Although there are no objections against such a methodology in order to simulate shipbank interaction effects for one particular ship in given loading conditions, the results can hardly be used for developing generic formulae covering a range of ships in varying operational and environmental conditions.
Fig.9. 
Ship model D: application point of additional lateral force due to shipbank interaction induced by propeller action (maximum propeller rate) as a function of shipbank distance for several values of forward speed and depth to draft ratio. 
For this reason, the number of terms in (67) was first reduced from 18 to 5, considering the most significant terms only. The results were discussed by Vantorre et al [11]; a clear relationship between the regression coefficients (α, β) and hull form parameters could not be found.
Taking account of the observations described in section 3.4, it was investigated whether the dependency on the Froude number in (67) could be avoided by replacing the nondimensional inverse gross under keel clearance T/(hT) by a nondimensional representation of the inverse net under keel clearance, T/(heffT), with
heff = h  Zm (8)
Zm being the average sinkage of the ship due to squat effects. In this way, the number of regression coefficients was reduced to 6:
The regression coefficients α and β were determined for the three ship models; the agreement appeared to be satisfactory. As a following step, it was checked whether a linear relationship between these coefficients and combinations of the nondimensional hull form parameters CB, B/L, B/T and T/L.
The following regression coefficients were obtained:
α^{(H)}10 = 4.61E01 + 3.68E01 CB^{1}
α^{(H)}11 = 1.73E01 + 1.14E02 CBLT^{1}
α^{(H)}12 = 6.34E03  4.60E04 CBLT^{1}
α^{(H)}20 = 1.36E+00  6.58E02 LT^{1}
α^{(H)}21 = 2.57E01  8.96E02 BT^{1}
α^{(H)}22 = 1.9 IE02 + 6.34E03 BT^{1}
β^{(H)}10 = 1.19E01 + 2.11E+00 TL^{1}
β^{(H)}11 = 3.54E02 + 1.95E01 BL^{1}
β^{(H)}12 = 2.29E04  6.92E05 BT^{1}
β^{(H)}20 = 1.3 4E01  2.35E+00 TL^{1}
β^{(H)}21 = 4.23E02 + 2.93E03 CBLT^{1}
β^{(H)}21 = 1.23E03  8.53E05 CBLT^{1} (11)
5.3 Effect of propulsion: bollard pull conditions
In bollard pull conditions, nondimensional formulations containing the square of the forward speed have to be avoided. For this reason, another reference velocity VT is introduced:
The effect of propeller action on the shi bank interaction force and moment, denoted Y^{(P)} en N^{(P)}, is modelled as follows:
with following numerical values for the regression coefficients:
α^{(P)}10 = 5.24E02  1.5 1E01 TB^{1}
α^{(P)}11 = 8.70E03  3.86E02 BL^{1}
α^{(P)}12 = 1.05E04  9.23E07 LB^{1}
α^{(P)}20 = 5.92E02  2.11E02 BT^{1}
α^{(P)}21 = 2.82E04  2.42E04 LB^{1}
α^{(P)}22 = 2.32E04  1.98E05 LB^{1}
β^{(P)}10 = 4.95 E03 + 1.25E01 CBTL^{1}
β^{(P)}11 = 1.29E03  5.37E03 TB^{1}
β^{(P)}12 = 2.68E04  8.78E04 TB^{1}
β^{(P)}20 = 3.81E03  1.29E02 CBTB^{1}
β^{(P)}21 = 3.44E03  1.10E03 BT^{1}
β^{(P)}22 = 4.88E04  1.52E03 TB^{1} (15)
5.4 Effect of propulsion combined with forward speed
As the effect of the propeller action on the shipbank interaction force and moment appear to be amplified if the ship has a nonzero forward speed, additional terms have to be added:
α^{(HP)} 10 = 2.37E0.1 + 4.22E01 TB^{1}
α^{(HP)} 11 = 2.89E02  2.20E03 LB^{1}
α^{(HP)} 12 = 6.57E03 + 1.18E03 LB^{1}
α^{(HP)} 20 = 4.19E01  4.79E02 LB^{1}
α^{(HP)} 21 = 4.49E02 + 9.98E03 LB^{1}
α^{(HP)} 22 = 1.06E02  4.24E02 TB^{1}
β^{(HP)} 10 = 2.89E01 + 5.71E+00 TL^{1}
β^{(HP)} 11 = 1.22E01 + 3.53E01 TB^{1}
β^{(HP)} 12 = 7.87E03  2.33E02 TB^{1}
β^{(HP)} 20 = 9.33E02 + 1.57E02 LB^{1}
β^{(HP)} 21 = 2.60E01 7.95E01 TB^{1}
β^{(HP)} 22 = 1.99E02 + 5.98E02 TB^{1} (18)
Note: in expressions (6), (7), (9), (10), (13), (14), (16) and (17) yB3 should be written as yB3｜y^{B3}｜.
6. CONCLUSION
By means of equations (918), a reasonable estimation of lateral forces and yawing moments acting on a ship due to interaction with a vertical bank can be made based on geometrical ship characteristics, water depth, shipbank distance and propeller loading. Reasonable agreement is obtained for the three tested ship models, but it should be emphasised that the validity of these formulae has not been tested yet for other ships and bank geometries such as sloping and submerged banks.
Following limitations must be respected when applying the formulae: 0.56 < C <B < 0.84; 6.0 < L/B < 7.3; 2.6<B/T<3.0; 17.8 < L/T < 21.5; h/T> 1.07.
It must be noted that an estimation of the average sinkage of the ship due to squat and of the propeller thrust has to be available as well.
The set of formulae in section 5 is certainly no definitive solution for simulation problems in which bank effects have a dominant effect. The phenomenon is determined by a large number of parameters, so that it is hard to cover the full range of conditions by an experimental program. Exchange of data between institutions is therefore highly recommended.
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