1. Turning Ability: L = 234.000 m∆ = 65000.000 t

1.1 Advance and Tactical Diameter Criteria: V= 7.716 m/s

0.810L/V = 30.327

Tactical Diameter and advance are to be determined from the turning circle test as defined in Table 1.

IMO requires that the tactical diameteris to be less than 5 ship lengths and the advance is to beless than 4.5 ship lengths (IMO 2002a):

Ad < 4.5 L …….(1)

Advance (Ad) = 1053.000 m.

Tactical Diameter (TD):

TD < 5L ….(1.1)

Tactical Diameter (TD) = 1170.000 m.

Provided that condition (eqn 1) is satisfied, the rating of turning ability is found from the following formulae.

4.155 < TD/L < 5.000 … Rtd = 1

3.525 < TD/L < 4.155 … Rtd = 2

2.685 < TD/L < 3.525 … Rtd = 3

2.055 < TD/L < 2.685 … Rtd = 4

2.055 > TD/L … Rtd = 5

Cb =

if (4.26-1.62.10^(-6) ∆).L < TD/ L< 5 then Rtd = 1

if (3.63 - 1.62.10^(-6) ∆).L <TD < (4.26 - 1.62.10^(-6)∆).L then Rtd = 2

if (2.79 - 1.62 .10^(-6)∆).L < TD < (3.63 - 1.62.10^(-6)∆).L then Rtd =3

if (2.16 - 1.62 .10^(-6)∆).L < TD < (2.79 - 1.62.10^(-6)∆).L then Rtd =4

if (2.16 - 1.62 .10^(-6)∆).L > TD then Rtd =5 …..(1.2)

2. Initial Turning / course changing and yaw checking Ability:

2.1 The First Overshoot Angle in the 10/10 Zig - Zag Maneuver Criteria

The first overshoot angle in the zig-zag test is a measure of the vessel's course checking ability.

following auxiliary function.

10.000 if L/V < 10 sec ….(A)

20.163 if 10 sec < L/V < 30 sec ….(B)

20.000 if L/V > 30 sec ….(C)

The first Overshoot angle in the 10/10 Zig-Zag test is to be rated as follows.

if:

11.838 < 20.163

Provided that condition (D) is satisfied:

11.838 20.163

Provided that condition (D) is satisfied:

9.218 11.838

if Condition (D) is not satisfied:

9.218 20.163

As measured in the 10/10 zig-zag test, the first overshoot angle, α101, is to be evaluated with

f101 L/V =

f101 L/V =

f101 L/V =

The rating for the first overshoot angle in the 10/10 zig-zag test, Rt α10 = 1, can be assigned only

10.04 + 2.22 Cb < f101 (L/V) …..(D)

if 10.04 + 2.22 CB < α101 < f101 (L/V) …… then Rtα10 =1 ….. (E)

< α101 <

if 7.42 + 2.22 CB < α101 < 10.04 + 2.22 CB …… then Rtα10 =2 ….. (F)

< α101 <

if 7.42 + 2.22 CB < α101 < f101(L/V) …… then Rtα10 =2 ….. (G)

< α101 <

Assignment of other ratingsdoes not depend on condition (D) and is to be done according to the following formulae.

5.718 9.218

3.088 5.718

3.088

2.2 The First Overshoot Angle in the 20/20 Zig-Zag Maneuver Criteria:

The Requirements below are the result of harmonization of the IMO standards (IMO 2002a)rating system based on the statisticsof the sea trials. As measured in the 20/20 Zig - Zag test,

23.686 25.000

18.436 23.686

11.436 18.436

6.186 11.436

6.186

if 3.92 + 2.22 CB< α101 < 7.42 + 2.22 CB …… then Rtα10 = 3 ….. (H)

< α101 <

if 1.29 + 2.22 CB< α101 < 3.92 + 2.22 CB …… then Rtα10 = 4 ….. (I)

< α101 <

if α101 < 1.29 + 2.22 CB …… then Rtα10 = 5 ….. (J)

α101 <

the first overshoot angle , α201 is to be rated as follows:

if 20.09 + 4.44 CB < α201 < 25 then Rtα20 = 1 …..(i)

< α201 <

if 14.84 + 4.44 CB < α201 < 20.09 + 4.44 CB then Rtα20 = 2 …..(ii)

< α201 <

if 7.84 + 4.44 CB < α201 < 14.84 + 4.44 CB then Rtα20 = 3 …..(iii)

< α201 <

if 2.59 + 4.44 CB < α201 < 7.84 + 4.44 CB then Rtα20 = 4 …..(iv)

< α201 <

if α201 < 2.59 + 4.44 CB then Rtα20 = 5 …..(v)

< α201 <

3. Initial Turning Ability Criterion:

The initial part of the Zig - Zag test is used to judge the vessel's initial turning ability.Specifically , with the application of a10 - degree rudder angle,the vessel must not travel more

than 2.5 ship lengths before the vessel's heading has changed 10 degrees.

The requirements below are the harmonisation of the IMO Standards (IMO 2002a) rating system based on statistics of the sea trials. Assignment of the initial turning ability rating is to be done as follows.

405.664 2.500 m.

374.877 2.240 m.

342.279 2.070 m.

295.193 1.890 m.

5.000 m.

where,

L = Vessel Length between perpendiculars, in meters.

distance that the vessel travels from the moment of first execute until the course angle reaches 10 degrees in the 10/10 Zig - Zag maneuver.

Rti = Rating for the initial turning ability.

if 2.24 < l10/L< 2.50 L then Rti = 1 ….(i)

< l10/L <

if 2.07 <l10/L< 2.24 L then Rti = 2 ….(ii)

< l10/L <

if 1.89 < l10/L< 2.07 L then Rti = 3 ….(iii)

< l10/L <

if 1.63 <l10/L < 1.89 L then Rti = 4 ….(iv)

< l10/L <

if l10 < 1.63 L then Rti = 5 ….(v)

l10/L <

l10 =

4. STOPPING ABILITY:

Stopping ability is measured by the "track reach" and "head reach"realized on a stop engine -fullastern maneuver performed after a steady approach at the test speed until ahead speed in ship co-ordinates changes sign (i.e, vessel starts going backward).

4.1 Track Reach Criterion:

The stopping ability of the vessel is judged using a full astern crash stop maneuver. Based on IMO requirements (IMO, 2002a), the track reach should generally not exceed 15 ship lengths.

TR = 15 L 3510.000 m. ….(i)

For low - powered large displacement vessels:

TR = 20 L 4680.000 m.

where,

TR = Track reach in meters.

L = Vessel Length in meters.

4.2 Head Reach Criterion:

Head reach Criterion in a form of rating is based on statistics of sea trials.

HR = 2035.800 m.

Provided that condition (i) is satisfied ,the head reach is to be rated as follows:

0.161

12.632 < HR/L

where,

HR = non - dimensional head reach , measured in ship lengths

if Fn(69.4 + 0.000139*∆) < HR/L then Rts = 1 ….(2.15)

Fn =

L = Vessel Length in meters

Froude Number , V/Sqrt (g*L)∆ = displacement in metric tons

g =t = test speed in m/s

Provided that the above condition (i) is satisfied, assignment of other ratings Is to be done according to the following formulae:

10.506 < HR/L < 12.632

6.254 < HR/L < 10.506

4.128 < HR/L < 6.254

HR/L < 4.128

5 Straight - Line Stability and Course Keeping Ability:

5.1 Definitions:

A vessel is a straight - line stable on a straight course if, after a small disturbance, it will soon settle on a new straight course without any corrective rudder. The resultant deviation from theoriginal heading will depend on the degree of inherent stability and on the magnitude andduration of the disturbance.

The Course - Keeping Quality is a measure of the ability of the steered vessel to maintain a straight path in a predetermined course direction without excessive oscillations of rudder or heading. In Most cases reasonable course control is possible where there is small straight - lineinstability. The relationship between rudder angle and yaw rate is used to quantify a

IMO Standards.

Fn =

gravity acceleration (9.807 m/s2)

if Fn (56.2 + 0.000139*∆) < HR/L < Fn (69.4 + 0.000139*∆) then Rts = 2

if Fn (29.8 + 0.000139*∆) < HR/L < Fn(56.2 + 0.000139*∆) then Rts = 3

if Fn (16.6 + 0.000139*∆) < HR/L < Fn (29.8 + 0.000139*∆) then Rts = 4

if < HR/L < Fn (16.6 + 0.000139*∆) then Rts = 5

magnitude of straight - line instability, in particular with unstable loop , αU as recommended by

5.2 PULL - OUT TEST:

The Pull - out test allows for the determination of whether a vessel is dynamically stable and able to keep the cousre.

After the completion of the turning circle test, the rudder is returned to neutral position, (zero for twin screw vessels, may not equal to zero for single screw vessels) and kept there until a

a steady turning rate is obtained. This test gives a simple indication of a vessel's dynamic stability on a straight course.If the vessel is stable, the rate of turn will decay to zero (within accuracy of vessel equipment) for turns to both port and starboard. If the vessel is unstable, then the rate of turn will reduce to some residual rate of turn. The residual rates of turn to port and starboard indicate the magnitude of instability at the neutral rudder angle.

Normally, pull-out maneuvers are performed in connection with the turning circle, Zig - Zag or

or initial turning tests, but they may be carried out separately.Note: This test should only be used to identify course instability.

5.3 Tests for Straight-line Unstable Vessels:

If the vessel is found to be straight-line unstable by the pull-out test, one of spiral tests may also be performed.

1. The direct spiral maneuver (Dieudonné Spiral) is an orderly sequence of turning circle tests

to obtain a steady turning rate versus rudder angle relation. The maneuver requires a very

long time and therefore is not recommended for sea trial.

2. The reverse spiral (Bech Spiral) test may provide a more rapid procedure than the direct

spiral test in developing the spiral curve and enables obtaining the dashed or unstable portion

of the yaw rate versus rudder angle relationship in Section 2, Figure 5 which is not obtainable

In the reverse spiral test, the vessel is steered to obtain a constant yaw rate, the mean rudder

angle required to produce this yaw rate is measured and the yaw rate versus rudder angle plot is created. Points on the curve of yaw rate versus rudder angle may be taken in any order.

If the vessel is found to be straight-line unstable (there is a residual turn rate after the rudder was

returned to the neutral position), the magnitude of the instability loop should be assessed in order to assure this capability, the following maximum value of the width of the instability ,

0.000 if (25.14719) < 9s

7.109 if 9 < 25.14719 < 45s

12.000 if (25.14719) > 45s

where .

L = Vessel Length in meters.V = speed measured in m/s.

No rating is assigned in relation to the width of the instability loop.

5.4 Maximum Width of Unstable Loop

αU, is specified by specified by the following formulae:

αU < fU < (L/V)

1. fU (L/V) = 0 if L/V < 9s

fU (L/V) =

2. fU (L/V) = ((1/3)(L/V) - 3) if 9 < L/V < 45s

fU (L/V) =

3. fU (L/V) = 12 if (L/V) > 45s

fU (L/V) =

Tactical Diameter and advance are to be determined from the turning circle test as defined in

IMO requires that the tactical diameteris to be less than 5 ship lengths and the advance is to be

Ad < 4.5 L …….(1)

TD < 5L ….(1.1)

Provided that condition (eqn 1) is satisfied, the rating of turning ability is found from the following formulae.

2. Initial Turning / course changing and yaw checking Ability:

2.1 The First Overshoot Angle in the 10/10 Zig - Zag Maneuver Criteria

The first overshoot angle in the zig-zag test is a measure of the vessel's course checking ability.

following auxiliary function.

The first Overshoot angle in the 10/10 Zig-Zag test is to be rated as follows.

Provided that condition (D) is satisfied:

Provided that condition (D) is satisfied:

if Condition (D) is not satisfied:

Assignment of other ratingsdoes not depend on condition (D) and is to be done according to the following formulae.

2.2 The First Overshoot Angle in the 20/20 Zig-Zag Maneuver Criteria:

The Requirements below are the result of harmonization of the IMO standards (IMO 2002a)rating system based on the statisticsof the sea trials. As measured in the 20/20 Zig - Zag test,

3. Initial Turning Ability Criterion:

The initial part of the Zig - Zag test is used to judge the vessel's initial turning ability.Specifically , with the application of a10 - degree rudder angle,the vessel must not travel more

than 2.5 ship lengths before the vessel's heading has changed 10 degrees.

The requirements below are the harmonisation of the IMO Standards (IMO 2002a) rating system based on statistics of the sea trials. Assignment of the initial turning ability rating is to be done as follows.

Vessel Length between perpendiculars, in meters.

distance that the vessel travels from the moment of first execute until the course angle reaches 10 degrees in the 10/10 Zig - Zag maneuver.

Rating for the initial turning ability.

co-ordinates changes sign (i.e, vessel starts going backward).

4.1 Track Reach Criterion:

The stopping ability of the vessel is judged using a full astern crash stop maneuver. Based on IMO requirements (IMO, 2002a), the track reach should generally not exceed 15 ship lengths.

For low - powered large displacement vessels:

Vessel Length in meters.

4.2 Head Reach Criterion:

Head reach Criterion in a form of rating is based on statistics of sea trials.

Provided that condition (i) is satisfied ,the head reach is to be rated as follows:

non - dimensional head reach , measured in ship lengths

Vessel Length in meters

Froude Number , V/Sqrt (g*L)displacement in metric tons

test speed in m/s

Provided that the above condition (i) is satisfied, assignment of other ratings Is to be done according to the following formulae:

5 Straight - Line Stability and Course Keeping Ability:

The Course - Keeping Quality is a measure of the ability of the steered vessel to maintain a straight path in a predetermined course direction without excessive oscillations of rudder or heading. In Most cases reasonable course control is possible where there is small straight - lineinstability. The relationship between rudder angle and yaw rate is used to quantify a

IMO Standards.

The Pull - out test allows for the determination of whether a vessel is dynamically stable and

After the completion of the turning circle test, the rudder is returned to neutral position, (zero for twin screw vessels, may not equal to zero for single screw vessels) and kept there until a

a steady turning rate is obtained. This test gives a simple indication of a vessel's dynamic stability on a straight course.If the vessel is stable, the rate of turn will decay to zero (within accuracy of vessel equipment) for turns to both port and starboard. If the vessel is unstable, then the rate of turn will reduce to some residual rate of turn. The residual rates of turn to port and starboard indicate the magnitude of instability at the neutral rudder angle.

Normally, pull-out maneuvers are performed in connection with the turning circle, Zig - Zag or

or initial turning tests, but they may be carried out separately.Note: This test should only be used to identify course instability.

5.3 Tests for Straight-line Unstable Vessels:

If the vessel is found to be straight-line unstable by the pull-out test, one of spiral tests may also be performed.

2. The reverse spiral (Bech Spiral) test may provide a more rapid procedure than the direct

spiral test in developing the spiral curve and enables obtaining the dashed or unstable portion

of the yaw rate versus rudder angle relationship in Section 2, Figure 5 which is not obtainable

In the reverse spiral test, the vessel is steered to obtain a constant yaw rate, the mean rudder

angle required to produce this yaw rate is measured and the yaw rate versus rudder angle plot is created. Points on the curve of yaw rate versus rudder angle may be taken in any order.

If the vessel is found to be straight-line unstable (there is a residual turn rate after the rudder was

returned to the neutral position), the magnitude of the instability loop should be assessed in order to assure this capability, the following maximum value of the width of the instability ,

No rating is assigned in relation to the width of the instability loop.