From d8c599fae6035902ceacff03210d2a94b29c1f80 Mon Sep 17 00:00:00 2001 From: mistangl Date: Wed, 12 Jun 2024 14:54:01 +0200 Subject: [PATCH 1/4] =?UTF-8?q?=C3=84nderung=20der=20Gleichungen=20bei=20F?= =?UTF-8?q?=C3=B6rderung=20bergab?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- Doku/Berechnung-foerderer-Längen.md | 25 +- Doku/bilder/SkizzeFördererAbwärtsStrecke.svg | 386 +++++++++++++++++++ 2 files changed, 410 insertions(+), 1 deletion(-) create mode 100644 Doku/bilder/SkizzeFördererAbwärtsStrecke.svg 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) } +$$ \ No newline at end of file diff --git a/Doku/bilder/SkizzeFördererAbwärtsStrecke.svg b/Doku/bilder/SkizzeFördererAbwärtsStrecke.svg new file mode 100644 index 0000000..82a9a2a --- /dev/null +++ b/Doku/bilder/SkizzeFördererAbwärtsStrecke.svg @@ -0,0 +1,386 @@ + + + + + + + + + + + + + + + + + + + + D HS + D HF + a'F + aS + L1 + LF + LS + + Hmax + H1 + H0 + + + + + + + + + + + + + + + + + + + + + + + + + From 89d4e02bd1901b5fb2f1424dd13b7f24e8bd3179 Mon Sep 17 00:00:00 2001 From: mistangl Date: Wed, 12 Jun 2024 15:10:41 +0200 Subject: [PATCH 2/4] =?UTF-8?q?Gleichungen=20f=C3=BCr=20F=C3=B6rderer=20ab?= =?UTF-8?q?w=C3=A4rts=20als=20Bild=20dazu=20gemacht,=20da=20MathMarkdown?= =?UTF-8?q?=20nicht=20unterst=C3=BCtzt=20wird?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- Doku/Berechnung-foerderer-Längen.md | 8 +++++++- Doku/bilder/Berechnung-Foerderer-abwaerts.png | Bin 0 -> 47652 bytes 2 files changed, 7 insertions(+), 1 deletion(-) create mode 100644 Doku/bilder/Berechnung-Foerderer-abwaerts.png diff --git a/Doku/Berechnung-foerderer-Längen.md b/Doku/Berechnung-foerderer-Längen.md index 7536a5d..1dff5fe 100644 --- a/Doku/Berechnung-foerderer-Längen.md +++ b/Doku/Berechnung-foerderer-Längen.md @@ -92,6 +92,9 @@ $$ # Förderer transportiert abwärts ![Alt text](bilder/SkizzeFördererAbwärtsStrecke.svg "Skizze von Förder und Strecke") +Formaln als Bild: +![Alt text](bilder/Berechnung-Foerderer-abwaerts.png) + 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: @@ -103,7 +106,10 @@ $$ \Delta{H_F} = H_0 - H_1 - \Delta{H_S} [3.2] $$ d.h. auf der rechten Seite haben alle Komponenten das jeweils inverse Vorzeichen. - +Anstatt wie oben +$$ + \Delta{H_F} = - H_0 + H_1 + \Delta{H_S} [3-Aufwärts] +$$ daraus ergibt sich für $L_F$: $$ L_F \cdot [tan(\alpha_F') + tan(\alpha_S) ] = - H_1 + H_0 + tan(\alpha_S) \cdot L_1 [9] diff --git a/Doku/bilder/Berechnung-Foerderer-abwaerts.png b/Doku/bilder/Berechnung-Foerderer-abwaerts.png new file mode 100644 index 0000000000000000000000000000000000000000..fd003beee7bcb80d8d2a0e67a130c33345f30c04 GIT binary patch literal 47652 zcmdSBWmH{Rw6=MG1cF0wcL@+YxCIFA0fKvQ5AGzvf_n%S9D=*M2Z9H83GVK_PO9#` z{f)leqx(nq9nDCMqE1f1*=w&k*PPG$&K;tpAc=}Zhy;N^P^G2BRUi;JM+gL_@) z@N`n0N~OCgB|XQckrAcQRC`u%)+W^<#ZGP=nwJxWw(P{}<78ADD>pZlR$tTTnPA69 zQu->1Ur?IwU{H?vLU+F^iD=H4e;)0-*Hmou%EmoxEP+fAHLDgS=S5Nw~OLjL_81&;UccbV9o zA`!vRFZyoQD5`(n$cD21_oZN!|1aP6fv~S$Q0Q*;9DQ_job04l@D?rOT53~=mX2a{ 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15:41:52 +0200 Subject: [PATCH 3/4] =?UTF-8?q?Gleichungen=20aufgel=C3=B6st?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- Doku/Berechnung-foerderer-Längen.md | 32 ++++++++++++++++++++++++++--- 1 file changed, 29 insertions(+), 3 deletions(-) diff --git a/Doku/Berechnung-foerderer-Längen.md b/Doku/Berechnung-foerderer-Längen.md index 1dff5fe..c0b3043 100644 --- a/Doku/Berechnung-foerderer-Längen.md +++ b/Doku/Berechnung-foerderer-Längen.md @@ -69,6 +69,9 @@ $$ $$ +## Zusammenfasung + + Es errechnet sich - $L_F$ aus Beziehung [9] - $L_S$ aus Beziehung [4] @@ -112,8 +115,31 @@ $$ $$ daraus ergibt sich für $L_F$: $$ - L_F \cdot [tan(\alpha_F') + tan(\alpha_S) ] = - H_1 + H_0 + tan(\alpha_S) \cdot L_1 [9] + L_F \cdot [tan(\alpha_F') - tan(\alpha_S) ] = H0 - H_1 - 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) } -$$ \ No newline at end of file + L_F = \frac{H_0 - H_1 - tan(\alpha_S) \cdot L_1} {tan(\alpha_F') - tan(\alpha_S) } +$$ + +## Zusammenfasung + +1. Berechnung von x_{Verhältnis}: + +$$ x_{Verhältnis} = \frac{\left( \tan(\alpha_F) - \tan(\alpha_S) \right) \cdot L_1}{H_0 - H_1 - \tan(\alpha_S) \cdot L_1} $$ + +2. Berechnung von L_F : + +$$ L_F = \frac{L_1}{x_{Verhältnis}} $$ + +3. Berechnung von L_S : + +$$ L_S = L_1 - L_F $$ + +4. Berechnung von $\Delta H_F$: + +$$ \Delta H_F = \tan(\alpha_F) \cdot L_F $$ + +5. 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