Wind Turbine 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)

Power Output (P):

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1. What is the Wind Turbine Power Equation?

The wind turbine power equation calculates the theoretical power available in the wind that can be converted to mechanical energy by a wind turbine. It's based on fundamental physics principles of kinetic energy in moving air.

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, typically 1.225 at sea level)
\( A \) — Swept area of turbine blades (m²)
\( v \) — Wind speed (m/s)
\( C_p \) — Power coefficient (dimensionless, max 0.59 per Betz's law)

Explanation: The equation shows that power output is proportional to the cube of wind speed, making higher wind speeds dramatically more productive.

3. Importance of Power Calculation

Details: Accurate power estimation helps in sizing wind turbines, predicting energy production, and assessing economic viability of wind energy projects.

4. Using the Calculator

Tips: Enter air density (default is sea level value), swept area (πr² 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 because both the mass flow rate and kinetic energy per unit mass increase with speed.

Q2: What is the Betz limit?
A: The theoretical maximum efficiency for a wind turbine is 59.3% (Betz's law), meaning no turbine can extract more than this fraction of the wind's power.

Q3: How does air density affect power output?
A: Power is directly proportional to air density. Colder air and lower altitudes (higher pressure) increase density and therefore power output.

Q4: What's a typical power coefficient for real turbines?
A: Most modern turbines achieve 35-45% efficiency due to mechanical and electrical losses beyond the Betz limit.

Q5: How do I calculate swept area?
A: For a horizontal-axis turbine, swept area is π × (blade length)². For a 50m blade diameter, A = π × 25² ≈ 1963.5 m².