Marine Propulsion

Prof. Anirban Bhattacharyya

Department of Ocean Engineering and Naval Architecture
Indian Institute of Technology, Kharagpur

Lecture - 13
Propeller Open Water Characteristics

Welcome to the 13th lecture of the course Marine Propulsion, today we will be discussing
Propeller Open Water Characteristics.

(Refer Slide Time: 00:33)

The key concepts covered in today’s class, are propeller open water diagram. The relation
between the open water characteristics and the blade element diagram that we have studied
earlier and the bollard condition and zero thrust condition for a marine propeller.
(Refer Slide Time: 00:51)

Now, let us look into the typical coefficients that we have discussed for a marine propeller.
The open water characteristics are actually the plot of these coefficients for different
operation conditions. So, the first one here we have the thrust coefficient KT which is the
thrust non-dimensionalized by ρ n2 diameter to the power 4 as we have seen in the
dimensional analysis and the second one is the torque coefficient KQ.

So, the open water characteristics of a marine propeller basically consists of the variation
of thrust and torque coefficients over an operation range of the propeller which is defined
by the advance coefficient J. Which is the velocity of advance VA/ n D when n is the
rotational speed in RPS.

Now, what is the efficiency the open water efficiency of the propeller? Here, in open water
we are considering that there is no ship in front of the propeller. So, it is the uniform
velocity of advance that the propeller is facing and it is generating a thrust T absorbing a
torque Q and we represent using non dimensional coefficients KT and KQ.

So, the open water efficiency in this condition will be thrust times the velocity of advance
which is the output power divided by the input power (2 π n multiplied by Q). So, if we
use these equations for KT and KQ, we will be getting this expression KT/ KQ × J/2π as the
open water efficiency of the propeller; so, this is the open water efficiency.
Now, how will this plot look like? The open water diagram for a propeller, the relation
between KT, KQ, ηO the open water efficiency with the advance coefficient J, this is what
we call the open water diagram. We have KT and 10 KQ here plotted as a function of J the
advance coefficient and ηO is the open water efficiency. Now, it is observed that the value
of KQ is much lower than KT that is why to put into perspective in the same diagram 10KQ
is plotted instead of KQ in the open water diagram this is the standard norm for marine
propellers.

So, we see that this curve KT and also 10KQ they decrease with the increase of J. Now,
what does increase of J imply? J is VA/n D; so, as J increases either VA can increase or n
can decrease for a propeller of a specific diameter ok or both can happen. So, as J increases
the thrust coefficient and torque coefficient decreases from a highest value at J equal to 0
here both these coefficients have the highest value and they gradually decrease at high J
values.

Now, in terms of propeller loading high values of J corresponding to lower propeller

loading and low values of J corresponding to high propeller loading. This is what will be
explained with the help of blade element diagram ok.

(Refer Slide Time: 05:15)

Let us explain this in the context of a representative section; so, the representative section
was basically a characteristic section of the propeller blade typically at 0.7R where the
characteristics of the section will be similar to that of the propeller. So, we will draw the
blade element diagram at that section and try to explain the open water diagram of the
propeller. How the thrust and torque behave with J with respect to the angles and forces
that we get for the blade element diagram at the characteristic section.

Now, this is the blade element diagram at 0.7R, we have the inflow velocity VA in the axial
direction, the rotational component, the tangential value 2 π n r. The resultant VR and the
three angles that we have the hydrodynamic inflow angle, the phase pitch angle phi, and
alpha which is the angle of attack nothing but ϕ - β.

Now, one thing you must understand that here we have not considered any induced
velocity. Just to keep it simple the blade element diagram is shown without any induced
velocity components that is why we have only VA and 2 π n r. Now, on the force side we
have the lift and drag force, the components of which gives the sectional thrust and torque
right.

Now, the total thrust and torque of the propeller blade section depends on the coefficient
of lift; and finally, the angle of attack of the particular section that is generated by this
particular section. Now, just to explain the open water diagram we assume that we are
drawing this blade element diagram for the characteristic or the representative section of
the propeller blade ok.

Now, we will see how the angle of attack changes with J which is the advance coefficient
of the propeller, because KT and KQ we have plotted as a function of J. So, in order to
understand the characteristics of the propeller in open water, we need to understand how
the angle of attack changes with J which is the advance coefficient of the propeller.
(Refer Slide Time: 07:50)

Now, let us take an extreme case of J = 0; now, J = VA /n D. So, J equal to 0 implies that
VA will be 0; so, at that case what will be your blade element diagram like, there is no
component in the axial direction. So, we have the resultant inclined at an angle ϕ which is
the phase pitch angle; so, β is 0 here, because VA is 0. Now, this corresponds to the point
on the open water diagram where J is 0.

In this case we have the angle of attack which is maximum because β is 0 in this case. So,
the section will produce the highest amount of lift as compared to other cases; hence, KT
and 10KQ here in the open water diagram will have the highest values at J equal to 0 which
is the case where the angle of attack is equal to the phase pitch angle of the blade section.

Now, let us try to advance towards the other conditions and gradually increase the value
of J and see how the diagram changes both the blade element diagram as well as the point
on the open water diagram.
(Refer Slide Time: 09:31)

Now, case two if we take a value of J as 0.1 here on the open water diagram what happens.
Now, again as I mentioned you can increase J in two ways, we do it here by increasing the
velocity keeping the rotational speed n same right. So, we give a small forward velocity
VA; so, that J increases to 0.1. Now, my blade element diagram is shown on the left, we
have a small velocity VA apart from 2 π r n and we have the resultant velocity VR which is
inclined to the horizontal by a small angle β.

So, we have now α is reduced as compared to the previous value because of the value of
VA now which is the axial velocity in the flow. Because of the decrease of α as compared
to case 1 what will happen, the sectional lift will decrease and which will result in a small
decrease of the thrust as well as torque. Because, we have seen that both thrust and torque
of the sections are related to the sectional lifts.

Drags also have a component; so, the lift and drag together will give the final sectional
thrust and torque ok.
(Refer Slide Time: 11:02)

Now, in a similar way let us go to case 3 and increase J further by increasing VA. So, we
go to the next step and again increase the VA such that J equal to 0.2 now and in the same
blade element diagram what happens now VR is inclined at a slightly higher angle which
results in a smaller angle of attack alpha compared to case 2 ok. So, in the same way our
KT and KQ will gradually reduce as we increase the value of VA. Now, VA increases
keeping the RPM same means that J is increasing.

(Refer Slide Time: 11:47)

(Refer Slide Time: 11:48)

(Refer Slide Time: 11:51)

Similarly, if we go on like this from 0.3 to 0.4 we see that the angle β gradually increases.
So, this angle β gradually increases which leads to the decrease of α; why? Because the
phase pitch angle ϕ of a particular blade section here we assume it at 0.7R which is
constant. So, if we gradually increase the J the angle of attack gradually decreases and the
sectional thrust and torque will decrease.
(Refer Slide Time: 12:24)

(Refer Slide Time: 12:26)

(Refer Slide Time: 12:29)

So, in this way if we go ahead to 0.7 and 0.8 the value of α decreases and KT and KQ will
gradually decrease. So, this gives an idea of the relation between the open water diagram
to the velocities of the blade element and the resultant forces. This is very important for
understanding the propeller open water characteristics. Now, we will go to the extreme
cases one by one.

(Refer Slide Time: 12:57)

Let us take up the case where α is 0, if we increase VA further such that the resultant VR is
inclined to the horizontal at an angle which is equal to the phase pitch angle; that means,
ϕ = β. Then we have the angle of attack of that particular blade section the characteristic
section that we have taken as 0. Now, what will happen to the open water diagram at this
point, because α is 0, the section will produce a very small amount of lift, why? Because,
typically these sections are cambered sections.

If this was a symmetric section, for symmetrical aerofoil sections that we have discussed
at 0 angle of attack they do not produce any lift. But for cambered sections if you remember
this lift coefficient with angle of attack for cambered sections even at 0 angle of attack it
has a finite value of lift coefficient right.

So, the section still produces a small amount of lift even at 0 angle of attack. But there will
also be drag and the resultant of lift and drag will be reflected in the final KT, because the
sectional thrust is a resultant of both lift and drag. So, let say if we neglect drag for now
because of that small lift, KT will have a very small value somewhere here. But it will still
not be 0; so, this is what is mentioned here the cambered section will still generate lift.

(Refer Slide Time: 14:55)

Now, let us go to the other case where J = 0; that means, the case where the propeller is
only rotating without any forward velocity. In the open water case, there is no ship; so, we
have considered that the propeller is rotating as well as the velocity of advance it is moving
forward at VA. In the open water case, the ship is not considered and the propeller is
rotating and moving at a velocity of advance VA.
What if we say that V A = 0? Which gives the condition J = 0? In naval architecture
terminology we mention this as the bollard pool condition. For tugs which are used for
towing duty, the bollard pool is very important where the tug or the boat is attached to a
bollard which is on shored and the propeller is rotated at different RPM and the pull exerted
on the tow dope is determined.

Now, in this process what is happening the ship is not moving forward, but the propeller
is rotating. Because the propeller is rotating as we have seen in the blade element diagram,
it has the highest angle of attack at J equal to 0; so, it will give a high value of thrust and
also there will be a high value of torque. So, this condition where the propeller revolves
without advancing forward is called the bollard pool condition or the static condition.

If we relate it to the slip that we have discussed in propeller geometry, this is the condition
of 100 percent slip because the propeller is not moving forward and only rotating. So, this
condition is the extreme case here for J equal to 0 where we have the highest value of KT
and KQ and by definition efficiency is 0, because efficiency is given by KT/ KQ × J /2 π
ok. So, at in the bollard pool condition we have the highest KT and KQ.

(Refer Slide Time: 17:11)

This is the blade element diagram we have already discussed where we have the highest
value of angle of attack equal to the phase pitch angle.
(Refer Slide Time: 17:22)

Now, on the other side what happens when KT is equal to 0, because we have considered
the case just now where the angle of attack is 0. So, even at 0 angle of attack the cambered
section will provide some lift and so, there will be a small value of thrust. But how do we
relate the condition where KT or the thrust coefficient is 0 in the open water diagram, how
do we relate it to the blade element diagram.

So, this is again the blade element diagram for the representative section, KT is 0, if we
neglect drag. Now, this is very important here, sectional drag also plays a role in lowering
the value of KT; let us, for simplicity neglect the drag first; so, to get KT equal to 0 the lift
should be 0. Now, the lift is 0 when the resultant velocity is inclined at an angle which is
in lined with the no lift line of the section.

So, again if I draw the lift coefficient versus angle of attack for the blade section here. This
is the value of α0 which is the negative angle of attack or the no lift angle of attack where
the lift generated by the section is 0. So, when VR the resultant velocity is aligned on the
other side; that means, on the line where the foil has no lift this angle α0, at that case we
will have the sectional lift is equal to 0.

So, if we neglect drag that will give us the condition where the thrust coefficient of the
propeller is 0, I hope this is understood. So, this α = α0, then we have the thrust coefficient
is equal to 0 when the VR is aligned with the no lift line. Now, what happens if we take
drag into consideration; if we do that lift will be 0, dL generated by the section because
the VR is aligned with the no lift line.

But in this particular condition dD will not be 0, because the section will have a small
value of drag; so, it will lead to a small negative value of KT. So, negative KT will arise
due to the contribution of the drag, this will cause a –dT/Z of that particular section which
will result in the negative KT. So, ideally for a realistic scenario if we take a representative
section the resultant velocity should be at an angle slightly less than the no lift angle shown
here.

So, that the small component from the lift generated is neutralized by the drag generated
from the section ok. To get the resultant KT of the propeller blade section as 0 ok. So, if
we consider the blade section the resultant value from the lift should cancel out the
component from the drag which gives the sectional thrust. So, that the total thrust
generated by the section will be 0 in a realistic scenario ok.

So, if we do not consider drag then VR is aligned with the no lift line for KT equal to 0, if
we consider drag the angle should be slightly lower because of the effect of drag and lift
to be cancelling each other ok.

(Refer Slide Time: 22:05)

So, now let us go to this condition it is called the feathering condition where KT equal to
0; so, again KT equal to 0 implies that the open water efficiency will also be 0. So, in the
propeller open water diagram the diagram should be drawn in such a way that ηO should
be 0 at the point KT is 0. And the nature of ηO, the open water efficiency is such that it
gradually increases and it reaches a maximum value and after that the value of ηO the drop
is very sharp. So, it sharply declines to a value of 0 at KT equal to 0.

But one must consider that at KT equal to 0, KQ is still not 0 KQ is still positive, why?
Because at KT equal to 0 the component of lift and drag will also give a small KQ. So, KQ
will become 0 at a J value which will be higher than the J at which KT is 0 ok. So, the
condition where the thrust coefficient is 0 is called the feathering condition and it
corresponds to the case where we call the effective slip is 0.

Now, the slip ratio as we have seen is defined by this expression where Pe is the effective
pitch of the propeller blade. And we have seen that the action of a marine propeller can be
defined with respect to a screw of the pitch which is equivalent to the propeller pitch. So,
using that concept of screw pitch we define the slip of the propeller blade and at zero
effective slip we will have the thrust coefficient 0 in the open water diagram.

So, if we substitute this, we will get at KT equal to 0 if we put the effective slip as 0 we
can get the advance coefficient J is given by the effective pitch by diameter at which the
KT is 0. Now, the case where KQ will be 0 will be slightly higher with respect to the J value
depending on the relative values of the thrust and torque generated by the blade section. If
we again think of the blade section diagram for the propeller blade ok.

So, propeller open water characteristics is very important in the context of marine
propulsion. Because, when we try to understand the characteristics of a propeller as a
separate entity open water diagram is the basic estimate of the propeller thrust and torque
with the change in the propeller loading condition which is J. So, different propellers will
have different thrust and torque characteristics which will be given with the help of open
water diagram; so, this is the most standard way of expressing propeller characteristics.

In the behind condition the properties of a propeller in terms of characteristic performance

its hydrodynamics will change because of the design of the ship the flow into the propeller
will change. But the open water characteristics are the intrinsic characteristics of a
propeller. So, this hydrodynamic performance is very important to estimate the design of
a propeller when it is used in a specific ship.
And we will use these open water characteristics to evaluate propeller design as well as
performance for different cases when we do ship powering. This will be all for today’s
class.