From 5a170b007610aa0c447daa6a5cc6ea9371e926d6 Mon Sep 17 00:00:00 2001 From: mistangl Date: Tue, 28 May 2024 15:28:17 +0200 Subject: [PATCH] =?UTF-8?q?Berechnung=20von=20ChatGpt=20Kontrolliert=20und?= =?UTF-8?q?=20vereinfachten=20Rechenweg=20f=C3=BCr=20Ein=20und=20Auslauf?= =?UTF-8?q?=20bestimmt?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- Doku/Berechnung-foerderer-Längen_extended.md | 93 +++++++----------- Doku/bilder/Berechnung-Foerderer-extended.png | Bin 0 -> 124766 bytes Doku/bilder/Berechnung-Foerderer.png | Bin 108084 -> 96385 bytes 3 files changed, 38 insertions(+), 55 deletions(-) create mode 100644 Doku/bilder/Berechnung-Foerderer-extended.png diff --git a/Doku/Berechnung-foerderer-Längen_extended.md b/Doku/Berechnung-foerderer-Längen_extended.md index 663a31d..d220d2a 100644 --- a/Doku/Berechnung-foerderer-Längen_extended.md +++ b/Doku/Berechnung-foerderer-Längen_extended.md @@ -1,22 +1,19 @@ ![Alt text](bilder/SkizzeFördererStrecke_mitEinAuslauf.svg "Skizze von Förder und Strecke") Bekannt: - +![Alt text](bilder/Berechnung-Foerderer-extended.png) $$ L_1, H_0, H_1, \alpha_F, \alpha_S,\\ H_{SEA}, L_{SEA}, H_{FEA}, L_{FEA} $$ Gesucht: - $$ L_F, L_S, \Delta H_F, \Delta H_S, H_{Max}, x_{Verhältnis} $$ Beziehungen: - - $$ \frac{\Delta{H_F} - H_{FEA}}{L_{F} - L_{FEA}} = tan(\alpha_F) [1] $$ @@ -41,60 +38,46 @@ $$ $$ L_1 = L_F \cdot x_{Verhältnis} [6] $$ -$L_1$ aus [6] in [5]: + $\Delta H_S$ aus [2.2] in [4.2]: $$ - L_S = L_F \cdot (x_{Verhältnis} - 1) [7] -$$ -$\Delta{H_S}$ aus [2.2] in [4.2]: -$$ - \Delta{H_F} = H_1 - H_0 + tan(\alpha_S) \cdot (L_{S}-L_{SEA}) + H_{SEA}[9] -$$ -$L_S$ aus [7] in [9]: -$$ -\Delta{H_F} = H_1 - H_0 + tan(\alpha_S) \cdot [L_F \cdot (x_{Verhältnis} - 1) - L_{SEA})] + H_{FEA}[10] -$$ -$L_F$ aus [6] in [10]: -$$ -\Delta{H_F} = H_1 - H_0 + tan(\alpha_S) \cdot \Bigl[\frac{L_1}{x_{Verhältnis}} \cdot (x_{Verhältnis} - 1) - L_{SEA})\Bigr] + H_{FEA}[11] -$$ -$\Delta H_F$ aus [1.2] in [11]: -$$ -tan(\alpha_F) \cdot (L_{F} - L_{FEA}) + H_{FEA} = H_1 - H_0 + tan(\alpha_S) \cdot \Bigl[\frac{L_1}{x_{Verhältnis}} \cdot (x_{Verhältnis} - 1) - L_{SEA})\Bigr] + H_{FEA}[12] -$$ -dann [12] auflösen nach x: -$$ -tan(\alpha_F) \cdot (L_{F} - L_{FEA}) - H_1 + H_0 + tan(\alpha_S) \cdot L_{SEA} = tan(\alpha_S) \cdot L_1 \cdot \Bigl[1 - \frac{1}{x_{Verhältnis}}\Bigr] -$$ -$$ -tan(\alpha_F) \cdot (L_{F} - L_{FEA}) - H_1 + H_0 + tan(\alpha_S) \cdot L_{SEA} - L_1 \cdot tan(\alpha_S) = - tan(\alpha_S) \cdot L_1 \cdot \Bigl[\frac{1}{x_{Verhältnis}}\Bigr] -$$ -$$ -\frac{tan(\alpha_F) \cdot (L_{F} - L_{FEA}) - H_1 + H_0 + tan(\alpha_S) \cdot L_{SEA} - L_1 \cdot tan(\alpha_S)}{- tan(\alpha_S) \cdot L_1 }= \frac{1}{x_{Verhältnis}} -$$ -$$ -x_{Verhältnis}= \frac{- tan(\alpha_S) \cdot L_1 }{tan(\alpha_F) \cdot (L_{F} - L_{FEA}) - H_1 + H_0 + tan(\alpha_S) \cdot L_{SEA} - L_1 \cdot tan(\alpha_S)} -$$ -$$ -x_{Verhältnis}= \frac{tan(\alpha_S) \cdot L_1 }{-tan(\alpha_F) \cdot 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