# Development of a Mobile Buoy with Controllable Wings: Design, Dynamics Analysis and Experiments
## 4 Dynamics Simulation Results
### Dynamic Responses in Glider Mode  
The sawtooth gliding performance can better reflect the maneuverability of the mobile buoy, which directly determines the ocean observation capability in a multiscale range. In this section, the dynamic characteristics of the mobile buoy in Glider mode are investigated using the proposed fluid-multibody coupling analysis method. For Glider mode, net buoyancy mass and wing rotation angle are crucial factors that affect gliding performance. Therefore, net buoyancy mass and wing rotation angle are considered as two control inputs and their variation ranges are set to conduct numerical simulations. The wing rotation angle \(\alpha_{w}\), as the key to attitude adjustment and mode switching, needs more attention regarding its effects on the motion performance of the proposed mobile buoy. Hence, the net buoyancy mass variation range stays constant, and the five  
Figure 9: Dynamic responses in Argo mode, showing (**a**) forward velocity, (**b**) have velocity, (**c**) pitch angle, (**d**) pitch moment, (**e**) angular velocity around the \(\mathbf{\gamma}\)-axis direction and (**f**) motion trajectory. variation ranges of the wing rotation angle, \(\alpha_{w}\in[-10^{\circ}\), \(10^{\circ}]\), \([-20^{\circ}\), \(20^{\circ}]\), \([-30^{\circ}\), \(30^{\circ}]\), \([-40^{\circ}\), \(40^{\circ}]\) and \([-50^{\circ}\), \(50^{\circ}]\), are given to analyze the dynamic responses. The relationship between wing rotation angle and velocity is shown Figure 10a,b, where the forward velocity shows a slight increase followed by a decrease as \(\alpha_{w}\) increases, while the heave velocity increases with the increase in \(\alpha_{w}\). Figure 10c shows the time domain curve of the angular velocity with different \(\alpha_{w}\). The smaller the angle of rotation of the wing, the more violent the fluctuations in pitching motion, and the less stable the buoy. Due to the periodic change of the wing rotation angle, the pitch angle of the buoy also undergoes a periodic variation, as shown in Figure 10d. In Figure 10e,f, notice that the \(F_{x-total}\) and \(M_{total}\) fluctuate greatly at 23 s. The main reason for this phenomenon is the simultaneous rotation of the wings during the buoyancy adjustment process, which puts the buoy into the climb phase and prepares it for the gliding motion that follows. In addition, it should be pointed out the buoy experienced the unstable and stable phases of the sawtooth glide successively, and its velocity, angular velocity and forces can be stabilized after a brief unstable state. Figure 10g illustrates the impact of the wing rotation angle on the motion velocity, clearly indicating that the motion velocity increases within a certain range of the wing rotation angle. In addition, it can be seen from Figure 10h that the motion trajectories of the buoy are different under different wing rotation angle. With the increase in the wing rotation angle, the horizontal displacement first increases and then decreases, and the horizontal displacement is maximum when the wing rotation angle is about \(30^{\circ}\). The net buoyancy mass \(m_{0}\) determines the buoyancy, which serves as the primary power source for the motion of the mobile buoy. In order to explore the dynamic response of the mobile buoy under different \(m_{0}\), five adjusting ranges of the net buoyancy mass, \(m_{0}\in[-0.1\) kg, \(0.1\) kg], \([-0.2\) kg, \(0.2\) kg], \([-0.3\) kg, \(0.3\) kg], \([-0.4\) kg, \(0.4\) kg] and \([-0.5\) kg, \(0.5\) kg], are analyzed, respectively. As shown in Figure 11a,b, the forward velocity and heave velocity are increased as net buoyancy mass increases. Figure 11c,d shows the time domain curve of the angular velocity and pitch angle with different net buoyancy mass. It can be found that the larger the net buoyancy mass, the more violent the pitching motion fluctuation, and the worse the stability of the mobile buoy.