5 . VELOCITY DEPENDENT TABULAR MODELS
5.1 Pure sway motion
The longitudinal force X'(β) measured during oblique towing is affected by the hull form and the water depth to draught ratio. For full ships the longitudinal hull force turns from a resistance force acting aft into a component acting forward as the drift angle increases (figure 11). The involved drift angle at which this effect occurs, is getting smaller as the water depth decreases (see also [7]). For slender ships this force component keeps on acting aft ward during a large range of drift angles and only becomes positive when the ship is moving astern.
Fig.11 |
Non-dimensional longitudinal force X'(β) modelled for full and slender ship based on oblique towing tests. |
Fig. 12 |
Non-dimensional lateral force Y'(β) modelled for full and slender ships based on oblique towing tests. |
The tabular models shown in figure 11 are based on hull forces measured during stationary and multi-modal oblique towing tests with propeller action [8].
Total lateral force and yawing moment measured during pure sway and pure yaw are caused by [3]:
□ ideal fluid effects
□ lifting effects
□ cross flow effects.
As the under keel clearance decreases, cross flow induces important lateral forces around 90° drift angle (figure 12). A part of this force must be attributed to the presence of the rudder.
Due to a non-dimensional description of the lateral force based on the lateral underwater surface Lppd, the tabular models for the tanker and the container carrier at 20% UKC differ hardly.
Nevertheless, for the ship moving astern the application point of this lateral force is situated more aft in the case of the tanker, compared to the container carrier (figure 13).
Additionally, the influence of a decreasing water depth on the yawing moment due to pure sway is more significant for the tanker than for the container carrier.
Fig. 13 |
Non-dimensional yawing moment N'(β) modelled for full and slender ships based on oblique towing tests. |
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