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Good morning, gentlemen. Today, we will start
on screw propellers and we will start with
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geometry.
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Every ship has an engine which is connected
to a propeller shaft, a sort of shafting system
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consisting of a number of units ultimately
as aft and the shaft is known as propeller
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shaft to which is attached the propeller;
this propeller is rotated by means of the
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moment or torque supplied by the engine at
a particular RPM, so once this propeller rotates
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it moves in a hydrodynamic medium and through
interaction of water and the propeller blade
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an axial force is generated, which is known
as thrust, in the direction in which the ship
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is moving. A ship when it moves forward it
experiences resistance to its motion in the
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reverse direction, this force generated by
the propeller known as thrust overcomes this
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resistance and allows the ship to move forward-
this is the principle on which the propeller
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works.
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Simply said or diagrammatically said it is
like this: you have the engine here somewhere,
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now, you have got a shaft coming here, and
then this comes out of the ships, out of the
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ship on which is housed the propeller; now,
the engine provides the moment to the propeller
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at a particular RPM, this propeller works
in this fluid medium- this medium is fluid,
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water- and produces a thrust or an axial force
in this direction, which is finally transmitted
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to the ship along the propeller shaft, and
since the propeller shaft houses a baring
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here, thrust baring, through the thrust baring
it is transmitted to the ship structure and
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the force is applied to the ship and the ship
moves forward overcoming this force, R, resistance,
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which is experienced by the ship at a particular
speed V .
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The propeller geometry is such that when it
rotates the one side of the propeller forms
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more or less a part of a screw- I suppose
all of you have seen a screw, a nut and bolt,
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a bolt on which a screw is carved out and
when you rotate a nut it travels in a particular
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fashion- a propeller blade surface, one of
the surfaces is a part of this screw surface
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and that is why a propeller fitted behind
a ship is called a screw propeller, so, this
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is, this is called a screw propeller. Before
we go further it is necessary for us to understand
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the geometry of a propeller.
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So, what have we got so far? The torque coming
out from the engine being applied on the propeller
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is called torque Q represented as capital
Q, and its unit is Newton meter- we are all
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talking about SI units; rotates the propeller
blade, rotates at rpm at revolutions per second
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denoted as small n, rps, unit be second inverse,
sometimes it is more convenient to say revolutions
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per minute in which case you write capital
N, rpm, which is equal to n into 60; and then
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we have thrust generated, which is called
thrust and the unit is that of force, Newtons.
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And this operates at a speed normally called
velocity of advance VA. Now, this velocity
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of advance varies from, varies as where the
propeller is working, if the propeller is
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working in open water, which will be seen,
the VA will be equal to the speed of water
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whereas, if it is working behind the ship,
it will also, the VA will be the mean velocity
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of water on to the propeller, which may be
less than the ship’s speed that is, if I
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write VS as ship speed, VA will be less than
VS- units of all speeds will of course be
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meters per second, or more conventionally
knots, which can be converted to meters per
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second by multiplying with 0.5144.
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I have got some propeller to show you here.
I will show you this propeller, this is- can
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you see this?- this is a model propeller having
three blades- can you see this?- this portion
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is called the boss of the propeller on which
there are three blades. So, this is a three
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bladed propeller and this boss has a hole
as you can see, which sits on the propeller
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shaft like this, so the shaft is on my right
and the ship is also on my right that means,
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this side is the aft side, or this is, this
portion is behind the ship, the ship is in
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front and it is moving that way. How is the
propeller rotating? This is, if you are looking
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from behind the propeller, behind the ship
let me say- still we have not said which is
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front and back of the propeller- suppose,
I am looking at the propeller from the from
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behind the ship that is, from this side, then,
if it rotates in the clockwise direction-
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is it the clockwise direction. this direction?
Anticlockwise- so, how will be the clockwise,
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how will it be clockwise here, this way? Right.
If it rotates.
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Looking from aft, looking from aft that is,
this side, if I rotate it like this, then
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this is clockwise, this is called the right
hand screw, right handed screw; if it rotates
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the other way, then it would be call the left
handed screw. Normally, single screw propellers
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are all right handed propellers, right hand
screws, but if I have a twins screw propeller
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that is, one on the fore side and one on the
stable side to balance the uneven forces that
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may be generated, I would like to rotate the
propellers, each propeller in the opposite
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direction, so, that means, one will be right
handed propeller and the other will be left
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handed propeller.
So, right now let us look at this right handed
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propeller, what are its characteristics? The
side that is facing you when you are standing
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behind the ship and propeller that is, this
side, is called the face of the propeller-
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this is the face- actually, it is behind from
the aft side, and this is the back of the
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propeller, and the edge that meets the water
first, if it is rotating like this, this is
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the edge that is meeting the water first,
so, that is called the leading edge of the
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propeller, and the other one is the trailing
edge, this edge trails the propeller- am I
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clear? The furthest point of the propeller
blade is called the propeller tip and the
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one that joins the propeller blade to the
boss is called the root. So, I have got the
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root, the tip, the leading edge, the trailing
edge, the face and the back. This would more
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or less define all the main features of a
propeller and number of blades of course,
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and along with RPM and torque it is supposed
to observe; what we have not defined yet is
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section shapes and the outline of the propeller
blade now, we will see how they can be defined.
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Showing it in the form of a diagram- can you
see this, is it visible to you, yes, clearly
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visible? So, this is the shaft where this
shaft is rotating in the clockwise direction
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looking from this side, and this is the face,
this is the back, leading edge, trailing edge,
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this is the boss, this is the tip and this
is the root where the propeller joins the
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boss- is that clear? Now, let us look at some
other features of the propeller blade.
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Now, you see here- is this visible, clear,
or should I draw it? So, if the propeller
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axis is perpendicular to the shaft center
line- this is the propeller center line, propeller
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axis as it is called, the shaft center line
on which the propeller sits is called the
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propeller axis- if the propeller blade as
in this case, as in this case, is the propeller
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blade is perpendicular to it in this plane,
if it is perpendicular like this, then this
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is called a propeller with no rake. But sometimes
it may be necessary to rake the propeller
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or tilt the propeller blade to one side of
the plane perpendicular to the propeller axis
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like it is shown in the next diagram, this
diagram- can you see it, is it understandable,
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can you understand?
What benefit do we give, do we get if I rake
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the propeller? You can see this distance between
the propeller trip and the hull here is less
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than the distance between the propeller trip
and the hull here. We know that propeller
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works in a velocity field, which is varying
and therefore, it is possible the propeller
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may transmit pulsating pressure forces on
to the ship hull, which may cause vibration
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in this overhang portion of the hull that
is, the stern, which may be transmitted to
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accommodation and the other areas. One way
to reduce the effects of this vibration is
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to increase the clearance between the propeller
tip and the hull- this minimum distance as
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I have discussed earlier is given by classification
societies. So, if you do not get adequate
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clearance here, rake propeller is one way
so that we can get increased clearance between
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the hull and the propeller.
Next, we have what is called skew of a propeller.
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Normally, propellers do not have forward rake
normally, they do not have forward rake, but
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can always have a forward rake, it is not
denied, but it is generally not there, because
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if you here forward rake the clearances reduce,
the way the propeller is fitted behind the
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ship.
Skew is, if I take the propeller axis like
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this and if it is perpendicular to this, it
is called no skew. So, there is another way
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to define this.
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This is the propeller boss, I have got a blade
here; now, at each section if I draw a radial
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section, radius here, and this is my section,
I draw the mid line here, midpoint, if I join
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the mid points of all sections like this,
all radial sections with this as center and
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I find they lie in one line, which is perpendicular
to the center like this, then this is called
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a propeller with no skew, but if I have this
blade shifted like this where the center point
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gets shifted to this, then this axis, the
propeller’s vertical axis is tilted to one
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side, then it is called skew.
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Now, some of these diagrams, this diagram
shows you various types of skew that exist;
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this is a propeller blade with no skew, this
is a propeller blade with slight skew and
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this is a propeller blade which is called
heavily skewed that is, the skew is very high.
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And you can see the center line of each blade
plotted here, and the measure of the skew
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is generally the angle between the propeller
non-skewed axis to the line joining the propeller
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center with the tip, that line, this is the
skew line and the measure is up to the tip,
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the skew at the tip, that angle- is that clear?
So, this is normally how propeller rake and
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skew are designed. Why is propeller blade
skewed, there should be some reason why we
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do these heavily skewed propellers, particularly,
one can appreciate that moderately skewed
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propellers can be designed to suit the geometry
and other constants, but why heavily skewed
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propellers? It has been found that heavily
skewed propellers can adopt themselves to
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varied weight field or varied velocity field
much better than normal propellers so therefore,
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these propellers have been advocated and have
been fitted to a number of ships who, where
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the velocity field is very uneven, which might
have caused vibration.
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Sir it been right handed skew also increase
the gap in both the ways
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Skew may increase gap, but may not because
skew is actually in this plane, so when the
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propeller blade rotates at someplace the gap
may reduce, someplace it may increase, but
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of course, a well designed, a well skewed
propeller may actually improve the gap.
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Now, let us look at this. Propeller geometry
is actually very interesting, it is a highly
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three dimensional geometry, the face and,
the propeller face forms a part of what is
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called a helicoidal surface. Now, what is
a helicoidal surface? We have already mentioned
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that it forms a part of the screw surface,
if I have an axis here like this and I have
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a line here perpendicular to the axis and
I rotate this line here, then the tip of this
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line will form a circle. But along with rotating
I also give a forward speed to this line that
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is, I not only rotate at a constant speed,
but I also move this along this axis, so,
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how will it form? It will go like this.
Now, the line that is formed by the tip is
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a three dimensional curve known as a helix,
the three dimensional curve is known as a
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helix, now, if this entire line I trace, it
will form a three dimensional surface, which
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is called a helicoidal surface- is that ok?
So, here what we have shown is this diagram,
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if you look at this diagram- can you see,
is that clear?- this is a cylinder of a constant
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radius R and on top of this I have tried to
move this R at a constant speed along the
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cylinder, it will move on the cylinder surface-
is it not?- because R is constant, so this
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is the, line A will trace a line like this,
a three dimensional line up to A1- it is shown,
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it is shown in a plane, but it is actually
a three dimensional curve, this line actually
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goes like this.
Now, there are two planes I have, we have,
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defined here: one is the perpendicular plane
to the, in one, one perpendicular plane to
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the propeller axis, which is called the theta
equal to 0 axis; and another one normal to
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the both this propeller axis as well as this
plane, which we have called as z axis. Why
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I have done this?
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Normally, we know Cartesian co-ordinate system;
in Cartesian co-ordinate system we defined
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the position of a point by x, y, z co-ordinates
in three dimensions- is that right?- in space
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if I define an axis system x, y and z, then
any point here will be defined by x, y, z;
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x is the distance this way, y is the distance
this way, z is the height, from this plane,
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how far it is. Now, in propellers since, it
is connected with a cylindrical movement it
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is easier for us to define the propeller,
a point on the propeller blade in what is
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called cylindrical cylinder co-ordinates-
this is Cartesian co-ordinates- that is R,
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theta and z- this z remains same as the Cartesian
co-ordinates, but r and theta that is, if
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I have got this propeller, this propeller
let us, let us compare this with this diagram
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that we have seen.
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This is the propeller blade, this is the propeller
blade, and a point here if I move, it will
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form a helix, this line, this plane is the
theta equal to 0 plane, this plane that means,
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if I take a radius r, I take a radius r here,
if this plane is defining theta equal to 0,
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then the point passing through that circle
that I have drawn would be theta equal to
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0, but any other point here we will have to
move through an angle theta- am I clear, Mr.
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Mukharji? So, this point can be defined by
R and theta, but it has also a co-ordinate
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in this direction, that I am calling z, if
I pass a plane here, a z equal to 0, then
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the point from that plane to this point will
be the z point; so, this point we will have
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a R co-ordinate, will have a theta co-ordinate,
which is how much it has moved angularly from
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this axis and the z co-ordinate that from
standard plane how far it has gone, how far
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deep it is, how deep it is- is that clear?
So, any point in space can be defined by three
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co-ordinates; in Cartesian co-ordinates we
had x, y, z, where all the three co-ordinates
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are measured linearly from the three defined
axis; in the cylindrical co-ordinate system
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we are defining by a point, by R theta and
z. So, R and theta define a point in a plane
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perpendicular to the propeller axis- R is
this distance and theta is the angle, and
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z is the distance from that plane- so, that
defines the co-ordinates of a propeller.
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So, that is what is shown here, the axis theta
equal to 0 and z equal to 0 are shown, so
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any point on this can be...Now, you see this
is the face of the propeller blade, this is
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propeller blade- this is the face corresponding
to the diagram we had seen earlier- this helix
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forms a part of that face, or rather the face
forms a part of this helix that has been shown
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here, this part of the curve. Now, if I open
this cylinder up, I have drawn this line on
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the cylinder now, I open it up, what do I
get? You see here, this is the cylinder of
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radius R, so if I open it up, it will open
up to 2piR and the distance here along this
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axis if it has moved, it has moved through
a distance called pitch- I have not defined
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pitch earlier that is, when this, when this
line moves through one revolution, the distance
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it has travelled longitudinally or axially
is called the pitch of the helix, or helicoidal
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surface if the entire surface is moving the
same distance.
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So, when I open this cylinder up, what do
I get? This side will be p and this side will
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be 2piR, this is what is shown here P is,
one side will be distance P the other side
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will be distance 2piR, and this helix will
convert itself to a diagonal, it started from
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one end and ended at the other end- do you
understand? So, this A, A1 that we had here
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is converting itself when I, when I open up
the cylinder into a diagonal of the rectangle
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the two sides of which are P and 2piR ; now,
this section that was here, this helix that
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was here on this face, face section that was
here that will now appear here on this diagonal.
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Now, this section that you have seen this
side is the face and this side is the back;
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now, I said that the face is a part of a helicoidal
surface, or at a particular radius it is a
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part of a helix, what is shown here is the
helix, but you will notice that if I expand
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this, this is the diagonal going and my section
shown here is something like this, is not
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actually, the face is not actually on this
line there is little bits of deviations from
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here, and this is the back, this is the face
– is it not?
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So, this is what is shown here, I have just
expanded this, you see here, the face is more
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or less falling on this helicoidal line just
slightly adjusted, slightly offset at the
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leading edge and the trailing edge, this is
the leading edge L and this is the trailing
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edge T, the projections of L and T on the
exact line is shown here as Ldash and Tdash.
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So, this is the actual section shape of the
blade at that radius R- am I clear? Now, if
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this, it is projector, in other views they
will look like this, I think we can skip it
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for the time being and proceed further- any
doubt so far regarding how wave propeller
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should behave?
Sir this ensures it will be flat face
00:31:04
No, it will not be a flat face. Of course,
it is a curved face, this is what I have shown
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here, this is curved, this is curved; this
is, this is face, this is supposed to be on
00:31:24
the helicoidal surface and this you can see
is not strictly on the helicoidal surface,
00:31:30
but it is slightly offset from the helix at
the ends that is, at the leading edge and
00:31:35
the trailing edge; back is not on a helicoidal
surface, we are not saying that same thing
00:31:42
for the back, we are more concerned about
the face, but it is more or less on a helicoidal
00:31:49
surface, this is what we are trying to say.
So, if the propeller actually moved as a helicoidal
00:31:56
surface in a solid medium, please understand,
if it moves in a solid medium, then there
00:32:03
will be no slip, when you move the propeller
forcible like a nut moves on a screw of a
00:32:10
bolt, it does not have any facility to slip
away unless the screw has broken. The nut
00:32:20
will move when you move it, one revolution-
sorry- one rotation, it will move a certain
00:32:27
fixed distance, if you move it ten times,
it will move ten times of that distance, that
00:32:35
distance, which it moves in one rotation is
called the pitch- and this is what we defined
00:32:41
pitch here. But since the propeller is moving
in a fluid medium it may not move, behave,
00:32:49
as if it is moving in a solid medium therefore,
there may be slip, its actual movement may
00:32:55
not be equal to P, if I defined P as pitch
that is, the distance moved in one revolution
00:33:06
of this helicoidal surface, the propeller
actually need not move P, it may move less
00:33:11
because it is in a fluid medium, it may slip-
this part we will see later.
00:33:17
Right now, let us just understand that though
we are defining the propeller blade as a helicoidal
00:33:23
surface and defining P as a distance moved
in one revolution, in an actual case, propeller
00:33:29
may not move distance P in one revolution
because the medium is not solid, there may
00:33:38
be many other reasons, but one of the main
reasons is it is not solid, to overcome the
00:33:43
resistance in a solid medium, we are actually
applying manual force to move it; in a fluid
00:33:50
medium what happens as we go along the course
we will see- have I been clear ?
00:34:03
So, most difficult part of propeller geometry
is representing it diagrammatically, showing
00:34:14
its various features.
So, if I bring back this diagram again, this
00:34:23
section that is shown here, this section is
what is called an expanded section that is,
00:34:31
if I expand the helix this is how the section
would look. Remember, what I have actually
00:34:37
drawn is, what I have actually done is I have
taken this propeller a at a constant radius,
00:34:45
a constant radius, it is not a flat line,
it is a constant radius, the section shape
00:34:51
what I have shown here, it is not a straight
line it is at a constant R; what I have shown
00:34:58
here is if that radial arc was made into a
straight line, how this section would look-
00:35:08
do you understand- we expanded this to a straight
line, is it not the helix?
00:35:13
This is a diagonal, it is a straight line.
So, this is as if we have expanded it along
00:35:20
this line and the angle of this line is phi
of pitch angle, you see this angle here, phi-
00:35:30
can see?- this angle is called the pitch angle
defined by the P and 2piR.
00:35:38
And what is pitch angle? You can tell me,
tan phi is equal to, tan phi equal to P by
00:35:50
2piR,P divided by 2piR is the tan phi. So,
pitch angle phi is tan inverse of P by 2piR
00:36:01
.
So, here you have got this line, which would
00:36:08
come on the helix if it was drawn in your
straight line at an angle to the 2piR line
00:36:17
phi, and this would be as if the section has
been straightened.
00:36:22
That is not the section of that part where
it is cutting
00:36:27
Yes, it is exactly that, it is exactly that.
If I take R here and cut it here, if I take
00:36:35
this R and cut it here, this is actually a
section in three dimensions, but if I have
00:36:41
expanded it, pulled it out along the helix,
then it becomes a straight line, the section
00:36:49
elongates in length along that line- do you
understand?- so, that is that section, it
00:36:58
would look like this and this is the actual
section with which we will be dealing, this
00:37:06
is called an expanded section- you got it?
Expanded section- am I clear, has it been
00:37:29
understood?- actually, it is on a three dimensional
plane, the section is in three dimensions,
00:37:34
it is as if I have pulled it out to a straight
line and that straight line is at an angle
00:37:39
to horizontal, then that section will look
like this.
00:37:43
Now, what I do is I now move it at that same
distance r, I make that line horizontal instead
00:37:52
of diagonal like this, I make this line like
this, horizontal, I made this line horizontal,
00:38:01
just physically moved it then, I get a line-
you see here, can you see this diagram clearly,
00:38:10
all of you can see it? This is that angle
phi, this is the angle phi, here is what I
00:38:20
have R theta L and R theta T- I do not know
whether I have explained this to you or not.
00:38:29
This distance, this distance here is called
r theta L, you see, this is, this distance
00:38:39
is actually how I would have seen it on the
arc- that is, that is the projection, this
00:38:50
distance is the projection into this plane,
in theta equal to 0 plane, projection is from
00:38:58
here to here- tell me if you are not understanding,
this is very important for us to define the
00:39:08
three areas, that are important to proceed
with later on.
00:39:25
What have we done? We have expanded the cylinder;
this is P, this is 2piR , the cylinder was
00:39:41
like this, in this it was like this, I have
expanded it, this is the helix that I had-
00:39:55
so far so good?- now, when I expanded the
helix since, at a particular radius of the
00:40:01
propeller blade the face I am saying is a
part of the helix that would come has a straight
00:40:08
line here actually, it is not straight will
it come as a straight line? So, let us say
00:40:15
the pitch was coming here, face was coming
here now, I am not giving any offset to face-
00:40:19
let us understand the geometry first- and
it has a back like this let us say, this is
00:40:26
my blade section, but if I look at the propeller
blade straight away like this, then this would
00:40:37
be my point, this is my projected length,
my projected length if I do a projection of
00:40:47
the propeller blade, it is here, but if I
expand that line, then the propeller blade
00:40:53
comes like this, elongated- this can be understood.
Sir Yeah.That part will be and that propeller
00:41:03
is a three dimensional. So, there is a difference
there also you are telling that
00:41:11
We have taken the pitch. We have taken the
pitch here, this is the length of the propeller
00:41:19
blade section, actual length.
that is the Yeah. Um.That the arc will be
00:41:29
a two dimensional curve.
This arc is a three dimensional curve, this
00:41:34
is a helix, the part of a helix, this arc,
this arc is also moving, it is part of a helix-
00:41:45
do you understand?- so, this is, now, as if
I have straightened the helix, so this is
00:41:54
a longer length, which I am actually not seeing,
what I am seeing is the projection here, this
00:42:01
much. So, this is actually the projected length
of that section, but this is the actual length,
00:42:10
if I measure the length, it would be this,
what is this, what is this? At constant R
00:42:18
if I measure, I take a thread put it from
here to here at constant and expand it this
00:42:24
is the length I will get.
That is a actual actual length.
00:42:30
Actual length at radius R- is that clear?
So, this is phi and I can say this is theta
00:42:45
equal to 0 line, what is the, see this is
theta equal to 0 line let say, and this is
00:42:51
R, so what is the length of this arc, projected
length? Now, let us say projection means I
00:42:58
will have a circle and a cylinder at a constant
section and I draw a line, what is that arc
00:43:07
length? R into theta, whatever is a theta,
so this distance is therefore, R into theta
00:43:15
L and this distance is R into theta T, trailing
edge this is L, this is T, the projections,
00:43:25
mind you- is it too difficult?
See here, let us make this surface flat for
00:43:42
the time being, what is the section you will
see? You will see this length, if I take a
00:43:49
photograph, what length I will see? This length
and that will be on this arc, so the length
00:44:00
of this will be R into theta, length of an
arc is R into theta, all I am saying from
00:44:06
standard co-ordinates the leading edge will
be R theta L and trailing will be R theta
00:44:13
T- that is the projection.
00:44:18
So, now when I draw the propeller outline
and come back to this diagram, when I draw
00:44:29
the propeller outline, if I draw an angle
phi here, my section would have come here,
00:44:36
that I am drawing on a horizontal plane. So,
this is R theta T and this is R theta L along
00:44:52
that diagonal line at angle phi and that when
I bring it to the horizontal plane it becomes
00:44:58
a longer line- do you understand? So, this
section is now known as the expanded section
00:45:10
drawn horizontally- have you understood, I
am asking you, you have understood? Good
00:45:32
But if I have, if I want to draw a projected
line, then it is only on that arc I put, if
00:45:41
I draw at an R, draw theta L and theta T this
side I get this L and theta lines and join
00:45:48
them I will get the projected line- projection
is very simple once I know the pitch and I
00:45:53
once I know the angles, theta L and theta
T, I can easily draw the projected outline.
00:46:00
The expanded outline I have to draw by drawing
this phi line, the pitch, and then projecting
00:46:07
it into a horizontal line, that would give
me an outline which is called the expanded
00:46:13
outline. So, you have got an expanded outline,
you have got the projected outline.
00:46:22
Now, there is a an outline called the developed
outline that is- see what we are getting-
00:46:34
the projected outline is if I had R here and
I drew it, if I took the photograph here,
00:46:39
how that line would look that is, this circle
T C and L – is it not- that is why I am
00:46:48
doing the projected line. Now, suppose I do
not actually make it into a straight line,
00:46:52
but bring this circle to a single plane, this
circle is in three dimensions if I bring this
00:47:01
out to two dimensions, then I will again get
a line which is more than the projected line-
00:47:08
can you understand?- that line is called the
developed line, where that will be horizontally
00:47:21
projected from L and T to give, here in this
case we have done Ldash and Tdash, which is
00:47:27
the along with the offset of the leading edge.
It is the horizontal line and it would come
00:47:34
on another circle, which will be geometrically
defined as, if you take P by 2pi this side
00:47:41
and angle phi here, you will get this center
and from there you draw a circle, which will
00:47:46
automatically give this Ldash and Tdash projected
horizontally on this circle to Ldoubledash
00:47:52
and Tdoubledash if you join them they are
called developed outline- have you understood?
00:47:59
Basically, what I have done if I take a radius
R a section if I draw it projected, same section
00:48:07
I get projected outline, if I that section
I bring to a single plane by expanding it,
00:48:13
not by making horizontal, but in that same
circle, then I get developed outline, that
00:48:19
circular line if I pull it and make it straight,
then I get expanded outline.
00:48:32
Actual expanded outline is not opening the
second curvature, well, yes, that is true,
00:48:42
in two different planes. We will stop now,
have a small gap and start again. Thank you.
00:49:10
We will continue with propeller geometry.
00:49:15
We have seen there are three outlines that
can define a propeller: the expanded outline,
00:49:22
the developed outline and the projected outline.
00:49:25
Correspondingly, there are three areas that
we can define that is: expanded area, developed
00:49:38
area and projected area. Now, the area that
is covered by the circle with radius R that
00:49:55
is, propeller radius, R is the radius up to
the propeller tip, that is called the disc
00:50:02
area, A0, which is equal to pi R square or
pi D square by 4, if D is the propeller diameter.
00:50:18
Expanded area normally is represented by AE;
developed area AD; and projected area AP.
00:50:25
So, non dimensionalising this we have three
area ratios that is, expanded area ratio,
00:50:40
which is equal to AE by A0; similarly, developed
area ratio is equal to AD by A0; and projected
00:50:53
area ratio, which is equal to AP by A0. So,
this is the definition of area.
00:51:04
Propeller diameter is given by D, and propeller
pitch as we have seen is given by p. Now,
00:51:11
this pitch will be constant at all radii if
the propeller face formed a single helicoidal
00:51:24
surface.
00:51:26
But sometimes we may not give a constant pitch
across the radius that is, the pitch may vary
00:51:35
like, if this is the radius R- this is full
radius- then your pitch distribution may be
00:51:49
constant; if it is a constant pitch, then
the pitch distribution will be like this to
00:51:56
the R, this is the pitch, at all radii the
pitch is constant. On the other hand, I may
00:52:06
decide that this pitch distribution is not
ok, I can reduce pitch at the root and increase
00:52:13
pitch at the tip, so in that case I can also
give a pitch distribution, which may look
00:52:18
like this; I can give a variable pitch distribution
to the propeller blade. In that case, what
00:52:30
will be the resultant pitch?
If I give a variable pitch distribution, the
00:52:40
resultant pitch of the propeller, if I want
to designate it by a single quantity, then
00:52:47
in the variable pitch case, resultant pitch,
you will, you can see, can be given as mind
00:52:57
you, the pitch is starting only after the
root, the boss, the blade is starting from
00:53:04
the root till the tip.
shape is known as aerofoil section where you
00:53:12
can see the leading edge is not really sharp,
it is rounded and the trailing edge is sharp-
00:53:21
that is how propeller blades are made- the
leading edge has a curvature, but the trailing
00:53:26
edge is sharp. There is another way of knowing
for which is the leading edge- the one that
00:53:33
is sharp is the trailing edge, the one that
is blunt is the leading edge and that is the
00:53:40
one that will be meeting a water first, so
you can also decide which way the propeller
00:53:44
rotates by just looking at the propeller if
it has the aerofoil section.
00:53:50
Now, as we have seen later, earlier, you can
also give some offset to the face from the
00:53:58
straight line and still it would be an aerofoil
section. This is the most commonly used section
00:54:06
for majority of propellers available in the
world. This on the another hand is called
00:54:14
a segmental section where the back of the
propeller section is a part of a circle- unlike
00:54:24
an aerofoil section you can see it is not
part of a circle, it is blunt forward and
00:54:29
sharp towards the trailing edge- here in the
segmental section the back is part of a circle,
00:54:40
this is many times used where there is a requirement
of a, typically these sections are used in
00:54:52
propellers for trollers where you require
not only free running speed, but also some
00:54:59
amount of pull that one must exert such as,
hauling a troll net or something like that.
00:55:09
In many propellers there is a combination
of both aerofoil section and segmental section
00:55:18
that is, aerofoil sections up to a certain
radius and then the section slowly change
00:55:23
to segmental section- we will see some of
these propellers later on.
00:55:28
Then, what we have is called a lenticular
section where the section is symmetrical about
00:55:35
its central line.
There will be a drag in the same direction,
00:55:41
but lift in the opposite perpendicular direction.
So, if you look at this lift, which is going
00:55:47
like this, most of its component is in the
axial direction; if I now compute it, one
00:55:56
is this direction, one is in this direction,
most of it is this way because perpendicular
00:56:01
to, perpendicular is very, making very small
angle to the axis of the propeller.
00:56:12
Thrust and lift are not same, are not different,
the axial component of lift is the thrust;
00:56:21
otherwise, what is thrust, how do you get
this axial force? This lift that I am getting,
00:56:29
the component of that in the axial direction
is what I call an element of thrust by any
00:56:35
point here, that thrust integrated over the
whole blades, all blades, gives me the total
00:56:42
thrust on the propeller- is that clear? I
am also loosing something in the form of drag,
00:56:52
so, ultimately, the propeller efficiency will
be, is a ratio between lift and drag- but
00:57:01
have you understood how lift is being generated?
00:57:04
So, let us look at this diagram a little bit.
We also know from aerofoil theory that if
00:57:13
you go on increasing this angle- this angle
alpha called the angle of attack- if I go
00:57:19
on increasing this angle of attack, lift increases
more or less linearly like this- as I have
00:57:27
shown here- that is, I get small lift if the
angle is small, and if my velocity angle of
00:57:36
attack is more and more, I get more and more
lift. But very strangely beyond a certain
00:57:43
lift angle, certain angle of attack- this
is angle of attack axis- lift suddenly drops
00:57:50
that means, you do not get any more lift-
this is called the stall angle, it is called
00:58:00
the stall angle. So, we have to design your
propeller that the lift is, the angle of attack
00:58:05
is within this. Now, when you go reducing
the angle, when it is at a particular angle
00:58:11
to the propeller there will be no lift, so
that angle is somewhat this- this is called
00:58:16
the no lift angle; only when the angle is
created with respect to that, start getting
00:58:20
lift till stall angle; so, our aim should
be to design the blade sections so that you
00:58:27
stay between no lift line and stall angle-
am I clear? We will stop here and next class
00:58:38
we will continue with propeller theories.
Thank you.
