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Wind Power Formulas
Wind power: P_w = ½ · ṁ · v² = ½ · ρ · A · v³
Turbine power: P_t = c_p · P_w = c_p · ½ · ρ · (πD²/4) · v³
Betz limit: c_p,max = 16/27 ≈ 0.593
- Theoretical maximum for ANY turbine
- Real turbines: c_p ≈ 0.35–0.45
⚡ Power scales with v³:
- Double wind speed → 2³ = 8× more power
- 10% more wind speed → 1.1³ ≈ 33% more power
Air density: ρ_air ≈ 1.225 kg/m³ at sea level
Full load hours: h = W_annual [MWh] / P_rated [MW]
- Onshore Germany: ~1,800 h/year
- Offshore Germany: ~3,500 h/year