13-08-2024

Dr. D. D. Ebenezer
1 13 Aug 2024

B. Tech. NA&SB. 2021-25. 20-215-0502

Department of Ship Technology
CUSAT, Kochi 682022
3 credits

Dr. D. D. Ebenezer
Adjunct Faculty
9446577239
ebenezer.cusat@gmail.com

Jul-Dec
2024 Only for personal use by CUSAT NA&SB students

Dr. D. D. Ebenezer
2 Course Content

Jul-Dec
2024

Dr. DD Ebenezer 1
 13-08-2024

Dr. D. D. Ebenezer
3 Module 3
Today
• 3.1 Design Cycle for Propellers
• 3.2 Propeller families and series

Jul-Dec
2024

Dr. D. D. Ebenezer
4 Carlton

A design is a solution to a
constrained optimisation problem

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Dr. D. D. Ebenezer
5 Carlton. Chap 22. Propeller Design.
• The finished propeller depends for its success on the satisfactory integration of
several scientific disciplines: these are hydrodynamics, stress analysis, metallurgy
and manufacturing technology, with supportive inputs from mathematics, dynamics
and thermodynamics.
• It may not be possible to find a single unique solution for a particular propulsion
problem
• Propeller design and manufacture commences with the definition of the problem
and this implies that a sufficient and unambiguous specification for the propulsion
problem has been produced. This design specification must include the complete
definition of the inputs and required outputs, including any permissible deviations
from these definitions, as well as any constraints that may be placed on the design.
• The design loop (see Fig. 22.1 and 22.2 in Carlton) must be flexible enough should an
unresolvable conflict arise with the original definition of the design problem, to
allow for an appeal to be made to change the definition of the design problem.
Jul-Dec
2024

Dr. D. D. Ebenezer
6 3.1 Propeller Design
• Carlton
• Design Constraints – more than one. Eg. Limits on the max dia of prop,
efficiency, and radiated noise
• Design involves constrained optimization

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7 3.1 Propeller Design
• Energy Efficiency Design Index (EEDI)
• CO2 production

Jul-Dec
2024

Dr. D. D. Ebenezer
8 USA Transportation 29%. World Shipping 3-4%
• The primary sources of greenhouse gas
emissions by economic sector in the
United States are:
• Transportation (29% of 2021 greenhouse
gas emissions) – The transportation sector
generates the largest share of greenhouse
gas emissions. Greenhouse gas emissions
from transportation primarily come from
burning fossil fuel for our cars, trucks,
ships, trains, and planes. Over 94% of the
fuel used for transportation is petroleum
based, which includes primarily gasoline
and diesel.
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Dr. D. D. Ebenezer
9
• Self-Study
• Hotel load is the amount of power
a ship needs to support its
everyday operations and keep it a
livable space. It's the electrical
load caused by all systems on a
ship other than propulsion, such
as lighting, air conditioning, and
galleys. Hotel load is independent
of the ship's forward speed.

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2024

Dr. D. D. Ebenezer
10 EEDI
• Self-Study

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11
• Methods to decrease
the Actual EEDI and
meet the
requirement

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2024

Dr. D. D. Ebenezer
12 Propeller Type

• Factors affecting choice of

propeller type. See Table
22.1 in the next slide.

• Efficiencies of various
types of propellers – see
L11S26.

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Dr. D. D. Ebenezer
13 Factors affecting choice of Propulsor
• Carlton
• Types of Propellers
• Fixed Pitch Prop
• Controllable Pitch Prop
• Ducted Prop
• Azimuth Prop
• Contra-rotating Prop
• Cycloidal Prop

• Details of some of these types will be presented in the last module

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2024

Dr. D. D. Ebenezer
14 Prop Design Basis

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15 Mission Profile
• The mission profile (next slide) shows that a “single design point” approach
may not be enough
• Design = choosing diameter, pitch distribution, blade area, section forms …

Jul-Dec
2024

Dr. D. D. Ebenezer
16 Ship mission profiles
• Percentage of time in which the ship travels
at each speed
• MCR = Maximum Continuous Rating. It is the
maximum power output the engine can
produce while running continuously (one
year average) at safe limits and conditions. It
is specified on the engine nameplate and in
the Technical File of the marine diesel engine.
• The 90% MCR is usually the contractual
output for which the propeller is designed.
• Ships usually operate at the nominal
continuous rating (NCR) which is 85% of
90% of the MCR. Thus, the usual output at
which ships are operated is around 75% to
Jul-Dec 77% of MCR. (0.85*0.9 = 0.765)
2024

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Dr. D. D. Ebenezer
17 Propeller Design Design basis =
power absorbed
by prop, prop rpm,
• Carlton. Fig. 22.22. ship speed
1of2
• Example of a simplified
design procedure

• Study this figure now. Study

it again at the end of the
sem when you will
understand it better.

No

Jul-Dec Yes
2024

Dr. D. D. Ebenezer
18 Propeller Design
• Carlton. Fig. 22.22.
2of2
• Example of a No
simplified design
Yes
procedure

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2024

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Dr. D. D. Ebenezer
19

Read books, magazines, and journals

and become outstanding Naval Architects

Jul-Dec
2024

Dr. DD Ebenezer 10
 23-08-2024

Dr. D. D. Ebenezer
1 23 Aug 2024

B. Tech. NA&SB. 2021-25. 20-215-0502

Department of Ship Technology
CUSAT, Kochi 682022
3 credits

Dr. D. D. Ebenezer
Adjunct Faculty
9446577239
ebenezer.cusat@gmail.com

Jul-Dec
2024 Only for personal use by CUSAT NA&SB students

Dr. D. D. Ebenezer
2 Course Content

Jul-Dec
2024

Dr. DD Ebenezer 1
 23-08-2024

Dr. D. D. Ebenezer
3 Module 3
Earlier
• 3.1 Design Cycle for Propellers

Today
• 3.2 Propeller families and series
• 3.3a Design using 𝐵 − δ charts

Later
• 3.3b Design using 𝐵 − δ charts. Numerical Example.
• 3.4 Cavitation Limit
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2024

Dr. D. D. Ebenezer
4

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5
• Carlton

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Dr. D. D. Ebenezer
6
Formats for (Series) Prop Data
• Molland Chap 12.1.2 and 12.1.3. Formats with various dependent and
independent variables.

• Molland Fig. 12.9 is a sample 𝐾 ,

𝐾 chart that shows how the
open water characteristics of a
prop can be presented. The next
slide shows a sample 𝐵 − δ
chart.

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2024

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Dr. D. D. Ebenezer
7 Prop Power Coefficient

• Carlton
• Prop Power Coefficient, 𝐵
• Prop Power Coefficient 𝐶
• 𝐵 =𝐶
• In many charts, 𝑃 has units
of hp and N is in rpm
• For 𝑃 see Carlton 22.6.1
• Power = force*velocity = kg (m/s2) (m/s)
• Some 𝐵 − 𝛿 charts show 1 imperial hp = 76 kg m/s. It
should be 76.07 kgf m/s or 745.7 watts. 1 metric hp =
Jul-Dec 735.5 watts.
2024

Dr. D. D. Ebenezer
8 Wageningen B4.40 propeller. Z = 4. BAR = 0.40
Molland
Fig.
16.5.
𝐵 and δ
are
P/D

dimen-
sional

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Dr. D. D. Ebenezer
9 𝐵 − δ chart
• In the 𝐵 − δ chart, 𝐵 is on the x axis and 𝑃/𝐷 is on the y axis.
• Constant δ and constant efficiency, 𝜂, (contour) lines are shown.
• 𝐵 is often an input for the prop design
• Use 𝐵 and find the δ and 𝑃/𝐷 at the maximum efficiency
• A dashed line runs through the max efficiency points. Its equation is known.

Jul-Dec
2024

Dr. D. D. Ebenezer
Principal Standard Series
• Carlton. Charts and equations are based on experiments. B series is the most widely used one.

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11
Typical
optimum
prop
efficiencies

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2024

Dr. D. D. Ebenezer
12 Standard Series Propellers

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Dr. D. D. Ebenezer
13 Standard Series Propellers
• Molland

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Dr. D. D. Ebenezer
14 Standard Series Propellers. Wageningen

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15 Standard Series Propellers. Japanese AU Series.

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2024

Dr. D. D. Ebenezer
16 Gawn
• Data presented by Gawn

BAR can be > 1. Explain.

• Larger dia of 503 mm
compared to Wageningen
which has 250 mm dia
• Uniform pitch does not
vary with r/R but pitch
angle varies
• Developed blade outline
is elliptical. See L11S30

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2024

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Dr. D. D. Ebenezer
17 Standard Series Propellers. Gawn
• The Blade Example of a non-filleted pole (left)
and a filleted pole (right)
Area Ratio,
BAR, can
be greater
than one.
Explain.
• Note the
radii of the
fillets (in
inches)

Jul-Dec
2024

Dr. D. D. Ebenezer
18 Gawn

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Dr. D. D. Ebenezer
19 KCA Gawn-Burrill Series
• Tested at various
cavitation
numbers

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2024

Dr. D. D. Ebenezer
20 KCA Gawn-Burrill Series

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21 CPP and Ducted Propellers
• Images on the next slide

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Dr. D. D. Ebenezer
22 Controllable Pitch Propeller
• https://global.kawasaki.com/en/mobility/marine/machinery/propeller.html
• Mechanisms inside the boss make it possible to change the pitch by rotating the blade about
an axis
• The blades are bolted to the hub

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Dr. D. D. Ebenezer
23 Ducted Propellers

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Dr. D. D. Ebenezer
24

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Dr. D. D. Ebenezer
25 Pumpjet Propulsor
• L. Lu et al. Numerical investigations of tip clearance flow characteristics of a
pumpjet propulsor, IJNAOE, 2018.

Jul-Dec
2024

Dr. D. D. Ebenezer
26
• Sub with
pumpjet
propulsion

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Dr. D. D. Ebenezer
27 Pumpjet Propulsors
• https://www.shapeways.com/product/6ZFNQFA3G/1-144-pump-jet-
seawolf-submarine-propeller
3D views of a pumpjet propulsor.

• G&G Fig. 12.10

Jul-Dec
2024

Dr. D. D. Ebenezer
28 AUV Propeller

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Dr. D. D. Ebenezer
29 AUV
• Figure 1. Portable AUV construction. 1: Propeller, 2: communication sonar, 3:
Global Positioning System (GPS), 4: wireless antenna, 5: strobe light, 6: rings
for the crane, 7: vertical rudder, 8: horizontal wing, 9: Doppler Velocity Log
and inertial navigation system, 10: bathymetric side scan sonar and 11: CCD.

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2024

Dr. D. D. Ebenezer
30

3.3a Design using 𝐵 − δ charts

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31

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Dr. D. D. Ebenezer
Symbols
32
• 𝐾 = Thrust Coefficient = 𝑇 / (𝜚𝑛 𝐷 ) • QPC = 𝑃 / 𝑃

• 𝐾 = Torque Coefficient = 𝑄 / (𝜚𝑛 𝐷 ) • QPC = 𝜂 𝜂 𝜂 = 𝑃 / 𝑃

• 𝑡 = thrust deduction factor
• 𝐾 = Torque Coefficient in Open Water
• 𝑤 = 𝑉 − 𝑉 /𝑉 = Taylor wake fraction
• 𝐾 = Torque Coefficient behind the ship
• 1 − 𝑤 = 𝑉 /𝑉
• 𝜂 = relative rotative efficiency = 𝐾 /𝐾
• 𝜂 = open water efficiency
• 𝐽 = mean advance coefficient = 𝑉 /(𝑛𝐷) = THP in open water/DHP
• 𝑃 = Power required to drive the ship = • 𝜂 = hull efficiency =
Resistance × Ship speed
• 𝜂 = 1 − 𝑡 /(1 − 𝑤 )
• 𝑃 = Power delivered by engine to the prop
= Angular speed × Torque = • 𝜂 =
2π𝐾 (𝜚𝑛 𝐷 )
Jul-Dec • 𝜂 =
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Dr. D. D. Ebenezer
33 Inputs for Prop Design aka Prop Design Basis
• aka = also known as
• The inputs usually used for the design are 1) the power absorbed = power
delivered to the prop or the resistance of the ship 2) ship speed 3) shaft rps

Jul-Dec
2024

Dr. D. D. Ebenezer

34 Propeller Design
• What is propeller design?
• It is the design or selection of all the details of the propeller that is optimum
(max efficiency) or best subject to the constraints. Design begins with inputs
and constraints and ends with design drawings based on which manufacturing
drawings can be prepared.
• What are the required inputs?
• Essential: 1) The speed of the ship 2) the resistance of the ship or the power delivered to the
prop
• The shaft rpm (see the prev slide) is often an input
• Additional: Desirable or undesirable frequencies, Thrust deduction, Velocity in the plane of
the prop, or the wake fraction,

• What are the outputs of the design?

• 1) Diameter 2) Area ratio 3) Number of blades 4) Series info or blade details 5) thrust
Jul-Dec
generated in the behind-ship condition 6) rpm if it is not an input
2024

Dr. DD Ebenezer 17
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Dr. D. D. Ebenezer
35 Steps in the Design of a Prop. See worked example.
1. Choose a type of prop. Eg. B Series.
2. Choose the number of blades. Eg. Z = 4
3. Choose a Blade Area Ratio. Eg. 0.40
. .
4. Use the inputs [𝑃 , 𝑁, 𝑉 = (1 − 𝑤 )𝑉 ] to find 𝐵 = 𝑁𝑃 /𝑉 . 𝑃 in hp, 𝑁 in
rpm, 𝑉 in knots.
5. Find the optimum efficiency by using a 𝐵 − δ chart or Eq. 22.2 in Carlton.
6. Find the corresponding 𝑃/𝐷 and δ = 𝑁𝐷/𝑉 . Use δ to find the dia, 𝐷.
7. Repeat for various Blade Area Ratios
8. Repeat for various number of blades
9. Repeat for various Series
Jul-Dec
2024
10. Find the ‘best’ propeller with the max efficiency

Dr. D. D. Ebenezer
36 Carlton
• 22.6.1 Determination of dia
• 22.6.2 Determination of P/D
• 22.6.3 Determination of open
water efficiency

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Dr. D. D. Ebenezer
37 Wageningen B4.40 propeller. Z = 4. BAR = 0.40
Molland
Fig.
16.5.
𝐵 and δ
are
dimen-
sional

Jul-Dec
2024

Dr. D. D. Ebenezer
38 Carlton
• See IntTest02.m
• Fig. 22.11 is shown later

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Dr. D. D. Ebenezer
39 Carlton

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Dr. D. D. Ebenezer
40

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Dr. D. D. Ebenezer
41 Design Considerations. Read Carlton Sec. 22.7
1. Direction of Rotation
2. Blade Number
3. Diameter, Pitch-Diameter Ratio and Rotational Speed
4. Blade Area Ratio
5. Section Form
6. Cavitation
7. Skew
8. Hub Form
9. Shaft Inclination
10. Duct Form
11. The Balance Between Propulsion Efficiency and Cavitation Effects
12. Propeller Tip Considerations
13. Propellers Operating in Partial Hull Tunnels
14. Composite Propeller Blades
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Dr. D. D. Ebenezer
42 Direction of Rotation

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43 Carlton. Chap 22.

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44

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45

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Dr. D. D. Ebenezer
46 Carlton. Chap 22.

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Dr. D. D. Ebenezer
47 Carlton. Chap 22.

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2024

Dr. D. D. Ebenezer
48 Carlton. Chap 22.

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Dr. D. D. Ebenezer
49 Carlton. Chap 22.

Jul-Dec
2024

Dr. DD Ebenezer 25
 02-09-2024

Dr. D. D. Ebenezer
1 02 Sep 2024

B. Tech. NA&SB. 2021-25. 20-215-0502

Department of Ship Technology
CUSAT, Kochi 682022
3 credits

Dr. D. D. Ebenezer
Adjunct Faculty
9446577239
ebenezer.cusat@gmail.com

Jul-Dec
2024 Only for personal use by CUSAT NA&SB students

Dr. D. D. Ebenezer
2 Course Content

Jul-Dec
2024

Dr. DD Ebenezer 1
 02-09-2024

Dr. D. D. Ebenezer
3 Module 3
Earlier
• 3.1 Design Cycle for Propellers
• 3.2 Propeller families and series
• 3.3a Design using 𝐵 − δ charts

Today
• 3.3b Design using 𝐵 − δ charts. Numerical Example.
• 3.4a Cavitation Limit

Jul-Dec
2024

Dr. D. D. Ebenezer
4

3.3b Design using 𝐵 − δ charts

Jul-Dec
2024

Dr. DD Ebenezer 2
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Dr. D. D. Ebenezer
5 Molland. Numerical Example.
• Design using a 𝐵 − δ chart

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2024

Dr. D. D. Ebenezer
6
• If the optimum diameter is less than the allowed
diameter, use the opt dia. Otherwise, use the

Fig. 16.5 is repeated on the next slide.

allowed dia.

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2024

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Dr. D. D. Ebenezer
7 Wageningen B4.40 propeller. Z = 4. BAR = 0.40
Molland
Fig. 16.5.

𝐵 and δ
are
dimen-
sional
P/D

Jul-Dec
2024

Dr. D. D. Ebenezer
8 Wageningen B Series
• For the Wageningen B Series propeller, charts are available for only the
combinations of Z and BAR shown in Carlton Table 6.4

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2024

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Dr. D. D. Ebenezer
9 Optimal B Series Propeller
• Choose many values of Z. Say Z = 3, 4, 5,

• For each value of Z, use the charts for many values of BAR= 𝐴 /𝐴 . Choose the values of BAR from
Carlton Table 6.4. For each combination of Z and BAR, there is a separate chart.
• Find the maximum efficiency for each propeller from the chart and fill the table below
• If the diameter corresponding to the max efficiency is greater than the allowed diameter, find the
efficiency for the specified values of 𝐷, 𝐵 and δ and enter it in the table below.
• Find the Z and BAR for the highest efficiency in the table
Wageningen B Series
BAR = 𝐴 /𝐴 0.35 0.50 0.65
Z=3
𝜂
BAR 0.40 0.55 0.70
Z=4
𝜂
BAR 0.45 0.6 0.75
Z=5
Jul-Dec 𝜂
2024

Dr. D. D. Ebenezer
10
• From the inset in Fig. 22.11a, note that as the BAR =
𝐴 /𝐴 increases, the optimum diameter decreases
• From the inset in Fig. 22.11b, note that as the BAR
increases, the optimum P/D is nearly constant and the
optimum efficiency reduces

BAR = 𝐴 /𝐴
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Dr. D. D. Ebenezer
11

• Will the propeller cavitate?

• Find out using Burrill’s and Keller’s Cavitation Criteria.
Jul-Dec
2024

Dr. D. D. Ebenezer
12 Carlton. 3rd Ed. P 82.

• 𝐵 − δ chart
cannot be used
when the 𝑉
tends to zero.
For tugs and
trawlers, 𝑉 is
very low.
• Max 𝐵 is 80
in the B4.40
chart. Min 𝐵
is about 2. The
scale is non-
Jul-Dec
linear.
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Dr. DD Ebenezer 6
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13
G&G. Cavitation at a
blade section

• Study this slide and the next

three slides together.

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Dr. D. D. Ebenezer
14

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3.4 Cavitation Limit
15 Ghose and Gokarn
• Cavitation occurs when the pressure drops below the vapour pressure.
• The answer in G&G is correct. See the next slide for the explanation and details.

Jul-Dec
2024

Dr. D. D. Ebenezer
16 Explanation for Example 1 in G&G. See L14S13&14
• Cavitation occurs on a blade section when the relative velocity is 32 m/s. This velocity is
based on only the velocity of advance and the rotational speed. When the water flows over a
blade section at radius 𝑟, it accelerates, the velocity increases to a certain value and the
pressure drops to the vapour pressure. Find the location on the blade where the pressure
equals the vapour pressure to find where cavitation occurs.
• When 𝑉 + 2𝜋𝑛𝑟 = 𝑉 = 32 cavitation occurs
• Bernoulli’s theorem: 𝑝 + 0.5𝜌𝑉 = 𝑝 + 𝜌𝑔ℎ + 0.5𝜌𝑉 = 141.546e3 + 0.5𝜌32 = K =
Constant
• 𝐾 = 141.546e3 + 0.5 ∗ 1025 ∗ 32 = 666.346e3
• When cavitation begins, 𝑝 + 0.5𝜌𝑉 = K and 𝑝 = 𝑝 = 1.704e3.
• Therefore, 0.5𝜌𝑉 = K − 1.704𝑒3 = 666.346e3 − 1.704e3 = 664.642e3

• 𝑉 = 664.642e3 /(0.5 ∗ 1025) = 36.012 m/s

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17 Cavitation Number. Various Definitions.

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Dr. D. D. Ebenezer
18

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19
Cavitation Number.
Values based on
Various Definitions.

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2024

Dr. D. D. Ebenezer
20

Jul-Dec
2024

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Dr. D. D. Ebenezer
21

Read books, magazines, and journals

and become outstanding Naval Architects

Jul-Dec
2024

Dr. DD Ebenezer 11
 03-09-2024

Dr. D. D. Ebenezer
1 03 Sep 2024

B. Tech. NA&SB. 2021-25. 20-215-0502

Department of Ship Technology
CUSAT, Kochi 682022
3 credits

Dr. D. D. Ebenezer
Adjunct Faculty
9446577239
ebenezer.cusat@gmail.com

Jul-Dec
2024 Only for personal use by CUSAT NA&SB students

Dr. D. D. Ebenezer
2 Course Content

Jul-Dec
2024

Dr. DD Ebenezer 1
 03-09-2024

Dr. D. D. Ebenezer
3 Module 3
Earlier
• 3.1 Design Cycle for Propellers
• 3.2 Propeller families and series
• 3.3a Design using 𝐵 − δ charts
• 3.3b Design using 𝐵 − δ charts. Numerical Example.
• 3.4a Cavitation Limit
Today
• 3.4b Cavitation Limit Charts

Jul-Dec
2024

Dr. D. D. Ebenezer
4 Pressure Distribution L10S06
• 𝑃 = free-stream static pressure = Reference pressure
• Positive angle of attack . High stagnation pressure near the nose.
• High (positive) pressure at the face. Local pressure > 𝑃 .
• Low (negative) pressure at the back. Local pressure < 𝑃 .
• Excess pressure = Pressure – Ref Pressure is shown. Far away
from the airfoil, the excess pressure is zero and the pressure is
equal to the reference pressure.
• Negative pressure means that the pressure is less than the
reference pressure

• At the stagnation point, the velocity is zero and

Jul-Dec the pressure is maximum.
2024

Dr. DD Ebenezer 2
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Dr. D. D. Ebenezer
L14S16
5 Explanation for Example 1 in G&G.
• Cavitation occurs on a blade section when the relative velocity is 32 m/s. This velocity is
based on only the velocity of advance and the rotational speed. When the water flows over a
blade section at radius 𝑟, it accelerates, the velocity increases to a certain value and the
pressure drops to the vapour pressure. Find the location on the blade where the pressure
equals the vapour pressure to find where cavitation occurs.
• When 𝑉 + 2𝜋𝑛𝑟 = 𝑉 = 32 cavitation occurs
• Bernoulli’s theorem: 𝑝 + 0.5𝜌𝑉 = 𝑝 + 𝜌𝑔ℎ + 0.5𝜌𝑉 = 141.546e3 + 0.5𝜌32 = K =
Constant
• 𝐾 = 141.546e3 + 0.5 ∗ 1025 ∗ 32 = 666.346e3
• When cavitation begins, 𝑝 + 0.5𝜌𝑉 = K and 𝑝 = 𝑝 = 1.704e3.
• Therefore, 0.5𝜌𝑉 = K − 1.704𝑒3 = 666.346e3 − 1.704e3 = 664.642e3

• 𝑉 = 664.642e3 /(0.5 ∗ 1025) = 36.012 m/s

Jul-Dec
2024

Dr. D. D. Ebenezer
6 • Historical
Cavitation Criteria
Criteria for no
Cavitation
• Thrust/𝐴 < 78
• 𝑣 = 𝜔𝑅 < 61 m/s
• Burrill (1943)
Criterion
• Keller (1966)
Criterion
• When several
criteria are in use,
check all of them
Jul-Dec
2024

Dr. DD Ebenezer 3
 03-09-2024

Dr. D. D. Ebenezer
7 G&G. Burrill’s Cavitation Diagram

• G&G

Thrust Loading Coefficient

When the cavitation number increases the upper limit for the
thrust loading coefficient increases
Jul-Dec
2024

Dr. D. D. Ebenezer
8 Carlton Burrill’s Cavitation Diagram
• This figure is from Carlton and has more
details than the fig in G&G

Jul-Dec
2024

Dr. DD Ebenezer 4
 03-09-2024

Dr. D. D. Ebenezer
9

𝜏 is based on 𝐴 . But
BAR = 𝐴 /𝐴 ≅ 𝐴 /𝐴

Jul-Dec
2024

Dr. D. D. Ebenezer
10
• Curve-fit
equations for
Burrill’s diagram

Jul-Dec
2024

Dr. DD Ebenezer 5
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Dr. D. D. Ebenezer
11 2.9 Prevention of Cavitation

Jul-Dec
2024

Dr. D. D. Ebenezer
12 Cavitation Bucket

Jul-Dec
2024

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Dr. D. D. Ebenezer
13 𝑃 −𝑃
𝐶 =
0.5𝜌𝑉
𝑃 −𝑃 ∆𝑝
= = <0
0.5𝜌𝑉 𝑞
• 𝑡/𝐶 is max
thickness / Chord
Length
• When 𝑡/𝐶 is
small, the angle
of attack in the
non-cavitating
region is small
but a lower value
of −𝐶 is
allowed
Note the minus sign in −𝐶 and in L14S14
Eqs. (6.3) and (6.4)
Jul-Dec
2024

Dr. D. D. Ebenezer
14
Burrill. See
the next slide
for details

• Note that Z
is not
mentioned
in the
analysis

Jul-Dec
2024

Dr. DD Ebenezer 7
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Dr. D. D. Ebenezer
15 Design using Burrill’s Cavitation Criterion

1. Find 𝑉 . and use it to find the cavitation number 𝜎 .

2. Use 𝜎 . and the Burrill chart or Eq. (6.14) to find the max thrust loading coeff 𝜏
3. Use the expression for 𝜏 in Eq. (6.10) to find the projected area 𝐴
4. Use 𝐴 and Eq. (6.11) to find the developed area 𝐴 ≅ expanded area 𝐴
5. Calculate the expanded blade area ratio 𝐴 /𝐴 = 𝐴 / 𝜋𝐷 /4
Jul-Dec
2024

Dr. D. D. Ebenezer
16

See Eq. (6.14)

See Eq. (6.11)

Jul-Dec
2024

Dr. DD Ebenezer 8
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Dr. D. D. Ebenezer
17 Twin Screw. Design using Keller’s Cavitation Criterion.

• See L15S11 Eq. (6.16)

• 𝑘 = 0 for twin screw
Jul-Dec
2024

Dr. D. D. Ebenezer
18 Twin Screw. Design using Keller’s Cavitation Criterion.

Two propellers
Z = number of blades

Jul-Dec
2024

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Dr. D. D. Ebenezer
19

FIG. 17. Comparison of coefficient of pressure at lowest and highest speed of

DARPA SUBOFF predicted using 2D axisymmetric simulation.
Jul-Dec
2024

Dr. D. D. Ebenezer
20 Angle of Attack and Cavitation

Jul-Dec
2024

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21

Jul-Dec
2024

Dr. D. D. Ebenezer
22
• See L15S21 for definition
of angles

Jul-Dec
2024

Dr. DD Ebenezer 11
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Dr. D. D. Ebenezer
23

Jul-Dec
2024

Dr. D. D. Ebenezer
24 Angle of Attack and Cavitation

Jul-Dec
2024

Dr. DD Ebenezer 12
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Dr. D. D. Ebenezer
25

Read books, magazines, and journals

and become outstanding Naval Architects

Jul-Dec
2024

Dr. DD Ebenezer 13
 09-09-2024

Dr. D. D. Ebenezer
1 Dr. D. D. Ebenezer 09 Sep 2024

B. Tech. NA&SB. 2021-25. 20-215-0502

Department of Ship Technology
CUSAT, Kochi 682022
3 credits

Dr. D. D. Ebenezer
Adjunct Faculty
9446577239
ebenezer.cusat@gmail.com

Jul-Dec
2024 Only for personal use by CUSAT NA&SB students
09/09/2024

Dr. D. D. Ebenezer
2 Course Content

Jul-Dec
2024 Dr. D. D. Ebenezer

Dr. DD Ebenezer 1
 09-09-2024

Dr. D. D. Ebenezer
3 Module 3
Earlier
• 3.1 Design Cycle for Propellers
• 3.2 Propeller families and series
• 3.3 Design using 𝐵 − δ charts
• 3.4 Cavitation Limit
Today
• 3.5 Design using 𝐾 and 𝐾 charts. Part I

Jul-Dec
2024 Dr. D. D. Ebenezer

Dr. D. D. Ebenezer
4

The Resistance vs Speed data are the inputs for design.

The 𝑃 is not known and 𝑛 is a variable.
If 𝑃 and 𝑛 are inputs, use the 𝐵 − δ chart.

Molland. Ship Resistance and Propulsion. Chap. 16. Propulsor Design Data

Carlton. Marine Propellers and Propulsion. Chap. 6.5 Standard Series Data

Jul-Dec
2024
Dr. D. D. Ebenezer 09/09/2024

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Dr. D. D. Ebenezer
5
1. Use the resistance, 𝑅,
and the speed of the
ship, 𝑉 .
• Molland
2. Find the required thrust,
• Before choosing
𝑇 = 𝑅/(1 − 𝑡), and the
the number of velocity of advance,
blades, choose the 𝑉 = 𝑉 (1 − 𝑤 ). These
Series. are the inputs for design.

• Note the 2 loops to

search in 2D space
of BAR and 𝑁

Jul-Dec
2024 Dr. D. D. Ebenezer

Dr. D. D. Ebenezer
6 Prop Design. Molland.
• For fixed 𝐷 and BAR,
• Molland: search in 2D space 𝑃/𝐷 , 𝑛 for the optimum prop
• Ebenezer: search in 2D space 𝑃/𝐷 , 𝐽 which is equivalent to 𝑃/𝐷 , 𝑛 as 𝑉 and 𝐷
are known.

• Details are on the following slides

Thrust = 486 kN
Dia = 5 m
Table 16.2 is on the next slide

Jul-Dec
2024 Dr. D. D. Ebenezer

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Dr. D. D. Ebenezer
7 Design Approach 1. Molland
1. Assume 𝐷 after considering constraints.
2. Choose 3 reasonable values of 𝑛. See Table 16.2. Ebenezer: Don’t do what
Molland has done! Choose 𝑛 such that 𝐽 is 0.4, 0.45, 0.5, 0.55, 0.6, 0.65, etc.
3. For 𝐷, 𝑛 , (𝐷, 𝑛 ), (𝐷, 𝑛 )
1. Calculate 𝐽 and 𝐾 for each set
2. From the chart, find 𝑃/𝐷 and 𝜂 for 𝑖 = 1, 2, 3
3. Draw a plot of 𝑛 vs 𝜂 . Interpolate and find the 𝑛 at which 𝜂 is max

4. Repeat for other values of 𝐷

Jul-Dec
2024 Dr. D. D. Ebenezer

Dr. D. D. Ebenezer
8 Molland Method – 3 interpolations
1. Choose a rps, 𝑛.
2. Calculate 𝐾 and 𝐽. Place a dot on the chart at (𝐽, 𝐾 )
3. Find the only (𝑃/𝐷)∗ at which the required 𝐾 and 𝐽 are met. This
involves finding a 𝐾 line that passes through your dot. See next 4 slides.
Interpolate 𝐾 (𝑃/𝐷) at a fixed 𝐽 to find (𝑃/𝐷). This (𝑃/𝐷) and the other
5 elements of the 6D space define a propeller that will deliver the 𝑇 at 𝑉 .
4. Find the 𝜂 of this prop. This involves the second interpolation as 𝑃/𝐷
found in the previous step will not be in the chart. See the next 4 slides.
5. Vary the rps, 𝑛. Interpolate the values of 𝜂 (𝑛) to find the 𝑛 at which the
𝜂 is max. This is the third interpolation. Then find the optimum 𝑛.
6. To make the interpolation easier, digital 𝐾 − 𝐽 can be used.
Jul-Dec
2024 Dr. D. D. Ebenezer

Dr. DD Ebenezer 4
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Dr. D. D. Ebenezer
9 Wageningen B4.40 Propeller
𝐾 Solid line
10𝐾 Dashed line
𝑱 = 0.627
𝜂 Solid line with a max (inverted U)

𝜂 = 0.57
,η

𝐾 = 0.263

Jul-Dec
2024 𝑱 Dr. D. D. Ebenezer

Dr. D. D. Ebenezer
10

𝑱 = 0.627

𝜂 = 0.570

𝐾 =
0.263

Jul-Dec
2024 P/D values are in parenthesis. Magenta (0.9), Cyan (1), Black (1.1), Red (1.2), Blue (1.3), Green (1.4)
Dr. D. D. Ebenezer

Dr. DD Ebenezer 5
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Dr. D. D. Ebenezer
11

𝑱 = 0.561

𝜂 = 0.582

𝐾 =
0.210

Jul-Dec
2024 P/D values are in parenthesis. Magenta (0.9), Cyan (1), Black (1.1), Red (1.2), Blue (1.3), Green (1.4)
Dr. D. D. Ebenezer

Dr. D. D. Ebenezer
12

𝑱 = 0.508

𝜂 = 0.575

𝐾 =
0.172

Jul-Dec
2024 P/D values are in parenthesis. Magenta (0.9), Cyan (1), Black (1.1), Red (1.2), Blue (1.3), Green (1.4)
Dr. D. D. Ebenezer

Dr. DD Ebenezer 6
 09-09-2024

Dr. D. D. Ebenezer
13 Interpolated Results
• Data from Molland Table 16.2 is plotted on this slide
• A 2nd order polynomial that fits the 𝐽 − 𝜂 data is found using Matlab. See
the figure. The max efficiency is 0.582 and the optimum 𝐽 is 0.559. The
Molland says that the max efficiency is 0.583 and the opt 𝐽 is 0.548 but does
not state if the 𝐽 − 𝜂 data was used. 𝑛 − 𝜂 data will yield a different
optimum 𝐽.

Jul-Dec
2024 Dr. D. D. Ebenezer

Dr. D. D. Ebenezer
14

Jul-Dec
2024
Dr. D. D. Ebenezer 09/09/2024

Dr. DD Ebenezer 7
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Dr. D. D. Ebenezer
15

Jul-Dec
2024 Dr. D. D. Ebenezer

Dr. D. D. Ebenezer
16

Jul-Dec
2024 Dr. D. D. Ebenezer

Dr. DD Ebenezer 8
 09-09-2024

Dr. D. D. Ebenezer
17

Jul-Dec
2024 Dr. D. D. Ebenezer

Dr. D. D. Ebenezer
18

Read books, magazines, and journals

and become outstanding Naval Architects

Jul-Dec
2024 Dr. D. D. Ebenezer

Dr. DD Ebenezer 9
 10-09-2024

Dr. D. D. Ebenezer
1 10 Sep 2024

B. Tech. NA&SB. 2021-25. 20-215-0502

Department of Ship Technology
CUSAT, Kochi 682022
3 credits

Dr. D. D. Ebenezer
Adjunct Faculty
9446577239
ebenezer.cusat@gmail.com

Jul-Dec
2024 Only for personal use by CUSAT NA&SB students

Dr. D. D. Ebenezer
2 Course Content

Jul-Dec
2024

Dr. DD Ebenezer 1
 10-09-2024

Dr. D. D. Ebenezer
3 Module 3
Earlier
• 3.1 Design Cycle for Propellers
• 3.2 Propeller families and series
• 3.3 Design using 𝐵 − δ charts
• 3.4 Cavitation Limit
• 3.5 Design using 𝐾 and 𝐾 charts. Part I
Today
• 3.6 Design using 𝐾 and 𝐾 charts. Part II
• 3.7 Types and advantages of propulsion plants
Jul-Dec
2024

Dr. D. D. Ebenezer
4
3.6 Design using 𝐾 and 𝐾 charts. Part II.
𝐾 = 𝒦𝐽 Method.

The Resistance vs Speed data are the inputs for design.

The 𝑃 is not known and 𝑛 is a variable.
If 𝑃 and 𝑛 are inputs, use the 𝐵 − δ chart.

Only one interpolation is needed.

Jul-Dec
2024

Dr. DD Ebenezer 2
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Dr. D. D. Ebenezer
3.6 Propeller Design. 𝐾 = 𝒦𝐽 Method.
5 • The inputs to prop design are 𝑇 and 𝑉
• The outputs of prop design are
1. Series. B Series is the most widely used one.
2. Number of blades, Z.
3. EAR
4. Diameter, 𝐷
5. rps, 𝑛
6. 𝑃(𝑟)/𝐷

• In general, search in a 6 dimensional space for the best prop with max 𝜂 .
• After the Series, Z, EAR, and 𝐷 are chosen, search in 2D space.
• The Molland and the 𝐾 = 𝒦𝐽 (MIT) methods for searching in 2D space are
Jul-Dec compared in the following slides
2024

Dr. D. D. Ebenezer
6

https://ocw.mit.edu/courses/mechanical-engineering/2-611-marine-power-and-propulsion-fall-
2006/

ocw.mit.edu. Marine Power and Propulsion.03kt_kq_design.pdf in CLASSROOM Study Material

Jul-Dec
2024

Dr. DD Ebenezer 3
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Dr. D. D. Ebenezer
𝐾 = 𝒦𝐽 Method using 1 interpolation
7
1. Given 𝑇 and 𝑉 , find the Series to be used, Z, EAR, and 𝐷, 𝑛, and 𝑃/𝐷 for optimum open water
efficiency. Note that the values of 6 parameters are to be chosen.
2. Eliminate 𝑛 and create a new parameter. As 𝐾 is inversely proportional to 𝑛 and 𝐽 is inversely
/ (𝜌 )
proportional to 𝑛, use =
/( )
= = 𝒦 which is independent of 𝑛. Find the value of
𝒦 by using the known values of 𝑇 and 𝑉 and assumed value of 𝐷.
3. In a 𝐾 − 𝐽 chart (𝐾 on the y axis and 𝐽 on the x axis), draw 𝒦𝐽 − 𝐽 also. See the next slide.
4. Choose a 𝑃/𝐷 which is on the chart. 𝑃/𝐷 = 0.5, 0.6, … or 1.4
5. For this 𝑃/𝐷, at the point of intersection of the 𝐾 − 𝐽 (red) and the 𝒦𝐽 − 𝐽 (purple) lines on the
next slide, the thrust provided by the propeller is equal to the thrust necessary to obtain 𝑉 .
6. Find 𝐽 at the intersection point. A prop with this 𝑃/𝐷 and 𝐽 delivers 𝑇at 𝑉 .
7. Find 𝜂 at that 𝐽.
8. Repeat for other values of 𝑃/𝐷. For each 𝑃/𝐷 the corresponding 𝐽 will be different. However, each
delivers 𝑇at 𝑉 at a specific 𝑛.
9. Interpolate the values of 𝜂 vs 𝐽 to find the 𝑃/𝐷 , 𝐽 at which the 𝜂 is max. This yields the
optimum 𝑛. Only one interpolation is involved in this method because 𝑃/𝐷 is the independent
Jul-Dec variable. See the Study Material from MIT.
2024

Dr. D. D. Ebenezer
8 Prop Design using One Interpolation
• This chart is for Z = 5, EAR = 0.75, and 𝑃/𝐷 = 1. 𝒦𝐽 − 𝐽 has been added.

𝑃/𝐷 = 1. Find the point of intersection of the 𝐾 and 𝒦

lines.
Find the 𝐽 and 𝜂.
𝒦

Jul-Dec
2024

Dr. DD Ebenezer 4
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Dr. D. D. Ebenezer
9 Prop Design with 𝑇 and 𝑉 as inputs

Repeat for various values of P/D.

Draw a line joining all the 𝜂
points.
Find the max in that curve.

Jul-Dec
2024

Dr. D. D. Ebenezer
10

Jul-Dec
2024

Dr. DD Ebenezer 5
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Dr. D. D. Ebenezer
11 Molland and MIT methods
• Both methods will yield the same results
• 𝐾 charts are in 3D with 𝑃/𝐷 and 𝐽 as independent variables. Slices of the
surface at discrete values of 𝑃/𝐷 and continuous values of 𝐽 are shown on 2D
charts. Starting with one of the discrete values of 𝑃/𝐷 (MIT method) and
finding the value of 𝐽 that yields the required 𝐾 is better than starting with a
value of 𝐽 (Molland method) and finding the 𝑃/𝐷.
• The 𝐾 = 𝒦𝐽 (MIT) method is considerably better if graphical charts are
used as only one interpolation is needed
• If digital charts are used, the MIT method is a little more convenient
• Next, … global optimization.
• Learn to use the digital charts for practical prop design

Jul-Dec
2024

Dr. D. D. Ebenezer
12 Prop design. Global optimum.
1. Given 𝑇 and 𝑉_𝑎, find the optimum prop for the chosen Series, Z, EAR, and
𝐷 by using the Molland or MIT methods.
2. Use the same Series, Z, and EAR. Choose a different 𝐷. Find 𝑃/𝐷 and 𝐽.
Repeat for various values of 𝐷. Find the prop with highest value of
𝜂 (𝑃/𝐷, 𝐽, 𝐷).
3. Vary the value of EAR. See the next slide for discrete values of EAR. Find
the prop with the highest value of 𝜂 (𝑃/𝐷, 𝐽, 𝐷, EAR).
4. Vary 𝑍. 𝑍 = 3, 4, 5, … Find the highest value of 𝜂 (𝑃/𝐷, 𝐽, 𝐷, EAR, 𝑍).
5. Vary the Series. B Series, BB Series, Au Series, … Find the highest value of
𝜂 (𝑃/𝐷, 𝐽, 𝐷, EAR, 𝑍, Series).
6. This prop is the global optimum one.
Jul-Dec
2024

Dr. DD Ebenezer 6
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Dr. D. D. Ebenezer
13 B series propellers
• Carlton
• E.g. It is seen from the table that data is available for props with 5 blades and
BAR = 0.45, 0.6, 0.75, and 1.05

Jul-Dec
2024

Dr. D. D. Ebenezer
14 Some useful sites
• https://www.caeses.com/news/2018/wageningen-b-series-online-
propeller-tool-released/

• https://www.simscale.com/blog/2019/06/how-to-optimize-propeller-
design/

• https://www.caeses.com/industries/case-studies/propeller-design-with-
openfoam/

Jul-Dec
2024

Dr. DD Ebenezer 7
 10-09-2024

Dr. D. D. Ebenezer
15

3.7 Types and Advantages of Propulsion

Plants

See L01 for various types of Propulsion Plants

Jul-Dec
2024

Dr. D. D. Ebenezer
16 Selection of Marine Propulsion Machinery
• In recent times, the Energy Efficiency Design Index (EEDI) has become a
very important factor in the selection of the engine and propeller.

Jul-Dec
2024

Dr. DD Ebenezer 8
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Dr. D. D. Ebenezer
17 Selection of Engine: main factors
• In passenger vehicles and ships, running cost plus maintenance cost is a
major factor to consider.

Jul-Dec
2024

Dr. D. D. Ebenezer
18 3.7 Types and Advantages of Propulsion Plants

Jul-Dec
2024

Dr. DD Ebenezer 9
 10-09-2024

Dr. D. D. Ebenezer
19 Types and Advantages of Propulsion Plants

Jul-Dec
2024

Dr. D. D. Ebenezer
20 Types and Advantages of Propulsion Plants

Jul-Dec
2024

Dr. DD Ebenezer 10
 10-09-2024

Dr. D. D. Ebenezer
21 Types and Advantages of Propulsion Plants

Jul-Dec
2024

Dr. D. D. Ebenezer
22 Types and Advantages of Propulsion Plants

Jul-Dec
2024

Dr. DD Ebenezer 11
 10-09-2024

Dr. D. D. Ebenezer
23 Types and Advantages of Propulsion Plants

Jul-Dec
2024

Dr. D. D. Ebenezer
24 Types and Advantages of Propulsion Plants

Jul-Dec
2024

Dr. DD Ebenezer 12
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Dr. D. D. Ebenezer
25 Diesel Electric and Gas Turbo Electric Engines
• Electricity is generated by using Diesel Engines or Gas Turbine Engines
• An electric motor is used to drive the propeller
• This is a p

Jul-Dec
2024

Dr. D. D. Ebenezer
26

Jul-Dec
2024

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Dr. D. D. Ebenezer
27 Steam Turbines
• How Does a Steam Turbine Work?
• In simple terms, a steam turbine works by using a heat source
(gas, coal, nuclear, solar) to heat water to extremely high
temperatures until it is converted into steam. As that steam
flows past a turbine’s spinning blades, the steam expands and
cools. The potential energy of the steam is thus turned into
kinetic energy in the rotating turbine’s blades. Because steam
turbines generate rotary motion, they’re particularly suited for
driving electrical generators for electrical power generation.
The turbines are connected to a generator with an axle, which in
turn produces energy via a magnetic field that produces an
electric current.
Jul-Dec
2024

Dr. D. D. Ebenezer
28

Read books, magazines, and journals

and become outstanding Naval Architects

Jul-Dec
2024

Dr. DD Ebenezer 14
 24-09-2024

Dr. D. D. Ebenezer
1 24 Sep 2024

B. Tech. NA&SB. 2021-25. 20-215-0502

Department of Ship Technology
CUSAT, Kochi 682022
3 credits

Dr. D. D. Ebenezer
Adjunct Faculty
9446577239
ebenezer.cusat@gmail.com

Jul-Dec
2024 Only for personal use by CUSAT NA&SB students

Dr. D. D. Ebenezer
2 Course Content

Jul-Dec
2024

Dr. DD Ebenezer 1
 24-09-2024

Dr. D. D. Ebenezer
3 Module 3
Earlier
• 3.1 Design Cycle for Propellers
• 3.2 Propeller families and series
• 3.3 Design using 𝐵 − δ charts
• 3.4 Cavitation Limit
• 3.5 Design using 𝐾 and 𝐾 charts. Part I
• 3.6 Design using 𝐾 and 𝐾 charts. Part II
• 3.7 Types and advantages of propulsion plants
Today
• 3.8 Design using 𝐾 and 𝐾 charts Part III

Jul-Dec
• 3.9 Design using Special Charts
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Dr. D. D. Ebenezer
4
• Birk. Chap 48.

• This is the best

sequence for
technical design.
However, other
considerations such
as lower lifetime
cost for certain
makes of engines
may also influence
the sequence.
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5

There is a preferred or chosen engine +

gearbox and the rpm is known
The engine will be chosen later

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6

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7 Service Margin

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8

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9 Engine Margin. Design Constants.

• First, design (or do the analysis) for calm water. Then, consider service
conditions and engine margin.
• See L11S16 regarding MCR = Maximum Continuous Rating and NCR =
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10 Optimum Diameter Selection

• Total cost or lifetime cost is the deciding factor. It includes capital cost,
operation cost, and maintenance cost.

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11 Find the Diameter
• 𝑃 , 𝑛, 𝑉 are known. Determine a “design constant” that is independent of the
diameter. Use it to find the best 𝜂 and the associated P/D.

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• Combine the known quantities in a way that eliminates the yet-to-be-found
12
diameter. 𝐾 /𝐽 depends only the known quantities and is indep of the diameter

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13 Task 1
• Example 1. Input data is on the next slide.

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14 Task 1.
• Do the analysis with 𝑍 = 4 and 𝐴 /𝐴 . Then, repeat for other values of 𝑍 and 𝐴 /𝐴 .

Service thrust is
used in Task 2.

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16

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• Use 𝐽 =
0.1, 0.15,
0.2, 0.25,
…
• Calculate
10𝐾 . Plot
Eq. (48.8)
on the 𝐾
vs 𝐽 chart.
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18
The chart has
values of
10𝐾 . So, plot
the curve for
10𝐾 /𝐽 on it.

At the
intersection of
the 10𝐾 and
the 10𝐾 /𝐽
curves, the
prop with a
particular P/D
can provide
the necessary
torque. Find
the 𝜂 and 𝐽.
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19
𝑛, 𝑉 are known. See L18S06.

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20

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21 Task 1. Optimum 𝜂 and P/D.

• Use the auxiliary curve of 𝜂 vs 𝐽 to find the optimum J.

• Then draw a graph of P/D vs J using the open circles in Fig. 48.4. Use it to
find the P/D at the optimum J. It is shown by an open square in Fig. 48.5.

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22 Optimum 𝑃/𝐷
P/D, there is a small reduction in the efficiency.
The reduction is much more if a lower P/D is
• If the P/Dis a little higher than the optimum

used.

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24 Check for thrust and
cavitation
• This diameter is optimal for only
the open water condition. The
optimum propeller diameter is
2%–5% smaller for the behind
condition. We will come back to
this “mystery” in the following
chapter. Birk Page 576.
• These two checks are very
important
• Find the thrust generated by the
optimum propeller. From
regression eqs. 𝐾 ≅ 0.174.
Thrust (service) =
0.174*1026*(108/60)^2*7.43^4
= 1762 kN which is = 1762 kN in
Eq. 48.10
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25 Use the chart only if you cant use the regression equations
• What is the 𝐾 at the optimum P/D of 0.9227 and J = 0.6202?
• At P/D = 0.8 and J = 0.6202, 𝐾 = 0.2-1.75*0.2/4.1 = 0.115
• At P/D = 1.0 and J = 0.6202, 𝐾 = 0.2+0.65*0.2/4.1 = 0.232
• At P/D = 0.9227 and J = 0.6202, 𝐾 = 0.115 + (0.9227-0.8) *(0.232-0.115)/
(1.0-0.8) = 0.187. But, using regression equations, 𝐾 = 0.174. See L18S24

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26 Design Task 2
• 𝑇, 𝑛, 𝑉 are known. Determine a “design constant” that is independent of the
diameter. Find 𝑃/𝐷, 𝜂 , and 𝐷.

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27 Design Task 2. Design Constant.

Service power is
used in Task 1.

• 1762.35e3*(108/60)^2 /(1026*8.295^4) = 1.1755

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28

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29 Design Task 2. Self Propulsion Points.
• Self propulsion points for task 2

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30 Design Task 2. Optimum 𝑃/𝐷.
• Compare the optimum propellers in Tables 48.3 and 48.4. They are for the
same ship but designed using different input data sets. Ideally, they should be
exactly the same but are not – read the last para of the previous slide.
• For the final answers, 2 significant digits should be enough for P/D, D, and 𝜂 .

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31 48.3 Optimum Rate of Revolution Selection. Design Tasks 3 and 4.

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32 Design Task 3
• 𝑃 , 𝑣 , and 𝐷 are known. Find 𝑛, 𝑃/𝐷, 𝜂 .

Task 1. Input is 108 rpm and

Output is Dia = 7.430 m.

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33
• Self
propulsion
points for
task 3

Task 3 output of 97.8 rpm is less than the Task 1

input of 108 rpm.

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34 Task 3 output of 𝜂 = 0.611 is a little higher
than the Task 1 output of 𝜂 = 0.605

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35 Design Task 4
• See Section 3.6. L16S18
• 𝑇, 𝑣 , and 𝐷 are known

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37

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Design using modified 𝐵 − 𝛿 charts.
38
Non-dimensional − charts.
Zero-interpolation method.

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Use this chart
to do Design
Task 1
without doing
any Maximum efficiency
interpolation curve
B4.85

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42 Optimum Propeller

• To find the optimum propeller at a particular value of , draw a vertical

line through that value. The efficiency contour that is tangent to the vertical
line is the maximum possible efficiency. At the tangent point, find the 𝑃/𝐷
and 1/𝐽.
• The maximum efficiency curve is shown on the chart. The intersection of this
line with the vertical line yields the 𝑃/𝐷 and 1/𝐽 of the optimum propeller.

• Check the above two paras by find the optimum propeller for = 1.4. The
max efficiency is 0.45.

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43 Optimum propeller for various 𝐴 /𝐴
• See Fig. 48.10 on the next slide

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44
• For a particular value of

, Fig. 48.10 shows

that when 𝐴 /𝐴
increases the optimum
efficiency decreases
and 𝑃/𝐷 increases.
• For each value of
𝐴 /𝐴 etc., check if the
required thrust is
produced and for
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45 Optimum Propeller for Behind Ship Condition

See Fig. 48.9

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46

Read books, magazines, and journals

and become outstanding Naval Architects

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