NA 2 Notes 1 - Propeller Geometry

Screw Propeller Geometry Description Screw propeller in its basic form consists of a number of blades fixed to a hub or a boss. Angle of these blades is fixed. When the propeller is rotated about its axis the tips of the blade trace out a circle. Diameter of this circle is called the diameter of the propeller. The boss is mounted on to a shaft through which the power of the ship's propulsion system is transmitted to the propeller. Torque is applied to the propeller which makes it turn or rotate about its axis with a certain rate of revolutions. The propeller by virtue of its geometry absorbs the torque and produces a thrust causing it to move ahead with respect to the surrounding water. Aim of Propeller design: to achieve -High propulsive efficiency -low levels of vibration and noise -minimum cavitation As ships have become larger and faster and propeller diameters are restricted by draft and other factors, unconventional propulsion devices are proposed for the ships in which performance of the conventional propellers is not fully satisfactory. Screw Propellers - Terminology A screw propeller consists of a number of blades attached to a hub or boss, as shown in the Figure below. The boss is fitted to the propeller shaft through which the power of the propulsion machinery of the ship is transmitted to the propeller. When this power is delivered to the propeller, a turning moment or torque Q is applied making the propeller revolve about its axis with a speed (“revolution rate”) n, thereby producing an axial force or thrust T causing the propeller to move forward with respect to the surrounding medium (water) at a speed of advance VA. Blade tip. The point on the propeller blade farthest from the axis of revolution is called the tip Blade Root. The blade is attached to the propeller boss at the root. Face: The surface of a propeller blade which faces downstream during ahead motion is called face or pressure side (when viewed from aft of a ship to the bow the visible surface of a propeller blade is called face or pressure side). Back: The surface of a propeller blade which faces generally direction of ahead motion is called back or suction side (when viewed from aft of a ship to the bow the unseen surface of a propeller blade is called back or suction side). Leading Edge: When the propeller rotating the edge piercing water is called leading edge. Trailing Edge: When the propeller rotating the edge trailing the leading edge is called trailing edge. Naval Architecture Lecture Notes

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Propeller Diameter. When a propeller revolves about its axis, its blade tips trace out a circle. The diameter of this circle is the propeller diameter D. Handing of Propeller. A propeller that revolves in the clockwise direction (when viewed from aft) when propelling the ship forward is called a right hand propeller. If the propeller turns anticlockwise when driving the ship ahead, the propeller is left handed. In a twin screw ship, if the starboard propeller is right handed and the port is left handed then, these are called outward turning propellers. This is the usual handing of the propellers in a twin-screw ship for reasons of cavitation and noise. The number of propeller blades is denoted by Z. The face of the propeller blade either forms a part of a helical or screw surface, or is defined with respect to it; hence the name "screw propeller". Therefore, a screw propeller may be regarded as part of a helical surface which, when rotating, ‘screws’ its way through the water. Helix and Helical Surface Consider a line AB perpendicular to the line AA’. AB is rotating at uniform angular velocity about AA’ and moving along AA’ at uniform velocity (See Figure). Each point on the line traces out a helix and the line AB sweeps out a helical surface. The distance the line advances in making one complete revolution is termed the pitch. Relationship of Propeller Blade and Helical Surface - Pitch

A conceptual propeller blade is drawn in the figure to show its relationship to a helical surface. If a propeller blade were made of constant thickness throughout, both the face and back of the blade could, in their simplest form, be true helical surfaces. Suppose that the face of the propeller blade shown in Figure is a true helical surface and that a cylinder of radius r concentric with the axis intersects the blade, producing the blade section shown shaded in the figure. The blade is then imagined to rotate one complete revolution, while advancing a distance equal to the pitch P as if it were a machine bolt thread being screwed into a tapped hole. If the intersecting cylinder of radius r is unrolled onto a flat surface, the path taken by a point on the face of the blade may be described by referring to the resulting diagram on the last page. The circumferential motion 2πr is laid out as the horizontal leg of the right triangle and the linear advance P is the vertical leg. The hypotenuse is the helix, which is the actual distance travelled Naval Architecture Lecture Notes BSW Page 25/158

by the point. Since it is a characteristic of the geometry of this blade section, the angle ϕ is called the pitch angle of the blade section such that. 𝑃𝑛 𝑃 𝑇𝑎𝑛𝜙 = = 2𝜋𝑛𝑅 2𝜋𝑅

Any cylinder coaxial with the propeller axis OO’ will cut the helical surface in a helix, and the angle between any such helix and a surface normal to the axis, such as SS, is called the pitch angle The angle will be constant for a given helix, i.e., at a given radius, but will increase in value from the tip of the blade inwards to the hub. Propellers can have any number of blades but three, four and five are most common in marine propellers. Face Pitch Ratio of Propeller Blade For simple propellers, the pitch is the same at all points on the face of the blade. This is called as the face pitch of the propeller and the ratio of this to the propeller diameter is the face pitch ratio Naval Architecture Lecture Notes

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𝑃 𝐷 In practice the pitch is not always the same at all radii, it being fairly common to have a reduced pitch towards the hub and, only in a very few cases, towards the tip. In such cases the pitch at 0.7 R is often taken as a representative pitch, as this is approximately the point where the maximum lift is generated. It is called as nominal pitch 𝑓𝑎𝑐𝑒 𝑝𝑖𝑡𝑐ℎ 𝑟𝑎𝑡𝑖𝑜 =

Propeller Blade section shapes As we have seen, section is a cut through the blade at a given radius, that is, it is the intersection between the blade and a concentric a cylinder of radius ‘r’. The section is actually along an arc of the circle but can be expanded (as described in expanded blade area) and laid out flat. The expanded blade sections used in propeller blades may generally be divided into two types: segmental sections and aerofoil sections. (a) Segmental sections: These were used in the olden days and are characterised by a flat face and a circular or parabolic back, the maximum thickness being at the midpoint between the leading and trailing edges, the edges being quite sharp (see Figure). (b) Aerofoil sections: Modern propellers use aerofoil sections. The face in the aerofoil section may or may not be flat. The maximum thickness is usually nearer the SEGMENTAL SECTION leading edge, which is often more rounded than the trailing edge.

(c) Lenticular Sections: More rarely, propellers may have lens-shaped or lenticular blade sections, (see Figure) such sections are used in propellers that are required to work equally efficiently for both directions of revolution. Propeller Reference Lines Propeller reference line. The line normal to the shaft axis is called either propeller reference line or directrix. In the case of controllable pitch propeller, the spindle axis is used as the reference line. Blade Reference Line. The line joining the mid points of chords drawn at successive radiuses. This line joins the mid point of root chord to the tip passing through mid points of chords at intermediate radiuses.

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Generator line: The line formed by intersection of the pitch helices and the plane containing the shaft axis and propeller reference line. The aero foil sections which together comprise the blade of a propeller are defined on the surfaces of cylinders whose axes are concentric with the shaft axis.

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Propeller Geometry: Cylindrical Coordinate system The shape of the blades of a propeller is usually defined by specifying the shapes of sections obtained by the intersection of a blade by coaxial right circular cylinders of different radii. These sections are called radial sections or cylindrical sections. Since all the Z propeller blades are identical, only one blade needs to be defined. It is convenient to use cylindrical polar coordinates (r, θ, z) to define any point on the propeller, r being the radius measured from the propeller axis, θ an angle measured from a reference plane passing through the axis, and z the distance from another reference plane normal to the axis. The z = 0 reference plane is usually taken to pass through the intersection of the propeller axis and the generating line of the helicoidal surface in the θ = 0 plane. Consider the section of a propeller blade by a coaxial circular cylinder of radius r, as shown in Fig.(a). The blade is pointing vertically up. The figure also shows the helix over one revolution defining the blade face at radius r, and the reference planes θ = 0 and z = O. The projections; of this figure on a plane perpendicular to the propeller axis and on a horizontal plane are shown in Fig. (b) and (c). If the surface of the cylinder is now cut along the line AAl, joining the two ends of the helix, and the surface unwrapped into a plane, a rectangle of length 2πr and breadth P (the pitch of the helix) is obtained, the helix being transformed into the diagonal as shown in Fig. 2.3(d). The radial section takes the shape shown in the figure, and this shape is the expanded section at the radius r. The angle ϕ = tan-1(P/2πr) is the pitch angle, and L and T are the leading and trailing edges at the radius r. Skew Consider the line obtained by joining the midpoints between the leading and trailing edges of a blade at different radii from the axis. If this line is straight and passes through the axis of the propeller, the propeller blades have no skew. Usually however, the line joining the midpoints curves towards the trailing edge, resulting in a propeller whose blades are skewed back. Skew is used to reduce vibration. Some modern propeller designs have heavily skewed blades. The angle θs between a straight line joining the centre of the propeller through midpoint of the root and a line joining the centre and the midpoint at the blade tip is a measure of skew. Skew at a radius is defined as the angle between the mid-chord position of the section at that radius and the directrix (θs(x)). The propeller skew angle (θsp) is defined as the greatest angle measured at the shaft centre line which can be drawn between lines passing from the shaft centreline through the mid chord position of any two sections. Generally these sections are the tip and root sections

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The skew can be classified into two types: (a) Balanced skew: Directrix intersects with the mid-chord line at least twice. (b) Biased skew: Mid-chord locus crosses the directrix not more than once normally in the inner sections. Rake The rake at the given radius is defined as the displacement from the propeller plane to the generator line in the direction of the shaft axis. If the line generating the propeller blade is perpendicular to the axis about which it rotates when advancing along it, then the helical surface and the propeller blade defined by it are said to have no rake. If, however, the generating line is inclined by an angle ϵ to the normal, then the propeller has a rake angle ϵ. Apart from the rake due to generator line, the propeller may have additional rake due to a skewed blade which is called as the skew induced rake. 𝑃𝑟𝑜𝑝𝑒𝑙𝑙𝑒𝑟 𝑟𝑎𝑘𝑒 = 𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑡ℎ𝑒 𝑟𝑎𝑘𝑒 𝑎𝑡 𝑡𝑖𝑝 𝑎𝑛𝑑 𝑟𝑎𝑘𝑒 𝑎𝑡 𝑟𝑜𝑜𝑡 𝑃𝑟𝑜𝑝𝑒𝑙𝑙𝑒𝑟 𝑟𝑎𝑘𝑒 𝑎𝑛𝑔𝑙𝑒 𝑇𝑎𝑛 𝜖 =

𝑃𝑟𝑜𝑝𝑒𝑙𝑙𝑒𝑟 𝑟𝑎𝑘𝑒 𝑅𝑎𝑑𝑖𝑢𝑠 𝑎𝑡 𝑡𝑖𝑝 − 𝑅𝑎𝑑𝑖𝑢𝑠 𝑎𝑡 𝑅𝑜𝑜𝑡

Propeller blades, are sometimes raked aft at angles up to 15 degrees to increase the clearance (space) between the propeller blades and the hull of the ship. Propeller Blade Areas Some geometrical ratios useful in defining propeller geometry and comparison of propellers are given below. We will not cover the geometrical construction to determine the parameters used only understand the definitions. Before we describe the ratios we must know some definitions of propeller areas.

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(a) Disc area: The area of the circle swept out by the tips of the blades of a propeller of diameter D. This equal to 𝐴𝑜 = 𝜋𝐷 2 /4 . 𝐴𝑜 includes the hub area also. (b) Projected area (AP): The area enclosed by the outline of the propeller blades outside the hub projected onto 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. A P does not include the hub area.

(c) Developed Area (AD): An approximation to the surface area of the Propeller blade 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 an arc whose radius of curvature, r1, is equal to the radius of curvature of the pitch helix given by r1= r/cos² φ where φ 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. AD does not include the hub area. (d) Expanded Area (AE): 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. AE does not include the hub area. Propeller Blade Area Ratios (a)

Projected Area Ratio: This is the ratio of the projected area to the disc area of the propeller

(b) Developed Area Ratio: This is the ratio of the developed area to the disc area of the propeller. This also called as Blade Area Ratio (BAR) (c) Expanded Area Ratio: This is the ratio of the expanded area to the disc area of the propeller. This also called as Expanded Area Ratio (EAR)

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Measurement of Propeller Pitch. The pitch of a propeller at a given radius may be measured without removing the propeller from the ship, by means of a simple instrument known as a Pitchometer. One form of this instrument consists of a protractor with an adjustable arm. The face of the boss is used as a datum, and a spirit level is set horizontal when the Pitchometer is set on the datum. The instrument is then set on the propeller blade at the required distance from the boss and the arm containing the level moved until it is horizontal, a reading of pitch angle or pitch may then be read from the protractor at the required radius (see Fig). An alternative method is to turn the propeller until one blade is horizontal. A weighted cord is draped over the blade at any given radius as shown in Fig. A batten is placed horizontally at the lower edge of the blade with the aid of a spirit level. The distances AB and BC are then measured. θ is the pitch angle, and 𝑇𝑎𝑛𝜃 = And

𝐻𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝐵𝐶 = 𝑉𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝐴𝐵 𝑃𝑖𝑡𝑐ℎ = 𝑇𝑎𝑛𝜃 × 2𝜋𝑟

Therefore, 𝑃𝑖𝑡𝑐ℎ =

𝐵𝐶 × 2𝜋𝑟 𝐴𝐵

Generally, the pitch is measured at radius 3R/4 for a four bladed propeller and at 2R/3 for three bladed propeller. Where R is the radius of the propeller

Example 10 In a propeller of 4.0 m diameter and 3.0 m constant pitch, each blade face coincides with its defining helicoidal surface. The distance. of the blade tip face from a plane normal to the axis is 263.3 mm, while the distance of a point on the face at the root section (radius 400 mm) from the same plane is 52.7 mm, both distances being measured in a plane through the propeller axis: The midpoint of the root section is 69.5 mm towards the leading edge from a plane through the propeller axis, while the blade tip is 1285.6 mm towards the trailing edge from the same plane. Determine the rake and skew angles of the propeller Solution

The tangent of the rake angle is given by 𝑃𝑟𝑜𝑝𝑒𝑙𝑙𝑒𝑟 𝑟𝑎𝑘𝑒 𝑎𝑛𝑔𝑙𝑒 𝑇𝑎𝑛(𝜖) =

=

𝑟𝑎𝑘𝑒 𝑎𝑡 𝑡𝑖𝑝 − 𝑟𝑎𝑘𝑒 𝑎𝑡 𝑟𝑜𝑜𝑡 𝑅𝑎𝑑𝑖𝑢𝑠 𝑎𝑡 𝑡𝑖𝑝 − 𝑅𝑎𝑑𝑖𝑢𝑠 𝑎𝑡 𝑅𝑜𝑜𝑡

263.3 − 52.7 2000 − 400

= 0.131625 Naval Architecture Lecture Notes

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𝑟𝑎𝑘𝑒 𝑎𝑛𝑔𝑙𝑒 𝜖 = 7.5𝑜 Sign convention: θ and distance to leading edge positive. The angles which the midpoints of the root section and the tip make with the reference plane are given by: 69.5 sin 𝜃𝑅 = = 0.17375 ⇒ 𝜃𝑅 = 10𝑜 400 sin 𝜃𝑇 =

−1285.6 = −0.64280 2000

⇒

𝜃𝑇 = −40𝑜

𝑆𝑘𝑒𝑤 𝑎𝑛𝑔𝑙𝑒 𝜃𝑆 = 10 − (−40) = 50𝑜

Example 11 In a propeller of 5.0 m diameter and 4.0 m pitch, radial lines from the leading and trailing edges of the section at 0.6R make angles of 42.2 and 28.1 degrees with the reference plane through the propeller axis. Determine the width of the expanded blade outline at 0.6R. Solution: Assuming a flat faced blade 𝑟 = 0.6𝑅 = 0.6 ×

5000 = 1500 𝑚𝑚 2

𝑃𝑖𝑡𝑐ℎ 𝑎𝑛𝑔𝑙𝑒 𝜙 = tan−1

4000 = 22.997𝑜 2𝜋 × 1500

𝜃𝐿 = 42.2𝑜 , 𝜃𝑇 = −28.1𝑜 . The width of the expanded outline at 0.6R is:

𝑐=

𝑟(𝜃𝐿 − 𝜃𝑇 ) 1500 (42.2 − (−28.1))𝜋⁄180 = = 1992.1 𝑚𝑚 cos 𝜙 cos 22.997

Example 12 The cylindrical polar coordinates (r, Ɵ, z) of a propeller, r being measured in “mm” from the propeller axis, Ɵ in degrees from a reference plane through the axis and z in mm from a plane normal to the axis, are found to be (1500, 10, 120) at the leading edge and (1500, -15, -180) at the trailing edge at the blade section at 0.6R. The blade section at this radius has a flat face. Determine the width of the expanded outline at this radius and the position of the reference line, Ɵ = 0, with respect to the leading edge. What is the pitch ratio of the propeller at 0.6R? The propeller has no rake. Solution

𝑟 = 1500 𝑚𝑚 𝜃𝐿 = 10𝑜 𝑧𝐿 = 120𝑚𝑚

𝜃𝑇 = −15𝑜 𝑧𝑇 = −180𝑚𝑚

𝐿𝑒𝑡 𝑃 𝑏𝑒 𝑡ℎ𝑒 𝑝𝑖𝑡𝑐ℎ, 𝜙 𝑏𝑒 𝑡ℎ𝑒 𝑝𝑖𝑡𝑐ℎ 𝑎𝑛𝑔𝑙𝑒 𝑎𝑛𝑑 𝑐 𝑏𝑒 𝑡ℎ𝑒 𝑒𝑥𝑝𝑎𝑛𝑑𝑒𝑑 𝑏𝑙𝑎𝑑𝑒 𝑤𝑖𝑑𝑡ℎ Then, 𝑧𝐿 = 𝑧𝑇 + 𝑐 sin 𝜙 𝑐=

⇒ 120 = −180 + 𝑐 sin 𝜙 𝑜𝑟 𝑐 sin 𝜙 = 300 𝑚𝑚

𝑟(𝜃𝐿 − 𝜃𝑇 ) 1500 (10 + 15)𝜋⁄180 = cos 𝜙 cos 𝜙

⇒ 𝑐 cos 𝜙 = 654.5 𝑚𝑚

… 𝑒𝑞 1 … 𝑒𝑞 2

Dividing eq1 by eq 2 tan 𝜙 =

300 654.5

⇒ 𝜙 = 24.625𝑜

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From eq 1 𝑐 =

300𝑚𝑚 sin 𝜙

⇒ 𝑐 = 720 𝑚𝑚

𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑙𝑖𝑛𝑒 𝑤𝑟𝑡 𝐿𝐸 = 𝑟 sin 𝜃𝐿 = 260𝑚𝑚 𝑃 = 2𝜋𝑟 tan 𝜙 = 2𝜋 × 1500 × 𝑃𝑖𝑡𝑐ℎ 𝑟𝑎𝑡𝑖𝑜 =

300 = 4320 𝑚𝑚 654.5

𝑃 4320 = = 0.864 𝐷 2 × 1500⁄0.6 Self-Study Questions

1.

Short answer type questions a. How you can differentiate between right handed and left handed propeller? b. How is propeller pitch measured? c. In a twin screw ship, the two propellers rotate in opposite directions. State the significance of the same. d. Explain skew of a propeller e. Explain the following terms: i. Right hand propeller ii. Outward turning propeller iii. Developed blade area of propeller f. State reasons for positioning the propeller at the stern of the ship.

2. Sketch a typical right handed screw propeller and indicate the following: (a) Leading Edge (b) Trailing edge (c) Hub (d) Root (e) Tip (f) Rake (g) Skew 3. A propeller of 6.0 m diameter and constant pitch ratio 0.8 has a flat faced expanded section of chord length 489 mm at a radius of 1200 mm. Calculate the arc lengths at this radius of the projected and developed outlines. 4. The cylindrical polar coordinates (r, θ, z) of the trailing edge of a flat faced propeller blade radial section are (1500 nun, -30°, -400 nun). If the pitch of the propeller is 3.0 m, and the expanded blade width is 2000 mm, determine the coordinates of the leading edge. 5. The pitch of a propeller is measured by means of a batten and cord. The horizontal ordinate is found to be 40cm while the vertical ordinate is 1.15m at a distance of 2.6m from the centre of the boss. Calculate the pitch of the propeller and the blade width at that point. (Ans 5.682 m, 1.218 m) 6. The pitch angle measured at a distance of 2 m from the centre of boss, was found to be 21.5 O. calculate the pitch of the propeller.

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Materials The following materials can be used for propellers • • • • • • • •

Gray cast iron Carbon and low-alloy steel Chromium stainless steel Chromium-nickel austenitic stainless steel Manganese bronze Nickel-manganese bronze Nickel-aluminium bronze Manganese-aluminium bronze

The castings are to comply with the requirements of the standards organizations. Where the use of other materials is proposed, details of the chemical composition, mechanical properties, and density are to be submitted for approval. For additional information see the rules of the standards organizations or the classification societies (Lloyd's Register of Shipping, American Bureau of Shipping, Det Norske Veritas, and others).

Diagram showing skew angle at the tip and reference line for propeller with skew back

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