FORCES ACTING ON THE MANOEUVRING SHIP
2.1. Categories of forces acting on the manoeuvring ship
Many different forces act on manoeuvring ship at sea or in harbour . These forces could be classified in different categories as follows:
hydrodynamic forces acting on ship hull
aerodynamic forces acting on the above water part of the ship
controlling forces of the rudder, thrusters and rudder propellers
forces of screw propellers or other propulsors
external pulling or pushing forces, executed by tugs, towing ropes etc
inertia forces
Hydrodynamic forces comprise forces acing on the ship hull in still water and also forces exerted by current and waves. Hydrodynamic forces are affected by the proximity of bottom, shore line, quays and jetties and also other ships.
Aerodynamic forces comprise aerodynamic force that appears in still air and the wind force.
Controlling forces are mainly rudder and thruster forces. To this category belong also forces exerted by special rudder propellers and similar devices.
Forces of propulsors include the thrust of the propeller, and that includes also the transverse thrust. With azimuting propellers the propeller thrust may be also used as a controlling force.
External forces include pulling or pushing forces of tugs, pulling force of towline in towing, forces exerted by nets or trawl, forces by replenishment equipment, etc.
Inertia force are mass forces acting when the linear or angular acceleration or deceleration occurs.
In this chapter considers only those forces that exist when the ship manoeuvres in still water and in still air. Therefore the forces of current, wave and wind are not considered.
2.2. Longitudinal and rotational motion
The simplest mode of the ship motion is when the ship is moving on a straight course at a constant speed. In this mode there are only two forces acting - the thrust of the propeller and the longitudinal hull hydrodynamic force - the resistance of the water. The forces are equal and act in opposite directions (fig. 2.1a).
In order to realise a pure rotational motion with no forward speed transverse forces are needed. They could be applied by using stern and bow thrusters acting in opposite directions. This could be also done using tugs pushing in opposite directions. Ship then turns around the point located approximately amidships (fig 2.1b). This point is called a pivot point (there is no ship lateral velocity at the pivot point).
Turning at speed could be executed by using a ship rudder. The rudder creates a transverse (lateral) force at the stern. When moving ahead the ship rotates around the pivot point located in the front part of the ship. When moving astern, the pivot point is close to the stern (fig. 2.1c).
A sideway motion (crabbing) could be executed by using bow and stern thrusters acting in the same direction (fig. 2.1d). Similarly, tugs pushing at the bow and the stern may create similar forces.
Fig. 2.1
2.3. The pivot point
Pivot Point “PP” is the point around which the ship rotates: when the ship rotates then at this point there is no transverse velocity (Fig. 2.2). The pivot point is a kinematic object - it tells about the transverse (lateral) velocity distribution on the ship's centre plane. The pivot point moves depending on the instantaneous set of forces acting on the ship
Fig. 2.2
With no forward speed and at steady rotational motion, when bow and stern swing in opposite directions the pivot point is located within the ship (often close to the midship).
When the ship is making headway, the pivot point moves forward.
When the ship is making sternway, the pivot point moves aft (Fig. 2.3).
Fig. 2.3
The position of the pivot point depends on the form of the hull. Its position - when moving ahead with a steady rate of turn - is between (0.12 to 0.25) L from the bow. In full-bodied ships, the pivot point is located closer to the bow, in slender ships it lies farther from the bow (fig. 2.4).
Full bodied ship CB≥0.8 PP close to the bow |
Slender ship CB<0.6 PP farther from the bow |
Fig. 2.4 |
|
The position of the pivot point is very important from the view point of manoeuvring. If it is close to the bow, then the ship has a better turning ability (smaller turning circle).
2.4. Rudder force and its effect
When the rudder is deflected to some angle it develops a force. The lateral component of the rudder force is used to control the ship motion. (fig. 2.5). This component causes sway motion, so drift angle appears and lateral hull force may develop. The lateral rudder force creates a torque that keeps the ship rotating around the pivot point. The rudder effectiveness increases with ship speed, it increases also with increased number of revolutions of the propeller, because the slipstream of the propeller increases, so the rudder force becomes larger.
Fig. 2.5
2.5. Transverse thrust of the propeller
In single-screw ships the turning propeller creates a non-symmetrical pressure field at the ship's stern. The pressure difference created on both sides causes that a transverse force is induced. This force is called the transverse thrust of the propeller.
If the propeller is a right-handed, then when making headway, the transverse thrust is directed to the starboard, and when making sternway, it is directed to the port (fig. 2.6).
With a left-handed propeller, the situation is reversed.
When ahead motion: transverse thrust to port;
When astern motion: transverse thrust to starboard.
Generally, the transverse thrust is small when making ahead, and it is much larger when making astern.
When the ship is making ahead, the hull is located on the suction side of the propeller. This causes that the asymmetry of the flow is rather small and the transverse thrust of the propeller is small (fig. 2.7a). It is hardly noticed by ship helmsman, because it is easily compensated by a small rudder angle.
When the ship is making astern, then the propeller pushes the water against the hull, which makes the asymmetry of the flow larger and the transverse thrust larger (fig.2.7b).
Fig. 2.6
Fig. 2.7
Simple formula for calculation of transverse thrust when making astern:
The value of the transverse thrust when making astern could be calculated by simple formula given below:
Roughly: Transverse thrust
(tons)
where: PA = astern power of the ship (in shp).
Example: Main engine power: P=30000 shp
Assuming engine power available: PA= 67% P = 20000 shp
Transverse thrust according to formula: TT= 10 to 20 tons
2.6. Effect of the transverse thrust of the propeller
The effect of the transverse thrust of the propeller is much more significant when making sternway than when making headway (fig. 2.8). This is because of different distances between the pivot point and the propeller for the two cases. When the ship is making headway, this distance is large (the pivot point lies in near the bow) and the transverse thrust small, therefore shifting sideways of the stern causes very small deflection of the bow. When the ship is making sternway, this distance is small, therefore even small shift of the stern causes large movement of the bow (fig. 2.9).
Fig. 2.8
Fig. 2.9
With a right-handed propeller swing due to transverse thrust of the propeller could be used to make mooring of the ship to the jetty easier. When moving ahead close to the starboard jetty, the stern of the ship will be pushed towards the jetty (fig.2.9). With astern motion the stern of the ship will be pushed away from the jetty and bow swings toward the jetty.
An unexpected effect may happen when the ship is very close to a solid jetty. With astern motion, the bow is not swinging toward the jetty, but away of it. The cause of this behaviour may be the “wedge effect” (fig.2.10)
Fig. 2.10
Water is pushed by the propeller working astern in the narrow space between the ship and the jetty causing higher pressure to arise on the ship's bow area. This results in creation a force F2 that may be larger than the transverse thrust F1. The ship swings then in the opposite direction to that which is expected.
2.7. Effect of thruster forces
Thrusters create forces perpendicular to the plane of the ship symmetry. With no forward speed, when bow and stern thrusters are working in the same direction, the ship is shifting sideways (swaying). If the bow thruster works in one direction and the stern thruster works in the other with the same force, then the ship rotates around the pivot point that lies approximately amidships (fig. 2.11). If the thruster forces are not equal the pivot point is shifted toward the stern (when the bow thruster force is larger) or to the bow (when the stern thruster force is larger).
Fig. 2.11
If only the bow thruster works (no forward speed of the ship), then the ship rotates around a pivot point located near the stern. If only the stern thruster works, the pivot point is located near the bow (fig. 2.12).
Fig. 2.12
The effectiveness of thrusters depends on whether the ship is moving ahead or astern.
Example: bow thrusters are more effective when the ship is moving astern (fig. 2.13).
Fig. 2.13
When the ship is making headway, the pivot point is moving forward. The bow thruster (or tug) is less effective, because it is pushing against opposite lateral hull force, arising due to the drift caused by the thruster work. When the ship is moving sternway, the opposing effect is created and the stern thruster (or tug) is less effective.
2.8. Differences in rudder and thrusters action
Very slow speed - swing to starboard
At the very slow speed the effect of using starboard rudder results in movement of the centre of gravity to port, then a swing to starboard follows. The position of the pivot point is thus in bow quarters. When using bow thrusters the centre of gravity moves to starboard, thus the pivot point is located in the stern quarters and (fig.2.14).
Fig. 2.14
At speed - swing to starboard
At speed, the starboard rudder causes the hull sway to port (the centre of gravity moves to port). The small drift toward port results in arising of hull lateral force located in bow quarters and directed toward the starboard. These two opposite lateral forces (rudder and hull) cause yaw torque and yaw motion to starboard - as intended when applying the starboard rudder. The pivot point in steady motion is located in bow quarters (fig.2.15).
At speed, when one intends to swing the bow to starboard using the bow thruster producing the lateral thrust directed to starboard then the effect of such an effort is lesser. The lateral thrust causes the hull to sway to starboard (initially the centre of gravity swings to starboard)., which induces lateral hull force directed to port - opposite to the acting thrusters force; the lateral hull force is located closer to midship then the thrusters force, so the thruster does provide a torque causing the ship to yaw to starboard - however, the yaw is smaller due to opposite action of lateral hull force. When the yaw motion to starboard develops then the pivot point settles in bow quarters of the ship. The motion of the centre of gravity changes to port, but the port swing velocity to port is smaller when compared to previous situation, when the rudder was used for turning. As an effect the drift at centre of gravity is small and for the ship master the bow thrusters seems to be ineffective as a turning device. Additionally, the lateral force produced by bow thruster decreases when the ship has forward speed due to outflow jet suction effects and further due to yaw motion that exposes the thrusters outlet to the flow incoming from the bow (fig.2.15).
Fig. 2.15
2.9. Lateral motion using rudder and bow thrusters
Lateral motion to port
With ahead power
Fig. 2.16
With a right-handed propeller a small transverse thrust of the propeller to starboard is easily compensated with the rudder force created by a full starboard rudder. Short kicks ahead at a dead slow engine create a high slipstream of the propeller and a large rudder force. A moderate amount of thrust of the bow thrusters to port is used to compensate the swing to starboard. However, even without the bow thrusters the high inertia of the ship against the rotation prohibits the swing to starboard (Fig.2.16).
With astern power.
The transverse thrust of the propeller pushes the stern to port. A moderate thrust of the bow thruster to port is used to compensate the possible swing (Fig.2.16).
Lateral motion to starboard
Fig. 2.17
With short kicks ahead, a full port rudder and the use of the bow thrusters to starboard there are no problems with controlling a lateral motion to starboard.
With astern power, there might be problems as shown in fig. 2.17. The bow is likely to swing to starboard because of the transverse thrust of the propeller to port. To control this transverse thrust of the right-handed propeller, the bow thruster force to port is used. This, together with the transverse thrust of the propeller, may cause an unintentional lateral motion to port, which, if much power is used, might be of considerable magnitude.
2.10. Effect of tug forces
When the ship has no forward motion or it is moving dead slow, the tugs pushing or pulling perpendicularly to the plane of ship symmetry exert forces having the same effect as the effect of thrusters - figs. 2.11 to 2.13 apply.
However, the effectiveness of tugs depends on their location. Few cases when two tugs working on the line or pushing are shown in fig. 2.18 to fig. 2.20.
However, if the tug pushes or pulls at a certain angle to the ship then the total tug force could be split into two components - one perpendicular to the plane of symmetry and the other parallel to it (fig.2.21). As shown in the figure, the result is that the bow of the ship is shifted sideways but at the same the ship is also moving ahead (or astern).
Ship dead in the water
Fig. 2.18
|
Pivot point at midship. Two tugs pulling or pushing sideways. Ship is shifting to one side without swing if both tugs develop equal pulling or pushing forces and force levers are the same. |
Ship making headway
Fig. 2.19 |
Pivot point shifts forward. Stern tug working on a large lever is more effective. Ship has a tendency to swing to port. |
Ship making sternway
Fig. 2.20 |
Pivot point shifts aft. Stern tug working on a small lever is less effective. Bow tug working on a large lever is more effective. Ship has a tendency to swing to starboard |
Fig. 2.21
2.11. Forces acting on the ship when turning
When the ship is making a turn, then apart of the propeller thrust also rudder force is active.
As the ship is now at a certain angle to the direction of motion (drift angle), the hydrodynamic force is no longer acting in the plane of the ship symmetry, but it is directed at a certain angle to the plane of symmetry. It is called now the total hydrodynamic force that could be split into two components - one opposite to the longitudinal direction of motion (longitudinal hydrodynamic force or water resistance) and the other perpendicular to it (transverse hydrodynamic force).
Ship is moving along the curvilinear path with the centre at point O. The distance between the centre of curvature and the centre of gravity of the ship is the radius of the instantaneous turn.
The ship's centre plane deviates from the tangent to the path of the centre of gravity by the drift angle. The line perpendicular to the ship's centre plane through the centre of rotation, marks the pivot point (PP). At this point, there is no transverse velocity in turning motion; for people on board it appears that the ship rotates around this point. In all other points along the ship there is a certain transverse velocity. In forward motion the transverse velocity is greatest at the stern. At the bow the transverse velocity is directed opposite to the stern transverse velocity. This is shown in fig. 2.22.
Fig. 2.22
Chapter 2. Forces acting on manoeuvring ship 2-3
*
*
No forward speed
At forward speed
P
P
Transverse speed
Right-handed propeller
AHEADD
ASTERN
a
b
*
P
High-pressure area
F2
F1
P
P
No forward speed
P
Total pushing force
Total pulling force
sway
Hull lateral force due to sway
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