1 GENERAL

SHIP GEOMETRY

RESISTANCE

PROPELLER

CAVITATION

SEAKEEPING

MANOEUVRABILITY

PERFORMANCE

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This section is concerned with propeller performance and various factor related thereto together with propeller geometry. Except where stated, the entries refer generally to screw propellers.

See: Rudder, active

(of propeller blade section) See: Angle, advance

(*J*)[-]

A parameter relating the speed of advance of propeller, V_{A} to the rate of rotation, *n*, given by

*J _{v}=V/nD*, where

(*δ*)

A parameter defined as:

<m>delta</m>=*nD/V _{A}=101.27/J*

where

(*λ*)[-]

A non dimensional speed parameter relating the speed of advance, *V*_{A} and the rotational tip speed, <m>pi</m>*nD*, given by:

<m>lambda</m>=*V*_{A}/<m>pi</m>*nD=J*/<m>pi</m>

where *J* is the advance coefficient, *D* is propeller diameter and *n* its rate of rotation.

See: Speed of advance.

See: Pitch, analysis

**(of a propeller blade section)** (*β*)[-]

The inflow angle to a propeller blade section determined by the rotative speed, *ωr*, the axial velocity of the fluid, *V*_{X}, and the tangential velocity of the fluid *V*_{θ}, according to the equation:

*β* = tan^{-1}{*V*_{X}(*r,θ*) / [*ωr*-*V*_{θ}(*r,θ*)]}

*r* is the radius of the blade section, *ω* the angular rate rotation and *θ* the angular position of the blade section.

A simpler definition, also in use is:

*β *= tan^{-1}(*V*_{A}*/ωr*)

where *r* is the radius corresponding to the section and *V*_{A} the advance speed.

The induced velocities are not included in the determination of the advance angle.

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

The angle measured in the plane containing the lift vector and the inflow velocity vector, between the velocity vector representing the relative motion between a body and a fluid and a characteristic line or plane of the body such as the chord line of an airfoil or hydrofoil positive in the positive sense of rotation about the y-axis. (See: Axes, co-ordinate in General Section)
. Synonymous with angle of incidence.

(<m>alpha</m>_{E})[-]

The angle of attack relative to the chord line including the induced velocities.

(<m>alpha</m>_{G})[-]

The angle of attack relative to the chord line of a section neglecting the induced velocities.

(<m>alpha</m>_{I})[-]

Angle of attack for thin airfoil or hydrofoil for which the streamlines are tangent to the mean line at the leading edge. This condition is usually referred to as a “shock free” entry or “smooth”.

(*β*^{∗})[-]

A propeller inflow angle defined by the equation:

*β*^{∗}=tan^{-1}(*V*_{A}/0.7*ωr*)

where *V*_{A} is the speed of advance and *n* is the rate of rotation, and *R* is the propeller diameter.

(*β*_{I})[-]

The inflow angle to a propeller blade section including the axial and tanential induced velocities given by the equation:
<m>beta_I=tan^-1 delim{[}{{V_X(r, theta) + U_A®}/{omega r-V_theta(r,theta)-U_T®}}{]}</m>

*U*_{A} and *U*_{T} are induced Axial and Tangential velocities respectively. For other items see Angle, advance.

[-]

The angle or angles made by a shaft axis with the centre-plane and/or the baseplane of a ship. If a craft significantly changes attitude at speed, the shaft angle may, if so indicated, be measured between the shaft axis and the direction of motion.

(*A*_{D})[L^{2}]

An approximation to the surface area of the propeller equal to the area enclosed by an outline of a blade times the number blades. The outline of a blade is constructed by laying off, at each radius *r*, the chord length along an arc whose radius of curvature, *r*_{1}, is equal to the radius of curvature of the pitch helix given by *r*_{1}=*r*/cos^{2}*φ* where <m>varphi</m> is the pitch angle at that radius. The outline is formed by the locus of the end points of the chord lines laid out in the above manner.

(*A*_{O})[L^{2}]

The area of the circle swept out by the tips of the blades of a propeller of diameter *D*:

A_{O} = <m> pi </m> D^{2}/4

(*A*_{E})[L^{2}]

An approximation to the surface area of the propeller equal to the area enclosed by an outline of a blade times the number of blades. The outline of a blade is constructed by laying off at each radius *r*, the chord length along a straight line. The outline is formed by the locus of the end points of the chord lines laid out in the above manner. (See figure below).

*Expanded aea of a propeller blade*

(*A*_{P})[L^{2}]

The area enclosed by the outline of the propeller blades outside the hub projected on to a plane normal to the shaft axis. The outline is constructed by laying off, along each radius *r*, the extremities of each section as determined in a view along the shaft axis. The locus of the end points of the chord lines laid out in the above manner is the required outline.

See: Induced velocity, axial.

The side of a propeller blade which faces generally in the direction of ahead motion. This side of the blade is also known as the suction side of the blade because the average pressure there is lower then the pressure on the face of the blade during normal ahead operation. This side of the blade corresponds to the upper surface of an airfoil or wing. \\

figura non presente nella versione 2011

\\
[-]

A term used to denote the ratio of either the developed or expanded area of the blades to the disc area. The terms expanded area ratio or developed area ratio are recommended in order to avoid ambiguity.

Most commonly taken to mean the shape of a propeller blade at any radius, when cut by a circular cylinder whose axis coincides with the shaft axis

unrolled generic propeller blade section

One of the possible positions of the blade of a controllable pitch propeller.
EXAMPLES:

**feathering position**

blade position at which the unrelated propeller produces the lowest resistance.

**zero thrust position**

blade position at which the rotating propeller with the ship speed at zero does not produce any thrust.

**trailing position**

defined blade position for the trailed propeller when the ship is going ahead.

[-]

If the maximum thickness of the propeller blade varies linearly with radius, then this variation of thickness may be imagined to extend to the axis of rotation. The hypothetical thickness at the axis of rotation, *t*_{0}, divided by the diameter, is known as the blade thickness fraction or blade thickness ratio. If the thickness does not vary linearly with radius, then the blade thickness fraction is not uniquely defined.

[MTL^{-2}]

The pull force exerted by a ship at zero ship speed. It is the sum of the propeller thrust and the interaction force on the hull.

See: hub

See: cone, propeller

**(of foil section)**

(*c*)[L]

The length of the chord line which is the straight line connecting the extremities of the mean line of
a hydrofoil section. It passes through, or nearly through, the fore and aft extremities of the section.
Synonymous with nose-tail line

(*C*_{LE})[L]

The part of the Chord delimited by the Leading Edge and the intersection between the Generator Line and the pitch helix at the considered radius.

*View of unrolled cylindrical section at radius r of a right-handed propeller (looking down) showing subdivisions of the Chord, Skewback and Rake.*

*Portion of an expanded blade of a right handed propeller, showing Chord subdivision.*

(*C*_{TE})[L]

The part of the Chord delimited by the Trailing Edge and the intersection between the Generator Line and the pitch helix at the considered radius.

*View of unrolled cylindrical section at radius r of a right-handed propeller (looking down) showing subdivisions of the Chord, Skewback and Rake.*

*Portion of an expanded blade of a right handed propeller, showing Chord subdivision.*

(*c*)[L]

The quotient obtained by dividing the expanded or developed area of a propeller blade by the span from the hub to the tip.

The straight line connecting the extremities of the mean line. The length of this line is called the chord length or simply the chord. It passes through, or nearly through, the fore and aft extremities of the section. Synonymous with nose-tail line.

*Propeller clearances*

The conical-shaped cover placed over the after end of the propeller shaft for the purpose of protecting the nut and forming a hydrodynamic fairing for the hub. Also known as a propeller fairwater or a propeller cap.

See: Propeller Types

See: Propeller Types

See: Area, developed

See: Propeller Types

See: Pitch, effective

(*η*_{M})[-]

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

<m>eta_M=P_S/P_I</m>

or

<m>eta_M=P_B/P_I</m>

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

(*η*_{B})[-]

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

<m>eta_B=P_T/P_D=TV_A/{2 pi Q_0 n}=eta_0eta_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.

(*η*_{O})[−]

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_O=P_T/P_D=TV_A/{2 pi Q_O n}</m>

*T* is the thrust, *Q*_{O} the torque in open water and *n* the rate of propeller rotation.

(*η*_{D})[-]

The ratio between the useful or effective power *P*_{E} and the power delivered to the propeller or the propulsion device *p*_{D}.

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

where *η*_{0}, *η*_{H}and *η*_{R} are the open water propeller, hull and relative rotative efficiencies respectively.

(*η*_{R})[-]

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_O</m>

[L]

The vertical distance from the top of the propeller tip circle to the at-rest water surface when the tips are exposed.

See: Area, expanded

The side of the propeller blade which face downstream during ahead motion. This side of the blade is also known as the pressure side because the average pressure on the face of the blade is higher than the average pressure on the back of the blade during normal operation. The face corresponds to the lower surface of an airfoil or wing.

See: Pitch, face

See: Propeller types

(*G*_{Z})[L]

The distance between the chord lines of two adjacent propeller blade sections measured normal to the chord. This distance is given by the formula:

*G*_{Z}=(2<m>pi</m>*r* sin<m>varphi</m>)*/Z*

where *r* is the radius in question, <m>varphi</m> is the pitch angle of the chord line at the radius *r* (geometric pitch) and *Z* is the number of blades.

The line formed by the intersection of the pitch helices and the plane containing the shaft axis and the propeller reference line. The distance from the propeller plane to the generator line in the direction of the shaft axis is called the rake. The generator line, the blade reference line, and the propeller reference line each intersect the shaft axis at the same point when extended thereto. Because of ambiguities which can arise in so extending the generator line and blade reference line when non linear distribution of rake and skew angle are used, it is recom-mended that these lines be defined each to originate at the reference point of the root section. The rake and skew angle of the root section will thus be defined to be zero and the propeller plane will pass through the reference point of the root section.

See: pitch, geometric

The central portion of a screw propeller to which the blades are attached and through which the driving shaft is fitted. Also known as the boss.

(*d*_{h})[L]

The diameter of the hub where it intersect the propeller reference line

**Hub diameter, fore**

(d[L] – Fore diameter of the hub, not considering any shoulder._{hf})**Hub diameter, aft**

(d[L] – Aft diameter of the hub, not considering any shoulder._{ha})

(lh) [L]

The length of the hub, including any fore and aft shoulder

**Hub length, aft**(*l*_{ha}) [L] – – Length of the hub taken from the propeller plane to the aft end of the hub including aft shoulder.**Hub diameter, fore**(*l*_{hf}) [L] Length of the hub taken from the propeller plane to the fore end of the hub including fore shoulder.

See: pitch, hydrodynamic

Synonymous with hydrodynamic flow angle. See: angle, hydrodynamic flow

A structure externally similar to an airplane wing designed to produce lift and which operates in water.

(*h*_{0})[-]

The depth of submergence of the propeller measured vertically from the shaft axis to the free surface.

A propeller which is not located on the centreline of the ship is said to have inboard rotation if the blade moves toward the centreline as they pass the upper vertical position. The opposite direction of rotation is called outboard rotation. Also called inward and outward rotation respectively.

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

The change in the velocity component in the direction parallel to the propeller axis due to the presence of the propeller but not including any change in the wake field due to propeller/hull interactions. Positive upstream. (See FIGURE 3)

FIGURE 3 ???

.
(*U*_{R})[LT^{-1}]

The change in the velocity component in the radial direction due to the presence of the propeller but not including any change in the wake field due to propeller/hull interactions. Positive outward.

(*U*_{T})[LT^{-1}]

The change in the velocity component in the tangential direction due to the presence of the propeller but not including any change in the wake field due to propeller/hull interactions. Positive clockwise looking forward. (See FIGURE 3)

Figure 3 ???

See: inboard rotation

Blade edge directed to the inflow under normal operating conditions starting from the blade root and ending at the blade tip.

*Leading and Trailing edges of a propeller blade*

(*L*)[MTL^{-2}]

The fluid force acting on a body in a direction perpendicular to the motion of the body relative to the fluid.

See: chord length, mean

The mean line is the locus of the midpoint between the upper and lower surface of an airfoil or hydrofoil section. The thickness is generally measured in the direction normal to the chord rather to the mean line. The maximum distance between the mean line and the chord line, measured normal to the chord line, is called the camber. The term camber line is often used synonymously with mean line.

See: pitch, mean

[-]

Mean expanded or developed chord of one blade divided by the propeller diameter. Equal to the inverse of one half the aspect ratio for a wing.

See pitch, nominal

A type of an airfoil or hydrofoil section having a straight face, a circular arc or parabolic back, maximum thickness at the mid chord, and relatively sharp leading and trailing edges.

A propeller which is not located on the centreline of the ship is said to have outboard rotation if the blades move away from the centreline as they pass the upper vertical position. The opposite direction of rotation is called inboard rotation. Also called outward and inward rotation respectively.

See: outboard rotation

(*P*)[L]

The pitch of a propeller blade section at the radius r is given by: *P = *2<m>pi</m>*r* tan<m>varphi</m> where <m>varphi</m> is the angle between the intersection of the chord line of the section and a plane normal to the propeller axis. This angle is called the pitch angle. Also called geometric pitch (which see).

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

The angle, measured about the transverse body axis, between the instantaneous position of the lon-
gitudinal axis of a ship when pitching (which see) and its position of rest. (Positive bow up). See: pitch.

Weighted value of geometric pitch when pitch is not constant. Both the radius and the thrust distribution (if known) have been used as weighting factors.

The pitch of a line parallel to the face of the blade section. Used only for flat faced sections where offsets are defined from a face reference line.

The pitch of the nose-tail line (chord line). It is equal to the face pitch if the setback of the leading and trailing edges of the section are equal.

The pitch of the streamlines passing the propeller including the velocities induced by the propeller at a radial line passing through the midchord of the root section. See: angle, hydrodynamic flow

- Generally synonymous with the effective pitch.
- The pitch of a constant pitch propeller which would produce the same thrust as a propeller with radially varying pitch when placed in the same flow.

Synonymous with face pitch. (See: pitch, face).

(*p*)[-]

The ratio of the pitch to the diameter of the propeller. Generally, the face pitch or geometric pitch at the 70 percent radius is used to compute the pitch ratio. Any measure of pitch can be used with the diameter to form a pitch ratio.

A propeller blade for which the pith is not the same at all radii is said to have variable pitch or varied pitch. A propeller which has the same pitch at all radii is said to be a constant pitch propeller.

See: propeller plane

(*K*_{P})[-]

The delivered power at the propeller, *P*_{D}, expressed in coeffie
icnt form:

*K*_{P}=*P*_{D}/<m>rho</m>*n*^{3}*D*^{5}

where *ρ* is the mass density of the fluid, *n* is the rate of the propeller rotation, and *D* is the diameter of the propeller.

(*B*_{P})

The horsepower absorbed by the propeller, *P*_{D}, expressed in coefficient form:

*B*_{P}=*n(P _{D})^{1/2}/(V_{A})^{5/2}*

where

(*B*_{U})

The thrust horsepower delivered by the propeller, *P*_{T}, expressed in coefficient form:

*B*_{U}=*n(P _{U})^{1/2}/(V_{A})^{5/2}*

where

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

The power absorbed by the propeller, *P*_{D}, expresse in coefficient form:

<m>C_P=P_D/{rho/2 V {3}under{A}(D^2 / 4)}</m>=(*K*_{Q}*/J*^{3})(8/<m>pi</m>)

where *ρ* is the fluid density, *V*_{A} is the speed of advance, and *D* is the propeller diameter. This coefficient may be defined in terms of the ship speed *V* and is then denoted by the symbol *C*_{PS}. *K*_{Q} and *J* are the torque and advance coefficient respectively.

The side of the propeller blade having the greater mean pressure during normal ahead operation. Synonymous with the face of the blade. Analogous to the lower surface of a wing.

See: area, projected

Most generally, any device which will produce thrust to propel vehicle. The most common form is the screw propeller, which basically consists of a central hub and a number of fixed blades extending out radially from the hub. Lift is generated by the blades when the propeller is rotated. One component of the lift force produces the desired thrust and the other compo-nent creates torque which must be overcome by the engine to sustain rotation.

*Screw propeller*

The plane normal to the shaft axis and containing the propeller reference line, i.e. contain the reference point of the root section. Also called the plane of rotation

* Diagram showing recommended reference lines (looking to port)*

(*R*)[L]

The largest distance from the shaft axis (x axis) of the extreme point of a blade (i.e. blade tip). Half the diameter of the propeller disk.

<m>R=D/2</m>

*Propeller radius*

<m>theta</m> angular coordinate, originating from z axis of the rectangular reference system, directed in the same direction as the direction of rotation of the propeller; r radial coordinate; x axis coincides with that of the rectangular reference system.

*Transverse metacentric parameters*

*Propeller reference system, cylindrical, looking forward*

x axis along the shaft centre line, directed forward; y axis normal to x and directed to port; z axis normal to x and y in order to form a right handed Cartesian system, directed upward. The z axis is positioned to pass through the reference point of the root section of a blade. This reference system is unchanged for right handed and left handed propellers.

*Figure 39: Propeller reference system, rectangular*

**The basic screw propeller**may be described as fixed pitch, subcavitating, open (unducted), and fully submerged. Variations on this basic type are listed below.**Adjustable-pitch propeller**- A propeller whose blades can be adjusted to different pitch settings when the propeller is stopped.**Contrarotating propeller**- Two propeller rotating in opposite directions on coaxial shafts.**Controllable pitch propeller**- A propeller having blades which can be rotated about a radial axis so as to change the effective pitch of the blade while the propeller is operating. This allows full power to be absorbed for all loading conditions. If the pitch can be ad-justed to the extent that reverse thrust can be achieved without reversing the direction of rotation of the shaft then the propeller is sometimes called a controllable reversible pitch propeller.**Cycloidal propeller**- A propeller consisting of a flat disc set flush with the under surface of the vessel with a number of vertical, rudder-like blades projecting from it. The disc revolves about a central axis and each of the blades rotates about its own vertical axis. The axis of each blade traces a cycloidal path. The blade motion can be varied so as to produce a net thrust in any desired direction in a plane normal to the axis of ro-tation. It is used where excellent manoeuvrability is required.**Ducted propeller**- A propeller with a short duct mounted concentrically with the shaft. The duct, or nozzle is shaped so as to con-trol the expansion or contraction of the slipstream in the immediate vicinity of the propeller. In one form (the Kort nozzle) the flow is accelerated, whereas in the other form (pump jet) the flow is decelerated. A pump jet is sometimes also defined as a ducted propeller with stator vanes regardless of whether the flow is accelerated or decelerated.**Fully cavitating propeller**- A propeller designed to operate efficiently at very low cavitation numbers where a fully developed cavity extends at least to the trailing edge of the blade. The blade sections of such propellers have relatively sharp, leading edges for more efficient supercavitating operation and thick trailing edges for strength. Also known as supercavitating propeller.**Interface propeller**- A propeller of the fully cavitating ventilated type designed to operated with only a portion of the full disc area immersed. These propellers are considered for high speed applications to vehicles such as surface effect ship where the appendage drag associated with the shafts and struts of a fully submerged propeller would result in a considerable increase in resistance. Also known as partially submerged or surface propellers.**Ring propeller**- A propeller with a very short duct attached to the tips of the blades and rotating with the propeller. Also called a banded propeller.**Steerable ducted propeller**- A ducted propeller in which the duct can be pivoted about a vertical axis so as to obtain a steering effect.**Supercavitating propeller**- See: Fully cavitating propeller.**Tandem propeller**- Two propellers fitted to the same shaft, one behind the other, and rotating as one.**Ventilated propeller**- A propeller of the fully cavitating type, but with provision to introduce air into the cavities in order to achieve fully developed, stable cavities at lower speed than would otherwise be impossible.**Vertical axis propeller**- Synonymous with cycloidal propeller.

(*i*_{G}, R_{k}(ISO))[L]

The displacement, iG, from the propeller plane to the generator line in the direction of the shaft axis. Aft displacement is considered positive rake. The rake at the blade tip or the rake angle are generally used as measures of the rake.

*View of unrolled cylindrical sections at blade root and at any radius r of a right-
handed propeller (looking down) showing recommended position of propeller plane.*

The rake angle is defined as:

<m>theta</m> = tan^{-1}[*i*_{G}(*r*)*/r*]

where *r* is the radius

*Diagram showing recommended reference lines (looking to port)*

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

The amount of axial displacement (rake) of a blade section which results when skew-back is used

It is the distance, measured in the direction of the shaft axis, between the generator line and the blade reference line and is given by: *r*<m> theta_S </m>*tan*<m>varphi</m>, where *r* is the local radius, *θ*_{S} is the local skew angle, and <m>varphi</m> is the local pitch angle. It is positive when the generator line is forward of the blade reference line.

The locus of the reference points of the blade sections

Sometimes used synonymously with generator line.

The straight line, normal to the shaft axis, which passes through the reference point of the root section. It lies in the plane containing the shaft axis and the generator line.

The point on the pitch helix to which the blade section offsets are referred. It usually the midpoint of the chord line. The point of maximum thickness and the location of the spindle axis for controllable pitch propeller, as well as other points, have also been used as blade section reference points.

See: propeller

(-)[L]

The displacement of the leading edge or trailing edge of a propeller blade section from the face pitch datum line when the section shape is referenced to that line. Also called wash-up. It is called wash-down if negative. The set back ratio is the set back divided by the chord length.

The duct portion of a ducted propeller concentric with the axis of rotation of the propeller blades. In some cases the duct may be rotated about a vertical axis to provide steering forces. Synonymous: duct, nozzle.

Intense discrete frequency sound radiated from the propeller due to resonant vibrations of the blades. Generally thought to be due to the shedding of Karman vortices from the trailing edge of the blades at a resonant frequency of the blade vibration.

(*θ*_{S})[-]

The angular displacement about the shaft axis of the reference point of any blade section relative to the generator line measured in the plane of rotation. It is positive when opposite to the direction of ahead rotation. This angle is the same as the warp. The skew angle at the blade tip is often used as a measure of the skew-back of a propeller.

(-)[L]

The displacement of any blade section along the pitch helix measured from the generator line to the reference point of the section

Positive skew-back is opposite to the direction of ahead motion of the blade section. Also called skew.

See: rake, skew induced

See: race

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

The translational speed of the propeller in relation to the body of water into which it is advancing. See also: Performance Section.

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

The torque acting about the spindle axis of a controllable-pitch propeller blade resulting from the hydrodynamic and centrifugal forces exerted on the blade. This torque is positive if tends to rotate the blade toward a higher positive pitch.

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

The torque acting about the spindle axis of a controllable-pitch propeller blade resulting from the hydrodynamic forces exerted on the blade. This torque is positive if it tends to rotate the blade toward a higher positive pitch.

(*K*_{SC})[-]

The centrifugal spindle torque, Q_{SC}, expressed in coefficient form:

*K*_{SC}=*Q*_{SC}/(<m>rho_P n^2 D^5</m>

where *ρ*_{P} is the mass density of the propeller blade material, *n* is the rate of propeller rotation, and *D* is the propeller diameter.

(*K*_{SH})[-]

The hydrodynamic spindle torque, Q_{SH}, expressed in coefient form:

*K*_{SH}=*Q*_{SH}/(<m>rho n^2 D^5</m>)

where *ρ* is the mass density of the fluid, *n* is the rate of propeller rotation, and *D* is the propeller diameter.

()[-]

The hydrodynamic spindle torque, *Q*_{SH}, expressed in coefficin form:

*Q*_{SH}/<m>lbrace 1/2 rho{[}V {2}under{A} + (0.7nD)^2{]} rbrace</m><m>( {pi D^3}/4)</m>

where *ρ* is the density of the fluid, *V*_{A} is the speed of advance, *n* is the rate of propeller rotation, and *D* is the diameter. This form of the spindle torque coefficient is useful when presenting propeller spindle torque characteristics over a range of advance coefficient extending from zero (*V*_{A} = 0) to infiity (*n* = 0). Usually presented as a function of

<m>beta</m>* = tan^{-1}[*V*_{A}/(0.7 *n*<m>pi</m>*D*)]

See: propeller types

The low pressure side of a propeller blade. Synonymous with the back of the propeller blade. Analogous to the upper surface of a wing.

See: propeller types

(*B*_{U}, *B*_{P})

See: power coefficient, Taylor’s

(*t*)[L]

The maximum thickness of a propeller blade section, generally measured in the direction normal to the chord line

(*t _{X}*)[L]
The thickness of a propeller blade section at any location along the X axis of the section reference system, generally measured in the direction normal to the chord line.

(*δ*)[-]

The ratio of the maximum thickness, *t*, of a foil section to the chord length, *c*, of that section.

The phenomenon of loss of thrust due to exces-sive cavitation on a subcavitating type propeller. The torque absorbed by the propeller is affected similarly and is called torque breakdown. Both the thrust and torque coefficient may increase slightly above noncavitating values near the initial inception of cavitation. In general, the changes in thrust and torque are such that propeller efficiency is reduced.

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

The thrust, *T*, produced by propeller expressed in coefficient form:

*K*_{T}=*T*/(<m>rho n^2 D^4</m>)

where *ρ* is the mass density of the fluid, *n* is the rate of propeller rotation, and *D* is the propeller diameter.

()[-]

A figure of merit for comparing the relative performance of propulsion devices at zero speed given by the equation:

<m>T/{({rho pi}/2)^⅓(P_D D)^⅔}=K_T/ {pi(K_Q)⅔ 2^⅓}</m>

The ideal upper limit for unducted screw pro-pellers is 1.0, while for ducted propellers the upper limit depends upon the area ratio of the down stream diffuser. When the area ratio is unity, i.e. no diffusion or contraction, the limit is 21/3 = 1.26; ρ is the fluid density, D propeller diameter, PD delivered power; KT and KQ are the thrust and torque coefficients respectively.

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

The thrust, *T*, produced by the propeller expresse inefficient form:

*C*_{T}* = <m> T/{1/2 rho [V {2}under{A}] + (0.7nD)^2]( pi D^2/4)} </m>

where ρ is the density of fluid, VA is the speed of advance, n is the rate of rotation and D is the propeller diameter. This form of the thrust coefficient is useful when presenting propeller thrust characteristics over a range of advance coefficients from zero (V_{A} = 0) to infinity (*n* = 0). Usually presented as a function of

<m>beta</m>* = tan^{-1}[*V*_{A}/(0.7 <m>pi</m>*nD*)]

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

The thrust, *T*, produced by the propeller expressed in coefficient form:

<m>C_Th = T/{rho/2 V {2}under{A} {pi D^2}/4}=K_T/J^2 8/ pi</m>

where *ρ* is the mass density of the fluid, *V*_{A} is the speed of advance, *D* is the propeller diameter, ( the symbol *C*_{TS} is used when this coefficient is based on ship speed instead of speed of advance).
Where *K*_{T} and *J* are the thrust and advance coefficient respectively.

See: thrust breakdown

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

The torque, *Q*, deliveredo the propeller expressed in coefficient form:

<m>k_Q=Q/{rho n^2 d^5}</m>

where *ρ* is the density of the fluid, *n* is the rate of propeller rotation, and *D* is the propeller diameter.

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

The torque, *Q*, absorbed by the propeller expressed in coefficient form:

*C*_{Q*} = <m> Q/{1/2 rho [V {2}under{A} + (0.7nD)^2]( pi D^3/4)} </m>

where *ρ* is the density of fluid, *V*_{A} is the speed of advance,*n* is the rate of rotation and *D* is the diameter. This form of the torque coefficient is useful when presenting propeller torque characteristics over a range of advance coefficients from zero (*V*_{a} = 0) to inity (*n* = 0). Usually
presented as a function of

<m>beta</m>* = tan^{-1}[*V*_{A}/(0.7 <m>pi</m>*nD*)]

See: rake, total

Blade edge opposite to the inflow under normal operating conditions starting from the blade root and ending at the blade tip

*Leading and Trailing edges of a propeller blade*

See: pitch, variable

See: Induced velocity (axial, tangential, and radial).

See: propeller types

Synonymous with cycloidal propeller. See: propeller types

See: setback

See: set-back

See: set-back

A form of propulsion in which water is taken into hull of the ship by means of ducting and energy is imparted to the water with a pump. The water is then ejected astern through a nozzle.

The rotation of a propeller caused by flow past the propeller without power being applied to the propeller shaft. This action may take place while the ship is moving under its own momentum, while it is being towed, or while it is being propelled by other means of propulsion.