A Primer of Inland Vessel Maneuverability

Liu, Jialun

doi:10.1007/978-3-030-47475-1_5

Cited by 1 publication

(2 citation statements)

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“…If we integrate r in Equation ( 16) from 0 to COP2 and from COP2 to L/2 and equate the two partial F D2 on either side of the COP2, we obtain the exact position of COP2. Rearranging Equation (17) and normalising to L/2:…”

Section: Free Body Diagrams and Mathematical Modelling Of A Turning Shipmentioning

confidence: 99%

“…Yoshimura [10] (p. 42, Figure 2), [11] (p. 78, Figure 1), [12] (p. 1, Figure 1), who also added the corresponding equations of motion; • Pérez and Clemente [13] (p. 519, Figure 1); • Carreño et al [14] (p. 81, Figure 11), [15] (p. 28, Figure 1), [16] (p. 101, Figure 3), who, in the latter two publications [15,16] added the equations of a rigid body in two dimensions, that is, forces in x-and y-directions, and moment about the z-axis; • Liu [17] (p. 109, Figure 5.6), who added the equations shown in [15]; • Huang and Wang [18] (p. 2251, Figure 1) showed an FBD, specifically labelled 'free body diagram', similar to [9], but also added rudder forces; furthermore, they listed the three equations of motion similar to [15], decomposing the x-and y-forces into propulsion, rudder and (hydrodynamic) hull resistance forces.…”

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confidence: 99%

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The Dynamics of a Turning Ship: Mathematical Analysis and Simulation Based on Free Body Diagrams and the Proposal of a Pleometric Index

Fuss

2023

Dynamics

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This study attempts to shed new light on the dynamics of a turning ship using the principles of free body diagrams (FBDs). Unexpectedly, the literature gap is defined by incomplete and flawed FBDs. The method behind this new approach involves the FBD of a turning ship, with all the essential forces included, namely propulsive force, sideward thruster force (producing the initial turning moment), drag force, lift force, centrifugal force, inertial force, and hydrodynamic force couple. From these forces, the force and moment equations are derived. The accelerations are calculated from the force and moment equilibria to simulate the dynamics from input parameters such as mass m, length L, draught D, and fluid density ρ. The turning dynamics are explained in terms of velocities, accelerations, forces, and moments, based on two conditions: flat and steep angles of attack (AoA) and long and short turning radii R. A critical result is the proportionality of lift and centrifugal forces, leading to the proposal of a pleometric index (m·L–2·D–1·ρ–1), which is nonlinearly proportional to the product of AoA and R/L, characterising the dynamics of a turning ship. The FBD approach of this study also identified missing databases required for accurate simulation of turning dynamics, such as drag and lift coefficients of different hull geometries.

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Section: Free Body Diagrams and Mathematical Modelling Of A Turning Shipmentioning

confidence: 99%