Vernier Software & Technology

# Turbine Efficiency

## Introduction

The efficiency of a wind turbine can be defined by the following equation:

$\text{Efficiency} = \frac{\text{Electrical power transformed by the wind turbine}}{\text{Power available in the wind}}$

For a wind turbine to be 100% efficient, all of the energy available in the wind would be converted into electricity. In other words, all of the energy in the wind would be transformed and the air would stop moving. This is not possible in practice because a rotor only spins if the wind passes over the blades. If a rotor were to stop all the moving air, the turbine would not be able to convert the wind’s kinetic energy to electrical energy.

A German physicist, Albert Betz, calculated that it is impossible to design a wind turbine that is able to convert more than 59.3% of the kinetic energy of the wind into mechanical energy turning a rotor. Known as the Betz Limit, 59.3% is the theoretical maximum efficiency for any wind turbine operating in real-world conditions (open air flow). In typical operating wind speeds, most modern wind turbines are 25–45% efficient.

The Betz Limit applies only to the transformation of the kinetic energy in the wind into mechanical energy in the rotating blades. The generator in the wind turbine, which transforms the mechanical energy into electrical energy, further reduces the total efficiency. To understand this process, imagine that the blades of a wind turbine convert 50% of the available power in the wind into mechanical energy (rotation). Then, the generator converts 80% of this mechanical energy into electrical energy. The overall efficiency of this wind turbine would therefore be 0.5 × 0.8 = 0.4, or 40% efficient.

When designing blades for a wind turbine, engineers try to maximize the efficiency of the rotor across a range of wind speeds—a wind turbine needs to be highly efficient at low wind speeds (4–8 m/s), which are most common, but it also needs to perform and survive in extreme wind speeds (>25 m/s)! Over time, engineers have experimented with many different shapes, designs, materials, and number of blades to find which work best. In this experiment, you will experiment with different blade designs to maximize efficiency.

## Objectives

• Measure the power produced by a wind turbine.
• Calculate the efficiency of a wind turbine.
• Evaluate data to determine which blade design is most efficient.

## Sensors and Equipment

This experiment features the following Vernier sensors and equipment.

You may also need an interface and software for data collection. What do I need for data collection?

## Renewable Energy with Vernier

See other experiments from the lab book.

 1 Renewable Energy: Why is it So Important? 2 What is Energy? 3 Project: Energy Audit 4 Voltage and Circuits 5 Current and Resistors 6 Mechanical Power 7 Generators 8 Exploring Wind Turbines 9 Effect of Load on Wind Turbine Output 10 Blade Variables and Power Output 11 Solidity 12 Turbine Efficiency 13 Power Curves 14 Power and Energy 15 Project: Maximum Energy Output 16 Project: Build a Wind Farm 17 Exploring Solar Panels 18A Effect of Load on Solar Panel Output 18B Fill Factor and IV Curve of a Solar Panel 19 Variables Affecting Solar Panel Output 20 Effect of Temperature on Solar Panel Output 21 Project: Build a Solar Charger 22 Exploring Passive Solar Heating 23 Variables Affecting Passive Solar Heating 24 Exploring Solar Collectors 25 Variables Affecting Solar Collectors 26 Project: Solar Cooker

### Experiment 12 from Renewable Energy with Vernier Lab Book

#### Included in the Lab Book

Vernier lab books include word-processing files of the student instructions, essential teacher information, suggested answers, sample data and graphs, and more.