3.1 Experimental Facilities

　

 For the investigation of ship hydrodynamics in relation with the concept, adaptation and operation of navigation areas, Flanders Hydraulics developed a shallow water towing tank, equipped with a planar motion carriage, a wave generator and an auxiliary carriage for ship-ship interaction tests. Full computer control allows automatic operation.

　

 The tank has an overall length of 88 m, with a useful part of 67 m, a width of 7.0 m and a maximum waterdepth of 0.5 m. Usually, the scale of the ship models is selected so that the model length is 3.5 to 4.5 m.

　

 As such ship models have a draft of about 0.20 m, the depth to draft ratio can be varied between 1 and 2.5, which is sufficient for studying ship behaviour in shallow water conditions in which ships navigate in approach channels and manoeuvre in harbour areas.

　

 For the ship-bank interaction tests, a vertical quay wall was mounted in the towing tank over a length of 20 m, see Figure 3. The ship model is equipped with rudder and propeller, and is only free to heave and pitch. The horizontal forces on and vertical motions of the ship model, the propeller thrust and torque and the rudder force components are measured and registered during the tests.

　

3.2 Ship Models

　

 Ship-bank interaction tests were carried out with three ship models, see Table 1.

　

　

3.3 Test Parameters

　

 For a given ship and a given bank configuration, bank effects depend on several parameters: ship-bank distance, forward speed, propeller action, depth to draft ratio. Table 2 gives an overview of the test parameters and their ranges.

　

　

4.1 General.

　

 In general, a captive ship model forced to follow a straight course parallel to a bank undergoes a lateral force towards this bank, while a yawing moment tends to turn the bow away from the bank. However, this general pattern is not always valid; some combinations of relevant parameters lead to adverse effects.

　

 Figures 5 and 6 give a selection of test results for the three ship models without propeller action. A selection of test results showing the effect of propeller action is displayed in figures 7 to 9.

　

4.2 Water depth to draft ratio (h/T).

　

 Most hydrodynamic forces acting on a manoeuvring ship in the horizontal plane increase with decreasing under keel clearance. To some extent, this is also valid for ship-bank interaction forces; especially the yawing moment tends to increase dramatically with decreasing h/T. The lateral force acting on a towed ship initially also tends to increase slightly with de-creasing under keel clearance. At very low h/T, however, the attraction force vanishes to zero and turns into a repulsion force. This transition takes place at a critical h/T value situated in the range 1.1 - 1.3.

　

4.3 Ship-bank distance.

　

 It is clear that the asymmetry of the flow around the ship will increase with decreasing ship-bank distance, so that stronger interaction forces may be expected.

　

 In many cases, this relationship between the non-dimensional ship-bank distance parameter yB and the interaction force and moment is approximately linear, as suggested by Norrbin, see (1).

　

 This is illustrated in figures 4 (Y: h/T = 1.5; N: h/T = 1.5, 1.2, 1.1) and 5 (Y: h/T = 1.5, 1.2). In some cases, however, non-linearities occur. For the lateral force, non-linear effects are rather restricted, and mostly amplify the linear relationship (figure 4, Y: h/T = 1.1, 1.07). The yawing moment, on the other hand, tends to decrease if the ship-bank clearance becomes very small; this is very clear in figure 5, where this kind of non-linearity disappears in very shallow water. This indicates that the application point of the lateral force is moving forward, towards the midship section.