1 GENERAL

SHIP GEOMETRY

RESISTANCE

PROPELLER

CAVITATION

SEAKEEPING

MANOEUVRABILITY

PERFORMANCE

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In this section the term seakeeping covers, in general, the behaviour and performance of a ship in a seaway including, in particular, ship motions and the sea states which cause them.

[M]

The total hydrodynamic force, per unit acceleration, exerted on a ship or other body in phase with and proportional to the acceleration.

(*A*_{ij})[-]

A non-dimensional coefficient expressing added mass in i^{th} mode due to j^{th} motion.

See: pitch angle

See: roll angle

See: trim, angle of

See: yaw angle

Referring to wave characteristics, a visible property of an irregular wave record as distinguished from a property of the components waves. Thus, an apparent wave height is a particular peak-to-trough distance.

The correlation between a random function of time, or space, and the same function shifted in time, or space, by a specified “lag” <m>tau</m>. The normalised auto correlation function is the auto covariance divided by the variance.

See: Ship geometry section under Keel

See: wave speed

A measured of the linear dependency of two random functions of time, or space, analogous to a correlation coefficient.

Influence of one mode of motion on another mode of motion, for instance, coupling between heave and pitch.

The correlation between two random functions of time, or pace, with one shifted in relation to the other by a “lag” <m>tau</m>.

That motion, or component of motion, caused by some action other than that of the main propulsion devices of a ship, such as wind, waves, current and like. See also: sideslip

(*β*)[-]

The horizontal angle between the instantaneous direction of motion of the centre of gravity of a ship and its longitudinal axis. It is positive in the positive sense of rotation about the vertical body’s axis.

()[L]

The relative vertical distance of a part (usually the bow) of an oscillating ship above the water surface; opposite to submergence.

(*Λ*)[-]

Ratio of excitation frequency to natural frequency or ratio of natural period of a motion to period of encounter. The tuning factor in heave, pitch and roll have the symbol

<m> wedge_z=omega_E/omega_Z wedge_theta=omega_E/omega_theta wedge_varphi=omega_E / omega_varphi</m>

or

<m> wedge_z=T_Z / T_E wedge_theta=T_theta / T_E wedge_varphi=T_varphi / T_E</m>

respectively

A force which tends to reduce the motion and, if assumed to be linear, is proportional to the velocity.

A fluctuating external force that causes motion of body, as for instance, a ship when encountering a train of waves.

(*f*)[L]

See: Ship Geometry Section

(*ω*)[T^{-1}]

In any cyclic motion, or in any periodic motion which may be represented by a cyclic motion, the circular frequency is the angular velocity. If *ω* is in radiant per second, then

<m>omega=2 pi/T</m> and <m>f= omega/{2 pi }</m>

where *T* is the period and *f* is the frequency.

(*f*_{W})[T^{-1}]

The number per unit time of successive crests of a train of waves at a fixed angle of encounter, *μ*; the reciprocal of the wave period *T*_{W}.

(*f*_{E})[T^{-1}]

The number per unit time of successive crests of a train of waves meeting a fixed point of a ship, at a fixed angle of encounter, *μ*; the reciprocal of the period of encounter TE. In deep water:

<m>f_E=f_W + {2 pi}/g Vf{2}under{W}cos mu</m>

where <m>f_W</m> is wave frequency and *V* ship speed

<m>f_Z, f_theta, or f_varphi T^-1</m>

The frequency of the periodic heaving, pitching or rolling motion of a ship.

<m>(omega_Z, omega_theta or omega_varphi [T^-1])</m>

Frequencyral, matural circular, of heave, pitch or roll has the following definitions respectively:

<m>{2 pi}/T_Z , {2 pi}/T_theta</m>, and <m>{2 pi}/T_varphi</m>, where <m>T_Z , T_theta</m> and <m>T_varphi</m> are the natural periods

(radius of gyration)

(*k*_{X}, k_{XX}, k_{Y}, k_{YY}, k_{Z}, k_{ZZ})[L]

The square root of the ratio of mass moment of inertia (referred to body axes) to the mass of a body. See General Section for body axes under axes, co-ordinate

(*ψ*)[ ]

The instantaneous direction of the projection of the forward longitudinal axis of a ship in a horizontal plane, defined by degrees of the compass or degrees azimuth.

The vertical oscillatory motion of a specified point in a vessel, usually the centre of gravity. Although the heaving of a ship is a motion which is confined to operation in waves, it is possible with a high-speed planing craft for such motion to occur in calm water under some conditions. (See Porpoising)

To maintain control of a ship, especially in extremely heavy weather, with minimum possible speed through the water.

A steady inclination of a ship about a longitudinal axis; to be distinguished from rolling, which is an oscillatory motion.

(*φ*)[-]

The angle, measured about a longitudinal axis, between a static inclined position of a ship and its normal upright position.

Analogous to aeroelasticity. The study of the interaction between the inertial, hydrodynamic and elastic forces in a structure subjected to hydrodynamic loading. Divided into dynamic hydroelasticity, where these three forces are coexistent, or static hydroelasticity where inertial forces are absent.

The down wind or down sea motion of a ship. More specifically, the lateral distance the ship has been forced off the desired path.

See: drift, angle of

See: heel

See: added mass

A moment which tends to reduce the motion and, if assumed to be linear, is proportional to the angular velocity.

A moment associated with a displacement from a position of equilibrium and tending to increase this displacement.

A fluctuating external moment that causes motion of a body or ship when encountering a train of waves.

(*I*_{X} ,I_{XX}, I_{Y} ,I_{YY}, I_{Z} ,I_{ZZ})

[L^{2}M]

The summation of products of elementary masses and the squares of their distances from the respective body axes through the centre of gravity – equal to the mass times the square of the gyradius or radius of gyration. See General Section for body axes under axes, co-ordinate.

A moment tending to return a body to its initial condition after being displaced by an external moment.

Exciting moment in roll. Moment, stabilising Moment associated with a displacement from a position of equilibrium and tending to decrease this displacement.

(*M*^{B}_{3} or *M*_{L}, formerly M_{BH})

[L^{2}MT^{-2}]

That part of the inertial lateral bending moment acting on a cross section of a hull which is caused by the action of waves and ship motions.

(M^{B}_{2} or *M*_{N} , formerly *M*_{BV})[L^{2}MT^{-2}]

That part of the internal vertical bending moment acting on a cross section of a hull which is caused by the action of waves and ship motions.

(*M*^{T} or *M*_{B})[L^{2}MT^{-2}]

That part of the internal torsional or twisting moment acting on a cross section of a hull which is caused by the action of waves and ship motions.

The all inclusive term to describe the various dynamic motions which may be made by a ship including the following which are defined separately:

*Rolling, Pitching*and*Yawing*(angular)*Heaving, Surging*and*Swaying*(translatory)

These motions may occur while the ship is stationary in the water or travelling through it.

(*T*_{Z}, *T*_{θ}, *T*_{ϕ})[Τ]

The time for one complete cycle of the motion resulting when a body or ship is displaced in calm water from its equilibrium position by an external force, then released.

A mechanism used to impose a controlled, known, oscillatory motion on a body. Also used to describe any oscillatory body.

(T)[T]

The time for one complete cycle of a periodic quantity or phenomenon. (See also: natural period of motions).

(<m>varepsilon_l</m>)[-]

The angle between two vector representing sinusoidal quantities of the same frequency.

Phase angle between output and input of a linear system performing forced motion, as a function of frequency.

(*θ*)[-]

The angle, measured about the transverse body axis, between the instantaneous position of the longitudinal axis of a ship when pitching and its position of rest. (Positive bow up).

The angular component of the oscillatory motion of a hull about a transverse axis. Although pitching of a ship is a motion confined to operation in waves, it is possible with a high-speed planing craft for such motions to occur in calm water under some conditions. (See: Porpoising)

The cyclic oscillation of a high-speed craft primarily in calm water in which heaving motion is combined with pitching motion. The motion is sustained by energy drawn from the thrust.

Described broadly as impacting between a water surface and the side or bottom of a hull. Pounding can perhaps be differentiated from slamming in that the impact, while heavy, is not in the nature of a shock. (See: Slamming)

(*P*_{AW})[L^{2}MT^{-3}]

The mean increase in power in wind and waves as compared with the water at the same mean speed.

A local pressure experienced by a hull when subjected to impact with the water. Usually associated with slapping, slamming or pounding.

See: gyradius

(*R*_{AW})[LMT^{-2}]

The mean increase in resistance in wind and waves as compared with the still water resistance at the same speed

The dynamical condition of a simple, uncoupled system where the excitation frequency is equal to the natural frequency. Note: In a coupled system, the dynamic condition where the excitation frequency corresponds to the frequency of maximum response to unit exciting force over a range of frequencies.

The square of the ratio of response amplitude to excitation amplitude of a forced harmonic motion applied to a linear system, as a function of frequency.

A complex function of which the modulus is equal to the response amplitude operator and the argument is equal to the phase response operator.

(*n*_{AW})[Revs. T^{-1}]

The mean absolute increase in rate of revolution (usually per minute), as compared with those in smooth water, necessary to maintain speed in wind and waves.

(<m>phi</m>)[-]

The angle measured about the longitudinal body axis, between the instantaneous position of a ship when rolling (which see) and its normal upright position. (Positive starboard down).

**Beam sea**- A condition in which a ship and waves, or the predominant wave components, advance at right angles, or nearly so.**Bow sea**- A condition in which a ship and the waves, or the predominant wave components, advance at oblique angles. This condition covers the direction between a head sea and beam sea.**Following sea**- A condition in which ship and the waves, or predominant wave components, advance in the same, or nearly the same direction.**Head sea**- A condition in which a ship and the waves, or the predominant components, advance in opposite, or nearly opposite directions.**Quartering sea**- A condition in which a ship and the waves, or the predominant wave components, advance at oblique angles. This condition covers the directions between a beam sea and a following sea.

In general, a term covering the study of the behaviour and performance of ship in a seaway. As an adjective, a term signifying a ship’s ability to maintain normal functions at sea.

The quality of behaving comfortably in a seaway; that property of ship which produces easy motions in a seaway.

(*F*_{L})[MLT^{-2}]

That part of the inertial lateral shearing force acting on a cross section of a hull that is caused by the action of waves and ship motions.

(*F*_{N})[MLT^{-2}]

That part of the inertial vertical shearing force acting on a cross section of a hull that is caused by the action of waves and ship motions.

The steady state lowering of a ship’s position of flotation in the water; to be distinguished from heaving, which is an oscillatory motion.

A phenomenon described broadly as severe impacting between a water surface and the side or bottom of a hull where the impact causes a shock-like blow. (See also: pounding and whipping).

A phenomenon described broadly as light impact between the water and the hull. A classification for impacts less severe than those associated with pounding. (See also: pounding).

The difference between actual pressure at a point under a wave profile and the static pressure corresponding to the actual distance below the surface.

(*S(ω)*)

A function of frequency whose integral over any interval represent the energy contribution of all the component waves of a random function in that interval; the Fourier transform of the auto-covarince function.

<m>S_varsigma(omega)d omega = sum{d omega}{}{1/2 varsigma {2}under{An}}</m>

<m>S_theta(omega)d omega = sum{d omega}{}{1/2 theta varsigma {2}under{An}}</m>

etc.
The subscript n denotes a particular component amplitude.

(*S(ω,μ)*)

A function of frequency and wave direction whose integral over any interval represents the energy contribution of all the component waves of a random function in that interval.

**Amplitude**- A function of frequency whose integral over any interval represents the squared amplitude of a wave at the central frequency having the same energy as all the component waves in that interval.**Co-spectrum**- The real part of a cross-spectrum (which see).**Cross-spectrum**- A complex function of frequency expressing the mutual properties of two random functions; the Fourier transform of the cross-covariance function, The real part, or co-spectrum, indicates the relationship between in-phase frequency components; the imaginary part, or quadrature spectrum, indicates the relation between 90° out-of-phase frequency components.**Quadrature spectrum**- The imaginary part of a cross-spectrum.

The decrease in speed, as compared with that in smooth water, caused directly by wind and waves at a constant setting of the main propulsion plant. Usually speed loss is determined at constant power (turbine plant) or constant torque (diesel plant).

The decrease in speed, as compared with that in smooth water, caused mainly by reducing the setting of the main propulsion plant in order to minimise the adverse effects ion the ship of wind and waves.

The continuous ship-hull vibration induced by the non-impulsive hydrodynamic forces acting on the ship hull. In particular, the vibratory response of the ship hull girder to short waves with frequencies of encounter close to the lower structural modes of vibration of the ship. See also: whipping.

The square root of the average of the squares of the deviations from the mean value; the square root of the variance.

See: wave steepness ratio.

()[L]

The relative vertical distance of a part (usually the bow) of an oscillating ship below the water surface; opposite to emergence.

The longitudinal oscillatory motion of a specified point in a ship, usually the centre of gravity (or origin of body axes).

(*T*_{AW})[MLT^{-2}]

The mean increase in thrust, as compared with that in smooth water, necessary to maintain speed in wind and waves.

(*Q*_{AW}) [ML^{2}T^{-2}]

The mean increase in torque as compared with that in smooth water, necessary to maintain speed in wind and waves.

See: Response function.

The steady-state longitudinal angular position of a ship; to be distinguished from pitching, which is an oscillatory motion.

(*θ*)[-]

The angle, measured about a horizontal axis, between the position of the longitudinal axis of a ship at rest and the horizontal plane.

The combined effect of the mass of the ship and added mass corresponding to the hydrodynamic forces in phase with and proportional to the acceleration. (See also: Added mass.)

A disturbance of the surface of a fluid that usually progresses across the surface as the result of circular or other local motions of the fluid components. A standing wave is special case of a wave that does not advance.

**Amplitude**(<m>varsigma_A</m>)[L] - The radius of orbital motion of a surface wave particle, equal to one half of the wave height .**Components**- The infinity of infinitesimal waves of different frequencies and directions which are found by spectral analysis to compose an irregular sea, or the large of finite wave used to approximate such an irregular sea.**Direction, angle of**(*μ*)[-] - The angle between the direction of a component wave and the <m>x_0</m> axis.**Encounter, angle of**(<m> mu </m>)[-] - The angle between the longitudinal axis of the ship and the direction of the wave encounter.**Encounter, period**(T_{E})[T] - The time between successive crests of a train of waves passing a fixed point in a ship, at a fixed angle of encounter <m>mu </m>; the reciprocal of the frequency of encounter fE (which see).**Frequency**(<m>f</m>)[T^{-1}] The reciprocal of wave period = 1*/T*, or circular frequency = 2<m>pi </m>*/T*.**Height**(*H*_{W})[L] - The vertical distance from wave crest to wave trough, or twice the wave amplitude of a harmonic wave.**Height, apparent**(*H*<sub<WV</sub>)[L ] - The vertical distance between a successive crest and trough, estimated by visual observation.**Height, significant**(*H*_{W1/3})- The average apparent height of the 1/3 highest waves in an irregular pattern.**Instantaneous elevation**(*η*)[L] - The instantaneous elevation of a point in a wave system above the level of the undisturbed surface.**Length**(*L*_{W},*λ*)[L] The horizontal distance between adjacent wave crests in the direction of advance.**Length, apparent**(*L*_{WV})[L] - The horizontal distance between adjacent wave crests of an irregular sea in the direction of advance.**Number**(<m>k</m>)[L^{-1}]

<m>K={2 pi}/lambda </m> or <m>{2 pi}/L_W</m>**Period**(*T*_{W})[T] - The time between the passage of two successive wave crests passed a fixed point.**Period, apparent**(*T*_{WV})[T] - The time elapsing between the occurrence of two successive crests of an irregular sea, or between two successive upward crossing of zero in a record, estimated by visual observation.**Profile**- The elevation of the surface particles of a wave plotted as a function of space in a fixed time.**Slope of surface**- The surface slope of a wave profile perpendicular to the crest in space co-ordinate. Maximum wave slope of a regular harmonic or trochoidal wave is π/2 x steepness ratio.**Speed celerity**(*c*_{W})[LT^{-1}] - The phase velocity of a surface gravity wave in deep water.

<m>C_W=sqr{gL_W/{2 pi}}</m>**Steepness ratio**- The ratio of wave height to length.**Train**- A continuous sequence of wave crests and hollows.**Trochoidal**- A profile closely approximating that of a regular surface gravity wave in a fluid; it can be geometrically constructed by tracing the path of a point on the radius of a circle as the circle rolls along the underside of a horizontal line.

(*T*_{E})[T]

The time between successive crests of a train of waves passing a fixed point in a ship, at a fixed angle of encounter *μ*; the reciprocal of the frequency of encounter <m>f_E</m>.

The quality of a part of the ship, usually the weatherdeck forward, with respect to its liability of being wet as a result of motions of ship and waves.

The transient ship-hull vibration which is induced by impulsive excitation forces. For example, fore-bottom slamming, bow-flare slamming, shipping of water and stern slamming. (See also: Springing).

(<m>X</m>)[-]

The angle, measured about the vertical body axis, between the instantaneous position of the longitudinal centreplane of a ship when yawing (which see) and its mean heading. (Positive bow to starboard).