## 2 Mooring Area Detection of Single Anchored MASS  
### Motion Law of Single Anchoring Ship  
The single anchoring method is one of the commonly used anchoring methods for ships. There are two modes in operation: the forward anchoring method and backward anchoring method. In most cases, the backward anchoring method against the wind flow direction of the ship is adopted, because the ship speed is opposite to the wind flow direction, which is convenient to control the residual speed of the ship and find the anchor position. Then, it is convenient for the anchor to break through the seabed and grip it firmly. When it comes to the forward anchoring method, the ship speed is in the same direction as the wind flow direction. After anchoring, the ship is forced to turn to the opposite direction of the wind flow, which requires a large turning space. Additionally, it is difficult to control the ship position because of the large inertia. Figure 1 shows the process of the backward anchoring method. After reaching the predetermined anchor position, the ship drops the anchor at the point \(A_{1}\). At this time, the position information displayed by the ship position sensor is \(A_{1}^{\prime}\). The ship retreats slowly under the influence of wind, wave and current and its own maneuverability. The anchor gradually grips the bottom material and finally stabilizes at the point \(A_{2}\) with the position displayed by the ship position sensor as the point \(A_{3}\).  
Once anchored, the single anchoring ship moves in a complex way under the comprehensive influence of wind, wave, rotary flow and reciprocating flow. Figure 2a shows the motion state of an anchoring ship under the influence of external forces, where point 0 is the anchor position and points A-G are the motion track of the bow. Figure 2b-f shows the hourly ship track of a real-scale ship in 12 h, 24 h, 5 day, 10 day and 15 day periods, respectively. In conclusion, when the external forces are relatively stable, the anchoring ship presents the characteristics of a short periodic yawing at anchor. When the external forces are unstable, the anchoring ship moves in an approximate circular motion  
Figure 1: Process of ship backward anchoring. (**a**) The predetermined anchor position. (**b**) The ship position after anchoring operation.  
in the long-period state. Its swing amplitude and circular radius are closely related to the external forces.  
On the vertical plane, the single anchoring ship produces a radial reciprocating motion under the influence of different external forces of wind, wave and current. The length of the anchor chain of the ship at point A in Figure 3 is \(S\); the catenary \(S_{S}\) is in a certain radian, and the horizontal chain \(S_{L}\) lies flat on the seabed. The resultant force of the gripping force \(P\) of the anchor and the friction force of the horizontal chain is greater than or equal to the external force \(F\). If \(F\) becomes larger, the ship moves from point A to point B and becomes stable at point B. If \(P\) is equal to \(F\), at this time, the catenary length becomes longer while the horizontal chain becomes shorter. If \(F\) continues to grow and exceeds \(P\), there is a risk of anchor dragging. If \(F\) becomes smaller, the anchoring ship will move from point B back to point A. Therefore, the above factors need to be taken into full consideration for the perspective of anchoring safety. In particular, the appropriate anchorage circle, anchor position and anchorage circle radius should be selected in the dense waters of ships.