Wind Turbine Power Formula

Wind Turbine Power Formula:

\[ P = 0.5 \times \rho \times A \times v^3 \times C_p \]

Air Density (ρ):

kg/m³

Swept Area (A):

m²

Wind Speed (v):

m/s

Power Coefficient (Cp):

(0-0.59)

Wind Turbine Power (P):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Wind Turbine Power Formula?

The Wind Turbine Power Formula calculates the theoretical power output of a wind turbine based on air density, swept area, wind speed, and power coefficient. This fundamental equation helps in designing and evaluating wind energy systems.

2. How Does the Calculator Work?

The calculator uses the wind turbine power formula:

\[ P = 0.5 \times \rho \times A \times v^3 \times C_p \]

Where:

\( P \) — Power output (Watts)
\( \rho \) — Air density (kg/m³)
\( A \) — Swept area of turbine blades (m²)
\( v \) — Wind speed (m/s)
\( C_p \) — Power coefficient (Betz limit: 0.59)

Explanation: The formula shows that power output is proportional to the cube of wind speed, making wind speed the most critical factor in wind energy generation.

3. Importance of Wind Power Calculation

Details: Accurate power calculation is essential for wind farm planning, turbine selection, energy production forecasting, and economic feasibility studies of wind energy projects.

4. Using the Calculator

Tips: Enter air density (typically 1.225 kg/m³ at sea level), swept area (π × radius² for circular blades), wind speed in m/s, and power coefficient (typically 0.35-0.45 for modern turbines).

5. Frequently Asked Questions (FAQ)

Q1: What is the Betz limit?
A: The Betz limit (59.3%) is the theoretical maximum efficiency for wind turbines, representing the maximum possible power extraction from wind.

Q2: Why is wind speed cubed in the formula?
A: Wind power is proportional to the cube of wind speed because kinetic energy increases with the square of speed, and mass flow rate increases linearly with speed.

Q3: How does air density affect power output?
A: Higher air density (colder temperatures, lower altitudes) increases power output, while lower density (warmer temperatures, higher altitudes) decreases it.

Q4: What is typical power coefficient for modern turbines?
A: Modern wind turbines typically achieve power coefficients between 0.35 and 0.45, well below the Betz limit due to practical constraints.

Q5: How do I calculate swept area?
A: For horizontal-axis turbines, swept area = π × (blade length)². For a turbine with 40m blades, area = π × 40² ≈ 5026.55 m².