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Introduction (8.1). SEAKEEPING. Seaworthiness defines the operational limits of our vessels!. USCG 47’ MLB. Introduction (8.1). SEAKEEPING. The ship is a system excited by external moments and forces. Excitations (inputs) are primarily wind and waves.

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seakeeping

Introduction (8.1)

SEAKEEPING

Seaworthiness defines the operational limits of our vessels!

USCG 47’ MLB

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Introduction (8.1)

SEAKEEPING
  • 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.
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Introduction (8.1)

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  • Ship response depends on two things:
    • 1. Size, direction, and frequency of the inputs.
    • 2. The seakeeping and structural characteristics of the ship.
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Waves (8.2)

SEAKEEPING
  • 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:
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The damage included bending the foremast 20 degrees and busting windows on the bridge 40 ft abv the deck! Taken off South Carolina in 1998.

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How Waves Are Made (8.2)

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Forces that make waves:

  • 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.
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SEAKEEPING

Wind Generated Wave SystemsFactors 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.
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SEAKEEPING

The Simplified Wave Equation for coastal waters!

This won’t be on the exam!

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Waves (8.2)

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  • 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.
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Wave Life Cycle (8.2)

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  • Birth - wind over water creates ripples; high frequency (f), low wave length ().
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Wave Life Cycle (8.2)

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  • Growing - freq  but length and ht  as wind continues and energy content of wave system grows.
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Wave Life Cycle (8.2)

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  • Fully Developed - sea stops growing with wave height and energy content maximized.
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Wave Life Cycle (8.2)

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  • 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.
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Wave Superposition (8.2)

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  • 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.
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Waves (8.2)

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  • Wave Spectrum: analyzing the sea in the frequency domain.
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Waves (8.2)

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  • 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!

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Waves (8.2)

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  • 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...

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Simple Harmonic Motion (8.3)

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  • 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.
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Simple Harmonic Motion (8.3)

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  • 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.
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Simple Harmonic Motion (8.3)

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  • The mathematics involves analysis of a 2nd order linear differential equation of motion with displacement (z) and time (t) and damping effects (c) =0:
  • the solution is a simple cosine.
  • where Z0 is the initial displacement and n is the natural (circular) frequency of the system.
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Simple Harmonic Motion (8.3)

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  • A plot of the displacement (z) against time (t):
  • The period (T) can be determined from the plot.
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Simple Harmonic Motion (8.3)

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  • 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).
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Simple Harmonic Motion (8.3)

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  • 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.
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Simple Harmonic Motion (8.3)

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  • 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.
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Simple Harmonic Motion (8.3)

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  • 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.
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Simple Harmonic Motion (8.3)

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  • The differential equation for the mass, spring, damper (=0) 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):
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Simple Harmonic Motion (8.3)

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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.
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Simple Harmonic Motion (8.3)

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  • 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...
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Ship Response (8.4)

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  • 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.

w=input freq. (Vs=0)

wn=natural freq.

(if Vs>0) then w= we

Recall

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Ship Response (8.4)

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

Where:

ww is the wave frequency

V is the ship speed in ft/s.

µ is the heading of the ship relative to the direction the waves are moving.

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Ship Response (8.4)

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  • For a given wave frequency (w), changing course or speed alters e. (Example?)
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Ship Response (8.4)

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  • 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.
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Ship Response (8.4)

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  • A ship has 6 degrees of freedom about the xyz axis system, 3 rotational and 3 translational. All are rigid body motions.
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Rigid Body Motions (8.4)

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  • 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.
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Rigid Body Motions - Heave (8.4)

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  • 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.
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Rigid Body Motions - Heave (8.4)

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  • 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).
    • ‘Narrow’ hulls like frigates, catamarans and SWATH have more gentle heave motions.
  • Heave is heavily damped.
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Rigid Body Motions - Roll (8.4)

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  • External wave slopes create internal righting moments to realign “B” and “G”. Rotation is about the X axis.

Roll

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Rigid Body Motions - Roll (8.4)

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  • 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.
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Rigid Body Motions - Roll (8.4)

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  • By rotational analogy to the mass-spring- damper system.
  • Similarly, the expression for the natural roll frequency (roll).
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Rigid Body Motions - Roll (8.4)

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  • 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)

What happens if B is increased?

T stays about the same! Huh?

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Rigid Body Motions - Roll (8.4)

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  • 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.
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Rigid Body Motions - Pitch (8.4)

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  • Pitch (about Y axis) wants to restore vertical alignment of “B” and “G”.
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Rigid Body Motions - Pitch (8.4)

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  • 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.
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Rigid Body Motions - Resonance (8.4)

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  • 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).
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Rigid Body Motions - Resonance (8.4)

SEAKEEPING
  • Heave and pitch 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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Ship Response - Structural (8.4)

SEAKEEPING
  • 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
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Ship Response (8.4)

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  • 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.
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Non-Oscillatory Dynamic Response (8.4)

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  • 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.
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Non-Oscillatory Dynamic Response (8.4)

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Forefoot emergence and slamming!

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Non-Oscillatory Dynamic Response (8.4)

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  • 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.
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Ship Response Reduction (8.5)

SEAKEEPING
  • 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.)
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DDG 51 Hull Advantages (8.5)

SEAKEEPING
  • 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.
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Ship Response Reduction (8.5)

SEAKEEPING
  • Recall pitch and heave are well damped but roll motion is sharply tuned, lightly damped, and very susceptible to the encounter frequency!
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Ship Response Reduction (8.5)

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  • “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
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Passive Anti-Roll Devices (8.5)

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  • Bilge Keel - very common, dampens 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.
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Active Anti-Roll Devices (8.5)

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  • 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.
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Passive and Active System Effects (8.5)

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  • 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).
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Ship Response Reduction (8.5)

SEAKEEPING
  • 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!
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Ship Response Reduction (8.5)

SEAKEEPING

A seaworthy design is only as good as the crew,

and you only appreciate the design when you need it!