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{"sheet":"Compound Interest","index":0,"n_rows":55,"n_cols":10,"rows_kept":55,"cut":false,"hidden":false,"merged":[]}
["interest rate","x0","Exact ans."]
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[]
["Annual Compounding",null,"Quarterly Compounding",null,"Monthly Compounding",null,"Bi-Monthly Compounding",null,"Continuous Compounding"]
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{"sheet":"PredatorPrey","index":1,"n_rows":144,"n_cols":7,"rows_kept":144,"cut":false,"hidden":false,"merged":[]}
["g_prey","a_prey","d_pred","b_pred","x0","y0","deltat"]
["# rabbits\n born/day/rabbit","fraction of rabbits \nkilled/day/lynx","# lynx \ndeaths/day/lynx","fraction of lynx\nborn/day/rabbit"]
[0.01,1E-3,4.0000000000000001E-3,1E-4,80,5,10]
[]
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{"sheet":"IwoJima","index":2,"n_rows":122,"n_cols":10,"rows_kept":122,"cut":false,"hidden":false,"merged":[]}
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{"sheet":"Square Law","index":5,"n_rows":119,"n_cols":13,"rows_kept":119,"cut":false,"hidden":false,"merged":[]}
["time","x-type","y-type",null,null,null,null,"delta",0.01]
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[0.53000000000000025,3.6267844165847767,4.5198619077384992]
[0.54000000000000026,3.5363871784300067,4.4835940635726512]
[0.55000000000000027,3.4467152971585535,4.4482301917883511]
[0.56000000000000028,3.3577506933227865,4.4137630388167652]
[0.57000000000000028,3.269475432546451,4.3801855318835372]
[0.58000000000000029,3.1818717219087804,4.3474907775580727]
[0.5900000000000003,3.094921906357619,4.3156720603389847]
[0.60000000000000031,3.0086084651508394,4.2847228412754088]
[0.61000000000000032,2.9229140083253311,4.2546367566239001]
[0.62000000000000033,2.8378212731928532,4.2254076165406467]
[0.63000000000000034,2.7533131208620403,4.1970294038087186]
[0.64000000000000035,2.6693725327858657,4.1694962726000986]
[0.65000000000000036,{"$f":"MAX(B66-delta*beta1*C66,0)","v":2.5859826073338636},{"$f":"MAX(C66-delta*alpha1*B66,0)","v":4.1428025472722396}]
[{"$f":"A67+delta","v":0.66000000000000036},2.5031265563884189,4.1169427211989014]
[0.67000000000000037,2.420787701964441,4.0919114556350173]
[0.68000000000000038,2.3389494728517408,4.0677035786153732]
[0.69000000000000039,2.2575954012794335,4.0443140838868556]
[0.7000000000000004,2.1767091196016963,4.0217381298740609]
[0.71000000000000041,2.0962743570042153,3.9999710386780438]
[0.72000000000000042,2.0162749362306545,3.9790082951080015]
[0.73000000000000043,1.9366947703284945,3.958845545745695]
[0.74000000000000044,1.8575178594135806,3.9394785980424101]
[0.75000000000000044,1.7787282874527324,3.9209034194482744]
[0.76000000000000045,1.7003102190637669,3.9031161365737472]
[0.77000000000000046,1.6222478963322919,3.8861130343831096]
[0.78000000000000047,1.5445256356446297,3.8698905554197869]
[0.79000000000000048,1.467127824536234,3.8544452990633404]
[0.80000000000000049,1.3900389185549673,3.8397740208179783]
[0.8100000000000005,1.3132434381386078,3.8258736316324287]
[0.82000000000000051,1.2367259655059593,3.8127411972510425]
[0.83000000000000052,1.1604711415609383,3.8003739375959831]
[0.84000000000000052,1.0844636628090187,3.7887692261803738]
[0.85000000000000053,1.0086882782854112,3.7779245895522835]
[0.86000000000000054,0.93312978649436551,3.7678377067694293]
[0.87000000000000055,0.85777303235897695,3.7585064089044855]
[0.88000000000000056,0.78260290418088729,3.7499286785808956]
[0.89000000000000057,{"$f":"MAX(B90-delta*beta1*C90,0)","v":0.70760433060926942},{"$f":"MAX(C90-delta*alpha1*B90,0)","v":3.7421026495390866}]
[0.90000000000000058,0.63276227761848769,3.735026606232994]
[0.91000000000000059,0.55806174549382781,3.7286989834568089]
[0.9200000000000006,0.48348776582469166,3.7231183660018705]
[0.9300000000000006,0.40902539850465425,3.7182834883436238]
[0.94000000000000061,0.33465972873778177,3.7141932343585773]
[0.95000000000000062,0.2603758640506102,3.7108466370711994]
[0.96000000000000063,0.1861589313091862,3.7082428784306933]
[0.97000000000000064,0.11199407374057234,3.7063812891176013]
[0.98000000000000065,3.7866447958220306E-2,3.7052613483801955]
[0.99000000000000066,0,3.7048826839006135]
[1.0000000000000007,0,3.7048826839006135]
[1.0100000000000007,{"$f":"MAX(B102-delta*beta1*C102,0)","v":0},{"$f":"MAX(C102-delta*alpha1*B102,0)","v":3.7048826839006135}]
[1.0200000000000007,0,3.7048826839006135]
[1.0300000000000007,0,3.7048826839006135]
[1.0400000000000007,0,3.7048826839006135]
[1.0500000000000007,0,3.7048826839006135]
[1.0600000000000007,0,3.7048826839006135]
[1.0700000000000007,0,3.7048826839006135]
[1.0800000000000007,0,3.7048826839006135]
[1.0900000000000007,0,3.7048826839006135]
[1.1000000000000008,0,3.7048826839006135]
[1.1100000000000008,{"$f":"MAX(B112-delta*beta1*C112,0)","v":0},{"$f":"MAX(C112-delta*alpha1*B112,0)","v":3.7048826839006135}]
[1.1200000000000008,0,3.7048826839006135]
[1.1300000000000008,0,3.7048826839006135]
[1.1400000000000008,0,3.7048826839006135]
[1.1500000000000008,0,3.7048826839006135]
[1.1600000000000008,0,3.7048826839006135]
[1.1700000000000008,0,3.7048826839006135]

{"sheet":"Minelayers","index":6,"n_rows":62,"n_cols":10,"rows_kept":62,"cut":false,"hidden":false,"merged":[]}
["Time","Mines","CntrLayer","Sweeper","ShipLoss","Layers"]
[0,0,30,6,30,20,null,null,10,"Mines Laid/Layer/Day"]
[{"$f":"A2+$I$10","v":1},{"$f":"MAX(B2+$I$10*($I$2*F2-$I$3*D2*B2-($I$4+$I$5)*B2-$I$6*C2*B2),0)","v":200},{"$f":"MAX(C2-$I$10*$I$6*C2*B2,0)","v":30},{"$f":"MAX(D2-$I$10*$I$7*D2*B2)","v":6},{"$f":"E2+$I$10*$I$4*B2","v":30},{"$f":"MAX(F2+$I$10*($I$9-$I$8*C2*F2),0)","v":9},null,null,0.1,"Mines swept/Sweeper/Mine/Day"]
[{"$f":"A3+$I$10","v":2},{"$f":"MAX(B3+$I$10*($I$2*F3-$I$3*D3*B3-($I$4+$I$5)*B3-$I$6*C3*B3),0)","v":161.39999999999998},{"$f":"MAX(C3-$I$10*$I$6*C3*B3,0)","v":29.4},{"$f":"MAX(D3-$I$10*$I$7*D3*B3)","v":4.8},{"$f":"E3+$I$10*$I$4*B3","v":34},{"$f":"MAX(F3+$I$10*($I$9-$I$8*C3*F3),0)","v":4.6000000000000005},null,null,0.02,"Mines exploded by Ships/Mine/Day"]
[3,122.99748400000001,28.925483999999997,4.0252800000000004,{"$f":"E4+$I$10*$I$4*B4","v":37.228000000000002},2.8952000000000004,null,null,0.02,"Mine attrition/Mine/Day"]
[4,97.163877224899778,28.569707824451772,3.5301806876044801,39.687949680000003,2.2202987744640001,null,null,1E-4,"Mines exploded/CntrLayer/Mine/Day"]
[5,80.902111230991764,28.292113466111143,3.1871746446923659,41.631227224497998,1.9516330290755035,null,null,1E-3,"Sweepers sunk/Sweeper/Mine/Day"]
[6,71.168552139697766,28.063224295051626,2.9293254870748675,43.249269449117833,1.8473165670192166,null,null,0.02,"Layers sunk/CntrLayer/Layer/Day"]
[7,65.747668454053652,27.863502390906586,2.7208496334138341,44.672640491911785,1.8104833837347158,null,null,1,"Layer reinforcements/Day"]
[8,63.150447560419437,27.680306359189981,2.5419601138028081,45.98759386099286,1.8015552219069377,null,null,1,"Delta_days"]
[9,62.412587616814591,27.505503985670742,2.3814341949354261,47.250602812201251,1.8042032125992873]
[10,62.923300235881285,27.333835017925711,2.2328027245903406,48.498854564537545,1.8116928394970941]
[11,64.301771489984702,27.161841507182611,2.0923074083834488,49.757320569255171,1.8212825759376754]
[12,66.313963651110399,26.987186054598407,1.9577683355227742,51.043355999054867,1.8318948025894271]
[13,68.818652579537996,26.808223327091369,1.827940957283622,52.369635272077076,1.8431410851907732]
[14,71.733183380001066,26.623732746349191,1.7021445236084123,53.746008323667837,1.8549143284881375]
[15,75.011994294220315,26.432752236013791,1.5800442783571456,55.180671991267857,1.8672194615072986]
[16,78.633204552259485,26.234474890022948,1.4615220059644038,56.680911877152262,1.8801044735815884]
[17,82.590215137687409,26.028184806988119,1.3465978471117763,58.253575968197453,1.8936334015256686]
[18,86.886392619460509,25.813217468702856,1.2353820412148679,59.905380270951198,1.9078765988937558]
[19,91.53163226204137,25.588935733927133,1.1280441521468423,61.643108123340411,1.9229079278798822]
[{"$f":"A21+$I$10","v":20},96.540054293835951,25.354716028369651,{"$f":"MAX(D21-$I$10*$I$7*D21*B21)","v":1.0247924296371913},63.473740768581237,{"$f":"MAX(F21+$I$10*($I$9-$I$8*C21*F21),0)","v":1.9388045801043363}]
[21,101.92837167721886,25.109941462171292,0.9258589128401048,65.40454185445796,1.9556477888433781]
[22,107.71464401508575,24.853999917556351,0.83148762145147281,67.443109288002333,1.9735237588737391]
[23,113.91724255311308,24.586285942209294,0.74192422830387705,69.597402168304043,1.9925245720668707]
[24,120.55392215456898,24.306205752293408,0.65740626603215302,71.875747019366301,2.0127489945525849]
[25,127.64094398838198,24.013184908679918,0.57815336221298697,74.286825462457685,2.0343031707662487]
[26,135.19222728522578,23.706678349688772,0.50435732129006439,76.839644342225327,2.0573012067677729]
[27,143.21853543545018,23.386182484925886,0.43617213167725033,79.54348888792984,2.08186564722237]
[28,151.72672362010672,23.051249004434158,0.37370419778067621,82.407859596638843,2.1081278485215562]
[29,160.71909275860438,22.701499955754755,0.31700328424833385,85.442394069040972,2.1362282491325071]
[30,170.19290706728142,22.336643508039916,0.26605480400244363,88.656775924213065,2.1663165390692338]
[{"$f":"A32+$I$10","v":31},180.14013829276746,{"$f":"MAX(C32-$I$10*$I$6*C32*B32,0)","v":21.956489678764033},{"$f":"MAX(D32-$I$10*$I$7*D32*B32)","v":0.22077416347005197},92.060634065558688,{"$f":"MAX(F32+$I$10*($I$9-$I$8*C32*F32),0)","v":2.1985517338940279}]
[32,190.54749675738489,21.560965170048405,0.18100387513108676,95.663436831414032,2.2331021648245679]
[33,201.39679621029111,21.150126375965815,0.1465140398214719,99.474386766561736,2.2701454048857239]
[34,212.66567581959333,20.724169606809586,0.11700658160160045,103.50232269076756,2.3098681607827007]
[35,224.32867006594893,20.283437653286381,9.2123297849955696E-2,107.75563620715943,2.3524661701141008]
[36,236.35857961626226,19.828421993973649,7.1457400961185844E-2,112.2422096084784,2.3981441522546056]
[37,248.72805920887953,19.359760228120901,5.4567831166930224E-2,116.96938120080365,2.4471158671889155]
[38,261.4113088794457,18.878228669291925,4.0995280425541861E-2,121.94394238498124,2.4996043384047644]
[39,274.38573867034694,18.384730422715418,3.0278650511621041E-2,127.17216856257015,2.5558422927415787]
[40,287.63347827856239,17.88027963898622,2.1970620625048624E-2,132.6598833359771,2.6160728616410021]
[41,301.14262245828229,17.365982936470722,1.5651134594727164E-2,138.41255290154834,2.6805505751989216]
[42,314.9081371760044,16.843019172165263,1.093791087842348E-2,144.43540535071398,2.7495426642138967]
[43,328.93239423797843,16.312618792972636,7.4934737391019884E-3,150.73356809423407,2.8233306680530763]
[44,343.22534564758746,15.776043917386243,5.028627480939755E-3,157.31221597899363,2.9022123297639042]
[45,357.80438606614553,15.234570104736601,3.3026750756612504E-3,164.17672289194539,2.9865037463252002]
[46,372.69397732363871,14.689470504405907,2.1209634478383159E-3,171.33281061326829,3.0765417324962048]
[47,387.92512080663539,14.142002785699376,1.330493144705396E-3,178.78669015974106,3.1726863517946677]
[48,403.5347625070184,13.593398971790355,8.14361430813155E-4,186.54519257587376,3.275323567290056]
[49,419.56520446240597,13.044858069215898,4.8573828423509275E-4,194.61588782601413,3.3848679670524287]
[50,436.06357921188061,12.497541214916534,2.8193940169477779E-4,203.00719191526224,3.5017655227877427]
[51,453.08142466546798,11.952568959564084,1.5899589707089683E-4,211.72846349949987,3.6264963438674718]
[52,470.67437861150677,11.41102026230293,8.695780951005079E-5,220.79009199280924,3.7595773912338122]
[53,488.90199701096071,10.873932775174655,4.6028996553489863E-5,230.20357956503938,3.9015651154525117]
[54,507.82768917329929,10.342304030260072,2.3525328218078041E-5,239.98161950525858,4.0530579797845689]
[55,527.51875588726489,9.8170931946186055,1.1578515152048059E-5,250.13817328872457,4.2146988222004946]
[56,548.04651300654302,9.2992231157731506,5.4706312440178216E-6,260.68854840646986,4.3871769997046641]
[57,569.48648198706326,8.7895824355462189,2.4724708667892077E-6,271.64947866660071,4.5712302443318258]
[58,591.91862950909001,8.2890275976107688,1.0644321310459169E-6,283.039208306342,4.7676461430434927]
[59,615.42763976788649,7.7983846120566893,4.3437492283177768E-7,294.8775808965238,4.9772631339368916]
[60,640.10320464032657,7.318450468476664,1.6704858929905893E-7,307.18613369188154,5.2009708892598816]

{"sheet":"FlakBomb","index":7,"n_rows":32,"n_cols":9,"rows_kept":32,"cut":false,"hidden":false,"merged":[]}
["Time","Attack_Ac","Supp_Ac","CumBomb","FlakSite","N",null,1,"Bombs per Attacker"]
[0,10,30,0,30,{"$f":"E2*EXP(-C2/(E2+0.000001))","v":11.036383603022704},null,1,"Missions per day"]
[{"$f":"A2+$H$9","v":1},{"$f":"MAX(B2+$H$9*($H$4-$H$3*F2),0)","v":9.5481808198488647},{"$f":"MAX(C2-$H$9*$H$6*E2,0)","v":29.4},{"$f":"D2+$H$9*$H$1*B2*(1-EXP(-0.5*($H$7/($H$8*(1+0.5*(F2/(B2+0.000001)))))^2))","v":1.8749149786997665},{"$f":"MAX(E2-$H$9*$H$5*C2,0)","v":27},{"$f":"E3*EXP(-C3/(E3+0.000001))","v":9.0879377970866244},null,0.05,"Prob Flak Kills Attack"]
[2,{"$f":"MAX(B3+$H$9*($H$4-$H$3*F3),0)","v":9.1937839299945328},{"$f":"MAX(C3-$H$9*$H$6*E3,0)","v":28.86},{"$f":"D3+$H$9*$H$1*B3*(1-EXP(-0.5*($H$7/($H$8*(1+0.5*(F3/(B3+0.000001)))))^2))","v":3.8332484684875112},{"$f":"MAX(E3-$H$9*$H$5*C3,0)","v":24.06},7.2503483320927691,null,0.1,"Attack resupply rate"]
[3,8.931266513389895,28.378799999999998,5.9181990864728888,21.173999999999999,5.5428439244657932,null,0.1,"Supp kills Flak"]
[4,8.754124317166605,27.955319999999997,8.1746887622428552,18.336120000000001,3.9919070399393606,null,0.02,"Flak kills Supp"]
[5,8.6545289651696375,27.588597599999996,10.645124045189606,15.540588000000001,2.6331857829392207,null,100,"Lethal Radius (meters)"]
[6,8.6228696760226757,27.277785839999996,13.361453407006174,12.781728240000001,1.5126958601822955,null,100,"Firing Error (meters)"]
[7,8.6472348830135601,27.022151275199995,16.333465646211046,10.053949656000002,0.68403296208448816,null,1,"delta"]
[8,8.7130332349093358,26.821072282079996,19.536433833769458,7.3517345284800024,0.19141187601771767,null,{"$f":"B2+C2","v":40},"Total A/C"]
[9,8.8034626411084496,26.674037591510395,22.907329650026249,4.669627300272003,1.5434334394956888E-2]
[10,8.9026909243887022,26.580645045504955,26.366545690417286,2.0022235411209635,3.4356714493545643E-6]
[11,9.0026907526051296,26.540600574682536,29.869480573299118,0,0]
[12,9.1026907526051293,26.540600574682536,33.411763364537833,0,0]
[13,9.2026907526051289,26.540600574682536,36.993393089805288,0,0]
[14,9.3026907526051286,26.540600574682536,40.614369749101478,0,0]
[15,9.4026907526051282,26.540600574682536,44.274693342426403,0,0]
[16,9.5026907526051279,26.540600574682536,47.974363869780063,0,0]
[17,9.6026907526051275,26.540600574682536,51.713381331162459,0,0]
[18,9.7026907526051271,26.540600574682536,55.491745726573598,0,0]
[19,9.8026907526051268,26.540600574682536,59.309457056013471,0,0]
[20,9.9026907526051264,26.540600574682536,63.16651531948208,0,{"$f":"E22*EXP(-C22/(E22+0.000001))","v":0}]
[21,{"$f":"MAX(B22+$H$9*($H$4-$H$3*F22),0)","v":10.002690752605126},{"$f":"MAX(C22-$H$9*$H$6*E22,0)","v":26.540600574682536},{"$f":"D22+$H$9*$H$1*B22*(1-EXP(-0.5*($H$7/($H$8*(1+0.5*(F22/(B22+0.000001)))))^2))","v":67.062920516979432},{"$f":"MAX(E22-$H$9*$H$5*C22,0)","v":0},{"$f":"E23*EXP(-C23/(E23+0.000001))","v":0}]
[22,10.102690752605126,26.540600574682536,70.998672648505519,0,0]
[23,10.202690752605125,26.540600574682536,74.973771714060334,0,0]
[24,10.302690752605125,26.540600574682536,78.988217713643891,0,0]
[25,10.402690752605125,26.540600574682536,83.042010647256177,0,0]
[26,10.502690752605124,26.540600574682536,87.135150514897205,0,0]
[27,10.602690752605124,26.540600574682536,91.267637316566976,0,0]
[28,10.702690752605124,26.540600574682536,95.439471052265475,0,0]
[29,10.802690752605123,26.540600574682536,99.650651721992716,0,{"$f":"E31*EXP(-C31/(E31+0.000001))","v":0}]
[30,{"$f":"MAX(B31+$H$9*($H$4-$H$3*F31),0)","v":10.902690752605123},{"$f":"MAX(C31-$H$9*$H$6*E31,0)","v":26.540600574682536},{"$f":"D31+$H$9*$H$1*B31*(1-EXP(-0.5*($H$7/($H$8*(1+0.5*(F31/(B31+0.000001)))))^2))","v":103.90117932574869},{"$f":"MAX(E31-$H$9*$H$5*C31,0)","v":0},{"$f":"E32*EXP(-C32/(E32+0.000001))","v":0}]

{"sheet":"FlakBomb (2)","index":8,"n_rows":32,"n_cols":13,"rows_kept":32,"cut":false,"hidden":false,"merged":[]}
["Time","u","Atk_Ac (in)","Supp_Ac(in)","Tot.A/C avail","Atk.A/C (out)","Supp A/C(out)","CumBomb","FlakSite","N",null,1,"Bombs per Attacker"]
[0,0.2,null,null,40,{"$f":"B2*E2","v":8},{"$f":"(1-B2)*E2","v":32},0,30,{"$f":"I2*EXP(-G2/(I2+0.000001))","v":10.324613973059741},null,1,"Missions per day"]
[{"$f":"A2+$L$9","v":1},0.2,{"$f":"MAX(F2+$L$9*($L$4-$L$3*J2),0)","v":7.5837693013470133},{"$f":"MAX(G2-$L$9*$L$6*I2,0)","v":31.4},{"$f":"C3+D3","v":38.98376930134701},{"$f":"B3*E3","v":7.7967538602694022},{"$f":"(1-B3)*E3","v":31.187015441077609},{"$f":"H2+$L$9*$L$1*F2*(1-EXP(-0.5*($L$7/($L$8*(1+0.5*(J2/(F2+0.000001)))))^2))","v":1.3492247884731423},{"$f":"MAX(I2-$L$9*$L$5*G2,0)","v":26.8},{"$f":"I3*EXP(-G3/(I3+0.000001))","v":8.3704473083219355},null,0.05,"Prob Flak Kills Attack"]
[2,0.2,{"$f":"MAX(F3+$L$9*($L$4-$L$3*J3),0)","v":7.4782314948533051},{"$f":"MAX(G3-$L$9*$L$6*I3,0)","v":30.651015441077607},{"$f":"C4+D4","v":38.129246935930915},{"$f":"B4*E4","v":7.6258493871861832},{"$f":"(1-B4)*E4","v":30.503397548744733},{"$f":"H3+$L$9*$L$1*F3*(1-EXP(-0.5*($L$7/($L$8*(1+0.5*(J3/(F3+0.000001)))))^2))","v":2.8368485424241632},{"$f":"MAX(I3-$L$9*$L$5*G3,0)","v":23.681298455892239},{"$f":"I4*EXP(-G4/(I4+0.000001))","v":6.5313005696829469},null,0.1,"Attack resupply rate"]
[3,0.2,{"$f":"MAX(F4+$L$9*($L$4-$L$3*J4),0)","v":7.3992843587020358},{"$f":"MAX(G4-$L$9*$L$6*I4,0)","v":30.029771579626889},{"$f":"C5+D5","v":37.429055938328922},{"$f":"B5*E5","v":7.4858111876657851},{"$f":"(1-B5)*E5","v":29.943244750663141},{"$f":"H4+$L$9*$L$1*F4*(1-EXP(-0.5*($L$7/($L$8*(1+0.5*(J4/(F4+0.000001)))))^2))","v":4.4946015242326993},{"$f":"MAX(I4-$L$9*$L$5*G4,0)","v":20.630958701017768},{"$f":"I5*EXP(-G5/(I5+0.000001))","v":4.8327636799113751},null,0.1,"Supp kills Flak"]
[4,0.2,{"$f":"MAX(F5+$L$9*($L$4-$L$3*J5),0)","v":7.3441730036702166},{"$f":"MAX(G5-$L$9*$L$6*I5,0)","v":29.530625576642784},{"$f":"C6+D6","v":36.874798580312998},{"$f":"B6*E6","v":7.3749597160625999},{"$f":"(1-B6)*E6","v":29.4998388642504},{"$f":"H5+$L$9*$L$1*F5*(1-EXP(-0.5*($L$7/($L$8*(1+0.5*(J5/(F5+0.000001)))))^2))","v":6.3551918815510335},{"$f":"MAX(I5-$L$9*$L$5*G5,0)","v":17.636634225951454},{"$f":"I6*EXP(-G6/(I6+0.000001))","v":3.3112730106090864},null,0.02,"Flak kills Supp"]
[5,0.2,7.3093960655321455,29.14710617973137,36.456502245263515,7.2913004490527031,29.165201796210813,8.4464830307391559,14.686650339526414,2.0159858482706419,null,100,"Lethal Radius (meters)"]
[6,0.2,7.2905011566391709,28.871468789420284,36.161969946059457,7.232393989211892,28.929575956847568,10.780977960444945,11.770130159905333,1.007714072957173,null,100,"Firing Error (meters)"]
[7,0.2,7.2820082855640331,28.694173353649461,35.976181639213493,7.1952363278426992,28.780945311370797,13.341412665915309,8.8771725642205759,0.3469251291414972,null,1,"delta"]
[8,0.2,7.2778900713856247,28.603401860086386,35.881291931472013,7.1762583862944034,28.705033545177614,16.069802994473577,5.9990780330834959,5.012171568186255E-2]
[9,0.2,7.27375230051031,28.585051984515943,35.858804285026253,7.1717608570052507,28.687043428021003,18.87829342931057,3.1285746785657342,3.259441112955722E-4]
[10,0.2,7.2717445597996857,28.624471934449687,35.896216494249373,7.1792432988498751,28.7169731953995,21.700062597126731,0.25987033576363361,2.6498833037462903E-49]
[11,0.2,7.2792432988498748,28.711775788684228,35.991019087534106,7.1982038175068217,28.792815270027287,24.524874721687688,0,0]
[12,0.2,7.2982038175068213,28.792815270027287,36.091019087534107,7.2182038175068222,28.872815270027289,27.3571472290161,0,0]
[13,0.2,7.3182038175068218,28.872815270027289,36.191019087534109,7.2382038175068217,28.952815270027287,30.197289123150259,0,0]
[14,0.2,7.3382038175068214,28.952815270027287,36.29101908753411,7.2582038175068222,29.032815270027289,33.04530040409017,0,0]
[15,0.2,7.3582038175068218,29.032815270027289,36.391019087534112,7.2782038175068227,29.112815270027291,35.901181071835822,0,0]
[16,0.2,7.3782038175068223,29.112815270027291,36.491019087534113,7.2982038175068231,29.192815270027292,38.764931126387225,0,0]
[17,0.2,7.3982038175068228,29.192815270027292,36.591019087534114,7.3182038175068236,29.272815270027294,41.636550567744372,0,0]
[18,0.2,7.4182038175068232,29.272815270027294,36.691019087534116,7.3382038175068232,29.352815270027293,44.516039395907271,0,0]
[19,0.2,7.4382038175068228,29.352815270027293,36.791019087534117,7.3582038175068236,29.432815270027294,47.403397610875913,0,0]
[20,0.2,7.4582038175068233,29.432815270027294,36.891019087534119,7.3782038175068241,29.512815270027296,50.298625212650308,0,0]
[21,0.2,7.4782038175068237,29.512815270027296,36.99101908753412,7.3982038175068245,29.592815270027298,53.201722201230446,0,0]
[22,0.2,7.4982038175068242,29.592815270027298,37.091019087534121,7.418203817506825,29.6728152700273,56.112688576616335,0,0]
[23,0.2,7.5182038175068246,29.6728152700273,37.191019087534123,7.4382038175068246,29.752815270027298,59.031524338807969,0,0]
[24,0.2,7.5382038175068242,29.752815270027298,37.291019087534124,7.458203817506825,29.8328152700273,61.958229487805355,0,0]
[25,0.2,7.5582038175068247,29.8328152700273,37.391019087534126,7.4782038175068255,29.912815270027302,64.892804023608477,0,0]
[26,0.2,7.5782038175068251,29.912815270027302,37.491019087534127,7.498203817506826,29.992815270027304,67.835247946217351,0,0]
[27,0.2,7.5982038175068256,29.992815270027304,37.591019087534129,7.5182038175068264,30.072815270027306,70.785561255631976,0,0]
[28,0.2,7.6182038175068261,30.072815270027306,37.69101908753413,7.538203817506826,30.152815270027304,73.743743951852352,0,0]
[29,0.2,7.6382038175068256,30.152815270027304,37.791019087534131,7.5582038175068265,30.232815270027306,76.709796034878465,0,0]
[30,0.2,7.6582038175068261,30.232815270027306,37.891019087534133,7.5782038175068269,30.312815270027308,79.68371750471033,0,0]

{"sheet":"Atlantic","index":9,"n_rows":42,"n_cols":11,"rows_kept":42,"cut":false,"hidden":false,"merged":[]}
["time(days)",".5mer_snk","subs","escorts"]
[0,0,50,100,null,null,null,null,null,0.01,"prob any given pack attacks any given convoy"]
[{"$f":"A2+$J$12","v":50},{"$f":"B2+5*$J$12*$J$6*$J$6*$J$3*$J$2*$J$4*C2/(D2*$J$5)","v":25},{"$f":"C2+$J$12*($J$10-C2*($J$9/$J$5+D2*(2*$J$2*$J$4/(100*$J$3*$J$5))))","v":82.6},{"$f":"D2+$J$12*($J$11-C2*D2*(2*$J$4*$J$2/(500*$J$3*$J$5)))","v":124.92},null,null,null,null,null,50,"cycle time for escort"]
[{"$f":"A3+$J$12","v":100},{"$f":"B3+5*$J$12*$J$6*$J$6*$J$3*$J$2*$J$4*C3/(D3*$J$5)","v":58.061159141850787},113.47052864,149.75490572800001,null,null,null,null,null,20,"patrol time for submarine in days"]
[150,95.946572006420524,142.57228602884885,174.48302143488979,null,null,null,null,null,50,"cycle time for submarine in days"]
[200,136.80220508073981,169.87927912855946,199.08499834306269,null,null,null,null,null,1,"rate at which convoys leave USA"]
[250,179.46721764884501,195.37847468311068,223.5438716870014,null,null,null,null,null,40,"convoy size"]
[300,223.16747058100165,219.06928284178917,247.84506111620198,null,null,null,null,null,4,"wolf-pack size"]
[350,267.36227556424046,240.96289234454915,271.97633727948829,null,null,null,null,null,0.04,"non-escort probability of sub loss per cycle"]
[400,311.66077865367117,261.08148026035582,295.927758001406,null,null,null,null,null,0.7,"submarine rate of production"]
[450,355.77314614896972,279.45732048121073,319.69157788765983,null,null,null,null,null,0.5,"escort rate of production"]
[500,399.48047843587352,296.13181552301063,343.26213545986951,null,null,null,null,null,50,"time interval (days)"]
[550,442.61541598531829,311.15447575216729,366.6357220298849]
[600,485.04915294218864,324.58186905166252,389.8104364958013,null,"The Battle of the Atlantic as Lanchester equations"]
[650,526.68244936820145,336.47656228530388,412.78603009494287,null,"The update equations in cols B:D are based on "]
[700,567.43922621550814,346.9060738446322,435.56374490509097,null,"statistics about convoy engagements from WWII."]
[750,607.26187880109273,355.94185419851971,458.14614956662552,null,"Change the green inputs to see how things might"]
[800,646.1077639553406,363.65830883292637,480.53697532709504,null,"have gone with different data or starting point."]
[850,683.94650764258643,370.13187537727805,502.7409551066288]
[{"$f":"A19+$J$12","v":900},720.75789844113149,375.44016415878048,524.76366786594747]
[950,756.53020768708029,379.66116898377686,546.61139014421701]
[1000,791.25882621107485,382.87255267546573,568.29095623442504]
[1050,824.9451402791741,385.15100984237864,589.8096280892114]
[1100,857.59559150104894,386.57170753881809,611.17497570723833]
[1150,889.22088073114924,387.20780292013393,632.39476844381204]
[1200,919.83528665618314,387.13003569394334,653.476877421935]
[1250,949.45607731225266,386.40639211566395,674.42918899183064]
[1300,978.10299817679015,385.10183645857126,695.25952899733738]
[1350,1005.7978243817573,383.27810528565271,715.9755974544222]
[1400,1032.5639674352608,380.99355944037904,736.58491312765273]
[1450,1058.4261289220215,378.30308843215693,757.09476740153139]
[1500,1083.409995190874,375.25806179536465,777.51218678163013]
[1550,1107.541968179534,371.90632202483408,797.84390332188696]
[1600,1130.8489283804188,368.29221381309031,818.09633225573691]
[1650,1153.3580265936816,364.45664451505991,838.27555610663558]
[1700,1175.0965016010989,360.43717102584787,858.38731456491359]
[1750,1196.0915212682139,356.26810856031381,878.43699944001355]
[1800,1216.3700448724921,351.98065715550996,898.42965402753532]
[1850,1235.9587046845113,347.60304206668081,918.36997626701361]
[{"$f":"A39+$J$12","v":1900},1254.8837050138784,343.16066458456402,938.26232510712373]
[{"$f":"A40+$J$12","v":1950},1273.1707370837946,338.67626015810794,958.11072953850908]
[{"$f":"A41+$J$12","v":2000},1290.844908226896,334.17006105598693,977.91889979934979]

{"sheet":"Control","index":10,"n_rows":23,"n_cols":10,"rows_kept":23,"cut":false,"hidden":false,"merged":[]}
[]
["Time","Merchants","Subs","Escorts","MOE1","MOE2","MerFrac"]
[0,50,15,8,{"$f":"3*C3-B3-D3","v":-13},{"$f":"3*C3+($B$3-B3)+($D$3-D3)","v":45},0.2,null,2,"Merchants lost/Sub/Day"]
[{"$f":"A3+$I$6","v":0.1},{"$f":"MAX(B3-$I$6*$I$3*C3*G3,0)","v":49.4},{"$f":"MAX(C3-$I$6*$I$4*D3,0)","v":14.2},{"$f":"MAX(D3-$I$6*$I$5*C3*(1-G3),0)","v":7.4},{"$f":"3*C4-B4-D4","v":-14.200000000000005},{"$f":"3*C4+($B$3-B4)+($D$3-D4)","v":43.8},0.2,null,1,"Subs lost/Escort/Day"]
[{"$f":"A4+$I$6","v":0.2},{"$f":"MAX(B4-$I$6*$I$3*C4*G4,0)","v":48.832000000000001},{"$f":"MAX(C4-$I$6*$I$4*D4,0)","v":13.459999999999999},{"$f":"MAX(D4-$I$6*$I$5*C4*(1-G4),0)","v":6.8320000000000007},-15.284000000000006,42.715999999999994,0.2,null,0.5,"Escorts lost/Sub/Day"]
[0.30000000000000004,48.293599999999998,12.7768,6.2936000000000005,-16.256800000000002,41.743200000000002,0.2,null,0.1,"Delta"]
[0.4,47.782527999999999,12.14744,5.7825280000000001,-17.122736000000003,40.877263999999997,0.2]
[0.5,47.296630399999998,11.5691872,5.2966303999999997,-17.885699199999998,40.114300800000002,0.2]
[0.6,46.833862912000001,11.039524159999999,4.8338629119999998,-18.549153344000004,39.450846655999996,0.2]
[0.7,46.392281945600004,10.556137868799999,4.3922819455999997,-19.11615028480001,38.883849715199993,0.2]
[0.79999999999999993,45.970036430848005,10.116909674239999,3.9700364308479998,-19.58934383897601,38.410656161023994,0.2]
[0.89999999999999991,45.565360043878407,9.7199060311551992,3.5653600438783997,-19.971001994291207,38.028998005708793,0.2]
[0.99999999999999989,45.176563802632202,9.3633700267673596,3.1765638026321916,-20.263017524962315,37.736982475037692,0.2]
[1.0999999999999999,44.802029001561507,9.0457136465041401,2.8020290015614973,-20.466917063610584,37.53308293638942,0.2]
[1.2,44.440200455701344,8.7655107463479904,2.4402004557013317,-20.583868672358705,37.416131327641295,0.2]
[1.3,44.089580025847425,8.5214907007778571,2.089580025847412,-20.614687949361265,37.385312050638731,0.2]
[1.4000000000000001,43.748720397816314,8.3125326981931167,1.7487203978162977,-20.559842701053263,37.440157298946737,0.2]
[1.5000000000000002,43.416219089888592,8.1376606584114874,1.4162190898885729,-20.419456204542705,37.580543795457295,0.2]
[1.6000000000000003,43.090712663552132,7.9960387494226302,1.0907126635521134,-20.193309078836357,37.806690921163643,0.2]
[1.7000000000000004,42.770871113575225,7.8869674830674192,0.77087111357520821,-19.880839777948175,38.119160222051825,0.2]
[1.8000000000000005,42.455392414252529,7.8098803717098981,0.45539241425251142,-19.481143713375346,38.518856286624654,0.2]
[1.9000000000000006,42.142997199384133,7.764341130284647,0.14299719938411548,-18.99297100791431,39.007028992085694,0.2]
[{"$f":"A22+$I$6","v":2.0000000000000004},41.832423554172749,7.7500414103462356,0,-18.582299323134041,39.417700676865962,0.2]

{"sheet":"SquareLawRnd","index":11,"n_rows":2000,"n_cols":22,"rows_kept":2000,"cut":false,"hidden":false,"merged":[]}
["time","x","y",null,null,null,null,"delta",1E-3,null,null,"time","x_det","y_det"]
[0,10,8,"Final difference x-y :",null,{"$f":"B2000-C2000","v":7},null,"alpha",1,null,null,{"$f":"A2","v":0},{"$f":"B2","v":10},{"$f":"C2","v":8}]
[{"$f":"A2+delta","v":1E-3},{"$f":"IF(RAND()<(beta*C2*delta),MAX(B2-1,0),B2)","v":10},{"$f":"IF(RAND()<(alpha*B2*delta),MAX(C2-1,0),C2)","v":8},null,null,null,null,"beta",2,null,null,{"$f":"A3","v":1E-3},{"$f":"MAX(0,M2-delta*beta*N2)","v":9.984},{"$f":"MAX(0,N2-delta*alpha*M2)","v":7.99}]
[2E-3,10,8,null,null,null,null,null,null,null,null,2E-3,{"$f":"MAX(0,M3-delta*beta*N3)","v":9.9680199999999992},{"$f":"MAX(0,N3-delta*alpha*M3)","v":7.980016}]
[3.0000000000000001E-3,10,8,null,null,null,null,null,null,null,null,3.0000000000000001E-3,9.9520599679999986,7.9700479800000004]
[4.0000000000000001E-3,10,8,null,null,null,null,null,null,null,null,4.0000000000000001E-3,9.936119872039999,7.9600959200320007]
[5.0000000000000001E-3,10,8,null,null,null,null,null,null,null,null,5.0000000000000001E-3,9.9201996801999357,7.9501598001599607]
[6.0000000000000001E-3,10,8,null,null,null,null,null,null,null,null,6.0000000000000001E-3,9.9042993605996159,7.9402396004797611]
[7.0000000000000001E-3,10,8,null,null,null,null,null,null,null,null,7.0000000000000001E-3,9.8884188813986569,7.9303353011191611]
[8.0000000000000002E-3,10,8,null,null,null,null,null,null,null,null,8.0000000000000002E-3,9.8725582107964183,7.9204468822377621]
[9.0000000000000011E-3,10,8,null,null,null,null,null,null,null,null,9.0000000000000011E-3,9.8567173170319435,7.9105743240269657]
[1.0000000000000002E-2,10,8,null,null,null,null,null,null,null,null,1.0000000000000002E-2,9.8408961683838889,7.9007176067099341]
[1.1000000000000003E-2,10,8,null,null,null,null,null,null,null,null,1.1000000000000003E-2,9.8250947331704683,7.8908767105415505,null,null,null,null,null,null,null,{"$f":"MAX(1,2)","v":2}]
[1.2000000000000004E-2,10,8,null,null,null,null,null,null,null,null,1.2000000000000004E-2,9.8093129797493859,7.8810516158083797]
[1.3000000000000005E-2,10,8,null,null,null,null,null,null,null,null,1.3000000000000005E-2,9.7935508765177683,7.8712423028286302]
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[5.0000000000000037E-2,10,7,null,"This sheet shows a probabilistic interpretation of ",null,null,null,null,null,null,5.0000000000000037E-2,9.2238818776579183,7.5192152858586807]
[5.1000000000000038E-2,10,7,null,"Lanchester's Square Law.  Press F9 to resample and",null,null,null,null,null,null,5.1000000000000038E-2,9.2088434470862008,7.5099914039810232]
[5.2000000000000039E-2,10,7,null,"see the extent to which results vary.  The final net",null,null,null,null,null,null,5.2000000000000039E-2,9.193823464278239,7.5007825605339367]
[5.300000000000004E-2,10,7,null,"difference of survivors is sometimes positive and",null,null,null,null,null,null,5.300000000000004E-2,9.1788218991571711,7.4915887370696588]
[5.4000000000000041E-2,10,7,null,"sometimes negative.  Use SimSheet to see a ",null,null,null,null,null,null,5.4000000000000041E-2,9.1638387216830317,7.4824099151705017]
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{"sheet":"Endgame","index":13,"n_rows":24,"n_cols":16,"rows_kept":24,"cut":false,"hidden":false,"merged":[]}
[null,null,null,null,null,"Blue Survivors (x or n) "]
[null,null,0,1,2,3,4,5,6,7,8,9,10,null,"beta:  y (or Red or m) lethality",1]
[null,0,"MOE",0,0,0,0,0,0,0,0,0,0,null,"alpha: x (or Blue or n) lethality",1]
[null,1,1,{"$f":"leftprob($B4,D$2,alpha,beta)*C4+(1-leftprob($B4,D$2,alpha,beta))*D3","v":0.5},{"$f":"leftprob($B4,E$2,alpha,beta)*D4+(1-leftprob($B4,E$2,alpha,beta))*E3","v":0.16666666666666666},4.1666666666666664E-2,8.3333333333333332E-3,1.3888888888888887E-3,1.9841269841269839E-4,2.4801587301587298E-5,2.7557319223985884E-6,2.7557319223985883E-7,2.5052108385441714E-8]
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[null,4,1,0.9916666666666667,0.91944444444444451,0.73968253968253972,0.5,0.28479111552028219,0.13890156525573191,5.9076930014430012E-2,2.2275583213083212E-2,7.5511800121175121E-3,2.3281538007480468E-3]
[null,5,1,0.99861111111111112,0.97599206349206358,0.88737599206349216,0.71520888447971787,0.5,0.3030372174122174,0.1607270497635081,7.552614727093894E-2,3.1827954033125168E-2,1.2161420544873755E-2]
[null,6,1,0.9998015873015873,0.99384920634920637,0.95835813492063493,0.86109843474426806,0.69696278258778255,0.5,0.31731456525727358,0.17914975497936808,9.0756674411622343E-2,4.1634640744904479E-2]
["R",7,1,0.99997519841269844,0.99861386684303355,0.98653714726631403,0.94092306998556996,0.83927295023649195,0.68268543474272647,0.5,0.32887986932232965,0.19493557218505678,0.10475855369084953]
["e",8,1,0.99999724426807757,0.99972056878306881,0.99612509018759021,0.97772441678691679,0.92447385272906113,0.82085024502063209,0.6711201306776704,0.5,0.33849530292150065,0.20864155334891671]
["d",9,1,0.99999972442680773,0.99994896885521878,0.99899299918831153,0.99244881998788237,0.96817204596687478,0.90924332558837762,0.80506442781494325,0.66150469707849935,0.5,0.34665344913100882]
[null,10,1,0.99999997494789161,0.99999147393244614,0.99976105668379978,0.99767184619925198,0.98783857945512632,0.95836535925509558,0.89524144630915048,0.79135844665108335,0.65334655086899129,0.5]
["S",11,1,0.9999999979123243,0.99999868653080459,0.99994776584930356,0.99934085394262318,0.99574639316528046,0.98255308707933287,0.9485985601131508,0.88239219655017509,0.77932165599364245,0.64631134361571752]
["u",12,1,0.99999999983940957,0.99999981222389467,0.99998940294897642,0.99982726569738811,0.99862700907029767,0.99326903507330933,0.97681149166693515,0.93904377362023117,0.87059143749455026,0.76864594027689903]
["r",13,1,0.99999999998852929,0.99999997495324466,0.99999799270244427,0.99995782164243097,0.99958815148350499,0.99759264103818013,0.99031923875824435,0.9707857282294774,0.92979715474700719,0.85973140932522107]
["v",14,1,0.99999999999923528,0.99999999686848651,0.99999964319212609,0.99999034951441601,0.99988450792733419,0.99919694786058799,0.99623771149314022,0.9869824448518083,0.96460559220210351,0.92090801600340255]
["I",15,1,0.99999999999995226,0.99999999963154451,0.99999994022497474,0.999997921128015,0.99996956782784474,0.9997488192657713,0.9986316486108433,0.99457975165117896,0.98333944185777566,0.95836687151602651]
["v",16,1,0.99999999999999722,0.99999999995905808,0.99999999052736066,0.99999957664749151,0.99999243169043273,0.99992599193825238,0.99953206136034523,0.99788129145728977,0.99264622560146476,0.97946185864552693]
["o",17,1,0.99999999999999989,0.99999999999569023,0.99999999857544086,0.99999991820821243,0.99999821672689881,0.99997937547768667,0.99984890886012878,0.99921927129122035,0.99694398624476643,0.99046912417097399]
["r",18,1,1,0.99999999999956901,0.9999999997961222,0.99999998496195674,0.99999960056303117,0.9999945442916951,0.99995376637085653,0.99972776788481466,0.99879984067146532,0.99582458477843261]
["s",19,1,1,0.99999999999995892,0.99999999997216293,0.99999999736169232,0.99999991469530458,0.99999862579843823,0.99998654826024314,0.99990987259344954,0.99955307661852599,0.99826738977711449]
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["(y or m)"]