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Frames of Reference
 10th International Towing Tank Committee (ITTC) initiated the
preparation of a dictionary and nomenclature of ship hydrodynamic
terms and this work was completed in 1975.
 The global reference frame proposed by the ITTC is a right-handed
rectangular Cartesian system.


 For propeller geometry it is convenient to define a local reference
frame having a common axis such that OX and Ox are coincident but
Oy and Oz rotate relative to the OY and OZ fixed global frame.


 The line normal to the shaft axis is called either propeller
reference line or directrix.


 Generator line: The line formed by intersection of the pitch
helices and the plane containing the shaft axis and propeller
reference line.


 The aerofoil sections which together comprise the blade of a
propeller are defined on the surfaces of cylinders whose axes are
concentric with the shaft axis.


 Face: The side 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 seen side of a propeller blade is
called face or pressure side).


 Back: The side 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 side 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.


 Consider a point P lying on the surface of a cylinder of radius r
which is at some initial point P0 and moves as to from a helix
over the surface of a cylinder.
 The propeller moves forward as to rotate and this movement
creates a helix.


 When the point P has completed one revolution of helix that
means the angle of rotation 360 deg.


 In the projection one revolution of the helix around the cylinder
measured normal to the OX axis is equal to 2πr.
 The distance moved forward by the helical line during this
revolution is p and the helix angle is given by:


 There are several pitch definitions:


 Nose-tail pitch: The straight line connecting the extremities of
the mean line or nose and tail of a propeller blade is called nose-
tail pitch line The section angles of attack are defined to the
nose-tail line.


 Face pitch: The face pitch line is basically a tangent to section’s
pressure side surface and you can draw so many lines to the
pressure side. Therefore its definition is not clear. It is rarely used
but it can be seen in older drawings like Wageningen B series.


 Effective or no-lift pitch: It is the pitch line of the section
corresponding to aerodynamic no-lift line which results zero lift.


 Hydrodynamic pitch: The hydrodynamic pitch angle (βi) is the
pitch angle at which the incident flow encounters the blade
section.
 Pitch values at different radii are called radial pitch distribution.


 Slip & Slip Ratio


 Skew
 It is the angle between the mid-chord position of a section and
the directrix (θs).
 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.


 Skew


 The skew can be classified into two types:
 i- Balanced skew: Directrix intersects with the mid-chord line at
least twice.
 ii- Biased skew: Mid-chord locus crosses the directrix not more
than once normally in the inner sections.


 The displacement from the propeller plane to the generator line
in the direction of the shaft axis is called rake. The propeller rake
is divided into two components: generator line rake and skew
induced rake.


 Propeller Outlines and Areas


 There are five different outlines and associated areas of propeller
in use. These are:
 1. Disc outline (area) (A0)
 2. Projected outline (Ap)
 3. Developed outline (AD)
 4. Expanded outline (AE)
 5. Swept outline (AS)


 Swept Outline: This outline is swept by the leading and trailing
edges when the propeller is rotating.
 In general, the developed area is greater than the projected area
and slightly less than the expanded area.


 Calculation of AE


 Propeller drawing methods


 Propeller section definition


 Propeller series


 Model ship & propeller tests
 1- Resistance Test
 2. Open water tests
 3. Self propulsion tests
 4. Cavitation tests
 5. Others (wake surveys, hull pressure tests, noise measurements,
etc.)


 1- Resistance Test
 In the resistance test the ship model is towed by the carriage and
the total longitudinal force acting on the model is measured for
various speeds. The breadth and depth of the towing tank
essentially governs the size of the model that can be used. Todd’s
original criterion that the immersed cross-section of the vessel
should not exceed 1 per cent of the tank’s cross sectional area
was placed in doubt after the famous Lucy Ashton experiment.
This showed that to avoid boundary interference from the tank
walls and bottom this proportion should be reduced to the order
of 0.4 per cent.


 The model, constructed from paraffin wax, wood or glass-
reinforced plastic, requires to be manufactured to a high degree
of finish and turbulence simulators placed at the bow of the
model in order to stimulate the transition from a laminar into a
turbulent boundary layer over the hull. The model is positioned
under the carriage and towed in such a way that it is free to heave
and pitch, and ballasted to the required draught and trim.


 In general there are two kinds of resistance tests:
 the naked hull and the appended resistance test. If appendages
are present local turbulence tripping is applied in order to prevent
the occurrence of uncontrolled laminar flow over the
appendages. Also the propeller should be replaced by a
streamlined cone to prevent flow separation in this area.


 2. Open water tests
 Open water tests of propellers can be performed either in a
cavitation tunnel or in a towing tank. Although the test procedure
applied to obtain open water characteristics of a propeller in a
cavitation tunnel is different from those in a towing tank, these
characteristics are the same used in the analysis of the Propulsion
Tests and the estimation of the required power.


 2.1 Open water test in Towing tank
 In a towing the model propeller is run without any hull ahead of
it, as shown in the figure.


 The drive shaft housing should not be too close to the model
propeller blades. A distance of not less than 1.5 D to 2.0 D is
recommended, where D is the propeller diameter. The drive shaft
should be arranged parallel to the calm water surface and the
carriage rails. A typical set up is shown in the above figure.
 The propeller immersion has to be selected such that air drawing
from the water surface is avoided at any test condition. As a
guideline, an immersion of the propeller shaft of at least 1.5 D is
recommended.


 The test procedure is as follows:
 1. The propeller advances through undisturbed water with a
known forward speed, V, which is the speed of the towing
carriage. Values of thrust, T and torque, Q are taken from the
dynamometer, and rate of rotation, n is recorded using a
tachometer.
 2. Usually measurements are taken during series of runs for T &
Q at varying J numbers so that n is kept constant and V is varied
from zero speed (i.e. J=0) to a high value ( ≈ J=1).
 3. The results are analised and coefficients are derived as similar
to those in cavitation tunnel.

 Self propulsion tests are carried out to estimate ship power at
various speeds and to derive propulsion factors, w, t, ηR.
 The hull model is equipped with an electric motor mounted
inside the hull and respective devices (dynamometer) fitted
inboard to enable the measurement of thrust, torque and rate of
revolutions of the model propeller(s). Appendages, such as
rudders, single brackets or A-brackets, propeller shafts, shaft
protection tubes, short bossings or bossings, extracted stabilisers
and openings in the hull such as for bow thrusters, should be in
the same condition as for the resistance experiment.


 The size of the propeller/propulsion unit model for propulsion
tests is determined automatically by the size of the ship model
and its scale ratio; this in turn means that the size of the model
propeller, or say a stock propeller, is also to be taken into
consideration when the scale for a ship model is selected.
 During a self propulsion test, an external tow force in propulsion
experiments should be applied along the same line of action as
the tow force in the resistance experiment.
 This external force comes from the skin friction correction such
that the skin friction coefficient of the model CFm is greater
than skin friction coefficient of the ship, CFs.


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