commit b95abbeeda95adc3153c1ec7c2def7fc730939fe
parent dd50ae6b0655ca2543c683bc37f5a844215b74b6
Author: Ivan Gankevich <i.gankevich@spbu.ru>
Date: Tue, 4 May 2021 13:31:09 +0300
balcony ftw
Diffstat:
| 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
