diff --git a/Doku/Berechnung-foerderer-Längen.md b/Doku/Berechnung-foerderer-Längen.md
index 8dfe7bd..7536a5d 100644
--- a/Doku/Berechnung-foerderer-Längen.md
+++ b/Doku/Berechnung-foerderer-Längen.md
@@ -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 $L_F$:
+$$ 
+  L_F \cdot [tan(\alpha_F') + tan(\alpha_S) ] = - H_1 + H_0 + tan(\alpha_S) \cdot L_1 [9]
+$$
+$$ 
+  L_F = \frac{- H_1 + H_0 + tan(\alpha_S) \cdot L_1} {tan(\alpha_F') + tan(\alpha_S) } 
+$$
\ No newline at end of file
diff --git a/Doku/bilder/SkizzeFördererAbwärtsStrecke.svg b/Doku/bilder/SkizzeFördererAbwärtsStrecke.svg
new file mode 100644
index 0000000..82a9a2a
--- /dev/null
+++ b/Doku/bilder/SkizzeFördererAbwärtsStrecke.svg
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