Regarding an assessment of the manoeuvring behaviour in the context of the present paper a short digression has to be conducted. Without going into details of the IMO interim standards it has to be recalled that the author already some years ago demanded a necessary revision, Oltmann (1998). This affects in particular the first overshoot angle of the 10°/10° zigzag manoeuvre. What revision was requested can be seen in Fig. 15, namely a constant limiting value of 17°independently from the speed of the ship.
Fig.15 
Manoeuvring Standards Regarding 10°/10°Zigzag Manoeuvre 
Fig.16 
Correlation Analysis for the Slope of the Spiral Curve rc(δR) at the Origin 
Fig. 16 shows the first overshoot angle of the 10°/10°zigzag manoeuvre for 70 data sets of ships all being unstable in yaw versus the reciprocal value of the slope of the spiral curve at origin. The correlation between both variables is not very evident (correlation factor r=.55). Nevertheless, the figure, additionally showing HSVA's limiting line, can be applied for an assessment. The figure shows that overshoot angles larger than 17°appear at abscissa values of approximately 0.9. This means that in the case of values ≥0.9, in order to be on the safe side, additional measures should be made.
Two measures are conceivable. First, tests with the freely manoeuvring ship model. Only two zigzag manoeuvres are necessary, namely the 10°/10°zigzag manoeuvre, which provides the true first overshoot angle, and for instance a 10°/1° zigzag manoeuvre with a reduced switching angle of 1° which gives qualitative information about the dynamic yaw stability, e.g. see Oltmann (1979). Second, captive model tests, to be performed with PMM or CPMC facilities, are feasible. In this case only three test runs are necessary to obtain the six hydrodynamic coefficients of Eq. (25) needed to determine the slope of the spiral curve and its reciprocal value, respectively.
6. CONCLUSIONS
The paper presents novel approaches for the main linear sway and yaw damping coefficients Y'v, Y'r, N'v, and N'r. With respect to the influence of the aft hull form this is an initial step in the right direction, but not yet the final solution. This is confirmed by the relatively large scatter shown in the comparisons of the estimated values with the corresponding data of HSVA's manoeuvring data base. Therefore, further efforts are necessary.
However, it also has to be kept in mind that the regression formulas presented show global characteristics which are as far as possible valid for different ship types like bulk carriers and container vessels.
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AUTHOR' S BIOGRAPHY
The author studied naval architecture between 1958 and 1964 at the Technical University Hanover and at Hamburg University. In 1964 he joined the Research Department of the Hamburg Ship Model Basin (HSVA) and was engaged in investigations on the reduction of ship's frictional resistance, interactions between passing ships, and the design of lateral thrusters. From 1972 to 1980 he worked for a special research pool for ship technology at the Institut für Schiffbau of Hamburg University. Thereby he was substantially concerned with the development of HSVA's Computerized Planar Motion Carriage (CPMC) put into operation in 1975. In 1978 he received his doctorate from the Technical University Hanover with a paper entitled "Determination of Manoeuvring Characteristics from Trajectories of Freerunning Ship Models". In 1980 he returned to HSVA and since then has been responsible for manoeuvring related problems. Between 1981 and 1990 Dr. Oltmann served as a member of the Manoeuvrability Committee of the International Towing Tank Conference (ITTC). Since 1988 he has been Chairman of the Manoeuvrability Committee of the German Society of Naval Architects (STG).
