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Report No. 1+1,

February

1966,

LABORATORIUM VOOR

SCH EEPSBOUWKUNDE

TECHNISCHE HOGESCHOOL DELFT

A STUDY ON HE MOTIONS OF A MODEL Q? TEE'

SXXTY ERIE8 EQUIPPED 1ITh FIXED AND

CONTROLLED BO AHIPICiING ?XNS.

By: Ir J.fl. Vugta,

(2)

i

pable of oontet8.

paf.

Liet of ermbola.

ii,

List of figuzee. V

List of tabtes.

8ummarr.

i

1. Introduction.

2

a. Th.

sthod of calculation and ita experimental Verification.

3

2.1. Theoretical calculation of the contribution of the fins. 3 2.2. Measurenents of the coetfotents in the equations of

otion.

7

2.3. Meaeuremortte of wave forces and momenta. 8

2.k. Çompari3on of seasured and calculated oton in waVes.

8

3. Controlled bow fine. 9

3.1. The control system. 9

3.2. The coefficients in the equations of motion. 11

3.3. Experimente. 12

3.k. Comparison of measured and calculated

cosUiotento when

pitching with controlled fine. 13

3.5. flesulte of the measurements of the rematnin coeffictente. 1k k. Analysie of the resulting ship motions for no fina, fixed fine

and controlled fina.

14

The

flow pattern about the tine.

16

Discussion ad conclusione.

19

App.ndx.

21

(3)

symbols.

a,b,o14,e,g1

Coefficients of the hull without fina in the coupled

pitch-A,B4O,D,E,GJ heave eqatione,

8, Lke,etib, Contribution o the fina to the above coefficiente.

AWL Waterplae aree,

AR Aspect ratio of fin at one aide of the ship. r

0y

Coefficient of the heave exciting force.

/

wLa

N

Coefficient of the pitch exciting moment.

flG

a

T

th

area at one aide of the ship.

fronde number.

F5 Heave exciting torce. Amplitude of F.

Longitudinal nioment of inertia of the waterplane about an axie through the ahip'e oefltre of gravity.

Vertical inertia force of * fin.

L Lift force.

Lift force due to the wave, orbital motion. Length between perpendiculars.

M9 Pitch exciting moment. Amplitude of M9.

11 3bip'c forward speed.

V Resulting velocity- at the fin.

o Chord length of the tn.

d Thickness of the hydrofoil seotion.

g Acceleration of gravity.

h Depth of mid.cbord pf tin below the water surface.

27E

Wave number.

k21

Non-dimensional control constant of the linear part of the

ocutrol meobanise.

ii.

(4)

iii

k2,, Non-dim.nsional control constant of the third harmonio part of the oovitrol mecbanjam,

T.ongitudinal distanoe bøtween the ship's oentre of zavity and the one quarter chord point.

Virtual masa of the fin associated with vertlOal translation. r

Eooentrjit

of 030il].ntor.

6 Fin span at one aide of the ship$ vortiosl motion of a point of the ship, relative bo the water surface.

s Amplitude of relative motiqn.

u Horizontal component of orbital velocity at the fin. y Vertical component of orbital velocity at the fin.

xyz

Right handed, orthogonal act of axes translating with the sbip'e forward speed.

z Heave displacement.

Heave amplitude. dO

Slope of the litt curve versus angle of attack.

Angle of attack at the fin in stili water.

oc Angle of attack caused by the orbital velocity at the restrajned

fin.

Angle betWeen the resulting velocity at the fin and the horizontal plano.

Maximum imposed angle of attack.

«al

Amplitude of the linear component of the angleof attack.

QCa3

Amplitude of the third harmbnio component of the angle of attack.

S Fin tilt.

1a1

Amplitude

of the linear component of the tin tilt.

Amplitude of the third

harmonio

component of the fin tilt.

Phase angle between and the w&ye at the ship's centre of gravity, Phase angle between MQ and the wave at the ship's centre of gravity. Phase angle between z and the wave at the ship's oeátre of gravity.

(5)

E

Pbaee angle between 9 and the wave at the ehip'e centre of gravity. L

b,aee angle between e and

the wave at the ahip's centre of

gravity-.

Wave displacement.

Wave amplitude.

Q Pitch angle.

Pitch amplitude. Wave length.

Mane denaity of water,

Reduced frequency of motion.

(u Wave frequency; frequency of oeoiUation.

e requenoy of encounter.

(6)

46t_c

RiW!

Iig.

I

- Coordinate aysteme.

2

Velocitp diagram at the fin in etui water.

3 - Velocity' diagram at the reotrained tin in wavee.

¿f

Pin A from[5}

5 - Comparison of measured and calculated coefficients for tin

A[51;

6 - Coefficiente and phases of wave exciting force and moment; 0.23.

7 - Comparison of measured and calculated response amplitude opera-tor ot the bare hull for heave.

8

Comparison of measured and calculated response amplitud. opera tor of the bare hull for pitch.

9 Comparison of measured and calculated response amplitude

opera-tor of the hull with fixed fine A[5] for heave.

10 Comparison of

measured and caloulated

response amplitude opera-tor of the hull with fixed fine

A[31

for pitch.

11

The angle

of attack versus time for passive and active fina.

12 Installation and dimensions of the controlled fine. 13 - Block diagram of the control ey'utem.

iLf - The controllable fin inetallation.

13 Comparison of measured and calculated B and e for controlled

fin.; F*0.20.

16 Comparison of measured and calculated A and d for controlled

17 - Comparison of measured and calculated e, b,D

and E4 FO.20.

-

Comparison of measured and calculated A, B, d and e for the fine

kept fixed; PO,20.

19 - Calculated response amplitude operators.and phase relatione;0,2O,

20 - Significant heave and pitch amplitudes in Neumann wave spectra. 21 - Reeponee amplitude operatoj for relative motion

(7)

vi

Fig. 22 Significant relative motions in Newnann Wave ßPeCtra F= 0.20. 23 - flow pattern at a static fin tilt of + 30 degrees and - 30. de

gre; model restrained; 0.20

2k - Flow

about

the fine during one period of forced pitching wtb controlled fine;

-max 25 degrees; a1 = iB.6 degrees

and 5 digress.

25 - Coapari.eon of expected and actual lift versus time.

Liat of tab,es..

Table I Particular, of model and fine A [s]. 2 - Static coefficient, for Fn = 0.25 3 Particulare of controlled fine.

k - Summary o! the teto done

with th. controllabl, fin installation.

5

Static coefficiente for the controllable fin itallatjon.

6

- 3uary and

particulars of photographed teste.

7 - Lift

force and its

vertical

cosponent according to linier

and

nonlinear

calculation.

8 Phase and reduction factor

of

lift

according to bon.etationary

(8)

A method of oalculatton of the effect of bow antipitohing fine is compared to the measured coefficiente and motions. It ebows to give quite satisfactory

reeults

both for fixed and for oofltrolled fine.

Next

the absolute

and z'e).ative ship motions are determined for the *

case of no tine, fixed fina and controlled fine. The oantrol systsa makes use of a nonlinear feedbao1 s.gnal of the pitch velöcit

By photographing eoae

particulars of the flow pattern

about

the fins

ers eStabljebed,

Wotf.

Tb. aign convention of the croes coupling cosUiciente d,e,g,D,E,G

in the equation. (1)

differ. from recent reporte of the Laborator7 on the pitch-heave problem, in which th. croce coupling terms are present-ed with a minus sign. Of

courea

this works through in

the other formu-. la. and in the figures presenting these Ooøfticiet It is regr.tt.4 if this causes confusion tnd in the future mors unit7 will be pursued. In the report the system of eigne 13 consistent, however, ao that it is easy to switch to the other eyateat by changing the signe of the u3.timat. resulta for d, D, e, , g and 'G. Phase relations of motions and

wvee are

not influenced.

2 -A Stud, ctnk the Motionsof a )lode] of the Sixty Seriea

Equipped with P'ixed and Controlled 8ow. AntiitohinAFirts.

(9)

ntroduction.

Several papers have dealt with

various aspeots of tie problem of

antipitohing fins,

am!ng othere[14J. Also in the

Shipbuilding

Labora-tory of the Technological University at Deift a serias of teats with fixed tine in regular waves was

run[5, 6].

Special attention dêserve a study of ocu[7J, dealing pri.marily with the vibrations induoed by the fins.

The purpose of the present study is thx'eofold. The

presence of the fins attribute to nearly all of the coefficients in the pitch and heave equations of motion. Firstly it is the intention to ahow that these addi-tiona]. ooeffloients can be culoulated quite reasonably by simple hydra.. foil theory, at least for bow fins. Secondly controllable fino are in-vestigated in which the control system consists of a nonlinear

feedback

signa]. of the pitch velocity. And thirdly the, flow pattern around the fin io examinad to find an explanation for some of the observed

phenome-na.

The whole experimental part of the study i.e perforaed witb'the aid of oscillator techniques in still water. This facilitates the analysis of the var&oua influences greatly. The alterations in the

system ahi» pluá

fin can be

seperated and studied in detail. Next the ship motion are calculated with the thus measured coefficientaof the pitch and

heave

equations,

Tbee can

be no doubt that this procedure leads to good re-eults as is shown by aomparion of tk* calculated and measured motions in actual waves.

or the

wozk reported here one type of fin and one type of control mechanism is selected,

1oreoyer only- the effect

of the fins

on pitch and

heave motions is considered. For a more comprehensive review of various matters4. associated with antipitobing fins, See reference[8].

(10)

3 -,

The

.th.d of

oulatto and ta X mental ver f .n.

2.1, Theoretical calculation of the oonr&ut1.on of the tins,.

If the following aseumptiona are adopted the forces on fixed fins are readily calculated.

The chip'. hull and the fine are mutually independent.

The flow around the tine te an undisturbed uniform flow with a velociø-ty equa]. to the ship's forward apead.

Thera

ero

fo eurfaóo effects, ventilation and cavitation.

¿+. Consequent linearization La allowed and fin drag may be neglected.

The coordinate

systems

are shown in Figure 1 and the velocity diagram at the fin in still water is given in Figure 2. The lift force is given by:

L

wh.re:

e

andi

VU.

¿L

In waves the orbital velocity cauces an additional angle of attack and an additional lift force Iig According to Figure

3;

'V-where y je the vertical orbital velocity at the point at one quarter of the chord length. In regular head waves the result is in a liflearized forms

=-

L

(,_U)c4(ú

Aé).

Th. inertia foro. of the fine may be expressed as:

Ki

where mf stande for the virtual mase of the fin in vertical translation.

Adding

afl. this to the equations of motion the heaving and pitching

of the model

plus

fini

is

described

by:

+2K

g

(1)

4*+8Ò+CG+D+EtGz

=

MQ+2L1 *2Lgl_2Kj i

(11)

¿CL

I_II-fi---.

Working this out..there raeulta:

(m)I#,thF)'+cz.

7'

dQtizp)c,

Ça)

(Ri2I

(Sf12)Ó

_eJ

+cZ

=

'd

(

-

(i

11,)

The ma3or

problem in

obtaining numerical resulte for the coefi..

ciente in the equations (2) is the deteriinat&on of the elope of th. lift curvi The many data on tbi quantity are all valid fr high Rsyn.lda

numbers,

infinite aspect ratio and a stationary

flow

pattern. It is genez-9117 stated that the

Reynolda number does

primarily affect the point of

lift breakdrownd xmttbspeafth,1iJtc vttamall

angles of attack. If this is acoepted, even for such low Reyø].ds

numbers as for

the mode],

fin

(about 6x1OZI), this inf].uøce Can be left out of ocnideratio in a1inCe riz.d approach. The correction for effective aspect ratio

is well knewn

in principle, Theoretically the relation iss

t3)

In Figure 18 of

(93

Mandel gives a curve determined from the

ezpez'jmenta:of

sCierai inveatigatòre which shows good agreement with

(3)

for values

of the

aspect ratte whjeh are of praòtioal interest (effeotiv.

AR2.5 or

3).

Th. influence ohe non'.etationary

v.].øoity

field is twofold1 The

stationary valu, of is reducid and a pb*ee difference between lift foros and angle of attack ansia, both depending on the magnitud. of the

reduced frequency The phaø difference will

man1y

develop a oo.

(12)

popent of the litt fora. i phas. with the motion (Qr the acceleration) of the

Bbjp,

which wifl be oriall relative to the inertia and spring cha-raoteristice of the model itself. Therefore the phase difference will b.

left out of contderation. The reduotton of however, is of direct importano. for the damping characteristics and can not be ignorad. Leute and Jecobe [IO] have proposed a mean reduction factor of 0.85 tor th. whole frequency range. They derived this valu, from some computa-tions based on the theory of Von Karmn and Sears. This practic. will be followed here. In the Appendix a little more attention wil). be paid

to the non.etationary charaot.r.

The other unknown cuantity is m. Por a flat plate the virtual mase is given 1) byz

¿2.

I

in

1C

and this will b. used as an approximation.

(13)

Table 1: Particulgrn of the model and

od,t

Length between erpendicu1sra 2.258 *

Length

on the waterline

2.296 m

Breadth

0.311

m

Draught

0.125 a

Volume of dis»laoeaent

o.o'ìo

¿

inaA

151.

"in eeotion

Mean epan

Chord length

MACA

0015

781O

rn

80xiO3

a

Aepoot ratio

0.98 Maximum thickneee

1210

a

Chord thicknese ratio 6.67

fln area (at orzo eid.) 1.20$ of A

O.629x1O2a2

Looatjon forward of C.D. 1.081. a

Location below water nurfaoe 0.10

Lift oire eLope 2.61

Block 000ffioiet

0.650

P'tsmatio ooeftoiant 0.661

Waterline coeff'jaiet

Z1idehip esotion coefficient 0.982

LOB aft j L» 0.0113

Longitudinal radiue of gyration 0.2

Waterplane area

O.525

a2

Longitudinal moment of tnertia of waterplan. O.1+2O

Centre o tfort of waterplan. aft

j

00598 a

(14)

2.2. Meaurements of the cotfoients i, theO e,uat one

o

mot on.

Foi' the model of the Todd Sixty $eries,blook coefficient o.6,

ueed in[5J and

[6:1 tor motion

measurements in

wavis, forced oscillation tests were parform.d with, the model's bar. hull and the hull equipped with fin A frorn [5], 'mrtioulmrs of model and fine are given

in Table

I and Figur.

,

The measuring technique of forced ooillation taste

usid at the Deift

kitpbuild1.ng Laboratory bas been explained in several

previous reports of the Laboratory and a new description will be omitted hors. The testa were carried out for two forward speeds, corresponding

to the Freude numbers 0.20 and 0.25. Two different eccentricities of

the

ooi11ator were used,

namely 2.0 and 3.0 cm; the dietanoe of the rode

is i a.

Using the measured values of the ban, hull me a starting point the

coefficiente for the mQdel equipped with fine were

calculated according to th. preceding section. The reulta of the measurements and the calcu-latione sr. shown in Figure 5 for ' 0.23 mc an example; for 0.20

the resulta are fully analogous. The

static ooeffioi.nta have for

= 0.25 the valueb given

in Table 2.

Table 2:

tatio co.ffiaiente for F

0.23.

-7

hull alone hull with

tine A[5]..

o O g G 52k,3 kg/rn

1k3,2 kg

25,

kg

25,5kg

52k,5 kg/rn

1ko,? kg

27,8 kg

(15)

2...Measuement

of wate forces nd rnomept.

Qn the retrajnod model the heave foTCe

and the

pttoh moment ex orted by waves was measured, both in the oase of tho bare bull and in

the case of hull p2us fins. The results for areoshown

in Fig

ura 6 in tho form of rondimenejonal coeffjoita

j07

A1,

4C

M

M0

There is not much difference between the two oases. B calculation it can easily be.ahown as well that there is only a alight influence of the fins on the exciting terms

The wave height used for the exi,e-imenta was 2 a'1pp lAO °r

2).. Compaxieon omoa8ure&azd calculated motions in wgvee,

With all the coo Ucients an4 the exciting force and moment for

the barO hull determined experimentally pitching and heaving of the mo-del can be solved from the euatjons o motion. These calculations are compared to the measured motions from[11J in the Pigures 7

and 8.Asoen

be seen the agreement is ver good, except for the peak values in heave. Probably this &s due to the tact that .n the frequenoy- range between

about

= 6 aoo and = 8 sec (corresponding to wave lengths of about 1,2 and i,1 t?imee the ship's length) water is shipped at the bow

[ii].

Of cou'ee this can

not be accounted for in the calculations.

Next the motion of the ship equipped with fins was calculated. For this purpose the equations (2) were solved using the same Oxperitnew tal values for a, A, b, B, etc. as in the pr.vioue Oase and the theoreti-cally determined contributions of the fins. In

[6)

the motiora were meae. urad for fin E, which is the

same as fin A but with

a longitudinal slot in it to reduce the vibration trouble. The two designs did not show much difference as far as the motions are concerned (see[5]snd[6)).

A comparison between the calculated mottons with tin A and the measured motions with fin E is made lit the Pigures 9 and 10. The agreement is quite satisfactory.

By these resulta it bao been shown that the

method of

caloulationia sufficiently

accurate

to predict themotlons of a chip equipped with fixed bow antipitohing fins in waves, when the coefficients of the hull Ltselt are known

(16)

q

3. Controlled bow fins.

,3.1.

h

contro

tern.

Of the various possibilities to control the fine

only a oontinuus

feedback system will be considered her., in which the control signal is

derivad from th. pitching motion. Xn its most general form the fin tilt

is

(Q,

,

).

As damping increase wi].l be the most effectiv, means

of pitch reduotion it

te obvious that should be made proportional to the pitch velocity Ô. On the other hand it must be prevented tb&t the

angle of attack becomes so large that

the fine 8t&ll. Depending on

the

amplitude and

the

frequency of the pitching motion the paasive angle of

attaok for

fixed fins can have very different magnitudes, reaching upto

30 or +0 degrees in serious conditions. Therefore the fin tilt

adjusted momentarily. When DÇ 'mc' the maximum permissiblé angle of

attack, Ö(, may be increased by

maX°v

(positive fin oontroL)

Wh., however,

<

>

f

must be

opposite to keep

down to D

(negativ, fin oontrol)a From this it

is olear that there is only a limi-ted possibility to increase pitch

damping by activation of the fins.

To get the highest possible advantage of the control action

a nonlinear component can be added to

f

and thereby to the damping coefficient.

mie is dne

by a third harmonio of

6, it is illustrated in Figuri

11.

Considering the cae. f a pure pitching motion the followinj formu-las apply

2,f

.-

.#

o=

9#OÇ

ir&Ç

f

()

As Q ie small compared to the sum of the other two componente and since it bas a phase diffu'enae of 90 degrees with them Q may be neglected in

(6).

For the harmonio pitching motion in regular WaVøs one obtains:

e=

1=

¿C&t

1a.

i

9g CU

J

¡ &a &7

=

I

()

-

10V-)J

(6)

(17)

=

21 Col 6 Co-I

AI

L.J.f_

u.

-

7'

a.,'

As the absolute magnitude nuet be restricted to OCmx further

yi.lde:

o'

±

}

(9)

The

eigne

depend on the position of the finsi They can be determined by considering that muet have the sign ot the passive angle of at-tack b(

and

that

D(3

muet be opposit. to DC' to subtract fros the

lin-ear peak value.

Therefor,

for bow fine (1>0) is:

4' O4

=

Substituting

(7)

and

(8)

the relations

(9)

give for the control constants:

=

=

r

lo

3

4ô' c(.4)0

96( C4)

Having obtained (10)

it

follows from (7) that:

-'°"*

û.Z c(,,,1

-*

tC

J

i

(S)

(18)

p.2. he ooeffioients jr theequatjone of motion.

A3

the control action only concerna the pitch velocity it is evident

that only the 3.. and the e-coefficient will

chango; the other' fin

contri-butions are identical to the case of fixed tins. The contribution of the controlled tine results from the substitution of the linearized angleof

attack into the formula for the lift torce. By (8) and (9) the linearized

angle of attack is iven Then there resulte:

=

.2

l2fI

(L18)e

6«L2F

2F.I.1r

i-e

/

where the subscript

ederiotee the fact that the tin

oontribution is the equivalent linear torxn of the fir3t and third harmonio part together.

,eI

Ex2erjmenthe

To judge the utily of controlled fins ao correctly as possible a different fin installatto was chosen, which could probably actually be realised. The axis of rotation of the tin at one quarter of the chord length was situated lO percent aft of the forward perpendicular and 76 percent of the draught below the load waterline. The part of the fina oloee to the hull was ooneruoted fixed for structural simplicity and to avoid large clearances between the hull nd the fine. The installa-tion is shown In 'igure 12. Partioulars are $Unmtariz.d in Table 3.

Fár the fins fixed experiments ware carried out analogous to the testa described in section 2. With the fins controlled only the pure pitching motion was repeated, because only- when pitching the control

ac-tion will give a tin tilt. The forces when heaving and the measuring of the wave forces are identical to the case of ti*ed fins.

(19)

12

Tabje

:

artouiars of optold_fina.

The teate were perform5d tor one forward speed, oorreaponding to

0.20, a little below the aervice apead of the model.

A scheme of

the testa done te preaented in Table k, The frequency

range runs from

¿0= 3 aeø_

to

CL

12 Beo.

Tabla ¿f3 8ummar' of the te8ts done with the

controllable fin ietallatjo.

fixed part controlled part

whole fin

Section

NACA - 0015

W

Span e

mn

21,7

8o

101,7

Çhord o

mm

80

8o

80

Aspect ratio AR

Q?71

1,0

1,271

Effectva Ai

-

2,5k

Thickneaa d

mm ¶2 12 12

cid

o

6,67

6,67

6,67

i (torward of G)

s

-

Q,911f5

Poaiton forward of

0,9032

h (under OWL)

s

-

O,o95

Poeitiou above bade line s

0,030

Fin area P

in

0,1736x102

0,6LfOx1O2

0,8136x102

F in percent of' A

L dC W

0,33

1,22

1,55

2,9k

2,9k

2,9k

-PwO.20

n

-fixed fine;

heavingandp4tchThg

-pitching with. cntrQjled fine

&'

15°

nl

20

01 max

r=1,Qca

r=2,Ocin

r*3,Qca

-x

x

x

x

*

X

x

x

6«)(ia

x

(20)

The OOUtiol signals could simply be obtained from the oscillator. Two resolvers

having a Circular frequencyofand 3

, respectively,

produced sinusoidal voltages. After apliftoation this Voltage was

pre

sented to a° serVomotor, which drove the fin shaft via a gøaD box anda belt transmission. The first and third harion1,o componente of the fin angle were adjusted to satiety the required magnitudes for every eepa rate teat, according to (ii). inoe ùo control system can work ideally, that is without any time 3.ag, it was necessary to compensate for phis. differences. This could easily be dona by turning the resolvers a little contrary to the phase lag, so that the produoed fin tilt was perfectly in phase with the pitch velocity, as assumed in the theoretical deriya

tion. A block diagram of the control system and a

photograph of the eet..

up is presented in the Figures 13 and 1k.

L

Comparison of rneaeure and calculated coefficients wheyitohin with oontro]4.ed tine.

Th. additional

(1)

and (te) are calculated a000rding to (12) and the total B and E are compared to the measurements in Figure 15. The agree.-ment io quite satisfactory, eapeciallr for the lower eccentricities rand

the emallsr D(. But also for an angle of attack of 5 degrees aitpli-tude the differences are not treat,

particularly not in the important

frequency range between eec and

eao.

In the calculation of (AB)5

and (e)

account has been takò of the fact that only a part of the fin arSa ib controlled and

the

other part is fixed.

The remaining pitch coefficiente A and d should not be changed by the control action, With respect to fixed fine. Th. measurements showed some nfluenoe, however, amounting to 10 or 15 percent in A for the lower

frequency range; Figure i6. This effect may be cateed by a number of'

oir-cumetancee. First of aU. the non.statiouary character

of the flow pattern

is probably more pronounced for controlled fins than for fixed fina,

re-sulting in a larger phase ditfrenoe between list

force and angle of

at-tok. Thereby a component

f the litt

proportional to the pitoh aooelera.

tion is developed.

Further will viscous damping of

the L'in movement b5in

phase with

t,

that is also proportional to *.

o

(21)

-.5.. Results ot the measurements of thç reyainin coeffioienta.

Measurements and calculations of the coefficients when heaving (a, b, D and E) are presenteá in Figure 17. Theee are va].i4 both for the oase of fixed end controlled fias. The pitoh coefficients A, B, d and e, when the fine are fixed a'e given in Figure 18, The agreement

la good. The restoring coeffioi.nts are given in Tab].. 5, also for 0.20,

Thlf

Statiooefficjents for jhe controllabli fin

inatallptiøn.

1.

Alyeis of the re8ultin,j shi, motions for no fina,fixed fina and

controlled fira.

To compare the behaviour of the ahi» in the three oaaea no fina, fixed fins and controlled fine the absolute and relativ. ship motions were computed for the installation described in section 3. br al]. of

the oom,putatjona the direotl3r measured quantities were used in the equa-tione of motion.

The pitching and heaving motion in regular waves are presented in th. tora of the response amplitude operators versus the frequency of

en-counter; see Figure 19, It is olear that the presence of the fine great.. ly reduces the maximum pitch angle; the peak is 0 to O percent lower., than for the bare hull. The advantage of the activatjo of the fina is not great, however, Zn heaving the influence of the fina consists mainly of a shift o! the response curve towards lower frequencies'. Th redue... tió'ot the maximum heaving in regular waves not being more than 11 to 15 percent. Here the control action even produces a slightly higher peak value than for fixed fins. The phase relation between pitch (or heave)

15

-FQ.2Q

hull

alone

sull

with fins

O C g G ' 52k,5 kg/zn

13

$2

km

23,5 kg

3,3kg

p24,5 kg/rn I 1 2 kgm a7,66kg

23,3kg

(22)

and the Wave elevatiofl at the centre of gravity.is aleo

gtven.*,n the

figures, The differences are not grsat, but themay obtain some impor-taflce for the relative motjons of bow arid stern; this will be discussed furor in thie section.

With the response amplitude operators from Figuro 19 the signifi-cant pitch angle

'a 1/3 and heave amplitud. were determined in

ir-regular head waves For this purpose the theoretical Ueumarni wave spec.. tre, were utilizad. The oomputatiQne were pert'orxned for the numbers 3, 6 7 and

8 of the Beautort-soale, corresponding to wind

velocities of

9i

2s, 30 and 37 knots respectively. The results are presented in Figure 20. The ourve should not be interpreted as absolute but as comprativedata since it is not quite known to what extefit the theoretical spectra

re-present aotuai ocean waves. Nor is it pretended that linear

superpoei-tion in severe ooridisuperpoei-tionB as B7and B8ta permitted, but the

computa-tians certainly show a tendency for serious motions. The curves reveal a pitch reduction of 30 to 35 percent for fixed fins in 5 and 6, and of 35 to #5 percent for controlled fine. In the more severe conditions the óffeotiveness decreases to about 20 and 30 percent respectively. Heaving is not significantly changed, the differences ranging fron about

minus 10 to plus 5 percent. This is an interesting result.

Despite the

modified

heaving n regular waves the irregular amplitude is flot

signi-floantly ohanged. Although this, of course, is not

a general proof it

looks reasonable to

suppose that this statement je not strictly limted

to the considered ship

tors.

The vertical motion of the ship relative to the water aurface at

a distance 1 from the centre

of gravity, is given by:

The amplitude operator 8a/*a can be determined trom the calculated model motions and phase relations with respect to the waves. This has

been done

for three points

along the length of the ship z forward and aft perpendi-ou3.ar ad the position of the fin shaft. Next the significant

displace-ments relative to the water surface can be computed

in the sanie Nuan

wave spectra as used for the

absolute motions. The

resulte are shown

in

the Figures 21 and 22. They

illustrate again that the

presence of fins

reduceetho, relative motions considerably, but that the advantage et fin

activation is only alight. It is noteworthy that for this ship the rela-tive motion of the stern is suppressed more than that of the bow, This may be one of the reaSons for the very favourable propu].sion

oharacteris-tias reported

i

f6J.

.. i6 -.

(23)

The oo*putatione have been performed for the ileasured coefficients to show the most realistic propertìes of the various cases. When the' theoretica]. t'in contributions are used the results wil]. be little dif-ferent, as has been checked For

an actual

prediction of ahip motions with controlled fine the accuracy utay then b not fully satisfactory. The relative merits of the various possibilities (no fthe, fixed fins,

controlled fine) or of diffevent tin

configurations will not be signifi..

cantly changed, however.

Therefore the method of calculation is still quite uab].e to judge of a possible application in the design stage.

3. The flow

attern about the lins.

The measurements of the

coefficients did not

reveal stalling arid

consequent

lift breakdown, although angles of attack of 30 to ko degrees were maintained. Xt

is known that very low aspect ratio wings do riot

stall before large anlee arid tbat,if they do, one can not speak Of 3

j

distinct breakdown of

the lift curve. The

effectjv. AX of the whole fin being 2.5k it was to be expected, however, that

a noticeable influsno.

could be observed. To make sure

whether

separation of

the flow

000urd

or not under&ter

photographe of the flow pattern were tauen in

vari-ous conditions.

First of all the restrained ship was given the test

speed of

019Le1 a/Bee (F0.20) while the

fins had a static tilt.

Next th. model performed a pitching motion with an amplitude oZ 0.0k rad

(2.28 degrees), the fins being fixed and controlled, respectively. At each frequency of motion a series of pictures was

taken

to cover

the whole period of

fin movement, The photographed teste

and their oir..

cumetanoes are SUjflmarjze

in Table 6.

(24)

11

')

Note ase page 18.

able 6g Sun7mar. and Partioulirß of photographed

tests.

- Restrained ship; tiria under conetant angle.

fin tilt remark ftn tilt remarks

+ 50 +100 _100 +15° _150 +200 -20° 1egula' flow regular flow regular flow separation regular flow separation regular flow separation. +250 5O +300 _3Q0

+33°

p.350 regular flow separation regu1a flow aeparatio

initial aeparation phenomena separation

Pitching ship; fina ixed. circular freR. aeo geometrica]. er,Lt,fattek

rica

)

4

6 8 10 12 13.2 10,10 15.00 19,6° 24.00 28.2° 30.5° no separation no separation

initial separation, only at underside of foil

8eparation at undereida

diatiot separation at underside, probably initial separation at upperside

separation at both aides

Pitching ship; controlled fine with & 25°. circular

-i

trsqac

O5

ç

remarks ) k 6

8

10 12

i86°

14.10

9,0

5.2° 0.8°

regular f ow at pporsjde, separation at underside

regtuar flow at Upporeide, separation at underside

regular flow at upPerside, separation at underside

Photographs not olear, but general picture the

se as above.

(25)

18

-Note Tab3.e 6: While pitching separation must be understood as to

oc-0u2' only during a part of the pitoh period.

At the higher trequnciee, both with fixed and with ooutroUed fina, th photographs are not good enough to show the flow pattern distinøtly. Nevertheless the general picture

95

described on be observed.

mi photographe of the first group, the

St9tto

tests, are very olear. For positive tin angles ¿ flow separation (at the uppereide) does not oc-cur before 0 or 35 degrees. But for negative fin angles the flow separa-tee at the lower' side of the fin at about ten degrees. This can be

attri-buted to two djffer'ent causes. In

the first place the potential flow a-round th. ship's body has a downward component at the bow' so that a zero

fin angle is actually a small negative

angle of attack of some degrees. Secondly the low pressure region at the upperside of the

fin pulla the

water surface down, thus smoothing the etrealine path and avoiding sepa-ration. Here the low preseure region interferes with the through of the

bow wave system. For £<o

a surface effect as described is not possible

and

separation occurs. Now the high pressure region is at the upparaid. of the fin and influences the bow wave too, This can be

noticed clearly

on the photographs reproduced in 'igure 23.

From the series of tests with controlled fins, performed under the satiegeometrical angle of attack no conclusion can be drawn as to

th.

in-fluence of the frequency of motion on the angle at which flow eepaz'ati.on starts. The higher the frequency of motion the lees clear the

photographe

show the flow pattern. An example of a reasonably good series of photos

i8

presénted in Figure 2k.'

It eau be understood now why no sharp decrease of the fin contribu-tious by stalling was observed. For! (geom.trical) angles of attack up to 30 or 35 degrees the flow is fully regular during one half of the period Separation only takes place during a part of the other half period.

Th.refore the lift force curve as a function of time wU]. only partly deviate from the theoretically expected curve, as illustrated in Figure 25, There is no cutting off of the

curve

at both sides of the zero line, but only

at

one side. For the overall effect

in

damping the ntsgrated lift curve is responsible and this will conceal most of the irregulari

(26)

6.

Diecueaio. and coçlusiona.

8oth for fixed and controlled bow fina the simple method of caloula. tian of the influence on ahip motions as outlined in eeotion 2.1 is quite eatietaotor3r. By using this method the characteristics of a ship equipped

with bow tine can be

determined beforehand when

the

ooeffioient

of the hu.0 itself ere known.

The results of the experiments justify th simplifying assumptions made for the calculation under 2.1, They will be inspected point by point.

-The hull is a three.djmensioyzal body which turns off the flow

down-ward; therefore nero angla of attack does not coincide

with QO

thin is merely a shift in

the zero

line of lift ad otbor quantities, which is of no importance for the ILarmonio oscillations.

-Th. velocity of the supposed uniform flow about the

fins is not U

due to the curvature of the hull. As tar forward as ten percent aft of the oz'ward perpendicular the potential flow about a Victory-hull indicated a velocity of about 5 percent lower than U at the load wa-terline, the deviatioudeoreeeÏng towards the bottom. At the bottom the Velocity was 2,3 percent higher. Along the length the differences nowhere amounted more than

8

percent. At some distano. from the hull the deviations will be still less. So this point can not have a sig-nificant influence.

-The fins are ot in a 8tattonary velocity field. The reduced fr.quen ay Qvaries between 0.15 and 0.50, a range which is. also importantin flutter. A non..stattonary approach produces considerably worse agree ment with the experimental results than the stationary calculation, however, see

the Appendix. This muet be

attributed, to three..dim.n*,

sional effects by the small aspect ratio and to surface effects. The stationary calculation with a reduction factor for the lift slope pröduo.s by far better results,

.Vetjlatio and cavitation were not noticed during the aecillation testa; in waves they may occur, how.ver. According to the pb.tsgrephe discussed in section 3. surface effeotsßre certainly present, but they can not be accounted for in computations.

-fly linearization the angle of attack is over-estimated afld the squared velocity considerably uMerrneetimatsd. Therefore i th1 néariy cairniIeà

For structura]. application this may Contain dange. roua 3.ements,

but the

vertical

oom»onent of

the lift force causing

o

(27)

20

-the alteration of -the coeffiotenta is quite correct. The following sable

S

i1lutrates this weU.

Table 7, LU foce and &ts vertical componer t

a000rdin

to linear an nonlinear calculation.

TOgSther'.Wttb th. fact that aven for large angles flow aepar'atien only OCCUrS during a part of the

pitching

pero6 it therefore may be con-eluded that for motion prediction linearization is not a esrious simpli-fication.

3,The advantage of controlled bow fina with respect to fixed fine is, gene rally speaking, too little to justify their application, because et the great technical problems

of

Construction and oontrol system. nl' for viry special purposes their additional merite may balance the difficulties and coste. The smallness of the gain is caused by a number of reasons: the passive fine already meet large angles of incidence, whioh can ñot be

in-creased much by activation; no distinct stalling phenomena

are observed,

which can be prevented by the control action and the coupled pitch-heave

performance as a whole will generally differ somewhat from the expects-tion when only the tncrease in pitch damping te considered.

4. The introductto of the nonZinear part in the control mechanism adds tan percent to the ß and e above the linear

contribution (see formula (12)),

which must be paid for br a complicated contro]. SyStem.

5.Antipitohing fina bave very little influence on the irregu].ar heaving. t is supposed that this statement is not strictly confined to the ap-,plication investigated here.

- 21 Q angl, of -attack degr.ee litt torce p of linear

-perdent

nonlinearpercent

linear percejit nonlinear. percent 10 20 30 40 100 loo lO 100 102 109 121 142 loo 100 100 loo

10,5

102,5 io4,8 108,7

(28)

In additiofl to the calculation of the ftn contributions according to stationary airfoil theory with a mean reduction factor of 0.85 some non-tationary computations wore performed with the object of explaining

the influence of the tine on A and 4 by the phase differsnoe between lift and angle of incideno. and giving a base to the factor 0.85. For thie purpose

th. data fromE12 were used, which are fully

analogousto those of Xtieener, Tbodoreon or Von Karthn and 8eare.

The th.or.tica2. data are valid tor a flat plate of infinite aspect ratto (two-dimensional flow) under verr high Reynolds numbers. For fixed

fne the then obtained reduction factors, with respect to th. theoretical = 27t , and phase angles between the lift forca and the angle of at-tack are summarized in Table

8.

Tbl. 8: Phase and reduction factor of lift acording to, non-statjoary airfoil theory (twt,-djmensional ).

A poeitie phase angle means that the lift foro. leads. the angle of attack

In the caloulatiòrs the intltenoe of the vibrating fluid about the plate has been taken into account.

These resulte lead to very small coeffiot.nte agreeing much worèe with the measurements than the etatiùnar7 Oa].øulationa. The tendency of fin con-tributions decreasing with frequency is opposite to the observations. For the lower frequencies in heave even a negativ virtual masa of the fina is indicated. Therefore suob Calculations can better be omitted. The reasons for the dteagreement probably being three-dimensional and aurfaøe effects. The influence of Reynolds number is very little provided that the transi-tion point of the boundary layer from

leinar

into turbulent flow is

fixed

[ia].

1or very low Røyoldo numbers the flow is fully laminar and there

will not

be any transition,

Heaving Pitching

phase red. factor phase rod factor

seo degrees degrees

4

0,170

.. 7.1

0./41

+ 8.4

6 O,256 4.1 0.668 +

6.3

0.650

8

0340

+ 0.7

0.647

+ 8.7

0.626

lo

o,46

+5.6

0.627

+12.1

o.6o

(29)

S

References.

[i] Pouznaras, tr.A. "Pitch Reduotion with Fixed Bow Fine

on a Model of

the Series 60, 0.60 Block Coefficient",

D.T.M.B. Report 1061,

October 1956.

Pouz.n*ras, IJ.A.t "A Study of the Sea Bohaviouj' of a flarjner-Q1as 8hip Equipped with Antipitching Bow

Fine',

DTJ1.B. Report. 10847 Oetober 1958,

Stefun, 0.1'.

"Model Exerienta with Fixed Bow

Antipitching Fins"

D.T.M.B. Report

iii8, December 1959,

Abkowitz, M.A..7 "The Effect of Antipitchi Fine on Ship Motion&', S.N.A.H.E. 1959,

Sonoda, Y., "Model experiments with Several Bow Antipitching Fins"7

Shipbuilding Laboratory of the Teohnologica].

University at Dolt t

Report 90. July 1962.

Son.da, Y.

"Antipitching Fina in Irregular Seae", Shipbuilding

Labo-ratory of

'the Teohnologion]. UniverGity at Deift, Report.93, October1962.

Ochi, IC.M.

"Hydroelatj0 8tudy of a Ship

Equipped

with an Antipitohing

Fin", S.L A.M.E. 1961.

Vugt., J.H,, "An Investigation of Fixed and ControU.abl. Antipitching Fine", Shipbuilding Laboratory of the TeabnoLogioal University at Dolt t Report 115,

May 196k.

Mand.l P., "Somo

Hy6x'odynamjc Aspects of Appendage Design", 3.N.A.M.E.

1953.

Lewi., E.V. and Jaoobe, W.B., "Preliminary Study of the Influence of

Controlled

Fine on Ship Pitching and Heaving", E.T.T. Nbte No.

379e 195?.

Garriteaa, J. and Beulc.].man, W.

"Ph. Influenc, of a Bulbous Bow on the

Motiona and the Propule.on in

Longitudinal Waves", Report No. 503 of

the N.tharland. Research Centre T.N.O. for

Shipbuilding, and Navigation,

April

1963.

Bergh, R., "Ret Meten van Luohtkrachton op Trjllende Vleugela"

Luchtaarbtóhyijäk

.69, No. 23, 7 June 1957.

A

i: 8]

[9]

[io]

[11] fia] (W&s 6125) - 22 I

(30)

o,

Ut

Fi'g.l Coordinate systems

zLè

Fig. 2 Velocity diagram at the fin in still water

V

Fig. 3 Velocity diagram at the restrained fin in waves

(31)

O

Fig. 1.

(32)

r m 20 15

fio

5 o + 5.0 u a) u D) $+25 O 2.5o 5 (j) 10 15

- sec

.

-e'-15 sec -40 30 E o Q, U) D) -X 20 10 +5 5

10

15 -1 sec

Fig. 5 a Comparison of measured and calculated coefficients

for fin A [5], F =0.25

I.

\

D

5iOi

o----o

model with.out fins (experiment)

-o- .- r = 2cm

s

.

model, with fins

(experiment)

-D

5- r= 3cm

model with fins

(calculation)

5 10 w 5 10 w o a) u)

r

O w sec-1

(33)

I. 2 1 o +2. C.) w D)

j'

2

5 10 15

i.

2 a +5 o

5.0

-

.5

Fig. 5b Comparison of measured and calculated coefficients

for fin A[5

F=0.25

5101!

0 5 10 1! D 5 10 1!

1

-m--sec w

- sec

w - sec w sec

.o---

model without fins (experiment)

o -- r= 2cm

.

model with fins

(experiment)

-o -.-

r= 3cm

(34)

1.00 0.75 L)

o

0.50 0.25 O +270 +180

90

+270

90

2a 1/40 L

D Ef N..

CF'

NCM

1111

2=1/i0 L

C\ \CM

D Ern .1 1.00 1.25 1.50 1.75

LIA

-Fig. 6b Coefficients and phases of wave exciting force and moment

for the model w.ith fixed fins A (5], F = 0.25

0.25 0.50 0.75 1.00 1.25

L/A

Fig. 6a Coefficients and phases of wave excitin.g force and

moment for the model without fins

Fn = 0.25

+90

J

O w 1.00 0.75 L) C-) 0.50 0.25 O 1.50 1.75

(35)

2.0 1.5 f (a N 0.5 o 2.0 1.0 O

Fig.7 Comparison of measured and calculated response

amplitude operator of the bare huit for heave

10.0 We 12.5 -1

sec

We

Fig. 8 Comparison of measured and calculated

response

amplitude operator of the bare hull for pitch

15.0

calculated F=O.20

o--o--.

measured

F=0.20

calculated F=0.25

---u

measured

F =0.25

,

r

/

calculated F=0.20

measured

F=0.20

calculated F=0.25

measured F=0.25

7

,>,t

UI O

25

5.0 7.5 7.5 10.0 12.5 150

sec

(36)

2.0 1.5 1.0 0.5 o 2.0 0.5 O We

Fig.9 Comparison of measured and calcuLate:d response amplitude

operator of the hull with fixed fins A[5) for heave

12.5

sec

Fig.10 Comparison of measured and calculated response amplitude

operator of the hull with fixed fins A[5] for pitch

15.0

o--o-- calculated F=0.20

measured F=0.20

calculated Fn=O.25

measured F=0.25

-D--D---u u m

calculated F=0.20

_-_-o__

s

measured F=0.20

-D----o---

calculated F=0.25

measured F=0.25

AÍI\

. u 2.5 5.0 7:5 10.0 12.5 150 We sec 2.5

50

7.5 10.0

(37)

/

/

/

/

Fig.11 The angle of attack vs.time for passive and active fins

mot o r gearbox

passive

osciLLator

power ampLi tier EÖ ,

gE

L_

jA.C. inductive

---r

rotary pick-off

/

/

/

/

/

/

/

,

resolver

summer

Fig.13 Blockdiagram of the control

system

Esinwt

amax

a

active nonlinear control

/

/

/

active by the linear part of the control

j

(38)

system-dimensions fn mm

timing belt

Fig. 12

InstalLation and dimensions of controlled fins

D

2

(39)

I

(40)

20 5 00 maxlSdeg r. 5 10 15 w sec 20 u 15 E O) X 10 5 o o 10 w U) a) = 25der. 5 5 w 10 sec1 15 2 u 15 E a) 10 5 10 w In O) o

j 35 dear.

w - sec1

w 10 sec'

model without fins (experiment) o---o--modei with controlLed fins (experiment), rlcm

modeL with controlled fins (calculation) o--o modeL with controLLed fins (experiment), r2cm A--6-- model with controLled fins (experiment), r=3cm Fig.15 Comparison of measured and caLcuLated B and e for controLLed finsi F=20

15

\

\.

5 10 15 5 w lo is sec

(41)

3 -2.5 amaxlSde. r. 4 amax2Sdegr. lOE 15 00 - sec 15 sec1 -25 4 amax 35degr. 5 10 15

u---- sec

model without tins (experiment) _.o-0--modeiwith controLLed fins(experiment); r.1cm

model with controLLed fins (calculation) o--o modeL with controlled fins (experiment); r2cm --_-o modeL with controlled fins(experiment)1 r3cm Fig 16 Comparison of measured and calcuLated A and d for controlLed fIns1 FO.20

5 lo 15 00 w sec1 5 10 w 15 sec 5 10 w

(42)

w

.-sec

5

1

sec

Fig.17 Comparison of measured and calcuLated a.b. D and E F=0.2O

5.0 10 5 10 1! C'J 'J) -x E ai D) m 20 15 10 5 E ai (n D) -x -D 40 30 20 10 w

- sec

w

model without fins

(experiment)

mode I with fixed fins (calculation)

o--o

model with fixed fins (experiment) r=2cm

a--o

model with fixed fins (experiment) r=3cm

00 5

lo

15 Oo 5

lo

15 U) sec Q ai u) D) -x p w

(43)

2

2.

- 5.' Oà 2 5 w

- sec

5 10 5 10 1 ) 5 10 U) sec w sec

model without fins

(experiment)

model with fixed fins (caLculation)

o----o

model with fixed f ins(experiment) r=2cm

__&__ò

model with fixed firis(experiment) r='3cm

Fig. 18 Comparison of measûred and calculated A. Bd. and e

for the fins kept fixed

Fn=O.2O

15 5 10 w -

sec1

10 w u' D)

15

w

(44)

2.0 1.5 Q 20 E u m ai w L D) a,

tc

0.5 +90 + 60

30

60

90

330 300 U) a) a, L D.) a, 240 w 210 180 150

Fig. 19 CaLculated response amplitude operators and phase relations) F =0.20

L)) N w

--

---"

-

=

-/

,,

O 25 50 7.5 10.0 12.5 15. We sec

Za/ca Cz

Za/ra Cz

°a/L Ce

ea/ca Ce

o.-o -,.-...-model without fins

,Do---.--6- model with controlled fins) a=25degr.

. s -'---model with fixed fins

-v--i,-model with controLled fins1 amax= 35degr.

O 2.5 50 7.5 10.0 125 15.0

(45)

i

In i E u

z

i

Beaufort number

Beaufort number

o

modeL without fins

model with fixed fins

a.----. modéL with controlled fins ama25 degrees

u

model with controlLed fins

max=35 degrees

Fig. 20 Significant pitch and heave ampLitudes in Neumann wave spectra F=0.2O

'J

(46)

12_rD - 2 lo 2 7 1 7. o o E

il

2 2 We - sec

modeL without fins

,

modeL with fixed fins

modeL with controLLed fins amax 25degr. mode L with controlled fins max 35degr. Fig. 21 Response amplitude operators for relative motions

0. 20

Beaufort number

Fig. 22 Significant relative motions in Neumann wave spectra' FnO2O

draught D

.

Uil

o 5

À

o'---

o 25

:7

5.0 75 10.0 125 15 Li 5 -o

immersion of propeLLer shaf

5

immersion of top of propelLer disk

05 6 7 8 u 5 o 5 n 0 75 100 125 15 u 5 o 2.5 5.0 7.5 10.0 12.5 15

We sec Beaufort number

5 6 7 8 Beaufort number We sec 2 E o ¿In

(47)

Fig. 23 FLow pattern at a static fin tilt of +3Odegr. and

- 30 degr.1

(48)

Fig. 2L FLow about the fins during one period of forced pitching with

controLled fins

(49)

/iiiì/1Iì/ÌÀ.

I/i//I/v

-

30

Fig. 25 Comparison of expected and actual lift

vs. time

t i me

actual curve

Cytaty

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e) The high levels of remittances were not only in the first years of the transition but during the years 2000s too, and have influenced in the foreign currency supply

We find no m ention in the Lithuanian Piarists re­ commended reading list of works from modern philosophy, general geography and politics, general and Polish

Pozbawienie praw publicznych zakaz porowadzenia pojazdów zakaz wykonywania zawodu nawiązka przepadek przedmiotów publiczne ogłoszenie wyroku. 8/ sposób i okoliczności popełnienia

Included were original studies that assessed the effects and/or elements of footwear or footwear characteristics on aspects such as fit, comfort, foot health, foot pain, balance,

nicy konferencji zwiedzili przygotowaną specjalnie wystawkę cenniejszych ma­ teriałów do dziejów medycyny, z archiwum w Brzegu oraz miasteczko Brzeg, przy czym

Jest jednak niewątpliwe, że konstrukcja szy­ bowa dawała większą efektywność procesu metalurgicznego, można było bowiem stwierdzić, że przy ściance o

Praoa jest kontynuacją badań autorki nad powstaniem rosyjskiej terminologii naukowej; pierwsza część pracy dotyczyła matematyki, astronomii i geografii i była

Estuaries are generally ' sunken' valleys in which marine and river sand and mud have deposited. In these deposits the rivers and tides have scoured channels and