# Development and Field Testing of a Wireless Data Relay System for Amphibious Drones
## 2 Materials and Methods
### Preliminary Selection of a Reinforcing Float for the Amplibious Drone System  
The amphibious drones that we used have a patented ability to flip automatically when overturned on water [18; 26]. However, because even the genuine floats by the drone manufacturer were not compatible with the auto-flip technology, the drones were not confirmed to reorient themselves on the water when they were used with our external water quality monitoring system [18]. The genuine floats were designed for horizontal operations on water [18], but we were unable to operate the drone with the floats in the field with aqueous plants. We added some floating materials for the drones to increase the floating stability during vertical operations (Figure 5) as a simple way of ensuring the floating stability of amphibious drones. We tried to arrange the water quality monitoring system symmetrically in the horizontal section of the drones, but restrictions on the arrangement (e.g., antenna of the drone, battery slot, camera) caused some asymmetry within the range of the maximum payloads. We compared the floating stability of the water quality sensing amphibious drones with those of commercially available floating materials placed symmetrically below each drone (quadcopter) arm.  
The amount of each float was estimated by minimizing the distance from the center of gravity to the center of buoyancy of the drone system (Figure 5). The metacentric height [27]\(H\) (Equation (1)) of the drone system should also be controlled (e.g., \(>\)0.15 m [27]) to maintain its position against reverting force [28]. Therefore, we tried to extend each drone arm to increase the inertial area moment within the range of shear strength of the float against the forces in a splashdown.  
\[H=\frac{I}{V}-L \tag{1}\]  
In that equation, \(I\) stands for the second moment of area of the horizontal section for the minor (weak) axis (m\({}^{4}\)), \(V\) signifies the volume of displaced water (m\({}^{3}\)), and \(L\) denotes the distance from the center of gravity to the center of buoyancy (m). In the worst case of floating stability of the present study, in which the maximum payload is placed above the drone while the floats push up the drone above the water as high as 7 cm, \(L\) extends to 0.1 m, but \(H\) is higher than 0.15 m with each of the candidate floating materials. The  
Figure 4: Slicer output images of the mountingers for water quality monitoring tools with amphibious drones. (**a**) Mounters for the SplashDroneTM 3+ with vertical installation of sensor electrodes; (**b**) mountingers for the SplashDroneTM 4 with horizontal installation of sensor electrodes (the holder is shown as a vertical image for 3D-printer output). GNSS-secure legs were used for sufficient space between the bottom of the upper mounter vessel and the GNSS antenna surface of each drone.  
estimated \(H\) values by a simplified top view (horizontal view) for the respective floats (Figure 6) were (a) 0.91 m, (b) 0.62 m, (c) 0.80 m, and (d) 0.18 m at \(V\) = 0.0042 m\({}^{3}\) (4.2 L, for 4.2 kg maximum flight weight at 1.0 kg L\({}^{-1}\) density of water). The increase in the inertial area moment by the drone arm extension avoids capsizing the amphibious drone on water. The actual floating stability was confirmed by a harsh splashdown on the waters using the tension of the tethering thread connected to the drone. The floating stability test was carried out on flat water where few aquatic (rooting) plants grew because surface plants would complicate the floating stability evaluation. We presumed that the system would only experience vertical splashdown and take-off.  
Figure 5: Simplified side-view of the amphibious drone system with an upper mounter and additional floating materials. Some points are identified: M, metacenter; G, center of gravity; B, center of buoyancy. The floating materials are sufficiently narrow to release airflow and minimize the distance from G to B.  
Figure 6: _Cont._