Vernier Software & Technology

# Solidity

## Introduction

Consider the wind turbines in Figures 1 and 2. What differences do you observe? These two examples are designed for two different purposes. The windmill in Figure 1 is designed to pump water; the turbine in Figure 2 is designed to generate electricity. In addition to variations in the tower design and number of blades, notice that the total surface area of the blades in each turbine is very different.

Solidity, the ratio of the total surface area for all blades to the total swept area, is calculated using the equation

$\text{solidity} = na/A$

where n is the number of blades, a is the area of a single blade, and A is the swept area of the turbine.

Turbines with a high solidity (e.g., greater than 0.80), rotate at a low speed, while turbines with a low solidity (e.g., 0.10), rotate at a higher speed.

Blade pitch dramatically affects the torque, speed, and the amount of drag experienced by the blades of the rotor. It also affects the solidity of the turbine. Blades with a shallow pitch (10–30°) have less drag, and provide greater solidity by presenting more of their surface to the wind. However, they can’t provide as much torque (turning force) to the generator. A greater pitch (30–60°) has less solidity and more drag, but can provide more torque to the generator.

In this experiment, you will calculate the planform area, the area the blade projects onto the plane of rotation, using the area of the blade and its pitch. You will use the total planform area (for all blades) to calculate the solidity of the wind turbine. You will then investigate how the turbine solidity affects electrical power output.

## Objectives

• Measure the total blade planform area.
• Calculate the total area swept by a wind turbine blade.
• Calculate solidity of a wind turbine.
• Investigate the relationship between power output and solidity.

## Sensors and Equipment

This experiment features the following Vernier sensors and equipment.

### Option 2

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 11 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.