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["\"Poor VPP\"",null,null,null,null,null,null,null,null,null,"©2001 Lester Gilbert"]
["A simple plaything to explore.",null,null,null,null,null,null,null,null,null,"(Approximate values:  speed in m/sec, time in sec, force in gm.)"]
[]
["True wind speed =",null,null,2.5,null,null,null,null,null,null,"Increment =",null,null,null,0.05,null,null,null,null,"\"On the wind\" works for headings from 0 to 180."]
["Heading =",null,null,90," degrees",null,{"$f":"IF(D5>=40,\"(OK)\",\"(Small for on the wind!)\")","v":"(OK)"},null,null,null,null,null,null,null,null,null,null,null,null,"\"Dead run\" is for a heading of 180 always."]
[]
["Boat","Drag forces",null,null,null,"On the wind",null,null,null,null,null,null,null,null,null,null,null,null,null,"Dead run"]
["Speed","Fric","Wave","Total",null,null,null,null,null,null,null,null,null,null,"Est",null,null,"Accum",null,null,null,null,null,null,null,"Est",null,"Accum"]
[null,null,null,null,null,"App wind",null,"AW","Sheet","Sail","Diff","Near max",null,null,"Max",null,"Time","time",null,"App wind","Sail","Diff","Near max",null,null,"Max","Time","time","Rn","Rn","Fn"]
[null,null,null,null,null,"speed",null,"angle","angle","Drive","Accel",null,null,null,"speed",null,null,"taken",null,"speed","Drive","Accel",null,null,null,"speed",null,"taken","sail","fin","hull"]
["(OK = don't worry about the ## here:)",null,null,null,null,null,"OK",null,null,null,null,null,"OK","OK",null,"OK",null,null,null,null,null,null,null,"OK","OK"]
[0,{"$f":"$B$39*A12^$C$40","v":0},{"$f":"$B$40*A12^$D$40","v":0},{"$f":"B12+C12","v":0},null,{"$f":"SQRT((SIN(PI()*$D$5/180)*$D$4)^2+(A12+COS(PI()*$D$5/180)*$D$4)^2)","v":2.5},{"$f":"180*ATAN((SIN(PI()*$D$5/180)*$D$4)/(A12+COS(PI()*$D$5/180)*$D$4))/PI()","v":90},{"$f":"IF(G12<0,G12+180,G12)","v":90},{"$f":"IF(H12-$H$40>90,90,H12-$H$40)","v":75},{"$f":"SIN(PI()*I12/180)*$K$40*F12^$J$40*(IF(I12=90,1+(($T$41-1)*(H12-90)/90),1))","v":60.370364143066766},{"$f":"J12-D12","v":60.370364143066766},{"$f":"IF(K12<=0,1,0)","v":0},{"$f":"IF(L12+L13=1,K12,\"\")","v":""},{"$f":"IF(L12+L13=1,K13,\"\")","v":""},{"$f":"IF(M12<>\"\",$A12+($O$4*M12/(M12-N12)),\"\")","v":""},{"$f":"IF(O12=\"\",\"\",I12)","v":""},{"$f":"IF(L12=0,IF(O12=\"\",$O$4*$Q$40/K12,(O12-$A12)*$Q$40/K12),0)","v":4.1411047216403325E-2},{"$f":"IF(Q12>0,Q12+R11,\"\")","v":4.1411047216403325E-2},null,{"$f":"$D$4-A12","v":2.5},{"$f":"$K$40*$T$41*T12^$U$40","v":79.166666666666657},{"$f":"U12-D12","v":79.166666666666657},{"$f":"IF(V12<=0,1,0)","v":0},{"$f":"IF(W12+W13=1,V12,\"\")","v":""},{"$f":"IF(W12+W13=1,V13,\"\")","v":""},{"$f":"IF(X12<>\"\",$A12+($O$4*X12/(X12-Y12)),\"\")","v":""},{"$f":"IF(W12=0,IF(Z12=\"\",$O$4*$Q$40/V12,(Z12-$A12)*$Q$40/V12),0)","v":3.1578947368421054E-2},{"$f":"IF(AA12>0,AA12+AB11,\"\")","v":3.1578947368421054E-2},{"$f":"IF(O12=\"\",\"\",68500*F12*$AC$40)","v":""},{"$f":"IF(O12=\"\",\"\",877200*O12*$AD$40)","v":""},{"$f":"IF(O12=\"\",\"\",O12/$AE$40)","v":""}]
[{"$f":"A12+$O$4","v":0.05},3.7500000000000006E-2,{"$f":"$B$40*A13^$D$40","v":1.2500000000000006E-4},{"$f":"B13+C13","v":3.7625000000000006E-2},null,2.5004999500099974,{"$f":"180*ATAN((SIN(PI()*$D$5/180)*$D$4)/(A13+COS(PI()*$D$5/180)*$D$4))/PI()","v":88.854237161824898},{"$f":"IF(G13<0,G13+180,G13)","v":88.854237161824898},73.854237161824898,60.058848504059277,60.021223504059279,{"$f":"IF(K13<=0,1,0)","v":0},{"$f":"IF(L13+L14=1,K13,\"\")","v":""},{"$f":"IF(L13+L14=1,K14,\"\")","v":""},"",{"$f":"IF(O13=\"\",\"\",I13)","v":""},4.1651933333730247E-2,8.3062980550133572E-2,null,2.4500000000000002,76.03166666666668,75.994041666666675,0,"","","",3.2897315962819453E-2,6.4476263331240513E-2,{"$f":"IF(O13=\"\",\"\",68500*F13*$AC$40)","v":""},{"$f":"IF(O13=\"\",\"\",877200*O13*$AD$40)","v":""},{"$f":"IF(O13=\"\",\"\",O13/$AE$40)","v":""}]
[0.1,0.15000000000000002,2.0000000000000009E-3,0.15200000000000002,null,2.5019992006393608,87.709389957361466,87.709389957361466,72.709389957361466,59.771076087347325,59.619076087347324,0,"","","","",4.1932887325145302E-2,0.12499586787527887,null,2.4,72.959999999999994,72.807999999999993,0,"","","",3.4336886056477313E-2,9.8813149387717819E-2,"","",""]
[0.15000000000000002,0.33750000000000008,1.0125000000000006E-2,0.34762500000000007,null,2.5044959572736385,86.566369637549485,86.566369637549485,71.566369637549485,59.506616295992231,59.15899129599223,0,"","","","",4.2259003157975823E-2,0.1672548710332547,null,2.35,69.951666666666668,69.604041666666674,0,"","","",3.5917454506054179E-2,0.13473060389377201,"","",""]
[0.2,0.60000000000000009,3.2000000000000015E-2,0.63200000000000012,null,2.5079872407968904,85.426078740099143,85.426078740099143,70.426078740099143,59.265011471644698,58.6330114716447,0,"","","","",4.2638096479301869E-2,0.20989296751255657,null,2.2999999999999998,67.006666666666646,66.374666666666641,0,"","","",3.7664972579899973E-2,0.17239557647367199,"","",""]
[0.25,0.9375,7.8125E-2,1.015625,null,2.5124689052802225,84.289406862500343,84.289406862500343,69.289406862500343,59.045778076673734,58.030153076673734,0,"","","","",4.308105127168655E-2,0.25297401878424314,null,2.25,64.125,63.109375,0,"","","",3.9613765783609804E-2,0.2120093422572818,"","",""]
[0.3,1.3499999999999999,0.16199999999999998,1.5119999999999998,null,2.5179356624028344,83.157226587369053,83.157226587369053,68.157226587369053,58.848408019911197,57.336408019911197,0,"","","","",4.36023128468708E-2,0.29657633163111397,null,2.2000000000000002,61.306666666666672,59.794666666666672,0,"","","",4.1809748918521156E-2,0.25381909117580292,"","",""]
[0.35,1.8374999999999997,0.30012499999999992,2.1376249999999994,null,2.5243811122728679,82.030389605678636,82.030389605678636,67.030389605678636,58.672370112180623,56.534745112180623,0,"","","","",4.4220593814287237E-2,0.34079692544540119,null,2.15,58.551666666666662,56.414041666666662,0,"","","",4.4315208166997432E-2,0.29813429934280034,"","",""]
[0.39999999999999997,2.3999999999999995,0.51199999999999979,2.911999999999999,null,2.5317977802344327,80.909723079177667,80.909723079177667,65.909723079177667,58.517111636252494,55.605111636252495,0,"","","","",4.4959895348363831E-2,0.385756820793765,null,2.1,55.86,52.948,0,"","","",4.7216136586839916E-2,0.34535043592964026,"","",""]
[0.44999999999999996,3.0374999999999992,0.82012499999999955,3.8576249999999987,null,2.5401771591761073,79.796026278268315,79.796026278268315,64.796026278268315,58.382060014663615,54.524435014663617,0,"","","","",4.5851002386868539E-2,0.43160782318063351,null,2.0499999999999998,53.231666666666662,49.374041666666663,0,"","","",5.0633894159971042E-2,0.39598433008961131,"","",""]
[0.49999999999999994,3.7499999999999991,1.2499999999999996,4.9999999999999982,null,2.5495097567963922,78.690067525979785,78.690067525979785,63.690067525979785,58.266624557971895,53.266624557971895,0,"","","","",4.6933704186176921E-2,0.47854152736681044,null,2,50.666666666666664,45.666666666666664,0,"","","",5.4744525547445258E-2,0.45072885563705656,"","",""]
[0.54999999999999993,4.5374999999999988,1.8301249999999991,6.3676249999999976,null,2.5597851472340407,77.592581472599264,77.592581472599264,62.592581472599264,58.170198275502109,51.802573275502112,0,"","","","",4.8260150836604711E-2,0.52680167820341517,null,1.9500000000000002,48.165000000000006,41.797375000000009,0,"","","",5.9812368599702716E-2,0.51054122423675929,"","",""]
[0.6,5.3999999999999995,2.5919999999999996,7.9919999999999991,null,2.5709920264364881,76.504266719204182,76.504266719204182,61.504266719204182,58.092159730465852,50.100159730465855,0,"","","","",4.990004050784997E-2,0.57670171871126519,null,1.9,45.726666666666659,37.734666666666662,0,"","","",6.6252075898378157E-2,0.57679330013513741,"","",""]
[0.65,6.3375000000000004,3.5701250000000009,9.9076250000000012,null,2.5831182706178981,75.425783801961259,75.425783801961259,60.425783801961259,58.031874921501256,48.124249921501253,0,"","","","",5.1948861625436667E-2,0.62865058033670185,null,1.85,43.351666666666667,33.444041666666664,0,"","","",7.4751730814033898E-2,0.65154503094917127,"","",""]
[0.70000000000000007,7.3500000000000014,4.8020000000000014,12.152000000000003,null,2.5961509971494339,74.357753542791272,74.357753542791272,59.357753542791272,57.988699173149662,45.836699173149661,0,"","","","",5.4541449212042223E-2,0.68319202954874403,null,1.7999999999999998,41.039999999999992,28.887999999999991,0,"","","",8.6541124342287487E-2,0.73808615529145871,"","",""]
[0.75000000000000011,8.4375000000000036,6.3281250000000044,14.765625000000007,null,2.6100766272276377,73.300755766006375,73.300755766006375,58.300755766006375,57.961979018540013,43.196354018540006,0,"","","","",5.7875254909870229E-2,0.74106728445861425,null,1.75,38.791666666666664,24.026041666666657,0,"","","",0.10405376110990683,0.84213991640136554,"","",""]
[0.80000000000000016,9.6000000000000032,8.1920000000000055,17.792000000000009,null,2.6248809496813377,72.255328374943062,72.255328374943062,57.255328374943062,57.951054058549936,40.159054058549927,0,"","","","",6.2252462330291018E-2,0.80331974678890528,null,1.6999999999999997,36.606666666666655,18.814666666666646,0,"","","",0.13287506200836241,0.97501497840972795,"","",""]
[0.8500000000000002,10.837500000000006,10.440125000000011,21.277625000000015,null,2.640549185302179,71.221966777554442,71.221966777554442,56.221966777554442,57.955258782916061,36.677633782916047,0,"","","","",6.8161430881739885E-2,0.87148117767064515,null,1.65,34.484999999999992,13.207374999999978,0,"","","",0.18928818179237011,1.1643031602020981,"","",""]
[0.90000000000000024,12.150000000000006,13.122000000000011,25.272000000000016,null,2.6570660511172846,70.201123645475079,70.201123645475079,55.201123645475079,57.973924340131866,32.701924340131853,0,"","","","",7.6448100545936259E-2,0.94792927821658135,null,1.5999999999999996,32.426666666666648,7.1546666666666319,0,"","","",0.34942228848304308,1.5137254486851413,"","",""]
[0.95000000000000029,13.537500000000009,16.290125000000021,29.82762500000003,null,2.6744158240632663,69.193208987288756,69.193208987288756,54.193208987288756,58.006380244456039,28.17875524445601,0,"","","","",8.871931986746856E-2,1.0366485980840499,null,1.5499999999999998,30.431666666666658,0.60404166666662817,0,0.60404166666662817,-6.5000000000000426,0.95425139445268836,0.35191235036393825,1.8656377990490796,"","",""]
[1.0000000000000002,15.000000000000007,20.000000000000018,35.000000000000028,null,2.6925824035672523,68.198590513648185,68.198590513648185,53.198590513648185,58.051956009916324,23.051956009916296,0,"","","","",0.10845066678613177,1.1450992648701817,null,1.4999999999999998,28.499999999999986,-6.5000000000000426,1,"","","",0,"","","",""]
[1.0500000000000003,16.537500000000009,24.310125000000021,40.847625000000029,null,2.7115493725912501,67.217594269518301,67.217594269518301,52.217594269518301,58.109982702789921,17.262357702789892,0,"","","","",0.14482378612719612,1.2899230509973778,null,1.4499999999999997,26.631666666666653,-14.215958333333376,1,"","","",0,"","","",""]
[1.1000000000000003,18.150000000000009,29.282000000000032,47.432000000000045,null,2.7313000567495327,66.250505507133227,66.250505507133227,51.250505507133227,58.179794405639164,10.747794405639119,0,"","","","",0.23260586364475933,1.522528914642137,null,1.3999999999999997,24.826666666666654,-22.605333333333391,1,"","","",0,"","","",""]
[1.1500000000000004,19.837500000000013,34.980125000000044,54.817625000000056,null,2.7518175811634027,65.29756977222867,65.29756977222867,50.29756977222867,58.260729587541149,3.4431045875410931,0,3.4431045875410931,-4.7198676233498489,1.1710897728093905,50.29756977222867,0.30626099604559964,1.8287899106877368,null,1.3499999999999996,23.084999999999987,-31.73262500000007,1,"","","",0,"",47124.876077423272,61636.79692250384,0.37059802937006026]
[1.2000000000000004,21.600000000000016,41.472000000000058,63.072000000000074,null,2.7730849247724096,64.358994175694704,64.358994175694704,49.358994175694704,58.352132376650225,-4.7198676233498489,1,"","","","",0,{"$f":"IF(Q36>0,Q36+R35,\"\")","v":""},null,1.2999999999999996,21.406666666666652,-41.665333333333422,1,"","","",0,"","","",""]
[1.2500000000000004,23.437500000000018,48.828125000000071,72.265625000000085,null,2.7950849718747373,63.434948822921996,63.434948822921996,48.434948822921996,58.453353732643741,-13.812271267356344,1,{"$f":"IF(L37+L38=1,K37,\"\")","v":""},{"$f":"IF(L37+L38=1,K38,\"\")","v":""},"","",0,{"$f":"IF(Q37>0,Q37+R36,\"\")","v":""},null,1.2499999999999996,19.79166666666665,-52.473958333333435,1,{"$f":"IF(W37+W38=1,V37,\"\")","v":""},{"$f":"IF(W37+W38=1,V38,\"\")","v":""},"",0,"","","",""]
[null,null,null,null,null,null,null,null,null,null,null,1,null,null,null,null,null,null,null,null,null,null,1]
["F scale",15,"F exp","W exp",null,"Cl max",null,"Attack",{"$f":"P39","v":50.29756977222867},"R exp","S scale",null,{"$f":"SUM(O12:O36)","v":1.1710897728093905},null,{"$f":"M39*COS(D5*PI()/180)","v":7.1737941285835581E-17},{"$f":"SUM(P12:P37)","v":50.29756977222867},"T mult",{"$f":"SUM(Q12:Q37)","v":1.8287899106877368},null,"Cd max","U exp",null,null,{"$f":"SUM(Z12:Z36)","v":0.95425139445268836},null,null,null,{"$f":"SUM(AA12:AA37)","v":1.8656377990490796},"S chord","F chord","sqrt(g)"]
["W scale",20,2,4,null,1.5,null,15,"Sheet",2,10,{"$f":"IF(SUM(L12:L37)<1,\"Err\",\"OK\")","v":"OK"},"Max",null,"VMG",null,50,"Accum",null,1.9,2,null,{"$f":"IF(SUM(W12:W37)<1,\"Err\",\"OK\")","v":"OK"},"Max",null,null,null,"Accum",0.25,0.06,3.16]
[null,null,null,null,null,null,null,null,"at max",null,null,null,"speed",null,null,null,null,"time",null,{"$f":"T40/F40","v":1.2666666666666666},null,null,null,"speed",null,null,null,"time"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"SUM(AC12:AC37)","v":47124.876077423272},{"$f":"SUM(AD12:AD37)","v":61636.79692250384},{"$f":"SUM(AE12:AE37)","v":0.37059802937006026}]
["INPUTS",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"OUTPUTS",null,null,null,null,null,null,null,null,null,null,"Sail","Fin","Hull"]
["True wind speed",null,"The wind speed.  Max for IOM around 2.5 when in 'A' rig.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Max speed",null,null,"Estimated max boat speed, on or off the wind.",null,null,null,null,null,null,null,"Rn","Rn","Fn"]
["Heading",null,"Boat heading with respect to true wind.  Use 40 when close-hauled.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"VMG",null,null,"Velocity made good directly to windward."]
["Increment",null,"Increment of speed.  Smaller for light wind, larger for stronger.  Start with 0.05.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Accum time",null,null,"Time to reach max speed, on or off the wind."]
[]
["Other input parameters",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Theoretical max",null,null,"(For IOM)",null,null,null,null,null,"Fn"]
["Attack",null,"Nominal angle of attack of sails to apparent wind.  Use 15 or so.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Hull waterline length (ft)",null,null,null,"LWL",null,null,null,3.28]
["F scale",null,"Multiplier for skin friction.  Use 15 or so to get something in grams.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Hull speed (knots)",null,null,null,null,null,null,null,{"$f":"1.32*SQRT(Z49)","v":2.3906216764682782}]
["W scale",null,"Multiplier for wave drag.  Use 20 or so to get something in grams.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Hull speed (mph)",null,null,null,null,null,null,null,{"$f":"1.15*Z50","v":2.7492149279385196}]
["S scale",null,"Multiplier for sail drive force.  Use 10 or so to get something in grams.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Hull speed (ft/sec)",null,null,null,null,null,null,null,{"$f":"Z50*6076/3600","v":4.0348381406170164}]
["T mult",null,"Multiplier to get the time to reflect something reasonable in seconds.  Try 50.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Hull speed (m/sec)",null,null,null,null,null,null,null,{"$f":"Z52/3.281","v":1.2297586530377984},{"$f":"Z53/AE40","v":0.38916413070816402}]
["F exp",null,"Exponent for skin friction.  Usually 2."]
["W exp",null,"Exponent for wave drag.  I use 4, other folks might prefer 3."]
["Cl max (reach)",null,"Coefficient of lift, reaching.  Something like 1.3 to 1.5."]
["Cd max (run)",null,"Coefficient of drag, running.  Something like 1.8 or 1.9."]
["R exp",null,"Exponent for drive from reaching.  Use 2."]
["U exp",null,"Exponent for drive from running.  Use 2."]
[]
["\"Max\"",null,null,"Set the heading required at the top of the spreadsheet."]
[null,null,null,"Use the \"Max\" macro (CTRL-m) to populate this table."]
[null,null,null,null,"(Heading is set to",null,null,null,{"$f":"D5","v":90}," here.)"]
[]
[null,null,null,null,null,{"$f":"F7","v":"On the wind"},null,null,null,{"$f":"T7","v":"Dead run"}]
[null,null,null,"Wind",null,"Max",null,"Time to",null,"Max","Time to"]
[null,null,null,"speed",null,"speed",null,"max",null,"speed","max"]
[]
[null,"Start",0.25,{"$f":"C69","v":0.25},null,0.19540617001296678,null,23.896286550562245,null,0.11878752207180694,15.550889837712701]
[null,"Incr",0.25,{"$f":"D69+$C$70","v":0.5},null,0.36738517376293633,null,14.21312312041508,null,0.23470142881539252,8.6040477671708757]
[null,null,null,{"$f":"D70+$C$70","v":0.75},null,0.51379872259105808,null,9.212769832012901,null,0.34523357794880977,5.921818194006681]
[null,null,null,1,null,0.63939064924139588,null,5.9267437848528735,null,0.44922464219041697,4.4955630139983933]
[null,null,null,1.25,null,0.75009371268560321,null,5.1894104074538498,null,0.54647941235441011,3.6257235488357997]
[null,null,null,1.5,null,0.84867485208851856,null,3.4276495115728238,null,0.63750051670685492,3.0622141968527137]
[null,null,null,1.75,null,0.93810080176362332,null,2.8542461099352865,null,0.72317253719897323,2.6998968792555424]
[null,null,null,2,null,1.0209270927058403,null,2.4967416594183804,null,0.80450345549738222,2.5077650337437523]
[null,null,null,2.25,null,1.0989899081236087,null,1.9720934055538739,null,0.88093633094831658,1.9049960795524723]
[null,null,null,2.5,null,1.1710897728093905,null,1.8287899106877368,null,0.95425139445268836,1.8656377990490796]
[]
["\"Polar\"",null,null,"Set the wind speed required at the top of the spreadsheet."]
[null,null,null,"Use the \"Polar\" macro (CTRL-p) to populate this table."]
[null,null,null,"If the resulting polar looks wrong, check the 'increment' used."]
[null,null,null,null,"(Wind speed is set to",null,null,null,{"$f":"D4","v":2.5}," here.)"]
["Heading","Max speed"]
[0,0]
[15,0]
[30,0.74288964359293164]
[45,0.97634670532529866]
[60,1.0996631441613316]
[75,1.1586183116327751]
[90,1.1710897728093905]
[105,1.1467056504659432]
[120,1.09134627541231]
[135,1.0348156106418442]
[150,0.98427752765606258]
[165,0.95606931884379098]
[180,0.95425139445268836]
[195,{"$f":"B96","v":0.95606931884379098}]
[210,{"$f":"B95","v":0.98427752765606258}]
[225,{"$f":"B94","v":1.0348156106418442}]
[240,{"$f":"B93","v":1.09134627541231}]
[255,{"$f":"B92","v":1.1467056504659432}]
[270,{"$f":"B91","v":1.1710897728093905}]
[285,{"$f":"B90","v":1.1586183116327751}]
[300,{"$f":"B89","v":1.0996631441613316}]
[315,{"$f":"B88","v":0.97634670532529866}]
[330,{"$f":"B87","v":0.74288964359293164}]
[345,{"$f":"B86","v":0}]

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