IntroductionCongratulations. Now you have $($almost$)$ made a cup calibration! In real life, we do things a littleCalibrate field data and calculate $10-$minute mean and turbulence intensity.

Load the file winddata.txt into a spreadsheet or workbook. The first column is a time stamp $($spaced by $1)$ and the second column is the measured cup rotational frequency. Apply the calibration values obtained from the previous section to obtain a third column of wind speeds. Plot this. It should look something like this:

What is the mean wind speed $\frac{?}{\text{b}\text{a}\text{r}}(V)?$

What is the standard deviation ${}_v?$

What is the turbulence intensity

differently but the basic principle is exactly the same. In particular we would do the following things for

a professional calibration:

have specific calibrations for the pitot tube

correct for the area that the cup fills in the tunnel cross$-$section $($blockage$)$

Perform the linear regression using mean values from the staircase plots where conditions are

constant $($avoiding the outliers when the speed changes$).$ You can try this if you like.

Calculate the uncertainty of the calibration.

Calibrate field data and calculate $10-$minute mean and turbulence intensity.

Load the file winddata.txt into a spreadsheet or workbook. The first column is a time stamp $($spaced by

$1$s$)$ and the second column is the measured cup rotational frequency. Apply the calibration values

obtained from the previous section to obtain a third column of wind speeds. Plot this. It should look

something like this:Calibrate field data and calculate $10-$minute mean and turbulence intensity.

Load the file winddata.txt into a spreadsheet or workbook. The first column is a time stamp $($spaced by

$1s$ and the second column is the measured cup rotational frequency. Apply the calibration values

obtained from the previous section to obtain a third column of wind speeds. Plot this. It should look

something like this:

What is the mean wind speed $\frac{?}{\text{b}\text{a}\text{r}}(V)?$

What is the standard deviation ${}_v?$

What is the turbulence intensity $ti?$

$(ti=\frac{100{}_v}{(\frac{?}{\text{b}\text{a}\text{r}}(V))}[\%])$

You have seen cup anemometers in the lectures. These are the most common instruments for

measuring wind speed in wind energy. Cup anemometers rotate at a speed that is very linearly

proportional to the wind speed. However, the physics are so complex that it is necessary to calibrate the

instrument in a wind tunnel in order to find the transfer function between rotational speed and wind

speed. In this exercise, you will calculate the transfer function of the cup anemometer and then use this

to determine some calibrated wind speeds from raw cup anemometer signals.

Learning objectives:

On completion of this exercise, you will be able to:

Explain how a cup anemometer measures wind speed

Calculate a cup anemometer calibration from wind tunnel measurements

Use a cup anemometer calibration to calculate calibrated wind speeds from field data.Plot the time series of reference wind speeds $($the data are recorded at $1$sca$\frac{n}{sec}.$ You will see a

'staircase' of wind speeds increasing up to about $20\frac{m}{s}$ and then returning in $3$ steps back to zero:

Plot the time series of the cup frequencies:Make a scatter $(x-$Y$)$ plot of the wind speed $(y-$axis$)$ and frequency $(x-$axis$)$:

The very high linear correlation is confirmed although there are a couple of 'outliers', probably when the

tunnel wind speed is changing very rapidly.

Insert a linear regression in the scatter plot. Now you are able to express the wind speed as a

function of the cup rotational frequency : $V_{\text{c}\text{u}\text{p}}=A{f}_{\text{c}\text{u}\text{p}}+B$ What are your values for A and $B?$

A non$-$zero $($positive$)$ value for the offset $B$ is expected. It represents the wind speed necessary to

start the cup anemometer.

You can test your results by going back to the input file and now calculating a new column of wind

speeds based on the your calibration values A and $B$ and the cup frequencies. These new wind

speeds should be very close to the speeds you calculated from the pitot tube

Congratulations. Now you have $($almost$)$ made a cup calibration! In real life, we do things a little

differently but the basic principle is exactly the same. In particular we would do the following things for

a professional calibration:

have specific calibrations for the pitot tube

correct for the area that the cup fills in the tunnel cross$-$section $($blockage$)$

Perform the linear regression using mean values from the staircase plots where conditions are