Abstract: A review of literature on ship-bank interaction is given, with the emphasis on experimental data and empirical formulae. The results of a systematic captive model test program carried out in the Towing Tank for Manoeuvres in Shallow Water (co-operation Flanders Hydraulics - Ghent University) in Antwerp (Belgium) are used for discussing the influence of the main parameters determining the hydrodynamic forces and moments. The test series were carried out with three ship models in parallel course along a vertical surface-piercing bank with varying water depth, lateral distance, forward speed and propeller rpm. Based on the results and published experimental material, new empirical formulae for predicting ship-bank interaction forces are proposed.

　

 In confined navigation areas, ship manoeuvring is affected by the presence of the boundaries of the waterway: the bottom, lateral restrictions such as banks and quay walls, other ships... Manoeuvring simulation runs, carried out for both waterway design and nautical training purposes, can only be sufficiently realistic if the mathematical manoeuvring model takes account of this modified behaviour. In particular, a reliable representation of ship-bank interaction forces and moments has to be included in the simulation model.

　

 Ship-bank interaction was investigated by several authors by means of numerical and experimental techniques. A few authors proposed empirical expressions formulating the interaction forces as a function of a number of variables describing the main ship characteristics, the environmental conditions and operational parameters. However, all formulations are based on a rather restricted number of model tests with a limited selection of ship models. Indeed, the number of parameters affecting the hydrodynamic forces is rather large: ship type and characteristics (L, B, T, CB・・・), bank configuration (slope, surface-piercing or flooded, ...), water depth, lateral ship-bank distance, ship speed, propeller rate, ... For this reason, a systematic model test program covering all these parameters is very time-consuming.

　

 The paper intends to give a review of literature on ship-bank interaction, with the emphasis on experimental data and empirical formulae. The results of a systematic captive model test program carried out in the Towing Tank for Manoeuvres in Shallow Water (co-operation Flanders Hydraulics - Ghent University) in Antwerp, Belgium will be used for discussing the influence of the main parameters determining hydrodynamic forces and moments. These test series were carried out with three ship models (cape size bulk carrier, panamax bulk carrier, post-panamax container carrier) moving in parallel course along a vertical surface-piercing bank with varying water depth, lateral distance, forward speed and propeller rpm. Based on the test results and on published experimental material, a set of empirical formulae is proposed.

　

 Several experimental studies on ship-bank interaction were reported in literature. Fujino [1] investigated the influence of water depth, bank distance, speed, bank slope, propeller action, drift and rudder angle on hydrodynamic forces acting on a manoeuvring ship in a canal by means of model tests with a tanker (Tokyo Maru, L = 2.000 m, B = 0.327 m, T = 0.110 m, CB 0.805) and a Mariner-type cargo ship (L = 2.500 m, B = 0.360 m, T = 0.116 m with 0.019 m stern trim, CB = 0.589). The hydrodynamic coefficients of these ships, including bank effects, at three water depth to draft ratios (h/T = 1.2, 1.5, 1.9) and three canal width to beam ratios (W/B = 3.05, 4.58, 6.11) were also published by Eda [2], who also gives results of captive tests at Davidson Laboratory with a propelled 250,000 dwt tanker model (L = 1.574 m, B = +0.247 m,T = 0.095 m,CB = 0.830).

　

 Norrbin [3], [4] carried out extensive experimental and analytical investigations on manoeuvring in general and bank effects in particular. Based on model tests with a propelled tanker model (L = 5.024 m, B = 0.852 m, T = 0.339 m, CB=0.821), the following formulations were obtained for vertical banks (see figure 1a):

　

　

 Norrbin also published expressions for sloping [3] and flooded [4] banks.

　

 Fuehrer & Römisch [5], [6], [7], discuss hydrodynamic forces, trim, sinkage, water level denivellations and backflow in four canal sections. Comprehensive tank investigations were carried out by Dand [8] with models of two tankers, a general cargo ship and a container carrier.

　

 Ch'ng et al [9] proposed a formulation for bank-induced hydrodynamic forces based on tests on two MarAd Series hull forms (L = 1.698 m, B = 0.340 m T = 0.077 m, CB = 0.85; bulbous and cylindrical bow) and a container ship model (L = 1.750 m, B = 0.254 m, T = 0.095 m, CB = 0.57). Non-dimensional formulations for sway force and yaw moment are given as a function of ship-bank distance, water depth to draft ratio, Froude number and thrust coefficient CT:

　

　

　

　

　

YB and YB3 are defined as (see Fig.2):

　

　

 The regression coefficients occurring in these formulations were found to be dependent on the non-dimensional ship geometry parameter CBB/T.

　

 Li et al [10] describe model tests carried out at SSPA (Gothenburg) with a tanker (L = 5.146 m, B = 0.930 m, T = 0.292 m, CB = 0.816), a ferry (L = 4.965 m, B = 0.773 m, T = 0.165 m, CB = 0.695) and a catamaran. (L= 1.723 m, B = 0.105 m, T = 0.084m, CB = 0.466). The effect of ship speed, water depth, bank distance, propeller action, bank slope, bank submergence was investigated.

　

 This list is certainly incomplete, and should be extended with theoretical and numerical studies.