Power Coefficient of Wind Machine Calculator

Power Coefficient Formula:

\[ C_p = \frac{P_e}{0.5 \times \rho \times \pi \times R^2 \times V_{\infty}^3} \]

Power Extracted by Rotor (P_e):

Watt

Density of Air (ρ):

kg/m³

Rotor Radius (R):

Meter

Free Stream Wind Speed (V_∞):

m/s

Power Coefficient (C_p):

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1. What is Power Coefficient of Wind Machine?

The Power Coefficient of Wind Machine is defined as the ratio of the power extracted by the rotor to the power available in the wind stream. It represents the efficiency of a wind turbine in converting wind energy into mechanical energy.

2. How Does the Calculator Work?

The calculator uses the Power Coefficient formula:

\[ C_p = \frac{P_e}{0.5 \times \rho \times \pi \times R^2 \times V_{\infty}^3} \]

Where:

\( C_p \) — Power Coefficient of Wind Machine
\( P_e \) — Power Extracted by Rotor (Watt)
\( \rho \) — Density of Air (kg/m³)
\( \pi \) — Archimedes' constant (≈3.1416)
\( R \) — Rotor Radius (Meter)
\( V_{\infty} \) — Free Stream Wind Speed (m/s)

Explanation: The formula calculates the efficiency of a wind turbine by comparing the actual power extracted to the theoretical maximum power available in the wind stream.

3. Importance of Power Coefficient Calculation

Details: The power coefficient is a crucial parameter in wind energy systems as it indicates how effectively a wind turbine converts wind energy into usable mechanical energy. It helps in evaluating turbine performance and optimizing design.

4. Using the Calculator

Tips: Enter power extracted in watts, air density in kg/m³, rotor radius in meters, and wind speed in m/s. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the theoretical maximum power coefficient?
A: According to Betz's law, the maximum possible power coefficient for a wind turbine is 16/27 ≈ 0.593.

Q2: How does air density affect power coefficient?
A: Higher air density increases the available wind power, but the power coefficient remains a measure of efficiency relative to the available power.

Q3: What factors influence the power coefficient?
A: Blade design, tip speed ratio, number of blades, and aerodynamic efficiency all affect the power coefficient.

Q4: Can power coefficient exceed the Betz limit?
A: No, the Betz limit represents the maximum theoretically possible efficiency for a wind turbine.

Q5: How is power coefficient used in wind farm design?
A: Power coefficient data helps in selecting appropriate turbine models and optimizing their placement for maximum energy production.