Power Extracted By Rotor Given Power Coefficient Of Wind Machine Calculator

Formula Used:

\[ P_e = C_p \times \left(0.5 \times \rho \times \pi \times R^2 \times V_{\infty}^3\right) \]

Power Coefficient of Wind Machine (C_p):

(dimensionless)

Density of Air (ρ):

kg/m³

Rotor Radius (R):

meters

Free Stream Wind Speed (V_∞):

m/s

Power Extracted by Rotor (P_e):

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1. What is Power Extracted by Rotor?

Power Extracted by Rotor is the rate at which mechanical energy is extracted by the rotor from the wind stream by reducing its kinetic energy. This represents the actual power that can be harnessed from wind energy using a wind turbine.

2. How Does the Calculator Work?

The calculator uses the wind power extraction formula:

\[ P_e = C_p \times \left(0.5 \times \rho \times \pi \times R^2 \times V_{\infty}^3\right) \]

Where:

\( P_e \) — Power Extracted by Rotor (Watts)
\( C_p \) — Power Coefficient of Wind Machine (dimensionless, 0-1)
\( \rho \) — Density of Air (kg/m³)
\( \pi \) — Mathematical constant pi (≈3.1416)
\( R \) — Rotor Radius (meters)
\( V_{\infty} \) — Free Stream Wind Speed (m/s)

Explanation: The formula calculates the maximum theoretical power that can be extracted from wind, modified by the efficiency coefficient (C_p) of the specific wind machine.

3. Importance of Power Extraction Calculation

Details: Accurate power extraction calculation is crucial for wind turbine design, energy production estimation, site selection for wind farms, and evaluating the economic viability of wind energy projects.

4. Using the Calculator

Tips: Enter power coefficient (0-1), air density (typically 1.225 kg/m³ at sea level), 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 typical range for power coefficient (C_p)?
A: The theoretical maximum (Betz limit) is 0.593, but practical wind turbines typically achieve C_p values between 0.35-0.45.

Q2: How does air density affect power extraction?
A: Power extraction is directly proportional to air density. Higher density (colder air) means more power can be extracted from the same wind speed.

Q3: Why is wind speed cubed in the formula?
A: The kinetic energy in wind is proportional to the cube of wind speed, meaning small increases in wind speed result in large increases in available power.

Q4: What factors affect the power coefficient?
A: Blade design, number of blades, tip speed ratio, and aerodynamic efficiency all influence the power coefficient of a wind turbine.

Q5: How accurate is this calculation for real-world applications?
A: This provides theoretical maximum. Actual power output may be lower due to mechanical losses, generator efficiency, and other system inefficiencies.