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Änderung der Gleichungen bei Förderung bergab

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This commit is contained in:
Michael Stangl
2024-06-12 14:54:01 +02:00
parent a02b5947ea
commit d8c599fae6
2 changed files with 410 additions and 1 deletions
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Doku/Berechnung-foerderer-Längen.md
+24 -1
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@@ -1,3 +1,5 @@
# Förderer transportiert aufwärts
![Alt text](bilder/SkizzeFördererStrecke.svg "Skizze von Förder und Strecke")
Formaln als Bild:
@@ -12,7 +14,7 @@ $$
Gesucht:
$$
L_F, L_S, \Delta H_F, \Delta H_S, H_{Max}, x_{Verhältnis}
L_F, L_S, \Delta H_F, \Delta H_S, x_{Verhältnis}
$$
@@ -87,4 +89,25 @@ $$
{tan(\alpha_F)} \geq {\frac{H_1 - H_0}{L_1}}
$$
# Förderer transportiert abwärts
![Alt text](bilder/SkizzeFördererAbwärtsStrecke.svg "Skizze von Förder und Strecke")
Unterschied ist hier, dass der Winkel $\alpha_F$ in einem anderen Ursprung definiert wird. Alternativ kann man bei gleichem Ursprung wie vorher über die Z-Winkel Beziehung $\alpha_F$ als negativen Winkel definieren, der dann als positiver Wert in $\alpha_F'$ eingesetzt wird.
Dadurch ändert sich Gleichung 3 in:
$$
H_0 = H_1 + \Delta{H_S} + \Delta{H_F} [3]
$$
oder
$$
\Delta{H_F} = H_0 - H_1 - \Delta{H_S} [3.2]
$$
d.h. auf der rechten Seite haben alle Komponenten das jeweils inverse Vorzeichen.
daraus ergibt sich für $L_F$:
$$
L_F \cdot [tan(\alpha_F') + tan(\alpha_S) ] = - H_1 + H_0 + tan(\alpha_S) \cdot L_1 [9]
$$
$$
L_F = \frac{- H_1 + H_0 + tan(\alpha_S) \cdot L_1} {tan(\alpha_F') + tan(\alpha_S) }
$$
Doku/bilder/SkizzeFördererAbwärtsStrecke.svg
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