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[]
[null,"Arbeitsdiagramm für Manson-Heissluft-Motor ( berücksichtigt Toträumen in der Maschine)"]
[null,"Eingabe-Grösse / Input parameter","Symbol","input"," "," "," "," ",null,null,null,null,null,"B"]
[null,"Durchmesser Arbeitskolben /-stange  (kalte Seite)","D1 [mm]",7.9," "," "," "," "]
[null,{"$f":"Value!A6","v":"Durchmesser desVerdrägerkolbens (warme Seite)"},"D2 [mm]",17.600000000000001," "," "," "," "]
[null,"Zylinderdurchmesser","DC [mm] ≥ D2",18.2]
[null,"Durchmesser der Steuerleitung","DV [mm] < D1",2]
[null,{"$f":"Value!A9","v":"Länge des Zylinders"},"LC [mm] ≥ LP+2*r",43]
[null," Länge des Verdrängerkolbens","LP  [mm] ",23," "," "," "," "]
[null," Länge der Steuerleitung","LV [mm] ",22.5]
[null,"Kurbelradius","r [mm]",10," "," "," "," "]
[null,"Pleuelstangenlänge","l [mm]  > 2*r",43," "," "," "," "]
[]
[null," Temperatur der Umgebung","Tu    [°C] ",20," "," "," "," "]
[null,"Temperaturänderung der kalten Seite im Betrieb","DTu    [°C] ",60]
[null,"Temperatur Arbeitsseite          (kalte Seite)","T1=Tmin [°C]",{"$f":"D14+D15","v":80}," "," "," "," "]
[null,"Temperatur Verdängerseite      (warme Seite)","T2=Tmax >T1 [°C]",300," "," "," "," "]
[null," "," "," "," "," "," "," "]
[null,"atmosphärischer Druck bei offenen Steueröffnungen","patm [105Pa=bar] ",1.0129999999999999," "," "," "," "]
[null,"Drehzahl (geschätzt / Annahme / Erfahrungswert)","n [1/min]",500," "," "," "," "]
[null,null," "," "," "," "," "," "]
[null,"Dichte der Luft","r [kg/m³]",1.2929999999999999]
[null,"allgemeine Gaskonstante","Rs [J/mol/°K]",8.3140000000000001]
[null,"spezielle Gaskonstante","Rs [m²/s²/°K]",287]
[null,"spez. Wärmekapazität (V=const)","Cv [ J/kg/K] ]",740]
[null,"spez. Wärmekapazität (p=const)","Cp [J/kg/°K ]",1025]
[null,"molare Masse der Luft","Mmol [kg/mol]",2.896E-2]
[]
[null,"Ausgangswinkel für Umlauf","j0  [-°]",0]
[null,"Schrittweite","Dj [-°]  ≥ 1",1," "]
[null,"Laufindex für Kurbelwinkel","i [-]",0," "]
[null," Kurbelwinkel aktuell","j    [-°]",{"$f":"D31*D30","v":0}," "]
[]
[null,"Ergebnisse / results"]
[null,"Wirkungsgrad des Motors","h  [-]",{"$f":"Calc!L60","v":4.3560924715851219E-2}]
[null,"zugeführte Energie pro Umdrehung (Zylinder)","Q [kg*m²/s²=Nm]",{"$f":"Calc!J57","v":0.49921655706777973}]
[null,"Arbeit pro Umdrehung (Zylinder)","W [kg*m²/s²=Nm]",{"$f":"Calc!L57","v":2.1746334859335997E-2}]
[null,"Motorleistung (Zylinder)","Pe [W ]",{"$f":"Calc!J60","v":0.18121945716113333}]
[null,"Wellenleistung (Kurbelwelle) / Wirkungsgrad an der Welle","PS [W]",{"$f":"Calc!V34","v":0.18020159703654459},{"$f":"D39/D38*E35*100","v":0}]
[null,"mittleres Wellenmoment ","Mt [Nm]",{"$f":"Calc!J61","v":"Mt [kgm²/s²]"}]
[null,"Fläche des Arbeitskolbens","A3 [m²] = p/4*D12",{"$f":"Value!E33","v":4.901669937763475E-5}]
[null,"maximaler Kolbenweg (Hub)","smax [m]",{"$f":"2*D11/1000","v":0.02}]
[null,"maximaler Druck                                                                                                                                      für die Umrechnung der dim.-losen Diagrammwerte auf absolute Druckwerte","pmax[105Pa=bar] ",{"$f":"Calc!I19/10^5","v":1.2609876646149292},"for Diagram 1"]
[null,"mittlerer Druck 0° ≤ j ≤ 180°","pm1 [105Pa=bar] ",{"$f":"Calc!$I$41","v":1.1279575902868695}]
[null,"athmosphärischer Druck","patm [105Pa=bar] ",{"$f":"D19","v":1.0129999999999999}]
[null,"mittlerer Druck 180° ≤ j ≤ 360°","pm2 [105Pa=bar] ",{"$f":"Calc!$I$45","v":0.90613181320018976}]
[null,"mittlerer Druck 0° ≤ j ≤ 360°","pm [105Pa=bar] ",{"$f":"(D44+D46)/2","v":1.0170447017435296},"for Diagram 54"]
[null,"Vorschlag zur Optimierung des Wirkungsgrades aus der Berechnung ohne Toträume / 1. Schritt für Näherung"]
[null,"Arbeitskolbendurchmesser (kalt) Metode 1","D1 [mm]",{"$f":"Optimierung!D36","v":8.2038279576556974},"[D2, DT]=const"]
[null,"Arbeitskolbendurchmesser (kalt) Metode 2","D1 [mm]",{"$f":"Optimierung!D37","v":0},"[D2, DT]=const"]
[null,"Arbeitskolbendurchmesser (kalt) Metode 3","D1 [mm]",{"$f":"Optimierung!D38","v":0},"[D2, DT]=const"]
[null,"Arbeitskolbendurchmesser (kalt)           für  [D2, T1,T2]=const","D1 [mm]",{"$f":"Opti!B11*1000","v":7.898169055353911}]
[null,"Nur sinnvolle Vorgaben führen zu einem vernünftigen Ergebnis."]
[null,"Prüfe deshalb Deine Angaben und das Diagramm auf Plausibilität!"]
[null,"Sensible inputs lead to a rational result only."]
[null,"Therefor check your inputs and the diagram for plausibility!"]

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[" "," ",null," "," "]
[" "]
[" "," ",null,"Eingabe","Umrechnung Rechenwert"]
["Eingabe-Grösse","Symbol",null,"Wert","Wert"]
["Durchmesser Arbeitskolben /-stange  (kalte Seite)","D1 [mm]","x 10-3 ®",{"$f":"Base!D4","v":7.9},{"$f":"D5/1000","v":7.9000000000000008E-3}]
[{"$f":"IF(D6>D7,\"Durchmesser des Verdrägerkolbens # zu groß # (warme Seite)\",\"Durchmesser desVerdrägerkolbens (warme Seite)\")","v":"Durchmesser desVerdrägerkolbens (warme Seite)"},"D2 [mm]","x 10-3 ®",{"$f":"Base!D5","v":17.600000000000001},1.7600000000000001E-2]
["Zylinderdurchmesser","DC [mm]","x 10-3 ®",{"$f":"Base!D6","v":18.2},1.8200000000000001E-2]
["Durchmesser der Steuerleitung","DV [mm]","x 10-3 ®",{"$f":"Base!D7","v":2},2E-3]
[{"$f":"IF(Base!D8<Base!D9+2*Base!D11, \"Länge des Zylinders     # zu kurz #\", \"Länge des Zylinders\")","v":"Länge des Zylinders"},"LC [mm]","x 10-3 ®",{"$f":"Base!D8","v":43},4.2999999999999997E-2]
[" Länge des Verdrängerkolbens","LP [mm] ","x 10-3 ®",{"$f":"Base!D9","v":23},2.3E-2]
[" Länge der Steuerleitung","LV [mm]","x 10-3 ®",{"$f":"Base!D10","v":22.5},2.2499999999999999E-2]
["Kurbelradius","r [mm]","x 10-3 ®",{"$f":"Base!D11","v":10},0.01]
["Pleuelstangenlänge","l [mm]","x 10-3 ®",{"$f":"Base!D12","v":43},4.2999999999999997E-2]
[]
[" Temperatur der Umgebung","Tu    [°C] ",".+273  ®",{"$f":"Base!D14","v":20},{"$f":"D15+273","v":293}]
["Temperaturänderung der kalten Seite im Betrieb","DTu    [°C] ","  ®",{"$f":"Base!D15","v":60},{"$f":"D16","v":60}]
["Temperatur Varbeitsseite          (kalte Seite)","T1=Tmin [°C]","Tu+DT+273  ®",{"$f":"Base!D16","v":80},{"$f":"D15+E16+273","v":353}]
["Temperatur Verdängerseite      (warme Seite)","T2=Tmax [°C]",".+273  ®",{"$f":"Base!D17","v":300},{"$f":"D18+273","v":573}]
[" "," "," ",{"$f":"Base!D18","v":" "}]
["atmosphärischer Druck bei offenen Steueröffnungen","patm [105Pa=bar] ","x 105 ®",{"$f":"Base!D19","v":1.0129999999999999},{"$f":"D20*10^5","v":101299.99999999999}]
["Drehzahl (geschätzt / Annahme / Erfahrungswert)","n [1/min]","x1/60 ®",{"$f":"Base!D20","v":500},{"$f":"D21/60","v":8.3333333333333339}]
["Winkelschwindigkeit","w [1/s]","p*n/30",{"$f":"PI()*D21/30","v":52.359877559829883},{"$f":"PI()*D21/30","v":52.359877559829883}]
[" "," "," ",{"$f":"Base!D21","v":" "}," "]
["spezifische Gaskonstante für Luft","Rs [m²/s²/°K]",".-.",{"$f":"Base!D24","v":287},287]
["spez. Wärmekapazität (V=const)","Cv [ J/kg/K] ]",".-.",{"$f":"Base!D25","v":740},{"$f":"D25","v":740}]
["spez. Wärmekapazität (p=const)","Cp [J/kg/°K ]",".-.",{"$f":"Base!D26","v":1025},{"$f":"D26","v":1025}]
["molale masse der Luft","Mmol [kg/mol]",".-.",{"$f":"Base!$D$27","v":2.896E-2},{"$f":"D27","v":2.896E-2}]
["Rechengrößen"]
["Pleuelverhältnis","l [-]"," r / l",{"$f":"D12/D13","v":0.23255813953488372},{"$f":"E12/E13","v":0.23255813953488375}]
["Kolbenhub"," smax[mm]","2 ∙r ",{"$f":"2*D12","v":20},{"$f":"2*E12","v":0.02}]
["Fläche der Arbeitsseite 1       (kalte Seite)","A1 [mm²]","p∙(D22-D12)/4",{"$f":"PI()/4*(D6^2-D5^2)","v":194.26823571635887},{"$f":"PI()*(E6^2-E5^2)/4","v":1.9426823571635886E-4}]
["Fläche der Verdrängerseite 2 (warme Seite) ","A2 [mm²]","p∙D22/4",{"$f":"PI()/4*D6^2","v":243.28493509399362},{"$f":"PI()*E6^2/4","v":2.4328493509399358E-4}]
["Kolbenstangenfläche ","A3 [mm²]","p∙D12/4",{"$f":"PI()/4*D5^2","v":49.016699377634751},{"$f":"PI()*E5^2/4","v":4.901669937763475E-5}]
["Maximum des variablen Volumens der Arbeitsseite (kalt)","V01max [mm³]","A1∙smax=A1·2·r",{"$f":"D31*D30","v":3885.3647143271774},{"$f":"E31*2*E12","v":3.8853647143271773E-6}]
["Maximum des variblen Volumens der Verdrängerseite (heiss)","V02max  [mm³]","A2∙smax=A2·2·r",{"$f":"D32*D30","v":4865.6987018798727},{"$f":"E32*2*E12","v":4.8656987018798717E-6}]
["Totvolumen der Arbeitsseite (kalt)","Vd1 [mm³]",null,{"$f":"PI()/4*((D6^2-D5^2)*(D9-D10-2*D12)/2+(D7^2-D6^2)*D9/2+D8^2*(D11-D10))","v":361.14178349341307},{"$f":"D36/10^9","v":3.6114178349341308E-7}]
["Totvolumen der Verdrängerseite (heiss)","Vd2 [mm³]",null,{"$f":"PI()/4*(D6^2*(D9-D10-2*D12)/2+(D7^2-D6^2)*D9/2+D8^2*D10)","v":434.96921085277313},{"$f":"D37/10^9","v":4.3496921085277311E-7}]
["Maximum des variables Arbeitseiten-Volumen (kalt)","V1max [mm³]","V01max+Vd1 ",{"$f":"D34+D36","v":4246.5064978205901},{"$f":"E34+E36","v":4.2465064978205904E-6}]
["Maximum des variables Verdränger-Volumen (heiss)","V2max [mm³]","V02max+Vd2",{"$f":"D35+D37","v":5300.6679127326461},{"$f":"E35+E37","v":5.3006679127326449E-6}]
["Minimum des variables Arbeitseiten-Volumen (kalt)","V1min [mm³]","Vd1 ",{"$f":"D36","v":361.14178349341307},{"$f":"D40/10^9","v":3.6114178349341308E-7}]
["Minimum des variables Verdränger-Volumen (heiss)","V2min [mm³]","Vd2",{"$f":"D37","v":434.96921085277313},{"$f":"D41/10^9","v":4.3496921085277311E-7}]
["Maximum des gesamten Volumens mit Toträumen","Vmax [m³]","V2max+Vd1",{"$f":"D39+D36","v":5661.8096962260588},{"$f":"D42/10^9","v":5.6618096962260589E-6}]
["Rechengrösse",null,"V1max/T1  + V2min/T2",".-.",{"$f":"E38/E17+E41/E18","v":1.2788872020340375E-8}]
["Rechengrösse",null,"V1min/T1  + V2max/T2",".-.",{"$f":"E40/E17+E39/E18","v":1.0273793884067006E-8}]
["Dimensionsloses Volumen",null,"V/Vmax=(V1+V2)/(V2max+V1min)",".-.",".-."]
["Masse des abgekühlten (erneuerten) Volumens (kalt) ","m1 [ kg]","patm∙V1max/(Rs∙T1)",".-.",{"$f":"E20*E38/E24/E17","v":4.2460454267475963E-6}]
["Masse des erwärmten(erneuerten) Volumens (heiss)","m2 [ kg]","patm∙V02max/(Rs∙T2)",".-.",{"$f":"E20*E35/E24/E18","v":2.9972166694056645E-6}]
[" "," ",null,null," "]
["Ausgangswinkel für Umlauf","j0 [-°]",{"$f":"Base!D29","v":0}]
["Schrittweite","Dj [-°]",{"$f":"Base!D30","v":1},null," "]
["Laufindex für Kurbelwinkel","i [-]",{"$f":"Base!D31","v":0},null," "]
[" Kurbelwinkel","i·Dj [-°]",{"$f":"Base!D32","v":0},null," "]

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[null,"Index","Kurbel-winkel",null,"Kolbenweg","Volumen                kalte Seite","Volumen            warme Seite","Rechen-größe","Druck","Verängtes Volumen","dimensionsloses pV-Diagramm  [-]  ",null,"pV-Diagramm",null,"Pleuelwinkel",null,"Pleuelstangenkraft",null,"Kurbelnkraft",null,"mittleres Wellen-moment","Wellen-Leistung","dimensionsloses pV-Diagramm  [-] "]
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[null,null,null,null,null,null,null,null,null,null,"Diagramm 1",null,null,null,"Check:",null,{"$f":"SUM(Q7:Q32)/25","v":6.5342693618574879E-2},{"$f":"SUM(R7:R32)/24","v":8.2235951830583409E-2},{"$f":"SUM(S7:S32)/24","v":-0.3281524551686788},{"$f":"SUM(T7:T31)/24","v":0.34415969905703897},{"$f":"SUM(U7:U31)/24","v":3.4415969905703895E-3},{"$f":"SUM(V7:V31)/24","v":0.18020159703654459},"Diagramm 2","Diagramm 3","Diagramm 4"]
[null,null,null,null,null,null,null,null,null,null,"Vvar","p'var","Vvar","pvar","Kräfte  / Momente / Leistung auf der Basis der Kinematik Kolben / Pleuel / Welle"]
[null,"i",{"$f":"Base!D32","v":0},{"$f":"PI()/180*C36","v":0},{"$f":"Value!$E$12*((1-COS(D36))+Value!$E$29/4*(1-COS(2*D36)))","v":0},{"$f":"Value!$E$31*(Value!$E$30-E36)+Value!$E$36","v":4.2465064978205904E-6},{"$f":"Value!$E$32*E36+Value!$E$37","v":4.3496921085277311E-7},{"$f":"F36/Value!$E$17+G36/Value!$E$18","v":1.2788872020340375E-8},{"$f":"IF(C36>=0,IF(C36<=180,Value!$E$20*Value!$E$43/(Calc!F36/Value!$E$17+Calc!G36/Value!$E$18),Value!$E$20*Value!$E$44/(Calc!F36/Value!$E$17+Calc!G36/Value!$E$18)))","v":101299.99999999999},{"$f":"E36*Value!$E$33","v":0},{"$f":"Calc!J36/(Value!$E$33*Value!$E$30)","v":0},{"$f":"I36/$I$19","v":0.80333854836664242},{"$f":"J36*10^6","v":0},{"$f":"I36/10^5","v":1.0129999999999999}]
[null,null,null,null,null,null,null,null,null,null,{"$f":"K36","v":0},0,{"$f":"M36","v":0},{"$f":"0","v":0}]
[null,null,null,null,null,null,null,null,null,null,"für Darstellung im p' V'-Diagramm 1"]
[null,null,null,null,null,null,null,null,"[bar]","[cm³]","V/Vmax[ - ]","pm/pmax[ - ]"]
[null,null,null,null,null,null,null,null,"pm1","V","V'","p'm1 ","0°- 180°"," "]
[null,null,null,null,null,null,null,{"$f":"Value!E20/(Value!E17/Value!E18*Value!E32/Value!E31-1)*LN(Value!E17/Value!E18*Value!E32/Value!E31)/10^5","v":1.1500733101660503},{"$f":"Value!E20/Value!E30*(Value!E31*Value!E30/Value!E17+Value!E36/Value!E17+Value!E37/Value!E18)/(Value!E31/Value!E17-Value!E32/Value!E18)*LN((Value!E31*Value!E30/Value!E17+Value!E36/Value!E17+Value!E37/Value!E18)/(Value!E32*Value!E30/Value!E18+Value!E36/Value!E17+Value!E37/Value!E18))/10^5","v":1.1279575902868695},{"$f":"0.9*J7*10^6","v":0},0,{"$f":"I41/I19*10^5","v":0.89450327068133262}," "," "]
[null,null,null,null,null,null,null,null,{"$f":"I41","v":1.1279575902868695},{"$f":"1*J20*10^6","v":0.98033398755269507},{"$f":"1.02*J42/$J$20/10^6","v":1.02},{"$f":"I42/I19*10^5","v":0.89450327068133262}]
[]
[null,null,null,null,null,null,null,null,"pm2  ","V","V=V'","p'm2","180° - 360°"]
[null,null,null,null,null,null,null,null,{"$f":"Value!E20/Value!E30*(Value!E32*Value!E30/Value!E18+Value!E36/Value!E17+Value!E37/Value!E18)/(Value!E31/Value!E17-Value!E32/Value!E18)*LN((Value!E31*Value!E30/Value!E17+Value!E36/Value!E17+Value!E37/Value!E18)/(Value!E32*Value!E30/Value!E18+Value!E36/Value!E17+Value!E37/ Value!E18))/10^5","v":0.90613181320018976},{"$f":"J41","v":0},{"$f":"K42","v":1.02},{"$f":"I45/I19*10^5","v":0.71858895897835562}]
[null,null,null,null,null,null,null,null,{"$f":"I45","v":0.90613181320018976},{"$f":"J42","v":0.98033398755269507},0,{"$f":"I46/I19*10^5","v":0.71858895897835562}]
[]
[null,null,null,null,null,null,null,null,"patm ",{"$f":"J44","v":"V"},"V=V'","p'atm "]
[null,null,null,null,null,null,null,null,{"$f":"Value!E20/10^5","v":1.0129999999999999},{"$f":"J45","v":0},{"$f":"K45","v":1.02},{"$f":"I49/I19*10^5","v":0.80333854836664254}]
[null,null,null,null,null,null,null,null,{"$f":"I49","v":1.0129999999999999},{"$f":"J46","v":0.98033398755269507},{"$f":"K46*10^5","v":0},{"$f":"I50/I19*10^5","v":0.80333854836664254}]
[null,null,null,null,null,null,null,null,null,"Q=Q*+W2",null,"W2 + W1","0°® 180°","180°® 360°","Q*=Q-W2"]
[null,null,null,null,null,null,null,null,"pmax","V","p'max","V'"]
[]
[]
[]
[null,null,null,null,null,null,null," ","Zugeführte Energie","Q [kg*m²/s²=Nm]","Arbei/Umdrehung","W [kg*m²/s²=Nm]","W2 [kg*m²/s²=Nm]","W1 [kg*m²/s²=Nm]","Q* [kg*m²/s²=Nm]"]
[null,null,null,null,null,null,null," ","energy input",{"$f":"Value!E25*Value!E47*(Value!E18-Value!E17)+Value!E30*Value!E33*(Calc!I41-Calc!I49)*10^5","v":0.49921655706777973},"energy output",{"$f":"($I$41-$I$45)*Value!$E$33*Value!$E$30*10^5","v":2.1746334859335997E-2},{"$f":"($I$41-$I$49)*Value!$E$33*Value!$E$30*10^5","v":1.1269683288537584E-2},{"$f":"($I$49-$I$45)*Value!$E$33*Value!$E$30*10^5","v":1.0476651570798415E-2},{"$f":"Value!E25*Value!E47*(Value!E18-Value!E17)","v":0.48794687377924217}]
[null,null,null,null,null,null,null,null,null,null,null,"h=W/Q",null,null,"Q*=CVm2(T2-T1)"]
[null,null,null,null,null,null,null,null,"Leistung","P [kgm²/s³=W]","Wirkungsgrad","h [-]"]
[null,null,null,null,null,null,null,null," engine power",{"$f":"L57*Value!E21","v":0.18121945716113333},"efficiency [-]",{"$f":"L57/J57","v":4.3560924715851219E-2}]
[null,null,null,null,null,null,null,null,"mittl. Moment","Mt [kgm²/s²]"]
[null,null,null,null,null,null,null,null,"mean moment",{"$f":"J60/Value!E22","v":3.4610366869949213E-3}]
[]
[]
[null,null,null,null,null,null,null,null,{"$f":"(I41+I45)/2","v":1.0170447017435296}]

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[]
["Zusammenhang von Temperatur und Flächenverhälnis für einen maximalen Wirkungsgrad "]
["Interrelationship of temperatur and area ratio for a maximum of efficiency"]
[]
["aktuelle Daten / actual values"]
["D1",{"$f":"Value!E5","v":7.9000000000000008E-3},{"$f":"B6*1000","v":7.9}]
["D2",{"$f":"Value!E6","v":1.7600000000000001E-2},{"$f":"B7*1000","v":17.600000000000001}]
["T1",{"$f":"Value!E17","v":353}]
["T2",{"$f":"Value!E18","v":573}]
["T2/T1",{"$f":"B9/B8","v":1.6232294617563738},{"$f":"B10","v":1.6232294617563738}]
["D1/opt",{"$f":"B7*(-0.002572*B10^4+0.043483*B10^3-0.27556*B10^2+0.82642*B10-0.582139)^0.5","v":7.8981690553539107E-3},{"$f":"B11*1000","v":7.898169055353911},"Näherung"]
["Ermittlung der Näherungsfunktion für optimalen Durchmesser D1 sind T1, T2, D2 bekannt, D1 kann ermittelt werden"]
["A1/A2   ","T2/T1=f(A1/A2)","y=D1/D2","y=[D1/D2]²"]
[0.48,{"$f":"1/A14*2.718181^(1/A14-1)","v":6.1549850080071939},{"$f":"(-(A14-1))^0.5","v":0.72111025509279791},{"$f":"-(A14-1)","v":0.52}]
[0.49,5.7784045027154924,{"$f":"(-(A15-1))^0.5","v":0.71414284285428498},{"$f":"-(A15-1)","v":0.51}]
[0.5,5.4363619999999999,0.70710678118654757,0.5]
[0.51,5.12480885747991,0.7,0.49]
[0.52,4.8402634468633057,0.69282032302755092,0.48]
[0.53,4.5797198636543026,0.68556546004010444,0.47]
[0.54,4.3405731134739769,0.67823299831252681,0.45999999999999996]
[0.55000000000000004,4.1205575001924331,0.67082039324993692,0.44999999999999996]
[0.56000000000000005,3.9176956483645866,0.66332495807107994,0.43999999999999995]
[0.56999999999999995,3.7302561354576338,0.65574385243020006,0.43000000000000005]
[0.57999999999999996,3.5567181287653868,0.64807406984078608,0.42000000000000004]
[0.59,3.3957417477471692,0.6403124237432849,0.41000000000000003]
[0.6,3.2461431270971843,0.63245553203367588,0.4]
[0.61,3.1068733558028208,0.62449979983983983,0.39]
[0.62,2.9770006253134329,0.61644140029689765,0.38]
[0.63,2.855695045191196,0.60827625302982191,0.37]
[0.64,2.7422156844625643,0.6,0.36]
[0.65,2.635899476848798,0.59160797830996159,0.35]
[0.66,2.5361516923698013,0.58309518948452999,0.33999999999999997]
[0.67,2.4424377297669069,0.57445626465380284,0.32999999999999996]
[0.68,2.3542760263258407,0.56568542494923801,0.31999999999999995]
[0.69,2.2712319159897576,0.55677643628300222,0.31000000000000005]
[0.7,2.1929122946942856,0.54772255750516619,0.30000000000000004]
[0.71,2.1189609748603733,0.53851648071345048,0.29000000000000004]
[0.72,2.0490546299185337,0.52915026221291817,0.28000000000000003]
[0.73,1.9828992453819727,0.51961524227066325,0.27]
[0.74,1.9202270059515865,0.50990195135927852,0.26]
[0.75,1.8607935589161047,0.5,0.25]
[0.76,1.80437560310167,0.4898979485566356,0.24]
[0.77,1.7507687601464708,0.47958315233127191,0.22999999999999998]
[0.78,1.6997856911861897,0.46904157598234292,0.21999999999999997]
[0.79,1.6512544273449503,0.45825756949558394,0.20999999999999996]
[0.8,1.6050168869052626,0.44721359549995787,0.19999999999999996]
[0.81,1.560927555818961,0.43588989435406728,0.18999999999999995]
[0.82,1.5188523114339871,0.42426406871192857,0.18000000000000005,null,"Zusammenhang von Temperatur- und Flächenverhälnis für einen maximalen Wirkungsgrad "]
[0.83,1.4786673720433192,0.41231056256176613,0.17000000000000004,null,"Interrelationship of temperatur- and area ratios for a maximum of efficiency"]
[0.84,1.4402583571902554,0.4,0.16000000000000003]
[0.85,1.4035194456528204,0.3872983346207417,0.15000000000000002]
[0.86,1.3683526197327136,0.37416573867739417,0.14000000000000001]
[0.87,1.3346669859353155,0.36055512754639896,0.13]
[0.88,1.3023781633837692,0.34641016151377546,0.12]
[0.89,1.2714077323930073,0.33166247903553997,0.10999999999999999]
[0.9,1.2416827365647718,0.31622776601683789,9.9999999999999978E-2,null,"Näherungslösung / Solution in the form of an approximation"]
[0.91,1.2131352325738052,0.29999999999999993,8.9999999999999969E-2]
[0.92,1.1857018825169963,0.28284271247461895,7.999999999999996E-2]
[0.93,1.1593235843066318,0.26457513110645897,6.9999999999999951E-2]
[0.94,1.1339451361192796,0.24494897427831791,6.0000000000000053E-2]
[0.95,1.1095149313741597,0.22360679774997907,5.0000000000000044E-2]
[0.96,1.0859846811187053,0.20000000000000009,4.0000000000000036E-2]
[0.97,1.0633091610522798,0.17320508075688781,3.0000000000000027E-2]
[0.98,1.0414459807286303,0.14142135623730956,2.0000000000000018E-2]
[0.99,1.0203553727494066,0.10000000000000005,1.0000000000000009E-2]
[1,1,0,0,null,"Näherungslösung  / Solution in the form of an approximation"]

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["← [D1/D2]²",{"$f":"Base!D4","v":7.9},{"$f":"Base!D5","v":17.600000000000001}]
[]
["← (Tmax-Tmin)/Tmax",{"$f":"Base!D17","v":300},{"$f":"Base!$D$16","v":80}]
["(Tmax-Tmin)/Tmax = 1,5813 [(D1/D2)²]0,8899"]
["(D1/D2)² = 0,5659 [(Tmax-Tmin)/Tmax]"]
[]
["Ermittlung der optimalen maximalen Temperatur Tmax ,  gegeben Tmin, D1, D2",null,null,null,"Input"]
["gegeben"]
["Umgebungstemperatur","Tu [°C]",null,{"$f":"Base!$D$14","v":20}]
["minimale Temperatur","Tmin [°C]",null,{"$f":"C3","v":80},"Ü"]
["Durchmesser Kolben (kalt)","D1 [mm]",null,{"$f":"B1","v":7.9},"Ü"]
["Durchmesser Verdränger (warm)","D2 [mm]",null,{"$f":"C1","v":17.600000000000001},"Ü"]
["Durchmesserverhältnis","[D1/D2]² [-]",null,{"$f":"(D11/D12)^2","v":0.20147856404958678}]
["optimale Temperaturverhältnis","(Tmax-Tmin)/Tmax"," 1,5813 [(D1/D2)²]0,8899 [°K/°K]",{"$f":"1.5813*D13^0.8899","v":0.38005593755579647}]
["optimale maximale Temperatur","Tmax [°C]",null,{"$f":"(D10+273)/(1-D14)-273","v":296.40621159956811}]
[]
[]
["Ermittlung des optimalen  Durchmessers D2 (warm),  gegeben D1, Tmin ,Tmax",null,null,null,"Input"]
["gegeben"]
[]
["Kolbendurchmesser (kalt)","D1 [mm]",null,{"$f":"B1","v":7.9},"Ü"]
["minimale Temperatur","Tmin [°C]",null,{"$f":"C3","v":80},"Ü"]
["maximale Temperatur (Verdränger)","Tmax [°C]",null,{"$f":"B3","v":300},"Ü"]
["optimale Temperaturverhältnis","(Tmax-Tmin)/Tmax","(Tmax-Tmin)/Tmax  [°K/°K]",{"$f":"(D23-D22)/(D23+273)","v":0.38394415357766143}]
["optimales Durchmesserverhältnis","[D1/D2]² [-]"," 0,5659 [(Tmax-Tmin)/Tmax]",{"$f":"0.5659*D24","v":0.21727399650959858}]
["optimaler Verdrängerdurchmesser","D2 [mm]","D2 /{0,5659 [(Tmax-Tmin)/Tmax]}1/2",{"$f":"D21/D25^0.5","v":16.948185739347426},null,null," "]
[]
["Ermittlung des optimalen Durchmessers D1 (kalt),  gegeben D2, Tmin ,Tmax",null,null,null,"Input"]
["gegeben"]
[]
["Kolbendurchmesser (warm)","D2 [mm]",null,{"$f":"Base!D5","v":17.600000000000001},"Ü"]
["minimale Temperatur","Tmin [°C]",null,{"$f":"D22","v":80},"Ü"]
["maximale Temperatur (Verdränger)","Tmax [°C]",null,{"$f":"D23","v":300},"Ü"]
["optimale Temperaturverhältnis","(Tmax-Tmin)/Tmax","(Tmax-Tmin)/Tmax  [°K/°K]",{"$f":"(D33-D32)/(D33+273)","v":0.38394415357766143}]
["optimales Durchmesserverhältnis","[D1/D2]² [-]"," 0,5659 [(Tmax-Tmin)/Tmax]",{"$f":"0.5659*D34","v":0.21727399650959858}]
["optimaler Verdrängerdurchmesser","D2 [mm]","D2 /{0,5659 [(Tmax-Tmin)/Tmax]}1/2",{"$f":"D31*D35^0.5","v":8.2038279576556974},null,null," "]

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[null,"(Tmax-Tmin)/Tmax",".=1-Tmin/Tmax",{"$f":"1-D3","v":0.5},0.55002249887505628,0.6,0.64998249912495631,0.7,0.75]
["2r//D2=0,4",null,"Tmax[°C]",327,393.7,477,584.1,727,927]
["D2=50",null,{"$f":"27","v":27},{"$f":"($C$3+273)/(D2+273)","v":0.5},0.44997750112494372,0.4,0.35001750087504374,0.3,0.25]
[null,null,null,"in °K/°K ","in °K/°K ","in °K/°K ","in °K/°K ","in °K/°K ","in °K/°K "]
["D2=50","D1/D2 [-]","[D1/D2]² [-]","h[-]","h[-]","h[-]","h[-]","h[-]","h[-]"]
[250,0,{"$f":"B6^2","v":0},0,0,0,0,0,0]
[250,0.2,{"$f":"B7^2","v":4.0000000000000008E-2},2.0199999999999999E-2,2.1399999999999999E-2,2.2599999999999999E-2,2.41E-2,2.58E-2,2.7799999999999998E-2]
[200,0.25,6.25E-2,3.0499999999999999E-2,3.2300000000000002E-2,3.44E-2,3.6700000000000003E-2,3.95E-2,4.2700000000000002E-2]
[166.7,0.3,0.09,4.1799999999999997E-2,4.4699999999999997E-2,4.7800000000000002E-2,5.1299999999999998E-2,5.5300000000000002E-2,6.0100000000000001E-2]
[142.9,0.35,0.12249999999999998,5.3400000000000003E-2,5.7700000000000001E-2,6.2199999999999998E-2,6.7100000000000007E-2,7.2900000000000006E-2,7.9500000000000001E-2]
[125,0.4,0.16000000000000003,6.4399999999999999E-2,7.0400000000000004E-2,7.6700000000000004E-2,8.3599999999999994E-2,9.1300000000000006E-2,0.1003]
[111.1,0.45,0.20250000000000001,7.3300000000000004E-2,8.1699999999999995E-2,9.0300000000000005E-2,9.9500000000000005E-2,0.10970000000000001,0.1215]
[100,0.5,0.25,7.8600000000000003E-2,9.01E-2,0.1016,0.1137,0.12690000000000001,0.14199999999999999]
[90.9,0.55000000000000004,0.30250000000000005,7.8100000000000003E-2,9.35E-2,0.1087,0.1245,0.1414,0.16039999999999999]
[83.3,0.6,0.36,6.8199999999999997E-2,8.9399999999999993E-2,0.1094,0.12959999999999999,0.1512,0.17499999999999999]
[76.900000000000006,0.65,0.42250000000000004,4.7100000000000003E-2,7.4200000000000002E-2,0.1002,0.12620000000000001,0.15329999999999999,0.18290000000000001]
[71.400000000000006,0.7,0.48999999999999994,7.1999999999999998E-3,4.2999999999999997E-2,7.6799999999999993E-2,0.1099,0.14399999999999999,0.18060000000000001]
[66.7,0.75,0.5625,-5.7599999999999998E-2,-1.06E-2,3.3000000000000002E-2,7.5200000000000003E-2,0.11700000000000001,0.16300000000000001]
[62.5,0.8,0.64000000000000012,-0.16309999999999999,-0.1007,-4.36E-2,1.0699999999999999E-2,6.4699999999999994E-2,0.1207]
["y","y'"]
["ax³","3ax²",null,-1.1997580000000001,-1.0960510000000001,-1.0069570000000001,-0.92983300000000002,-0.85812999999999995,-0.80560399999999999]
["bx²","2bx",null,-0.39427499999999999,-0.35494199999999998,-0.32349,-0.298626,-0.28304099999999999,-0.25870700000000002]
["cx","c",null,0.49271999999999999,0.522088,0.55435400000000001,0.59143199999999996,0.63581900000000002,0.68648600000000004]
["d",null,null,0.49271999999999999,0.522088,0.55435400000000001,0.59143199999999996,0.63581900000000002,0.68648600000000004,"Optimierungrechnung"]
["[D1/D2]² = f (hmax)",null,0,{"$f":"-2*D22/(3*D21)/2+((2*D22/(3*D21)/2)^2-D23/(3*D21))^0.5","v":0.27632483262955121},0.30488691692807168,0.33447495324660165,0.36568450717774681,0.39904076228408497,0.43655867355393541,{"$f":"(L25/M25)^2","v":0.25},"← [D1/D2]²",50,100]
["hmax[-]","Test",{"$f":"1.5813*C23^0.8899","v":0},{"$f":"D21*D25^3+D22*D25^2+D23*D25","v":8.0732170851840493E-2},9.5120533806570859E-2,0.11154836659235763,0.13087374320984202,0.15412192643826475,0.18335918532070428,"**********"]
["(Tmax-Tmin)/Tmax = 1-Tmin/Tmax",null,{"$f":"1.5813*C24^0.8899","v":0},0.5,0.55000000000000004,0.6,0.65,0.7,0.75,0.46050000000000002,"← (Tmax-Tmin)/Tmax",800,27]
["(Tmax-Tmin)/Tmax= f ((D1/D2)²)",null,{"$f":"1.5813*C25^0.8899","v":0},{"$f":"1.5813*D25^0.8899","v":0.50342392790683654},0.54947682351653293,{"$f":"1.5813*F25^0.8899","v":0.59668543936689478},0.64598554446846235,0.69816734491165255,0.75628972407008965,0.46051214118421296,"(Tmax-Tmin)/Tmax = 1,5813 [(D1/D2)²]0,8899"]
["[D1/D2]²= f ((Tmax-Tmin)/Tmax)",null,{"$f":"0.5659*C27","v":0},{"$f":"0.5659*D27","v":0.28294999999999998},0.31124499999999999,0.33953999999999995,0.36783499999999997,0.39612999999999993,0.42442499999999994,{"$f":"0.5659*J27","v":0.26059694999999999},"(D1/D2)² = 0,5659 [(Tmax-Tmin)/Tmax]"]

{"sheet":"Temp+Spiel","index":6,"n_rows":81,"n_cols":20,"rows_kept":81,"cut":false,"hidden":true,"merged":[[80,1,80,2],[14,0,14,1],[20,1,20,8],[32,0,32,7],[70,1,70,2]]}
[null,null,"http://upload.wikimedia.org/wikipedia/commons/9/98/Kerze_zonen.png"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Durchmesser","Wandstärke ","dim.-lose Wandst","Temperatur "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"D [mm]","s [mm]","d=[D-d]/D [-]","DT [-°C]"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,20,3.5,{"$f":"R4/Q4","v":0.17499999999999999},260]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,17,2,{"$f":"R5/Q5","v":0.11764705882352941},297]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,15,1,{"$f":"R6/Q6","v":6.6666666666666666E-2},393]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,14,0.5,{"$f":"R7/Q7","v":3.5714285714285712E-2},345]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,13,0,{"$f":"R8/Q8","v":0},250]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null," "]
["http://de.wikipedia.org/wiki/Kerze"]
["Zone 1","600°C-800°C"]
["Zone 2","1000°C"]
["Zone 3","1200°C"]
["Zone 4","1400°C"]
["gilt nur bei freier Flamme"]
[]
[]
[]
[]
[]
["eigener  Versuch","mit Holzylinder mit Aussen-Ø/ Innen-Ø/ Innere Länge:  da/di/li"]
["Wärmeerzeuger","Tu  [°C]","Tmax [°C]","DT  [°C]","da/di/li  [mm/mm/mm]","Datum","Zeit [min]","Wandstärke [mm]","Bemerkung",null,"da",null,"di"]
["Kerze ",21,238,{"$f":"C23-B23","v":217},"17 / 13 / 28 ","2010-04-05","~ 30",2,"starke Rußbildung"]
["Spiritusbrenner",21,318,297,"17 / 13 / 28 ",40287,25,2,"keine Rußbildung"]
["Spiritusbrenner",22,320,298,"17 / 13 / 28 ","2010-04-19","~25",2,"keine Rußbildung",null,null,null,"     li"]
["Spiritusbrenner",20,413,393,"15 / 13 / 28 ","2010-05-11","~20",1,"keine Rußbildung"]
["Spiritusbrenner",20,420,400,"15 / 13 / 28 ","2010-05-12","~25",1,"keine Rußbildung"]
["Spiritusbrenner",22,367,345,"14 / 13 / 28 ","2010-05-14","~26",0.5,"keine Rußbildung"]
["http://www.pahmeyer.homepage.t-online.de/motor22.html"]
[null,"Kalte Seite","Warme Seite"]
["Messung",80,300]
[]
["Ermittlung desr Durchmesserspieles zwischen Zylinder und Kolben:   smittel = D-d "]
["Durchmesserspiel:",null,"Basisdaten unveränderlich","1a                sehr grob"," 1b                            geeignet"," 1c                   gut geeignet"," 1d                   noch geeignet","input"]
["gegeben"]
["mittl. Spaltdurchmesser","dm [mm]",17.5,{"$f":"0.975*Base!$D$5","v":17.16},{"$f":"0.975*Base!$D$5","v":17.16},{"$f":"0.975*Base!$D$5","v":17.16},{"$f":"0.975*Base!$D$5/0.975","v":17.600000000000001}," ←"]
["mittl.Kolbenlänge","leff  [mm]",42,{"$f":"Base!$D$9","v":23},{"$f":"Base!$D$9","v":23},{"$f":"Base!$D$9","v":23},{"$f":"Base!$D$9","v":23}," ←"]
["Kolbenhub","h [mm]",13.6,{"$f":"2*Base!$D$11","v":20},{"$f":"2*Base!$D$11","v":20},{"$f":"2*Base!$D$11","v":20},{"$f":"2*Base!$D$11","v":20}," ←"]
["Drehzahl","n  [min-1]",500,".-.",".-.",{"$f":"Base!D20","v":500},".-."," ←"]
["gesucht:",null,null,null,null,null,null,"output"]
["mittl.Zyl./ Kolben-Spiel","smittel  [mm]",1,{"$f":"(D37/D36*D43)^(1/3)","v":0.82350537269863089},{"$f":"(E43*E36*E37*E38)^(1/3)","v":0.92430710041432196},{"$f":"(F43*F36*F37*F38*F39)^(1/3)","v":0.92430710041432196},{"$f":"0.02*G36","v":0.35200000000000004},"®"]
[]
["unveränderlich",".-.",null,{"$f":"C36/C37","v":0.41666666666666669},{"$f":"C41^3/(C36*C37*C38)","v":1.0004001600640257E-4},{"$f":"C41^3/(C36*C37*C38*C44)","v":2.0008003201280511E-7},0.02]
["unveränderlich","n0 [min-1]",{"$f":"C39","v":500}," "," "," ",null," "]
[null,null,"Stirlingmotor               Frank Arbeiter",".-.","n [min-1]                   unbekannt","n [min-1] bekannt","2% D2-Regel          A. Fröbel"]
[]
[]
["Dichte","Alu",2.7,"kg/dm³"]
[null,"Messing",8.5,"kg/dm³"]
[null,"Stahl",7.85,"kg/dm³"]
[]
["Wärmeleitfähhigkeit","Alu",235,"W/m/K"]
[null,"Messing",120,"W/m/K"]
[null,"Stahl",48,"W/m/K"]
[null,null,null," "]
["Wärmeausdehnung","Alu","23,8*10-6","mm/mm/*°C"]
[null,"Messing","18,4*10-7","mm/mm/*°C"]
[null,"Stahl","11,5*10-8","mm/mm/*°C"]
[]
["spez.Wärmekapazität","Alu",897,"J/kg/°C"]
[null,"Messing",377,"J/kg/°C"]
[null,"Stahl",420,"J/kg/°C"]
[]
["Schmelzpkt.","Alu",934,"°C"]
[null,"Messing",900,"°C"]
[null,"Stahl",1535,"°C"]
[]
[]
[]
["2010-10-24"]
[null,"Temperatur [ °C]"]
[null,"UT","OT"]
["Stange","56  -60","85 - 85"]
["Führung","72 - 75","78 - 80"]
["KH","90 - 100","100 -90"]
["KM","100 - 110","104  -107"]
["KV","110 - 125","110 - 115"]
["WH","115 - 125","110 - 117"]
["WM","155 - 155","130 - 130"]
["WV (Flamme)","220 - 220","180 - 215"]
[null,"1-flammiger Brenner"]

{"sheet":"Kinematik","index":7,"n_rows":68,"n_cols":8,"rows_kept":68,"cut":false,"hidden":false,"merged":[[6,3,6,6],[35,2,35,7],[39,3,39,7]]}
[]
[null,null,"Pleuellänge:",{"$f":"Base!D12/1000","v":4.2999999999999997E-2},"Verhältnis r/ l=l",{"$f":"D3/D2","v":0.23255813953488375}]
[null,null,"Kurbelradius:",{"$f":"Base!D11/1000","v":0.01}]
[]
[]
[null,null,"UT"," j=0°"]
[null,null,"Winkel ","dimensionsloser Weg / Vergleich der exakten Lösung mit Näherungen"]
[null,null,"j [°]","Sexakt [m]","Sapp/1 [m]","Sapp/2 [m]","Smoteurmanson","1+cosj"]
[null,"UT",0,{"$f":"(1+COS(PI()/180*$C9)-1/$F$2*(1-(1-$F$2^2*SIN(PI()/180*$C9)^2)^0.5))","v":2},{"$f":"(1+COS(PI()/180*$C9)-$F$2/4*(1-COS(2*PI()/180*$C9)))","v":2},{"$f":"(1+COS(PI()/180*$C9)-$F$2/2*SIN(PI()/180*C9)^2)","v":2},{"$f":"(1+COS(PI()/180*$C9)+$F$2/2*SIN(PI()/180*$C9)^2)","v":2},{"$f":"1+COS(PI()/180*C9)","v":2}]
[null,null,15,{"$f":"(1+COS(PI()/180*$C10)-1/$F$2*(1-(1-$F$2^2*SIN(PI()/180*$C10)^2)^0.5))","v":1.9581295378913286},{"$f":"(1+COS(PI()/180*$C10)-$F$2/4*(1-COS(2*PI()/180*$C10)))","v":1.9581366055788612},{"$f":"(1+COS(PI()/180*$C10)-$F$2/2*SIN(PI()/180*C10)^2)","v":1.9581366055788612},{"$f":"(1+COS(PI()/180*$C10)+$F$2/2*SIN(PI()/180*$C10)^2)","v":1.9737150469992752},{"$f":"1+COS(PI()/180*C10)","v":1.9659258262890682}]
[null,null,30,1.8368567045969633,1.8369556363425783,1.8369556363425783,1.8950951712262993,1.8660254037844388]
[null,null,45,1.6485687932762465,1.6489672463028264,1.6489672463028264,1.7652463160702685,1.7071067811865475]
[null,null,60,1.4118879377305376,1.4127906976744187,1.4127906976744187,1.5872093023255813,1.5]
[null,null,75,1.1489249265937964,1.1503291960452859,1.1503291960452859,1.3673088941597555,1.2588190451025207]
[null,null,90,0.88210473326529693,0.88372093023255816,0.88372093023255816,1.1162790697674418,1]
[null,null,105,0.63128683638875482,0.63269110584024435,0.63269110584024435,0.84967080395471395,0.74118095489747915]
[null,null,120,0.41188793773053767,0.41279069767441878,0.41279069767441878,0.58720930232558166,0.50000000000000022]
[null,null,135,0.23435523090315161,0.23475368392973159,0.23475368392973159,0.35103275369717346,0.29289321881345254]
[null,null,150,0.10480589702808583,0.10490482877370083,0.10490482877370083,0.16304436365742175,0.13397459621556129]
[null,null,165,2.6277885313192195E-2,2.6284953000724726E-2,2.6284953000724726E-2,4.1863394421138872E-2,3.4074173710931799E-2]
[null,null,180,0,0,-1.7453357401918362E-33,1.7453357401918362E-33,0]
[null,null,195,2.6277885313192084E-2,2.6284953000724628E-2,2.6284953000724628E-2,4.1863394421138747E-2,3.4074173710931688E-2]
[null,null,210,0.10480589702808595,0.10490482877370091,0.10490482877370091,0.16304436365742189,0.1339745962155614]
[null,null,225,0.23435523090315138,0.23475368392973139,0.23475368392973139,0.35103275369717324,0.29289321881345232]
[null,null,240,0.411887937730537,0.41279069767441823,0.41279069767441823,0.58720930232558088,0.49999999999999956]
[null,null,255,0.63128683638875505,0.63269110584024457,0.63269110584024457,0.84967080395471417,0.74118095489747937]
[null,null,270,0.8821047332652967,0.88372093023255793,0.88372093023255793,1.1162790697674416,0.99999999999999978]
[null,null,285,1.148924926593796,1.1503291960452855,1.1503291960452855,1.3673088941597551,1.2588190451025203]
[null,null,300,1.4118879377305376,1.4127906976744187,1.4127906976744187,1.5872093023255813,1.5]
[null,null,315,1.6485687932762465,1.6489672463028264,1.6489672463028264,1.7652463160702685,1.7071067811865475]
[null,null,330,1.8368567045969628,1.8369556363425779,1.8369556363425779,1.8950951712262989,1.8660254037844384]
[null,null,345,1.9581295378913286,1.9581366055788612,1.9581366055788612,1.9737150469992752,1.9659258262890682]
[null,null,360,2,2,2,2,2]
[null,null,"Mittelwert",{"$f":"SUM(D9:D32)/24","v":0.94125720172649086},{"$f":"SUM(E9:E32)/24","v":0.94186046511627908},{"$f":"SUM(F9:F32)/24","v":0.94186046511627908},{"$f":"SUM(G9:G32)/24","v":1.0581395348837208},{"$f":"SUM(H9:H32)/24","v":1}]
[null,null,"mittl. Abweichung",".-.",{"$f":"E34/$D34*100-100","v":6.4091237621525465E-2},{"$f":"F34/$D34*100-100","v":6.4091237621525465E-2},{"$f":"G34/$D34*100-100","v":12.417682748438978},{"$f":"H34/$D34*100-100","v":6.2408869930302444}]
[null,null,"Kolbenweg in Abhängigkeit vom Kurbelwinkel "]
[null,null,null,null,"x = s"]
[null,null," "]
[null,null,"OT"," j=0°"]
[null,null,"Winkel ","dimensionsloser Weg / Vergleich der exakten Lösung mit der Näherungen"]
[null,null,"j [°]","xexakt [m]","xapp1 [-]","xapp1 [-]","Smoteurmanson","xapp2 [-]"]
[null,"OT",0,{"$f":"(1-COS(PI()/180*$C42)+1/$F$2*(1-(1-$F$2^2*SIN(PI()/180*$C42)^2)^0.5))","v":0},{"$f":"(1-COS(PI()/180*$C42)+$F$2/4*(1-COS(2*PI()/180*$C42)))","v":0},{"$f":"(1-COS(PI()/180*$C42)+$F$2/2*SIN(PI()/180*C42)^2)","v":0},{"$f":"(1-COS(PI()/180*$C42)-$F$2/2*SIN(PI()/180*$C42)^2)","v":0},{"$f":"1-COS(PI()/180*C42)","v":0}]
[null,null,15,{"$f":"(1-COS(PI()/180*$C43)+1/$F$2*(1-(1-$F$2^2*SIN(PI()/180*$C43)^2)^0.5))","v":4.1870462108671291E-2},{"$f":"(1-COS(PI()/180*$C43)+$F$2/4*(1-COS(2*PI()/180*$C43)))","v":4.186339442113874E-2},{"$f":"(1-COS(PI()/180*$C43)+$F$2/2*SIN(PI()/180*C43)^2)","v":4.186339442113874E-2},{"$f":"(1-COS(PI()/180*$C43)-$F$2/2*SIN(PI()/180*$C43)^2)","v":2.6284953000724635E-2},{"$f":"1-COS(PI()/180*C43)","v":3.4074173710931688E-2}]
[null,null,30,0.16314329540303674,0.16304436365742175,0.16304436365742175,0.10490482877370083,0.13397459621556129]
[null,null,45,0.35143120672375333,0.35103275369717335,{"$f":"(1-COS(PI()/180*$C45)+$F$2/2*SIN(PI()/180*C45)^2)","v":0.35103275369717335},0.2347536839297315,0.29289321881345243]
[null,null,60,0.58811206226946244,0.58720930232558133,0.58720930232558133,0.41279069767441851,0.49999999999999989]
[null,null,75,0.85107507340620359,0.84967080395471406,0.84967080395471406,0.63269110584024446,0.74118095489747926]
[null,null,90,1.1178952667347031,1.1162790697674418,1.1162790697674418,0.88372093023255804,0.99999999999999989]
[null,null,105,1.3687131636112451,1.3673088941597555,1.3673088941597555,1.1503291960452859,1.2588190451025207]
[null,null,120,1.5881120622694622,1.5872093023255811,1.5872093023255811,1.4127906976744184,1.4999999999999998]
[null,null,135,1.7656447690968484,1.7652463160702685,1.7652463160702685,1.6489672463028264,1.7071067811865475]
[null,null,150,1.8951941029719144,1.8950951712262993,1.8950951712262993,1.8369556363425783,1.8660254037844388]
[null,null,165,1.9737221146868078,1.9737150469992752,1.9737150469992752,1.9581366055788612,1.9659258262890682]
[null,"UT",180,2,2,2,2,2]
[null,null,195,1.9737221146868078,1.9737150469992752,1.9737150469992752,1.9581366055788612,1.9659258262890682]
[null,null,210,1.8951941029719142,1.8950951712262991,1.8950951712262991,1.8369556363425781,1.8660254037844386]
[null,null,225,1.7656447690968486,1.7652463160702685,1.7652463160702685,1.6489672463028269,1.7071067811865477]
[null,null,240,1.5881120622694629,1.5872093023255818,1.5872093023255818,1.4127906976744191,1.5000000000000004]
[null,null,255,1.3687131636112451,1.3673088941597555,1.3673088941597555,1.1503291960452859,1.2588190451025207]
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