.168.3917.93NoNo 73.4109/06/2023400-2023061212210.070.711.352.754.325.9817.84NoNo 51.2709/06/2023
SYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLAreaMeas.DateComment400-20230612122217.6317.6317.639.939.94145.9209/06/2023
CRUISER/RACER REQUIREMENTS*
Accommodation length13.5 mTable area0.66 m²Headroom1.87 mMinimum number of berths6Personal gear stowage0.24 m³Fresh water capacity225 lMinimum number of seats in cockpit6Food stowage0.36 m³Fuel capacity120 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.