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,
i
pable of oontet8.
paf.
Liet of ermbola.
ii,
List of figuzee. V
List of tabtes.
8ummarr.
i
1. Introduction.
2a. 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.
72.3. 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 whenpitching 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.
14The
flow pattern about the tine.16
Discussion ad conclusione.
19
App.ndx.
21symbols.
a,b,o14,e,g1
Coefficients of the hull without fina in the coupledpitch-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
aT
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 theocutrol meobanise.
ii.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.
E
Pbaee angle between 9 and the wave at the ehip'e centre of gravity. Lb,aee angle between e and
the wave at the ahip's centre ofgravity-.
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.
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 fineA[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 finekept 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
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 itsvertical
cosponent according to linierand
nonlinearcalculation.
8 Phase and reduction factor
of
lift
according to bon.etationaryA 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 patternabout
the finsers 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. Ofcourea
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 andwvee are
not influenced.
2 -A Stud, ctnk the Motionsof a )lode] of the Sixty Seriea
Equipped with P'ixed and Controlled 8ow. AntiitohinAFirts.
ntroduction.
Several papers have dealt with
various aspeots of tie problem of
antipitohing fins,am!ng othere[14J. Also in the
ShipbuildingLabora-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 nonlinearfeedback
signa]. of the pitch velocity. And thirdly the, flow pattern around the fin io examinad to find an explanation for some of the observedphenome-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 andheave
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 finson pitch and
heave motions is considered. For a more comprehensive review of various matters4. associated with antipitobing fins, See reference[8].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:
oÇ
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 pitchingof the model
plusfini
isdescribed
by:+2K
g
(1)
4*+8Ò+CG+D+EtGz
=MQ+2L1 *2Lgl_2Kj i
¿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 stationaryflow
pattern. It is genez-9117 stated that theReynolda number does
primarily affect the point oflift breakdrownd xmttbspeafth,1iJtc vttamall
angles of attack. If this is acoepted, even for such low Reyø].dsnumbers 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 isst3)
In Figure 18 of
(93
Mandel gives a curve determined from theezpez'jmenta:of
sCierai inveatigatòre which shows good agreement with
(3)
for valuesof the
aspect ratte whjeh are of praòtioal interest (effeotiv.AR2.5 or
3).
Th. influence ohe non'.etationary
v.].øoity
field is twofold1 Thestationary 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.
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.
Table 1: Particulgrn of the model and
od,t
Length between erpendicu1sra 2.258 *
Length
on the waterline
2.296 mBreadth
0.311
mDraught
0.125 a
Volume of dis»laoeaent
o.o'ìo
¿
inaA
151."in eeotion
Mean epan
Chord length
MACA0015
781O
rn80xiO3
a
Aepoot ratio
0.98 Maximum thickneee1210
aChord 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
0.650P'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
a2Longitudinal moment of tnertia of waterplan. O.1+2O
Centre o tfort of waterplan. aft
j
00598 a
2.2. Meaurements of the cotfoients i, theO e,uat one
omot on.
Foi' the model of the Todd Sixty $eries,blook coefficient o.6,
ueed in[5J and
[6:1 tor motionmeasurements 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 givenin 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, correspondingto 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 0.20the 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
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 inthe 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 thesame 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 sufficientlyaccurate
to predict themotlons of a chip equipped with fixed bow antipitohing fins in waves, when the coefficients of the hull Ltselt are knownq
3. Controlled bow fins.
,3.1.
h
contro
tern.
Of the various possibilities to control the fine
only a oontinuusfeedback 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, meansof 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 theangle of attack becomes so large that
the fine 8t&ll. Depending onthe
amplitude and
thefrequency 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 tiltadjusted momentarily. When DÇ 'mc' the maximum permissiblé angle of
attack, Ö(, may be increased by
maX°v
(positive fin oontroL)Wh., however,
<>
f
must beopposite to keep
down to D
(negativ, fin oontrol)a From this it
is olear that there is only a limi-ted possibility to increase pitchdamping by activation of the fins.
To get the highest possible advantage of the control action
a nonlinear component can be added tof
and thereby to the damping coefficient.
mie is dne
by a third harmonio of6, 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&Çf
()
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 CUJ
¡ &a &7=
I
()
-
10V-)J
(6)
=
21 Col 6 Co-IAI
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
thatD(3
muet be opposit. to DC' to subtract fros thelin-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
34ô' c(.4)0
96( C4)Having obtained (10)
it
follows from (7) that:-'°"*
û.Z c(,,,1-*
tC
J
i
(S)
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 angleofattack into the formula for the lift torce. By (8) and (9) the linearized
angle of attack is iven Then there resulte:
=
.2dÇ
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
Ex2erjmentheTo 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.
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
CL12 Beo.
Tabla ¿f3 8ummar' of the te8ts done with the
controllable fin ietallatjo.
fixed part controlled part
whole fin
Section
NACA - 0015
WSpan e
mn21,7
8o
101,7
Çhord o
mm80
8o
80
Aspect ratio AR
Q?71
1,0
1,271
Effectva Ai
-
2,5k
Thickneaa d
mm ¶2 12 12cid
o6,67
6,67
6,67
i (torward of G)
s
-
Q,911f5Poaiton forward of
0,9032
h (under OWL)
s
-
O,o95
Poeitiou above bade line s
0,030
Fin area P
in0,1736x102
0,6LfOx1O2
0,8136x102
F in percent of' A
L dC W0,33
1,22
1,55
2,9k
2,9k
2,9k
-PwO.20
n
-fixed fine;
heavingandp4tchThg
-pitching with. cntrQjled fine
&'
15°
nl
20
01 maxr=1,Qca
r=2,Ocin
r*3,Qca
-x
x
x
x
*
Xx
x
6«)(ia
x
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 deriyation. 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 randthe 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 andthe
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 patternis probably more pronounced for controlled fins than for fixed fina,
re-sulting in a larger phase ditfrenoe between list
force and angle ofat-tok. Thereby a component
f the litt
proportional to the pitoh aooelera.tion is developed.
Further will viscous damping ofthe L'in movement b5in
phase witht,
that is also proportional to *.o
-.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 andcontrolled 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
alonesull
with finsO C g G ' 52k,5 kg/zn
13
$2km
23,5 kg3,3kg
p24,5 kg/rn I 1 2 kgm a7,66kg23,3kg
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 of9i
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 aboutminus 10 to plus 5 percent. This is an interesting result.
Despite themodified
heaving n regular waves the irregular amplitude is flotsigni-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 shiptors.
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 significantdisplace-ments relative to the water surface can be computed
in the sanie Nuanwave spectra as used for the
absolute motions. Theresulte are shown
inthe Figures 21 and 22. They
illustrate again that thepresence 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 -.
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 aridconsequent
lift breakdown, although angles of attack of 30 to ko degrees were maintained. Xtis known that very low aspect ratio wings do riot
stall before large anlee arid tbat,if they do, one can not speak Of 3j
distinct breakdown of
the lift curve. The
effectjv. AX of the whole fin being 2.5k it was to be expected, however, thata noticeable influsno.
could be observed. To make surewhether
separation ofthe 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 testspeed of
019Le1 a/Bee (F0.20) while thefins 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 coverthe whole period of
fin movement, The photographed testeand their oir..
cumetanoes are SUjflmarjzein Table 6.
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 aeparatioinitial 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 separationinitial 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
O5ç
remarks ) k 68
10 12i86°
14.109,0
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.
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 beattri-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 zerofin angle is actually a small negative
angle of attack of some degrees. Secondly the low pressure region at the upperside of thefin pulla the
water surface down, thus smoothing the etrealine path and avoiding sepa-ration. Here the low preseure region interferes with the through of thebow 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 benoticed 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 thephotographe
show the flow pattern. An example of a reasonably good series of photosi8
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 onlyat
one side. For the overall effectin
damping the ntsgrated lift curve is responsible and this will conceal most of the irregulari6.
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 whenthe
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 coincidewith 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 than8
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
verticaloom»onent of
the lift force causingo
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 bein-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
nonlinearpercentlinear percejit nonlinear. percent 10 20 30 40 100 loo lO 100 102 109 121 142 loo 100 100 loo
10,5
102,5 io4,8 108,7In 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 isfixed
[ia].
1or very low Røyoldo numbers the flow is fully laminar and therewill not
be any transition,
Heaving Pitching
phase red. factor phase rod factor
seo degrees degrees
4
0,170
.. 7.1
0./41
+ 8.46 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
+12.1o.6o
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", ShipbuildingLabo-ratory of
'the Teohnologion]. UniverGity at Deift, Report.93, October1962.Ochi, IC.M.
"Hydroelatj0 8tudy of a ShipEquipped
with an AntipitohingFin", 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,
April1963.
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 Io,
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
O
Fig. 1.
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 +5 510
15 -1 secFig. 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-1I. 2 1 o +2. C.) w D)
j'
2
5 10 15i.
2 a +5 o5.0
-.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
1.00 0.75 L)
o
0.50 0.25 O +270 +18090
+27090
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 1.75LIA
-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 1.752.0 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
WeFig. 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
---umeasured
F =0.25
,
r
/
calculated F=0.20
measured
F=0.20
calculated F=0.25
measured F=0.25
7
,>,t
UI O25
5.0 7.5 7.5 10.0 12.5 150sec
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 mcalculated F=0.20
_-_-o__
smeasured 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 2.550
7.5 10.0/
/
/
/
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
summerFig.13 Blockdiagram of the control
system
Esinwt
amax
a
active nonlinear control
/
/
/
active by the linear part of the control
j
system-dimensions fn mm
timing belt
Fig. 12
InstalLation and dimensions of controlled fins
D
2
I
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 sec3 -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
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
wmodel 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 5lo
15 U) sec Q ai u) D) -x p w2
2.
- 5.' Oà 2 5 w- sec
5 10 5 10 1 ) 5 10 U) sec w secmodel 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.2O15 5 10 w -
sec1
10 w u' D)15
w2.0 1.5 Q 20 E u m ai w L D) a,
tc
0.5 +90 + 6030
6090
330 300 U) a) a, L D.) a, 240 w 210 180 150Fig. 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 secZa/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
i
In i E uz
iBeaufort 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 degreesFig. 20 Significant pitch and heave ampLitudes in Neumann wave spectra F=0.2O
'J
12_rD - 2 lo 2 7 1 7. o o E
il
2 2 We - secmodeL without fins
,
modeL with fixed finsmodeL 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 5À
o'---
o 25:7
5.0 75 10.0 125 15 Li 5 -oimmersion 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