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25-Nav-A2 Hydrodynamics of Ships (I)_ Resistance and Propulsion · Undated paper

Question 5 of 10: Propeller Geometry Definitions

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

National Exams — May 2019 — 16-Nav-A2 Hydrodynamics of Ships I: Resistance and Propulsion. Three-hour, closed-book exam; a data sheet, a Wageningen B4-55 propeller chart and a Burrill cavitation chart are supplied. Format: Questions 1–8 are compulsory (attempt all eight), then one of Questions 9 or 10. All ten are solved below for completeness.

Reference texts: Larsson & Raven, Ship Resistance and Flow (SNAME) — model-scale resistance testing, Froude/Reynolds scaling, boundary-layer estimates and the ITTC 1978 performance-prediction method; Lewis (ed.), Principles of Naval Architecture, Vol. II — Resistance, Propulsion and Vibration (SNAME) — propeller geometry, wave-pattern interference, open-water B-series design and wake-induced blade loading; Carlton, Marine Propellers and Propulsion (Butterworth-Heinemann) — Wageningen B-series charts, the Burrill back-cavitation criterion and open-water model testing.

Question 5: Propeller Geometry Definitions (10 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Approach. Each term is defined against the blade-section (2-D unrolled cylindrical cut) and side-view (rake) geometry shown in the figure, then sheet cavitation is described physically since it is a flow phenomenon rather than a geometric one.

Blade section (i)(iii)(v) pitch datum line leading edge (v) trailing edge camber line (iii) face side (v) — pressure surface back side (v) — suction surface φ (pitch angle) chord length c (v) Pitch $P=2\pi r\tan\varphi$ (i) Rake (ii), side view plane ⊥ shaft axis rake angle generator line shaft axis
Figure 2 — Left: expanded blade section showing the pitch datum line, pitch angle $\varphi$, chord, camber line, face (pressure) and back (suction) surfaces, and leading/trailing edges. Right: blade generator line rake, measured as the fore-aft offset from the plane perpendicular to the shaft axis.
  1. (i) Pitch datum, pitch angle, pitch. The pitch datum line is the reference (nose-tail) line of a blade section against which pitch is measured — conventionally the line joining the leading and trailing edges at zero camber, or a specified datum on the face. The pitch angle $\varphi$ is the angle this datum line makes with the plane of rotation (perpendicular to the shaft axis) at a given radius $r$. The pitch $P$ is the axial distance the blade section would advance in one revolution if it moved along the helix defined by $\varphi$: $$P=2\pi r\tan\varphi.$$
  2. (ii) Propeller rake & rake angle. Rake is the fore-aft (axial) displacement of the blade's generator line from the plane perpendicular to the shaft axis, usually quoted at the blade tip and expressed as a length or as a fraction of diameter. The rake angle is the angle between the generator line and that perpendicular plane; positive (aft) rake tilts the blade tip toward the stern, which is common practice to increase tip clearance from the hull.
  3. (iii) Camber line & camber. The camber line (mean line) is the locus of points midway between the face and back surfaces of the blade section, analogous to an airfoil's mean camber line. The camber is the maximum perpendicular distance between the camber line and the chord (pitch datum) line, usually expressed as a fraction of the chord length; it sets the section's lift-generating curvature independent of angle of attack.
  4. (iv) Sheet cavitation. Sheet cavitation is a thin, smooth, glassy, attached vapour cavity that forms on the blade's back (suction) surface, typically starting near the leading edge, where the local pressure has dropped below the vapour pressure of water due to high local velocity/angle of attack. Unlike bubble or cloud cavitation it stays attached to the surface as a continuous sheet whose extent grows and shrinks cyclically as the blade sweeps through the non-uniform wake (largest where local angle of attack is highest); it collapses downstream of the low-pressure region, producing noise, erosion (pitting) of the blade surface, and added vibration.
  5. (v) Chord, face, back, leading edge. The chord length $c$ is the straight-line distance from the leading edge to the trailing edge of a blade section. The face side is the high-pressure (pressure) surface of the blade — the side that pushes water aft, traditionally the surface seen looking at the propeller from astern. The back side is the low-pressure (suction) surface, the curved forward-facing surface. The leading edge is the edge that first meets the incoming relative flow as the blade rotates.