# Wind Speed Measurement via Visual Recognition of Wind-Induced Waving Light Stick Target
## 3 Wind Speed Calculation
### Wind Tunnel Calibration  
To calibrate the relationship between the stick yaw angle and wind speed magnitude, a wind tunnel test was conducted in the environmental simulation tunnel at High-Speed  
Figure 10: Relationship between the stick and the thin wire reinforcement. (**a**) Real stick; (**b**) Stick schematic.  
Figure 9: Imaging model in coupled view. (**a**) Cone motion decomposition; (**b**) hexahedron motion decomposition.  
Train Research Center in Central South University. The wind tunnel enables sand blowing, anemometer calibration, and more importantly, aerodynamic tests for many objects. Two test sections are included in the wind tunnel: low-speed and high-speed test sections (Figure 11). In the low-speed test section, the wind speed can be adjusted from 1.5 m/s to 15 m/s in the 3000 mm \(\times\) 2000 mm \(\times\) 1600 mm chamber, respectively denoting its length, width, and height. In the high-speed test section, the wind speed ranges from 5 m/s to 60 m/s in its 3400 mm \(\times\) 800 mm \(\times\) 1000 mm chamber. Calibration was carried out in the high-speed test section between stick yaw angle and wind speed magnitude, in terms of anemometer calibration.  
The stick is 225 mm long and fixed at a height of 440 mm away from bottom plate, at a displacement of 340 mm away from the side wall. The stick was suspended from a horizontal circular rod which passes through a hole cut through the calibrated protractor board, which is 40 mm behind the stick. The rod is fixed to another cantilevered structure which supports the entire weight of the setup. The entire system is configured such that the target's swing is unrestrained along the wind flow direction and is loosely centered along the width of the wind speed test section.  
During the test, the wind loading cases are set from 5 m/s to 30 m/s at the interval of 2.5 m/s. In the 11 wind test cases, the yaw angle is read at the protractor board, the minimum scale of which is 1\({}^{\circ}\). However, because of the non-negligible width of the stick target, the angle reading is selected as the medium value of two board readings at stick boundaries. After the tests, results between wind speed magnitude and yaw angle readings are listed in Table 1 and plotted in Figure 12 as below.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline
**Test Case** & **1\#** & **2\#** & **3\#** & **4\#** & **5\#** & **6\#** & **7\#** & **8\#** & **9\#** & **10\#** & **11\#** \\ \hline Wind speed \(v_{w}\) (m/s) & 5 & 7.5 & 10 & 12.5 & 15 & 17.5 & 20 & 22.5 & 25 & 27.5 & 30 \\ Yaw angle \(\alpha\) (\({}^{\circ}\)) & 25 & 41 & 52 & 59 & 64 & 68 & 70 & 73 & 75 & 76 & 77 \\ \hline \end{tabular}
\end{table}
Table 1: Wind tunnel calibration results between wind speed and stick yaw angle.  
Figure 11: Schematic of the experimental wind tunnel set-up for stick waving calibration.  
As seen from the above, the yaw angle climbs as the wind speed increases. However, when the wind varies in high speed above 20 m/s, it becomes more difficult to achieve the same yaw angle increment as in the low-speed range. This is because when the stick is slightly lifted, more wind load acts on the stick, while as the yaw angle increases, the payload required to further lift the stick becomes much greater because the pressure-acting area becomes much smaller. It is hard to observe the theoretical relationship between wind speed and yaw angle if using regular fitting formulae.