7.8 KiB
7.8 KiB
Gleichungen Förderer aufwärts
violett ist F wie Förderer
hellblau ist S wie Strecke
AS ist Ausschleus- Element
ES ist Einschleus- Element
Gegeben
H_0, H_1, L_1, \alpha_F, \alpha_S, L_{ES}, H_{ES}, L_{AS}, H_{AS}
Gesucht
L_F, L_S, H_F, H_S
Grundgleichungen (H_1 > H_0, Förderrichtung: von H_0 nach H_1)
(1) Horizontal:
L_1 = L_{ES} + L_F + L_S + L_{AS}
(2) Vertikal:
H_1 - H_0 = H_F - H_S - H_{ES} - H_{AS}
(3) Neigung F:
\tan(\alpha_F) = \frac{H_F}{L_F} \quad \Rightarrow \quad H_F = L_F \cdot \tan(\alpha_F)
(4) Neigung S:
\tan(\alpha_S) = \frac{H_S}{L_S} \quad \Rightarrow \quad H_S = L_S \cdot \tan(\alpha_S)
Lösung (Einsetzen von (3),(4) in (1),(2))
(I)
L_F + L_S = L_1 - L_{ES} - L_{AS}
(II)
L_F \cdot \tan(\alpha_F) - L_S \cdot \tan(\alpha_S) = (H_1 - H_0) + H_{ES} + H_{AS}
Ergebnis
L_F = \frac{(H_1 - H_0 + H_{ES} + H_{AS}) + (L_1 - L_{ES} - L_{AS}) \cdot \tan(\alpha_S)}{\tan(\alpha_F) + \tan(\alpha_S)}
L_S = (L_1 - L_{ES} - L_{AS}) - L_F
H_F = L_F \cdot \tan(\alpha_F)
H_S = L_S \cdot \tan(\alpha_S)
Gleichungen Förderer abwärts
Gegeben
H_0, H_1, L_1, \alpha_F, \alpha_S, L_{ES}, H_{ES}, L_{AS}, H_{AS}
Gesucht
L_F, L_S, H_F, H_S
Grundgleichungen (H_0 > H_1, Förderrichtung: von H_0 nach H_1)
(1) Horizontal:
L_1 = L_{ES} + L_F + L_S + L_{AS}
(2) Vertikal:
H_0 - H_1 = H_{ES} + H_F + H_S + H_{AS}
(3) Neigung F:
\tan(\alpha_F) = \frac{H_F}{L_F} \quad \Rightarrow \quad H_F = L_F \cdot \tan(\alpha_F)
(4) Neigung S:
\tan(\alpha_S) = \frac{H_S}{L_S} \quad \Rightarrow \quad H_S = L_S \cdot \tan(\alpha_S)
Lösung (Einsetzen von (3),(4) in (1),(2))
(I)
L_F + L_S = L_1 - L_{ES} - L_{AS}
(II)
L_F \cdot \tan(\alpha_F) + L_S \cdot \tan(\alpha_S) = (H_0 - H_1) - H_{ES} - H_{AS}
Ergebnis
L_F = \frac{(H_0 - H_1 - H_{ES} - H_{AS}) - (L_1 - L_{ES} - L_{AS}) \cdot \tan(\alpha_S)}{\tan(\alpha_F) - \tan(\alpha_S)}
L_S = (L_1 - L_{ES} - L_{AS}) - L_F
H_F = L_F \cdot \tan(\alpha_F)
H_S = L_S \cdot \tan(\alpha_S)
Zusammenfassung
Wobei \alpha_S normalerweise immer bei 3° liegt und \alpha_F von 3,6,9,12,15.. 51° läuft.
#!/usr/bin/env python3
"""
Förderer-Berechnung in 2D – Markdown-Ausgabe
=============================================
"""
import math
# ============================================================
# KONSTANTEN [alle in Meter / Grad]
# ============================================================
H0 = 2.0
H1 = 5.0
L1 = 8.0
L_ES = 1.0
H_ES = 0.3
L_AS = 1.0
H_AS = 0.3
ALPHA_S = 3.0
ALPHA_F_LIST = [3, 6, 9, 12, 15, 18, 24, 27, 33, 39, 45, 51]
def berechne(delta_h, l1, l_es, h_es, l_as, h_as, alpha_f_deg, alpha_s_deg):
alpha_f = math.radians(alpha_f_deg)
alpha_s = math.radians(alpha_s_deg)
tan_f = math.tan(alpha_f)
tan_s = math.tan(alpha_s)
l_rest = l1 - l_es - l_as
if abs(tan_f - tan_s) < 1e-12:
return None
l_f = (delta_h - h_es - h_as - l_rest * tan_s) / (tan_f - tan_s)
l_s = l_rest - l_f
h_f = l_f * tan_f
h_s = l_s * tan_s
return {"L_F": l_f, "L_S": l_s, "H_F": h_f, "H_S": h_s}
def validierung(erg):
probleme = []
for key in ("L_F", "L_S", "H_F", "H_S"):
if erg[key] < 0:
probleme.append(f"{key} < 0")
return (len(probleme) == 0, probleme)
def md_tabelle(fall_name, h_anfang, h_ende):
"""Erzeugt eine Markdown-Tabelle. ΔH = |H_Ende - H_Anfang| (immer positiv)."""
delta_h = abs(h_ende - h_anfang)
lines = []
lines.append(f"### {fall_name}")
lines.append(f"H_Anfang = {h_anfang:.3f} m, H_Ende = {h_ende:.3f} m, "
f"ΔH = {delta_h:+.4f} m\n")
lines.append("| α_F [°] | L_F [m] | L_S [m] | H_F [m] | H_S [m] | Status |")
lines.append("|--------:|--------:|--------:|--------:|--------:|--------|")
for alpha_f_deg in ALPHA_F_LIST:
erg = berechne(delta_h, L1, L_ES, H_ES, L_AS, H_AS, alpha_f_deg, ALPHA_S)
if erg is None:
lines.append(f"| {alpha_f_deg} | — | — | — | — | ⚠ α_F = α_S |")
continue
gueltig, probleme = validierung(erg)
status = "✓ gültig" if gueltig else f"✗ {', '.join(probleme)}"
lines.append(
f"| {alpha_f_deg} "
f"| {erg['L_F']:.4f} "
f"| {erg['L_S']:.4f} "
f"| {erg['H_F']:.4f} "
f"| {erg['H_S']:.4f} "
f"| {status} |"
)
lines.append("")
return "\n".join(lines)
def main():
md = []
md.append("# Förderer-Berechnung (2D-Modell)\n")
md.append("## Gegebene Werte\n")
md.append("| Parameter | Wert |")
md.append("|-----------|-----:|")
md.append(f"| H₀ | {H0:.3f} m |")
md.append(f"| H₁ | {H1:.3f} m |")
md.append(f"| L₁ | {L1:.3f} m |")
md.append(f"| L_ES | {L_ES:.3f} m |")
md.append(f"| H_ES | {H_ES:.3f} m |")
md.append(f"| L_AS | {L_AS:.3f} m |")
md.append(f"| H_AS | {H_AS:.3f} m |")
md.append(f"| α_S | {ALPHA_S:.1f}° |")
md.append("")
md.append("## Ergebnisse\n")
# Fall 1: aufwärts – von H0 nach H1
md.append(md_tabelle("Aufwärts (H₀ → H₁)", h_anfang=H0, h_ende=H1))
# Fall 2: abwärts – von H1 nach H0, ΔH ebenfalls +3.0
md.append(md_tabelle("Abwärts (H₁ → H₀)", h_anfang=H1, h_ende=H0))
result = "\n".join(md)
with open("/mnt/user-data/outputs/foerderer_ergebnisse.md", "w", encoding="utf-8") as f:
f.write(result)
print(result)
if __name__ == "__main__":
main()
Förderer-Berechnung
Gegebene Werte
| Parameter | Wert |
|---|---|
| H₀ | 2.000 m |
| H₁ | 5.000 m |
| L₁ | 8.000 m |
| L_ES | 1.000 m |
| H_ES | 0.300 m |
| L_AS | 1.000 m |
| H_AS | 0.300 m |
| α_S | 3.0° |
Ergebnisse
Aufwärts (H₀ → H₁)
H_Anfang = 2.000 m, H_Ende = 5.000 m, ΔH = +3.0000 m
| α_F [°] | L_F [m] | L_S [m] | H_F [m] | H_S [m] | Status |
|---|---|---|---|---|---|
| 3 | — | — | — | — | ⚠ α_F = α_S |
| 6 | 39.5767 | -33.5767 | 4.1597 | -1.7597 | ✗ L_S < 0, H_S < 0 |
| 9 | 19.6794 | -13.6794 | 3.1169 | -0.7169 | ✗ L_S < 0, H_S < 0 |
| 12 | 13.0226 | -7.0226 | 2.7680 | -0.3680 | ✗ L_S < 0, H_S < 0 |
| 15 | 9.6759 | -3.6759 | 2.5926 | -0.1926 | ✗ L_S < 0, H_S < 0 |
| 18 | 7.6531 | -1.6531 | 2.4866 | -0.0866 | ✗ L_S < 0, H_S < 0 |
| 24 | 5.3092 | 0.6908 | 2.3638 | 0.0362 | ✓ gültig |
| 27 | 4.5624 | 1.4376 | 2.3247 | 0.0753 | ✓ gültig |
| 33 | 3.4934 | 2.5066 | 2.2686 | 0.1314 | ✓ gültig |
| 39 | 2.7537 | 3.2463 | 2.2299 | 0.1701 | ✓ gültig |
| 45 | 2.2009 | 3.7991 | 2.2009 | 0.1991 | ✓ gültig |
| 51 | 1.7637 | 4.2363 | 2.1780 | 0.2220 | ✓ gültig |
Abwärts (H₁ → H₀)
H_Anfang = 5.000 m, H_Ende = 2.000 m, ΔH = +3.0000 m
| α_F [°] | L_F [m] | L_S [m] | H_F [m] | H_S [m] | Status |
|---|---|---|---|---|---|
| 3 | — | — | — | — | ⚠ α_F = α_S |
| 6 | 39.5767 | -33.5767 | 4.1597 | -1.7597 | ✗ L_S < 0, H_S < 0 |
| 9 | 19.6794 | -13.6794 | 3.1169 | -0.7169 | ✗ L_S < 0, H_S < 0 |
| 12 | 13.0226 | -7.0226 | 2.7680 | -0.3680 | ✗ L_S < 0, H_S < 0 |
| 15 | 9.6759 | -3.6759 | 2.5926 | -0.1926 | ✗ L_S < 0, H_S < 0 |
| 18 | 7.6531 | -1.6531 | 2.4866 | -0.0866 | ✗ L_S < 0, H_S < 0 |
| 24 | 5.3092 | 0.6908 | 2.3638 | 0.0362 | ✓ gültig |
| 27 | 4.5624 | 1.4376 | 2.3247 | 0.0753 | ✓ gültig |
| 33 | 3.4934 | 2.5066 | 2.2686 | 0.1314 | ✓ gültig |
| 39 | 2.7537 | 3.2463 | 2.2299 | 0.1701 | ✓ gültig |
| 45 | 2.2009 | 3.7991 | 2.2009 | 0.1991 | ✓ gültig |
| 51 | 1.7637 | 4.2363 | 2.1780 | 0.2220 | ✓ gültig |