From 2b2c3229bb6e9fd97d53c9e925f4167d422b5b66 Mon Sep 17 00:00:00 2001
From: Simon Schmutzler <s.schmutzler@schoenenberger.de>
Date: Mon, 27 May 2024 17:46:46 +0200
Subject: [PATCH] =?UTF-8?q?GPT=20L=C3=B6sung=20der=20F=C3=B6rdererberechnu?=
 =?UTF-8?q?ng=20hinzugef=C3=BCgt?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 Doku/Berechnung-foerderer-Längen_extended.md | 43 ++++++++++++++++++++
 1 file changed, 43 insertions(+)

diff --git a/Doku/Berechnung-foerderer-Längen_extended.md b/Doku/Berechnung-foerderer-Längen_extended.md
index 128e54d..5ee3320 100644
--- a/Doku/Berechnung-foerderer-Längen_extended.md
+++ b/Doku/Berechnung-foerderer-Längen_extended.md
@@ -89,3 +89,46 @@ $$
 $$
 {tan(\alpha_F)} \geq {\frac{H_1 - H_0}{L_1}}
 $$
+
+///
+
+C-GPT
+
+# Bekannte Werte:
+L1, H0, H1, alpha_F, alpha_S, H_SEA, L_SEA, H_FEA, L_FEA
+
+# Gesucht:
+# L_F, L_S, ΔH_F, ΔH_S, (→ H_Max)
+
+# Beziehungen:
+# [1]    (ΔH_F - H_FEA) / (L_F - L_FEA) = tan(alpha_F)
+# [1.2]  ΔH_F = tan(alpha_F) * (L_F - L_FEA) + H_FEA
+# [2]    (ΔH_S - H_SEA) / (L_S - L_SEA) = tan(alpha_S)
+# [2.2]  ΔH_S = tan(alpha_S) * (L_S - L_SEA) + H_SEA
+# [4]    H_0 + ΔH_F = H_1 + ΔH_S
+# [4.2]  ΔH_F = H_1 - H_0 + ΔH_S
+# [5]    L_1 = L_F + L_S
+# [6]    L_1 = L_F * x_Verhältnis
+
+# Umstellen der Gleichungen für ΔH_F und ΔH_S:
+ΔH_F = tan(alpha_F) * (L_F - L_FEA) + H_FEA
+ΔH_S = tan(alpha_S) * (L_S - L_SEA) + H_SEA
+
+# Einsetzen von L_S = L_1 - L_F:
+tan(alpha_F) * (L_F - L_FEA) + H_FEA = H_1 - H_0 + (tan(alpha_S) * ((L_1 - L_F) - L_SEA) + H_SEA)
+
+# Auflösen nach L_F:
+tan(alpha_F) * L_F - tan(alpha_F) * L_FEA + H_FEA = H_1 - H_0 + tan(alpha_S) * L_1 - tan(alpha_S) * L_F - tan(alpha_S) * L_SEA + H_SEA
+
+# Gruppieren der Terme:
+tan(alpha_F) * L_F + tan(alpha_S) * L_F = tan(alpha_S) * L_1 + H_1 - H_0 - tan(alpha_F) * L_FEA - H_FEA + tan(alpha_S) * L_SEA - H_SEA
+
+# L_F isolieren:
+L_F = (tan(alpha_S) * L_1 + H_1 - H_0 - tan(alpha_F) * L_FEA - H_FEA + tan(alpha_S) * L_SEA - H_SEA) / (tan(alpha_F) + tan(alpha_S))
+
+# Berechnung von x_Verhältnis:
+x_Verhältnis = L_F / L_1
+x_Verhältnis = (tan(alpha_S) + (H_1 - H_0 - tan(alpha_F) * L_FEA - H_FEA + tan(alpha_S) * L_SEA - H_SEA) / L_1) / (tan(alpha_F) + tan(alpha_S))
+
+# Vereinfachte Formel für x_Verhältnis:
+x_Verhältnis = (tan(alpha_S) + ((H_1 - H_0) - tan(alpha_F) * L_FEA - H_FEA + tan(alpha_S) * L_SEA - H_SEA) / L_1) / (tan(alpha_F) + tan(alpha_S))