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5. STRAIGHT-LINE STABILITY: THE RESIDUAL RATE OF TURN RATIO
 When free sailing tests are performed, it is a normal procedure to perform the turning circle test and the pull-out test in one procedure. During model tests, this is standard procedure (at least with large enough basins). During full-scale trials, this could be more problematic due to the influence of the wind on the "residual rate of turn". The residual rate of turn ratio can be derived from a turning circle test at hard over rudder (35 degrees or the maximum rudder angle, whichever is the smallest) with a pull-out manoeuvre. In Figure 7 such a manoeuvre is given.
 The time trace of the rate of turn of a turning circle / pull-out manoeuvre will show that the rate of turn decreases from the constant rate of turn during the turn after the rudder has been put to zero to a rate of turn which stabilises after having travelled a few ship lengths (between 10 to 15 ship lengths). This rate of turn at zero rudder angle is called the residual rate of turn. The residual rate of turn ratio is the ratio between the rate of turn at zero rudder angle and the rate of turn at the maximum rudder angle. Such a value is related to the height of the instability curve as illustrated in Figure 8.
 
Fig. 7 Turning circle / pull-out test
 
Fig. 8 Residual rate of turn ratio
 
 The criterion is that the rate of turn ratio should be smaller than 0.3. The psychology behind this criterion is that the helmsman should encounter a large difference in visual perception (in general: the rate of turn) between steering with maximum rudder and steering with smaller rudder angles. Therefore, the rate of turn achieved with maximum rudder should be significantly higher than the rate of turn with a small rudder angle. This has been reduced to a single criterion derived based on bridge simulations in the eighties at MARIN, being the factor 0.3.
 This criterion can be determined using free sailing model tests or captive tests followed by simulations.
 
6. HEEL ANGLES
 The heel angle during turns is much more important than it received attention in previous criteria. The maximum heel angle is of importance. It needs to be said that the maximum heel angle is often much larger (factor 2 to 4) than the constant heel angle during a turn. The maximum heel angle is a function of speed, drift angles, roll damping and build-up of the dynamic manoeuvre.
 From interviews, it appears that a heel angle of 10 degrees is much higher than acceptable. In Figures 9 and 10, these heel angles are illustrated. An IMO resolution has been written on the maximum heel angle: the criterion was set at 10 degrees. Furthermore, the "panic" angle has been determined at 9 degrees. If this angle is present for a longer time, and builds up slowly, this is a frightening effect. Therefore, it needs to be avoided. From a lot of model tests at MARIN, it was observed that heel angles are achieved up to 30 degrees.
 To keep things practical, the maximum heel angle during a turning circle test is set at 13 degrees. This is valid for any steering angle. The maximum angle during the constant turning is set at 8 degrees, as it should be clearly below the panic angle.
 The best way to verify this before the sea trials is to use free sailing model tests. It is also possible to do this using captive tests, but it is more elaborate and requires a larger set of tests.
 
Fig. 9 
Heel angle during forced roll tests seen through bridge window
 
Fig. 10 
Heel angle during turning circle on frigate (source: internet)
 
7. SPECIAL STEERING DEVICES
 As the IMO criteria are defined for ships with rudders, one could say that they are not valid for ships with pods, azimuthing thrusters or other units with vectored thrust. However, from an operator point of view, there is no distinction between "hard-over rudder" or "hard-over pod", just as there is no difference in criteria for normal rudders and high-lift rudders. So, also podded driven vessels should fulfil the IMO criteria. The values of 10 degrees rudder angles apply to 10 degrees pod or thruster angles in the same way. In general, ships equipped with vectored thrust devices do not have problems with respect to their turning ability. It is, however, a myth that there are no "manoeuvring problems". Ships with vectored thrust devices often have course keeping problems. It should always be kept in mind that the role of the rudder is namely not only to steer the vessel, but also to stabilise the vessel. The stabilising effect of a thruster or a pod is in general less than the combination of a rudder with a propeller in front of it. Toxopeus and Loeff [6] have demonstrated that the overshoot angles of vessels with pods are larger than the overshoot angles of vessels with rudders. Therefore, the course keeping ability of vessels equipped with thrusters or pods needs to be investigated.







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