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DEVELOPMENTS OF SHIP'S AFTERBODIES,

PROPELLER EXCITED VIBRATIONS

by

E VOSSNACK nd A, YOOGD

SECOND LIPS PROPELLER SYMPOSIUM

(2)

PROPELLER EXOTED VIBRATIONS

by

E. VOSSNACK) snd A VOOGD)

Abstract

In the actual development of shipbuilding, there is a distinct tendency to increased dimensions in

the tanker and bulkcarrier field on the one hand and to higher speeds in the container ship and

Ro-Ro area on the other hand. Both developments are responsible for the installation of

continuous-ly increasing power. It is doubtful, however, whether such related problems as vibration and

cavitation are given sufficient attention. In support of this proposition the present paper reviews:

Introduction

As representatives of a shipowner on the one

hand, and of a propeller manufacturer on the

other, we would like to describe some of the

difficulties we encounter when a new ship is

or-dered. The shipowner primarily wants a good

ship but for a reasonable price. In view of

sharply increasing prices, he starts looking for

standard designs of different yards.

In order to be competitive, a yard likes to offer

a ship with an overall length as short as

pos-sible. The shipowner's requirements in regard

to loading capacity persuade the yard to seek

the 'gain' in length by designing a short

after-body.

In consequence of this, the homogeneous flow

of water into the propeller disc is disturbed.

causing high wake peaks in the propellers' top

) NedLloyd - N. S. U. Rotterdam, Holland. ) Lips Propeller Works B. V., Drunen. Holland.

IV Fins, tunnels and nozzles as

wake-equal-izers.

V A new design philosophy for big ships with

pram-type afterbodies.

VI Free-flow propellers.

position and, very possibly, leading to vibration

and cavitation problems. Seve re requirements in

the shipowner's specifications regarding

vibra-tionandnoiselevelappearedtobe of little help in

this respect, and not infrequently a great amount

of money is spent afterwards to conduct

expens-ive vibration measurements and complicated

theoretical calculations in order to solve these

problems. Desperate measures are sometimes

taken, in order to keep the ship running, as

often as not on a trial and error basis.")

In our opinion, many of these problems could

be avoided if proper contact were established at

an early stage between Owner, Shipyard, Model

basin. Classification

Society and

Propeller

Manufacturer, in order to attack vibration and

cavitation problems by making the wake field of

the ship as homogeneous as possible.

) According to Det Norske Ventas 20% of casco damages are found in aft

peak tank.

I

Historical development of sternframes.

II Results of investigations on a 50 000 t.d.w.

tanker model with variations in afterbody

shape.

III Flow patterns of ships with extreme

U-shaped afterbodies.

(3)

the propeller to rotate (Figure lA). A first

at-tempt at improvement is shown in Figure lB.

The sternframe shape shown in Figure 1C has

been used for many years. It is obvious that no

attention has been paid to a favourable inflow

into the propeller - note the position of zinc

anodes. A simple improvement is

shown in

Figure 1D. An identical development is given in

Figures lE and 1F. A step forward could be

made by introducing the free-hanging rudders.

and omitting the sole piece (Figures 1G and 1H).

At that time wider clearances were already

being applied in order to obtain a more

homo-geneous wake field (Figure 1H). However, the

importance of a homogeneous wake field in

con-nection with vibrations and cavitation was not

fully recognized.

The examples in Figures 11 - iL all suffer from

severe vibrations.

Adhering to the

philosophy of keeping the

afterbodv as short as possible, requirements

for further equalizing the wake field led to the

application of stern-bulbs (Figure 1M). Although

regard to vibrations.

Finally the present state of the art in

obtain-ing a homogeneous wake field

is shown in

Figures 1P and 1Q, a roll on-roll off carrier

and a Lash-carrier respectively - both designed

in the

¡J. S. A.. The wake field of both single

screw ships is completely comparable with that

of twin screw arrangements. To prove that new

developments in this respect do not always gain

general

recognition, examples are given

in

Figures 2A and 2B, showing sternframes of a

Japanese built tanker - 1962 - of 50 000 t.d.w.

and a tanker of 271 000 t.d,w. -

under

con-struction. Despite the fact that the installed

power of the latter is almost 3 times greater.

the shape of the sternframe has been hardly

alted.

Figure 3A shows the propeller arrangement

of a twin screw container-ship which proved to

be extremely good from a vibration point of

view; Figures 3B

3E, show proposed

after-bodies, for very large tankers, single and twin

screw.

(4)

GEDE -4-1928 Inst.5200 s.h.p. x 95 rev serv. 4000 s.h.p. 14 kn.

Figure 1C. Normal bad construction 1950-1960. High maintenance costs. Strong thrust and torque variations. Wear of sterntube and sim-plex rudder bearings. Loosening of cone in sole piece. Cracks in sole piece at hull con-nection. Cavitation at propeller tips.

00

0 0 Inst. 10500 s.h.p. x 115 rev serv. 8500 - 9500 s.h.p. 18-18 1/2 kn. IlL k I,OM

Figure lE. Cast steel. Vibration level in

ac-commodation just acceptable.

lQQQ M

Inst. 5000 s.h.p. x 95 rev

Figure 1D. Improved construction 1955. Low maintenance on rudderbearings. No cavitation. However still high wake peaks in top and bottom position.

1929

00 °Oooc\c.o

5-LL.OYD jH Inst. 10500 s.h.p. x 115 rev serv. 8500 -9500 s.h.p. 17 1/2 - 18 kn. k !Q.QQ l

Figure 1F. Wide sternframe (all welded con-struction). Improvement in relation to lE.

Figure lB. Bad aringement. Rudder was a

Figure lA. Good arrangement cudgel, being too fat. Bad course keeping. Later on skeg fitted.

(5)

1967

TLMNTIC -5-W-KEK

Inst. 17000 s.h.p. x 115 rev

l000'1

Figure 11. Suffering from vibrations. Too small clearance before propeller. Heavy solepiece ahead of propellertip. Crack below sterntube. High

main-tenance on cone of rudder.

inst. 20000 s.h.p. x 115 rev

20 kn.

Figure 1K. Too small tip-clearance. Hull vortex

cavitation. Changed to smaller prop.dia., 7 blades.

(on sis tership fins above propeller were fitted).

000 M

000M

Figure iL. Slow barge carrier 'Lash'.

Design Goidman-Somitono. o :1:--:::== 1972 inst. 16700 s.h.p. x 120 rev serv. 14200 s.h.p. 20 1/4 - 20 1/2 kn.

Figure 1J. Suffering from vibrations. Too small clearance before propeller. Heavy solepiece ahead of propellertip. Bilderdijk

h:

inst. 26700 s.h.p. serv. 22000 s.h.p. lSkn. 1971

Figure 1G. Good construction.No vibrations. Figure 1H. Good construction. No vibrations. Just acceptable rumbling in stearinggear-flat Rudderhorn too small for hard-over at full speed. because of small tipclearance. Heavy load on rudderpintle.

(6)

..w.

10.00 M

-Figure 1Q. Optimum waterfiow to propeller.

Bare shaft between tailshaft and sterntube. Fairing caps should be 100% fixed. Difficult to obtain reliable corro-sion protection of shafting.

Ponce de Leon, Trailership

1968

i inst. 32000 s. h.p. X 128 rev

22-23 kn.

Figure 1P. Good waterfiow to propeller.

A hollow torque tube between tailshaft and sterntube. Difficulties with corrosion protection.

Far East containerships 2952 containers

Thomas e Cuffe

1970

fast barge carrier

Lash type design Goldman inst. 32000 s.h.p. x 105 rev 21-21 1/2 kn. inst. 2 x 40500 s. h.p. x 136 rev serv. 2 x 36000 s. h.p. 26 kn.

Figure 3A. Good waterfiow to propeller - no vibration troubles. Large tip clearance. Propeller extended on Mannesmann tube supported by brackets. Covered shafting is always accessible. Bearings could eventually be adjusted if necessary.

(7)

Figure 1 M. Suffering from vibrations in afterbody above 26000 s. h.p. Too small clearance of aperture above propellers. Rudder and propeller to be located more aft. (Fortunately tiie accomodation is located away from stern.

rl

10.00 M

Figure iN. Good construction. No propeller excited vibrations.

Texaco Oregon Japan 47000 ts tanker 162 inst. 19000 s.h.p./105 rev serv. 17100 s.h.p. C O O /

i

le r,Q .' inst. 14000 s. h.p./115 rev serv. 12000 s. h.p. ___\_

4.

- L-inst. 32450 s.h.p. x 110 rev serv. 26600 s. h.p. = 82% 21-21 1/2 kn. M 00M

Figure 10. Good construction.

No propeller excited vibrations. Good steering at low speed. No maintenance on rudder. Newbuilding 271000 ts tanker Japan 1973 inst. 37000 s. h.p. /90 rev b ON

Figure 2A. Propeller excited vibrations. Figure 2B. Cavitation and heavy propeller excited Too small aperture. Big sole piece. High maintenance vibrations. Too small apertures. Big sole piece.

on rudder. High maintenance.

WRLCH EREN , o o o

- 37000 t.d.w.

(8)

T

?M

T= i?.- M FL1 loaded ballast

J

Tr11 r

-r

-H.

L AT PEA< 36000 s.h.p. x 85 rev

Figure 3D. Relatively small aperture with simplex balance rudder.

Cheap construction, small steering gear, good stearing. Possibility of repairs on rudder: cone, bearings,

couplingflange, sole piece. High wake peak (-75%) in bottom position. Heavy variations of torque and thrust with 4-bladed propeller are to be expected. (Gearing and thrustblock). Possibility of fore and aft movement of superstructure in ballast. Can full power be maintained in ballast? (Application of fin?). With 5 or 7 -bladed propeller, free vertical and horizontal forces on sterntube bearing, which might cause sterntube-wear-down. Extra 10M 40,30 M

J

318000 t.d.w. tanker Block coeff. 0.84 Afterbody 0.78 HOLTE M

Figure 3E. Proposal for improvement was considered to be impossible because of

standard-ships-production-program of shipyard. "Owners have to accept standard designs".

(9)

+ M

Q.00M

Figure 3B. Considered to be utmost limit for power on single screw. Relatively slender waterline endings above propeller shaft.

540000 t.d.w. tanker Proposal for twin screw

inst. 2x40000 s.h.p. x 80 rev.

ser'. 2x32000s.h.p.

Figure 3C. Pramwith twofree flow propellers. 22° angle to be adjusted according speed-length ratio. Oblique flow should be taken into account for cavitation investigations.

(10)

Results of investigations ou a 50 000 t.d.w.

tanker model with variations in afterbody

shape

Systematic model experiments have been

car-ried out in the Netherlands Ship Model Basin

with six tanker models of practically the same

principal dimensions, but with systematic

varia-tion of the sternframe and afterbody shape.

Results of resistance and propulsion tests are

summarized in Table 1. from which it

can be

seen that different afterbodies can increase the

resistance rernarkably, whereas the effect on

thrust deducti6ñ is even more pronounced. For

each variant, the wake-pattern and the radial

wake variation at 70% and 90% of the propeller

diameter are given in Figures 4A - 4E. To make

direct comparison possible, the radial

wake-variations for all tested models are also plotted

ma single diagram (Diagram I). From this

dia-gram it can be seen that the wake-variation is

strongly dependent on the shape of afterbody.

The section shapes of the different models

are given in Figure 5. Of all the variations A

CHAPTER lI

(m.s. 'Onoba') andE (m.s. 'Doelwijk') have

ac-tually been realised. The final lines of

alter-native E (m. s. 'Doelwijk') are given in Figure

GA and the afterbodies are given in Figure 6B.

Results of torque variation measurements for

both ships are given in Diagram II, from which

it can be observed that the amplitude of torque

variation is considerably reduced by increasing

clearance. This effect is stronger than to be

ex-pected from model test wake patterns.

The influence of the afterbody shape on the

flow around it is shown by streamline tests

(Figure 9).

From these investigations, it finally can be

con-cluded, that the waterflow does not follow the

'cigar', but boils up around the turn of the bilge

at the aft-sections, where bilge radius is very

important. It is clear that flow separation

oc-curs along the upper part of the 'cigar' and the

propeller has to cope with 2 counter-rotating

vortices in the upper half of the disc.

Even with the model no. 6 broad transom stern

and slender hog.

(11)

Table 1. Results of investigations on a 50 000 t.d.w. tanker model with variations in afterbody shape. AT 16 KNOTS 15310 SHP 15210 SHP 15540 SHP 17115 SHP 16197 SHP

SHP 100% 99'%

10i%

112% 105%

WAVE+FORM/FRICTION 3430 +7730 3430 + 7730 3540 +7740 3859 +7774 4110-4-7774 EFFECTIVE POWER EHP 11160 11160 11280 11633 11884

EHP 100% 100% 101% 104% 106% 0,729 0 734 0 726 0 680 0 734 SHP Propulsive efficiency 100%

i00%

99% 97% 101% Revs/mm. 101,5 104,4 107,1 102,3 100,0

Resistance 98,6 ton 98,6 ton 99,8 ton 102,8 ton 105,0 ton Thrust 121,8 122,6 122,6 150,6 ,, 140,6

Thrustdeduction 19,0% 19,5% 18,7% 31,7% 25,3%

CAD_D 2/3 V3

463

-

466 456 415 438

SHP

ONOBA HOGNER HOGNER

Test 15436 Test 15437 Test 15660 Test 17458 'l'est 17531

MODEL No. 1574 No. 1574 No. 1574 c No. 1959 No. 1959 A

LENGTH O-20 M 216,400 M IDEM IDEM IDEM IDEM

LWL M BEAM M DRAUGHT M 222,024 M 31,240 M 11,547 M ,, ,, 221,370 IDEM 221,370 IDEM DISPL. M3 61265 M3 IDEM 61255 M3 61273 M3 61273 M3 WETTED AREA WITHOUT APPENDAGES 9721 M2 9698 M2 9761 M2 9761 M2 WITH RUDDER 9797 = 100% ,, 9778 9881 = 101% 9881 =101%

PROP. BLADES No. 2503-5 No. 2522-4 No. 2522-4 No. 2503-5 No. 2503-5 DLAMETER 0 = 6800 0 = 6900 0 = 6900 0 =6800 0 =6800 PROP. PITCH O,7R H=5282 H=5134 H=5134 H=5282 H=5282

(12)

Test 17532 Test 17459 Test 17550 Test 17731 Test 18710 Test 19605 No. 1959 A No. 1960 No. 1960 No. 1959 B

IDEM IDEM IDEM IDEM

221,370 222,700 222,700 226,400

IDEM IDEM IDEM IDEM IDEM IDEM

61273 M3 61241 M3 61241 M3 61304 M3

9761 M2 10087 M2 10087 M2 9746 M2

9881=101% 10218=104% 10218=104% 9869 M2

SPARE PROP. WORKING PROP. LIMA BRONZE CUNIAL

No. 2611-5 No. 2503-5 No. 2611-5 No. 2522-4 NC). 3164-4 No. 3336-4 = 7000 = 6800

H=5200 H=5282

0,579 0,570 0,579 0,523 0,544 0,538

has been made has been made with 1.24% more pitch 15403 SHP 15320 SHP i00% 100% IDEM IDEM 98% 98% 443 436 443 465 461 463 HOGNER DOELWIJK 0,742 0,706 0,717 0,716 0,710 0,714 102% 97% 98'%

98%

97% 98% 96,5 103,7 99,7 105,2 102,5 103,2

good pitch too small 105,0 ton 101,4 ton 101,4 ton 96,6 ton 96,6 ton 96,6 ton

140,6 135,1 132,1 127,3 127,6 ,, 127,6 25,3% 24,9% 23,2% 24,1% 24,3% 24,3% 16009 SHP 16259 SHP 16017 SHP 15263 SHP 104% 106% 104%

99%

4110+7774 3448+8032 3448-4-8032 3180+7755 11884 11480 11480 10935 106% 103% 103% 98% = 7000 0 = 6900 0 = 6900 0 = 6900 H=5200 H=5134 H=5196 H=5196 D D E

(13)

hull form 'Onoba'

Figure 4A. High wake peak in top - cavitation. High wake peak in bottom position.

With 4 bI. prop. strong variations in torque and thrust.

With 5 bi. prop. strong variations in transverse forces on sterntube and bending moments in tailshaft.

o

Figure 4A'. Sole piece removed. Not much improvement.

e.h.p. = 100% i = 0.729

(14)

Figure 4A". Example of type 4A'. Not much improvement.

s.s. Caltex Amsterdam.

e.h.p. = 101% î = 0.726

s.h.p. = 99 1/2 %

Figure 4B. Rounded hull shape below propeller shaft. Large improvement in bottom position. No improvement in top.

(15)

Figure 4C. Fat Hogner cigar. Two vortexes excited, p and s, contra rotating tangential flow in propeller disk. Flow separation above propeller shaft, bhmt waterline endings at 8 m did increase s.h.p. value.

e.h.p. = 104% '= 0.680

s.h.p. = 112%

e.h.p.= 106 1/2 % r = 0.734

s.h.p.= 105 1/2 %

(16)

A

Al

E

LI

4

Figure 4D. Slender Hogner cigar below transom stern. Two vortexes excited. Insufficient wake filling of wake field according to model test. How will be the wakefield on the ship?

-IQ.OQ

\... 's ''-O.. 5

-s

Axial wake at 0. 7 R measured with normal pitot tube

-O--e.h.p. = 103% rj = 0.706

s.h.p. =106%

variation of angle of attack

(17)

Figure 4E.

DOELWUK

Normal afterbody A

WI

Hogner afterbody C

Figure 5. Hogner cigar and transom stern D

(18)

Figure 7. Esso Essen. A. G. Weser stern.

Note the difference in clearance above propeller shaft.

UIILUIW

11t!

:'.I

-.

-Figure 8A. Doelwijk.

Note the difference in clearance above propeller shaft.

Figure SB. Doelwijk.

- Wide aperture - no vibration troubles.

- Free Oertz rudder - expensive.

Good steering and course keeping. Low maintenance costs.

TORaUE VARIATION

Diagram II. 'Onoba' and 'Doelwijk'. Reduction of vibrations by increasing clearance. Figure GB. 50 000 t. d. w. tankers

(19)

C. Hogner afterbody. D. Hogner cigar + transom stern.

C. Hogner alterbody. D. Hogner cigar + transom stern. Note separation of flow at bilge rounding.

Type C. Hogner afterbody. D. Honer cigar + transom stern. Figure 9. Netherlands Ship Model Basin.

(20)

Flow patterns of ships with extreme L.shaped

aftvrbod íes

As mentioned in the historical review, short

afterbodies combined with stern-bulbs are

com-mon nowadays. In this section two such

after-bodies will be discussed: a L.N.G. -carrier and

a container ship, both single screw.

Streamline

tests

and

3-dimensional wake

measurements have been carried out for the

L.N.G.-model (Figures 10 and 11).

The streamline test shows that flow separation

occurs aft of section 2' above the turn-up of the

bilge.

Due to the broad, flat bottom under the engine

room the inflow into the lower half of the

propel-ler disc is strongly decepropel-lerated. This vessel is

a pure blunt-ended wake-maker. 'Engine

funda-tion far-aft creates high wake values'.

The axial wake variations vary the angle of

attack of the propeller blades. From Figure 11

the attempt to obtain a homogeneous wake field

would seem to have been very successful in this

case, provided one restricts oneself to axial

components on model scale. However, because

of scale effect in the wake, the result might

turn out less favourably in a full-size

ship.

Moreover, the tangential wake components will

create fluctuating

entrance

velocities at the

propeller tip sections. It may well be that the

'camel'-type vibration (diagram with humps, at

one - and two-times blade - frequency,) as found

from vibration measurements on many single

screw vessels, can be explained as

follows:

During one revolution, the blade is struck by the

axial wake peak at top position and, shortly

CHAPTER III

afterwards, by the counter-rotating flow at

ap-proximately the 30° to 50° blade position. This

counter rotating flow on SB side increases the

propulsion efficiency however simultaneously

excites vibration.

More extended tests have been performed on

a container vessel. 'Abel Tasman'. The results

of these tests are given in the Figures 12 and

13. Because of the lower block coefficient of

this fast vessel, section number two is far less

full (Figure 14). The fact that the propeller disc

is not completely filled-up with wake, causes

large radial variations.

In this case too, tangential wake components are

present. Although the cavitation pattern itself is

acceptable (Figure 15) its influence on

hull-ex-cited forces is such that severe vibrations

oc-cur above 80% of the nominal power.

Pressure fluctuation measurements on model

scale and on full size have been carried out

(Fig-ures 16) Ref. [1] [2].

Sketches of the streamlines around the

after-body, as deduced from painttests and pitot tube

measurements, are given in Figure 17, From

these it

can be seen that there is a strong

vertical component inherent to the U-shaped

afterbody sections. The wake peak in top

posi-tion could be reduced, for example by the

ap-plication of a fin or tunnel (Figure 17D), and

improvement of the vibration level caused by

hull vortex cavitation could be expected.

How-ever

it

must be stated, that fitting fins or

tunnels above the propeller cannot reduce

vibra-tions caused by the tangential inflow (Figure 17 E).

(21)
(22)

axial wake

tangential wake

o

Gastanker 34000 s.h.p. x 110 revs, i = 0.74

40.00M

3 dimensional wake-field (5 hole pitot tube) N.S.M.B.

A5 TAN KR SPC&D OÇS4IP V - oo o

OT

SO' V.o Sg, 0. 49 ',

V

V,,,.

S. S.S .. 'g

Figure 11. Variations of resultant speed. Small variations of angle of attack (as far as model tests).

._____ _.

00

_i

.

i!JlJâ

TH'jj

(23)

s.s. Abel Tasman containership 32450 s.h.p. x 110 revs = 0.62.

3 dimensional wake-field (5 hole pitot tube) N.S.M.B.

O .n no 141

Figure 12 Variations of resultant speed. Strong variations of angle of attack.

10 O - . . . 8o V...o.So. I.8,_ Z. '% tE'." 10

...,

T. 10 .Oft;,

,

RC

j

PS»

W W W

a 5

-

g .'

_ ia

.ò -: t0

:.

:-D0.

(24)

Figure 13.

(25)

a

Figure 1M. Dummy of afterbody in cavitation tunnel (N.S.M.B.). Note pressure gauges above propeller.

Figure 15. Cavitation pattern on model propeller. 32450 s. h.p. x 110 rev.

0.5 0.4 0.3 0.2 0.1 o

1UUU

UUUAU

100

R.S. pim.

PR3RB UaJA18 (i'op - Top )

Figure 16B. Full size pressure fluctuations. Because of contra rotating vortex on SB side, pressure fluctua-tions are much stronger.

mean top-top

(26)

\

\

/ ,' N

\

J N

,.. /,

N.

-.---'

,'///'1

'

\

\

/

/ /

B. Excited vces strongly influenced by trim and

shallow water.

Figure 17.

A. Excited vortex by small bilge roundings.

/

/

/

¡ 1 f ', .,* I /

(,(çf('

i

/ / / /

/

,1

,/

/

/

/

/

z

/

/

,/

,/

j/

/

/

/

/

/

/

/

/

/

/

f

/

/ / /

/

/

/

/

/

or tunnel. Directing flow to

Function of Ito D.

propeller equalizing wake by reducing the wake peak in top position. However not influencing

(27)

or nozzles. However, these modifications have

nearly always been carried out after the troubles

had manifested themselves. Only nozzles have.

in some cases, been decided upon at an earlier

stage. For the first time, a fin has recently

been installed as original equipment on the m. s.

'Carl D. Bradley' (Reference [3]),

shown in

Figure 18. The results obtained were as follows

according to the report:

The fin reduced the vibration amplitude to

one-fifth of its

previous value in deep water, and

two-fifths of its previous value even in shallow

water.

The psychological improvement was great. To

the crew the vibration had completely

clisap-pea red.

All the difficulties existing before the fin was

fitted had vanished completely. It was a

spec-tacular difference to those who had lived with

annoying vibrations for so many years'.

Interesting investigations of the effect of fins

have been carried out on the 230 000 t.d.w.

tankers 'Thorshammer 'and 'Norse King'

(Refer-ence [41). On both ships the purpose of the fins

was to reduce propeller induced hull pressures

and cavitation. Figure 19A shows a general

ar-rangement of the construction and position of fin

and propeller, as well as the position of

trans-ducers for measuring pressure

fluctuations.

Figure 19B gives comparative values of full

scale pressure fluctuations and vibration levels,

measured without and with fins.

The results of wake measurements in a towing

tank (Figure 19C) show that the influence of fins

on the wake patterns is remarkable, especially

with propeller.

As a result, the cavitation patterns will also be

favourably affected (Figure 19D).

From these investigations it can be concluded

that the introduction of afterbody fins

signifi-cantly improved the cavitation performance of

the propeller and favourably affected the

propel-1er -induced forces on the hull. Figure 20 shows

it was concluded that the wake had very high

local values in the upper part of the propeller

disc, and this was considered to be the main

cause of the vibration problem. In order to

im-prove the water flow through the propeller disc,

flow accelerating fins were placed on the stern

above the propeller. From measurements

car-ried out by Lloyd's, it appeared that the

im-provement on the wake field was such that, for

certain points, the amplitude of vibration had

been reduced to about 1/3 of previous values. In

this case, the fitting of fins reduced vibration to

an acceptable level. Two examples in which the

fitting of tunnels cured vibration problems are

given in Figures 21 and 22, a suction dredger

and a container ship. For both cases the tunnels

were designed by the Netherlands Ship Model

Basin.

The

single

screw

container

ship

'Abel

Tasman' has a relatively small aperture above

the propeller shaft. As mentioned in Chapter III,

severe hull vibrations occur when running the

turbine above 80% of its maximum loading. In

our opinion the stern-bulb does not contribute

much in reducing propeller-induced vibrations

and it would have been better if propeller and

rudder were located more aft. To improve the

vibration characteristics in the existing vessel,

proposals were made for fin-alternative tunnel

constructions (Figures 23 and 24).

The influence of fins on the axial wake can once

more be observed from Figures 25 and 26

-where results of wake measurements, carried

out at the Norwegian Ship Model Experiment

Tank, Trondheim, are shown for a ship without

and with fins.

Ducted propellers have been used for many

years to improve the efficiency at high propeller

loadings (Figure 27). The possibilities of a

non-symmetrical nozzle in equalizing propeller

in-flow, however, deserve more attention from all

concerned with propeller-induced vibrations,

Ref. [6].

(28)

o 355 350

Figure 17E. Two contra rotating vortexes on ss 'Abel Tas man'

(29)

Figure 18.

Fin installed on Great Laker 'Carl D. Bradley' which

suffered from heavy fantail vibration SNAME 1952 [3].

(30)

230000 T D W TANKER THORSP-IAMriER + NOSE-KiNG 310.98 M 8 48)0 M r 0.44 M i .844

M r.

T 130 M n, Fïgure 19A. O4 M 3 ..,5. L4.%

1971-72 Vibration investigation on 230 000 ts dw tanker by Swedish State Experimental Tank and Det Norske Ventas [4,4A].

Mod.i *3)5.

Fait Sc,I.;Thor.ho.m., 5 bi wth.,t lins

Wtb

D N.. K.ng 6 bI wN t'ss

WL 2

Fr0 Fr 1/4

Positions of transducers. For measuring pressure

(31)

02

0.1

Ampi mm

Figure 19B.

- -o- - Fnr .hp;Thoruor 6v wOfl.6 i'o

.-- Sfld lP;No. Kin0'6bi

Mees. pool Dl 02 03 Dl 02 03 1)4 05 Direct of vibr V L ir V L ir V V V

Vibration levels in deckhouse. Numbers indi-cate approximate number of rev, per min.

Ampi mm O OS 04 03 02 0.1 0.1 O

Measpoint V2 V2 VI. VI. V5 VS

--°--Firsl Ship horshamrner"5blwjthout fins -.--Second ShipNorse King 6 bi with fins

V2 VI. VS Vt V3 V6 V6

Vibration levels in wing tank No. 5, SB. Numbers indicate approximate number of

rev, per min.

62 Ballast

/

/

/

/

/

/

//'

/

.

--

Fully loaded

7-ijoode d

----k

__'i

-es Baltast -\ /\ / Fully loaded

IAri.

q 7

A\w

V

es 65 BALLAST B/. - FULLY LOADED /l

/

q40 78o ¡ i 62 L I o I / I 58o /

i\

.i 68

''1

¡ I / '62

i,

i, 8 61 84

.-04368 81 73 ' 75 30 50 70 90 Number of revs/mm

Pressure fluctuations in full scale. Pressure fluctuations in full scale. T/T 'Thorshammer' (first ship) with and T/T 'Norse King' (with fins 6-bladed

without fins. propeller).

520

als

010

oc

(32)

00

0(Tj

0 45 90

os ,

ieo

Figure 19C. Results of wake measurements in towing tank. Radius, R = 70 mm. Results without propeller measured in the propeller plane. Results with propeller measured 68 mm forward of the propeller. Note reduction of wake-peak in top position (00) by fin.

i

Model with fins, 5-bladed propeller

ÍqTh' FINS sÇflOJT FINS

_,_ .fl_

OtflL 75 50 Mx 75 50 ¡s o o o o

Model without fins, 5-blded propeller

Figure 19D. Tests in cavitation tunnel. Cavitation patterns in different blade positions. Different hull-propeller configurations. Fully loaded condition, 16 knots.

FU.LY ¿I4V *Th UEP a5 90 os 'do 45 w os . ,

\

NNJ

--w

loo 7! 50 ¡5 o o 45 90 05 9. 50 25 C,

(33)

s,

CE

Figure 20. 1969 Installation of flow accelerating fins in 33000 ts bulkcar-riers 'En Gedi' and 'Avedad',

propos-ed by SSPA, S + SR March 6-1970.

p 2

Fins PSB

Transmitter in

11200 a. p. k. /135 rev

Figure 21. 1972 Installation of tunnel on dredger deepstone. Proposed by N. S. M. B. A large reduction of vibration was obtained.

3

For certain points the amplitude of vibration is reduced to about 1/3.

(34)

Figure 22. 1973 Containervessel SL 181 being fitted with a tunnel, as designed by N. S. M. B. - from the 32000 s. h.p. installed, only 25000 s. h. p. could be applied because of vibrations, - after installation of tunnel it is possible to use 29000 s. h. p.

(35)

Figure 23. s.s. 'Abel Tasman'. Fin-arrangement proposed by S.M.T., Trondheim.

Installed 32450 s.h.p./11O revs. Normally in service, without fin or tunnel: 26600 s.h.p. = 82% can be used without suffering from heavy fantail vibration.

(36)

Investigations on a tanker model by S. M. T. Trondheim.

270

Figure 26. Wake pattern with fin.

i 90

Figure 25. Wake pattern without fin.

180

(37)

1970 'Golar Nichu' TS Tanker fitted with Kort nozzle. 215000 Ts d.w., 30000 s.h.p. x 90 rev.

Figure 27. Better steering and course keeping. Less variations in propeller revs in a rough sea.

Clearance forward of propeller should be increased to obtain in conjunction with nozzle reduction of vibrations.

(38)

A new design philosophy for big ships with

pram-type afterbodies

To avoid vibration and cavitation problems on

L. N. G. -carriers and half million tons oil

tan-kers, wake-making

afterbodies

fitted

with

stern-bulbs, where the propeller has to pass

wake peaks of 50 to 70% causing enormous

variations in blade loading, should be abandoned

(Figures 28A-B and 29). A better solution is to

aim at a free flow of water into the propeller

disc by mounting the propeller in the end of a

long tube, supported by brackets, as far as

pos-sible from the hull.

The hull

itself should be of the roud-bottom

form, i.e. a pram which is completely different

as compared to usual tanker bulbs. Extreme

U-shaped sections should be replaced by flat

sections, allowing an easy upward flow. As a

result, the overall length of the ship has to be

increased, resulting in higher building costs.

The latter could partly be compensated by using

developable hull surfaces (Figure 28C). The

de-creased course keeping qualities of the

pram-type hulls can be improved by the use of

hard-chine seams.

Obviously, the block coefficient and prismatic

coefficient of the afterbody are not determinant

ChAPTER V

for the likelihood of flow separation, because

these coefficients say nothing about the direction

of flow. For pram-type hulls, the flow direction

with respect to the propeller shalt is the

deter-minant parameter.

A proposal of a pram-type afterbody design

for a half million tons tanker is shown in Figure

29B. This ship can be equipped with either two

or three propellers. The twin screw installation

with a skeg at the centre line represents a sound

solution,

yielding

acceptable

manoeuvring-properties, and enabling the ship to be

drydock-ed on centre line dock blocks. The construction

of this ship type necessitates an extra length of

about 15 m as compared with a conventional

ship.

The increase in length can be restricted to about

3. 5 m by application of a stepped configuration

(Figure 30).

Admittedly, problems are then

transferred to the engineering department. The

critical angle of turn-up of the ship's bottom is

determined by

the

speed-length

ratio. The

situation of the gearing foundation, the propeller

tip clearance and the position of the rudder in

the propeller race are determinant for the ship's

length.

(39)

Figure 29A. Extra r Figure 29B. I H

Pi: I

.

.-

r

!uwIu

E-DOCK 0-KECK C-DECK 8-DECK A-DECO Inst. 34000 s.h.p. x 110 revs Counter rotating-vortexes.

ROPO5KL FREE-FLow-pRopEu.ROpen stern variant. Increase

of length 12 m. Simple deve1

opable hull surface.

450000 t.d.w. shallow draft tanker Verolme design.

inst. 45000 s.h.p. x80 rev.pm.

530000 t.d.w. tanker.

inst. 2 x 32000 s.h.p.

Proposal of pram-type stern with free flow propellers in-crease of length 15 m.

(40)

Figure 30. Proposal of pram-type with small increase of length. Problems and extra costs are transferred to engine -room.

'hIIiIPAIUPni

UIL Ull!U!UhllW4

iuh'

ILU1

iiiiuuiu

Figure 29A. 450000 t. tanker. Shallow draft. Verolme design.

-Figure 29B. Developable hull surface. Better course keeping. Small increase in s. h. p.

/

Figure 29B. Extended skeg on centreline. For course keeping and good steering.

(41)

timum is obtained, according to model tests,

with moderate U-shaped afterbody sections,

resulting in a relatively high effective horse

power in combination with a high propulsive

ef-ficiency (propeller operating in a region of high

wake). However, the regaining of energy from

the wake is counter-balanced to a large extent

by thrust deduction phenomena.

This was demonstrated by Van Lammeren,

Reference [7], in his model experiments on the

'Simon Bolivar'. By systematically moving the

propeller further aft, it was found that the

max-imum propulsive efficiency was obtained when

the propeller was located twice its diameter

behind the usual position (Figure 31). The

con-clusion is that the propeller-rudder arrangement

should be located as far aft as possible.

The free flow principle, as a means to cope with

vibration and cavitation problems, is therefore

not necessarily in conflict with performance

op-timization.

Figure 32 shows some typical examples of

ships where free-flow propellers have been

ap-plied.

For twin screw ships the optimum is obtained

by creating a hull with lowest attainable

effect-ive horse power in combination with maximum

propeller efficiency and minimum appendages

resistance.

Model tests indicate that twin screw vessels

require about 5% more horse power than their

single screw equivalents. This difference could

not be confirmed by full-scale

observations

performed on the large fleet of twin and single

screw ships of the Royal Rotterdam Lloyd.

The

wake scale effect and the scale effect in

append-ages drag tend to reduce the observed difference

on model scale. In addition, the open water

ef-ficiency of the twin screw configuration

com-pared to the single screw is favourably affected

by the following factors:

- higher speed of advance

- smaller blade area ratio

- lower optimum r. p. m. at equal diameter.

over the last 20 years can be summarized as

follows. Severe difficulties with regard to

vibra-tions were encountered when the power of ships

having sharp and narrow sternframes had to be

increased. Omitting the sole piece of the

aper-ture did not relieve the problem because the

wake peaks in the bottom position remained

un-changed (Figures 33A and B). However, moving

the propeller and rudder as far aft as possible

resulted in a large reduction of vibration level.

Cavitation erosion was reduced and steering was

improved, Figures C and D.

Mounting the propeller on a thick walled tube

and fixing this tube in the stern is difficult and

expensive. Vibration calculations of the free

supported tube with propeller should be carried

out to check that the resonance frequency is well

below blade frequency in service condition. The

consequences of a possible damage to one

pro-peller blade presents another problem. A simple

and relatively cheap solution consists of a

con-struction in which the shafting, covered by an

excentric

tube,

is supported by

a

slender

bracket underneath the stern.

We propose that this development be continued

for both single and twin screw fast container

ships.

Figure 34 (References [81,[91,[10I,[11I, [12])

illustrated the anticipated trend in the

develop-ment of container ships with regard to hull form,

propulsion and general arrangement:

- Free-flow

propellers instead of propellers

behind 'onions'.

- Considerably increased clearances.

- Super

structure located more forward, to

prevent the accomodation from whipping. This

will reduce the container capacity by about

one percent.

- Trend from U-shaped

afterbodies to flat

bot-toms.

- Large rudders, preferably with a large fixed

skeg area to compensate the reduce stability

on a straight course clue to the flat bottom

afte rbody.

(42)

Experience with the large Far East twin screw

container ships proved that with free flow

pro-pellers (tube in brackets. Grimmsche Welle.

slender bossings) hardly any vibration was

ex-cited. Model tests in the cavitation tunnel

show-ed that pressure fluctuations were about 1/6 or

1,'7 of the values measured for conventional

single screw container ship models.

The wake field of these 2 x 40 000 HP twin

screw ships is remarkably homogeneous (Figure

35). with axial and tangential wake values up to

20 and 14

respectively. The comparable

Sea-Land twin screw container. - U S construction of open shafts,

- Careful attention should be paid to fairing-caps.

single screw ship of 32 000 HP. on the contrary

shows axial wake variations from 5 to 55

anda

tangential wake up to 20

(Figure 12).

Results of investigations on streamline and

wake pattern at different appendages are given

in Figures 36A and 3GB, whereas results of

pressu re fluctuation measurements at diffe rent

longitudinal

propeller locations are shown in

Figure 36C.

Constructional details of shafting arrangement

of the twin screw container ship are shown in

Figures 37A and 37B.

(43)

807 307

o

Figure 31. Analysing propulsive components. s.s. 'Simon Bolivar model without rudder.

Toe-stand

N0

ON

e s

i-e

FL;

ps T1p ps N/mm a A 0,745

0,287 0,236

1, 072

0,695 0,674

1, 031 75, 0 B 0, 778 0,218 0, 144 1, 096

0,710 0,702

1, 012 75, 9 C 0,793

0,173 0,087

1,105

0,718 0,715

1,005

77,1

D 0,783

0,107 0,044

1,070

0,732 0,728

1,006

79,8

0, 734 0 0 1, 000

0,734 0,734

1, 000 84, 4

(44)

C3 vessel 1942. 8500 s. h.p. /85 r. p. m.

'Leuve Lloyd'. 17000 s. h.p. /115 r.p.m.

Figure 32.

'Brunsbjittel'. Ir. E. van Dieren.

'S. -Lloyd' 1949. 10500 s. h.p. /115 r. p. rn.

(45)

Figure 33A

LEUVE LL.OY

17000/115 r.p.m.

op

Conventional underwater bodies with transom stern.

5TT NGMK

STRRT N. ¿bQYk LZOV $ - 7OOO I 16700/115 r. p. m. 'L Figure 33 B. Small tip-clearance. Rumbling of steering.

Gear flat.

Small clearance before propeller. Suffering from vibrations.

piece. Big sole

(46)

'M -Lloyd'

Effect of moving. The propeller aft. Smaller wake

peak.

Figure 33C.

From the model test wake field it could be con-cluded that the wake peak evoked by the skeg is noticeable far behind it, but this effect is reduced on full scale. RUDR TRQU Increased rudder torque. Figure 33D 1-2% less h. p. required.

Dependent on thickness of rudder. Less cavitation. Less vibration. NOME NT 1ERtNC N IMT / -1'

ml /

\

i

\

tilo I -\ 'i I \

L

Improved steering. i I

(47)

Encounter Bay' h.d.w. 32000 s.h.p./136.

:::::.

p:_: L_4.-1,-_4.

::L:::

--- -

-w

--==-- = =

= =

r-

: iI*IiIt-:EI

______

-i.. '2I -

_____ _______ .1

- -

-'Sydney'/'Abel Tasman'. 32450 s.hp./110.

Project South Africa. 36000 s. h.p. /121.

I

-:1:-.! L

'Bremen Express'/NedLloyd 'Dejima'. 2 x 40500/136. Development of container ships trend towards: - Free flow propeller.

- Superstructure away from stern.

(48)
(49)

-

Al OiR AT OIR

Clearance between propeller and tunnel too large.

Figure 34C. A. G. Weser stern bulb not effective in top quadrant.

-I

California Star

Encounter Bay

(50)

-

4000 M

Wake field tending to pattern of a twin screw bossing configuration.

Wake field tending to pattern of a twin screw bracket configuration.

Westlander Project

Ir. E. van Dieren

lo0

NedLloyd De ji ma

DM CROf bOO

(51)

Figure 34E.

S- ..

Z1. S DSP?T

I Sa, rs D'SP

Increased:

- Axial wake peak

- Tangentialwake

-

.,J2

__-Shalt supported by brackets.

FT C GOIP QFF'iRS B

Hogner cigar.

FAT CRLP4EE Df

-Narrow sector of moderate axial wake

- Small tangential wake. Due to slender shalt tube.

'ITs

I

«ill

Ai

'JA

u

IWa

2,

(52)

°R0PELLEÑ Ø 6300 I I I I I j 0 IO 00 30 40 TNG.Rfl. WAKE Ø $900

PIPE +STRUTS 86

5-1OLE- PlTOT-WQKE

PA fAIT CONTAINeR - NfD.OVDDCI,.lA

n Oc UCTATIOM AT all 6000 Io lo 1 ¼ 'z ¼

t

. I4S.O . ,b.. OIO V. aoJo.,., 4. V.0

100 V. 14J.lA5.It.3 I'_ IÇ.141.0.11.1r,o..

(53)

Bos sing

Pipe with struts. 700 angle.

Pipe with struts. 86° angle.

Paint test at N. S. M. B.

(54)

Figure 36B.

Bossing with small clearance ahead of propeller.

AXIAL- PITOT- WAKE

Pipe without Struts.

05

05_O7wAK

04 40

lo

4

Note small influence of struts on wake.

q-

--Bossing with increased clearance.

AXIAL- PITOT-WAKL

Al o.85 R.

FAT OSSING

5LENOE BOSSINC

PIPE WITH $TUTS

-PIPE wITI4OV-r

Pipe with struts 70°.

\/AKE

TWIN SCREW CONTA INR 5HIP

05

AXIAL TOT

:i-

5EPM-o-r

5010

AXIAL-PlTo-r- WAI<C AXIAI.-PITOT WAI<

ojo 04F I 04

j"

O 854 064 03 20 40 00 365/0 IO ANGLE N DEGREES 90

(55)

o OZ 50Z 4OZ 30% TIP-CLEARANCE % ØPROP s,"' ."ti a .t

/.a

.s .4 .s . .° ., . î .5,

Figure 36C. Aft most location of propeller is less suitable for good steering. The middle position was elected.

Mannesman tube to cover shafting.

(56)

--EXOENTRIC-PiPE Ø10o.35O) TTrT1r H Lii

i

1iiÌ

m

liuuiiiiiuìiïià,1

tXJT5IDE OIAMTER 1QOO',, WLLTHICKHE.S5 3O35,,n,

t .

__--,

Figure 37B. Construction details of shafting arrangement. Stiffening inside tube is not necessary, and due to excentric shaft position, easy access is possible.

(57)

Figure 38. Some typical shafting arrangements.

1" ree flow propeller on single screw Ro-Ro vessel. Designed by Transaflantic in combination with SSPA. Slow turning diesel engine out of centreline because of 3 Ro-Ro lanes in cross section.

Twin screw tube in brackets. Far East con-tainerships.

(58)

NedLloyd Dejima

Figure 39. Far solution to obtain optimum inflow of water in propeller disc of side propellers of triple screw. Far East container 'Nihon'. Intermediate tube covers shafting.

(59)

Nice triple screw arrangement of 'Selandia'- Far East. container.

(60)

Obstacle on sole piece causes cavitation and vibration.

'W-kerk' small aperture. Heavy sole piece.

Heavy propeller excited vibrations. High wake peak.

(61)

40000 30000 20000 toaDo 50000 SHP inst 50000 40000 30000 20000 tO 000

Free flow propellers giving no vibration troubles. AREL TASCAS ò; 500010W ASCE

/

/

2T1000 TOW IRR. TANKER

/

ENC OAT ATL.STAR

/

elLROhJR /

/

/

/

TEXACO OREGON CALIF STAN 500KO T TAIlS ER DOECWI,R ONEREI L.LL000

/

REERT/OALCRtfi0R ;!CL000 STO.006ASORI I, SOSTO N000E

III

. 20500010W TARIT ER 4P01 40'

-425000 T ARROI TANKER Tw

f'

271000 OAE 2300007 TORREO SORSE RING WINOS T AR RET ne / 1500007 RILOENTIIR AÎL.S'AR 51100070W c TOSMAN, 720000 0,0 RUSIA CONTAIS eAR ' ROCCE EAST LASS RE LEON EIICOLÑTER OULECORT. CALIF.SIA'R

/

STELL TUNEE 500007

-TE NACO MLLODSLLOOO lAP TAIIREft00540060

.1,.LLOROfe" OOELWIJR WAjCRERER R.ERR

0OTAU50''

- I,. ROTA BARDE

I I I I I I I

Nv

I I T

2 3 4M

TIP- CLEARANCE

Practical diagrams for determining clearances where character of wake peak should be taken into account.

3 4 5 5 7 8 9M

(62)

St a t em en t

Regarding experiences in the past and looking

into the future, with sharply increasing shaft

horse powers the authors ask for severe

re-qui re ments regarding propeller clearances by

the Classification Societies.

Still more practical research on ships in

ser-vice is necessary and model testing on propeller

excitation should have priority at Research

In-stitutions.

Rekreiiees

Jonk, A., Kooy, J.v.d. , Hylarides, S.,

'Perform-ance and propeller-induced hull pressure fluc-tuations of containership t. s. s. 'Abel Tasman'. Report No. 70-364-DWT/ST. Tests carried out at Netherlands Ship Model Basin. October 1972.

Netherlands Ship Research Centre T. N. O. Wevers, L.J. , 'Full scale pressure fluctuation

measurements on board of t. S.S. 'Abel Tasman'.

Prelimenary report of IWECO-TNO,

Nether-lands Ship Research Centre,December 1972. Baier, L. A. , Ormondroyd, J., 'Vibration at the

stern of single screw vessels', S. N.A. M. E.

May 1952.

Lindgren, H., Johnson, C.A. and Simonsson, E., 'Propulsion and cavitation investigation on 230,000 ton dwt tankers', Full scale and model experiments.

4A. Johnson, C. A. , Sntvedt, T. , 'Propeller excita-tion and response of 230. 000 tdw tankers', Det Norske Ventas, Publication no. 79.

Shipbuilding and Shipping Record, 'After-body

vibration reduced by modifying wake distribu-tion', March 6, 1970.

Minsaas, K. J. , 'Golar Nichu', Shipping World and

Shipbuilder, June 1971.

Lammeren W.P.A. van., 'Analyse der Voort-stuwings componenten in verband met schaal-effect by scheeps modeiproeven', Dissertation 1938.

Kringel, H., Schneider, B. ,

'Schwingungsunter-suchungen an den Containerschiffen 'California

Star' und 'Columbia Star'. Hansa, 1971,page 2145 -2173. 'Melbourne Express', Schiff und

hafen, 1970, page 1011.

Acknowledgement

The authors would

like

to express

their

gratitude

to Mr. De Ridder, Mr. Scheer and

Mr. Koch of NedLloyd, and Miss Karen

Rin-kema, Miss Corne van Essen and Mr. Ruimers

of Lips Propeller Works for their kind and

patient cooperation in the preparation of this

paper.

Meek, M.,

'Encounter Bay - The first

O. C. L. containership'. R.I.N.A. 1969. Motorshipl969/ April.

Conn, R.B., Erotokritos, N.R., Joy, A.W., and

Wilishare, G. T. , 'The propeller excited vibra-tion characteristics of a 30. 000 tdw

container-ship', B.S.R.A. , December 1970.

Langenberg, H. , Schönfeldt, H., Schwiers, G.

'Containerschiff 'Sydney Express '/'Abel Tas

-man'. Blohm & Voss. Schiff und Hafen, page

891, 1970.

Kringel, H. , Albert, R., 'Containerschiff 'Bremen Express', Bremen Vulkan. Hansa, 1972, page

2043.

MS 'Widar' -145. 000 Bulkcarnier FRIGGA REDERI,

Blohm & Voss. Schiff und Hafen, 1971, page

453.

Does, J. Ch. de, Rijksen, I. H.W. , 'Investigation

on a 425 000 tdw shallow shaft tanker', Verolme Shipyard. Schiff und Hafen, 1971, page 770. Reports of Netherlands Ship Research Centre T. N. O. regarding several tests, carried out at Netherlands

Ship-Model Basin on

Far East Containership Model 3865. Bremer Vulkan 977, 978, 979, 980.

'Bremen Express', 'Hongkong Express', 'Nedlloyd

Dejima', 'Nediloyd Delft'

Resistant and Propulsion - Appendages -Wakefields Hull Pressure Fluctuations

Cavitation Manoeuvring Seekeeping.

Cytaty

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