693
1 INTRODUCTION
The theme of the development of remote‐controlled
underwater vehicles has long been popular
throughouttheworld. Over thepast decade, alarge
number of devices of various shapes and sizes,
capableofperformingworkbothinthewatercolumn
and on the seabed have appeared. Underwater
apparatus
canbehabitableanduninhabitable.Inthe
framework of this paper, uninhabited underwater
apparatus,orunderwaterrobots,areconsidered.
In accordance with the classification proposed in
[1],thenumberofuninhabitedunderwaterapparatus
includes: remote‐controlled, autonomous, towed,
bottom,drifting,etc.,which differ inpurpose,shape
ofcontours,movementparameters.
Theshapeofthe
contours,as a rule,is determined bythe purpose of
the apparatus. Most studies on UUV (Unmanned
Underwater Vehicles) reveal practical operating
experienceorhydrodynamicresearchresults[2‐4].
The purpose of this paper is a mathematical
description of the movement options of the selected
structureof
anunderwateruninhabitedapparatus.
The tasks of the work are the analysis of the
existingformsofthehullsofunderwaterdevices,the
study of the geometric shape of the proposed
apparatus, its movement and control systems with
methodsforthemotionparameterscalculationofan
alternative design, methods of
the apparatus
positioningontheflow,theapparatusmovementina
verticalplane.
2 THEHULLSHAPEOFTHEEXISTING
UNDERWATERVEHICLES
The existing types of devices can be divided into
devicesofawellstreamlinedshapeanddevicesofa
poorlystreamlinedshape.
Justification for the Body Construction Selection of the
Unmanned Uninhabited Underwater Apparatus
M.P.Lebedeva,A.O.Lebedev&A.A.Butsanets
A
dmiralMakarovStateUniversityofMaritimeandInlandShipping,Saint‐Petersburg,Russia
ABSTRACT:Thepaperexploresthepossibilityofcreatinganunderwaterapparatusintheformofabodyof
rotation. Theform ofthe devicewill allowto effectivelyexamine the foundunderwater objects, thebottom
topography, measurement of other
parameters of the underwater environment or objects. The devices of a
differentstreamlinedbodyformareconsidered.Theapparatusintheformofarotationbodyisproposed.The
geometricshapeoftheproposed apparatus,thesystemofmotionand controlareinvestigated.Methods for
calculatingthemotionparameters,methods
forthevehiclepositioningintheflowandtheunderwatervehicle
movementintheverticalplaneareproposed.Thestudyconfirmstheabilityoftheunderwatervehicletomove
under water in a horizontal and vertical directions. The study confirms that the device possess stability at
rectilinearmotion,goodturningability
andatthesametimeitisabletopositionitselfduringtheflow.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 12
Number 4
December 2018
DOI:10.12716/1001.12.04.07
694
Thedevicesofwellstreamlinedshape.Themost
common form of the body of such a device is an
oblong torpedo‐shaped form [5‐6], sometimes with
ballast [7] or flattened in a vertical or horizontal
plane, with underwater wings [8‐9]. Devices with
bodies of similar shape provide a
sufficiently high
speedoflongitudinalmovementatasufficientlylow
turningability.Thesedevicesaremainlydesignedfor
prospecting, hydrographic work, as well as for
monitoring of extended bottom structures, for
example, oil pipelines. The works on the study of
motion during deformation of the hull at high
pressure of
dense sea water are known [10].The
devices of well streamlined shape, as a rule, are
autonomous.
The devices of poorly streamlined shape. The
devices of poorly streamlined shape are a frame
structurewithabuoyancycompartment.Theattached
implements of a widenomenclature is on the frame
structure.Themainadvantage
oftheapparatusofthis
designistheversatilityofequipment,sincethereisno
needtofitintothebodycontourspre‐installedbythe
designer.Themaintypesofbodystructures,attached
implements and the main achievements of
underwatervehiclesofpoorly streamlinedshapefor
thelast20
yearsaredescribedinthearticle[11].The
disadvantageisthegreatresistanceof theapparatus
shape and, as a result, the increased energy
consumptionformovingandpositioning.Thedevices
of such a composition are used for detailed local
studies or works, for example, surveys of a flooded
object[1].
Thedevicesofpoorlystreamlinedshape,as
arule,aretethered.
Traditional control system of the underwater
apparatus. The control system of the devices, both
well‐streamlined shape and poorly‐streamlined
shape,isahelicalcomplexcomprisingfromoneto8
propellers. Propellers can be equipped with guide
nozzles, can
be placed in tunnels, and can be made
stationaryorrotary.
The composition scheme of the control complex
andthelocation oftheequipment foreachdevice is
individual.Theincrease inthenumber ofpropellers
leadsnotonlytoincreasedenergyconsumption,but
also to the complexity of the composition
of the
underwaterapparatus.
Underwater apparatus of alternative design.
Amongthealternativethedesignswithflappingwing
areknown[12‐13],wheretheauthorsnoteimproved
hydrodynamiccharacteristicsincomparisonwiththe
torpedoshape.
Amongtheunderwaterdevicesofunconventional
form,itisnecessarytosingleouttheworkof
[14‐15];
theydevelopedaroboticfishofslidingbycombining
themechanismsofslidingandreduction.
These works indirectly confirm that research to
search for the optimal shape of an unmanned
underwaterapparatusisnecessaryandrelevant,and
descriptions ofthe waysof movement of alternative
structuresrequirestudy.
The
authors of the article propose an alternative
solutionfortheunderwaterapparatus,combiningthe
advantagesofthetypesofdevicesdescribedabove.
Thebodyoftheapparatusintheformofadiskis
equipped with two stationary propellers placed
diametricallyrelativetoeachother.Ageneralviewof
the
apparatusisshowninFigure1.
Themanagingofdevicewithrespecttothevertical
axis of symmetry is carried out by measuring the
stopsofthepropellers.Thechangeofrollandtrimis
carriedoutbythedeviationofthecenterofgravityof
theapparatusfromtheneutral
position.Thelatteris
achieved by the displacement of cargoes located
insidethebody.
The shape of the body can be described
analytically, which greatly simplifies the
mathematical description of the parameters of its
movement.Ananalysisoftheliterature[16]confirms
thatthisdesignisofinteresttoresearchers.
In this article, the authors provide a brief
description of the geometry and laws of machine
controlwiththeanalyticalformofthecontours,made
onthebasisoftheCassinioval.
3 GEOMETRYOFTHEAPPARATUSOF
ALTERNATIVEDESIGN
Thedevicehascontoursofananalyticalformanditis
a body of rotation, the cross section of which is the
Cassinioval.Generallyspeaking,itispossibletouse
any form of contours. Using the contours of the
analyticalformwillsignificantlysimplifythestudyof
hydrodynamicsattheinitialdesignstage.
The waterlines of the apparatus are concentric
circles(Figure1).
The body of the apparatus and all the quantities
necessary for calculation of the motion parameters
(displacement, moments of inertia, added masses,
etc.)are easyto calculatewith minimal involvement
of the model experiment. The shape and size of the
device body can be determined on the basis
of the
known total weight and overall dimensions of the
carriedequipment.
Figure1.Schemeoftheunderwaterapparatus
If you install the equipment on a special round
framemountedonthescales,itiseasytoensurethe
centerofgravitypositioninthecenterofthevolume.
Calculatedspecificallyfortheselectedcompositionof
X
Y
P1
P2
695
the equipment, the body will allow to simplify the
procedureofdevicetrimming.
4 MOVEMENTANDCONTROLSYSTEMFOR
APPARATUSOFALTERNATIVEDESIGN
The propulsion system of the apparatus should
include two permanently fixed propellers located
symmetricallyrelativetothelongitudinalaxis(Fig.1)
intheplaceofthegreatest
width.Theselectionofthe
propeller diameter and the evaluation of engine
powerwillbedeterminedbycalculationusingknown
methods.
The calculation of the required thrust of the
propellerscanbeperformedbytheformula[2]
0
DVJ5.0
D)J(k
2С
222
0p
2
pp1
x
where
x
Ñ –thedimensionlessresistanceforceofthe
apparatus body,
)J(k
p1
– coefficient of propeller
thrust,
p
J
– instant advance of propeller,
0p
J
–
initial advance of propeller,
p
D
– propeller
diameter.
Whenmovinginahorizontalplaneintheabsence
offlow,thedevicecanbecontrolledbypropellersby
changingthethrustofoneofthem.
The calculation of the needful moment of the
propellerscanbeperformedbytheformula
0
DVJ5.0
D)J(k)J(k
Ñ
2
a
22
0p
2
p2p11p1
mz
where
1p
J and
2p
J – pitch ratio,
a
D – machine
diameter.
For maneuvering in the vertical plane it is
supposed to use the movement of the center of
gravityoftheapparatusby changingthepositionof
thecargoesinsidetheapparatus.
Figure2.Trimanglechangesystem.
It is known that the cargo movement within the
system [2], leads to the occurrence of the moment
causingthetrimor rollof theapparatus, depending
on the direction of the cargo movement and the
accepted system of designations. The mechanism of
thesystemoperationwillbethesame.
The
relationship between the cargoes movement
andtheanglevalueoftrimisdeterminedbyasimple
formula[17]
0
W
xg
Ñ
11
my
,
where
my
Ñ – dimensionless hydrodynamic
moment on the device body,
1
g
– total weight of
displaced cargoes,
1
x – the distance over which
cargoesaremoved,
–trimangle.
When the trim angle changes, the vertical
component of the force will exist for a short
evolutionaryperiodofmotion.Atsteadymotion,the
apparatus will move in a straight line, experiencing
onlytheactionofthelongitudinalcomponentofthe
force(resistanceforce).
The immersion speed
at a constant mode of the
propeller operation will be determined by the
projectionofthespeedoftheapparatusmovementin
thediametricalplaneontheverticalaxis,thatis,the
valueofthetrimangle.
Figure3. The controlled movement of the device in the
verticalplane.
Itispossibletochangethedirectionofmovement
oftheapparatusinthesamewayascontrollingitina
horizontal plane, that is, using the propellers
operation.
To prevent a strike about the bottom during the
apparatus descent, it is necessary to control the
distancetotheobstacleand
leveltheapparatusasit
approaches,thatis,tobecontrolledinthesameway
asaircraftcontrollingduringlanding.
5 METHODSFORCALCULATIONOFMOTION
PARAMETERS
Thesystemofsixdifferentialequationsofmotioncan
beusedtocalculatetheparametersof theapparatus
motion, as it is usually
done when calculating the
parameters of ships movement [2]. Due to the
symmetry of the body, the equations of motion and
theexpressionsforhydrodynamiccharacteristicsused
inthemwillbesignificantlysimplified.
Thevaluesofhydrodynamicforces andmoments
actingontheapparatusinanarbitrarymotionwillbe
written
inthefollowingform:
‐longitudinalforce
4
D
VV5.0CX
2
2
x
2
0
x
;
x
z
x1
g
2
g
1
X
Z
x
z
Vx
VZ
696
‐lateralforce
4
D
VV5.0CY
2
2
y
2
0
y
;
‐verticalforce
4
D
VV5.0CZ
2
2
z
2
0
z
;
‐momentrelativetothelongitudinalaxis(roll
moment)
4
D
VV5.0CM
3
2
х
2
0
mxx
;
‐momentrelativetothelateralaxis(trimmoment)
4
D
VV5.0CM
3
2
y
2
0
myy
;
‐momentrelativetotheverticalaxisz(momentof
yaw)
4
D
VV5.0CM
3
2
z
2
0
mzz
;
where
x
С ,
y
С
,
z
С
,
mx
С ,
my
С
,
mz
С
‐
dimensionless hydrodynamic characteristics of the
apparatus depending on the shape of the contours,
0
V – speed at the beginning of the maneuver,
x
V ,
y
V ,
z
V ‐changeofspeedintheprocessofmaneuver
inprojectionson thecoordinateaxes,
D –machine
diameter.
Due to the fact that the apparatus is a rotation
body, the body shape remains unchanged in the
direction of the axes
x
and y . Due to this, the
hydrodynamic and inertial forces will lie on one
straightlinepassingthroughthecenterofgravity.
Atthesametime,theconditionofequalityofthe
dimensionless components of the longitudinal and
lateral hydrodynamic forces is satisfied, that is
yx
ÑÑ ,andthemomentoftheseforcesrelativeto
thecenterofgravitywillbezero,thatis
0
Mz
Ñ .
Theverticalforcewillbedeterminedbythebody
shape in the plan, and will depend on the angle of
rotation relative to the direction of rotation, i.e.
z
z
ÑÑ .
Dimensionless hydrodynamic moments with
respect to the axes
x
and
y
will change with
changingofroll
andtrim
angles.However,it
isnotedthatforthecorrespondingvalues
and
themomentsvaluesareequal,thatis,
mymx
ÑÑ .
Whenmovingnearthebottomatadistanceofless
than two widths of the body, the device will
experiencearepulsiveforceduetothescreeneffect.
At low speeds, this will allow it to move at a
constantdistancefromtheplane.
6 THEDEVICEPOSITIONINGONTHE
FLOW
In the presence of a flow, the apparatus completely
immersedinitcanbepositionedatapointprovided
thatitisabletotakeapositionalongtheincidentflow
anditspropellerscanprovidethenecessarythrust.
The device is not able to extinguish the lateral
component
of speed. However, a controlled lag
movementontheflowispossibleifweallowasmall
anglebetweenthelineofthepropellersthrustandthe
direction of the flow. At the same time, the lateral
componentofthehydrodynamicforcewillappearon
the apparatus body, under the action
of which the
apparatuscanmoveinthedesireddirection,andthen
turnaroundtowardstheflow.
7 THEDECLINEOFTHEAPPARATUSINTHE
VERTICALPLANE
Ensuringthecontrolledmovementofthedeviceina
vertical plane, when the device is immersed with a
minimumdeviationfromthevertical
axis,ispossible
usingamaneuver(fig.4).
Figure4. The scheme of the apparatus movement in a
verticalplaneusingthemaneuver
The maneuver is performed while simultaneous
changing the speed magnitude and movement
directionoftheapparatusandthetrimangle.
8 CONCLUSION
The device, made in the form of a body of rotation
and equipped with two stationary propellers, is
capabletomoveinsidethewatercolumn,bothinthe
horizontal
and in the vertical directions. The device
has the stability of straight motion, good
maneuverability and at the same time is able to
positionitselfontheflow.
Due to the listed properties, it can be used for