MARINE CRAFT DESIGN &
CONSTRUCTION
Mechanical Engineering 4450
LECTURE 5: Monday February 7th, 2005
2.0 Ship Motions in a Seaway
2005 Winter Term
Marine Craft Design & Construction
(Mech 4450) − Lecture 5
Dept. of Mechanical Engineering
1
2.0
Ship Motions in a Seaway
Encounter frequency / period
• as far as ship motions are concerned, it is the period of
encounter with the waves that is important rather than the
absolute period of the wave
• the ship is moving relative to the waves and it will meet
successive peaks and troughs in a shorter or longer time
interval depending on whether it advances into the waves
or is travelling in the same direction as the waves
• the situation can be generalized by considering the ship at
an angle to the wave crest line as shown:
2005 Winter Term
Marine Craft Design & Construction
(Mech 4450) − Lecture 5
Dept. of Mechanical Engineering
2
2.0
Ship Motions in a Seaway
Encounter frequency / period
2005 Winter Term
Marine Craft Design & Construction
(Mech 4450) − Lecture 5
Dept. of Mechanical Engineering
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2.0
Ship Motions in a Seaway
Encounter frequency / period
• measured at a fixed point, the wave period is:
T = Lw / V w
• if the ship travels at Vs at α to the direction of
wave advance, in time T E (encounter time), the
ship will have travelled distance T EVs cos α in the
wave direction and the waves will have travelled
TEVw
• if TE is the period of encounter, then:
2005 Winter Term
Marine Craft Design & Construction
(Mech 4450) − Lecture 5
Dept. of Mechanical Engineering
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2.0
Ship Motions in a Seaway
Encounter frequency / period
Lw
Tw
TE =
=
Vw − Vs cos α 1 − Vs cos α
Vw
• if the ship travels in the same direction as the waves, the
period of encounter is greater than the wave period, if it is
running into the waves, the period of encounter is less
• this is the frequency / period that would be seen in the
spectrum of the ship motions, not the actual frequency of
the wave as it would appear in an inertial reference frame
2005 Winter Term
Marine Craft Design & Construction
(Mech 4450) − Lecture 5
Dept. of Mechanical Engineering
5
2.0
Ship Motions in a Seaway
Encounter frequency / period
encounter spectra in
head seas
2005 Winter Term
Marine Craft Design & Construction
(Mech 4450) − Lecture 5
Dept. of Mechanical Engineering
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2.0
Ship Motions in a Seaway
Wave aspects
waves encountered
by moving ships
2005 Winter Term
Marine Craft Design & Construction
(Mech 4450) − Lecture 5
Dept. of Mechanical Engineering
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2.0
Ship Motions in a Seaway
Synchronous roll
2005 Winter Term
Marine Craft Design & Construction
(Mech 4450) − Lecture 5
Dept. of Mechanical Engineering
8
2.0
Ship Motions in a Seaway
Synchronous roll
• when the encounter period is the same or nearly
the same as the natural period of the ship, a
superposition of inclining energies exists, and the
result is very heavy roll
• this is analogous to an elastically mounted rigid
mass being forced at its natural frequency
• such heavy rolling is not uncommon and it can be
clearly distinguished from rolling due to a lack of
stability
• synchronous rolling is NOT due to a lack of
stability
2005 Winter Term
Marine Craft Design & Construction
(Mech 4450) − Lecture 5
Dept. of Mechanical Engineering
9
2.0
Ship Motions in a Seaway
Synchronous roll
• ship of large GM or large static righting moments
are those that are more apt to encounter
synchronous roll
• ship of low GM are much less frequently subject
to such rolling
• follows from, rolling in a seaway:
T=
CB
GM
where : C is an empirical constant (0.38 - 0.55, depending upon ship and loading)
B is extreme beam (ft)
2005 Winter Term
Marine Craft Design & Construction
(Mech 4450) − Lecture 5
Dept. of Mechanical Engineering
10
2.0
Ship Motions in a Seaway
Synchronous roll
• the roll period varies inversely as the root of the
metacentric height
• therefore, the greater the GM for the same ship
beam, the shorter is the natural roll period
• at the same time, for larger vessels, the shorter the
period of roll (12 seconds and lower), the greater
the probability for synchronizing with the wave
period e.g. large Atlantic storm waves are 500 –
600 ft in wavelength and have a period of 10 – 11
seconds
2005 Winter Term
Marine Craft Design & Construction
(Mech 4450) − Lecture 5
Dept. of Mechanical Engineering
11
2.0
Ship Motions in a Seaway
Synchronous roll
• under such conditions, a large ship of low GM
would have a period in excess of the period of
these waves and would be safe from synchronous
roll
• on the other hand, a similar ship of large GM with
a period of about 10 – 11 seconds would be
susceptible to synchronous roll
2005 Winter Term
Marine Craft Design & Construction
(Mech 4450) − Lecture 5
Dept. of Mechanical Engineering
12
2.0
Ship Motions in a Seaway
Coupled pitching and heaving
• pitch considered analogous to roll except that the
axis of rotation is 90 degrees to the roll axis in the
same plane
• undamped natural pitch is typically between 1/3
and 2/3 of the natural period of roll
• with pitch, yaw, and heave, more difficult to
describe ship motion as an isolated phenomenon
as you can in roll
• pitch and heave are inter-related and affected by
roll, yaw, sway and surge
2005 Winter Term
Marine Craft Design & Construction
(Mech 4450) − Lecture 5
Dept. of Mechanical Engineering
13
2.0
Ship Motions in a Seaway
Coupled pitching and heaving
• pitch and heave motion in a real sea are coupled
and produces undesirable ship operation
conditions, namely: speed reduction, slamming,
and wet decks and their interference with human
and machinery functions
• more convexity in the forward and after sections
of a ship can reduce these undesirable effects
• these requirements often conflict with those for
high cruising speeds
2005 Winter Term
Marine Craft Design & Construction
(Mech 4450) − Lecture 5
Dept. of Mechanical Engineering
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•
•
Ship Motions in a Seaway
Yawing
ship yaw is the result of three possible mechanisms:
1. inequality of static pressures on the hull]
2. orbital motions of the water in a seaway
3. gyroscopic action
in general, the wave profile on the port and starboard
sides of the ship are not the same therefore, the
longitudinal position of the center of pressure on one side
of the submerged portion of the ship is offset
longitudinally and vertically from that on the other side
2005 Winter Term
Marine Craft Design & Construction
(Mech 4450) − Lecture 5
Dept. of Mechanical Engineering
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Ship Motions in a Seaway
Yawing
2005 Winter Term
Marine Craft Design & Construction
(Mech 4450) − Lecture 5
Dept. of Mechanical Engineering
16
2.0
Ship Motions in a Seaway
Yawing
• this creates a rotating couple about the vertical
axis – this manifests as a yawing and heeling
moment
• as the wave profiles change with the seas, the
yawing couple changes in magnitude and
direction, producing an oscillation
• this oscillation occurs at the apparent period of the
waves passing the ship
• could correct by anticipating the motion and then
compensating with appropriate rudder action
2005 Winter Term
Marine Craft Design & Construction
(Mech 4450) − Lecture 5
Dept. of Mechanical Engineering
17
2.0
Ship Motions in a Seaway
Yawing
• dynamic yawing action also produced by the orbital
rotation of the water in a wave
• as shown in the diagram, a ship moving in quartering sea
or the sea at an angle to the bow is subjected to a yawing
couple
• as the wave passes the ship, changing form the crest to the
trough at the bow and from the trough to the crest in the
after portions of the ship, the couple direction is reversed
• net result is a yawing oscillation with the same period as
the period of encounter of the waves
• rudder compensation for dynamic yaw and orbital motions
is difficult – every half wavelength, the water in the
vicinity of the rudder will be moving in the same direction
Dept. of Mechanical Engineering
2005as
Winter
Marine Craft Design
& Construction
theTerm
ship and a reduced
turning
couple
is
the
result
(Mech 4450) − Lecture 5
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2.0
Ship Motions in a Seaway
Why roll mitigation
• small waves of frequency equal to the ship's natural
frequency cause the ship to roll heavily
2005 Winter Term
Marine Craft Design & Construction
(Mech 4450) − Lecture 5
Dept. of Mechanical Engineering
19
2.0
•
Ship Motions in a Seaway
Motion-damping devices
all stabilization systems depend on the motion of mass
and can be classified as follows:
1. type of force used
a.
counterweight – gravitational force
b.
acceleration – inertial force
2. location of system
a.
internal
b.
external
3. type of mass
a. solid
b. liquid
2005 Winter Term
Marine Craft Design & Construction
(Mech 4450) − Lecture 5
Dept. of Mechanical Engineering
20
2.0
Ship Motions in a Seaway
Motion-damping devices
• only those devices that are frequently used are
discussed next
• for anti-roll:
– bilge keels
– controllable fins
– anti-rolling tanks
– active gyrostabilitizers
2005 Winter Term
Marine Craft Design & Construction
(Mech 4450) − Lecture 5
Dept. of Mechanical Engineering
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2.0
Ship Motions in a Seaway
Bilge keels
2005 Winter Term
Marine Craft Design & Construction
(Mech 4450) − Lecture 5
Dept. of Mechanical Engineering
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Ship Motions in a Seaway
Bilge keels
model of design with
twin bilge keels
2005 Winter Term
Marine Craft Design & Construction
(Mech 4450) − Lecture 5
Dept. of Mechanical Engineering
23
2.0
Ship Motions in a Seaway
Bilge keels
• long fin-like projects attached to ships along the
the turn of the bilge and extending from ½ to 2/3
of the length
• simple, well tested, economical, successful for
anti-roll
• continuous attachment of a single, heavy steelplate structure that projects 2 – 4 ft form the hull
and roughly perpendicular to the hull surface
• on large ships may be a v-shape cross-section and
fitted solidly to prevent damage when docking or
grounding
2005 Winter Term
Marine Craft Design & Construction
(Mech 4450) − Lecture 5
Dept. of Mechanical Engineering
24
2.0
Ship Motions in a Seaway
Bilge keels
• regardless of shape or fitting, bilge keels operate
according to a simple theory, recall: T = 1.108k x
φ
GM
where kx = radius of mass gyration
• with bilge keels projecting from the sides of the
ship, have an increased mass of water to roll with
the ship, value of kx in above equation is increased
=> period of roll is increased
• under forcing by waves, with the increased natural
period the amplitude of roll is decreased overall
• major effect of bilge keels is the increased
resistant to roll
2005 Winter Term
Marine Craft Design & Construction
(Mech 4450) − Lecture 5
Dept. of Mechanical Engineering
25
2.0
Ship Motions in a Seaway
Bilge keels
• bilge keels more effective when moving ahead through
waves than when stopped (i.e. sitting in water)
• there is hydrodynamic lift created on the forward section of
the bilge keels which resists the lateral forces of roll and
adds stability to the ship – i.e. a special case of fixed
stabilizing fins
• will not get complete elimination of roll
• disadvantage: added drag in forward motion
• if dynamically suppressed roll is desired should use active
stabilizing fins
2005 Winter Term
Marine Craft Design & Construction
(Mech 4450) − Lecture 5
Dept. of Mechanical Engineering
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2.0
Ship Motions in a Seaway
Active stabilizing fins
2005 Winter Term
Marine Craft Design & Construction
(Mech 4450) − Lecture 5
Dept. of Mechanical Engineering
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2.0
Ship Motions in a Seaway
Active stabilizing fins
• used on some large ships and pleasure craft
• consists of a projecting fin – one on each side at the bilge
line and forward of amidships
• some fins are retractable (axially or radially) and when
fully extended can rotate within a limited arc in a similar
manner to a stabilizing fin on an aircraft of the dive planes
on a sub
• fin angle-of-attack is controlled
• a gyroscopic sensing device actuates the motors, which
creates a response to, and anticipates, the wave roll force
• transmission of motion to the fins produces, at the right
time, the desired angle and results in a force at the fins that
opposes the heeling or rolling wave forces Dept. of Mechanical Engineering
2005 Winter Term
Marine Craft Design & Construction
(Mech 4450) − Lecture 5
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Ship Motions in a Seaway
Active stabilizing fins
• port and starboard fins operate simultaneously
with a 180 degree phase relationship to produce a
correcting roll moment (i.e. one that is opposite to
that created by the waves)
2005 Winter Term
Marine Craft Design & Construction
(Mech 4450) − Lecture 5
Dept. of Mechanical Engineering
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Ship Motions in a Seaway
Active stabilizing fins
effect of employing active stabilizing fins
2005 Winter Term
Marine Craft Design & Construction
(Mech 4450) − Lecture 5
Dept. of Mechanical Engineering
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Ship Motions in a Seaway
Anti-rolling tanks
2005 Winter Term
Marine Craft Design & Construction
(Mech 4450) − Lecture 5
Dept. of Mechanical Engineering
31
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Ship Motions in a Seaway
Anti-rolling tanks
• the Frahm anti-rolling tank consists of a U-shaped
tank system transversely arranged from side to
side (e.g. port to starboard)
• when the system is half-filled with water, it is
designed so that the natural period of oscillation of
the water (the sloshing) is approximately equal to
that of the ship (or slightly less)
• motion of ship is transferred to the water which
then dissipates it
• located above the ship CG
2005 Winter Term
Marine Craft Design & Construction
(Mech 4450) − Lecture 5
Dept. of Mechanical Engineering
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Ship Motions in a Seaway
Anti-rolling tanks
• effectiveness of anti-rolling tanks
• success of the anti-roll tank is that the motion of the water
should always be in harmony with the wave excitation
• only happens if frequency of the exciting waves is equal to
the natural frequency of the tank
• at other frequencies motion of water can even cause an
increase in roll motion; in the following graph it is evident
that the roll motion has in fact doubled at 0.4 rad/s.
2005 Winter Term
Marine Craft Design & Construction
(Mech 4450) − Lecture 5
Dept. of Mechanical Engineering
33
2.0
Ship Motions in a Seaway
Anti-rolling tanks
2005 Winter Term
Marine Craft Design & Construction
(Mech 4450) − Lecture 5
Dept. of Mechanical Engineering
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