Wind Power and the Wind Rose (rev. 01/16)

Wind Power and the Wind Rose (rev. 01/16)

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Wind Speed, Energy, and Power:
Energy is the ability to do work, and power is the rate at which energy is produced or consumed. The amount of energy a wind turbine can convert to electricity is

dependent on the wind speed. It is also important to know the distribution of wind speeds and the frequency of the varying wind directions if a viable wind farm is to

be constructed. When these data are presented graphically, the result is called a wind rose. In this laboratory, you will prepare a wind rose based on observations of

wind speeds and wind directions collected by the Oklahoma Mesonet.

How can the energy content of wind be determined? Wind is just the movement of a column of air. The energy of motion is called kinetic energy. The kinetic energy of

any object is given by K.E.= 1/2mv2, where m is the mass of the object in kilograms, and v is the velocity of the object in meters per second. The energy is then

given in joules, J.

Imagine a column of air 1.00 meter long and having a diameter of 1.128 meters traveling at a certain velocity, v. That column would look like the one shown in this


The mass of the air is given by the density of the air multiplied by the volume of the air column. The density of air depends on the atmospheric pressure and the

temperature. At sea level and 25 degrees Celsius, the density of air is can be approximated to be 1.2 kg/m3. The volume of the column of air is πr2L, where r is the

radius of the column (diameter/2) and L is the length of the column. In the diagram above, L=1 m, and r = 0.564 m. As mass is defined as the product of density and

volume, we have all the necessary variables to compute the energy of the wind.

Power is defined as the amount of energy produced per second, J/s or watts, W. Suppose there was a wind turbine with a rotor diameter of 1.128 m. When the wind blows

3.00 m/s, three columns of air (each 1 m long like that shown above) would strike the rotor blades every second. Knowing the kinetic energy of one column of air and

knowing how many columns of air strike the blades of a wind turbine per second, the power can be calculated. Think about this for a moment. Do you see that the power

potential of the wind must vary with the cube of the average wind speed, v3? That is, if the wind speed is two times greater it contains 23 (2 x 2 x 2) or eight times

as much energy.

Since the diameter of the column of wind determines the volume of air striking the rotor blades, the size of the rotor blades also affects the amount of power that can

be obtained from the wind. The diameter of the column of air shown above would strike a turbine with a rotor diameter of 1.128 m. Suppose the rotor diameter were

increased to 3.39 m, three times larger. How much more power could be obtained? Since the diameter is three times larger, the radius of the air column is three times

larger. The volume of the air column depends on the square of the radius, so tripling the radius causes the volume to increase by 32 or a factor of 9!

The prototype of the NEG Micon 1500 kW Turbine was commissioned in September 1995. The original model had a 60 meter rotor diameter and two 750 kW generators operating

in parallel. A more recent version is the 1,500/750 kW model (with two 750 kW generators) with a 64-meter rotor diameter. A photograph of the NEG Micon 1500 kW Turbine

is shown below.

Wind Speed Measurement and the Wind Rose:
Measurement of wind speeds is made using an anemometer. A cup anemometer has a vertical axis and three cups that capture the wind. The number of revolutions per

minute is registered electronically. Normally, the anemometer is fitted with a wind vane to detect the wind direction. Other anemometer types include non-mechanical

anemometers, like ultrasonic or laser anemometers. The advantage of non-mechanical anemometers may be that they are less sensitive to icing in winter; however, cup

anemometers with electrically heated shafts and cups are available.

The nice thing about the Oklahoma Mesonet data is that wind speeds are measured near prospective wind turbine sites. Unfortunately the anemometers are located only 10

m off of the ground. While it is best to fit an anemometer at the same height as the expected hub height of the wind turbine to be used, the Mesonet data should

provide a conservative estimate of the available wind power. (Generally the higher from the ground one gets, the less turbulence and the greater wind power potential.)

At any location, strong winds usually come from a particular direction. When planning a wind farm it is important to know the distributions of wind speeds, and the

frequency of the varying wind directions. Once these data are collected they can be displayed graphically. This graphical presentation is called a wind rose. In

this lab, Mesonet observations of wind speeds and wind directions will be used to generate a wind rose for a site selected based on the previous laboratory.

To produce a wind rose the compass is divided into 16 sectors, one for each 22.5 degrees of the horizon. In a 16-sector wind rose the directions are N, NNE, NE, ENE,

E, ESE, etc. (A wind rose may also be drawn for 8 or 12 sectors.) The 16-sector wind rose for Bixby for January 2001 is shown below.

How does one read a wind rose? The outer circle represents the 25% mark and the inner circle the 12.5% mark. The radius of the outermost, blue wedge gives the

relative frequency that the wind blows from that direction. The middle, black wedge gives the normalized wind speed in that direction. To get the normalized wind

speed, the average wind speed in a particular direction is multiplied by the percent of the time that the wind is blowing from that direction, divided by the sum of

all the values and multiplied by 100 percent. It sounds complicated, but essentially this just indicates the windier directions. The innermost, red wedge is most

important. It gives the normalized wind power available from each direction. Remember, it is obtained from the cube of the average wind speed in each particular

location. The result is again normalized to add up to 100 percent. This wedge indicates how much potential power the wind has at a particular location from each

sector or direction.

Questions and Exercises:
Submit both a Word Document and an Excel Spreadsheet for this lab that answers the following:

1. Using the equation for kinetic energy (1/2mv2), calculate the kinetic energy (in joules) of a column of air 9.0 meters long passing through a turbine with a blade

diameter of 4.00 meters moving at a speed of 7.0 m/s (15.7 miles per hour). Assume the density of air to be 1.3 kg/m3. Report the result of your calculation.

2. Calculate the kinetic energy of a column of air with a density of 1.3 kg/m3 that is 9.0 meters long passing through a turbine with a blade diameter of 4.00 meters

moving at a speed of 3.5 m/s (7.8 miles per hour). Compare the results of this question to that in question 1. What is the ratio of the kinetic energy in this

question over the kinetic energy in question 1? (This is the factor that halving the wind speed has on the kinetic energy of the wind)

3. The density of air at 0oC is roughly 1.300 kg/m3 while the density of air at 15oC is nearly 1.235 kg/m3. By what factor will the kinetic energy of the wind

increase/decrease when the temperature changes from 0oC to 15oC? (Compute the ratio of the kinetic energy at 15oC over 0oC). Interpret this value.

4. Use Excel to make a graph that plots the power potential of the wind striking rotor blades (assuming a surface with a 0.8-m diameter; density of air = 1.2 kg/m3)

over the range of 0 m/s to 30 m/s at 3 m/s intervals. Be sure both axes are labeled with the appropriate units.

5. Again use Excel to make a graph that shows the power potential of the wind moving at 1 m/s striking a turbine with a 4-meter blade diameter versus a changing air

density. Use the range of 1.15 kg/m3 to 1.4 kg/m3, which are the air densities at 35 oC and -20 oC. Compare the shapes of the two graphs.

6. Select one of your Mesonet sites for which you analyzed data for Laboratory #2. On an Excel spreadsheet show the wind direction and the average wind speed for each

day of the year. (In lab, your instructor will show you how to “cut and paste” data electronically from the .html file.) After inputting all 365 days of data (or as

many days as are available from the site), use the “sort” command to sort the data by direction. This will allow you to calculate the number of days of that year that

the wind was blowing from each direction. That number, divided by 365 (or the appropriate number of days) and multiplied by 100% gives the percent of time the wind

plows from that direction. Do this for all 16 sectors. Now calculate the average wind speed in each direction. Draw the wind rose for your location. Use the wind

rose calculator excel file on Harvey.

When calculating a wind rose, you are required to know the wind frequency and the average wind speed for each direction. The entries correspond to the directions shown

in the table below:

Entry Direction # Days Wind Frequency Mean Wind Speed
1 N
3 NE
5 E
7 SE
9 S
10 SSW
11 SW
12 WSW
13 W
14 WNW
15 NW
16 NNW

Tables such as the one above will help you organize your data before you enter it into the wind rose generator. Your table should be in almost this exact same format.

Enter your data and click on the “plot” button. Within a few seconds your wind rose will be constructed. Capture the image (you will have to get it from a

screenshot) and paste it into your Word Document. Make sure the image is fully visible in the Word Document. In your report, interpret the results of your wind rose.

What direction should your wind turbine face to generate the most power? Suppose there were mountains at your location. Where should you place the turbine so that the

mountains do not inhibit the wind flow? If a wind farm with multiple turbines were to be constructed at your site, along which direction should the turbines be lined

up to prevent them from blocking each other?

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