Wind Turbine Calculator

Wind power is a rapidly growing source of renewable energy, harnessing the kinetic energy of the wind to generate electricity. The Wind Turbine Calculator allows you to explore the fundamental principles of wind energy by estimating the potential power output of a horizontal-axis wind turbine based on its size and the prevailing wind conditions.

How Do Wind Turbines Generate Electricity?

A wind turbine works on a simple principle: instead of using electricity to make wind—like a fan—it uses wind to make electricity. The wind turns the large, propeller-like blades of a turbine around a rotor. This rotor is connected to a main shaft, which spins a generator to create electricity.

The amount of power a turbine can produce is heavily dependent on the wind speed and the size of its blades.

How to Use the Calculator

This calculator uses the standard formula for wind power to estimate a turbine's output.

Step-by-Step Guide

1. Enter Blade Radius (meters): This is the length of a single turbine blade, from the center of the rotor to the tip. The total area swept by the blades is a critical factor.
2. Enter Wind Speed (m/s): Input the speed of the wind passing through the blades. Power output increases exponentially with wind speed.
3. Set Turbine Efficiency (%): This is the power coefficient (Cp), representing how efficiently the turbine can convert the kinetic energy of the wind into electrical energy. The theoretical maximum efficiency is 59.3% (known as Betz's Law), but real-world turbines are typically in the 35-45% range.
4. Calculate Power: Click the "Calculate Power Output" button to see the estimated power in kilowatts (kW) and megawatts (MW).

The Formula Behind the Calculation

The power available in the wind is calculated using the following formula:

Power (Watts) = 0.5 × ρ × A × v³ × Cp

Where:

• ρ (rho) is the density of air, approximately 1.225 kg/m³ at sea level.
• A is the swept area of the blades in square meters, calculated as A = πr².
• v is the velocity of the wind in meters per second (m/s).
• Cp is the Power Coefficient or efficiency of the turbine (a decimal value, e.g., 0.40 for 40%).

The most important takeaway from this formula is that power is related to the cube of the wind speed (v³). This means that doubling the wind speed increases the available power by a factor of eight!

A Practical Example

Let's calculate the power output for a typical utility-scale wind turbine.

• Scenario: A wind turbine with a blade radius of 50 meters is operating in a 12 m/s wind. Its efficiency is 40%.
• Inputs:
  • Blade Radius (r): 50 m
  • Wind Speed (v): 12 m/s
  • Efficiency (Cp): 40%
• Calculation:
  • Swept Area (A) = π × (50 m)² = 7854 m²
  • Power (W) = 0.5 × 1.225 × 7854 × (12)³ × 0.40
  • Power (W) = 0.5 × 1.225 × 7854 × 1728 × 0.40
  • Power (W) ≈ 3,313,939 Watts
  • Power (MW) ≈ 3.31 MW

This single turbine could generate approximately 3.31 megawatts of power, which is enough to power over 1,000 average homes while it is operating.

Real-World Turbine Operation

While the formula provides a snapshot of power at a specific wind speed, real-world turbines have a more complex operating profile:

• Cut-in Speed: The minimum wind speed (usually 3-4 m/s) required to start generating power.
• Rated Speed: The wind speed at which the turbine generates its maximum, or "rated," power.
• Cut-out Speed: A high wind speed (usually around 25 m/s) at which the turbine shuts down to prevent damage.

Frequently Asked Questions (FAQ)

What is Betz's Law?

Betz's Law, formulated in 1919 by German physicist Albert Betz, states that no turbine can capture more than 59.3% of the kinetic energy in wind. This is because if a turbine were 100% efficient, it would stop the wind completely, and no more wind could flow through it. The 59.3% limit is the theoretical maximum.

Why is turbine height important?

Wind speeds are generally faster and more consistent at higher altitudes, away from ground-level obstacles like trees and buildings. This is why utility-scale turbines are placed on very tall towers.

Are wind turbines noisy?

Modern wind turbines are designed to be relatively quiet. From a distance, the aerodynamic swoosh of the blades is often the most noticeable sound, which is typically quieter than the background noise of the wind itself.

Internal & External Resources

Internal Links

• Hydroelectric Power Calculator
• Solar Panel Calculator
• Power Converter

External Resources

• U.S. Department of Energy - How Do Wind Turbines Work?
• WINDExchange - U.S. DOE Wind Energy Technologies Office