Hydrodynamic derivatives on ship manoeuvring

Development of a core mathematical model for arbitrary manoeuvres of a shuttle tanker

“…Finally, it must be noted that the original mathematical model by Inoue et al [19,21] is 4DOF involving also the roll equation and dependence of the yaw moment on the instantaneous roll angle. The back influence of the roll may become significant for relatively fast vessels.…”

“…. ., N r|r| are functions of the hull's particulars and trim and are estimated according to Inoue et al [21]. Then, the regressions (17) and (18) can be re-written in terms of the same variables as (19) using the relation r ≈ r − 1 2 r 3 and then asymptotically matched to (19).…”

Verification and validation of ShipMo3D ship motion predictions in the time and frequency domains

“…Hull maneuvering forces are considered when evaluating motions in both the frequency and time domains, and are evaluated using the approach of Inoue, Hirano, and Kijima (1981). Care has been taken to avoid duplication of terms when merging hull maneuvering and seakeeping force terms.…”

Study on Ship Motions and Capsizing in Following Seas (Final Report)

“…(11) , Froude-Krylov force X(F.K) is given in the form : (13 ) where A(x) is the sectional area of instantaneously immersed volume and L the ship length. The integral with respect to the sectional area A(x) can be described as (14 ) where the breadth B(x) of equivalent barge section is equal to that of the actual ship section, the sectional area A(x) of barge is the same as that of the actual ship and the draft d(x) of equivalent barge section is determined to be the same sectional area as that of the actual ship. Using the average value, the integral of Eq.…”