Wind Power Calculation Formula

Wind Power Formula:

\[ P = \frac{1}{2} \rho A v^3 C_p \]

Air Density (ρ):

kg/m³

Rotor Area (A):

m²

Wind Velocity (v):

m/s

Power Coefficient (C_p):

Wind Power (P):

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1. What is the Wind Power Calculation Formula?

Definition: This calculator estimates the power available in the wind based on air density, rotor area, wind velocity, and turbine efficiency.

Purpose: It helps engineers and renewable energy professionals determine the potential power generation from wind turbines.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ P = \frac{1}{2} \rho A v^3 C_p \]

Where:

\( P \) — Power (Watts)
\( \rho \) — Air density (kg/m³)
\( A \) — Rotor swept area (m²)
\( v \) — Wind velocity (m/s)
\( C_p \) — Power coefficient (turbine efficiency)

Explanation: The formula calculates the kinetic energy in moving air that can be captured by a wind turbine.

3. Importance of Wind Power Calculation

Details: Accurate power estimation is crucial for turbine design, site selection, and energy production forecasting in wind farms.

4. Using the Calculator

Tips: Enter air density (default 1.225 kg/m³ at sea level), rotor area, wind speed, and power coefficient (default 0.35). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the Betz limit?
A: The maximum theoretical power coefficient is 0.59 (59% efficiency), known as the Betz limit.

Q2: How does air density affect power?
A: Power is directly proportional to air density. Higher altitudes with lower density produce less power.

Q3: Why is wind velocity cubed in the formula?
A: The kinetic energy in wind increases with the cube of velocity, making speed the most critical factor.

Q4: What's a typical power coefficient for modern turbines?
A: Most turbines operate between 0.35-0.45 due to practical limitations below the Betz limit.

Q5: How do I calculate rotor area?
A: \( A = \pi r^2 \) where r is the blade length (radius) of the turbine.