# Leading-Edge Vortex Characteristics of Low-Aspect-Ratio Sweptback Plates at Low Reynolds Number
## 2 Materials and Methods  
A robotic arm can precisely adjust the sweptback angle \(\beta\) as well as the angle of attack \(\alpha\) of the model flat plates (Figure 1a). Three servo motors (XH430, Robotis(r)) were mounted on the arm, and each encoder inside the motors provides an angular position with a resolution of 0.088 deg/step. The motors are in charge of the \(\alpha\), \(\beta\), and a sweeping angle (fixed in this study), respectively, and we used two motors, Motor 1 and Motor 2, to adjust the two angles. This robotic arm was connected to a laptop computer, and was controlled by an in-house code written in LabVIEW(tm) via RS485 protocol. The baud rate was 2 Mbps, which was sufficient for high-speed motor control. The three model flat plates in this study were made of a 1 mm-thickness carbon fiber sheet. The spanwise lengths of the plates are 130, 200, and 288 mm, while the chord length is fixed as 64 mm. Corresponding ARs are, therefore, 2.03, 3.13, and 4.50, respectively. In order to check the possible deformation during the test, we applied a classical beam theory with a drag coefficient of 1.2, which is known as the value at \(\alpha=90\) deg. It was estimated as 0.144 mm at the aspect ratio of 4.50, which corresponds to 0.22% of the chord length. Figure 1b shows the open test section of the wind tunnel B at the Technical University  
Figure 1: Experimental setup. (**a**) A robotic arm consisting of three servo motors; (**b**) The test setup in the wind tunnel B at the Technical University of Munich; (**c**) The gram-scale force/moment bending-beam loadcell; (**d**) A relation of the measured moments and force on the loadcell. of Munich. The rectangular nozzle has a size of 1.20 \(\times\) 1.55 m. The turbulent intensity of the test section freestream is less than 0.4% in all directions, and the angle divergence of the freestream is below 0.5 deg. The maximum blockage of the model plate (at AR = 4.5, \(\alpha\) = 90 deg, and \(\beta\) = 0 deg) is less than 1.0%. The atmospheric pressure was 95.4 \(\pm\) 0.35 kPa and the temperature was maintained within 19.7 \(\pm\) 0.9 \({}^{\circ}\)C during the test; the ranges of the density and kinematic viscosity were then 1.135 \(\pm\) 0.01 kg/m\({}^{3}\) and 1.53 \(\pm\) 0.9 \(\times\) 10\({}^{-5}\) m\({}^{2}\)/s, respectively. The dynamic pressure was settled in the range of 26.4 \(\pm\) 0.4 Pa, the freestream velocity was yielded as 6.82 \(\pm\) 0.07 m/s; stall flutter appeared at AR = 4.50 beyond this speed. The corresponding Reynolds number based on the chord length is Re \(\approx\) 2.85 \(\times\) 10\({}^{4}\). One issue in this study was that most commercial force/moment sensors are not adoptable to such a low Reynolds number due to an excessively low aerodynamic load (e.g., the maximum aerodynamic load on the AR = 2.03 plate only reaches ~0.2 N). In order to tackle this issue, we fabricated a customized gram-scale force/moment bending-beam loadcell (Figure 1c). This loadcell was composed of two pairs of tandem straingauges (1-LY93-3/350E, HBM), and gives us two bending moments at two different positions where the two pairs of straingauges were attached. We then computed the normal force using the two bending moments and the distance between the two. Figure 1d explains the relation between the two moments and the normal force (refer to [23; 24] for more details). Two bending moments M\({}_{1}\) and M\({}_{2}\) collected by each set of the straingauges can be expressed as:  
\[M_{1}=\int_{a}^{b}yf(y)dy \tag{1}\]  
\[M_{2}=\int_{a}^{b}(y-d)f(y)dy \tag{2}\]  
The normal force is then obtained with the relation of the two moments, that is,  
\[F=\int_{a}^{b}f(y)dy=\frac{M_{1}-M_{2}}{d} \tag{3}\]  
During the calibration test, voltage outputs for the bending moments showed clear linearity; the root-mean-square errors were less than 1.6 \(\times\) 10\({}^{-4}\). Based on the maximum input voltages of the DAQ of \(\pm\)5 V, the maximum range of the force and moment are \(\pm\)4 N and \(\pm\)120 N-mm, respectively.