1.2 Manoeuvring characteristics

  1.2.1.1 In the following discussion, the assumption is made that the ship has normal actuators for the control of forward speed and heading (i.e., a stern propeller and a stern rudder). However, most of the definitions and conclusions also apply to ships with other types of control actuators.

  1.2.1.2 In accepted terminology, questions concerning the manoeuvrability of a ship include the stability of steady-state motion with "fixed controls" as well as the time-dependent responses that result from the control actions used to maintain or modify steady motion, make the ship follow a prescribed path or initiate an emergency manoeuvre, etc. Some of these actions are considered to be especially characteristic of ship manoeuvring performance and therefore should be required to meet a certain minimum standard. A ship operator may choose to ask for a higher standard in some respect, in which case it should be remembered that some requirements may be mutually incompatible within conventional designs. For similar reasons the formulation of the IMO Standards for ship manoeuvrability has involved certain compromises.

  1.2.2.1 At a given engine output and rudder angle δ, the ship may take up a certain steady motion. In general, this will be a turning motion with constant yaw rate ψ, speed V and drift angle β (bow-in). The radius of the turn is then defined by the following relationship, expressed in consistent units:

  1.2.2.2 This particular ship-rudder angle configuration is said to be "dynamically stable in a turn of radius R". Thus, a straight course may be viewed as part of a very wide circle with an infinite radius, corresponding to zero yaw rate.

  1.2.2.3 Most ships, perhaps, are "dynamically stable on a straight course" (usually referred to as simply "dynamically stable") with the rudder in a neutral position close to midship. In the case of a single screw ship with a right-handed propeller, this neutral helm is typically of the order δ_o = -1° (i.e., 1° to starboard). Other ships which are dynamically unstable, however, can only maintain a straight course by repeated use of rudder control. While some instability is fully acceptable, large instabilities should be avoided by suitable design of ship proportions and stern shape.

  1.2.2.4 The motion of the ship is governed mainly by the propeller thrust and the hydrodynamic and mass forces acting on the hull. During a manoeuvre, the side force due to the rudder is often small compared to the other lateral forces. However, the introduced controlling moment is mostly sufficient to balance or overcome the resultant moment of these other forces. In a steady turn there is complete balance between all the forces and moments acting on the hull. Some of these forces seeming to "stabilize" and others to "destabilize" the motion. Thus the damping moment due to yaw, which always resists the turning, is stabilizing and the moment associated with the side force due to sway is destabilizing. Any small disturbance of the equilibrium attitude in the steady turn causes a change of the force and moment balance. If the ship is dynamically stable in the turn (or on a straight course) the net effect of this change will strive to restore the original turning (or straight) motion.

  1.2.2.5 The general analytical criterion for dynamic stability may be formulated and evaluated with the appropriate coefficients of the mathematical model that describes the ship’s motion. The criterion for dynamic stability on a straight course includes only four "linear stability derivatives" which together with the centre-of-gravity position, may be used to express the "dynamic stability lever". This lever denotes the longitudinal distance from the centre-of-pressure of the side force due to pure sway (or sideslip) to the position of the resultant side force due to pure turning, including the mass force, for small deviations from the straight-line motion. If this distance is positive (in the direction of positive x, i.e. towards the bow) the ship is stable. Obviously "captive tests" with a ship model in oblique towing and under the rotating arm will furnish results of immediate interest.

  1.2.2.6 It is understood that a change of trim will have a marked effect mainly on the location of the centre-of-pressure of the side force resulting from sway. This is easily seen that a ship with a stern trim, a common situation in ballast trial condition, is likely to be much more stable than it would be on an even draught.

  1.2.2.7 Figure 1 gives an example of the equilibrium yaw-rate/rudder angle relation for a ship which is inherently dynamically unstable on a straight course. The yaw rate is shown in the non-dimensional form for turn path curvature discussed above. This diagram is often referred to as "the spiral loop curve" because it may be obtained from spiral tests with a ship or model. The dotted part of the curve can only be obtained from some kind of reverse spiral test. Wherever the slope is positive, which is indicated by a tangent sloping down to the right in the diagram, the equilibrium balance is unstable. A ship which is unstable on a straight course will be stable in a turn despite the rudder being fixed in the midship or neutral position. The curvature of this stable turn is called "the loop height" and may be obtained from the pullout manoeuvre. Loop height, width and slope at the origin may all be regarded as a measure of the instability.

  1.2.2.8 If motion is not in an equilibrium turn, which is the general case of :notion, there are not only unbalanced damping forces but also hydrodynamic forces associated with the added inertia in the flow of water around the hull. Therefore, if the rudder is left in a position the ship will search for a new stable equilibrium. If the rudder is shifted (put over "to the other side") the direction of the ship on the equilibrium turning curve is reversed and the original yaw tendency will be checked. By use of early counter-rudder it is fully possible to control the ship on a straight course with helm angles and yaw rates well within the loop.

  1.2.2.9 The course-keeping ability or "directional stability" obviously depends on the performance of the closed loop system including not only the ship and rudder but also the course error sensor and control system. Therefore, the acceptable amount of inherent dynamic instability decreases as ship speed increases, covering more ship lengths in a given period of time. This results because a human helmsman will face a certain limit of conceptual capacity and response time. This fact is reflected in the IMO Standards for ship manoeuvrability where the criterion for the acceptable first overshoot in a zig-zag test includes a dependence on the ratio L/V, a factor characterizing the ship "time constant" and the time history of the process.

  1.2.2.10 In terms of control engineering, the acceptable inherent instability may be expressed by the "phase margin" available in the open loop. If the rudder is oscillated with a given amplitude, ship heading also oscillates at the same frequency with a certain amplitude. Due to the inertia and damping in the ship dynamics and time delays in the steering engine, this amplitude will be smaller with increasing frequency, meaning the open loop response will lag further and further behind the rudder input. At some certain frequency, the "unit gain" frequency, the response to the counter-rudder is still large enough to check the heading swing before the oscillation diverges (i.e., the phase lag of the response must then be less than 180°). If a manual helmsman takes over the heading control, closing the steering process loop, a further steering lag could result but, in fact, he will be able to anticipate the swing of the ship and thus introduce a certain "phase advance". Various studies suggest that this phase advance may be of the order of 10° to 20°. At present there is no straightforward method available for evaluating the phase margin from routine trial manoeuvres.

  1.2.2.11 Obviously the course-keeping ability will depend not only upon the counter-rudder timing but also on how effectively the rudder can produce a yaw checking moment large enough to prevent excessive heading error amplitudes. The magnitude of the overshoot angle alone is a poor measure for separating the opposing effects of instability and rudder effectiveness, additional characteristics should therefore be observed. So, for instance, "time to reach second execute", which is a measure of "initial turning ability", is shortened by both large instability and high rudder effectiveness.

  1.2.2.12 It follows from the above that a large dynamic instability will favour a high "turning ability" whereas the large yaw damping, which contributes to a stable ship, will normally be accompanied by a larger turning radius. This is noted by the thin full-drawn curve for a stable ship included in figure 1.

  1.2.2.13 Hard-over turning ability is mainly an asset when manoeuvring at slow speed in confined waters. However, a small advance and tactical diameter will be of value in case emergency collision avoidance manoeuvres at normal service speeds are required.

  1.2.2.14 The "crash-stop" or "crash-astern" manoeuvre is mainly a test of engine functioning and propeller reversal. The stopping distance is essentially a function of the ratio of astern power to ship displacement. A test for the stopping distance from full speed has been included in the Standards in order to allow a comparison with hard-over turning results in terms of initial speed drop and lateral deviations.

 The IMO Standards for ship manoeuvrability identify significant qualities for the evaluation of ship manoeuvring characteristics. Each has been discussed above and is briefly defined below:

• .1 Inherent dynamic stability: A ship is dynamically stable on a straight course if it, after a small disturbance, soon will settle on a new straight course without any corrective rudder. The resultant deviation from the original heading will depend on the degree of inherent stability and on the magnitude and duration of the disturbance.

• .2 Course-keeping ability: The course-keeping quality is a measure of the ability of the steered ship to maintain a straight path in a predetermined course direction without excessive oscillations of rudder or heading. In most cases, reasonable course control is still possible where there exists an inherent dynamic instability of limited magnitude

• .3 Initial turning/course-changing ability: The initial turning ability is defined by the change-of-heading response to a moderate helm, in terms of heading deviation per unit distance sailed (the P number) or in terms of the distance covered before realizing a certain heading deviation (such as the "time to second execute" demonstrated when entering the zig-zag manoeuvre).

• .4 Yaw checking ability: The yaw checking ability of the ship is a measure of the response to counter-rudder applied in a certain state of turning, such as the heading overshoot reached before the yawing tendency has been cancelled by the counter-rudder in a standard zig-zag manoeuvre.

• .5 Turning ability: Turning ability is the measure of the ability to turn the ship using hard-over rudder. The result being a minimum "advance at 90° change of heading" and "tactical diameter" defined by the "transfer at 180° change of heading". Analysis of the final turning diameter is of additional interest.

• .6 Stopping ability: Stopping ability is measured by the "track reach" and "time to dead in water" realized in a stop engine-full astern manoeuvre performed after a steady approach at full test speed. Lateral deviations are also of interest, but they are very sensitive to initial conditions and wind disturbances.