1 GENERAL

SHIP GEOMETRY

RESISTANCE

PROPELLER

CAVITATION

SEAKEEPING

MANOEUVRABILITY

PERFORMANCE

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This Section is concerned essentially with performance in the context of power required to propel a ship at a given speed and various factors and matters related thereto. The propelling device is generally understood to be a screw propeller.

A quasi-dimensionless coefficient used for assessing or comparing the performance of ship.
Admiralty coefficient = <m>{Delta^{2/3} V^3}</m>/P,

where Δ is the displacement, *V* speed and *P* any corresponding power.

See: Speed of advance.

See: Resistance, wind.

See: Rudder angle and rudder angle ordered.

See: Slip ratio, apparent.

(*β*)[-]

A factor taking account of the effect of scale between model and ship on the resistance of appendages. It is defined by a factor β, where:

<m>R_APS/{1/2 {rho_S V{2}under{S} S_S}} = beta R_APM/{1/2 {rho_M V{2}under{M} S_M}}</m>

Where *R*_{AP} is the appendage resistance (See: Resistance, appendages), *ρ* the fluid density, *V* the speed and *S* the wetted surface.

See: Run, approach.

The area of the above-water hull, superstructure, deck erections, funnels, masts, and like, as projected onto either the vertical *x-z* or *y-z* plane of the ship. (See: General Section under Axes, co-ordinate).

See: Power, brake.

See: Admiralty coefficient.

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

This is the addition which has to be made to the resistance of the “smooth” ship, as predicted from the model results, to bring it into agreement with the actual ship performance determined from full scale trial or service result. The correlation allowance depends upon the method used to extrapolate the model results to the “smooth” ship, the ship length and type, the basic shell roughness of the newly-painted ship, fouling, weather conditions at the time the ship measurements were taken and scale effects on the factor making up the model and ship propulsive coefficients.

(K_{2})[-]

The scale effect between the rate of propeller rotation of model n_{M} and ship n_{S} is defined by the factor K_{2}, such that

<m>K_2 = eta_S/eta_M sqrt{lambda}</m>
where λ is the scale factor.

(K_{1})[-]

The scale effect between the propulsive efficiencies of the model and ship is defined by the factor K_{1}, such that

<m>K_2 = eta_DS/eta_DM </m>

where the efficiencies *η*DS and *η*DM for ship and model respectively are derived at corresponding speed and propeller loading.

The mean direction which a ship moving. This is defined by degrees of the compass or degrees of azimuth in a horizontal plane.

A straight measured course, which is used for speed trials of a ship. When such a course is one nautical mile in length it is often referred to as a measured mile.

( )[-]
The mean heading of a ship, defined by degrees of the compass or degrees of azimuth in a hori-zontal plane

(<m>psi_0</m>)[-]

The course at the beginning of a manoeuvring test, defined by degrees of the compass or degree of azimuth in a horizontal plane. (See Figure 7-1 and Figure 7-2).

A current in the water caused by the tide and influenced by the coastline and contours of the seabed.

See: Power, delivered.

See: Power, effective.

See: Wake fraction, effective.

(<m>eta_G</m>)[-]
The ratio of the power output to the power input of a set of reduction – or multiplying – gears between an engine and propulsion device:

<m>eta_G = P_S/P_B</m>

where *P*_{S} and *P*_{B} are the shaft and brake powers respectively (which see).

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

The ratio between the useful work done on the ship and the work done by the propeller or other propulsion devices in a given time that is effective power P_{E} and thrust power P_{T} respective.

<m>eta_H = P_E/P_T = {R_T v}/TV_A = {1-t}/{1-w}</m> in Taylor notation or

<m>eta_H = (1+ W_F)(1-t)</m>

in Froude notation. Where R_{T} is the total resistance, *V* the ship speed, *T* the propeller thrust and V_{A} the speed of advance; *t* is the thrust deduction fraction; *w* and *w*F are the wake fractions according to Taylor and Froude respectively (which see).

which links for “which see” (Taylor, Froude) ?

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

The ratio between the power output and the power input of any machinery installation.

<m>eta_M = P_S/P_1</m>

or

<m>eta_M = P_B/P_1</m>

where *P*_{S} and *P*_{B} are the shaft and brake powers respectively and *P*_{I} is the indicated power (which see)

on pdf it links to “indicted power” but only “indicated power exsist”

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

The ratio between the power *P*_{T}, developed by the thrust of the propeller and the power *P*_{D} absorbed by the propeller when operating behind a model or ship:

<m>eta_B = P_T/P_D = TV_A/{2pi Q_n} = eta_0 eta_R</m>

where *T* is the thrust, V_{A} speed of advance, *Q* shaft torque and *n* rate of propeller rotation; *η*0 and *η*R are the open water propeller and relative rotative efficiencies respectively.

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

The ratio between the power developed by the thrust of the propeller P_{T}, and the power absorbed by the propeller P_{D} when operating in open water with uniform inflow velocity V_{A}:

<m>eta_0 = P_T/P_D = TV_A/{2pi Q_0 n}</m>

where *T* is the thrust, *Q*0 the torque in open water and n the rate of propeller rotation.

<m>eta_D</m>[-]

The ratio between the useful or effective power PE and the power delivered to the propeller or the propulsion device P_{D}.

<m>eta_D = P_E/P_D=eta_0 eta_H eta_R</m>

where *η*O, *η*H and *η*R are the open water propeller, hull and relative rotative efficiencies respectively

<m>eta_P</m>[-]

The ratio between the useful or effective power P_{E}and the brake power P_{B}.

<m>eta_P = P_E/P_B=eta_0 eta_H eta_R eta_S eta_G</m>

where *η*0, *η*H *η*R *η*S and *η*G are the open water propeller, hull relative rotative shafting and gearing efficiencies respectively (which see).

<m>eta_R</m>[-]

The relative rotative efficiency is the ratio of the propeller efficiencies behind the hull and in open water, as already defined.

<m>eta_R = eta_B/eta_0</m>

<m>eta_S</m>[-]

The shafting efficiency is a measured of the power lost in shaft bearings and stern tube:

<m>eta_S = P_D/P_S</m>

where *P*_{D} and *P*_{S} are the delivered and shaft powers respectively (which see).

See: Form factor.

See: Power prediction factor.

(*F*_{D})[LMT^{-2}]

The towing force applied to a model to compensate for the increased specific frictional resistance of the model and to achieve the ship point of self-propulsion.

The difference between the viscous resistance of a model or a ship and the two dimensional friction resistance of a flat plate of the same length and wetted area and at the same speed in a given fluid. The difference arises because of the augmented speed of flow around the ship form as compared with along a flat plate and the pressure resistance of viscous origin. See also: Form factor.

(*k*)[-]

The ratio between the total viscous resistance coefficient of a model or a ship *C*_{V} and the two dimensional frictional resistance coefficient of a flat place *C*_{F0} at the same free stream Reynolds number. It may be expressed in two ways, either:

<m>k={C_V-C_F0}/C_F0</m>

or

<m>k={C_V-C_F}/C_F</m>

See: Power prediction factor.

See: Thrust deduction factor.

on document it links to “Thrust deduction faction” but this item does not exist, there' s only Thrust deduction factor, that's linked now

See: Wake fraction.

See: Water, standard fresh.

See: Wake, frictional.

See: Efficiency, gearing.

One of a series of models which differ in absolute size but are geometrically similar. It is a contraction of the expression “geometrically similar model” and was first used by Dr. E. V. Telfer.

See: Speed, ground.

(*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. See also Fig.24.

See: Efficiency, hull.

See: Surface, smooth.

See: Power, indicated.

(1+*x*)[-]

See: Power prediction factor.

(*x*)[-]

<m>X= eta_D P_D/P_E -1</m>

where P_{D} and P_{E} are the delivered and effective powers respectively and *η*D the quasi-propulsive efficiency (which see).
See also: Power prediction factor.

See: Course, measured.

See: Efficiency, mechanical.

See: Course measured.

See: Power prediction factor.

See: Wake, potential.

(P_{B})[L^{2}MT^{-3}]

The power measured at the engine coupling by means of mechanical, hydraulic or electrical brake.

(P_{E})[L^{2}MT^{-3}]

The power required to tow a ship, usually without its propulsive device, at constant speed *V* in unlimited undisturbed water:

*P*_{E} = *R*_{T}*V*

The power may be for ship either with or without appendages. If the latter, it is usually known as the naked or bare hull, effective power.

(P_{I})[L^{2}MT^{-3}]

The power developed in the cylinders of a reciprocating engine, either steam or diesel, as determined from the pressure measured by an indicator or similar device.

(1+*x*)[-]

A factor based on the correlation of ship and corresponding model data, which is introduced in estimating ship power to allow for the method of extrapolating model results to ship, scale effects on resistance and propulsion and the effects of hull roughness and weather conditions such that:

<m>P_D={P_E(1+x)}/eta_D</m>

where P_{D} and P_{E} are the delivered and effective powers respectively and *η*D the quasi-propulsive efficiency (which see). The results of model propulsion experiments are analysed for a propeller loading equivalent to the power prediction factor. The factor (1+x) is sometimes known as the *load factor* and the factor *x* as the load fraction (which see).

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

The power developed by the propeller thrust *T*, at the speed of advance *V*_{A}:

P_{T}=*TV*_{A}

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

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

See: Efficiency, propeller.

See: Efficiency, propulsive.

See: Efficiency, propulsive.

See: Slip ratio.

See: Wind, relative.

(R_{AP})[LMT^{-2}]

The increase in resistance relative to that of the naked, or bare hull resistance, caused by appendages such as bilge keels, rudders, bossings, struts, etc.

(*a*)[-]

The thrust *T* required to propel a model or ship at speed *V* is greater than the resistance R_{T} of the hull when towed at the same speed. The increase (*T-R*_{T}) is called the augment of resistance, and the resistance augment fraction is:

<m>a={T - T_T}/R_T</m>

<m>T=(1 + a)R_T</m>

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

The model-ship correlation allowance R_{A} (which see) expressed in coefficient form:

<m>C_A=R_A/{1/2 rho V^2 S}</m>

where *ρ* is the water density, *V* speed and *S* wetted surface.

(*C*_{AA})[-]

The ratio between the air or wind resistance on a ship or body R_{AA}, and the force corresponding to the dynamic pressure times a specified area. It is customy texsed it as :

<m>C_AA=R_AA/{1/2 rho V {2}under{R} S}</m>

Where *A* is the appropriate above water area of the ship, *V*_{R} the relative wind velocity (which see) and *ρ* the air density.

(R_{AR})[LMT^{-2}]

The increase in resistance relative to the resistance of a hydraulically smooth hull due to the effect of roughness. The hull roughness may be of different types such as:

- Structural roughness caused by method of shell construction, waviness of plating, scoops, valve openings etc.
- Paint roughness depending on the type of paint as well as how it is applied.
- Corrosion roughness due to breakdown of the paint film and corrosion of the shell plat-ing.
- Fouling roughness caused by marine organisms depositing shell, grass etc.

See: Resistance, wind.

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

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

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

The fore and aft component of the resistance of above water form of a ship due to its motion relative to still air or wind. When there is no natural wind, this is called the still air resistance. See also: Resistance coefficient, wind.

See: Water, restricted.

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

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

See: Surface, rough.

(*Δ*C_{F})[-]

Now obsolescent, See: Resistance coefficient, incremental for model-ship correlation (*C*_{A})

(*K*_{S})[L]

Equivalent sand roughness is used as a convenient measure of the roughness of a surface and is determined by equating the frictional resistance of a surface of random roughness with that of a flat plate completely covered with sand grains of a sensibly uniform size as in Nikuradse’s experiments. It is the average diameter of the Nikuradse sand grains.

(*k*)[L]

A length dimension expressing the height of a roughness element on a surface exposed to liquid flow. It is often expressed as some form of average such as root mean square or mean apparent amplitude.

See: Resistance, roughness.

(*δ*_{R})[-]

The angular displacement of a rudder about its stock relative to the neutral position and measured in a plane normal to the stock. See also: Manoeuvrability Section.

(*δ*_{RO})[-]

The ordered angle set on the steering control apparatus. This may differ from the rudder angle δ_{R}, depending on the lag and lost motion in the steering control and gear.

The path taken by a ship when accelerating during the approach to a measured course to attain a steady speed corresponding to give engine setting.

See: Water, standard salt.

The change in any force, moment or pressure coefficients, flow pattern, or the like, due to a change in absolute size between geometrically similar models, bodies or ships. These variations in performance due to differences in absolute size arise from the inability to satisfy simultaneously all the relevant laws of dynamical similarity (e.g. gravitational, viscous and surface tension).

See: Power, shaft.

See: Efficiency, shafting.

See: Water, shallow.

(S_{A})[-]

This is similar to the real slip ratio (which see) except that the ship speed V is used instead of the speed of advance *V*_{A}, that is:

<m>S_A={P_n-V}/P_n = 1 - V/P_n</m>

(S_{R})[-]

This is defined by the ratio:

<m>S_R={P_n-V_A}/P_n = 1 - V_A/P_n</m>

where *P* is the nominal, geometrical pitch, or the effective pitch of the propeller (i.e. advance per revolution at zero thrust), *V*_{A} is the speed of advance and n the rate of propeller rotation.

See: Surface, smooth.

(*V*_{A})[LT^{-1}]

Speed of advance of a propeller in open water. When a propeller behind a ship or model is producing the same thrust at the same rate of rotation as in open water the corresponding speed VA determined from the open water propeller characteristic is termed the speed of advance of the propeller. This is usually less than the ship speed V. (See also: Wake fraction, effective). This is based on thrust identity. There is another corresponding speed based on torque identity.

The speed of a ship *V*_{S} related to that of a model *V*_{M} , or vice-versa, according to Froude’s Law of comparison:

<m>V_S=V_M sqrt{lambda}</m>

where *λ* is the scale factor.

The speed of a ship relative to the ground, that is the speed including the effects of tide and currents. When the ship is moving through still water the ground speed is the same as the true water speed.

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 on the ship of wind and waves.

See: Resistance, wind.

A surface free from irregularities sensible to the touch or visible to the naked eye. A surface is called hydraulically smooth when there is no increase of resistance due to the surface irregularities.

A surface, which may be either smooth or rough, in which there are undulations of relatively large curvature.

(*t*)[-]

It is logical to view the effect of the propeller behind the hull as causing an increase in resistance- See: *Resistance augment fraction*. However, it is also common practice to look upon this increase in R_{T} as a deduction from the thrust *T* available at the propeller, i.e. to assume that of the total thrust *T* only R_{T} is available to overcome resistance. This “loss of thrust” (*T - R*_{,}), expressed as a fraction of the thrust *T*, is called the thrust deduction fraction, *t*, where

<m>t={T-R_T}/T</m>

or

<m>R_T=(1-t)T</m>

See: Power, thrust.

A trial carried out on a measured mile course to determinate the performance characteristics of a ship, namely ship speed, corresponding rate of rotation of propeller shaft, power, and also thrust where practicable.

See: wind direction or velocity, true.

The wake is a term used to describe the motion imparted to the water by the passage of the ship’s hull. It is considered to be positive if its direction is the same as that of the ship.

(*w, w*_{F})[-]

The difference between the ship speed *V* and the speed of advance *V*_{}A is called the wake speed(*V - V*_{A}). Froude expressed the wake speed at the position of the propeller as a fraction of the speed of advance, calling this ratio the wake fraction *w*_{F}, such that

<m>w_F={V-V_A}/V_A</m> and V_{A}=<m>V/{1+W_F}</m>

Taylor expressed the wake speed at the position of the propeller as a fraction of the ship speed, such that

<m>w={V-V_A}/V</m> and <m>V_A=V(1-w)</m>.

(*w*_{Q})[-]

A propeller will develop the same torque *Q* at the same revolutions per unit time, *n*, when working behind a hull advancing at speed *V* and in open water at a speed of advance *V*_{A}. The torque wake fraction will then be

<m>w_Q={V-V_A}/V</m>

This depends on identity of torque.

(*w*_{T})[-]

A propeller will develop the same thrust *T* at the same revolutions per unit time, *n*, when working behind a hull advancing at speed *V* and in open water at a speed of advance V_{A}. The thrust wake fraction will then be

<m>w_T={V-V_A}/V</m>

This depends on identity of thrust.

[-]

Wake fractions calculated from speed measured at the propeller position by Pitot tube, vane wheels, etc. in the absence of the propeller are called nominal wakes.

The component of the wake which results from the frictional action of the water when moving along the solid surface of a body or ship.

The component of the wake due to the potential flow around a body or ship, with velocity and pressure relationship in accordance with Bernoulli’s Theorem.

A term describing a body of water in which the boundaries are close enough to the ship to affect its resistance, speed, attitude, manoeuvring, and other performance characteristics, as compared with the corresponding characteristics in an open, unlimited, body of water. Principally, “restricted” applies to the proximity of the water boundaries in a horizontal direction.

A term describing a body of water in which the boundaries are closed enough to the ship in a vertical direction to affect its resistance, speed, attitude, manoeuvring, or other performance characteristics as compared with its corresponding characteristics in water of unlimited depth.

Water having zero salinity and a temperature of 15°C (59°F) with:

density *ρ* = 999.00 kg/m3 (1.9384 lb s^{2}/ft^{4}.)

Kinematic viscosity *ν* = 1.13902 * 10^{-6} m^{2}/s. (1.22603 10-5 ft^{2}/s)^{*}

Water having 3.5 per cent salinity and a temperature of 15°C (59°F) with:

density *ρ* = 1,02587 Kg/m3 (1.9905 lb s^{2}/ft^{4})

Kinematic viscosity *ν* = 1.18831*10^{-6} m^{2}/s. (1.27908*10^{-5}ft^{2}/s)^{*} See also relevant items in General Section under Liquid Properties and Physical Constants

See: Surface, wavy.

(*β*_{AW})[-]

The direction of the relative wind with respect to a ship’s heading. The resultant direction of the wind induced by the ship’s motion and the true wind, if any.

(*θ*_{W})[-]

The direction of any natural or atmospheric wind blowing over the ground or over the surface of the sea, measured from the true North.

See: Resistance wind.

(*V*_{WR})[LT^{-1}]

The velocity of the wind relative to the ship. It is the resultant of the wind induced by the ship’s motion and the true wind, if any.