5.3 Traffic lane width and bend radius
For one speed and different settings of the main rudder angle and the bow thruster power some special results of the simulations were plotted in Fig. 15. The bend radius was calculated using formula (7).
Theoretically it is possible to obtain the traffic lane width by using the radius R and the drift angle β then applying the geometry of Fig. 13 and adapting it to inclined motion.
Fig. 15 Traffic lane width versus curve radius
A different method was used in the simulation program. For each time step inward and outward points of the vessel's outline being at the farthest distance from the center of the curve radius are calculated and the right and left envelope for this path is generated. The traffic lane width is the orthogonal distance of these two new curves. The reason for this complicated method is the possibility to generate the path of rather complicated vessel outlines as they may occur in inland navigation with coupled barge trains.
There are two basic curves in this diagram. The obtained traffic lane width with the corresponding curve radius for the ship manoeuvring with the main rudder (at different rudder angles) only and the ideal traffic lane width moving with a zero drift angle. A third curve is indicated showing the manoeuvring performance of the vessel only using the bow thruster as control device.
From the main curve "Main rudder only" the sub-curves indicating the increased setting of the bow thruster power with constant rudder angle start at the values marked with a square. The results of reducing the drift angle by a combination of main rudder and bow thruster can be followed up to the optimum point at the curve "Ideal traffic lane width". From there on the thruster-lines become steeper and require more space in traffic lane due to the increasing drift angle with its changed sign.
If the thruster power increases beyond the optimum point the performance of the vessel will become even worse than that of the ship using the main rudder only. The lines for "Bow thruster only" and the small rudder angles 5° and 10° clearly show it.
Similar results can be obtained by the application of a bow rudder. The only difference is that the maximum effect is obtained at high speed while the thruster looses efficiency as it can be seen in Fig. 9.
5.4 Influence of Current
Using formula (1) for the influence of the current in a river the results in Fig. 1 5 can be converted. In order to keep the new diagram readable only the curve Main rudder only" and the Thruster-line for a main rudder angle of 15° are displayed in Fig 16. Five different values of current are used: 6 km/h and 3 km/h, both running upstream and downstream and of course the still water case.
For the case sailing upstream the virtual curve radii for a ship become smaller, because the yaw rate of the vessel does not change, but the time this manoeuvre is taking rises due to the reduced speed over ground. Vice versa, the curve radii of a ship sailing downstream are increased with the current speed. This is the reason for the fact, that on the river Rhine pushed barge trains consisting of 6 barges type EIIb are allowed in the coupling 3 in length / 2 in breadth sailing up and 2 in length / 3 in breadth sailing down.
Fig. 16 Traffic lane width versus curve radius including current
The investigations carried out for this paper demonstrate the influence of bow steering systems on the manoeuvring behaviour of ships. Both active (thruster) and passive (rudder) devices can be used to control the bow of the vessel. They can help to reduce the drift angle by moving the pivot to the center of the ship. Thereby the traffic lane width can be reduced down to the theoretical minimum.
Simulation runs can give the answer on how big the force acting on the bow has to be to reduce the drift angle to zero. This information can be valuable to define regulations and limitations for vessels operating on narrow rivers and canals. The other way round it can be proofed for existing vessels whether they meet the statuary requirements or not.
 A. Gronarz "PMM-Tests with the Model of an Inland Cargo Vessel on Different Water Depths" VBD-Report 1243 (in German), Duisburg, Germany, 1989
 A. Gronarz "Determination of the Hydrodynamic Coefficients for the Simulation of Pushed Barge Trains" VBD-Report 1286 (in German), Duisburg, Germany, 1990
 A. Gronarz "Numerical Simulation of the Ship's Motion in Manoeuvres with Special Consideration of the Dependency of the Water Depth", PhD-Thesis, Gerhard- Mercator-Universität, Duisburg, Germany, 1997
 M.A. Abkowitz "Lectures on Ship Hydrodynamics - Steering and Manoeuvrability", Hydro- og Aerodynamisk Laboratorium, Report No. Hy-5, Lyngby, Denmark, 1964
 I.W. Dand "On Modular Manoeuvring Models" International Conference on Ship Manoeuvrability, RINA, London, 1987
 A. Gronarz "A Mathematical Model for Manoeuvring Simulation on shallow Water", Proceedings Marsim '93, St. Johns, Newfoundland, Canada, 1993
 P. Oltmann, S.D. Sharma "Simulation of Combined Engine and Rudder Manoeuvres using an Improved Model of Hull-Propeller Interactions" 15. ONR-Symposium, Hamburg, Germany, 1984
On 21.2.1956 Andreas Gronarz was born in Homberg (now Duisburg). As a schoolboy and student he had the chance to gain deep insight in inland navigation by working several weeks on motor vessels and push boats on the Rhine. He had his military service with the German navy. Since 1976 he studied at the RWTH Aachen, where he specialised in naval architecture and finished in February 1983 as certified engineer. After that he was scientific employee at the institute for naval architecture, design and dynamic (Prof. Schneekluth).
Since autumn 1985 he is member of the staff of the Versuchsanstalt für Binnenschiffbau, e.V. in Duisburg and specialised in the field of manoeuvrability. He worked on research and industrial projects dealing with PMM-tests and the simulation of the ship's motion. This led to his doctoral which was submitted to the Gerhard-Mercator-Universität Duisburg in 1997. From 1995 to 97 he led the research department of the VBD, where he is now working on the fields of hydrodynamics, data processing and European research contacts and special projects as for example development of ground effect crafts.