Unit 1 Wind Power

AOE Summer Math Bridge Program

Unit 1

Wind Power

Student Resources

Resource / Description
Student Resource 1.1 / Engineering Notebook Instructions
Student Resource 1.2 / Engineering Notebook Template
Student Resource 2.1 / Introduction to Wind Power
Student Resource 2.2 / Labeling Rulers
Student Resource 2.3 / Building the Tower: Specifications
Student Resource 2.4 / Tower Construction Checklist
Student Resource 2.5 / Heights and Lengths
Student Resource 3.1 / Understanding Angle of Attack
Student Resource 3.2 / Measuring Angles
Student Resource 3.3 / Setting Up a Graph
Student Resource 3.4 / Understanding Angle of Attack: Experiment Instructions and Specifications
Student Resource 3.5 / Angle of Attack Checklist
Student Resource 4.1 / Multiplication and Finding Area
Student Resource 4.2 / Rectangular Blades: Experiment Instructions and Specifications
Student Resource 4.3 / Rectangular Blades Checklist
Student Resource 4.4 / Practice with Area and Perimeter
Student Resource 5.1 / Percentage of Scrap Material
Student Resource 5.2 / Design Your Own Rotor: Instructions and Specifications
Student Resource 5.3 / Rotor Design Checklist
Student Resource 5.4 / Design Contest: Efficient Power Production
Student Resource 5.5 / Design Contest: Power at the Lowest Wind Speed

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Unit 1 Wind Power

Lesson 1 The Engineering Notebook

Student Resource 1.1

Engineering Notebook Instructions

You will be keeping an engineering notebook for the duration of the class. Engineers keep a record of all of their ideas, plans, calculations, and data in one place. It makes it easier to find information when you need it, and it also provides proof of the date that you had an idea or completed a task for legal reasons.

Each entry into your notebook must contain the following:

  • The date
  • The names of all the people you are working with on that project
  • Any data charts and observations
  • Any calculations
  • Any new ideas and thoughts about the project
  • Any planning sketches and drawings
  • Your signature, verifying that the work is yours

Never Erase Anything. Engineering notebooks record all of your work, not just what you think is correct at the time. If you must strike something out, like an incorrect calculation, just draw a single line through it.

Record all changes to your original plans or designs. Instead of erasing the old plan, write down a list of changes in an organized way. Make another sketch of the design for clarification, if needed, but leave all original sketches alone. You never know when you might need them.

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Unit 1 Wind Power

Lesson 1 The Engineering Notebook

Student Resource 1.2

Engineering Notebook Template

Name

Other Group Members

Date

Write what this notebook entry will contain.

Example: “Sketches and calculations for blade shape experiment”

Heading and Work #1

Example: “Blade Sketch #1 with Dimensions”

Heading and Work #2, etc.

Strike out incorrect work with a single line.

Blade material: Wet tissue paper. It’s cheap.

Change in blade material: cardboard.

Still cheap, but stronger.

Signature and Date

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Unit 1 Wind Power

Lesson 2 Introduction to Wind Power

Student Resource 2.1

Introduction to Wind Power

In early history, people discovered that the kinetic energy in wind can be transferred into mechanical energy to do work. You’ve probably heard of a windmill. They are tall towers with propellers spun by wind power. The earliest known windmill dates back to the time period between 500 and 900 A.D. in Persia. The earliest windmills used wind power to grind grain or pump water.

Today, windmills are used to transform wind energy into electricity. When used for this purpose, they are called wind turbines. Wind is a free and renewable resource. It is relatively nonpolluting, except for the amount of noise wind turbines make when spinning. Many people, including engineers, hope that wind power can replace a large part of the electricity that currently comes from fossil fuels.

The first wind turbine was invented in 1888 in Cleveland, Ohio. By the 1930s, many wind turbines existed, mostly on farms, to make enough electricity for a single family. Today, many countries have wind farms that produce enough electricity for entire communities. There are wind farms in the hills of California, the mountains of Spain, and even in the offshore waters of Europe. The world’s largest wind farm is located in Texas. It’s called Horse HollowWind Energy Center. It has 421 wind turbines on almost 60,000 acres of land and provides 735 megawatts of electricity, which can power more than 200,000 households.

The major parts of a wind turbine are the tower, the propeller-like rotor, and the generator that transforms the rotor’s mechanical energy to electricity. The tower is often very tall because wind is more reliable and less turbulent at higher altitudes. Depending on the intended use and surrounding environment, the rotor can have from one to dozens of blades, with many different shapes and sizes.

General Electric, for example, makes a 1.5 megawatt wind turbine that is used on wind farms. It has a rotor diameter that spans 77 meters (253 feet) and a tower that stands 100 meters (328 feet). An individual household, on the other hand, might have a wind turbine with a 30-foot tower and a rotor diameter of 4 or 5 feet.

There are many types of wind turbines. Traditional wind turbines need their rotors pointed into the wind to produce electricity. The Darrieus wind turbine, patented 1927, is a vertical axis wind turbine that can use wind that blows from any direction. Another type of wind turbine, Magenn Power’s Air Rotor System, is also being developed. It is as big as a house, filled with helium, and floats 1000 feet in the sky where wind constantly blows. This flying wind turbine is tied down with a copper wire that transfers its electricity to the ground.

In this unit, you will design and build a small traditional wind turbine from craft sticks, cardboard, and an electric motor, which will work in reverse as a generator. Your rotor will be attached to the shaft of an electric motor. A fan will provide the wind to spin your rotor, which will then rotate the motor’s shaft and produce electricity.

The rotor’s design is important. An efficient rotor will transfer more wind energy to the generator’s shaft and produce more electricity. You will experiment with different blade shapes, sizes, and pitch angles to understand how these factors affect the amount of wind energy transferred to electricity.

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Unit 1 Wind Power

Lesson 2 Introduction to Wind Power

Student Resource 2.2

Labeling Rulers

PART I

How many equal pieces does the mark divide this unit length into? Write the appropriate number for that mark.

a)

Do the same thing for b–d.

b)

c)

0

d)

Which numbers from the rulers above represent the same length?

Use a–d to label each length mark between 0 and 1 unit on this ruler with the simplest form of the fraction it represents.

How many equal pieces do these marks divide this unit length into? Label each mark with the appropriate number.

Name the pairs of numbers that stand for the same length on the ruler.

PART II

Label the following rulers:

Can you divide the following ruler into equal pieces that will contain all of the fractional measurements in the previous two rulers? Label each mark you make with of the number it represents. (Hint: There will be more than 5 marks on the ruler!)

Label the marks on these rulers:

Divide this ruler into equal pieces that will contain all of the fractional measurements in the previous two rulers. Label each mark with the simplest form of the number it represents.

What is the relationship between the number of pieces you came up with in your answer and the number of pieces in the original two rulers?

PART III

Which is larger, or ? Draw one ruler with an appropriate number of equal pieces to show how you know. (How many equal pieces are needed to show both 3rds and 7ths?)

Which is larger, or ? Divide one ruler into equal pieces to show how you know.

PART IV

Use this ruler to measure lengths a, b, and c. Name each of those lengths in at least two different ways:

Example:

a)

b)

c)

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Unit 1 Wind Power

Lesson 2 Introduction to Wind Power

Student Resource 2.3

Building the Tower: Specifications

Materials

  • No more than 25 craft sticks
  • Masking tape

Constraints

1)The tower may use no more than 25 craft sticks.

2)The tower “footprint” (the area of ground space it requires) must fit inside an 8 × 8 in square.

3)The tower must be between 9 and 12 in tall, not including the generator or blades.

4)The tower must have a flat surface (parallel to the ground) on the top. This surface must be stable enough to attach the generator and windmill blades to. The generator will be attached with masking tape.

5)The tower must not block the free rotation of the wind generator blades. The blades will extend no more than 6 in from the center of the hub.


Directions

1)Working in pairs, you will be designing and building your own tower for your wind generator.

2)In your engineering notebook, sketch a design for your tower. Both partners need to have a sketch in their notebooks.

3)You will be given one craft stick. Measure the length of the craft stick with a ruler. Use it as a guide to calculate the height and footprint of your design to make sure that it satisfies the given constraints. Make any necessary changes to your design and record the measurements in your notebook.

4)Calculate the number of craft sticks used in your design and record it in your notebook. Make sure that it satisfies the given constraints. Make any necessary changes to your design. Note the changes in your notebook.

5)Check to make sure constraints 4 and 5 are satisfied. Record any changes to the design in your notebook.

6)Ask your instructor to approve your design and give you the exact number of craft sticks you require, based on your calculations.

7)Build your tower. Note any difference between the number of craft sticks you originally asked for and the number you actually used.

8)Measure the actual length, width, and height of your tower and record it in your notebook. If the constraints are not satisfied, change your design and record all changes.

9)Make a drawing of your final product with the actual dimensions in your notebook.

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Unit 1 Wind Power

Lesson 2 Introduction to Wind Power

Student Resource 2.4

Tower Construction Checklist

Task or Constraint / Completed/Constraint Satisfied
Materials Constraint
Explain the constraint in your own words:
Write the constraint with mathematical symbols:
Tower Footprint Constraint
Explain the constraint in your own words:
Write the constraint with mathematical symbols:
Height Constraint
Explain the constraint in your own words:
Write the constraint with mathematical symbols:
Generator Attachment Constraint
Explain the constraint in your own words:
Free Rotation Constraint
Explain the constraint in your own words:
Initial sketch in notebook
Theoretical height and footprint calculations in notebook
Calculations for number of craft sticks needed in notebook / Number of craft sticks needed:
Design approved by instructor, and craft sticks received
Tower built
Final drawing of tower with all dimensions labeled in notebook

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Unit 1 Wind Power

Lesson 2 Introduction to Wind Power

Student Resource 2.5

Heights and Lengths

Use your ruler or tape measure to figure out the following problems.

1)Renysha builds a tower that is in tall. The wind propeller adds in to the top of the tower. How tall is the entire wind generator and tower?

2)Jose built a tower that is in high. How much does he have to reduce the height of his tower to make it in?

3)The base of Elena’s tower is a rectangle. The width is in, and the length is in. How many craft sticks did Elena need to build the perimeter of her tower base? How much length of stick was left over when she finished building it?

The previous problems used regular rulers that are divided into in lengths. The following problems use rulers divided into other lengths. For each problem,

a)Decide how many equal pieces the ruler needs to be divided into.

b)Sketch an appropriate ruler.

c)Solve the problem using the ruler.

4)Deandre has a rope that is yd and ties another yd of rope to it. How long is the entire rope (in yards)?

5)When relaxed, a rubber band measures in long. Stephen stretches it another in. How long is the stretched rubber band?

6)Valerie builds a rectangular tower whose footprint is in wide, and in long. What is the perimeter of the tower’s footprint?

Explain how to figure out the number of equal pieces a ruler should be divided into when solving addition and subtraction problems.

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Unit 1 Wind Power

Lesson 3 Angles of Attack

Student Resource 3.1

Understanding Angle of Attack

The angle of attack is an important factor in how a blade moves in the wind, which effects how much energy is captured by a wind turbine. Here is what you need to know to accurately measure an angle of attack.

Angle of Attack: the angle created by the relative direction of the wind and an airfoil’s chord line. The angle of attack is often denoted by the Greek letter (pronounced “alpha”).

Airfoil: A streamlined surface that produces useful movement when air flows around it. Wind turbine rotor blades, airplane wings, and kites are all examples of airfoils.

Chord Line: The straight line that connects the leading edge to the trailing edge.

Leading Edge: The edge of the airfoil that hits the oncoming wind first.

Trailing Edge: The edge of the airfoil that hits the oncoming wind last.

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Unit 1 Wind Power

Lesson 3 Angles of Attack

Student Resource 3.2

Measuring Angles

We will be measuring all angles in degrees.Write the measure of each angle next to that angle.

Using a protractor, draw a rotor blade whose angle of attack is

a)10 degrees

b)50 degrees

c)90 degrees

d)125 degrees

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Unit 1 Wind Power

Lesson 3 Angles of Attack

Student Resource 3.3

Setting up a Graph

Example 1: Set up a graph for the following data to fill half a sheet of paper.

Time (minutes) / 5 / 8 / 15 / 22 / 30 / 45 / 51 / 63
Amount of food left (percent) / 97 / 90 / 84 / 71 / 66 / 57 / 43 / 32

Step 1: On a half sheet of graph paper, 25 units are available in the x direction and 20 units in the y direction.

Step 2: The range of values for x is 5–63. The range of y values is 32–97.

Step 3: All the values in the chart are positive, so I only need the first quadrant in my graph.

Step 4: On the x-axis, I want to go from 0 to about 70 in 25 units. If I make every unit represent 3 minutes, I’ll reach 75 before I run out of squares, which is good enough.

On the y-axis, I need to go from 0–100 because it doesn’t make sense to go higher than 100%. That means I need to scale 100 onto 20 units. If I make each unit represent 5%, I’ll make 100 exactly.

Steps 5–7: I set up the graph like this:

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Unit 1 Wind Power

Lesson 3 Angles of Attack

Student Resource 3.4

Understanding Angle of Attack:
Experiment Instructions and Specifications

Materials

  • Built tower
  • Rotor blades of different shapes
  • Paperclips
  • Rotor hub
  • Generator
  • Wind source
  • Voltmeter/multimeter
  • Wires and alligator clips
  • Protractor
  • Graph paper

Angles of Attack

0, 20, 45, 60, 90 degrees

Blade Shapes (Your group will be responsible for one shape.)

Square / Rectangle / Equilateral triangle / Right triangle / Trapezoid / Parallelogram (nonrectangular)


Directions

1)You will be assigned one blade shape for this experiment. Your instructor will give you three blades of your assigned shape to use during this experiment.

2)Create an organized data table for the experiment in your notebook for this experiment. The data table should include 3 columns: angle of attack, range of voltage output, and average voltage output.

3)Attach the three blades equidistant from each other to the rotor hub using paperclips. Set the angle of attack of each blade to 0 degrees.

4)Attach the rotor to the generator by pushing the hub onto the shaft securely. Make sure that when the rotor rotates, the shaft rotates with it. Tape the generator to the top of your tower.

5)Wire the generator to the multimeter, following the diagram.

6)Set up the fan 1½ ft away from the wind tower so that the wind will blow perpendicular to the front of the rotor hub.

7)Set the multimeter to read millivolts (mV).

8)Turn on the fan and record the range of voltage generated in the organized table in your notebook.

9)Repeat steps 3–8 for the rest of the angles of attack.

Graph the data for your blade shape and post the graph for the rest of the class to see. Use the average value of the voltage output for your data points. Make the angle of attack the x-axis and the voltage the y-axis. Include the following:

a)A title that makes sense

b)Appropriate scale for both axes that will make the graph fill at least a half page

c)Labels for both axes

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Unit 1 Wind Power

Lesson 3 Angles of Attack

Student Resource 3.5

Angle of Attack Checklist

Task or Constraint / Completed or Constraint Satisfied
Three blades received from instructor.
Blade shape assigned:
Organized data table for the experiment created in notebook.
Wind turbine attached to tower and wired to multimeter correctly.
Wind source is correct distance from the generator.
Voltage measured and range recorded as an inequality: 0 degrees
Voltage measured and range recorded as an inequality: 20 degrees
Voltage measured and range recorded as an inequality: 45 degrees
Voltage measured and range recorded as an inequality: 60 degrees
Voltage measured and range recorded as an inequality: 90 degrees
Average voltage output for each angle of attack calculated and recorded.
Produced graph of data with:
Correct scale
Correctly labeled x-axis and y-axis
Appropriate title
At least one-half page in size

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