SEAKEEPING Introduction (8.1) Seaworthiness defines the operational limits of our vessels! USCG 47’ MLB.

SEAKEEPINGIntroduction (8.1)

Seaworthiness defines the operational limits of our vessels!

USCG 47’ MLB


• The ship is a system excited by external moments and forces.

• Excitations (inputs) are primarily wind and waves.•“RAO” : response amplitude operator

• Responses (output) are motions in the six degrees of freedom, plus structural loading.

EXCITATIONEXCITATION SHIP RAO’s RESPONSE

- WAVES- WIND

- MOTION- STRUCTURALLOADS


• Ship response depends on two things:

1. Size, direction, and frequency of the inputs.

2. The seakeeping and structural characteristics of the ship.

SEAKEEPINGWaves (8.2)

• Wind and waves are both important but our study is limited to wave systems as this is the dominant input load.

• Waves are created by energy supplied to water (from wind, ship’s bow, etc.).

• Wave energy is related to wave height by:

W a ve E n e rg y f ( W a ve H e ig h t ) 2

The damage included bending the foremast 20 degrees and busting windows on the bridge! Taken off South Carolina in 1998.

SEAKEEPINGHow Waves Are Made (8.2)

• Wind: Most common. Energy transfer through shear stresses.

• Geological Events: Seismic activity on the sea bed (i.e. underwater volcanoes, landslides and earthquakes). “Tsunami’s”

• Currents: Interaction of ocean currents. Greatly influenced by the coastline’s shape.

Forces that make waves:

SEAKEEPINGWind Generated Wave Systems

Factors for Wave Size (8.2)

• Wind Strength: Faster wind = more energy transferred. Strong winds form large waves.

• Wind Duration: Longer = larger waves.

• Water Depth: Different relationships for deep and shallow water.

• Fetch: Area influenced by wind. Larger area = more energy transfer.

SEAKEEPING

The Simplified Wave Equation for coastal waters!

This won’t be on the exam!


• Energy transfer is constantly occurring in a wave.

– Water viscosity dissipates wave energy by viscous friction. Dissipation increases with wave height.

– To maintain the wave height, the energy lost to friction must be replaced.

SEAKEEPINGWave Life Cycle (8.2)

• Birth - wind over water creates ripples; high frequency (f), low wave length ().

Wind Energy > Wave Energy Dissipation


• Growing - f but as wind continues and energy content of wave system grows.

Wind Energy > Wave Energy Dissipation


• Fully Developed - sea stops growing with wave height and energy content maximized.

Wind Energy Wave Energy Dissipation


•Reducing - wave system no longer maintained as winds reduce. Waves dissipate (from high to lower freqs) as energy content drops.

• Swell - Eventually the wave system consists of low freq, long waves associated with an ocean swell.

Wind Energy < Wave Energy Dissipation

SEAKEEPINGWave Superposition (8.2)


• Confused seas are modeled as a destructive/constructive interference pattern.

• The wave systems are modeled by superimposing sinusoidal wave components, each with their own wavelength, speed, and amplitude.

Bottom Line: We must look at spectral densities and statistical analysis methods to determine wave system and sea properties.



• Wave Spectrum: analyzing the sea in the frequency domain.



• Modal wave periods from the Sea Spectra Chart are easily converted to modal (or circular) wave frequencies by the following relationship:

Don’t confuse this with linear frequency, f=1/T!


• Each sea state has a predominant modal frequency and significant wave height.

• Direction of the seas is assumed to be the same as local, observed wind.

• So, we now know the magnitude, direction, and frequency of the Excitation Forces!

The next step is understanding the ship motions...

SEAKEEPINGSimple Harmonic Motion (8.3)

• A harmonic motion is a system where a mass displaced from its “at rest” location experiences a linear restoring force resulting in an oscillating motion.

– Linear - size of force or moment is proportional to displacement. “Non-linear” restoring forces work, too.

– Restoring - force or moment opposes the direction of motion.


• Common Model:

– Mass is displaced, the spring is either in compression or tension with a restoring force trying to return it to the original location.

– The size of the force will be proportional to the amount of displacement - a linear force. (F=k·x)

– Motion will continue indefinitely if no damping is in the system.


• The mathematics involves analysis of a 2nd order linear differential equation of motion with displacement (z) and time (t) and damping effects =0:

• the solution is a simple cosine.

• where Z0 is the initial displacement and n is the natural (circular) frequency of the system.


• A plot of the displacement (z) against time (t):

• The period (T) can be determined from the plot.


• From the period the natural frequency can be calculated and checked against the observed natural frequency calculated from the known system parameters, mass (m) and spring constant (k).


• Amplitude of spring, mass, damper system may reduce with time due to damping or dissipation effects.

• Three conditions:

– Under damped: continued oscillations.

– Critically damped: one overshoot.

– Over damped: no oscillations, slow recovery.



• Forcing Function and Resonance

– For spring- mass-damper system to remain oscillating, energy must be put into system (if damping 0).

– This energy is required to overcome the energy being dissipated by the damper. In

this system it would be applied as an external force, often called an external forcing

function.


• To create maximum displacement, the forcing function has to inject its energy to coincide with the movement of the mass (i.e. be in phase).

• So to maintain system oscillation, a cyclical force is required that is at the same frequency as the SHM system.

• When this occurs, the system is at resonance and maximum amplitude oscillations will occur. If the forcing function is applied at any other frequency, the amplitude of oscillation is diminished.


• The differential equation for the mass, spring, damper system with forcing function becomes:

• where F is the size of the forcing function and is the

frequency at which it is applied.

• The solution becomes (still neglecting damping):

Z FK

1

1 ( n

)2Cos t


When << n Z = F/K F = forcing function K = spring rate

When >> n Z = 0 When = n Z = • System motion amplitude versus the forcing function frequency.

Z FK

1

1 ( n

)2

Cos t

Amplitude

Frequency n


• The figure below compares a system that is sharply tuned and one that is not.

• Lightly damped systems are more “sharply tuned” and are more sensitive to forcing function frequency than those with high damping. Ships are often sharply tuned in some motions...

SEAKEEPINGShip Response (8.4)

• As we saw in 8.1, the system output depends on the magnitude and frequency of the excitation force and the ship’s RAO’s.

•Excitation force frequency depends on the wave frequency (from sea state table) and ship speed and heading.

Z FK

1

1 ( n

)2

Cos tRecall

=input freq. (Vs=0)e=encounter freq.(Vs>0) then = e


Encounter frequency (e) accounts for the relative velocity between ship and waves.

Where:

w is the wave frequencyV is the ship speed in ft/s. µ is the heading of the ship relative to the direction the waves are moving.


• For a given wave frequency (w), changing course or speed alters e. (Example?)


• Knowing encounter frequency, we can predict ship responses.

• The 3 major sets of response can be grouped as:

1. Rigid Body Motions.

2. Structural Responses.

3. Non-oscillatory Dynamic Responses.


• A ship has 6 degrees of freedom about the xyz axis system, 3 rotational and 3 translational. All are rigid body motions.

R o l l

P i t c h

Y a w

H e a v e

SEAKEEPINGRigid Body Motions (8.4)

• Heave (Z axis translation)

– Imbalance between displacement and the buoyant force creates a resultant force

which attempts to restore the ship to its original waterline.

= FB

Zero Resultant Force

DWL

ResultantForce

FB

DWL

ResultantForce

CL CL CL

•

•B

G

•

•

G

B

•

•

G

B

FB

SEAKEEPINGRigid Body Motions - Heave (8.4)

• The vertical motion is completely analogous to the mass-spring-damper system.

• It is possible to predict the natural heave frequency (heave) of a ship.

Spring Constant (k) TPI Mass (M) g

SEAKEEPINGRigid Body Motions - Heave (8.4)

• TPI depends heavily on area of the DWL.

• Larger waterplane area for a given displacement equals greater restoring forces.

• ‘Beamy’ ships (e.g. tugs) will have short period oscillations and high accelerations (less comfortable).

• Heave is heavily damped.

SEAKEEPINGRigid Body Motions - Roll (8.4)

• External wave slopes create internal righting moments to realign “B” and “G”.

Rotation is about the X axis.

G

S

B

FB

B

FB

G Z

S

•

• •

•

Remember Chapter 4?!

Roll


• Righting moment depends on righting arm and ship displacement.

• For small angles (in radians) this becomes:

• This creates a linear restoring moment which is a rotational SHM.

Righting Moment GZ

Righting Moment GMT


• By rotational analogy to the mass-spring- damper system.

• Similarly, the expression for the natural roll frequency (roll).

Spring Constant (k) GMT Mass (M) Ixx


Combining empirical knowledge and the relationship between natural roll frequency (roll) and period of roll Troll.

– where B is the ship’s Beam – C is a constant whose value can range from 0.35 - 0.55

s/ft½ when GMT and beam are measured in ft. (0.44

when damping unknown)

T ro ll C B

G M T

What happens if B is increased?


• GM=f(B3)!, so T=f(1/B0.5)• Accelerations are higher and F=ma• Typical of B/L ratios >~0.3

RightingArm

Angle of Keel

Stiff GZ Curve - Large GMT

Tender GZ Curve - Small GMT

Too much GM is uncomfortable and ...


• GMT value is a compromise between good seakeeping (small GMT) and good stability (large GMT).

• Naval Architects design for a GMT of between 5 -8% of beam as a compromise.

SEAKEEPINGRigid Body Motions - Pitch (8.4)

• Pitch (about Y axis) wants to restore vertical alignment of “B” and “G”.

S

G

B

F B

S

G

B

F B

•

••

SEAKEEPINGRigid Body Motions - Pitch (8.4)

• Internal righting moment acting to restore the ship is linear and depends on MT1" value.

• As in roll, rotational motion is analogous to the mass- spring-damper system.

• Large MT1" = large moments & accelerations

• Motions heavily damped in all cases.

S p r in g C o n s ta n t (k ) M T 1 M a ss (M ) I y y

SEAKEEPINGRigid Body Motions - Resonance (8.4)

• Resonance - if freq of the forcing function = natural freq of the system: then maximum amplitudes!

• To minimize undesirable motions, resonance must not occur.

• Since heave, pitch, and roll are SHM, it is important that they do not match with encounter frequency (e).

Z FK

1

1 ( n

)2Cos t

SEAKEEPINGRigid Body Motions - Resonance (8.4)

• Pitch and heave are well damped and as such are not “sharply tuned” (amplified).

• Roll motion is sharply tuned, lightly damped, and very susceptible to the encounter frequency.

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HEAVE ROLLPITCH

heave pitch

roll

SEAKEEPINGShip Response - Structural (8.4)

• Distinct from rigid body motion, waves can negatively impact ship structural components.

• Primary structural loads:

1. Longitudinal bending: hogging and sagging

2. Torsion: twisting effect upon the ship structure

3. Transverse stresses: hydrostatic pressure of the sea


• Non-Oscillatory Dynamic Response

– Caused by the relative motions of the ship and sea.

– Maximized when a movement of the ship due to heave, pitch, or roll

superimposed with a wave peak or trough.

SEAKEEPINGNon-Oscillatory Dynamic Response (8.4)

• Shipping Water - bow of the ship submerged, considerable loads on the

ship structure.

• Forefoot Emergence - bow unsupported, severe structural loads.

• Slamming - severe structural vibration from forefoot emergence.

• Racing - propeller leaves the water.


Shipping Water!


Forefoot emergence

and slamming!


• Large following seas at speeds close to the wave speed may cause undesirable responses:

– Broaching - sudden and uncontrollable turning of a ship to a “beam on” orientation with a risk of capsize.

– Loss of Stability - ship surfs, can adversely effect stability.


SEAKEEPINGShip Response Reduction (8.5)

• Historically, seakeeping has been less important than hull resistance, strength and space efficiency considerations. (Heck, who cares about the crew’s comfort?!)

• DDG-51 hull form was the first to be created with seakeeping as a high priority. (In order to expand the mission envelope.)

SEAKEEPINGDDG 51 Hull Advantages (8.5)

• The hull shape was designed to reduce accelerations.

• Forward and aft sections are V-shaped, giving nonlinear MT1”, reducing pitch accelerations.

• Similarly, volume distributed higher (above DWL); limits Awp and TPI, reducing heave accelerations.

• Wider water plane forward and higher G reduces the stiffness of the GZ curve giving reduced roll accelerations.


• Recall pitch and heave are well damped but roll motion is sharply tuned, lightly damped, and very susceptible to the encounter frequency.


• “Anti-Roll Devices” are used to damp roll motion more effectively.

• Two categories of Anti-Roll Devices

– Passive- no external input required

– Active- require some kind of power or control system

SEAKEEPINGPassive Anti-Roll Devices (8.5)

• Bilge Keel - very common, reduces roll up to 35 %.

• Tank Stabilizers - ‘throttled’ fluid flow across a transverse tank.

• Others - tried w/o much success such as delayed swinging pendulums, shifting weights, and large gyroscopes.

SEAKEEPINGActive Anti-Roll Devices (8.5)

• Fin Stabilizers - common systems found on many ships, use control hydraulics to move fin.

• Others - again with only limited success such as pumping tanks and moving weights with hydraulics.

SEAKEEPINGPassive and Active System Effects (8.5)

• Resonance can still occur, however roll amplitude at resonance is reduced.

• Anti-roll devices have little impact on the motions of heave and pitch (which are heavily damped anyway).


• Responses are significantly influenced by the encounter frequency.

• If e is near any n , angular and vertical accelerations may cause severe negative consequences!

• Altering course and/or speed may be the easiest solution!

1

1

2

e

n

Recall,


A seaworthy design is only as good as the crew,

and you only appreciate the design when you need it!

SEAKEEPING Introduction (8.1) Seaworthiness defines the operational limits of our vessels! USCG 47’ MLB.

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