basic concepts and basic theories of ship maneuverability ,Standards for Ship Maneuverability , Coupled motions ,Heel angle in a turning. ,Steering and maneuvering tests for full scale ships in sea trials : 1 - Dieudonne spiral maneuver. 2 - Bech reversed spiral 3 - Pull-out Maneuver 4 - Weave Maneuver 5 - Turning circles. 6 - Kempf or zig-zag maneuver. 7 - Stopping trials.

1. REPRESENTED BY :
• AHMED TAHA
• MAYAR MOHAMED
• NOURAN MAGED
Coupled motions in turning
&
Full Scale Maneuvering Trials

2. Contents :
 Recall
 Ship maneuverability
 Coupled motions in turning
 Heel angle in a turning.
 Steering and maneuvering tests for full scale ships in sea trials
1. Dieudonne spiral maneuver.
2. Bech reversed spiral
3. Pull-out Maneuver
4. Weave Maneuver
5. Turning circles.
6. Kempf or zig-zag maneuver.
7. Stopping trials.

3. Recall
• Degrees of freedom
• Port and Starboard
δ

4. Coordinate systems
X˳
y˳
y
X
Ū
G
X˳ɢ
y˳ɢ
u
v
Ψ
δ
β
Ψ : heading angle
δ : rudder angle
β : drift angle
r, Ψ ̊: yaw rate
O˳
O
r

5. Equations of motion in horizontal plan
• Surge : X = m (ů̊G - vG Ψ ̊)
• Sway : Y = m (v̊G + uG Ψ ̊)
• Yaw : N = Iz Ψ ̊ ̊
# Move the original point to midship point :
X = m (ů - vΨ ̊ - XG Ψ ̊²)
Y = m (v̊ + uΨ ̊+ XG Ψ ̊ ̊ )
N = Iz Ψ ̊ ̊ + m XG (v̊ +u Ψ ̊ )
y
X
C.G
y
X
C.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 ̊

6. 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 ̊ - vr - XG r ²)
Y = m (v ̊ + u r + XG r ̊ )
N = Iz r ̊ + m XG (v ̊ +u r )

7. Hull Forces in Linear Formulation
X = 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 =
𝝏𝑿
𝝏𝒖
( u - V) +
𝝏𝑿
𝝏𝒗
v
Y =
𝝏𝒀
𝝏𝒗
v +
𝝏𝒀
𝝏𝒗 ̊
v ̊+
𝝏𝒀
𝝏𝒓
r +
𝝏𝒀
𝝏𝒓 ̊
r ̊
N =
𝝏𝑵
𝝏𝒗
v +
𝝏𝑵
𝝏𝒗 ̊
v ̊+
𝝏𝑵
𝝏𝒓
r +
𝝏𝑵
𝝏𝒓 ̊
r ̊
Hydrodynamic Derivatives

8. Hydrodynamic Derivatives
X 𝒖 =
𝝏𝑿
𝝏𝒖
, X 𝒗 =
𝝏𝑿
𝝏𝒗
: surge hydrodynamic derivatives
Y 𝒗 =
𝝏𝒀
𝝏𝒗
, Y 𝒗 ̊ =
𝝏𝒀
𝝏𝒗 ̊
: sway hydrodynamic derivative by transversal component of velocity and accelerations
Yr =
𝝏𝒀
𝝏𝒓
, Y 𝒓 ̊ =
𝝏𝒀
𝝏𝒓 ̊
: sway hydrodynamic derivative by yaw rate and yaw acceleration
N 𝒗 =
𝝏𝑵
𝝏𝒗
, N 𝒗 ̊ =
𝝏𝑵
𝝏𝒗 ̊
: yaw hydrodynamic derivative by transversal component of velocity and accelerations
N 𝒓 =
𝝏𝑵
𝝏𝒓
, N 𝒓 ̊ =
𝝏𝑵
𝝏𝒓 ̊
: yaw hydrodynamic derivative by yaw rate and yaw acceleration

9. 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
Hydrodynamic Forces on the Hull

10. 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 stability
2. Course keeping ability
3. Initial turning/course changing ability
4. Yaw checking ability
5. Turning ability
6. Stopping ability

11. 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.

12. Original course
Disturbance
Final course
Y
X
Stable ship
Unstable ship
For a dynamically unstable ship, it
will ultimately enter into an
arbitrary unsteady turning motion.

13. 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

14. • 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.

15. 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.

16. Heel angle in a steady turning
G
E
H
K
FR = Yδ δr
FH = Y 𝒗v+ Yr r
FG=
mv²
𝑹
FR
FH
FG
𝒇𝒚
FH - F R = mv²
𝑹
𝑀
Moment causing Heel = (FH - F R )* KG + F R * KH – FH * KE
= (FH - F R )* GE – FR EH
Mg GM 𝒔𝒊𝒏 ∅ = (FH - FR )GE
Mg GM 𝒔𝒊𝒏 ∅ =
mv²
𝑹
GE
GE
GM
= 𝑹 g
𝒔𝒊𝒏 ∅
v²
𝒔𝒊𝒏 ∅ =
v² GE
𝑹 𝒈 GM
Z axis
Y axis
FR
FG
Y𝒗

17. G
B'
W
B

M
B

18. 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.

19. Conditions of Trials
Maneuverability 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.

20. Dieudonne spiral maneuver
There 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 test
which are performed to evaluate :
1. Ship dynamic stability “straight line stability”.
2. Course keeping ability “directional stability”.

21. Steps
• The direct spiral test is an orderly series of turning circle tests
1. 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

22. ẟ : Rudder Angle
r : Rate of Turn
PORT
STARBOARD
PORT
STARBOARD
5 10 15 20- 20 -15 -10 - 5

23. 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.

24. Conclusion:
ẟ
Ψ ̊ r
ST.BoardPort
ST.Board
At 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

25. • 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.

26. 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.

27. 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.

28. 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

29. 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 ̊

30. 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.

31. 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.
Starboard
4. 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

32. 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 .

33. Turning Circle
Used 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

34. 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.

35. Turning Circle
The 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

36. tactical diameter
For 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

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

38. v●
β
δ
r●
r ̊ ( yaw acceleration )
Phase 3Phase 2Phase 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)

39. 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

40. 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.

41. 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)

42. 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.

43. time
Ships heading
Rudder angle
(δ)
Overshoot angle
(ψ)
Period
(Ԑ)
Overshoot
time
(Ti)
Angle(degree) 20/20
20
-20

44. Stopping Test
The 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.

45. Stopping Test
During stopping tests a ship’s speed is reduced
from some initial steady value to zero by
applying full astern power.

46. 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 the
ship's initial course.
the track reach :
the total distance travelled along the ship's
path

47. Stopping Test
Ships 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.)

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