JPRS ID: 9420 TRANSLATION BIONICS

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i S. . ~ ~ ~ r~

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JPRS L/9420
1 December 1980
Translatio~
Bion,~cs
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JPRS L/9420 _
1 December 1980
~IONICS "
~tiev HIONIKA, in Russian 1979 signed to press 14 Juae 79 No 13, pp 2-100 =
[Translr.tion of the book BIONIKA. RESPUBLIKANSKIY MEZSVSD~ISTVENNYY
SHORNIK. OSNOVAN V Z965 g. (Bionics. Republic Interaqenay Collectioai.
Founcled i.n 1965.) from the Academy of Sciences UkSSR, Iuatitute of
Hydromechanics, Editor-in-Chief G.V. Logvinovich, izdatel'stva "Naukova
- Dumka", 1,000 COp1e8, 100 pdqe8]
CONTENTS -
i1(ItIV ~ U ;.hll ~ � . � ~ � � . . . � � � . . � . . � . � � � � . � � � � � � � � � � . s . � � . . ~ ~ . . � � . . � � ~ � � � � � . . � . � � � � ~ 1
'i'he Hy~lradynamic~ of Aquatic Animals F~ith Lunate Caudal Fin
(L. Kozl~v) 2
_ Thp flydrodyna~nic Characteristics of the Caudal Fin of the Dolphin
~V. P. Kayan) .........e IO
_ A't'hin rerme~Ule Lifting Surface in ar Incompressible Fluid Flow
- (t. I. Yefremov) 19 -
Nydrodynamic ~ffects of a Travelling Wave ~
(Yu. N. Savchenko) 24
'Th~ Mc,uoflipper--A Promieing Wave Impeller for Fast Swimming in the
~'nNttlon of nolphi.ne
(S. V. P~rsF~i.n~ G. N. Orlov) 31
Itgg~.+l~ced tiyclroelr~etic ~ffect in the Fina of the Largest and Fastest
. ~~lphi.n, tha hiller Whale
(5. V. Per~hin, et al.) 45
_ [nvpetlgc~r.ing the Skin Elasticity of Live Dolphins
(V. V. Bubenko) 56
~nv~~tignting the Propagation Speed of Oacillations on the Skin of the
Ac~lphin
(S. M. Kidun) 68
- a - [I - USSR - C F~UO]
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. Some Results of 5pectral Analysia of Fluctuationa in t~ne Boundary
Layez o� ~etaceane -
(A. A. Vishnyakov, et al.) 7b
Distr~hution of Body Maes and Red Mueclee of the Tuna Along Its Length
(V. Ye. Pyatetekiy) 81
The Role of Hearing Mechaniema in the Spatisl Orientation of Animals
(V. A. Saprykin~ et al.) 85
MorplioEunctional Analysis of the I.igam~:at-Articular Apparetue of the
Larynx and 'Trachea of Dolphins
(A. P. Manger~ I. V. Karyeheva) 90
� 'ChP I'roblem c~f Sound Porception in Fish 97
(A. Yu. Heproshin)
_ t'de~ibiliey of Creating Analog Probability of a Model of the Sea
(I. V. Popov) 122
~
,
- -b-
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ANNO'TATION
~Ftt~: COLLECTION IS DEVOTED TO HYDRADYNI":MIC PROBLEMS OF BIONICS.
INDIVIDUAL PROBLEMS OF GENERAL HYDROMECx*ANICS ARE CONSIDERED
WT.TH RESPECT TO SWIMMING OF AQUAT~C ANIM2~~L5 AND SOI~ HYDRODYNAMIC
- F~ROBLEMS OF SWIMMING OF AQUATIC ANIMALS ARE I7EV~LOPED. THE MOR-
pHOIAGICAL STRUCTURE AF THE SKIN OF MARIN",E ANIMALS IS DESCRIBED.
xHL; POSSIHILITIES OF USING THE DERIVED I~`ORMATION FOR TECHNICAL
YURPOSES ARE INVESTIGATED. ~
TFiE COI.LECTION IS INTENDED FOR SCIENTIFIC WORKERS, TEACHERS IN -
WZES AND POST~RADUATE STUDENTS INVOLVED IN PROBLEMS OF BIONICS.
1
~ ~na nsr~T~TAt. i1CF. (1NT.Y
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UDC 591.524.1~591.177 -
7'H~ FIYARODYNHMICS OF AQUATIC ArTIMALS WITH LUNATE CAUDAL FIN
~ ttfRV PtANxKA in Ruc~aian No 13, 1979 siqned to pre~s 14 J~,n 79 pp ?~9
(Article by L. F. ICozlov, Inatitute of Hydromechanics of the Ukrainian SSR Academy
o! ~c~ancos, trom th~: collection "Bionika," Izdatel'stvo Naukova Dumka, 1,000
, copiea, lA0 gaqeel
- ~TAx~) The epproximate hydrodynAmic theory oi ewimming of aquatic animals with
lun~~~ cnudnl fin ~a proposod in [3]. The baei~ of thia work ia t~e hypcthesi~
that the oAaillatory emplituds of the body of an aquatic animal during ewimming
motione h~e a aon~tent value along the entire lenqth of the body. Hflw~ver, analy- :
ai~ o! movie lila~e of the ewimming ot numerous claeeee of a~quatic animals showed
that the oeaillatory emplitude of the body of the eAiQ ar~ia~ls varies approximateiy
eacording to linear law from the nose to ite hiqheet value in the r~gion of the
- GauAnl lin. A movie film of a ewimming stuzgeor? ie presented in Figure 1 as an
ex~m~lm Af t,hie type of ewimminq. Th~ autnbers 1-6 in this figure denote the se-
quentiAX paaitiona of its body durinq a eingle period of oacillation of the caudal
~Sn. S~~ah remnrkable ewimmere ae Scombridae, bonito, tuna of the Scombridae family,
~rwc~rd~i~h of tha Xiphii8ae femily, sailfish, spearfish, marlin of the xstinphoridae
lamily, vazioue epaciee of dolphina of tha D~lphinidae fiunily and other fast�ewim-
- ming ~quatic ariimale alao belong to t}~e~e clasaes of animals.
~,At us con~ider th~ forces actinq on the Zunate caudal fin of an aquatic animal.
Elonqetion of this ceud~l fin is evaluated in the hydrodynamic genee by the formula
,
(1)
wh~+xe ~ in blongation, 2R is apa~n and S ie the area of the caudal fin.
_ ` r7"
- f:~,.:~r.' -
/
~'iqure 1. Diagram ot Oscillations Made by the Body and Fins of Sturgeon
_ 2
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To calculnte tlie thrust created by the caudal fin of an aquatic animal (Figure 2),
let uq uen the main propositions of the theory of a hiqh-aspect wing, outlined in
(4). AcGarding to th� mentioned the;sty, we have the expressions
cp, m~nx~--' c'~ (1 + a~, c z~
~,a ~3~
c~m~2 .
Z'he rtnl3.owin~~ additional notationa are ueed here: Cpi is the induced drag factor, _
CL is tho lit't coefficlent, a ie the angle of attack of the caudal fin and (Z + d)
Sr~ a fecCar which takea into account deviation of the geometric shape of the caudal
~in !.n lsyout from the optimum shape in the sense of lenat inductive losees.
- Mor~ovar -
� Q z z
(1 b) ~ n .61 2 Az 3 ~ ~ ( 4 )
n~1 A~ A~
. whure 1~,~ iA the et111 unknown coefficients of axpansion of the rate of circulation �
~lonc7 the wing epan in the form of a trigonometric aeries with reapect to sines.
7'h~~~ cosf~iciente4 are dependnnt on the geometric ah~.-acteriatics of the winq and
the dngle of attack ~nd alao eatisfy an infinite syetem of algebraic equations
- ~ -
. ~(a R n-~sin6}A*sin~e=a R assin d, (5)
~ i
_ ~..i
�
- wh~r~ cxl ~ a- aQ is the angle of ~Ctack with respsct ~o zero lift, b(z) is the
crom~~r~ational chord of th~ caudal fin in the x0y pl+~ne, rp is the circumferential
rn~liu~ !n the auxiliary plane and a~ 2~rrp/b.
ii~ aquation (5), a and a(b/1) are known functians of coordinate z and parameter A
lx~unc9 tc> i~. 2'hc~ unknown valuee ara coegficienta An. it is recommended that
_ Clauerx'~ well~kriOtN1'! method, outlined in (4], be used to eolve the system of alge-
brai.c aqueti~ns (5).
Y
f~ 1 J
Q
- x p ~ =
,t ~ h
- f/ (
~'igurc~ 2. Coordinate System and Main Geametric Charecteristics of Aqua~ic
Animal
Sinco oxprASeion (4) is the sum of significantly positive terms, ~he minimum value
- of i.nduved dra~g Cp~, will be enauxed at 8~ 0. Consequently, in this case An = 0
3
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~
at n' 1. 'rhi~ corrASponds to the aptimum ahnpe of the raudsl fin in the xOz
pl~ne.
i.~t u~ nc~t~ tha following with regnrd to determ~nation oF the value of S f~r t-he
cau~lesl ~4n~ of equatic r~nimr?ls. The main pzoposition of hydrobionics, which ghould '
~c] ah ba vnlic~ f.or the hydrodynamics of the swimminq of aquettic animals, includes
the i'~c~ ~hat tho fozm of swimming oP, r~n aquatic animal ehould be very cloee to
c~~timum. '.rh~rafare, let ue assume the value d~ 0 in further calcula~tions wtth re-
~;f~e+r.t Cc~ a caudal fin in the ehnpe of (2) . Moreovar, even a eignificant deviation
a~ th~ qaom~trfv shape o~ the caudal ~in nf an aquatic animal from the optimum
nhrc~A oE a wing yf~ld~ slight corrections which can be disregarded in approx~mate
et~ginceting calculntione. 'Thue, for ur.ewept winge which differ eignificantly from
th~ aptimum in the sense OE Z@d8~ induced drag, the extent ~f this correct~.on com-
~r,ig~s the rollowing valuee~: -
- 3 fi 8 11 `
8, Q 02 0.05 0 A& 0.08
" ThQ given f.igures shaw that this ccrrection comprise8 approximately 2-3 percen*_ for -
caudxl fina enceuntered in aquatic animale with lunate fin (a a 1-3) and it can be
c3l~regerded in approximate calculatione.
~ot u~a note that interpolatior, formula (3) for the lift coaff~cient i~ in satis-
~eot~ry agreemerit with the numeroua ava~ilable experimental data (see Fiqure 3). _
F'c~r ~xample, far 4 accnrcling to the Fedyayevekiy formula dCi,/da ~ 3.88 and the _
ax~ori,mcen~al v+~lue comprie~s dCx,/da + 3.80. Conseqaently, the ezror of the value
ci~t~rminmd by tozmul.a compriaes eQproximatoly 2 parcent in thie cr~se. 2t is
interaotinc~ to note that the formule tor calculating lift used in (3I yielda a value
~P AC~,/dcx r 4.19 ~or the giv~n value of a$nd the corresponding error comprises more a
tihnn lo porcent comnared to oxperimental data. There are some advantages of _
~ormul~ (3) .Ln thie sense to determiae the lift coefficient for high-aspect wings.
J
?
/
0 ! ? J "
~'ic~ure 3. Compariaon of Experimen~al Dntn of Derivative dCl,,~da to Values
Calcul~ted by Formula (3) for Different Winq Aepect Ra~ios:
= adli~l lin~s--theoretical d~tai circle~s--experimental data
It ~l~oul~l .also ba noted th~st formula (3) is va,11d only for absolutely rigid hydro-
dynemic wing~, wh~roag the caudal fins ~uring swimming of aquatic animals are de-
~c~rmsd nomawhat due t4 the effect of incident flow. However, the mentioned de-
- f~rmeti.ons mu~~ be disregasded at the sC.age of studying the areation of thrust by
nqu6tic r~nimala under considera~ion.
4
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L~~t u~ nubeec;uantly c9leregarc9 thg rotdtion of the caudal ~in with reapec~ t~ the
a~rootion of in~tnntmneous epeed, i.e., let us as~ume that Q~ m 0 in equation (6).
Thi~ l~ypathosie must be ma~e ~ince there ia eeeentially no information about the =
val.ua af thie 8ng1a durinq ewimming of variaus tiypee of aquatic nn3mals. Aa ma- _
tsii.~l in aecumula~ted on the vdlues of angle ~ for various types of aquatic ani:-
n~~ld, 1.t will, be Aaey to refine the calculatione made in tYi~,s pa~er.
t.~t ur~ turn to celculation of thP speeda ~nd forces acting on the caudal fin of an
- aquatia ~n1mA+., re~ardefl r~s a rigid high-aspect wing (Figure 4). Zt follaas from
- thF~ giv~n layout that th~ inetantaneous thruet coe~ficient of a caudal fin is de-
tc~rmined tn? ~..,o formul,a ~
(6~
s� ~L ~~r T~' - CD,~
where tti~ additional natatiiong are introduced: n(x, t) is daviation of the center
~.ir~o a~ an aqua~tic enimal from coosdina~te axis y, t is tim, 2n/nt ~ nt ie the -
tranaveree velocity of ~he center line of an aquatic animal, nt/V is the elope of
the dirnction of inatantana~s~s speed of the center line to the direction of motion
- of ~n aquatic e~nimal, ~ is the angle of rotation ~f the caud~~ fin with respect to
- tha direr,tion of instanta~neoua speec~ of the centar lina and V ie the speed of -
ewimmfnq of an eauetic enima2.
_ ~ a
/ ~ r
~ /m~4o
_ C, y
C~ ~ 0
k'~c~ur~ 4. Diagram oi Speede ~nd Forces for Caudal Fin of Aquatic Animal _
A~ theoretical ~nd experimental dnta are accumulated on the effect of hiqh-aepect
win~1 deforma?tion oa the lift coefficient, one aan introduce the appropriate cor-
reati~n~n Co the calculations. Zt ehould lae assumed that the mentioned corrections
elcy nat mako any fundament~al chnnges in the derived valuea of~the lift coefficients.
Aco~rA.ing ta tha previously poetulated problem, let ue assume that the oscillatory =
ecnplitude of the center line of the body o! an aquatic ar~imal increasee by linear
- lew ae tho pnint under conaideration movae from the aose to the tail point xZ. In
other ~vorda, lat us ns~ume that the following formula? is applicable to deecribe the
a~c3.~lati~n ot the boc~y of mn aquatic animnl
am 1.~.~, r~ 3L _ 1~ ~ 7~
TI ~lo x- x s~fl ~l x- x
t 1
ttdre i~Q i~ the Ascillatory atnplitude of the tail point of the caudal fin, L is the
l~ngttti of the wave travdlling along the body of ar~ aquatic animal, n ie the number
5
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o~ wrsveg a?dded on the length of the body of an aquatic animal, c ia the speed of
' pra}~agntion of a weve traveli:.r.g nloaq tha body of an aquatic ~?nimal and Y.~ ~ -
` 2�ni..~ M xl - x1 ie the l~r?gth o! ths ba9y o! an aquetic animal. From the graph
yiv~n in ~'iqura 4, toz the anqle o! attaok we find _
c,--u~" ..~~~-V ~I ~ _
os as
w1�r~ vn i~ L�he normal epeed componeat of the tail point of the caudal fin.
- Let un calculato the values of the darivatives in formula (8). To do this, let us
aifferenti.at~ the values of ;7) with respect to coordinate x and tin?e t. After
calculntion, we lind ~
xJ. ~x ~ x~ - zl . (9 )
~ ~ L C L C~ ( -~-I ~ _
P
e.-~-sin(~--~)-I-~-~ ~cos( ~ � (io)
Then the nortnr~l apeed component for the caee under consideratian has the form _
un~ ~.c,-x~~_..y~~os ~~-~)-}-~Vsin(~--z-
L-xl � (11)
~p ` ~ /
- L~t us ca~loula~e the pulling coefficient. Subetitutinq the values of the lift and
induoed dYeg coeffiQiantB into equation (6) according to formulas (2) nnd (3),
atter eimple? traneformations we find
~ v 2
C~ = v ~ 4 2 IT ( dt V ~ ( : 4 21� l V ) ' (12 )
- I~et un then calculn~s the value of the pulZing coe~ficieat during periad 'r ~ 2~r(i,/C}
s
- {C,~} = z ~ Cadt. (13 )
o -
U~iny the le~w of averaging (L3) permite one to find the expreseion
{Ca}~ ~+4-1-2~1~/ ~'~}4-i-2)' /Z~ ~ (14) e
. Let ue turn to calculation of the indi~~idudl terma of the expression.
The celculatione made previougly in (2] made it poseible to find the expreasiona
6
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- j~ t-T-l1~ L 12-}- 2(~L l~ ~x'LA z~ ~ V 1)2' (15)
l ! \ I ~ ~ ,
~\~1 \~l~~m ~ \~l1\x
Lp !s~\y~1/ ~ (16)
sub~+:lr.uting them into equa.tion (14), Co calculate the pulling coefficient we find
tha Pi.na1 nxp~eeRion
'`~n).4+2r~13 c ~c 1/\x px)s-
{Ca} o. r ; ~ _V (1 ~ ) .
4nA 1 ~0 1 1!~ \1(z - x~) c 3
~ , + 4 + 2~, L 2 ` ~ } + 2 I ~ 1 - 11
\ I \ 1
Sincn tror~ expreeeion (1) for the typical aree we have -
S~ -
- r~n~i l:lta~ rQduced maas at the tnil point is _
- m~ m pnR',
th~n
p~ S~2
ThE~n the moan valuns of pulling are
{A} ~ {CA} P~' S (C~} + ( ie )
c~r, ue~inc~ ex~ree~loti (17) , we finally find
- {A} ~ 2 lZ /s ~s l~ - 1~ C~)s -l-
- 4 + .
Y~r-~~, 2[ p (19)
Tt~a~e expr~asione can be found by aimildr ealcule?tions.
- mh~ mean value for the section force ia _
.
_ tP} ~ 4~ ~ ~ ~1~ 2 ( L ~(~r 1)~' (20) _
, ~
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'i'Iz~ meaan velue of the kin~tic energy comi~ng nff the caudal fin to the hydrodynamic
wake ip equ~l t~
{E} L l~ V a,~- 4
i( L~1 ~X~ L xi) _ rla Va, ( 21)
~ ~ ~ 1 P ~
~1~t~H qenorna. ~xproeEiion f.or the hydrndynar,iic efficiency haa the torm
. {~p}~ ~t.4} -I- P V (22)
( ~i- } ) V +
Su1~~titutinc~ exX~rc~~ei~ng (19)- (21) inta equality (22) after simple traneformations =
rtnr e~Pficicncy, w~ find the final expression
l~~
; ~4 Z ~ ~ - 1) _ , + 4 + 2[ 2 + - 1)Z ] } + .
1 1 c x
4 +i~~y---i~
~~I?~`'~ 2 c jc 1l_ 4 l fc ~ la (23)
V~-}- 4~- 2 l~`~ ~ 1 V~
4-}- 2~`V l 1~
f 1 c lY -
+ 4 ~ 3 \~~1/
'1'ho~ func:tiany nf hydrodynt~mic ef.ficiency {~'lp} and the din~ensionleas coefficient of =
- wave velocit c/v t
thruHt far different values of travelling y
ar~ cnlcul~ted k~y uRing formulas (19)-(23). The resulta of these calculations are -
~~r~*a,~oiat~c9 in ric~ure 5 for aquatic animale with lunate caudal Eir? having aspect
ratic, c,f a m 4.
.
4e . ?o _
q6 ~ ~ /,3
- J
- q4 ~ ~o
~
Q~ as
i
- o 0
i,o il is ~e ~o ~v
t~igur~ Gomparieon of Resulta of Calculating the Pull and Hydroflynamic
Efficiency for an Aqua~ic Animal with Lunate Caudal Fin:
solid line~--according to fornulas (19)-(23)j dashed lines-- -
accazding to data of G. V. Logvinovich [3]
- a ~
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it p}~~uld }~e �oted thnt or,e ahoi:ld take int~ account the effect of thr, r.ydrody-
namic weke occusriny behind the body on the ~r+rk of the ce~udal fin ae an imneller
wh~n calculating the hydrodynamic efticiency of the caudal fin of an aquatic ani-
- mal by fonnula (22). Thie is usunlly teken into account in shipbuildinq by intro-
ducing the conc~ept o! hull effi.ci~ncy. Thie coefticient represeats the fcllo~+iag
reletion in th~ cne~ ur~der consideration
1-t
~lK�t~-$ ' (24)
wh~r.e ~y i~a t;+~ wake~ frnction, t is the suction coefficient nnd i is the coefficien*_ _
- ~f the etfect ot velocity tie2d nonuniformity at the location of the caudal fin. -
Calculatione carried out by the known data of Haswald (see (1~) showed that the _
Pollowing vnluee can be used foz aquatic animals: i~ 1 and 1- t= 1- t~, i.e., _
t~ull efficiency for f~st-aw~m~ning aquatic animal~ is approximately equal to unity.
Coneequently, the usa of formula (24) in the case ui~der coneideration to calculate
_ the k~yAzodynnmic efficiency is quite valid. Zn those casee when nk differs con-
- Aieerably trom unity, the formula for determininq ~he hydrodynamic afficiency has
thn f.orm _
} ({~i) {P}) V _
~ {~1P u ~1k~- } ' (25)
w~a rwto that thc F~roblem of ewimmi~g of various types of aquatic animale continues
- to bF~ of ~roat ecientific in~erest nnd merits sezious atudy both in the theoretical
~r~~i in the~ oxperim~nt~sl eense.
- BIBLIOGRAPHY
1. vc~ytkunKkiy, Yn. I., R. Ya. Pershin and Z. A. Titov, "Spr3vochnik po teorii
korablya" [Handbook on Ship 'I'heory) , Leninqrad, Sudostroyenfye, 1973.
7., Y.ozlnv, L. F. and R. A. Oleynik, "The Hydrodynamics of Aquatic Animala Swim-
_ ming in Scombroid F'~shion," DOId. AN USSR, SER. A., No 11, 1976.
;3. Logvinovi.ch, G. V. ,"The Hydrodynamics of Swimming of Fiahes," BIONIKA, No
1973.
a, r~dyr~yevekiy, Y.. x., Ya. 2. ~loytkunskiy an8 Yu. T. F$ddeyev, "Gidromekhanika" -
(flydromochanics], I.eningrad, Sudostroyeniye, 1968.
9
- F(1R f1RRT(;tAT, TTSF ONLY
I
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~
UDC 591.177
_ Z'itE 11Y:}'r.~'%q:N11MIC CHARACTERTSTICS OF THE CAUDAL FIN OF THE DOLPHIN
Kt~v ~I~NIKA in Ru~~la.*~ No 13, 1979 aiqne8 to preae 14 ~un 79 pp 9-15
_ ~ArticAU~OeY~ ~from h e~collectiontesion kar'~Izdatelestvo Naukovait1DumkaSS1~000d~y
_ o~ Sci ,
c:opioe, 100 ~aqee~
~ [Text1 inveetfqating the hydrodyr.amica of swimminq of fast-swinaning aqua~~c ani- _
mal~ is of grdat interest on tne part of inveetigators working in the field of -
- hydrobioaics. Gf ~pecia: interest are ania~?ls which move by means of bending,
ascillatoty motions of the caudal fin working like a flapping wing (specifically,
dol~hin~).
we prefvinuely touad the hydrodynamic cheracteristics of swimaning of the aphal~ine
8olphin by the kinema?tics of bendinq-oscillatory motAons of ~he ~er~b�s~ and by
thn calculating mathod based on G� V� Logvinovich's theory [ l�
idial hydromechanical e~ficiency of ti.1ze dolphin impeller and also the coeffici.ents -
e~ tha hydre~dynamic drag of the dolphin were determined ae functions of the Reynol.ds
numb~t anci the meen value during oecil2ation and the sign of variation of speed of
- awimminq (5~.
N~w~v~r, ~ince a number of aeaumptior.s wa~ introduced into the calcul8tinq formulas,
it would be interesting to find the eame characterietics by a different methc~3 for
~:omp~riron. 'i'he resulte of calculating the propulsive characteristics of the caudal
fin of n~lQiphin workiag like a flapping wing with known law of }t~ �thesis of~
- anqular oacillations ere presented below. A method based on the hypo
Atability, i.e., on the assumption thati the instantaneous forces occurriny an the _
_ winq during unsteedy flow of a fluid over it, are determi.n~ anly by the values of
the inetnnteaeous angle o� attack ai and speed V~ of the wing, was ~ssed for the
caZculation. _
~Pha func3amentals of the theory of an oscillatingerimental investiqatianshenpstudy
of A. I. NekraAOV (8] and L. I. Sedov [10]. ExP
af. tl~e f~rcre end moments occurring on a rigid wing ma}cing angular and v~rtical
oRCil.letions in a fluid were ca?rried out at 3ifferent times by,H. Hertel [14], -
Yu. N. Savchenko (9l and E. P. Grebeshov and 0. A. Sagoyam [3]. Unswept [3, 14~, -
ellipticnl and Iow-nepect delta wings (9~ were tested. -
Sincs Lh~ l.itatature containa no data on the hydrodynamic characteris~i~s of the -
- cauc~el ~in of dolphing, some simplifications were made for calculation. The wing
1Q
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= wa~ raqarded as rigid and the natural shape of the caudal fin of the aphaline
dolphin was replaced by a aw~pt wing with aspect ratio of a~ 12/s = 4 and taper
, n� hl/bZ ~ 4, where 1= 0.52 m is t;he wing spa~n and b2 = 0.059 m is the end chord
o~ the winy (Figure 1), equnl to the caudal !in in aren S= 0.077 m2 and by the
v~lue o~ the root chozd bl ~ 0.236. The mean aerodys~amic chord bSAI(h o~ thia wing
1~ daterminoQ by the knowa method I11 and is equA~ to 0.164 meter.
Q1~~ 6~ ~ -
a~as
v
, ~j .
.
, ~ _
�
_ ~
i'igurA 1. Shdpe of CnUdal Fin of Hottlenoaed Dolphin and of Equal Area uf
Swept Wing
The N]1CA-0018 eyY~m?etrical profile [6], whose aerodynamic characteristics for an
unnwopt wing of 6 are known and are presented in Figure 2(C1, is the lift co-
effiolent, Cx ie the drag factor, k~ CY/CX is wing efficiency and a is the anqle
of att~ck of the wing), wes selected from the catalog as the wing profile. Fiqure -
3 servee ae juetification for selection of NACA-0018 profile. Profiles 3 and 4 in
the lorward part elmcaet completely coincide, while thoy have a slight difference in
the tail part. -
vartation of the hydrodynamic coefficients of the winq upon transition from unswept
- at a~~ t~ ywept at 7~ ~ 4 and ?1~ 4 is shown in Fiqure 4. The functions Cy(a) and
rY(rx), foun~9 by wind-tunnel testing for plntes in the form of wings of different
qh~pg, ar~ shawn on the qraph. Thus, by introducing the correcting coefficieat to =
tuncti~n~ ~Y(a) and Cx(~) presented in Figura 2, we find the coe~ticients Cx and `
CY f.or. e rigid wing of the adopted shape with NACA-0018 nroffle.
c7a~ Cen then detormine the hydr.odynamic forces on this wing a~t aach moment of time -
by th~ ~~rmulaa (1J
s
)(i 'a C:t P
Zt S� (1) _
4 (2
Yt ~ Cri P~ s.
mh~� unknnwn velues of ai and Vi are determined from the trajectories of motion of
~ r.hu caud~l f.in of the dolphin, found by making motion pictures in a biohydrodynamic
channei (12, 13J. Th~e investigations were carried aut with six bottlenosed dolphins
h~vinc~ lenqth of r, ~ 2.35-2.65 meters [5]. The components of the kinen?atics of
motion of the caudal fin of the animal i:nder investigation were recorded with the
lI
Ff1R (1FFT!'.TAT. TTSE nN1.Y
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Knnvae-nvtomat movie camara wi~th Rp-ZZM objective having focal length of 50 mm.
An electric timer wae used to record the time intervals between a?ovie frames [12].
`
/6 .
e
_ o c` -
_ ~
a~e
Q~t ~ -
Q~ .
o,a~
o~
�
ae -
~
o ~ e i1 ;e ~ avq,~ood -
Fiqure 2. Dependence of Aerodynamic Coefficients and Efficiency on
Anqle of Attack a
1~..." o-~
.l
4H s -
~ ~
~
- 0 Ql Q1 4J Q< QS Q6 Q1 qa plG,u~ ~
I'iqure 3. Comp~rison of Mean Cross-sectional Span Profii~s of Caudal Fin
of Bottlenoaed Dolphin (1) [11), of the White-Finned PnrpoiSe ~2~
[15] and Their Mean Value (3) to NACA-0018 Profile (4) [6]
Condition~ where the dolphin moves in straight line and where the plane of the
cnudal fin doea not mnke rotary motions around the root chord, i.e., the caudal fin -
ie proiected onto the longitudinal vertical plane ~OY only by the root profile -
which was replnced by a straight-line seqment equal to the root chord (Fiqure 5, a), _
wer~ eelacted tor subsequent processtng,. _
12 -
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lS Cy -
- ~
. IO ~~/J? J ~ -
QS ~ '
/
0 A7 ~c.ipfi~ Q!r Ql C~ -
E
Fiqur~ Aerodynamic Characteristica of Plata in the Shape of Ur.swept
and Sra~pt Winq: 1--unewept winq with ~~~t 2--With J~ ~ 6f
3--awept winq with a ~ 4 and n~ 4
Koy:
1. pegree
Le~t uo plot the path travelled by the caudal fin in the longitudinal direction,
tha numbar of lrnmee on the movie film and time t in seconds on the ~-axis. Let
- ua plot the ecqpYitude of verticel oscillations Ap of the caudal fin oP the dolphin
aloa~ t?:a y axi~. Variation of the eaimming ~peed Vp of the dolphin is showri in
~'iqure 5, b aafl of the spaed Vy of ~he caudai fia in the verticai plane during the
period Qf o~cillation is ahown in Figure 5, c, while curve Vy(t) is the same as
- func.tion Ap(t), but ie shi~ted in pheee by ~r/2. The transverse speed of the fin
ie de~~rmined e~s a tusction of the a~aplitucie of vertical oecillatione:
vy'~ ~ o.'t (A~' ( 3 )
'Tho inmtantaneoue? apaed of the center ~f preseure of the caudal fin is determined
by the lormula
y, YVo . -
(4)
Th~ angle of nttack a of a rigid ewep~t win~ (here the angle of attack of the root
chord) ia ~ouad ae the differeace o! the anqla of downwash y(i.e., the angle of ~
~lope of tho inetaataneoue speed vector to the direction of forward motion di the
c~nter at gravity of the dolphin's body) and the engle of motion of the wing ~
;i.~., the iastantanaous anqle of i.aclination of the profile chord to the direction
~Y f~rward motion of the centas of gravity of the dalphin's body). An sxample of
veriation of aagl~e Y and ~ durinq tl-de period o~ osc~.llations of the eaudai fin is
!shown in Fiqure 5, d.
w~ ~ind aaqle Y from the zatio of speada Vp and Vy:
tgY~-~, l5)
and angle S is found graphically directly from the trajectory of the caudal fin
(Fiqute 5, s). Anqle S is alao the amplitudo of the angulnr oscill~tions of the
profile around ite awn preseuze center. It followa from comparisian of Figure 5, a
And 5, d that the phaee shearing angle d of vertical and angular oscillations of
~
13
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the prafil~ is equal to '~/2. In the case of variable 8, this corresponds to the
mnximum efficiency of an impeller o~ the flapping wing typp, all things being
- oqual t:~) .
l3~~~111'~~ 7l ~ 6/~
~
- -
s~
~ ~ ~i ~ ~ -
- 1 t11
/ J 3 7 0!! 1311 1/ ?J?3177~.~.~fJ3 JI d9414.f ~1 ~t140S/SJdf31,f~F/M~+rd~~
0 Ql !!2 QJ~ 4~ Q5 46 41 40 Qp l0 1,1 l? lJ
a
~o
1,4 -
2~1
0
- ~ 1 S ~ l3 /7 !S 7~ JU Jl til ~3 4P SJ 51 61 65 _
~y b
/,6
Qe
,
- ~ S 0 IJ !1 2! 23 ?9 J~1 J7 y/ 43 40 3J 37 6; 63
�QB _
-/,6
1~ c
Y,P.tOoe t2 ~
JD
~ ~ ~
~n
~ l 3 9 /J /7 Il ?S ?9 JJ J1 ~i! 43 4~ .fJ S7 6/
�10
- ' ,~0
s10 ~
- ~
s
(x~ y) E S.
~!',qu~tioa (l.A) cen aleo be faund by ueing the vortex acheme of n finite-span wing
and by r~plecing the latter w~th continuous diatribution of U-ehaped vortices with
psaki the wtng points [5]. _
~ Let ud aor~oiSer arr unswept wing
x- a
' 1 1 +b ~I) 1 _ ~ ~ _ f ~ 11 ~ -
'~Y ~X~ an y - n) ~ + Yc~~+~~ ~ ~ .
('I7~o ~~.vial in~egral should be underatood in the sense of Maazgler [5~ Let us _
u~a the di~cxate v~rtex method for numeric~l eolution of equation (11). Zb Qo this,
1~~ us divic~e tha }~ai~-span og the wing in~ko K part~ and let ue nssume tha~ the
intea~ity ot the U~shaped vozticee ineide each seqmeri~ is independent of n. Let us
~ntisty th~ boundary condition (4) in the middle of the amall interval. Let us uee
th0 "3/4" m~thod in the direction of the chord [ll. Thus, we find a eyatem of
linaar ulgebreic equations -
21
~ L+/~p /1TAL~T/+TAT iSCF nNT~.Y
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,
. _ _ ,
FOR OFFICIAL USE ONLI'
, K , 1 v~~-~~,, + ~ ~ r..
- xYr� ~nM ~ ~ Y/~ ~I?� ~Iv [ + xr - ! _
I-~ v�t
~f l y~ xt ~"'1'_~� l
U-~- nv_~ xt 1 J r -
N L
_ ~ i'~z~- ~)'+cb,,-ny>� ~ 1 X ~ia) -
_ U� _ ~V I 1 x~ _ ~ y� --+1,~-i
l
. x 1 1 V (x~ - ~~)s + ~U� ~v-1~s_ I~ a~t
( + xi - J ax ~
~
~aha~rg 1\ 1 3 1
xi=jc--- 4 IM : F,~~~j-- 4~~-? _
\ / ~
1 b b
y�~(�._-~1~; ~~~.v~-; (13)
~ 1
(i,~~1,2~...~N? (�~v)~+1~2~...,K.
a~4
~ 4
1
/
Q? '45
:
Q1 q! Q? QJ Qx e
m,ic~ur.d 2. Va.riati~n of Pasition of Pressure Center of Unswept Wing as a
- Funation of Coefficient o~ Permeability
- At'tie~e ~nl~stion oE ayetPm (12 the aerodynamic characteristics of a permeable -
winR i~ ~oun~l by the �ormules
/ 2 M K 2 M K ~14) -
C ~ ~ ~ Y~Y~ CTri a ~ ~ ~ b~Y~y�
~ ~w
~Che calculntions were made* on a BESM-6 computer using FORTRAN algorithmic language.
*
'~he oaloula~ions on the computer were mad~ by M. E. Marko.
22
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, Th~ mimbAr of wing divi~sion~ along the span to K and along the chord M was va:ied
in th~ calculntions ag a function of aspect ratio. Thus, K� 12 and M~ 5 at
- 2b ~ A dnd K~ 5 nnd M~ 12 at 0.5. The results of calculntion of CZ and
r,tn atA ptp~entsQ in Yrigure 1. Hencs, it is obvioue that the eflect of permenbility
on rhn vrs].uA o~ ~hA litt coetficient bocomea weak ae aspect ratio decreaeee. How-
' ~v~r, th~ center ct pre~euze ia shittsd toward the osnter oP the chord ao pertneabil-
ity incroaMaN (~iRura 2). 7'his ehitt ie espec:.ally Appreciable at loa eepect
znti~a. The lond dietribution alonq the apari also becomse more uni~orm and de-
c;reanee ehnrply in value only near the lateral edqes. The indiceted c3rcumetance
t'or n eala i~+ v~ry und~eirable siace it leadB to an incrense of the rollinq mament.
BSBLIOGRAPHY
1.. Nelataorkovekiy, S. M. ,"Tonkaya nesushchaya poverkhnoAt' v dozvukovom potoke
ctaza" (A Thin Lifting Surface in a Subsonic Gas Flaw] , Moacow, Nnuka, 1965.
2. Nekraeov, A. I. ,"Teoriyn kryla v neetatsionarnom potoke" [Theory of a Wing
in n TranAient Flow), Moscow, Izd-vo AN SSSR, 1947.
3. I~Anchenkov, A. N., "Teoriya potenteialn uskoreniy" I7'heory of Acceleration _
~otential), Irkutsk, Izd-vo irkutekaqo univeraitete, 1970.
4. f~nkhmetulin, iQi. A. ,"Flow 4ver e~ Permeable Body," VESTN. MOSK. UN-TA. SER.
i'i~.-MAT. I YFSTF.STV. NAUK, No 2, 1950. _
- 5. Anhl~ay, N. and M. Lindall, "Aerodinamika korpusov i kryl'yev leta~el'nykh
+~ppsratov" (The Aerodyna~mica of Aircraft Eodiee and W~nqs~ , Nbscow, Mashino-
e~~royeniys, 1969.
c,. AarakaC, R., "IncompreBeible Flow Around Poroue Tw~o-Dimensional Sails and
Wl.1?a~+;" ~7. MATH. ANf~ PHYSICS~ VOl 47~ NO 3~ 1968.
23 ~
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UDC 591.524j591.177
IiYl7ROI~YNAMIC EFP'ECTS OF' A TRP?VELLING WAVE
Kiev BIONIKA in Russian No 13, 1979 eiqned to preae 14 Jun 79 pp 19-24
(Artiale by Yu. N. Savchenko, Znstitute of F3ydrosaechanics of the Ukrainian SSR
AcsQemy og Sci~ncee, from the collection "Bionika," Izdatel'etvo Navkova Dum3ca,
1 ~OOp copi8n ~ 1.00 pe?gee]
(Text~ Zntereet in study of flows along a travelling surface wave wae aroused by
the bioaic iriveetigatione of Essapian ar~d ICramer, who sugqeated that the "travel-
_ ling t~lds" on the skia eurfnce of the dolphin may affect ewimming speed [5, 10~.
~the investigatorr teel that detsiled etudy of the hydrodyr~amics of travellinq wa?ves
would yield dats of funQemental importau~ce for hydraomachaaics.
~ioni,c abROrvatioas r~quire scientilic expla~nations and a subesquant nutaber of
papore leid the l~aeis ~or the new treaQ of investigatione in hydrrnaechanice related
tio tr~vollinq waves a~ e poseible mschani~ of draq reduction (1, 2, 4, 6]. _
x`tte hopss of inveetigatore were justified: digital computer calculatione aad direct
nx~erimnnta in a hydradynamic lr~boratory ehowed that m vortex flow, cleariy visible
an photayrnphs with prolonged exposure of the travalling wave model (Fiqure l, a-b),
iN ~ormod in the depressions between travelling waves under specific conditions.
A g~u+cial model of the travelling wave which permits consideration of the flow
tormad in coordinnte eyetem OXY boutzd to the wave ctest and moving at phase veloc-
ity V~ in an incident Pluid flow a?t velocity Vo~ was used both in theaexper ~en+s~,
+snd ,in digital computer calculation. The wavy surface boundery Y
1n thi~ coordinate system becomes a lixed surfece in ~dhich each point slidse along
the tiangent toward the incident wave at velocity of -Vq. The relative velocity in
this case ia equal to Ve ~ V~, - Vg a~r~d Vg ~ Vg.
An ~x~arim~nt ~n Plow visuelizetion was conducted in a flow channel c~n a model con-
taining four wnve~ of length 110 man and amplitude 2A ~ 45 mm on its surface at
iteynolda numbsrs of RL ~ V8L/v ~ 0.12�106-0.3�106 and RJ~ = VeJ~/v = 0.2�105-0.5�105.
Frnm ~omparieon o� the flow patterne tound by digital co~a?pute: =~�~culation [2]
(~'iqurA 1, c) arsd obeerved in, experiment during water flow over ~~e ~ad_1; their
totei ngreement is obvious.
'Phe invagtigatioae showed that stable periodic flow in the form of vortices between
wava creste occuta only in the case whea the phase ~velocity of the wavas camprises
24
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-t
~ half the incident flow velocity, i.e., Vf/Ve ~ 1/2. The value of this ratio appa:- _
ontly corresponds to the minimum tnngent stresaes in interaction of the resulting -
vortax tlow with ealid boundary and external flow.
~x~~rimanz~ to msaeure the torce interaction of a surface with a trnvell.iag wave
~.r~Q tlzm ~low nround i~ [6~ showed that the drag co~flicient Cx ~ 2Rx/ VZS is
attonqly dependent on the value of the relative phaea velocity Vg and may bec~me
1~q~ at Vg + 0.6 thasi that of an equivalent smooth plate [6]. The dtag coefficient
Cx i~ no lonqer dependent on Rey�olds number in thie ca,sa, which can be explained
by ~ormetf~:n ~f. a etable periodic flov+ alonq the entire surface when the drag coef-
~ici~nt ot eeci~ of tihe celis of the travelling wave ia no longer dependent on its
panition in the row. _
Unliko a gurface with fixed boundary on which neqntive work is carried out to re-
duce the energy of the incident flow, a travellinq wave on the surface may increase -
~he tlow ener~y, which is observed in the case of forme?tion of a stnble secondary
vort~x flow in the depreseions~ between travelling waves when the directions of the '
normal vslc~city components of the boundary and flow coincide.
2t i~ obvious Lhs~ apecific war:ci ~.etermined by enerqy expenditures to form a
- vortox flow dnd to maintnin it on the flow eurface, must be canpleted to increase
th~ @1ow energy. Tlie enerqy expenditure to create a stable eyetem of secondary
vc~rtex tlow cen ba estimated in the lollowing manrier.
t,Qt u~ con~ider a vortex pinch of radiu9 r and length 1 rotatinq a?t a~ngular rate _
~ V,~/2t ir~ the c~epr~0eion between ttavelliny wavea in the coordinate syetem XOY
- baund to th~ cmnter of the vortex (Figu.re 2).
ThR mom~~n~ c,f tho viscoue �or.ces applied on the boundary of the vortex pinch rotat-
inq ~K a aingle whola from the direction of the surroundinq fluid can be estimated _
by tiAing the known solution of the Navier-Stokes equations far a vortex in an in-
f~nite fluid (8li
M ~ 4n}uul~. ( i )
- Takiny int~ account that a specific number of wav~a n~ L/~ ie added aimultaneously -
an the flow ~urfaco of length L and width 1, we find for the enerqy expende3 per -
uni.t timA ro maint~in the entire voztex 8ystem
NA ~ ie11~1~ ~ 4nvpw=r'lL/~. (2)
Th~g tormula permite vne to estinu~te the value of the viacoue losses to disaipation _
of th~ vortsx ey~tem of the secondary flow along the entire surface with travelling
wavaa. '1'he+ enargy expended on tormation of vorticas is equal to the kinetic enerqy
c~f tlie vortices formed per unit time on the flow surface. -
AcCarding to experimental data, a sta?ale secondary flow is formed at phase v~locity
af. trAVelling waveN of Vg ~ Ve/2. Tn this case nl a Ve/2~ vortices whose centera
er~ maved alang tha eurface at velocity Ve/2 are formed per unit time. Since the
k~�9tic anerqy af the forward motion of the fluid included in the formed vortices -
. is aqual t4 Np � lptrrzVe/4~ upon inleakAqe to a eurface with a travelling wave and _
, 25
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~inc;e N~ a lp'rtr2V3/16?~ on :.:~e surfa~~, itself Anc~ in the wake, the energy expended
- rer unit timo to ~rake the forward ~�,~tion of the fluid is determined by the formula -
'A
_
~ \ �
~ `
~ \
_ ~ \
_ � ' ~ \ a _
C
S~~ y:
.
`FI
~ ~
.t
E'i~ure~ 1. Flow Pattern Along Trsvelling Wave: a--flow in depression between
wave cros ts at Vf = Ve ~ 0; b--at Vp/Ve = 1/2; c--diqital computer
celculati on of.flow pattern; d--flow along surface of model at
Vf/Ve ~ 1/2 -
9Pnr~Vel (3 )
Nn ~s J11p - Ne = 1 �
26
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~
~ '
~ ~ ~ ~ ~
~
- ~
~'iqurE~ nierr+~m of Vortex Arrangernent Alonq Surface of Travelling Waves
Z'ho kin~tic: anarqy c~f the vnrL�ex eyatem during ite rotetional motion at rate
w ~ VA/~r in faund by the formul~
a
N, ~ 2 Jao=i ~ ~
vt ~ ( 4 )
whor.s J~(1/2)pnr4 ie tha moment of inertia of the circulnr cross-section of
_ r.ec~lus r.
- Adding expreseaions (2)-(4), we fi:zd the approximate estimate of the energy taken
- ~rom th~ incident f.low by the vortex eyatem of a travelling wave: -
_ Nx ~ NA -F' Nn -k- ~1s e ~ Py~lv (1-F- ~ ~ ~ ReL, , ( 5 )
'
whera Re~, ~ VAL/v is Reynolde number along the length of the model L.
CnMpasing tho value of NE ta the energy consumpci:,~ per unit time in a turbulent
baundnry lr~yez (9)
- v~ _ t Pys (6)
N,,,~ d ~ p-~'- lL ~ 0~0307 (Re~) ~ !L, -
. w~ k~nd eome roAff.iCiez~t of boundary wa~e effectiveness
- N~ n L i ~ 3 4 (7)
- ~ s N;,~ o,
o - Rel [ReL 32 ( ~ ) 1 � _
I" ~V~ or ~C/V~ > l.
One can sleo follow Purther in similar fasnion lrom frame to fram~ and one can dlso
eup~rimpase the line o! propaqation o! the extrea~ value with the higheet point of
th� trxvellinq wave ana ~o on if poasible.
The ~paco-tim~ data of the movie fil~ of the type of Figure 6 can be used to _
dstarmin0 the parameters of the travelling wave, bearing in mind that it contains -
n~ fewer thnn three petirs of correaponding points with cne low~est and highest posi- _
tiony aE twa wave trajectories--for the center of bo8y qravity and the center o�
~hs terminnl eflqe of the monoflipper paddle. This permits one to eagily construct -
th~ reduce(i qza~ph x(t) on which straiqht lines of minimum and maximum propagation
of both wave trajectoriee cnn be drawn through each pair of indicated points and
= 38
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th~ length of. the travelling wave X and velocity C can be determined. In the con-
eidsred cnee X" 2.10 metere, C= 3.0 m/s and therefore C/V ~ 1.33 or V/C ~ 0.75.
With an athlete's height of H� 1.82 metere, the total length of hie body together
with erm~ and Qaxt of the monoflippar extended ie equal to L= 2.82 meters. A
Vb111A af i,~x ~ 1.34 ot the trnvelling wavA is con~t;ained on thie length.
R~turninq t~ Figure 7, we note the remarkable fdct that ~he ~low boundaries were _
viauali,zed undex condition~ o� an athlete swinL~ning a heat in a pool. Here a is the
vi~iblA outet bounderiee of the region of water di.sturbancea caused by the swimming
ng sn ~a~hl~tn u~inq a~ mono�lipper, b is the boundaries of the water jets flowing -
~r~m th~e t~~mtl,al edge Qf the monoflipper paddle and d is some individual region -
of. ellipticnl a}iap~ in the vertical plane. It is obvious that the upper external
c:urvilineat boundnry should be the bende and protruding parts of the athlete's body
n~n~ tttie monoilipper, it lags quite fnr behind them and the region of water disturb-
ancae ie vary wide. 'Phie iz~dicates interrupted fLow over the athlete's body and
, f+rim~rily flow over the poosly streamlined cylindrical compreseed aiz tnnk located -
in i`.ront of tt~e athlete. The water j~ts leave the monofllpper paddle along the
tenqont, by wliich the Zhukovskiy-Chaplyqin postulate is sati~fie~~ with regard to
rogion d, ita boundaries are cZearly diatinguished on the movie fr~mea, but its
_ netur~ remr~ins uncle~r. it is poasible that this is one of the concentrated vor-
ticem, but the problem requires additional special inveetigation.
The fUrAgoing provides the basis to uae G. V. Logvinovich's formulas (4, 5~ on the _
hycircx9ynamice o~ a deformsd body and t~ use th~ "penetrated layer" coacept to cal-
_ cuiata the awimming of an athlete usinq a monoflipper. Since the exiatiag mono-
fli,pp@rd hnva aepect ra~io of 12/F ~ 0.9-1.7, where 1 is the width of the mono-
fl.i~p~r aloaq thA ~utlet edge and F is the lifting aren of the monoflipper (on one
aiAe), ~he calculetin~ formulas, nccording to (4], will be the following (in our
notaL�ioa~).
'~ha me~n velue nf tho active tr.ruet ie
A~fip~\xlsl\~~s-1JVs. (3)
Tho i~ydrnliynamic afficiency ia
~ ~ ~ ~ 1-}- . (4 ) :
A~ can bo r.+aen, the rc~lative parameters of the travelling wave A/X and C/V which _
aharactarixe ite eteepnees and propa?qation speed an8 also the width 1 of the mono-
lli~per elnng thA outlet e8ge are of main siqnificance in the giv~n the~~y for
thruat. All. these parameters are squared in the fotmula of [3], i.e., the depend-
oncc on them is strong. Thie requires sufficiently accurate management of the kine-
matic experiment, which ia not always achievable in the case of hydzobionts. _
i Subbti~uting the calculated values given above into formulas (3) and (4), we find _
p� 3A.A kq r~nd r1 ~ 0.87 in the coneidered case. Taking the known prerequisites
39 =
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~w -
ro~ ~
0
m ,b 0 4 * /
~ � ~ 1 ~
a~~ ~
_ ~ ~ -
~o ~
~ e d J
~ /
~ _
s j .
_ . t ~
- ~ ~ ` ,
_ ~ � ~
_ i~
~
/ .
/ ' K~~
~
QS ~0 . t,0 J~0
Figur~ 9. neper~der?ce of Drag on Speed of Towing and Swimming of Treined
Athletes Without Flippere (Males, Mean Values for Groups of
- 3 to 10 Persons): 1--towinq of athletes in level ~osition with
extended armsi by wir~ch, average height of 1.75-1.80 meters and
weight ~f approximately 80 kgt 2--the same, with average heiqht
n! 1.70 met~re end weight of 65 kg~ ~--active ewintming of ath-
let~s ia lree style and breast stroka on surface of water oppo-
' rite the current ir. a phyaiological swimming pool, height of
1.80 metere and weight of 75 Dcq (sccording to "c"), or ordinary
ewimn?ing in a pool, average heiqht oP athletes of 1.75 meters
aad weight of 78 kg (acaox~ding to "d")
x~y~
1. lt~logramg 2. M/e
sr�i e~~~w~pt�c~ne thie theory into accourit~ we assume thdt both values are some-
what axxegerated. To detarmine the mean thruet over the entl.re swin~ning 8i.stance
a! 400 metere, we took the absoluts value of the mean apeed of rne heat o� V=
_ ~ 1.94 m/e in valculation nccordir?g to (3), according to the accurately recorded
ro~ult oP 3 minutee 26.2 aeconcis (utilike the relative values of A,'X and C/V found
~or a eingle typical aycle. St is of interest to compare the derived value of
thru~nt P to the total drag of the athlete R, assuming that on the average P m R.
We proaeee~d the experiA?ental data avaiinble ia the literature (Figure 8) to de-
t~rmine the letter. T'h~ primary source of theee experiments was underwafier towing _
40 -
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of 9-10 nthletee without flippere in the poQl of the L'vov Institute of Physical
aweriul sound preR~ure sources (for example, the uoise of fishinu
vc~sact~), the acou~tic oscillations from which are propagated zor tens o~ kilom-
Q~er.~, ip techni.cally poesible, one would also expect fish to respond to them at
th~ aame ~tietanca~, wlii.cis ie not observed in raality J and 4) it i~ pointad out in
_ C~i ) r.t~�~t ramoval o E~.ndividuel reaaptors (the air bladder, otolyth, sngittus ,
utriculua anc3 the c~ntire labyrinth) causes only a renuction of the aenaitivity
threnhol~iH at ~re~c~uency of 150 Hz to various degrees, but it is still difficult
th andwer tlie quastinn of tha essFnce of the perceived components of sound due to
L�}i~ compl~xity o~ ~our~d perception by different receptr~rs.
�,fp
~
�~+0
sra j
~ ~o ~
.~p s
, ~ y
) ~
~ 0
y 'N
~ JO ( 2 )
- .l
so ioo svo ~ puao ir~,
L'tyuro Audiogram of Fiah in Which There is No Contact of tha Air
F3lndder to the Tnner Ear ~42~ : 1--Lutinephauls r~podus ;
2--TY.alaseoma bifnsciatumj 3--Prianotue scitulus; 4--Holo-
ces~trua voxillarious; S--Haemulon saiurusj 6--Holocentrus
e~c~naionus
x~ay ;
l. ~7.cTnnl level with r~epect to 1 ubar, dB 2. Hz
, mllo fr.oquo~~~y range p~rceived by Eish in which there is no connection of the air
blac~Q~~r to tt~a inrer oar is very narrow and occu,pies the r~gion from 100 to 1,000
t~z wi.th maxim~un in the ~z~c~uenay zange of 300-600 Hz and very rarely re~ches fre-
qua~nci~s above+ 2,000 ~Iz, while their sensitivity to eound varies over a wide range
tr.om +2C to -4Q dB (with L spect to 0.1 Pa), which can apparently be oxplained by
th~! ~col.flgianl characteristics of each of the apeciea (Fiqure 3).
'1'he a?ir bladcier combf.nocl with the innex ear. Although there ~.s e large diversity
ni: mor~hoJ.oc~ical characterietics in the structurea of recaption af acoustic oscil-
lcatian~ in fie~h in which the sir bl~dder participates, they can be divided into two
groupe--reco~~tion uaing Weberian'~ mechanism and using the processes which connect
~ho k~laddor ta thc inner ear.
103
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o "~p
_ f~ ~ ~
` x?
�a
_ ~
0
~ �ro
_ ~ [
~L ~ J
~ ~
SA~O
~
ao a~ ,sc+ca~rc~o,~aa~r.r~
P'igurQ a. Audi~gram of ~'ish Having Cnnnection of Int~er Ear to Air Bladder
[42)s 1--Ictnrulua nebulosust 2--Leuoaepiua deline~tusr 3-- -
Ci~rinua carpiv
Key :
~ 1. Signal level with reapect to 1 ubar, d8 2. Hz _
i
~1~h~ fir.ek typc~ o~ ~rdnsducer is based on tr,e use of a number of bones which trans-
fnrm tha Porcea occutring duzing oscillntion of the air bladder and tranamit them
to the rer~r wa].1 of the unpnired sinus anc thu~ provides contact with the tirans-
- v~x�~c~ ahennel of the labyrinth and the lagena [23, 41~. These oscillations are
- tr~n~emitted to the otolythe in the lagena and saggitus where they also excite the
w~xy c~l~,e of the mnculus. Thie machrsniem is typical. for aazp, mainly fre~hwater
tt~h.
~tfi~ ~c~nand ty~� of connection is provided by the processee connecting the bladder
nc~~ ahc?mb~r.u of. the inner enr. The working principle of this system ia similar
t~ th~+ pz~viou~ ono. ~xhe indiaated mechenism of eound perception exiats in some -
m~r.~.no ti.nh ~~6] .
'1`hc+ trer{u4ncy ranqe oP heerSng in fieh with Weberian app.aratug is the widest and
~ r~nc:?iAa ~rom th~ lowest to 5~000-8,400 Hz in some of them, although the maximum
r~or~~s~~i.vity ~.g observed only in the low frequency range (500-1,000 Hz). As can be
~uon Pram the audiogratn of Figure 4, the variation in eenaitivity ie not very wide
~ c~nd fluctuntoe in the rnnqe of (-30) to (-45) dB (with raepect to 0 dB = 0.1 Pa).
In ~inh releted to the second group, the upper bound of the rnnqe of hearing does f
n~r. oxoeed 3~400 Hz, while maximum seneitivity is in the eame range as for the
C~ir~t grou~ of fish.
One ~hould conclude Ezom analysis of available data on the sansitivity af fiah to
~nunde thr~t tihe highest aensitivity for almost all investiqated epecies is equal to
-40 to -45 d9 n~nd is located in the range of 300-1,000 Hz. 7,'hese parameters coin-
oia0 wi~h the hearing aensitivity ar.d range of man I40].
104
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~ ~,ro
~ ~o
~ a
u
~ �f0 J
~ a ~ ~si . . . ' f/'y~2 ~
d0 ;AD ~ JAV.ta~ ~ aoioio
t~ i,ri ic~ water. Tha reaeon may be various factors, including water temperature,
ri~],inlty aiicq e~tetic pzes~ure. Air bubblee play a no lesa important role in thia
r.nrsG. ~Ch~ cc~mpresaibility of. the water may vazy twenty.fold and accordinqly the
ri~a~mc3 nf ~ounc~ mav be roduced by n factor df 4.5 at depths up to 10 meters, where
k~ut>t~'loA w.ith diamet:ar af 1 mm are found.
'PmmX~nr~~t:ur.o, ~alinity and depth (presaure) also predetermine the direction of motion
o~ thA ar.oug~i~c wr~ve, whi.ch i~ bent toward the region with lower speed of sound
p~'of~+~~c~Ci.nt~.
�eatinq thE~ surfec~ watere, related to seaaonal changes of �4emperature conditions
a.n thc~ rr~gi.c~ns of. th~ oce~n, causes bendinq of the acoustic beams. Thus, the beams
ar�+ bpnt dawnward during summer dus to an increase of temperature of the surface
],ay~r and their path ia turned toward the aurfuce in wi.nter. ~
'1'h~? bQama aro b~nt to tho side of prASeure watez in coastal regions with complex
diyCrf.t~uti.on of seJ.ine and f~esh water.
xh~ tliarmal barrier in whi.ch temperature and denaity vary sharply has a significant
c~fect on tha pr~th of beama. It may be impenetrable to acouetic beams at high
c~rad.i~nke of tl~eee parametere in ahallow water.
117
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ro ,
~ � (2)
~0 s ~ ,~'t3 )
_ ~ ~ ~a Q
t ~ QSO ~ W
t1~ ~o
JQ~
'!0
~ ~ .
� 0
qatQal ai qt 4s ~ t s roi~r� t4 )
- F~igure 12. 5pectYal Characterie~~ics of Ocean Noise ,as a~ F'unction of Its
~ur~acQ 5tgte ~47] ~
K~y : '
- 1. i,~tntx~pia ncai~ae, 8~
2 , vni t~
3. ,ound pra~suze relatlve to 2�10'5 Pa, dB
- 4 , kFi2
ronaluntane. Tha purpoee of this paper wae to give preliminary consideration to
+nome f~roblem~ of eound perception by fish from the viewpaint of physiology and
- hydroacau,stlcss, to oompesre the hearing range ta the spectrum of signals emitted
k~y ~~,~h nnd th preaent a mode7. of percepti~n and geparation of these sounde on the
_ nai~y beckgxound of the medium. One can make the followinq conclueions from
~an~tyai~a of Che materials from the literature and the reeults of experimeatal
inv~~i:ic~n,tion ~
sr~i~noA hag now accumulated a sufficient amount of informatfon on the audi-
tiory caFyRbilitiee Af fieh in order to determine the }~oundaries of auditory per-
cspki~n which aan be used to solve problema of controlling fisn behavior using
r~o~u~~ic ~i,o~