REPRESENTED BY :• AHMED TAHA• MAYAR MOHAMED• NOURAN MAGED

Coupled motions in turning &

Full Scale Maneuvering Trials

Contents : Recall Ship maneuverability Coupled motions in turning Heel angle in a turning. Steering and maneuvering tests for full scale ships in sea trials1. Dieudonne spiral maneuver. 2. Bech reversed spiral3. Pull-out Maneuver4. Weave Maneuver5. Turning circles. 6. Kempf or zig-zag maneuver. 7. Stopping trials.

Recall• Degrees of freedom

• Port and Starboard

δ

Coordinate systems

X˳

y˳

y

XŪ

G

X˳ɢ

y˳ɢ

u

v

Ψ

δ

β

Ψ : heading angleδ : rudder angleβ : drift angler, Ψ : yaw rate

O ˳

O

r

Equations of motion in horizontal plan• Surge : X = m (uG - vG Ψ ) • Sway : Y = m (vG + uG Ψ ) • Yaw : N = Iz Ψ

# Move the original point to midship point :X = m (u - v Ψ - XG Ψ ²) Y = m ( + uΨ +v XG Ψ ) N = Iz Ψ + m XG ( +u Ψ )v

y

XC.G

y

XC.G ¤

C.G ( XG , 0 , ZG )

Assuming that the ship is symmetrical about its longitudinal centerplane .

Ψ = r Ψ = r uG = u vG = v + XG Ψ

Equations of motion Now we have equations of motion, with the original of the coordinate system lying on the midship point :

X = sum of all forces acting on the hull in ship-fixed abscissa axis or surge or axial forces .Y = sum of all forces acting on the hull or sway forces .N = sum of all moments acting on the hull in horizontal plane or yaw moments .u = surge or axial component of instantaneous speed .u = surge or axial acceleration .v = sway velocity . v = sway acceleration . r = yaw rate or yaw angular velocity .r = yaw acceleration . m = vessel mass . Iz = mass moment of inertia of a vessel relative to vertical axis Z . XG = abscissa of the center of gravity

X = m (u - v r - XG r ²)Y = m (v + u r + XG r ) N = Iz r + m XG (v +u r )

Hull Forces in Linear FormulationX = Fx (u, v, u , v , r, r ) Y = Fy (u, v, u , v , r, r ) N = Fψ (u, v, u , v , r, r ) • Fx, Fy = components of the hydrodynamic force . • Fψ = hydrodynamic moment in the horizontal plane . Final linear formulae for the hull forces are: X = ( u - V) + v Y = v + v + r + r N = v + v + r + r Hydrodynamic Derivatives

Hydrodynamic Derivatives

X= , X = : surge hydrodynamic derivatives

Y = , Y = : sway hydrodynamic derivative by transversal component of velocity and accelerations

Yr , Y = : sway hydrodynamic derivative by yaw rate and yaw acceleration

N= , N = : yaw hydrodynamic derivative by transversal component of velocity and accelerations

N = , N : yaw hydrodynamic derivative by yaw rate and yaw acceleration

Rudder Forces

XRd = 0

YRd = Yδ δR

NRd = Nδ δR

δ

C.G

HeadingDrag

Thrust

Rudder Lift force

lever

The moment of lift force deviates the

vessel from its original course

δ C.GDrag

Thrust

Rudder Lift force

Lift force

Hydrodynamic Forces on the Hull

Ship Maneuverability is the ability of a ship to keep or change its state of motion under the control actions, i.e., to keep the straight- ahead course with constant speed.• Ship maneuverability includes the following contents : 1. Inherent dynamic stability2. Course keeping ability3. Initial turning/course changing ability4. Yaw checking ability5. Turning ability6. Stopping ability

Dynamic stability “straight line stability”• A ship is dynamically stable on a straight course .

The resultant deviation from the original course will depend on :

1. Degree straight line stability of the ship 2. Magnitude and duration of the disturbance.

Original course

Disturbance

Final course

YX

Stable shipUnstable ship

For a dynamically unstable ship, it will ultimately enter into an

arbitrary unsteady turning motion.

Course keeping ability “directional stability”• Is the ability of the steered ship to maintain its original course direction.

Original course

Disturbance

Y

X

Final course

• Initial turning ”course changing ability” :The ability of ship to change its heading as response to a control action. A ship with good initial turning ability will quickly get into turning or change its original course after the control action.

• Yaw checking ability : the ability of the steered ship to respond to the counter rudder action applied in a certain state of turning. • Turning ability :

the ability of ship to turn under the hard over rudder action. • Stopping ability:

the ability of ship to stop with engine stopped (inertia stop) or engine full astern (crash stop) after a steady approach at full speed.

Coupled motions in turning• Heel during turning occurs as a result of the intrinsic coupling of sway, yaw, and roll caused by the center of gravity. • In a surface vessel, the fluid forces act below the waterline, but

the center of gravity is near the waterline or above.

Heel angle in a steady turning

G

E

H

K FR = Yδ δrFH = Yv+ Yr rFG =

FRFH

FG

FH - F R = Moment causing Heel = (FH - F R ) * KG + F R * KH – FH * KE

= (FH - F R ) * GE – FR EH

Mg GM = (FH - FR ) GE Mg GM = GE = g

=

Z axis

Y axis

FR

FGY

G

B'

W

B

M

B

Required and Recommended Maneuvers

Sea trials are the final confirmation of a vessel’s maneuvering qualities and its maneuverability prior to its delivery.

The required maneuvers are:• Turning test : For initial turning and steady turning ability . • 20/20 zig-zag test : For yaw checking ability and course-keeping ability . • Stopping test (Crash Stop) : For emergency stopping ability .

The recommended maneuvers are:• Pull-out test : For straight-line stability . • One of the spiral tests : For straight-line stability if the pull-out test indicated that the vessel is directionally unstable.

Conditions of TrialsManeuverability of a vessel may be significantly influenced by hydrodynamic interaction with the sea bottom, banks and other vessels passing nearby. In addition, winds, waves, currents and tides .

In order to get credible results, sea trials are to be carried out in the following conditions:• Deep and unrestricted waters : 1. Water depth at the trial site is to be more than four times of vessel draft at midship. 2. The site should be free from other traffic and far enough from banks that any maneuver

would not make any bank closer than two ship lengths.• Winds and waves • Tides and currents : It is recommended to avoid places with strong current and/or tidal influence when choosing a trial site. If current cannot be avoided, it should be uniform and the tests should be performed both for initial following and initial ahead current.

Dieudonne spiral maneuverThere are two kinds of spiral test :1. Direct spiral test, also called Dieudonné’s spiral test 2. Reverse spiral test, also called Bech’s reverse spiral testwhich are performed to evaluate :3. Ship dynamic stability “straight line stability”.4. Course keeping ability “directional stability”.

Steps• The direct spiral test is an orderly series of turning circle tests1. Accelerate ship up to full speed 2. changes the rudder angle ẟ in sequence of

+15° » +10 ° » +5 ° » 0 ° » » -15° » -10 ° » -5 ° » 0 °3. Record the rate of turn “r” , when it become constant.4. plot the Relation between Rudder Angle and Rate Turn

: ẟ Rudder Angle

r : Rate of Turn

PORT

STARBOARD

PORT

STARBOARD

5 10 15 20 - 20 -15 -10 - 5

Bech Reversed Spiral (In-direct)This is a manoeuvre aimed at giving a feel for a ship’s directional stability.

Steps:1. Accelerate ship up to full speed 2. The spiral maneuver is to be steering a constant rate of turn of 35 deg/sec.

To starboard with a minimum of rudder movement.3. When steady conditions have been reached the mean rudder angle

required to maintain this constant rate of turn, should be noted.4. The rate of turn is then to be reduced to 35 deg. Starboard and the

corresponding rudder angle should be noted.5. The same procedure is followed for a range of rates of turn.

Conclusion:

ẟ

Ψ r

ST.BoardPort

ST.BoardAt zero rudder angle, there is a value for rate of turn Ψ ( different from starboard and port ).

It is impossible to predict the direction of ship

Range of unstable angles of rudder

• Stable: If the ship is stable there will be a unique rate of turn for each rudder angle• Unstable: If the ship is unstable the plot has two ‘arms’ for the smaller rudder

angles, depending upon whether the rudder angle is approached from above or below the value.

• It is impossible to predict which way the ship will turn, let alone the turn rate, as this will depend upon other disturbing factors present in the ocean.• The manoeuvre does not give a direct measure of the degree of stability,

although the range of rudder angles over which response is indeterminate is a rough guide.

The difference between Dieudonne spiral ( direct spiral ) and Bech Reversed spiral (in-

direct):

• For the dis-advantages of Dieudonne spiral, Bech proposed an alternative approach, where instead of holding the rudder steady until a constant rate of turn is achieved, the ship is actively steered at a constant rate of turn using the rudder.

• In general, the results of Dieudonne method and Bech method are similar but the latter gives in the unstable part of the rate of turn versus rudder angle.

Pull-out Maneuver:Developed as a simple test to give a quick indication of a ship’s course stability.

Steps:1. Accelerate up to full-ahead speed.2. The ship is held on a steady course and at a steady speed.3. Commence maneuver with application of 20 deg. Port rudder.4. When rate of turn is steady, return rudder to amidships.5. Record rate of turn.6. Repeat maneuver for 20 deg. Starboard rudder.

Conclusion:Ψ r

Port

ST.Board

T

20 If the ship is stable, the rate of turns will decay to zero for turns to both port and starboard.

Rudder returned to amidship

Rudder returned to amidship

Ψ r

Port

ST.Board

T

If the ship is unstable then the rate of turn will reduce to some residual rate of turn

Range of un stable rate of turns

If the ship has a steering bias, then port and starboard turns will decay to the same small rate of turns on which ever hand the bias exists.

20

Weave Maneuver:

• Consider as a complementary to the pull-out maneuver and was developed to determine the minimum rudder angle necessary to produce a reversal rate of turn and so application to ships with little or no course stability.

Steps:1. Accelerate up to full-ahead speed with the ship’s head to wind.2. Commence maneuver with the application of 10 deg. Port rudder.3. When a steady rate of turn has been achieved put the rudder over to 10 deg.

Starboard4. If the ship’s heading changes from port to starboard apply 6 deg. Port rudder

and reverse the rate of turn ( without return rudder to amidship).5. The procedure of reducing the rudder angle is continued until the point is

reached where the rudder angle is not sufficient to change the ship’s heading

Notes:

• The rudder angle at which this failure to respond to the rudder will be different for port and starboard application, they will correspond to the rudder dead band-width .

Turning CircleUsed to determine :

The effectiveness of the rudder to produce steady-state turning characteristics

Advantages of the trial :Being economic in terms of time ,but if strong wind are experienced it is preferable to arrange all the approach runs in the same direction relative to wind

Turning Circle• When the rudder is put over initially, the force acting on the rudder

tends to push the ship bodily to port of its original line of advance.

• As the moment due to the rudder force turns the ship's head, the lateral force on the hull builds up and the ship begins to turn.

Turning CircleThe essential information to be obtained from this manoeuvre consists of :

• tactical diameter• advance• transfer• loss of speed on steady turn• time to change heading 90 degrees• time to change heading 180 degrees

tactical diameterFor 180 degrees change heading

Maximum transfer

Transfer of 9o degree change of heading

Steady turning radius

Drift angle,Must be zero so that the ship can rotate

Advance of 90 degree change of heading

3rd phase2nd Phase

1st Phase

Turning Circle

Advance.(after 90 degree of heading) The distance travelled by the center of gravity in a direction parallelto the original course after the instant the rudder is put over.

Transfer.The distance travelled by the center of gravity perpendicular to theoriginal course. It should be noted that the tactical diameter is not the maximum value of the transfer.

Tactical Diameter of steady turning circle. The maneuver should be obtained until 180 degree change of heading has been completed ,so that the advance and tactical diameter can be determined .

Maximum transfer and maximum advance .Which are measured at the points of max. translation of the ship’s center of gravity

Turning Circle

v● β δr●

r ( yaw acceleration )

Phase 3 Phase 2 Phase 1

T

Turning Circle

δr (angle of rudder is kept fixed)

R (becomes constant)

β (drift angle)

v (acceleration starts high then reduced till become zero)

Zigzag Manoeuver (Z-Manoeuver)

The zig-zag manoeuver, sometimes called a Kempf manoeuver, after G.Kempf, is carried out to study more closely the initial response of a ship to rudder movements

This trial was proposed as a means of :

1- investigating the qualities of a free-running model

2- qualitative measure of the effectiveness of the rudder to initiate and check changes of heading

A typical manoeuver would be as follows:

1-accelerate ship up to full speed ,with the ship’s head to wind

Zigzag Manoeuvre (Z-Manoeuver)

2- the rudder is put over to 20 degrees and held until the ship's heading changes by 20 degrees.

3-The rudder angle is then changed to 20 degrees in the opposite sense and so on.

The manoeuver is repeated for a range of approach speeds and for different values of the rudder angle and heading deviation.

Zigzag Manoeuvre (Z-Manoeuvre)

Important parameters of this manoeuver are:

(a) the time between successive rudder movements

Zigzag Manoeuvre (Z-Manoeuvre)

(b) the overshoot angle which is the amount by which the ship's heading exceeds the 20 degree deviation before reducing.

time

Ships heading

Rudder angle(δ)

Overshoot angle (ψ)

Period (Ԑ)

Overshoot time (Ti)

Angle(degree) 20/20

20

-20

Stopping TestThe stopping test is performed to evaluate the stopping ability.

A full astern stopping test is conducted to determine :the track reach of ship from the time when an astern order is given until the ship is stopped dead in the water.

• Track reach :the total distance travelled along the ship's path.

Stopping TestDuring stopping tests a ship’s speed is reduced

from some initial steady value to zero byapplying full astern power.

Stopping Test

the head reach : distance travelled in the direction of the ship's initial course

the lateral deviation : the distance toport or starboard measured normal to theship's initial course.

the track reach :the total distance travelled along the ship's path

Stopping TestShips usually are directionally uncontrollable during this manoeuvre so that the trajectory (path) is, to a large extent, determined by :-the ambient disturbances- initial conditions - rudder actions.

(Although existing procedures allow rudder activity to keep the ship as close to the initial course as possible, it should be noticed that IMO requires the rudder to be maintained at midship throughout the trial.)

REPRESENTED BY :• AHMED TAHA• MAYAR MOHAMED• NOURAN MAGED