Wind Turbine Power Calculation Example

Wind Turbine Power Equation:

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

Air Density (ρ):

kg/m³

Swept Area (A):

m²

Wind Velocity (V):

m/s

Power Coefficient (Cp):

dimensionless

Wind Turbine Power (P):

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1. What is the Wind Turbine Power Equation?

The wind turbine power equation calculates the theoretical power output of a wind turbine based on air density, swept area, wind velocity, and power coefficient. It represents the maximum extractable power from wind energy.

2. How Does the Calculator Work?

The calculator uses the wind turbine power equation:

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

Where:

\( P \) — Power output (watts)
\( \rho \) — Air density (kg/m³)
\( A \) — Swept area of turbine blades (m²)
\( V \) — Wind velocity (m/s)
\( C_p \) — Power coefficient (dimensionless)

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

3. Importance of Wind Power Calculation

Details: Accurate power calculation is essential for wind farm planning, turbine sizing, 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 velocity 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 coefficient.

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

Q3: What factors affect air density?
A: Air density decreases with altitude and increases with lower temperatures. Standard sea level density is 1.225 kg/m³ at 15°C.

Q4: How is swept area calculated?
A: For horizontal axis turbines, swept area = π × (blade length)². For vertical axis turbines, it's height × diameter.

Q5: What are typical power coefficient values?
A: Modern wind turbines typically achieve Cp values between 0.35-0.45, which is about 60-75% of the Betz limit.