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{"sheet":"Tabelle1","index":0,"n_rows":214,"n_cols":114,"rows_kept":214,"cut":false,"hidden":false,"merged":[]}
[null,"Quelle der Formeln: wikipedia.org/wiki/Great-circle_navigation",null,null,null,null,null,null,null,null,null,null,"Ingo Mennerich, Januar 2019"]
[null,null,null,null,null,null,null,null,null,null,null,null,"VBA-Code: Philipp Eisenbarth"]
[null,"Wohin, bitte, geht´s nach Neuseeland?",null,null,null,null,null,null,null,null,"Geographische Breite (j)",null,"Südliche Breite negativ!"]
[null,"Großkreisnavigation, Orthodrome = kürzester Weg auf dem Globus",null,null,null,null,null,null,null,null,"GeographischeLänge (l)",null,"Länge westlich Greenwich negativ!"]
[null,null,null,null,"mit Spur"]
[null,"Start",null,null,"ohne Spur",null,"Nach (km)",null,"d (km)=",{"$f":"K29","v":17971.290426203734},null,"Kompasskurs",null,"Start (°)",{"$f":"E62","v":41.762258658125837}]
[null,null,null,"https://en.wikipedia.org/wiki/Equirectangular_projection",null,null,null,null,null,null,null,"https://commons.wikimedia.org/wiki/File:Kompassrose.svg"]
[null,"j1 (°)",50]
[]
[null,"l1 (°)",10]
[]
[null,"Ziel"]
[]
[null,"j2 (°)",-35]
[]
[null,"l2 (°)",175]
[]
[null,"Dl (°)",{"$f":"C42","v":165}]
[]
[null,"Midpoint"]
[]
[null,"j=",{"$f":"E152","v":36.635941271587463}]
[]
[null,"l=",{"$f":"E169","v":134.99999999999994}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"j=",{"$f":"C28","v":50.000000000000007}]
[null,"nach km:",{"$f":"H6","v":0}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"l=",{"$f":"I36","v":10}]
[null,"j=",{"$f":"E187","v":50.000000000000007},null,null,null,null,null,"Zentriwinkel  (°)",null,{"$f":"E86","v":161.43883530022802}]
[null,null,null,null,null,null,null,null,"Distanz Start-Ziel  (km)",null,{"$f":"(K28/360)*K30","v":17971.290426203734},null,null,"Kurs (°) ",{"$f":"E214","v":41.762258658125845}]
[null,"l=",{"$f":"E200","v":10},null,null,null,null,null,"U Äquator (km)",null,40075.019999999997]
[]
[]
[]
[null,"l1 + 360 =",{"$f":"C10+360","v":370},null,null,"Karte"]
[null,null,null,null,null,"Start","Ziel","Midpoint","l / j",null,null,"Plot 1","Plot 2","Plot 3","Plot 4","Plot 5","Plot 6","Plot 7","Plot 8","Plot 9","Plot 10","Plot 11","Plot 12","Plot 13","Plot 14","Plot 15","Plot 16","Plot 17","Plot 18","Plot 19","Plot 20","Plot 21","Plot 22","Plot 23","Plot 24","Plot 25","Plot 26","Plot 27","Plot 28","Plot 29","Plot 30","Plot 31","Plot 32","Plot 33","Plot 34","Plot 35","Plot 36","Plot 37","Plot 38","Plot 39","Plot 40","Plot 41","Plot 42","Plot 43","Plot 44","Plot 45","Plot 46","Plot 47","Plot 48","Plot 49","Plot 50","Plot 51","Plot 52","Plot 53","Plot 54","Plot 55","Plot 56","Plot 57","Plot 58","Plot 59","Plot 60","Plot 61","Plot 62","Plot 63","Plot 64","Plot 65","Plot 66","Plot 67","Plot 68","Plot 69","Plot 70","Plot 71","Plot 72","Plot 73","Plot 74","Plot 75","Plot 76","Plot 77","Plot 78","Plot 79","Plot 80","Plot 81","Plot 82","Plot 83","Plot 84","Plot 85","Plot 86","Plot 87","Plot 88","Plot 89","Plot 90","Plot 91","Plot 92","Plot 93","Plot 94","Plot 95","Plot 96","Plot 97","Plot 98","Plot 99","Plot 100","Plot 101","Plot 102","Plot 103"]
[null,"l2 + 360 =",{"$f":"C16+360","v":535},null,null,{"$f":"C10","v":10},{"$f":"C16","v":175},{"$f":"E169","v":134.99999999999994},{"$f":"IF(AND(G198>180),G198-360,(IF(AND(G198<-180),G198+360,G198)))","v":10},null,"l"]
[null,null,null,null,null,{"$f":"C8","v":50},{"$f":"C14","v":-35},{"$f":"C22","v":36.635941271587463},{"$f":"C28","v":50.000000000000007},null,"j"]
[null,"Dl",{"$f":"IF(C36>C34,C36-C34,-(C34-C36-360))","v":165},"° nach Osten"]
[null,null,null,null,null,"Kompass"]
[null,"Dl",{"$f":"C38-360","v":-195},"° nach Westen",null,"Distanz X",{"$f":"H6","v":0},"Distanz A-B",{"$f":"K29","v":17971.290426203734}]
[null,null,null,null,null,360,{"$f":"O29","v":41.762258658125845},{"$f":"F41*SIN(RADIANS(G41))","v":239.77485816418277},{"$f":"F41*SIN(RADIANS(90-G41))","v":268.52936039164513}]
[null,"Differenz",{"$f":"IF(C40*-1<C38,C40,C38)","v":165},null,null,null,null,{"$f":"F42*SIN(RADIANS(90-G42))","v":0},{"$f":"F42*SIN(RADIANS(G42))","v":0}]
[]
[]
[null,null,"(Zentri)Winkel zwischen P1 und P2"]
[]
[null,null,"cosg = ",null,{"$f":"SIN(RADIANS(C8))*SIN(RADIANS(C14))+COS(RADIANS(C8))*COS(RADIANS(C14))*COS(RADIANS(C16-C10))","v":-0.94798438413149932},null,"cosg = sind1 * sind2 + cosd1 * cosd2 * cosDa"]
[]
[null,null,"g = ",null,{"$f":"DEGREES(ACOS(E47))","v":161.43883530022805},"Grad (Zentriwinkel)"]
[]
[]
[null,null,"Kurswinkel a1 und a2 in P1 und P2"]
[]
[]
[null,null,"Zähler",{"$f":"COS(RADIANS(C14))*SIN(RADIANS(C18))","v":0.21201214989665487}]
[null,null,"Nenner",{"$f":"COS(RADIANS(C8))*SIN(RADIANS(C14))-SIN(RADIANS(C8))*COS(RADIANS(C14))*COS(RADIANS(C18))","v":0.23743726695491663}]
[]
[null,null,null,{"$f":"D55/D56","v":0.89291859115321881}]
[]
[null,null,null,{"$f":"DEGREES(ATAN(D58))","v":41.762258658125837}]
[null,null,null,null,null,null,null,null,null,null,null,"Figure 1. The great circle path between (φ1, λ1) and (φ2, λ2)."]
[null,null,null,"a1",{"$f":"IF(AND(D55<0,D58>0),D60-180,(IF(AND(D55>0,D58<0),D60+180,(IF(AND(D55<0,D58<0),D60,D60)))))","v":41.762258658125837},null,null,null,null,null,null,"Aus Wikipedia, Great Circle Navigation"]
[null,null,null,null,null,"Auf Quadranten achten!!!!"]
[]
[]
[null,null,null,"Zähler",{"$f":"COS(RADIANS(C8))*SIN(RADIANS(C18))","v":0.16636567534280211}]
[null,null,null,"Nenner",{"$f":"-(COS(RADIANS(C14))*SIN(RADIANS(C8))-(SIN(RADIANS(C14))*COS(RADIANS(C8))*COS(RADIANS(C18))))","v":-0.27138177814760406}]
[]
[null,null,null,null,{"$f":"E66/E67","v":-0.61303185673842897}]
[]
[null,null,null,null,{"$f":"DEGREES(ATAN(E69))","v":-31.509623885049162}]
[]
[null,null,null,"a2",{"$f":"IF(AND(E66<0,E69>0),E71-180,(IF(AND(E66>0,E69<0),E71+180,(IF(AND(E66<0,E69<0),E71,E71)))))","v":148.49037611495083}]
[]
[]
[null,null,"Zentriwinkel (s12) zwischen P1 und P2"]
[]
[null,null,"Sigma (s12)"]
[null,null,null,"ZÄHLER",{"$f":"SQRT((COS(RADIANS(C8))*SIN(RADIANS(C14))-SIN(RADIANS(C8))*COS(RADIANS(C14))*COS(RADIANS(C18)))^2+(COS(RADIANS(C14))*SIN(RADIANS(C18)))^2)","v":0.3183168349974943}]
[null,null,null,"NENNER",{"$f":"SIN(RADIANS(C8))*SIN(RADIANS(C14))+COS(RADIANS(C8))*COS(RADIANS(C14))*COS(RADIANS(C18))","v":-0.94798438413149932}]
[]
[null,null,null,null,{"$f":"E79/E80","v":-0.33578278326717576}]
[]
[null,null,"Sigma (s)","s12=",{"$f":"DEGREES(ATAN(E82))","v":-18.561164699771972}]
[]
[null,null,null,null,{"$f":"IF(AND(E79<0,E82>0),E84-180,(IF(AND(E79>0,E82<0),E84+180,(IF(AND(E79<0,E82<0),E84,E84)))))","v":161.43883530022802}]
[]
[]
[]
[]
[null,null,"Kurswinkel a0 im Knoten (Äquator)"]
[]
[null,null,null,"ZÄHLER",{"$f":"SIN(RADIANS(E62))*COS(RADIANS(C8))","v":0.42812307761745566}]
[null,null,null,"NENNER",{"$f":"SQRT(COS(RADIANS(E62))^2+SIN(RADIANS(E62))^2*SIN(RADIANS(C8))^2)","v":0.90372043819499737}]
[]
[null,null,null,"QUOTIENT",{"$f":"E93/E94","v":0.47373397737086342}]
[]
[null,null,null,"ARCTAN",{"$f":"DEGREES(ATAN(E96))","v":25.348504780104349}]
[]
[null,null,null,"a0",{"$f":"IF(AND(E93<0,E96>0),E98-180,(IF(AND(E93>0,E96<0),E98+180,(IF(AND(E93<0,E96<0),E98,E98)))))","v":25.348504780104349}]
[]
[]
[]
[null,null,"Zentriwinkel s01 zwischen A und P1 und Zentriwinkel s02 zwischen P1 und P2"]
[]
[null,null,"Sigma (s)"]
[null,null,null,"ZÄHLER",{"$f":"TAN(RADIANS(C8))","v":1.19175359259421}]
[null,null,null,"NENNER",{"$f":"COS(RADIANS(E62))","v":0.74591488997679212}]
[]
[null,null,null,"QUOTIENT",{"$f":"E107/E108","v":1.5977072030715052}]
[]
[null,null,null,"ARCTAN",{"$f":"DEGREES(ATAN(E110))","v":57.957677724745167}]
[]
[null,null,null,"s01=",{"$f":"IF(AND(E107<0,E110>0),E112-180,(IF(AND(E107>0,E110<0),E112+180,(IF(AND(E107<0,E110<0),E112,E112)))))","v":57.957677724745167}]
[]
[]
[null,null,"Sigma (s)","s02=",{"$f":"E114+E86","v":219.39651302497319}]
[]
[]
[]
[]
[null,null,"Die geographische Länge des Knotens (Überquerung des Äquators)"]
[]
[null,null,null,"ZÄHLER",{"$f":"SIN(RADIANS(E98))*SIN(RADIANS(E114))","v":0.36290128088160167}]
[null,null,null,"NENNER",{"$f":"COS(RADIANS(E114))","v":0.53054554140151589}]
[]
[null,null,null,"QUOTIENT",{"$f":"E124/E125","v":0.68401532491055028}]
[]
[null,null,null,"ARCTAN",{"$f":"DEGREES(ATAN(E124/E125))","v":34.372726102097921}]
[]
[null,null,null,"l01",{"$f":"IF(AND(E124<0,E127>0),E129-180,(IF(AND(E124>0,E127<0),E129+180,(IF(AND(E124<0,E127<0),E129,E129)))))","v":34.372726102097921}]
[]
[]
[]
[null,null,null,"l0",{"$f":"C10-E131","v":-24.372726102097921},null,null,null,null,null,null,"Figure 2. The great circle path between a node (an equator crossing) and an arbitrary point (φ,λ)."]
[null,null,null,null,null,null,null,null,null,null,null,"Aus Wikipedia: Great Circle Navigation"]
[]
[]
[]
[null,null,"Um den Mittelpunkt der Route zu berechnen setze σ = ½(σ1 + σ2) "]
[]
[null,null,null,"Sigma (s)",{"$f":"0.5*(E114+E117)","v":138.67709537485916}]
[]
[null,null,"Breite und Länge des Mittelpunkts"]
[]
[]
[null,null,null,"ZÄHLER",{"$f":"COS(RADIANS(E98))*SIN(RADIANS(E142))","v":0.59672835983138428}]
[null,null,null,"NENNER",{"$f":"SQRT(COS(RADIANS(E142))^2+SIN(RADIANS(E98))^2*SIN(RADIANS(E142))^2)","v":0.80244330925800988}]
[]
[null,null,null,"QUOTIENT",{"$f":"E147/E148","v":0.7436392738860983}]
[]
[null,null,null,"ARCTAN",{"$f":"DEGREES(ATAN(E150))","v":36.635941271587463}]
[]
[null,null,null,"j=",{"$f":"IF(AND(E147<0,E150>0),E152-180,(IF(AND(E147>0,E150<0),E152+180,(IF(AND(E147<0,E150<0),E152,E152)))))","v":36.635941271587463}]
[]
[]
[]
[null,null,null,"ZÄHLER",{"$f":"SIN(RADIANS(E98))*SIN(RADIANS(E142))","v":0.28269049931291346}]
[null,null,null,"NENNER",{"$f":"COS(RADIANS(E142))","v":-0.75100023047344111}]
[]
[null,null,null,null,{"$f":"E158/E159","v":-0.37641865853316903}]
[]
[null,null,null,null,{"$f":"DEGREES(ATAN(E161))","v":-20.627273897902153}]
[]
[null,null,null,null,{"$f":"IF(AND(E158<0,E161>0),E163-180,(IF(AND(E158>0,E161<0),E163+180,(IF(AND(E158<0,E161<0),E163,E163)))))","v":159.37272610209786}]
[]
[null,null,null,null,{"$f":"E135+E165","v":134.99999999999994}]
[]
[null,null,null,"l=",{"$f":"IF(AND(E167>180),E167-360,(IF(AND(E167<-180),E167+360,E167)))","v":134.99999999999994}]
[]
[]
[]
[null,null,"Um den Punkt a mit der Distanz X vom Start zu finden setze s = s01 + d/R"]
[]
[null,null,"Sigma (s)",null,{"$f":"E114+360*H6/K30","v":57.957677724745167},null,"σ = σ01 + d/R"]
[]
[]
[null,"Beliebiger Punkt auf der Strecke mit d=",null,null,{"$f":"H6","v":0},"km"]
[]
[null,null,null,"ZÄHLER",{"$f":"COS(RADIANS(E100))*SIN(RADIANS(E175))","v":0.76604444311897812}]
[null,null,null,"NENNER",{"$f":"SQRT(COS(RADIANS(E175))^2+SIN(RADIANS(E100))^2*SIN(RADIANS(E175))^2)","v":0.64278760968653925}]
[]
[null,null,null,"QUOTIENT",{"$f":"E180/E181","v":1.1917535925942102}]
[]
[null,null,null,"ARCTAN",{"$f":"DEGREES(ATAN(E183))","v":50.000000000000007}]
[]
[null,null,null,"j=",{"$f":"IF(AND(E180<0,E183>0),E185-180,(IF(AND(E180>0,E183<0),E185+180,(IF(AND(E180<0,E183<0),E185,E185)))))","v":50.000000000000007}]
[]
[]
[]
[null,null,null,"ZÄHLER",{"$f":"SIN(RADIANS(E100))*SIN(RADIANS(E175))","v":0.36290128088160167}]
[null,null,null,"NENNER",{"$f":"COS(RADIANS(E175))","v":0.53054554140151589}]
[]
[null,null,null,"QUOTIENT",{"$f":"E191/E192","v":0.68401532491055028}]
[]
[null,null,null,"ARCTAN",{"$f":"DEGREES(ATAN(E194))","v":34.372726102097921}]
[]
[null,null,null,null,{"$f":"IF(AND(E191<0,E194>0),E196-180,(IF(AND(E191>0,E194<0),E196+180,(IF(AND(E191<0,E194<0),E196,E196)))))","v":34.372726102097921},null,{"$f":"IF(AND(E200>180),E200-360,IF(AND(E187<0),E200+360,E200))","v":10}]
[]
[null,null,null,"l=",{"$f":"E135+E198","v":10}]
[]
[]
[]
[null,null,null,"Kurswinkel a an Punkt a mit Distanz d"]
[null,null,null,"a"]
[]
[null,null,null,"ZÄHLER",{"$f":"TAN(RADIANS(E100))","v":0.47373397737086342}]
[null,null,null,"NENNER",{"$f":"COS(RADIANS(E175))","v":0.53054554140151589}]
[]
[null,null,null,"QUOTIENT",{"$f":"E207/E208","v":0.89291859115321903}]
[]
[null,null,null,"ARCTAN",{"$f":"DEGREES(ATAN(E210))","v":41.762258658125845}]
[]
[null,null,null,"a",{"$f":"IF(AND(E207<0,E210>0),E212-180,(IF(AND(E207>0,E210<0),E212+180,(IF(AND(E207<0,E210<0),E212,E212)))))","v":41.762258658125845}]