Wind Turbine Output — Power & Energy from Wind Speed and Blade Size

How This Wind Calculation Works

We use the standard wind power relation: P_avail = ½ · ρ · A · v³. The turbine extracts a fraction via the power coefficient Cp, then we apply a system efficiency η. Cut-in/out and an optional rated cap keep estimates realistic.

• Swept area: A = π·(D/2)²
• Mechanical power: P_mech = ½·ρ·A·v³·Cp
• Electrical power: P_elec = P_mech·η
• Limits: If v < cut-in or v > cut-out ⇒ P = 0; optional clamp to rated kW
• Energy (option 1): Annual kWh ≈ rated kW × 8760 × capacity factor
• Energy (option 2): Daily kWh ≈ P_elec × hours/day; Annual = daily × days/year

Tip: Small turbines often see capacity factors around 10–30% depending on site. Cp for 3-blade HAWTs is commonly ~0.3–0.45.

Wind Turbine Basics: From Wind Speed to Usable Energy

This calculator turns a few simple inputs—wind speed, rotor diameter, and reasonable performance assumptions—into a friendly estimate of wind power and energy. The core idea is that moving air carries kinetic energy. A rotor sweeps an area and converts a portion of that energy into shaft power, which a generator converts into electricity. The physics are compact but powerful: the available wind power scales with air density (ρ), swept area (A), and the cube of wind speed (v³). That cube relationship is why a modest increase in wind speed can dramatically boost output.

Key Concepts

• Swept Area (A): For a horizontal-axis turbine, A = π · (D/2)², where D is rotor diameter. Doubling the diameter quadruples the swept area and, all else equal, quadruples potential power.
• Betz Limit & Cp: No turbine can capture all the wind’s energy. The theoretical cap is about 59.3% (the Betz limit). Real rotors achieve a power coefficient (Cp) typically around 0.3–0.45 for well-designed, three-blade machines at optimal operating conditions.
• System Efficiency (η): Mechanical and electrical losses—bearings, gearbox (if any), generator, rectifier, wiring—reduce delivered power. An overall efficiency between ~80–95% is common for small systems when operating near their sweet spot.
• Cut-in / Cut-out: Below the cut-in speed, the machine cannot overcome losses and remains idle. Above the cut-out speed, the turbine shuts down to protect itself from extreme loads. Between those points, control systems (pitch, stall, or electrical loading) shape the power curve.
• Rated Power: Nameplate (rated) power is the output at a specified wind speed on the manufacturer’s curve. The calculator can optionally clamp power to an entered rated value for realism at high winds.

From Power to Energy

Power is instantaneous (kW). Energy integrates power over time (kWh). There are two practical ways to estimate energy: (1) multiply rated power by hours in a year and a capacity factor (a single, site-dependent efficiency number capturing wind variability and control behavior), or (2) multiply the calculated power at your representative wind speed by the number of generation hours per day. Capacity factor is convenient when you know your site’s wind distribution or have a long-term average; hours-per-day is handy for quick sensitivity checks.

Siting Tips for Better Results

• Height matters: Wind generally increases with height. If you can, use wind measured at hub height. A simple rule of thumb is that a taller mast often pays back in energy.
• Avoid turbulence: Buildings, trees, and ridgelines can create gusty, turbulent flow that lowers Cp and stresses components. Clear exposure improves performance and longevity.
• Air density shifts: Colder or lower-altitude air is denser, nudging power higher. Hot, high-altitude sites see lower density and thus lower power, all else equal.

Interpreting Results

Treat the outputs as awareness-level estimates rather than guarantees. Real turbines have detailed power curves, and real sites have changing wind speeds, directions, and turbulence across seasons. For quick planning: try a few wind speeds (e.g., 4–8 m/s), vary Cp within a realistic band, and compare both the capacity-factor and hours-per-day methods. If you later obtain a wind histogram or Weibull/Rayleigh parameters for your location, you can refine energy by integrating across the full wind distribution.

Bottom line: rotor size and wind speed dominate. Improve siting, aim for smooth flow, and use realistic assumptions for Cp, efficiency, and control limits. The calculator keeps those pieces transparent so you can learn, iterate, and plan with confidence.