marine craft design & construction mechanical...

2005 Winter Term Marine Craft Design & Construction (Mech 4450) − Lecture 5

Dept. of Mechanical Engineering

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MARINE CRAFT DESIGN & CONSTRUCTION

Mechanical Engineering 4450

LECTURE 5: Monday February 7th, 2005

2.0 Ship Motions in a Seaway



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2.0 Ship Motions in a SeawayEncounter 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:



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• measured at a fixed point, the wave period is:T = Lw / Vw

• if the ship travels at Vs at α to the direction of wave advance, in time TE (encounter time), the ship will have travelled distance TEVs cos α in the wave direction and the waves will have travelledTEVw

• if TE is the period of encounter, then:



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• 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

αα cos1cosw

s

w

sw

wE

VV

TVVL

T−

=−

=



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encounter spectra in head seas



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2.0 Ship Motions in a SeawayWave aspects

waves encountered by moving ships



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2.0 Ship Motions in a SeawaySynchronous roll



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• 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



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• 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:

(ft) beam extreme is loading) and shipupon depending 0.55, - (0.38constant empiricalan is :where

BC

GM

CBT =



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• 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



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• 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



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2.0 Ship Motions in a SeawayCoupled 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



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2.0 Ship Motions in a SeawayCoupled 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



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2.0 Ship Motions in a SeawayYawing

• 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 seaway3. 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



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• 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



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• 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 as the ship and a reduced turning couple is the result



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2.0 Ship Motions in a SeawayWhy roll mitigation

• small waves of frequency equal to the ship's natural frequency cause the ship to roll heavily



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2.0 Ship Motions in a SeawayMotion-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 forceb. acceleration – inertial force

2. location of systema. internalb. external

3. type of massa. solidb. liquid



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2.0 Ship Motions in a SeawayMotion-damping devices

• only those devices that are frequently used are discussed next

• for anti-roll:– bilge keels– controllable fins– anti-rolling tanks– active gyrostabilitizers



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2.0 Ship Motions in a SeawayBilge keels



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model of design with twin bilge keels



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• 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 steel-plate 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



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• regardless of shape or fitting, bilge keels operate according to a simple theory, recall: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

GM

kT x108.1

=φ



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• 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



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2.0 Ship Motions in a SeawayActive stabilizing fins



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• 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



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• 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)



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effect of employing active stabilizing fins



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2.0 Ship Motions in a SeawayAnti-rolling tanks



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• 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



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• 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.



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