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Wind measurements exercise Calibrating and using a cup anemometer Introduction 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. Cup anemometer calibration The first step is to determine the transfer function between cup rotational speed and wind speed. To do this, we put the cup anemometer in a wind tunnel as shown below. The reference wind speed can be controlled and is set to a number of different values in succession. For each different wind speed, the rotational frequency of the cup anemometer is determined from its electrical signal and the differential pressure measured by the pitot tube is simultaneously logged. Such a set of recordings is available to you in file Calibration _ data.txt . Now perform these steps: Load this data into a spreadsheet, a Python data – frame or something similar From the differential pressure d P , calculate the reference wind speed V for each row of the dataset, using the equation V = 2 * d P ρ where ρ is the air density. For the test period, the air temperature t was 2 7 . 2 ° C and the barometric pressure B was 1 0 0 7 . 0 hPa. Use the equation ρ = 1 . 2 2 5 2 8 8 . 1 5 t + 2 7 3 . 1 5 B 1 0 1 3 . 3 [ k g m 3 ] to obtain the value of ρ for the actual conditions under the calibration. [ Hint: For a differential pressure of line of the file ) the wind speed will be 5 . 9 4 m s . ] Plot the time series of reference wind speeds ( the data are recorded at 1 sca n s e c ) . You will see a ‘staircase’ of wind speeds increasing up to about 2 0 m s and then returning in 3 steps back to zero: Plot the time series of the cup frequencies: Notice that this looks very similar to the wind speed plot, just with different values and units on the y axis. This indicates that the speed and frequency are quite highly correlated. 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 c u p = A f c u 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 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 1 0 – 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 s
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![Wind measurements exercise Calibrating and using a cup anemometer Introduction 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. Cup anemometer calibration The first step is to determine the transfer function between cup rotational speed and wind speed. To do this, we put the cup anemometer in a wind tunnel as shown below. The reference wind speed can be controlled and is set to a number of different values in succession. For each different wind speed, the rotational frequency of the cup anemometer is determined from its electrical signal and the differential pressure measured by the pitot tube is simultaneously logged. Such a set of recordings is available to you in file Calibration _ data.txt . Now perform these steps: Load this data into a spreadsheet, a Python data – frame or something similar From the differential pressure d P , calculate the reference wind speed V for each row of the dataset, using the equation V = 2 * d P ρ where ρ is the air density. For the test period, the air temperature t was 2 7 . 2 ° C and the barometric pressure B was 1 0 0 7 . 0 hPa. Use the equation ρ = 1 . 2 2 5 2 8 8 . 1 5 t + 2 7 3 . 1 5 B 1 0 1 3 . 3 [ k g m 3 ] to obtain the value of ρ for the actual conditions under the calibration. [ Hint: For a differential pressure of line of the file ) the wind speed will be 5 . 9 4 m s . ] Plot the time series of reference wind speeds ( the data are recorded at 1 sca n s e c ) . You will see a ‘staircase’ of wind speeds increasing up to about 2 0 m s and then returning in 3 steps back to zero: Plot the time series of the cup frequencies: Notice that this looks very similar to the wind speed plot, just with different values and units on the y axis. This indicates that the speed and frequency are quite highly correlated. 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 c u p = A f c u 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 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 1 0 – 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 s](https://numengineering.com/wp-content/uploads/2025/01/Screenshot_30-1-2025_145136_.jpeg)
Latihan pengukuran angin Mengkalibrasi dan menggunakan anemometer cangkir Pendahuluan Anda telah melihat anemometer cangkir di kuliah. Ini adalah instrumen yang paling umum untuk mengukur kecepatan angin dalam energi angin. Anemometer cangkir berputar dengan kecepatan yang sangat linier berbanding dengan kecepatan angin. Namun, fisikanya sangat kompleks sehingga perlu untuk mengkalibrasi instrumen di terowongan angin untuk menemukan fungsi transfer antara kecepatan rotasi dan kecepatan angin. Dalam latihan ini, Anda akan menghitung fungsi transfer anemometer cangkir dan kemudian menggunakannya untuk menentukan beberapa kecepatan angin yang dikalibrasi dari sinyal anemometer cangkir mentah. Tujuan pembelajaran: Setelah menyelesaikan latihan ini, Anda akan dapat: Menjelaskan bagaimana anemometer cangkir mengukur kecepatan angin Menghitung kalibrasi anemometer cangkir dari pengukuran terowongan angin Gunakan kalibrasi anemometer cangkir untuk menghitung kecepatan angin yang dikalibrasi dari data lapangan. Kalibrasi anemometer cangkir Langkah pertama adalah menentukan fungsi transfer antara kecepatan rotasi cangkir dan kecepatan angin. Untuk melakukan ini, kami meletakkan anemometer cangkir di terowongan angin seperti yang ditunjukkan di bawah ini. Kecepatan angin referensi dapat dikontrol dan diatur ke sejumlah nilai yang berbeda secara berurutan. Untuk setiap kecepatan angin yang berbeda, frekuensi rotasi anemometer cangkir ditentukan dari sinyal listriknya dan tekanan diferensial yang diukur oleh tabung pitot dicatat secara bersamaan. Kumpulan rekaman semacam itu tersedia untuk Anda di file Kalibrasi _ data.txt . Sekarang lakukan langkah-langkah ini: Muat data ini ke dalam spreadsheet, data Python – bingkai atau sesuatu yang serupa Dari tekanan diferensial d P , hitung kecepatan angin referensi V untuk setiap baris kumpulan data, menggunakan persamaan V = 2 * d P ρ di mana ρ adalah kerapatan udara. Untuk periode pengujian, suhu udara t adalah 2 7 . 2 ° C dan tekanan barometrik B adalah 1 0 0 7 . 0 hPa. Gunakan persamaan ρ = 1 . 2 2 5 2 8 8 . 1 5 t + 2 7 3 . 1 5 B 1 0 1 3 . 3 [ k g m 3 ] untuk mendapatkan nilai ρ untuk kondisi aktual di bawah kalibrasi. [Petunjuk: Untuk tekanan diferensial garis file) kecepatan angin akan menjadi 5 . 9 4 m s . ] Plot deret waktu kecepatan angin referensi (data direkam pada 1 sca n s e c ) . Anda akan melihat ‘tangga’ kecepatan angin meningkat hingga sekitar 2 0 m s dan kemudian kembali dalam 3 langkah kembali ke nol: Plot deret waktu frekuensi cangkir: Perhatikan bahwa ini terlihat sangat mirip dengan plot kecepatan angin, hanya dengan nilai dan satuan yang berbeda pada sumbu y. Ini menunjukkan bahwa kecepatan dan frekuensi cukup berkorelasi. Buat plot hamburan ( X – Y ) dari kecepatan angin ( y – sumbu ) dan frekuensi ( x – sumbu ) : Korelasi linier yang sangat tinggi dikonfirmasi meskipun ada beberapa ‘outlier’, mungkin ketika kecepatan angin terowongan berubah sangat cepat. Masukkan regresi linier dalam plot sebar. Sekarang Anda dapat menyatakan kecepatan angin sebagai fungsi dari frekuensi rotasi cangkir: V c u p = A f c u p + B Berapa nilai Anda untuk A dan B? Nilai non – nol (positif) untuk offset B diharapkan. Ini mewakili kecepatan angin yang diperlukan untuk memulai anemometer cangkir. Anda dapat menguji hasil Anda dengan kembali ke input file dan sekarang menghitung kolom kecepatan angin baru berdasarkan nilai kalibrasi Anda A dan B serta frekuensi cangkir. Kecepatan angin baru ini harus sangat mendekati kecepatan yang Anda hitung dari tabung pitot Selamat. Sekarang Anda telah (hampir ) membuat kalibrasi cangkir! Dalam kehidupan nyata, kita melakukan sesuatus sedikit berbeda tetapi prinsip dasarnya persis sama. Secara khusus kami akan melakukan hal-hal berikut untuk kalibrasi profesional: memiliki kalibrasi khusus untuk tabung pitot yang benar untuk area yang diisi cangkir di penampang terowongan ( penyumbatan ) Lakukan regresi linier menggunakan nilai rata-rata dari plot tangga di mana kondisinya konstan ( menghindari outlier ketika kecepatan berubah ) . Anda dapat mencoba ini jika Anda suka. Hitung ketidakpastian kalibrasi. Kalibrasi data lapangan dan hitung rata-rata 1 0 menit dan intensitas turbulensi. Muat file winddata.txt ke dalam spreadsheet atau buku kerja. Kolom pertama adalah stempel waktu (diberi jarak 1 detik) dan kolom kedua adalah frekuensi rotasi cangkir yang diukur. Terapkan nilai kalibrasi yang diperoleh dari bagian sebelumnya untuk mendapatkan kolom ketiga angin s
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