Theoretical Analysis Method for Roll Motion of Popup Data Communication Beacons

The popup data communication beacon (PDCB) can send data to the shore and ships through the BeiDou navigation satellite system (BDS) when it surfaces. The data can be collected by a deep-sea landing vehicle (DSLV) and transmitted using a magnetic induction coil. PDCBs can reduce the cost of DSLV recovery and redeployment. Whether the data can be successfully sent mainly depends on the outlet height and roll angle of the PDCB. Thus, accurately assessing the effect of the roll angle on data transmission is crucial. In this study, first, the differential equation of roll motion was preliminarily established using the small-amplitude wave theory along with the shape characteristics of the PDCB. Next, the nonlinear term of the recovery moment was processed using the Linz Ted Poincaré method. Then, the wave current force was analyzed using the Morrison theoretical formula along with an additional inertia moment calculation formula that is suitable for slender cylindrical small buoys. Finally, the theoretical calculation results were verified using the computational fluid dynamics (CFD) method and pool test. The roll angle error of the theoretical calculation was within 5%. Thus, the heave and roll response of PDCBs can be evaluated using theoretical calculation methods. The proposed calculation formula of additional inertia moment has guiding significance for the further optimization of the structure.