Machinery and Propeller Design · 2019-03-30 · approximately double the effective power calculated by MAXSURF Resistance. The selected machinery matches that of similar vessels

VILUCE MARINE DESIGN PTY LTD REVISION 1.0 |DATE OF LATEST AMENDMENT: 30-MAR-19

Machinery and Propeller Design “MAFALDA” FERRY

Machinery and Propeller Design

i

ABSTRACT

Following an estimate of effective power required in the previous design phase, this report details the accurate

assessment of power requirements, the selection of suitable drive train machinery and the design of an appropriate

Marin BB Series propeller. The total powering requirement was found to be 2120 kW which is, as expected,

approximately double the effective power calculated by MAXSURF Resistance. The selected machinery matches that

of similar vessels from the published data. Design of the propeller to Marin BB definitions was hindered by the

relatively small space for the propeller between the shaft and the hull, however simple modifications and allowances

were made to be able to accommodate a propeller of sufficient diameter to provide the required thrust. The

resultant propulsion system consists of MTU 12V 2000 M72 main engine, ZF5050 V-drive gearbox and 1.29 m

diameter 5-blade propeller per demihull.


ii

Table of Contents

Abstract .............................................................................................................................................................................. i

1 Introduction .............................................................................................................................................................. 1

2 Powering Design Point .............................................................................................................................................. 1

3 Brake Power .............................................................................................................................................................. 2

4 Machinery ................................................................................................................................................................. 3

4.1 Main Engine ...................................................................................................................................................... 3

4.2 Gearbox ............................................................................................................................................................. 4

5 Propeller Design ........................................................................................................................................................ 5

6 Propeller Design Details ............................................................................................................................................ 6

6.1 Blade Lengths .................................................................................................................................................... 8

6.2 Thicknesses ....................................................................................................................................................... 8

6.2.1 Trailing and Leading edge thickness ....................................................................................................... 10

6.3 Offsets ............................................................................................................................................................. 10

7 Conclusion ............................................................................................................................................................... 12

Appendix A ...................................................................................................................................................................... 13

Appendix A.1 – MTU 12V 2000 M72 Datasheet ......................................................................................................... 13

Appendix B ...................................................................................................................................................................... 15

Appendix B.1 – Z5050V Gearbox ................................................................................................................................ 15

Appendix C ...................................................................................................................................................................... 17

7.1 Appendix C.1 – Values of V1 and V2 ............................................................................................................... 17


iii

List of Figures

Figure 1 Brake Power Requirement .................................................................................................................................. 2

Figure 2 V-Drive gearbox diagram .................................................................................................................................... 4

Figure 3 Propeller Principle Design ................................................................................................................................... 5

Figure 4 Thickness and Offset Dimensions ....................................................................................................................... 6

Figure 5 Definitions for Blade Lengths .............................................................................................................................. 6

List of Tables

Table 1 Propeller Details Input ......................................................................................................................................... 6

Table 2 Marin BB Series Dimensions ................................................................................................................................. 7

Table 3 Blade Lengths ....................................................................................................................................................... 8

Table 4 Blade Thicknesses for r/R = 0.25 and 0.6 ............................................................................................................. 8

Table 5 Blade Thicknesses ................................................................................................................................................. 9

Table 6 Leading Edge Thicknesses .................................................................................................................................. 10

Table 7 yFACE offsets for P > 0. All values in mm. ............................................................................................................. 10

Table 8 yBack offsets for P>0. All values in mm. ............................................................................................................... 11

Table 9 yFACE offsets for P<0. All values in mm. ............................................................................................................... 11

Table 10 yBACK offsets for P<0. All values in mm. ............................................................................................................ 11

Table 11 – V1 Values ....................................................................................................................................................... 17

Table 12 – V2 Values ....................................................................................................................................................... 18

List of Graphs

Graph 1 Trials Resistance Curve ........................................................................................................................................ 1

Graph 2: Blade thickness vs radius ................................................................................................................................... 9


1

1 INTRODUCTION

The determination of the propulsion system is a cyclic process requiring an estimation of propeller diameter and

RPM to obtain the required thrust of the propeller and match it with both off-the-shelf engine and gearbox options

and to enable the propeller to be designed to Marin BB definitions. Two pre-prepared Excel sheets were utilised

alongside with extensive market research of machinery available to a ferry operating out of Townsville, QLD. Upon

selection of the machinery, the principal dimensions of the propeller are found. These allow for a complete and

detailed design of the propeller as undertaken to provide the end point to an optimal drive train for this vessel.

2 POWERING DESIGN POINT

From the resistance vs speed curve from the previous design phase, a ‘Trials resistance curve’ was created by

effectively adding an additional 0.5 kn to each speed at which a resistance was calculated. This provides a margin for

error by assuming the resistance of the vessel is slightly higher than calculated. The design point for powering this

vessel for a operational speed of 25 kn would then be powering for a resistance calculated for the vessel at 25.5 kn.

With this increase in resistance, the Trials resistance curve was created, and the design point found as per Graph 1.

Graph 1 Trials Resistance Curve

The total resistance at the design point was found to be 82.58 Kn, or 41.29 kN per demihull.

0.00

20.00

40.00

60.00

80.00

100.00

120.00

10 15 20 25 30

Res

ista

nce

(kN

)

Speed (kn)

Speed vs Total Resistance


2

3 BRAKE POWER

Calculation of the brake power required the determination of a few key particulars, the first of which is the proposed

propeller diameter. Initially a diameter of 1.26 m was selected to ensure plenty of clearance between the hull and

propeller blade tips, however a propeller of this diameter was found to either not provide the required thrust or to

break the Marin BB definitions. The best results were found by maximising the propeller diameter to 1.29 m, leaving

plenty blade tip clearance before the rake of the blades is considered. Some assumptions were made in establishing

other important inputs, including the Taylor wake fraction, the thrust deduction fraction and the efficiencies of the

shaft transmission and gearbox. The Taylor wake fraction can typically range from 0.05-1.5 yet the professional

opinion is that the value is at the lower end of this spectrum for high-speed catamarans and so was set at 0.07. The

thrust deduction value was suggested to be a similar value of 0.07. The gearbox and shaft efficiency were chosen to

be 97% and 98% respectively as average values in the industry. Furthermore, a 10% de-rate was applied due to the

effects of the tropical climate of Townsville.

By iteratively testing rotation speeds for the propeller, it was also found that the most efficient rotation speed

occurs at the lowest RPM that allows the pitch to diameter ratio of the propeller to stay within range of the Marin BB

series. Overall, the smallest break power requirement for the vessel was obtained to be 889 kW per hull using a 1.29

m propeller rotating at 545 RPM. Any RPM lower than this requires an increase in blade pitch beyond the range of

the Marin BB Series, as demonstrated in Figure 1.

Figure 1 Brake Power Requirement


3

4 MACHINERY

4.1 MAIN ENGINE The propulsion machinery must supply 889 kN of brake power at 90% of its Maximum Continuous Rating (MCR). As

such, the MCR of the selected engine must be at least 1000 kW, as shown below.

𝑀𝑅𝐶𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 =889

0.9

= 988.12

≈ 1000 kW

Besides the base power requirement, the following factors were considered in the main engine selection:

• Size: The engine block must fit into the demihulls, which are 2.5 m wide each. The smaller the engine block,

the more accessible the engine room is for maintenance and the lighter the engine.

• Availability of parts: As Townsville is the operating area of the vessel, major shipping ports attract the

presence of most large engine manufacturers. This includes: MAN, Caterpillar, Wartsilla, MTU and Cummins.

• Efficiency and Ecology: The client expressed a strong preference for a vessel which is both environmentally

friendly and fuel efficient. A qualitative judgement was made on the relative consumption and

environmental impact of each engine considered over their lifetime

• Machinery Common to Industry: The published data reflects the accumulated knowledge and experience of

different naval architects and marine engineers from similar vessels to Mafalda. This limits the risk of

choosing an engine not appropriate for fast-ferry propulsion.

After extensive research, MTU 12V 2000 M72 was selected. This is a high-speed, 4-stroke diesel engine which

outputs 1060 kW at 1950 RPM in Category 1B of MTU. The reasoning for this selection is that this engine is widely

used in the high-speed aluminium ferry industry, popular for vessels in the 25 – 35 m range. Moreover, the engine is

only 1.385 m wide, allowing maximum access space in the engine room. Category 1B for MTU is defined to be ideal

for passenger ferry operations where the vessel operates at full load 60 – 80% of the time, with no large load

fluctuations. Selection the appropriate engine is necessary to optimize the lifespan of the engine under expected

operations. The data sheet for the engine can be found in Appendix A.1.

The total installed brake power of the vessel is 2120 kW, which exceeds published data vessels. This is due to

previous vessels underwent far more cycles in the design spiral, fairing the hull and reducing the total resistance of

the vessel. As explained in the resistance calculation report, the appendage resistance is considered to be a large

portion of the total resistance of the vessel and reducing it could reduce the total resistance considerably.


4

4.2 GEARBOX The transmission selection was simplified to be a selection of ZF Marine Group gearbox, as they have a big global

presence and provide a large range of compatibility with all major engines. At 90% MCR, the gearbox must be able to

handle 1755 ERPM and step it down to 545 SRPM, requiring a reduction ratio of 3.222. It must also withstand 954

kW (90% of 1060 kW) at 1755 ERPM and up to 1060 kW at 1950 ERPM (100% MCR).

The ZF 5050 V satisfies the requirements by a healthy margin up to 1114 kW at 2000 RPM with a reduction ratio of

3.222. This allows the machinery and the propeller to run at their most efficient speeds while avoiding over stressing

the gearbox. The gearbox weights 768 kg each, which is quite heavy, and size could be stepped down to save over

250 kg per gearbox, but it is not worth the risk to slightly exceed its suggested operational limits.

The reasoning for selecting a V drive gearbox is to allow the shaft to exit the hull far further forward in to the vessel,

increasing the propeller clearance and decreasing the shaft exit angle. Therefore, this gearbox selection addresses

the lack of propeller clearance and, more significantly, addresses the detrimental effect of the shaft exit angle as a

significant source of appendage resistance.

Figure 2 V-Drive gearbox diagram


5

5 PROPELLER DESIGN

The optimal Marin BB Series propeller is designed based on two key particulars, the diameter of the propeller and

the pitch to diameter ration (P/D) of the blades. The propeller needs a diameter of at least 1.26m to meet the P/D <

1.4 criteria of the series for the thrust required. As seen in Figure 3, the power delivered to the propeller is 816 kW

at the operational speed of 90% MCR of the engine which can be satisfied by a 1.29 m, 5 bladed propeller with a P/D

of 1.3455 and an area ratio (Ae/Ao) of 0.915, both of which are at the design boundaries of the series. However, as

they are within bounds. Thus, the designed propeller produce 44.53 kN of pull, safely more than the 44.40 kN

required pull, which takes into consideration the thrust deduction factor, determined at the design point.

Figure 3 Propeller Principle Design


6

6 PROPELLER DESIGN DETAILS

This section details the calculation of the blade lengths, thicknesses and offsets for the accurate construction of this

propeller to the Marin BB series definition. All constants and formulae are derived from the Ship Propulsion Notes by

Phil Helmore. These details describe the cross-section of the propeller at each discrete radius using the dimensions

shown in Figure 4 and 5 below.

Figure 4 Thickness and Offset Dimensions

Figure 5 Definitions for Blade Lengths

The input values for the calculations are provided in Table 1,

Table 1 Propeller Details Input

Input Value Unit

Z 5 -

D 1290 mm

P/D 1.3455 -

AE/AO 0.915 -

A 345 mm

P 1735.695 mm

Revs 1950 RPM

P 1060 kW

RR 3.222 -

G 7.5 g/cm^3

U 46

B 0.915

N 5

E0.25 1

E0.6 1.25

F0.25 2.146

C 1

R 605.21

M 7.55

F0.6 5.85

M0.6 6.88

C0.6 1.60


7

where:

Z = Number of blades

D = Diameter of propeller, in mm P/D = Pitch ratio

A = Rake of the propeller, in mm. Blade propellers lose negligible effect until tilted past 15o backwards, thus the rake of blade was calculated to be 345 mm

A = 𝑅 tan (𝜃)

= 1290 tan (15) = 345 mm

Revs = RPM of engine at 90% MCR P = Brake power of the engine, in kW

RR = Reduction ratio

G = Density of manganese aluminium bronze, which is the material selected for the propeller, anticorrosive marine metal, in g/cm3

U = Allowable stress of manganese aluminium bronze, in N/mm2 B = Ae/Ao N = Z

E0.25 = Through to C0.6 are constants as derived from the series definition and are found using P/D

M = 3.75𝐷

𝑃+ 2.8

𝑃

𝐷

F = P/D + 0.8

For the Marin BB Series, the following dimensions are provided,

Table 2 Marin BB Series Dimensions

r/R

CrZ/DAEAO ar/cr br/cr

- - -

0.2 1.6 0.581 0.35

0.3 1.832 0.584 0.35

0.4 2.023 0.58 0.351

0.5 2.163 0.57 0.355

0.6 2.243 0.552 0.389

0.7 2.247 0.524 0.443

0.8 2.132 0.48 0.486

0.9 1.798 0.402 0.5

0.95 1.434 0.318 0.5


8

6.1 BLADE LENGTHS To find the blade lengths, it is a simple matter of multiplying or dividing these dimensions by the appropriate input

values to isolate ar, br and cr. The results are provided in Table 3.

Table 3 Blade Lengths

Cr ar br

(mm) (mm) (mm)

377.7 219.5 132.2

432.5 252.6 151.4

477.6 277.0 167.6

510.6 291.1 181.3

529.5 292.3 206.0

530.4 278.0 235.0

503.3 241.6 244.6

424.5 170.6 212.2

338.5 107.7 169.3

6.2 THICKNESSES The blade thicknesses were calculated at 0.25R and 0.6R as per Lloyd’s Rules for the Classification and Construction

of Ships, as shown in Table 4. T0.25 and T0.6 were found to be 59.46 mm and 25.62 mm respectively.

Table 4 Blade Thicknesses for r/R = 0.25 and 0.6

Variable Value Unit

K 7994.03 -

L0.2 377.71 mm

L0.3 432.48 mm

L0.25 405.10 mm

T0.25 59.46 mm

T0.6 25.62 mm

Where:

K = 𝐺𝐵𝐷3𝑅2

675

L = Length of blade section at 25 (L0.25) and 60 (L0.6) percent radius, as appropriate

T = 𝐾𝐶𝐴

𝐸𝐹𝑈𝐿𝑁+ 100 √

3150𝑀𝑃

𝐸𝐹𝑅𝑈𝐿𝑁 in mm, for thicknesses of 25 and 60 percent radius

B = Developed area ratio E = 1 at 0.25R and 1.25 at 0.6R


9

The maximum thickness of each station is assumed to be linear between 0.2R to 0.6R, followed by a tangential curve

to a tip of 4 mm, as shown in Graph 2. The linear gradient was found by interpolation between T0.25 and T0.6.

Table 5 Blade Thicknesses

r/R T (mm)

0.2 64.3

0.25 59.5

0.3 54.6

0.4 45.0

0.5 35.3

0.6 25.6

0.7 19.6

0.8 12.7

0.9 7.6

0.95 5.6

1 4.0

Graph 2: Blade thickness vs radius

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

0.2 0.4 0.6 0.8 1

Tick

nes

s T

(mm

)

Percentage Radius

Blade Thickness from Base to Tip


10

6.2.1 Trailing and Leading edge thickness

The thickness of the trailing and leading edge has been set to a constant thickness of 4 mm beside the region of the

leading edge between 0.2R to 0.55R. Within this range, the leading edge thickness decreases from 0.55R linearly to

4mm.

0.2TLE = 0.2𝑇

6

= 10.7 mm The resulting leading edge thicknesses are summarised in table 6 as follows,

Table 6 Leading Edge Thicknesses

r/R TLE

(mm)

0.2 10.7

0.25 9.8

0.3 8.8

0.4 6.9

0.5 5.0

0.55 4.0

0.6 4.0

6.3 OFFSETS The offsets are calculated from the tabulated functions V1 and V2, which are simple non-dimensional functions of

the blade thickness, R and P, the proportion of the distance from the position of the maximum thickness. The offsets

have been calculated for 0.2R to 0.95R for both the face and back of the blades on both the leading side forward of

the point of maximum thickness where P is positive (Table 7 and Table 8), and the trailing side where P is negative

(Table 9 and Table 10).

Table 7 yFACE offsets for P > 0. All values in mm.

yFACE

r/R P1 P0.95 P0.9 P0.8 P0.6 P0.4 P0.2 P0

0.95 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.9 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.7 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.6 0.8 0.4 0.1 0.0 0.0 0.0 0.0 0.0

0.5 4.0 2.4 1.6 0.7 0.1 0.0 0.0 0.0

0.4 8.9 6.0 4.5 2.6 0.8 0.1 0.0 0.0

0.3 14.8 11.1 8.9 6.0 2.5 0.7 0.1 0.0

0.25 18.1 13.9 11.5 8.1 3.7 1.2 0.2 0.0

0.2 21.7 17.0 14.2 10.2 4.8 1.8 0.3 0.0


11

Table 8 yBack offsets for P>0. All values in mm.

yBACK

r/R P1 P0.95 P0.9 P0.8 P0.6 P0.4 P0.2 P0

0.95 4.0 4.1 4.2 4.3 4.6 4.8 4.9 4.9

0.9 4.0 4.2 4.5 4.9 5.6 6.1 6.4 6.5

0.8 4.0 4.7 5.4 6.6 8.6 10.0 10.7 11.0

0.7 4.0 5.6 7.0 9.4 12.9 15.3 16.6 17.0

0.6 4.8 7.6 10.0 14.0 19.6 23.0 24.9 25.6

0.5 8.0 11.9 15.1 20.4 27.5 31.8 34.4 35.3

0.4 12.9 17.9 21.7 28.0 35.9 40.7 43.8 45.0

0.3 18.8 24.6 29.1 36.0 44.6 49.9 53.5 54.6

0.25 22.1 27.7 32.3 39.8 48.8 54.6 58.2 59.5

0.2 25.7 30.4 35.3 43.0 52.7 59.3 63.1 64.3

Table 9 yFACE offsets for P<0. All values in mm.

yFACE

r/R -1P -0.95P -0.9P -0.8P -0.6P -0.4P -0.2P 0P

0.95 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.9 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.7 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.6 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.5 1.6 1.3 1.0 0.6 0.1 0.0 0.0 0.0

0.4 5.6 4.6 3.7 2.4 0.8 0.2 0.0 0.0

0.3 10.6 11.0 8.2 6.1 2.9 0.9 0.2 0.0

0.25 12.9 11.8 10.5 8.2 4.5 1.7 0.4 0.0

0.2 15.1 14.1 12.9 10.5 6.5 4.9 0.9 0.0

Table 10 yBACK offsets for P<0. All values in mm.

yBACK

r/R -1P -0.95P -0.9P -0.8P -0.6P -0.4P -0.2P 0P

0.95 4.0 4.1 4.2 4.3 4.6 4.8 4.9 4.9

0.9 4.0 4.2 4.5 4.9 5.6 6.1 6.4 6.5

0.8 4.0 4.7 5.3 6.5 8.5 9.9 10.7 11.0

0.7 4.0 5.3 6.5 8.7 12.3 14.9 16.5 17.0

0.6 4.0 6.1 8.1 11.7 17.9 22.2 24.8 25.6

0.5 6.5 9.1 11.6 16.4 24.6 30.6 34.2 35.3

0.4 12.5 14.9 17.5 22.6 31.9 39.1 43.6 45.0

0.3 19.4 23.5 24.7 30.3 40.0 47.6 52.9 54.6

0.25 22.7 25.1 28.1 34.0 44.3 51.9 57.5 59.5

0.2 25.9 28.2 31.4 37.6 48.5 58.4 62.2 64.3


12

The coordinates were calculated by means of the following formulas,

yFACE = V1(Tmax -TLE) for P > 0

yBACK = (V1 + V2)(Tmax – TLE) + TLE

yFACE = V1(Tmax -TTE) for P < 0

yBACK = (V1 + V2)(Tmax – TTE) + TTE

The values of V1 AND V2 can be found in appendix C

7 CONCLUSION

With specified propulsion machinery and a purpose-built Marin BB series propeller, this vessel is prepared to make

speed during sea trails. The main engine is a size larger than initially expected, leading also to a large gear box.

However, selected set up for the V-drive gearbox couple with a dimensionally small engine will allow for more

streamlined shafting and this is expected to considerable reduce drag and effectively increase the engine

performance and efficiency. Furthermore, the V-drive set up allows for sufficient propeller clearance as without it

the propeller would have to have been designed smaller and thus less efficient. The propeller details have been

calculated to provide a blueprint for construction of the optimal propeller for this vessel. The results of this design

phase match expectations for the most part and so support the resistance calculations of the previous phase and

assure the client that this vessel is on track to deliver to the design brief with satisfaction.


13

APPENDIX A

APPENDIX A.1 – MTU 12V 2000 M72 DATASHEET


14


15

APPENDIX B

APPENDIX B.1 – Z5050V GEARBOX


16


17

APPENDIX C

7.1 APPENDIX C.1 – VALUES OF V1 AND V2 Table 11 – V1 Values

r/R P1 P0.95 P0.9 P0.8 P0.6 P0.4 P0.2 P0

0.95 0 0 0 0 0 0 0 0

0.9 0 0 0 0 0 0 0 0

0.8 0 0 0 0 0 0 0 0

0.7 0 0 0 0 0 0 0 0

0.6 0.0382 0.0169 0.0067 0.0006 0 0 0 0

0.5 0.1278 0.0778 0.05 0.021 0.0034 0 0 0

0.4 0.2181 0.1467 0.1088 0.0637 0.0189 0.0033 0 0

0.3 0.2923 0.2186 0.176 0.1191 0.0503 0.0148 0.0027 0

0.25 0.3256 0.2513 0.2068 0.1465 0.0669 0.0224 0.0031 0

0.2 0.36 0.2821 0.2353 0.1685 0.0804 0.0304 0.0049 0

r/R -P1 -P0.95 -P0.9 -P0.8 -P0.6 -P0.4 -P0.2 -P0

0.95 0 0 0 0 0 0 0 0

0.9 0 0 0 0 0 0 0 0

0.8 0 0 0 0 0 0 0 0

0.7 0 0 0 0 0 0 0 0

0.6 0 0 0 0 0 0 0 0

0.5 0.0522 0.042 0.033 0.019 0.004 0 0 0

0.4 0.1467 0.12 0.0972 0.063 0.0214 0.0044 0 0

0.3 0.2306 0.24 0.179 0.1333 0.0623 0.0202 0.0033 0

0.25 0.2598 0.2372 0.2115 0.1651 0.0899 0.035 0.0084 0

0.2 0.2826 0.263 0.24 0.1967 0.1207 0.092 0.0172 0


18

Table 12 – V2 Values

r/R P1 P0.95 P0.9 P0.8 P0.6 P0.4 P0.2 P0

0.95 0 0.097 0.19 0.36 0.64 0.84 0.96 1

0.9 0 0.097 0.19 0.36 0.64 0.84 0.96 1

0.8 0 0.105 0.2028 0.3765 0.6545 0.852 0.9635 1

0.7 0 0.124 0.2337 0.414 0.684 0.866 0.9675 1

0.6 0 0.1485 0.272 0.462 0.72 0.879 0.969 1

0.5 0 0.175 0.3056 0.5039 0.7478 0.888 0.971 1

0.4 0 0.1935 0.3235 0.522 0.7593 0.8933 0.9725 1

0.3 0 0.189 0.3197 0.513 0.752 0.892 0.975 1

0.25 0 0.1758 0.3042 0.4982 0.7415 0.8899 0.9751 1

0.2 0 0.156 0.284 0.4777 0.7277 0.8875 0.975 1

r/R -P1 -P0.95 -P0.9 -P0.8 -P0.6 -P0.4 -P0.2 -P0

0.95 0 0.0975 0.19 0.36 0.64 0.84 0.96 1

0.9 0 0.0975 0.19 0.36 0.64 0.84 0.96 1

0.8 0 0.0975 0.19 0.36 0.64 0.84 0.96 1

0.7 0 0.0975 0.19 0.36 0.64 0.84 0.96 1

0.6 0 0.0965 0.1885 0.3585 0.6415 0.8426 0.9613 1

0.5 0 0.095 0.1865 0.3569 0.6439 0.8456 0.9639 1

0.4 0 0.0905 0.181 0.35 0.6353 0.8415 0.9645 1

0.3 0 0.08 0.167 0.336 0.6195 0.8265 0.9583 1

0.25 0 0.0725 0.1567 0.3228 0.605 0.8139 0.9519 1

0.2 0 0.064 0.1455 0.306 0.5842 0.7984 0.9446 1

Documents

Machinery and Propeller Design · 2019-03-30 · approximately double the effective power calculated by MAXSURF Resistance. The selected machinery matches that of similar vessels