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May 2004

Article selected from our quarterly magazine dedicated to the largest and most luxurious boats with information, interviews, technical articles, images and yachting news



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Article by
Angelo Sinisi


In previous articles I discussed the choice of the hull on the basis of speed and seakeeping ability, taking into consideration stability for safety yet neglecting maneuverability. In this article I will try to explain, in simple words, ship maneuverability.

The maneuvering characteristics of ships have been the object of extended studies and experiences all over the world, mainly for big ships, which, for their nature, generally have a poor maneuvering ability and a more or less emphasized directional instability. This not only is harmful to the efficiency of the ship, but it also affects its safety qualities, which are important especially when the hull has full shape aft and when sailing with following sea.

Ship maneuverability is considered to be the capability of maintaining and changing speed and direction with suitable means, depending on the needs resulting from the nature of the ship. Of course, the ship responds in several ways to a steering command and this depends on her geometric, kinematic and dynamic characteristics, on the type and size of the control units, on the reciprocal interaction between control elements and ship, and finally, on all external forces occurring at sea that disturb the motion.

Examining the straight and evolutionary motion of the ship on the horizontal plane, one must identify the most important aspects both of the ship's reactions to control actions when these are intended to change the ship's direction, as well as of her tendency to maintain or not the a straight line path, following actions caused by external forces.

These reactions, identified as physically representative of the various aspects of direction steering are called steering "qualities" and allow to evaluate, isolatedly or comparatively, the effective possibilities and capabilities of the ship and of her steering units, while maintaining or changing a given direction.

Trying to examine this very important chapter of ship dynamics in the simplest way possible does not seem useless. Ship dynamics together with seakeeping are very often ignored or at least unsuitably interpreted by way of empirical relationships, which, is obvious, scarcely represent the completeness of the problem. The design of steering units is just a part of the study of maneuverability and it would be irrational to carry it out on its own, separately from the hull on which they have to be installed.

The steering qualities are defined as follows: DIRECTIONAL STABILITY, MANEUVERABILITY and STEADY TURN CAPABILITY.

DIRECTIONAL STABILITY is associated with the basic concept of stable equilibrium of a physical phenomenon, when the initial conditions of the phenomenon, changed with the onset of an accidental cause, are reestablished when the perturbing cause disappears.

MANEUVERABILITY is the more or less accentuated capacity that a ship has of responding to the steering controls, which may tend to make her change direction from the straight line path motion or to return to the original heading, if some disturbance may have modified it.

STEADY TURN CAPABILITY is the capability of a ship of inverting direction, under the action of steering controls in restricted stretches of waters.

One can also add to such qualities the capability of being able to change the speed of the motion in a given period of time, that is the capability of accelerating and decelerating. Even though such capability is part of the maneuverability in a general sense, it greatly depends on the power of the engine and on the type of propulsion.

Fig. 1

The conditions of a straight line path of a ship, once the perturbing causes disappear, may be spontaneously reestablished in three different ways, as shown by the figure shown on Fig. 1, and these are:

Case I : straight line path stability when the ship, once the disturbance disappears, spontaneously follows the straight line path with a different heading from the original one.

Case II and III : directional stability when the ship, once the disturbance disappears, after a phase during which motion is in several directions, follows the original direction but on a different path as compared with the original one.

Case IV : positional motion stability when the ship, once the disturbance disappears, follows the same original path.

In the four above-mentioned cases, the actions carried out by control units are not considered, because, from the hydrodynamic point of view, the concept of straight line path is associated with the spontaneous capability of the ship of returning to the initial conditions. In practice, one should observe that a ship may have, at the most, the intrinsic quality of straight line path.

Fig. 2

The straight line path stability may be increased with fixed steering means, such as deadwoods (Fig. 2), thus obtaining, sometimes, ships that are too stable. In this case rudder maneuverability may be jeopardized.

In general, the stability characteristics on the horizontal plane with fixed steering means are independent from speed, that is, if a ship has a straight line path stability at low speed, the same is true for higher speeds and vice versa.

A ship with a high moment of mass inertia (big masses distributed at bow and stern) shall not suddenly change its heading and shall not easily return to it. A ship with a low moment of mass inertia shall immediately change its heading, nevertheless it will also return to it more easily. In the first case, in order to change heading more easily, a rudder that with small rudder angles generates big forces shall be installed; on the other hand, in the second case a rudder that at the same rudder angles will generate smaller forces shall be installed.

Very often dissymmetry of the propelling system thrusts and/or resistance to progress, the latter due to the dissymmetry of the flow on the hull, allow the straight line path to be maintained only with a given rudder angle.

The flow along a ship with a hull having symmetrical sides and which moves without rudders, in calm water, is symmetrical. The athwartship forces, which may be produced by the motion of the water along the hull, for the ship symmetry, are reciprocally balanced. As soon as the rudder is taken to a rudder angle α, a force P that does not lie on the symmetry plane of the ship is generated. Generally, this force generates an athwartship motion of the ship and rotations around three reciprocally perpendicular axes.

Only rotation around the vertical axis shall be maintained; the other types of rotation are to be considered secondary and undesirable.

Fig. 3

The forces that generate the ship's motion on the horizontal plane generate three different phases of the motion. (Fig. 3).

The first phase starts when the rudder is turned ad an angle and ends as soon as the ship starts rotating around the vertical axis.

During the second phase, the angular speed of rotation increases, while in the third one the angular speed is constant and the ship describes the so-called "steady turn".

As soon as the rudder is moved at an angle and the first phase starts, force P is generated and it acts perpendicularly to the rudder symmetry plane.

Fig. 4

The longitudinal component of force P , generated by the rudder, P sen α , acts in the same direction as the ship's drag or resistance and, therefore, it slows down its speed. The athwartship component, P cos α , gives the ship an athwartship motion and it also generates a couple which must overcome the moment of inertia of the ship's mass. Initially, force P sen α predominates so that the ship makes leeway to the left if the tiller is pushed to the right, without any considerable rotation around the vertical axis (Fig. 4).

In the second phase, as a consequence of the leeway, occurring in the first phase, and of the beginning of rotation, drag W to the ship's progress, originally acting on the longitudinal plane of symmetry, gradually changes into drag W' and acts at an angle β with the longitudinal plane of symmetry, on the left side of the rudder if the tiller is pushed to the right. The longitudinal component W' cos β , together with force P sen α , slows down the ship's motion, and the athwartship component W' sen β opposes force P cos α , so that the leeway to the left, occurring in the first phase, stops (Fig. 4). Now the ship follows a round path, whose turning radius diminishes as the angular velocity increases.

Because force W' acts on a point included between the center of gravity G and the bow, the ship advances with the bow on the inside and the stern on the outside of the trajectory of the center of gravity.

In the first two phases the forces and the motions vary, while in the third phase the conditions are constant. Once the two forces, occurring in the first two phases are balanced, the third phase starts. Both positive and negative angular accelerations in the opposite direction to that of tangent speed Vt stop, while the centrifugal force is balanced by the hydrodynamic forces that are generated with motion. The turning radius R becomes constant and the center of gravity of the ship traces a steady turn. The ship's speed, which diminished in the first two phases, now remains constant.

One of the undesirable secondary results of using the rudder is the ship's heeling around a longitudinal axis. This is due to the fact that the athwartship forces act on different vertical positions. Moreover, these forces vary as the ship passes through phases one and two, so that the heeling depends, in all instances, on the phase in which the ship is in that moment.

Fig. 5

In the first phase, the athwartship forces involved are the component of the force generated by the rudder, P cos α , and the component of drag W' sen β . As W' sen β is small at the beginning of the turn, and therefore of minor importance, P cos α provokes the heeling to the right when the tiller is pushed to the right and vice versa. Then, force W' sen β gradually increases and the heeling slowly diminishes (Fig. 5).

Fig. 6

As soon as the ship starts turning in the second phase, the centrifugal force (D' / g) (Vt² / R) cos δ (δ = leeway angle) comes into play. As a consequence, the ship tends to heel to the left if in the first phase the tiller is pushed to the right and vice versa (Fig. 6). The greatest angle of heeling φ is reached immediately after the heeling changes from right to left because due to its mass inertia, the ship heels beyond its position of static balance. In this condition, if the tiller was taken back at midships, the rudder force P cos α would disappear and it would not counteract force W' sen β , thus increasing the heeling to the left.

This is to be considered with attention, because the helmsman, fearing an excessive heeling, could set the tiller back at midships or worse, push the tiller to the opposite side thus worsening the situation; the only safe action would be, on the contrary, to slow down the ship by stopping the propelling systems. It is clear that the risk of capsizing in such circumstances is greater on ships that have some or all of the following characteristics: a high center of gravity, a little metacentric height, a high speed or a small steady turning radius.

Steady turning diameter R is approximately 3 to 7 times the ship's length. This ample variation of diameter R may be influenced by the hull shape or by the rudder shape and type.

Fig. 7

Above, we have seen that in order to increase straight line path stability the deadwood must be the greatest possible, vice versa for small steady turning diameters the deadwood should be removed. This means that straight line path stability and a small steady turn diameter are two characteristics that cannot be obtained simultaneously. Therefore, speed reduction resulting during a steady turn is a function of the size of the diameter of the turn and of the type of hull, that is of her block coefficient Cb (Fig. 7).

The other tests that highlight the steady turning qualities of a vessel are the "spiral" and "zig-zag" maneuvers.

The spiral maneuver is the most proper test to identify the directional qualities, because it also provides the quantity of the type of instability, when it exists.

The zig-zag maneuver provides the indexes of the steady turning capability and of maneuverability when the motion is not uniform, therefore it is more realistic.

It is important to note that the suitably analyzed data collected during the various tests supply the necessary elements for proportioning the servomechanisms of the automatic steering systems.

After explaining maneuverability, without specifying the details and without developing mathematical formulas relative to the different cases and tests, I remembered an interview made by a journalist to an architect. To the question "Is the study of the hull important?" the answer was "No. Everything is optimized by the computer programs..." Yet, I ask myself how can a computer program decide on: a deadwood, a small or big radius stempost, a rather full shape aft combined with hydrodynamic stern or vice versa (the geometrical shape on the three planes is very well carried out by the computer), a beam that may satisfy the stability requirements (for crew safety), the hydrodynamic criteria, etc.? Let alone the structure!