Squat prediction in muddy navigation areas
Introduction
Squat, defined as the sinkage and trim of vessels due to their own forward speed, is of particular importance in shallow water areas. Small under keel clearances cause large return currents which lead to important sinkages and higher risks of bottom touching as already mentioned by Constantine (1960).
In shallow navigation areas the presence of a soft fluid mud layer on the bottom is not exceptional, but its effect is mostly neglected in the formulation of squat. As a consequence pilots and scientists may disagree on the safety of navigation. Mostly pilots have to rely on the high frequency echo to determine the water depth. As the latter detects the top of the mud layer and not the solid (or nautical) bottom level, they may still be able to navigate safely through a muddy navigation area, even in case the ship is navigating at a zero (or even negative) under keel clearance according to the echo sounder. In cases where common squat formulae would predict grounding of a ship navigating in a shallow fairway at a rather high speed, the presence of a mud layer may prevent such grounding.
Indeed a limited or even negative under keel clearance referred to a mud layer does not necessarily lead to impracticable manoeuvres as mentioned by Delefortrie et al. (2007). When initially the ship has a small under keel clearance referred to the mud layer, she may hit the mud layer due to squat. This mud, having a larger density than water, will affect the buoyancy of the ship and will probably smoothen the squat effect. However, to be sure about the mud effect additional research had to be carried out, because the literature offers very limited results on this topic.
Section snippets
General research on squat
Scientific research on squat took off with Constantine (1960) who discussed the different squat behaviour for subcritical, critical and supercritical vessel speeds. In the subcritical domain (Frh<1) Tuck (1966) proved that for open water conditions of constant depth the sinkage and trim of the vessel to be linear with the parameter
In which represents the depth related Froude number
This theory was later extended to dredged channels by Beck et al. (1975). Naghdi and
Test facilities
The new squat formulae presented in this article are all derived from experimental research carried out from 2001 until 2004 at the Towing Tank for Manoeuvres in Shallow Water—cooperation Flanders Hydraulics Research, Ghent University. The formulae are valid within the range of conditions covered by this experimental research. The shallow water towing tank (88 m×7 m×0.5 m) is equipped with a planar motion carriage, a wave generator and an auxiliary carriage for ship–ship interaction tests. Thanks
Undulations of the water mud interface
Fig. 3 gives an example of the measured undulations of the water mud interface, which seem to behave as a Kelvin pattern. The maximal amplitude closest to the ship is represented in Fig. 4. The rising increases with increasing speed, but this increase is limited once the undulations are behind the ship, see Fig. 5. This is especially the case with low density mud layers (c, d).
When the vessel navigates above the mud layer the rising will increase faster with the velocity when the density and
Definitions
A mathematical model will be built to predict the ship’s squat when sailing straight ahead based on the measurements carried out with the 6000 TEU container carrier. The effect of a rotating propeller will be taken into account. According to Tuck (1966) the mean sinkage of the vessel in the subcritical speed range can be modelled asWith s0 a coefficient to be derived from regression analysis. An analogous relationship is valid for the vessel’s trim
This relationship is also
Conclusions and recommendations
For a same small under keel clearance referred to the solid bottom the sinkage will be mostly smaller when a mud layer is present. This is not always the case for the ship’s trim. The squat of the ship can be related to the observed undulations of the water mud interface, that become dominant once the viscosity of the mud layer is below a critical one.
A mathematical model predicting fairly well the ship’s squat for container carriers has been built taking into account the bottom conditions and
Acknowledgements
The data presented in this article were obtained during the research project Determination of the nautical bottom in the harbour of Zeebrugge: Nautical implications, which was carried out co-operatively by Ghent University and Flanders Hydraulics, commissioned by T.V. Noordzee & Kust (Ostend, Belgium) in the frame of the optimisation of the maintenance dredging contract for the harbour of Zeebrugge, financed by the Department Maritime Access, a division of the Mobility and Public Works
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