commitb95abbeeda95adc3153c1ec7c2def7fc730939feparentdd50ae6b0655ca2543c683bc37f5a844215b74b6Author:Ivan Gankevich <i.gankevich@spbu.ru>Date:Tue, 4 May 2021 13:31:09 +0300 balcony ftwDiffstat:

main.tex | | | 72 | ++++++++++++++++++++++++++++++++++++++---------------------------------- |

1 file changed, 38 insertions(+), 34 deletions(-)diff --git a/main.tex b/main.tex@@ -104,8 +104,8 @@ of which are determined from the spectrum, and phases are random variables: \begin{align*} & V(t) = \overline{V} + \sum\limits_{j=1}^{n} \left( A_j \sin\omega_jt + B_j \cos\omega_jt\right), \\ -& A_j = \sqrt{\frac{1}{2} S_j \Delta\omega} \sin\phi_j, \\ -& B_j = \sqrt{\frac{1}{2} S_j \Delta\omega} \cos\phi_j. +& A_j = \sqrt{\frac{1}{2} S_j \Delta\omega} \sin\phi_j, \quad + B_j = \sqrt{\frac{1}{2} S_j \Delta\omega} \cos\phi_j. \end{align*} Here \(S_j\) is spectrum value at frequency \(\omega_j\), \(\phi_j\) is random variable which is uniformly distributed in \([0,2\pi]\). @@ -360,19 +360,34 @@ coefficient equals the raw sensor value that is equivalent to the wind speed of m/s (table~\ref{tab-coefficients}). \begin{table} - \centering - \caption{Calibration coefficients for each arm of three-axis anemometer: - \(C_1\) is for negative values and \(C_2\) is for positive values. - \label{tab-coefficients}} - \begin{tabular}{lll} - \toprule - Axis & \(C_1\) & \(C_2\) \\ - \midrule - X & 11.19 & 12.31 \\ - Y & 11.46 & 11.25 \\ - Z & 13.55 & 13.90 \\ - \bottomrule - \end{tabular} + \begin{minipage}[t]{0.35\textwidth} + \centering + \begin{tabular}{lll} + \toprule + Axis & \(C_1\) & \(C_2\) \\ + \midrule + X & 11.19 & 12.31 \\ + Y & 11.46 & 11.25 \\ + Z & 13.55 & 13.90 \\ + \bottomrule + \end{tabular} + \caption{Calibration coefficients for each arm of three-axis anemometer: + \(C_1\) is for negative values and \(C_2\) is for positive values. + \label{tab-coefficients}} + \end{minipage} + \begin{minipage}[t]{0.55\textwidth} + \centering + \begin{tabular}{ll} + \toprule + Time span & 36 days \\ + Size & 122 Mb \\ + No. of samples & 3\,157\,234 \\ + No. of samples after filtering & 2\,775\,387 \\ + Resolution & 1 sample per second \\ + \bottomrule + \end{tabular} + \caption{Dataset properties.\label{tab-dataset}} + \end{minipage} \end{table} We noticed that ambient temperature affects values reported by our load cells: @@ -429,20 +444,6 @@ for the purpose of the research. \label{fig-intervals}} \end{figure} -\begin{table} - \centering - \begin{tabular}{ll} - \toprule - Time span & 36 days \\ - Size & 122 Mb \\ - No. of samples & 3\,157\,234 \\ - No. of samples after filtering & 2\,775\,387 \\ - Resolution & 1 sample per second \\ - \bottomrule - \end{tabular} - \caption{Dataset properties.\label{tab-dataset}} -\end{table} - \section{Results} \subsection{Anemometer verification} @@ -643,22 +644,25 @@ determinate its mean direction becomes, and the slower the flow is the more indeterminate its mean direction is. Three-axis anemometer disadvantages are the following. -\begin{itemize} -\item The arm for the \(z\) axis is horizontal, and snow and rain put additional load on this cell distorting the measurements. -\item Also, thermal expansion and contraction of the material changes the resistance of load cells and distorts the measurements. -\item Pressure force on the arm is exerted by individual air particles and +Pressure force on the arm is exerted by individual air particles and is represented by choppy time series, as opposed to real physical signal that is represented by smooth graph. -\end{itemize} The first two defficiences can be compensated in software by removing linear trend from the corresponding interval. The last one make anemometer useful only for offline studies, i.e.~it is useful to gather statistics, but is unable to measure immediate wind speed and direction. +We used a balcony for long-term measurements and open field for verification +and calibration. We found no clues that the balcony affected the distributions +and ACFs of wind speed. The only visible effect is that the wind direction is +always parallel to the wall which agrees with physical laws. Since we measure +pressure force directly, the mean wind direction does not affect the form +of the distributions, but only their parameters. + \section{Conclusion} In this paper we proposed three-axis anemometer that measures wind speed for