The Effect of Blade Angle on the Power Output of a Wind Turbine in Low-Wind Areas (Hands-on and modelling)

“It seems to me that the natural world is the greatest source of excitement; the greatest source of visual beauty; the greatest source of intellectual interest. It is the greatest source of so much in life that makes life worth living.”

—David Attenborough, English broadcaster and naturalist

Research Question Since I was a child, I have always been fascinated by nature and by the life and beauty that surrounds us. Thus, I have continuously dedicated my time and energy towards environmental awareness.

When brainstorming topics in physics, I immediately remembered an article I had read recently. It discussed Rhode Island’s plans for the first offshore wind farm in the United States, the Block Island wind farm. This farm actually has the potential to provide large amounts of energy due to the

strong coastal winds. Yet this lead me to question, what about areas with low wind speeds? Shouldn’t we also focus on how to optimize turbine designs in places where wind energy needs improvement? From here, I began looking at the factors that can affect the output of a wind turbine – turbine structure, number of blades, gear ratio, and more – and one in particular caught my eye: blade angle. It seemed so insignificant, leading me to ponder how it actually affects a turbine’s power output.

Thus, my research question is: how does the blade angle of the blades on a wind turbine in an area with low wind speeds affect its power output?

Background InformationBefore I can begin my investigation, I must first deepen my understanding of the background principles regarding wind turbines. Here is some of my research:

Image: Wind turbines in a wind farmSource: http://c1cleantechnicacom.wpengine.netdna-cdn.com/files/2014/04/wind-turbines17.jpg

How a wind turbine works:Wind turbines are made with careful precision. Basically, the blades are attached to a low-speed shaft that turns with them. At the other end of this low-speed shaft is a gearbox. The gearbox is very important. The blades usually turn very slowly, not even close to fast enough to generate any electricity. However, the gears in the gearbox can translate, for example, 18 rotations per minute into 1800 rpm, depending on the design. These gears are attached to a high-speed shaft, which ultimately turns the coil inside the electromagnetic generator.

How an electromagnetic generator works:The high-speed shaft is connected to a coil that is placed between two opposite magnets. These magnets are held apart, and create a magnetic field in the space between them. The field is made up of lines of force, and when these lines are cut by an electric conductor, electricity is produced. In the generator, the coil is the conductor, and is rotated whenever the high-speed shaft turns, which is moved by

the low-speed shaft, which in turn is rotated with the blades. But how exactly do the blades turn?

How the blades work:Depending on the type of wind turbine, blades can look extremely different. However, looking only at the horizontal axis designs that will be used in this experiment, most blades have a couple things in common. When the wind blows, it goes around both sides of the blade. The blades are made uneven, thicker on one side and thinner on the other, causing uneven air pressure, and ultimately making the blades spin around the center of the turbine. In order to keep the turbine spinning with the wind, there is a wind vane connected to a computer in the back.

Image: Diagram of electromagnetic generatorSource: https://sasco54.files.wordpress.co

Image: Diagram of inside of wind turbineSource: http://www.cleanlineenergy.com/sites/cleanline/media/Parts_of_wind_turbine_l

Experimental DesignIn order to accurately judge the optimum wind turbine blade angle, I will need to make sure that other factors that could potentially alter the power output of the turbine are made constant. The first is the style of the turbine – there are two options: classic, which consists of three pointed blades and is the most commonly seen, and windmill-style, which consists of a minimum of 6 blades which are almost rectangular and resemble the image shown above. Upon researching, I found that the windmill-style turbines are more commonly used in lower wind regions, so I decided to keep that as the model for the basic structure. Since this design generally has a minimum of 6 blades and tends to otherwise vary, I chose six blades as a safe constant. Lastly, when looking at the gear ratio, I decided to keep it at 1:3, which would be the easiest to turn at a low wind speed, ensuring that the most data possible is obtained. In order to test for the highest power output, I chose to use a multimeter to measure current and voltage and then use P = Iv to get power. I will take 10 readings from each of 5 trials twice, one for voltage and the second for current, and record the data.

Experimental Independent Variables, Dependent Variables, ConstantsThe independent variable in this experiment is the angle at which the blades on the turbine are turned. It will be tested at 0⁰, 10⁰, 20⁰, 30⁰, and 40⁰.

The dependent variables in this experiment are the current in milliamps and the voltage in volts.

The controlled variables in this experiment are the fan, the wind speed (3.5 mph, based on lowest national average wind speed data), the set-up and position of the turbine model, the location of the model (100 cm distance from the fan and 26 cm above the floor), the multimeter used to measure current and voltage, the generator in the turbine, the windmill-style structure of the turbine, the number of blades (6), and the gear ratio (1:3).

Materials114.3 cm house fan – provides constant wind speed of 3.5 mph at 100 cm distance

Tape measure – used in measurements to keep position (height, distance) constant

26 cm. tall base – used to keep model at constant height high enough to catch wind directly

Weight to hold down wind turbine – keeps it in place through changes in design throughout experiment

Protractor – used to measure the blade angle in the experiment

Left: Windmill-style wind turbineSource: http://turbotricity.com/wp-content/uploads/6-blade-sm-jpeg-260x300.jpg

Windmill model

Gears (2 small [2.03 cm diameter], 2 medium [4.06 cm diameter], 2 big [6.1 cm diameter])

41.91 cm pole (1)

22.86 cm rectangular blades (6) – for windmill-style turbine

15.24 cm Axle (2)

Electromagnetic generator (1)

Digital multimeter – measures current and voltage

Experiment Method1. First, I had to build the basic skeleton of the model of the windmill. In order to do this, I used a set of 2 small, 2 medium, and 2 large gears. I put one of each size in order from smallest to largest on one axle, and put the others in order from largest to smallest on the other. After securing in the two axles, I attached an axle connector that fit both blade types on the first axle. For the second axle, on the opposite side, I attached the electromagnetic generator. This entire mechanism I then attached to the 16.5” pole, putting two brick weights on the base in order to hold the turbine down.

2. Next, I had to figure out the best possible placing for the windmill, which turned out to be keeping the turbine model at a 100 cm distance from the fan, and on top of a 26 cm stool so it could catch the most wind at a constant speed of 3.5 mph at 100 cm distance

3. Once everything was set up, I used a protractor to change the blade angles and noted results. For each, I took 10 readings from each of 5 trials twice, one for voltage and the second for current, and recorded the data. Upon getting the results, I finished recording the data and began to draw conclusions.

Raw DataThe measurement uncertainty of the digital multimeter used is + 1%

Due to the sensitivity of the multimeter device, values displayed in each trial continuously change. Thus, the following table displays 10 of the values from each trial.

Blade Angle vs. Raw Output Values

Blade Angle Voltage (V) + 1% Current (mA) + 1%Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 1 Trial 2 Trial 3 Trial 4 Trial 5

0⁰

0.00 0.00 0.00 0.00 0.00 0.0 0.0 0.0 0.0 0.00.00 0.00 0.00 0.00 0.00 0.0 0.0 0.0 0.0 0.00.00 0.00 0.00 0.00 0.00 0.0 0.0 0.0 0.0 0.00.00 0.00 0.00 0.00 0.00 0.0 0.0 0.0 0.0 0.00.00 0.00 0.00 0.00 0.00 0.0 0.0 0.0 0.0 0.00.00 0.00 0.00 0.00 0.00 0.0 0.0 0.0 0.0 0.00.00 0.00 0.00 0.00 0.00 0.0 0.0 0.0 0.0 0.00.00 0.00 0.00 0.00 0.00 0.0 0.0 0.0 0.0 0.00.00 0.00 0.00 0.00 0.00 0.0 0.0 0.0 0.0 0.00.00 0.00 0.00 0.00 0.00 0.0 0.0 0.0 0.0 0.0

10⁰

0.07 0.06 0.12 0.06 0.07 77.5 89.7 90.2 63.8 90.60.07 0.08 0.11 0.11 0.08 57.0 99.7 66.6 62.8 80.90.08 0.06 0.11 0.08 0.07 85.0 110.3 65.4 57.4 80.90.06 0.05 0.06 0.12 0.08 64.6 67.1 98.7 39.9 57.70.09 0.10 0.09 0.10 0.13 49.8 64.7 77.8 81.9 48.70.09 0.07 0.12 0.14 0.07 86.3 52.7 65.0 38.3 64.20.10 0.10 0.10 0.12 0.10 92.5 59.4 107.4 89.5 88.30.13 0.10 0.11 0.11 0.14 93.1 89.7 130.4 72.7 94.80.11 0.07 0.09 0.08 0.13 95.5 89.6 112.4 71.3 111.40.13 0.11 0.08 0.09 0.12 93.1 100.2 81.3 51.5 99.5

20⁰

0.27 0.37 0.44 0.46 0.44 175.6 191.3 200.0 194.0 169.20.28 0.38 0.45 0.45 0.40 176.1 202.2 200.0 194.5 178.50.33 0.37 0.43 0.46 0.39 166.5 202.2 192.1 197.5 163.90.32 0.35 0.47 0.46 0.28 189.6 200.7 201.3 183.1 168.50.34 0.38 0.46 0.42 0.40 190.8 193.1 196.8 191.3 172.50.33 0.42 0.42 0.43 0.45 194.1 200.1 201.9 197.8 172.40.35 0.43 0.41 0.44 0.41 200.4 201.8 200.7 190.0 185.00.34 0.41 0.42 0.43 0.38 179.5 191.8 200.0 195.4 198.40.36 0.41 0.43 0.42 0.36 197.1 200.0 191.0 194.1 193.40.39 0.46 0.44 0.43 0.33 201.4 198.6 187.4 188.5 178.20.14 0.12 0.25 0.25 0.22 110.4 132.4 114.1 85.4 128.3

30⁰

0.16 0.15 0.27 0.25 0.21 102.5 138.2 109.9 96.2 119.50.18 0.18 0.25 0.24 0.23 97.9 124.5 110.2 100.3 146.40.11 0.20 0.24 0.25 0.22 92.4 99.3 96.8 120.7 131.50.13 0.24 0.25 0.26 0.24 90.5 106.6 96.8 118.7 111.20.19 0.22 0.25 0.25 0.19 90.5 127.4 102.3 135.2 83.70.15 0.22 0.26 0.24 0.22 109.3 123.1 127.6 94.5 85.90.11 0.22 0.24 0.25 0.22 120.2 109.8 132.2 98.8 88.40.14 0.23 0.25 0.22 0.24 111.2 118.6 83.5 102.0 113.60.13 0.24 0.26 0.21 0.23 111.2 118.2 92.1 105.3 101.7

40⁰

0.08 0.06 0.09 0.07 0.06 63.5 67.0 83.2 77.2 83.50.07 0.07 0.07 0.05 0.07 67.2 59.2 79.4 76.5 90.20.08 0.07 0.04 0.05 0.08 53.9 52.4 61.1 76.5 90.20.08 0.06 0.04 0.07 0.07 64.6 81.9 61.1 62.8 93.30.07 0.08 0.06 0.09 0.05 71.9 83.2 61.1 74.5 86.10.06 0.07 0.04 0.08 0.08 71.8 80.2 64.9 54.6 82.90.09 0.05 0.09 0.06 0.06 75.6 79.4 72.6 63.2 72.40.08 0.06 0.07 0.05 0.05 64.1 86.3 65.2 68.9 65.80.09 0.05 0.05 0.06 0.05 77.7 91.3 81.0 75.3 65.80.09 0.08 0.06 0.09 0.04 81.3 54.2 81.4 78.7 61.6

Processed DataResultsTo simplify the data, I took averages of all the values from each trial and displayed them in the following table:

The uncertainties in the mean were found using the formula: ∆ X= Range2

=Max−Min2

Blade Angle vs. Trial Output Averages

Blade Angle

Trial # Average Voltage

Absolute Uncertainty Voltage (V) Percentage

UncertaintyAverage Current

Absolute Uncertainty

Current (mA)

Percentage Uncertainty

0⁰

Trial 1 0.000 0.000 0.00 0 0.00 0.00 0.00 0Trial 2 0.000 0.000 0.00 0 0.00 0.00 0.00 0Trial 3 0.000 0.000 0.00 0 0.00 0.00 0.00 0Trial 4 0.000 0.000 0.00 0 0.00 0.00 0.00 0Trial 5 0.000 0.000 0.00 0 0.00 0.00 0.00 0

10⁰Trial 1 0.093 0.035 0.09 + 0.04 38 79.44 22.85 79 + 20 29Trial 2 0.080 0.030 0.08 + 0.03 38 82.31 28.80 82 + 30 35Trial 3 0.099 0.030 0.10 + 0.03 30 89.52 32.70 90 + 30 37

Trial 4 0.101 0.040 0.10 + 0.04 40 69.91 25.60 70 + 30 37Trial 5 0.099 0.035 0.10 + 0.04 35 81.70 31.35 82 + 30 38

20⁰

Trial 1 0.331 0.060 0.33 + 0.06 18 187.11 17.45 190 + 20 9Trial 2 0.398 0.055 0.40 + 0.06 14 198.18 5.45 200 + 5 3Trial 3 0.437 0.030 0.44 + 0.03 7 197.12 7.25 200 + 7 4Trial 4 0.440 0.020 0.44 + 0.02 5 192.62 7.35 190 + 7 4Trial 5 0.384 0.085 0.38 + 0.09 22 178.00 17.25 180 + 20 10

30⁰

Trial 1 0.144 0.040 0.14 + 0.04 28 103.61 14.85 100 + 20 14Trial 2 0.202 0.060 0.20 + 0.06 30 119.81 19.45 120 + 20 16Trial 3 0.252 0.015 0.25 + 0.02 6 106.55 24.35 110 + 20 23Trial 4 0.242 0.025 0.24 + 0.03 10 105.71 24.90 110 + 30 24Trial 5 0.222 0.025 0.22 + 0.03 11 111.02 31.35 110 + 30 28

40⁰

Trial 1 0.079 0.015 0.07 + 0.02 19 69.16 13.70 69 + 10 20Trial 2 0.068 0.015 0.07 + 0.02 22 73.51 19.45 74 + 20 26Trial 3 0.061 0.020 0.06 + 0.02 33 71.10 11.05 71 + 10 16Trial 4 0.072 0.020 0.07 + 0.02 28 70.82 12.05 71 + 10 17Trial 5 0.061 0.020 0.06 + 0.02 33 79.18 15.85 79 + 20 20

In order to further simplify the data and see clearer patterns, I took averages of all the values from each different angle, combining the trials, and displayed them in the following table:

The uncertainties in the mean were found using the formula: ∆ X= Range2

=Max−Min2

Blade Angle vs Overall Average Output

Blade Angl

e

Average Voltage

Absolute Uncertainty Voltage (V) Percentage

UncertaintyAverage Current

Absolute Uncertainty

Current (mA)

Percentage Uncertainty

0⁰ 0.000 0.0000 0 0 0.00 0.00 0 010⁰ 0.094 0.0105 0.09 + 0.01 11 80.58 9.81 81 + 4 1220⁰ 0.398 0.0545 0.40 + 0.05 14 190.61 10.09 190 + 10 530⁰ 0.212 0.0540 0.21 + 0.05 25 109.34 8.10 110 + 8 740⁰ 0.068 0.0035 0.07 + 0.003 6 72.75 5.01 73 + 5 7

To find the average power output, the formula P = Iv will be used, where P is power in watts, I is current in amperes, and v is voltage in volts.

To find the average power output in milliwatts, the results in milliamperes will be multiplied by the results in volts.

Final results:

Blade Angle Avg. Power Output (mW)

0⁰ 010⁰ 8 + 2

20⁰ 76 + 14

30⁰ 23 + 8

40⁰ 5 + 0.6

These results appear to demonstrate a relationship between the angle of the blade on a wind turbine and the power that it subsequently generates. In order to see even more clearly how these two variables relate, I will graph them.

Graphs

0 5 10 15 20 25 30 35 40 450

10

20

30

40

50

60

70

80

Blade Angle vs Power Output

Blade Angle (⁰)

Avg.

Pow

er O

utpu

t (m

W)

For these graphs, I started by plotting the points in order to see what the general pattern was. Based on this, I drew out a general line of best fit in order to help make the trend clearer.

ConclusionWhen looking at the data, there seems to be a trend in the data that shows that the average power output peaks at 20 degrees as the blade angle. This is interesting, yet the shape of the graph makes it impossible to linearize this relationship. Thus, the best way to model this graph would be by finding best-fit curves that suit the relationship between each of the data points; it would essentially require splitting the graph up and finding individual curves. Nonetheless, the result can be used to represent the experimental relationship between the angle at which the blade is set and the power the turbine would produce, when put in the exact environment with the same settings. Also, the relationship will have to have a y-intercept at (0, 0), because the 0 degree angle had no output whatsoever.

Potential ErrorsThere was room for errors in a few of the steps. For instance, one of the most prominent errors comes into consideration when considering that there are many variables in the design of a wind turbine, and the combination of factors that I chose represents only on of countless different structures for a turbine to have. Thus, it is possible that the optimum blade angle may vary depending on other factors in the turbine. Even within this model, however, there are potential errors in measurement. Even though numerous trials and readings were taken, there is still uncertainty in every data value, since the device itself has a 1% error range. When calculating averages and using formulas, the uncertainty continues growing. The error bars in

particular are a useful mean of determining the extent of uncertainty, as it varies for each value. Additionally, there is room for error in this experiment due to the need for distinct values in the independent variable. This experiment shows that the peak, in comparison to 0, 10, 30, and 40 degrees, is at 20 degrees, but in reality, the peak could just be in the vicinity of 20 degrees. And looking at the graph, which shows a less steep slope of the right side of the maximum, it is likely that the true peak lies somewhere between 20 and 30 degrees.

ReflectionUpon concluding my experiment, I was very surprised by the results, as I had originally anticipated that the difference in the power output would be very small. Instead, I saw drastic differences, which was very fascinating. I very much enjoyed getting to conduct this experiment, so I began thinking of ways to possibly expand upon what I had already done. Here are some more possible experiments I’d like to look into:

1. What is the overall optimum design for a wind turbine in low-wind areas?

Instead of looking at just one factor, it could be very interesting to consider multiple factors and find all their combinations and test to see the optimum overall design and whether or not the factors affect each other and how they do.

2. Will forcing wind through a smaller space (a cover around the turbine), generate more power?

When researching, I saw that some theories claimed that certain structures, if shaped correctly, could increase the wind speed coming into the turbine when placed around it. One of these was a structure shaped as an airplane wing, which I thought was very interesting and would be fascinating to experiment with.

3. What is the best blade shape for a wind turbine’s blades?

Another important factor that I could not test in this experiment is the shape of the turbine’s blades. I had to use preset shapes, but looking at the surface area and inclusion of curves and sharp edges could be very interesting and impactful to the design.

4. What are the trends relating to vertical-axis wind turbines, and how do they relate to traditional, horizontal axis turbines?

A lesser known style of wind turbines is the vertical axis turbine, which as its name explains, has a vertical axis rather than the typical horizontal ones. These turbines have a completely unique structure and very different blade shapes as well, as the blades of a vertical axis turbine typically curve and twirl around the axis. There are many unique designs to this kind, so there are many factors to test within that category. Aside from that, it is also possible to test how the

horizontal axis turbines compare to the vertical axis turbines in terms of power output at varying wind speeds.

Overall, I was amazed at the clarity of the results and was very satisfied with the experiment. I look forward to expanding upon this in the near future and working to further promote environmental sustainability!

Bibliography"American Classic Wind Power Turbines." POTOMAC WIND ENERGY. N.p., n.d. Web. 11 Jan.

2013.

Brain, Marshall. "HowStuffWorks "Generators"." HowStuffWorks "Science". N.p., n.d. Web. 11

Jan. 2013.

"Breakdown of a Turbine Blade from Gurit." Gurit - Delivering the future of composite solutions.

N.p., n.d. Web. 11 Jan. 2013.

"Energy 101: Wind Turbines - YouTube." YouTube. N.p., n.d. Web. 11 Jan. 2013.

"How DC Generators Work - YouTube." YouTube. N.p., n.d. Web. 11 Jan. 2013.

"Sinusoidal Waveform or Sine Wave in an AC Circuit." Basic Electronics Tutorials and Revision.

N.p., n.d. Web. 11 Jan. 2013.

"Wind Energy Science Fair Projects & Experiments." The Orchid Grower: A Juvenile Science

Adventure Novel. N.p., n.d. Web. 11 Jan. 2013.

"Wind Program: How Do Wind Turbines Work?." U.S. DOE Energy Efficiency and Renewable

Energy (EERE) Home Page. N.p., n.d. Web. 11 Jan. 2013.

"Wind Turbines - Kinetic wind energy generator technology." Alternative Energy News. N.p.,

n.d. Web. 11 Jan. 2013.