;
Manoeuvring characteristics
The "manoeuvring characteristics" addressed by the IMO Interim standards for
ship manoeuvrability are typical measures of performance quality and handling ability
that are of direct nautical interest. Each can be reasonably well predicted at the design
stage and measured or evaluated from simple trial-type manoeuvres.
1.2.1 Manoeuvring characteristics: general
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.
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 Interim standards for ship manoeuvrability has involved certain
compromises.
1.2.2 Manoeuvring characteristics: some fundamentals
At a given engine output and rudder angle d, the ship may take up a certain
steady motion. In general, this will be a turning motion with constant yaw rate y,
speed V and drift angle b (bow-in). The radius of the turn is then defined by the
following relationship, expressed in consistent units:
R = V / y
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.
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 do = -1° (i.e., 1 degrees 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.
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.
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.
The value of the dynamic stability lever typically varies from 0.1L (where L is
ship length) for a stable, fine form cargo liner to -0.1L for a full form wide-beam
tanker. 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.
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 pull-out
manoeuvre. Loop height, width and slope at the origin may all be regarded as a
measure of the instability.
If motion is not in an equilibrium turn, which is the general case of motion,
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, indicated by the
arrows and small circles shown in figure 1. 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.
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 Interim 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.
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 degrees). 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 degrees to 20 degrees. At present
there is no straightforward method available for evaluating the phase margin from
routine trial manoeuvres.
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.
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.
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.
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.
1.2.3 Manoeuvring characteristics: selected quality measures
The IMO Interim standards for ship manoeuvrability identify six significant qualities for
the evaluation of ship manoeuvring characteristics. Each has been discussed above and
is briefly defined below:
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.
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.
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).
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.
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 degrees change of heading" and "tactical diameter" defined by the "transfer at 180 degrees change of heading". Analysis of the final turning diameter is of additional interest.
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.