Wind Turbine Output Calculator

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 Speed (v):

m/s

Power Coefficient (Cp):

(dimensionless)

Wind Turbine Output (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 of the blades, wind speed, and the turbine's power coefficient. This fundamental equation helps in assessing potential energy production from wind turbines.

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 in watts
\( \rho \) — Air density (kg/m³)
\( A \) — Swept area of the blades (m²)
\( v \) — Wind speed (m/s)
\( C_p \) — Power coefficient (dimensionless, max 0.59)

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

3. Importance of Wind Turbine Output Calculation

Details: Accurate power output estimation is crucial for wind farm planning, energy production forecasting, and turbine sizing. It helps determine the economic viability of wind energy projects.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: Why is wind speed cubed in the equation?
A: The kinetic energy in wind increases with the cube of velocity, making higher wind speeds dramatically more productive.

Q2: What is the Betz limit?
A: The maximum theoretical power coefficient is 0.59 (Betz limit), meaning no turbine can capture more than 59% of the wind's kinetic energy.

Q3: How does air density affect output?
A: Colder, denser air contains more mass and thus more energy. Output decreases at higher altitudes where air is less dense.

Q4: What's a typical swept area for turbines?
A: A 2 MW turbine might have 80m diameter blades (swept area ≈ 5,027 m²). Area increases with the square of blade length.

Q5: Why don't turbines produce rated power all the time?
A: Wind speed varies, and turbines have cut-in/cut-out speeds. They only produce rated power at specific wind speeds.