• STOPPING OF SHIPS

4.1. Forces acting when stopping

There are two basic ways of stopping of the ship (or at least, easy to analyse):

1. Inertia stopping

2. Stopping with engine reversed

The behaviour of a ship during a stopping manoeuvre is complicated. However, assuming for simplification that stopping trajectory is a straight path, only the following forces acting on a ship might be taken into account: (fig. 4-1):

Fig. 4-1	Inertia stopping
		Stopping with engine reversed
		Symbols: m - mass of the ship mx - added mass v - velocity v ^' - acceleration R - resistance TE - effective thrust

Assuming that the hull resistance is proportional to the square of the ship's speed, the added mass is constant during the stopping manoeuvre, and propeller revolutions change linearly, the above stopping equation can be solved analytically:

From the above results that for a given ship the stopping distance depends mainly on:

• effective thrust astern T_E which is a function of engine's type

• time t_r for reversing the main engine

• ship resistance R₀ (or hull braking force)

• approach speed V₀.

4.2. Stopping process

Inertia stopping is a manoeuvre of stopping of the ship sailing at nominal speed when the main engine is stopped by closing down the fuel supply.

All relevant quantities change then in time according to the diagram shown in fig.4-2.

Fig. 4-2

Active stopping (crash stopping) is a manoeuvre of stopping of the ship using its main engine working in astern condition. All relevant quantities change in time as shown in the diagram in fig.4.3.

Fig. 4-3

Stopping distance during crash stop depends on the propeller thrust developed in astern condition. This, in turn, depends on the power available in astern condition. Fig. 4-4 shows the power available in astern condition for diesel engine and steam turbine propulsion. It is seen that the turbine propulsion develops much less power in astern condition than the diesel propulsion. The result is, that the stopping distance is much larger for turbine-driven ships.

Fig. 4-4 effect of engine characteristics on stopping manoeuvre

The other important quantity on which the stopping distance depends is the time needed for reversing the main engine - t_r. For large ships the time t_r may attain even several minutes.

Fig. 4-5 Non-dimensional time needed for reversing the main engine for ships with Diesel engine

The stopping distance considerably increases with increased time t_r due to the distance travelled during this time. The values of t_r for diesel propulsion versus ship size are shown in fig. 4-5.

Another important factor is the ship resistance R₀ at the approach speed V₀: the increase of the resistance R₀ shortens the stopping distance, thus any manoeuvre or procedure that can increase the R₀ result in shortening the stopping distance.

4.3. Different ways to stop the ship

Apart from inertia stopping and crash stop there are also other possibilities to stop the ship, such as:

1. Hard turn

2. Rudder cycling

3. Tactics called “Stopping in narrow waterway”

The principal reason for introducing the above strategies is the desire to shorten the stopping distance by judicious use of the hull and rudder braking forces while maintaining the ships controllability (which means to be able to generate the desired rudder force).

Hard turn could be used when there is an obstacle in front of the ship but the distance is too small to stop the ship by reversing the engine (crash stop). The distance travelled by the ship is then equal to the advance, that according to the IMO standard should be less than 4.5 ship lengths (see chapter 3). However, there should be enough free space available sideways, because the ship makes a turning circle with the tactical diameter up to five lengths of the ship.

Rudder cycling procedure is a procedure where the engine and the rudder are used in order to stop the ship. In this procedure the longitudinal component of the rudder force and the longitudinal component of the total hull hydrodynamic force (that is larger than the ship resistance) are used to reduce the stopping distance. The ship is put at a certain angle (drift angle) to the direction of motion, as in the first phase of turning circle manoeuvre (fig.4.6), and next part of turns are performed. This procedure is shown in fig. 4.7. Drift and rate of turn increase the longitudinal hull force. The proper sequence of propeller RPM reduction also puts the propeller into turbine mode, thus developing a braking force on the propeller. The stopping distance (head reach) when using this procedure is smaller than in crash stop.

Fig. 4-6

Fig. 4-7. Rudder cycling procedure

Stopping in narrow waterway. This procedure is used when the ship has to stop in a narrow fairway. It is similar to rudder cycling, but the ship has to be kept out from going outside the fairway. Because the full advantages of rudder cycling procedure can not be used, the head reach is much larger. This procedure is shown in fig. 4-8.

The principal idea of this procedure is:

• Use the propeller astern to slow down the ship

• Use the astern propeller power and the propeller side force to turn the bow and to initiate the turn in desired direction (the drift and the yaw rate increase the hull longitudinal braking force),

• Use the propeller kicks ahead with full rudder to put ship back into the waterway while also increasing the hull braking force

Fig.4-8. Stopping in narrow waterway procedure

4.4. Comparison of different stopping procedures

Fig. 4-9 shows comparison of different stopping procedures. The stopping distances were estimated by computer simulation for a bulk carrier 32 000 DWT.

Fig. 4-9.

Fig. 4.10.

The figure shows clearly the effect of the type of engine (diesel or turbine), and also the effect of installation of the controllable pitch propeller. The controllable pitch propeller has higher efficiency in astern condition than fixed-pitch propeller because of significantly shorter time for the thrust direction reversal (t_r) , therefore the stopping distance is smaller.

It is also clear that the hard-over turn provides the smallest head reach.

Fig.4-10 shows the comparison of the effect of rudder cycling procedure versus crash stop procedure taken from the tanker ESSO BERENICA trials.

4.5. Stopping characteristics

Inertia stopping

Average distances travelled (head reach) and average times to stop the ship as a function of deadweight are shown in fig. 4-11.

Inertia stopping distances for different initial engine settings could be estimated in operation using diagram similar to that in fig.4-12.

Fig. 4-12. Curves of stopping characteristics of inertia stopping

Crash stop distances

Head reach in crash stop manoeuvre could be estimated approximately using the following empirical formulae:

For ships with diesel propulsion:

For ships with turbine propulsion:

where: Hr = head reach

V₀ = initial speed in knots

Δ = ship displacement in tons

P_A = astern power in HP

The formulae provide rather too large distances

General effect of the ship size on stopping distance - head reach - in a crash stop manoeuvre is shown in fig. 4-13

Fig. 4-13. General effect of ship size on stopping head reach (Crane, 1973)

Fig. 4-14 shows average values of head reach and times to stop in crash stop manoeuvre for ships with diesel propulsion.

Similar diagram for ships with turbine propulsion is shown in fig. 4-15.

4.6. Effect of environment condition on stopping trajectory

As the rule one can say that during the stopping manoeuvre using crash-astern or coasting procedures the ship's captain is incapable of controlling the ship's heading. Stopping trajectory will depend mainly on weather condition and the final position of the ship when dead in water is difficult to predict with sufficient accuracy. Fig. 4-16 shows stopping trajectories for the same ship obtained in different weather conditions.

Fig. 4-16. Stopping trajectories for the same ship in function of actual weather condition ( tanker Esso Bernicia 278 kDWT)

References:

[1] - Revision of the Explanatory Notes to the Standards for Ship Manoeuvrability

DE 47/21 IMO 2004;

[2] - A. Nowicki: Wiedza o manewrowaniu statkami morskimi, Trademar Gdynia

2002;

[3] - M. Aucher: Stopping of Ships. A General Survey. ITTC 1972

4-3

Chapter 4- Stopping of ships

Longitudinal component of hull hydrodynamic force

Braking component of rudder force

Total hull hydrodynamic force

Head reach/L

Head reach- miles

Head reach/L

miles

minutes

10

20

30

40

50

5

10

15

0

25

50

75

0 50 100 150 200 250 300

Deadweight T x 10³

Fig.4-14

2

4

6

8

10

2

1

0

0.5

1.5

5

10

15

20

Head reach/L

Head reach- miles

Time to stop- minutes

Time to stop- minutes

0 50 100 150 200 250

deadweight Tx10³

Fig. 4-11

Head reach/L

miles

minutes

5

10

15

1

2

3

30

20

10

0

0 50 100 150 200 250 300

deadweight Tx10³

Fig.4-15

Time to stop-minutes

Head reach -miles

Head reach/L

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