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FC1.3 Design of an Underwater Glider with Fore and Aft Buoyancy Engines Jui-Min Tung, Ming-Feng Guo, Jenhwa Guo, Forng-Chen Chiu, Sheng-Wen Cheng Department of Engineering Science and Ocean Engineering National Taiwan University, Taipei, Taiwan, R.O.C. Abstract - In this paper, we discuss design issues in applying buoyancy (C.B.). In other words, the lengths between buoyancy engines as the device to vary net buoyancy and to C.B. and water tanks are identical. To gain the best alternate the position of the center of gravity of a glider. The moment from the change of the water mass, fore and aft buoyancy engines arrangement contains two tanks located at buoyancy engines are configured at the head and end parts the fore and end aft part of the hull. Buoyancy engines of the hull. High external water pressure causes large considered here are those of piston-type. Forces equations energy consumption when expelling water out of tank. To which model buoyancy, gravity, and hydrodynamic forces in avoid wasting energy, some operational constrains of glider gliding are derived. Performances of different sizes of have to be confirmed. buoyancy engines are compared. Operational constrains In section II, forces equilibrium in gliding are considering the power consumption of buoyancy engines are established. In section III, the performance of gliders with also specified. Gliders with rectangular wings of various fore and aft buoyancy engines are calculated. Energy shape and wing location are then examined in terms of the expenditure of the buoyancy changes are estimated with a energy cost for gliding controlled by buoyancy engines. simplified model. Glide angle that corresponds to the least amount of energy in operating the buoyancy engines are specified. In section IV, design considerations with fixed I. INTRODUCTION wings to minimize energy cost and to enlarge the working envelop using the fore and aft buoyancy engines Buoyancy engine is a device which changes net configuration is proposed. Finally, section V gives the buoyancy of an underwater vehicle by attracting and conclusions. expelling water. Underwater gliders equipped with buoyancy engines can be driven by net buoyancy forces to II. GLIDING IN EQUILIBRIUM travel in the vertical plane. Existing underwater gliders, such as Seaglider, Spray and SLOCUM are configured The glider hull considered here is a cylindrical hull with single buoyancy engine and a longitudinally mass with nose, tail and fixed wings. Assuming that the hull, shifting device by which pitch angle are varied by moving nose and tail are all symmetrical with respect to the their center of gravity. The buoyancy engine on Seaglider horizontal plane of the hull and the wings are flat. The and Spray include a high-pressure reciprocating pump and body of the glider considered in this paper is 2m in length an external bladder [1,2]. For SLOCUM Battery, buoyancy and 0.22m in diameter. The total mass of glider is divided engine is a piston driven by a motor. Modeling and control into the stationary mass ms and the variable mass mv. of ocean gliders driven by buoyancy engines and The body coordinate is fixed on the center of stationary mass-shifting device can be found in [3]. Nonlinear mass. The stationary mass center is located right below the dynamic equations are derived, and feedback control laws C.B.. mv has two components: the longitudinally moving for the linearized system were developed in [4]. The mass, m2 and the ballast mass mb. rp and rb are stability of this nonlinear system using linearization control their position vector, respectively. The position vector of was shown by numerical simulations. Equilibrium points mv is calculated by of the nonlinear glider model were also derived in [4]. An m r + mbrb estimation of energy cost for the buoyancy engines rv (1) operating at different water depths was shown in [5]. In [6], mP + mb design considerations of gliders and wings were described. The mass of displaced water is m and position Maximum velocities of gliders with various body sizes and v in buyac egnecaaite wer stde in 6. vector iS rd . Excess mass for buoyancy iS then defined by, buoyancy engine capacities were studiedin [6]. In this paper, we discuss design issues regarding applying buoyancy engines as the device to vary net me =mV - md (2) buoyancy force and to alternate the position of the center The glider is assumed to be even keel at me of gravity. This kind of buoyancy engines arrangement because of the requirements of symmetrical ascending and contains two tanks located at the fore and end aft part of descending paths and glide velocities. The pistons are the hull. Buoyancy engines considered here are those of infused with a half tank of water at me =0 For piston-type. The glider does not use longitudinal symmetrical gliding paths, the excess masses are mass-shifting device. To glide with symmetrical gliding designated to be me and -me in ascending and path in ascending and descending, positions of both water descending operations. The ballast masses and position of tanks are assumed to be symmetrical to the center of l-4244-1208-0/07/$25.00 ©2007 IEEE. 446 UT07+SSC07, Tokyo, Japan, 17-20 April 2007.

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FC1.3

Design of an Underwater Glider with Fore and AftBuoyancy Engines

Jui-Min Tung, Ming-Feng Guo, Jenhwa Guo, Forng-Chen Chiu, Sheng-Wen ChengDepartment of Engineering Science and Ocean Engineering

National Taiwan University, Taipei, Taiwan, R.O.C.

Abstract - In this paper, we discuss design issues in applying buoyancy (C.B.). In other words, the lengths betweenbuoyancy engines as the device to vary net buoyancy and to C.B. and water tanks are identical. To gain the bestalternate the position of the center of gravity of a glider. The moment from the change of the water mass, fore and aftbuoyancy engines arrangement contains two tanks located at buoyancy engines are configured at the head and end partsthe fore and end aft part of the hull. Buoyancy engines of the hull. High external water pressure causes largeconsidered here are those of piston-type. Forces equations energy consumption when expelling water out of tank. Towhich model buoyancy, gravity, and hydrodynamic forces in avoid wasting energy, some operational constrains of glidergliding are derived. Performances of different sizes of have to be confirmed.buoyancy engines are compared. Operational constrains In section II, forces equilibrium in gliding areconsidering the power consumption of buoyancy engines are established. In section III, the performance of gliders withalso specified. Gliders with rectangular wings of various fore and aft buoyancy engines are calculated. Energyshape and wing location are then examined in terms of the expenditure of the buoyancy changes are estimated with aenergy cost for gliding controlled by buoyancy engines. simplified model. Glide angle that corresponds to the least

amount of energy in operating the buoyancy engines arespecified. In section IV, design considerations with fixed

I. INTRODUCTION wings to minimize energy cost and to enlarge the workingenvelop using the fore and aft buoyancy engines

Buoyancy engine is a device which changes net configuration is proposed. Finally, section V gives thebuoyancy of an underwater vehicle by attracting and conclusions.expelling water. Underwater gliders equipped withbuoyancy engines can be driven by net buoyancy forces to II. GLIDING IN EQUILIBRIUMtravel in the vertical plane. Existing underwater gliders,such as Seaglider, Spray and SLOCUM are configured The glider hull considered here is a cylindrical hullwith single buoyancy engine and a longitudinally mass with nose, tail and fixed wings. Assuming that the hull,shifting device by which pitch angle are varied by moving nose and tail are all symmetrical with respect to thetheir center of gravity. The buoyancy engine on Seaglider horizontal plane of the hull and the wings are flat. Theand Spray include a high-pressure reciprocating pump and body of the glider considered in this paper is 2m in lengthan external bladder [1,2]. For SLOCUM Battery, buoyancy and 0.22m in diameter. The total mass of glider is dividedengine is a piston driven by a motor. Modeling and control into the stationary mass ms and the variable mass mv.of ocean gliders driven by buoyancy engines and The body coordinate is fixed on the center of stationarymass-shifting device can be found in [3]. Nonlinear mass. The stationary mass center is located right below thedynamic equations are derived, and feedback control laws C.B.. mv has two components: the longitudinally movingfor the linearized system were developed in [4]. The mass, m2 and the ballast mass mb. rp and rb arestability of this nonlinear system using linearization control their position vector, respectively. The position vector ofwas shown by numerical simulations. Equilibrium points mv is calculated byof the nonlinear glider model were also derived in [4]. An m r + mbrbestimation of energy cost for the buoyancy engines rv (1)operating at different water depths was shown in [5]. In [6], mP + mbdesign considerations of gliders and wings were described. The mass of displaced water is m and positionMaximum velocities of gliders with various body sizes and v inbuyac egnecaaite wer stde in 6. vector iS rd . Excess mass for buoyancy iS then defined by,buoyancy engine capacities were studiedin [6].In this paper, we discuss design issues regarding

applying buoyancy engines as the device to vary net me =mV - md (2)buoyancy force and to alternate the position of the center The glider is assumed to be even keel at me 0°of gravity. This kind of buoyancy engines arrangement because of the requirements of symmetrical ascending andcontains two tanks located at the fore and end aft part of descending paths and glide velocities. The pistons arethe hull. Buoyancy engines considered here are those of infused with a half tank of water at me =0 Forpiston-type. The glider does not use longitudinal symmetrical gliding paths, the excess masses aremass-shifting device. To glide with symmetrical gliding designated to be me and -me in ascending andpath in ascending and descending, positions of both water descending operations. The ballast masses and position oftanks are assumed to be symmetrical to the center of

l-4244-1208-0/07/$25.00©2007 IEEE. 446 UT07+SSC07, Tokyo, Japan, 17-20 April 2007.

the buoyancy engines are mb, , mbb and rbamb, g(r, cosO+r3 slnG)-md g.(rd cosO+rd sinO)respectively. The total ballast mass, mb is the summationof the fore ballast mass, mba, and the aft ballast mass, =MDL +MMK

Mbb . mh =mh +mh (3) where r,,, rv( are positions of m, in the x and z axis,Mb=Mba+ Mbb (3) respectively. rd , rd are positions of md in the x and zaxis, respectiveiy.3Now, we consider the glider model in the X-Z plane of

the global coordinate as shown in Fig.1. In Fig. 1, 0 is the III. PERFORMANCE OF GLIDERS WITH FOREpitch angle, ; is the glide angle, and a is the attack AND AFT BUOYANCY ENGINESangle, V represents the forward velocity of the glider. Fig.1 illustrates the relationship between a and . L represents In this section, performance in terms of achievablethe lift force, while D is the drag force. minimum and maximum glide angle for gliders equipped

with buoyancy engines is discussed. Small glide angleswith a high speed are desirable for long range glider

r operations. There is a smallest glide angle in the case ofequilibrium. The smallest glide angle for gliding trajectory

L , X \ / can be found using the lift and drag characteristics of the0 4 \ X hull form. The ratio of lift and drag forces in different

attack angle can be described by,

W/ I aXL CL CLIa 2 (12)D CD CDO +CD2a2

Fig. 1 Lift, drag forces and viscous, Munk moments. In this paper, CDS, CLS are estimated using thedatabase DATCOM [8]. There is a maximum in L / D at

The hydrodynamic forces which include drag and lift a ±=±VSCD / CD2 The positive a is the ascending glideforces are modeled as, angle, and negative a is the descending glide angle. The

smallest glide angle, .fin is then,D =-p Sref (CD) V2 (4)

CD= CD, +CDaa2 (5) Cot min 2-CDI (13)

L=-P2Sref(CL) V2 (6) However, the glide angle, qmin is not always

-CL=C7 aachievable due to the limitations of intake capacity ofC a(7) buoyancy engines. Ballast masses, mba , mbb at forward

Here, CD , CL are the drag, life coefficients, velocities of 0.2 m/s, and 0.6 m/s are drawn for ascendingrespectively. Sref is the reference area for the calculation and descending trajectories in Fig.2. In Fig. 2, a volumeof the lift and drag forces, and p is the density of water.MDL is the moment which is generated by drag and lift caact of 1 lter for each buoyancy engne S used. Thereforces. The Munk moment is are two buoyancy engines and no mass-shifting device in

the hull. It is assumed that rb, rb are time-invariant inMMK = (mf3 -mf)*uw (8) this case andrb =-r , rba = rbb 3

Then equilibrium

where m, , mf are the added masses in the x and z axis, equations could be written asrespectiveiy. u, w are the velocities in the x and z axis,respectively. Equations representing forces in equilibrium (mb +mb ) gcondition in the vertical plane were derived in [6, 7]. m b (14)

L 2 CL CDO (mba -mbb).g.rba cosO+(mb +mbb).g-rb3 sinO=cotq or ax + 1tan;q.a+ 0=O (9)+m.r-mrd)gsO

megg-D.sinq+L.cosq (10) +(mp .rp -md*rd1).g.cosO 15MDL +MK

447

A Vol 2Fm / 16V=02 /s V=0.2 m/s net Lb a ( J1+Lm b (20 (16)nba (fore) \<1 nba (fore)

0.8 mbb (aft) 0.8 mbb (aft)

E|0 E8° 0.8 0 tl0mbb (a2ft0 2)

06 0- 0 2

A Vol=21 m -mo 1+ in Ilp (17ThV 0.4 V0.4 L 2L L 2h

0.2 0.2

-°o70 -60 -50 -40 -30 -20 -10 910 20 30 40 50 60 70 80wglide angle (degrees) glideangle(degrees) where .represents the absolute value. Assumingthataccelerations of the piston are ignored since the piston

(a) V=0.2m/s. (left: descending; right: ascending) expels and attracts water with small speeds. The work doneon the glider by buoyancy engines is positively related to

6V=06/s V=06m/s AnetVol while the energy cost of the fore and aft buoyancy08 mba(fore) ' ba(fore) " ' engine is positively related toiAVol. For example, the

0.8 mbb (aft) 0.8 mbb (aft) isrlae tolthI -2 energy cost will be larger than the work done on the gliderU0.6 .0.6 by two buoyancy engine as one attracts and the other

1iiO4-v 1iiO4 expels water. Atol and netol can be deternined at0.2 0.2 a fixed forward velocity as shown in Fig. 4. Within the

-°8°~70-60 -50 -40 -30 -20 -10 D 20 30 40 50 60 70 80 envelope of the possible glide angles, it is found that thereglide angle (degrees) glide angle(degrees) is a single glide angle that uses the least amount of energy

as indicated in Fig. 4. Fig. 4 shows the volume changes of(b) V=0.6 m/s. (left: descending; right: ascending) buoyancy engines at the transition point from descent to

ascent. It is required that mbb > Mba and mba <m /2 forFig. 2 Ballast masses of fore and aft buoyancy engines ascent.nt is ired that mbb . i. and Vol cinci2eo^ . , ,. ,. ~~~~~ascendant gliding. As shown in Fig. 4, At01 Vol coincidesfor symmetrical gliding with AnetVoll at Mbb <mO /2 , and AtolVol >1 Anet VolIwhen mb > mO / 2 . The least-energy-cost glide angleThen, mb and mb are calculated with respect to glide bb /.ht s h,b bb ........,corresponds to the constraint of mb = mO / 2 . That iS, theangles at dif$ferent forward velocities. Fig. 3 illustrates cob

possibleglid angles at various forward velocitis for glider ascends under the control of the fore buoyancypsbglide,angle at var forard velcites. fo engine alone. Fig. 5 illustrates that, as the velocities getglder employi oforea buoyancy engine*s the higher, the larger the total volume change is needed and thevolume capacity Of the buoyancy engine limits the les-nryctgidagehslrervusmagnitude of operating speed. With small capacity, the least-energy-cost glide angle has larger values.glide angles are bounded by the volume capacity both frombelow and from above. At lower speeds, the glide angles V=0.4 m/sare bounded by the hull form from below, and are bounded 2by the volume capacity from above. Gliders with larger total volume changecapacity are able to generate higher speed with wider a1.5boperating interval of the glide angle. In general, practical --glide angles are smaller than 450 and gliding with lowspeeds cost less power. L,

Let the volume capacity of a buoyancy engine is mo0. EFor gliders with fore and aft buoyancy engines, values of >

the net and total volume change denoted by AnetVOl I

Ato/Vol respectively, could have different values. °10 20 30 40 50 60 70 80glide angle (degrees)

Fig. 4. The magnitude of net volume change (dash line)and total volume change (solid line).

oD 1 .- 2 f, -Xo X,O 1..55

10 2 30 4 V=0.2 rn/s

min or max glide angle (degrees) ___l V=0.6 rn/s_

Fig. 3 Performance envelope of gliders with fore and glide angle (degrees)aft buoyancy engines. Fig. 5 Total volume change at fixed velocities.

448

IV. WING DESIGN = 14°-2.58

Underwater gliders are driven by net buoyancy force. E 2.59 ' AR=10In equilibrium gliding, a) + AR=15

~"-2.6D V l (18) - AR=20

(18) ~ ~~~~-2.61meg Vsinq -2.62

Eq. 18 indicates that the power supplied by net E2.63\buoyancy force is consumed by drag force. For gliders cn

working at the same velocity and glide angle, smaller me ais desired because the gliding has lower power 0-2.65consumption. In this paper, the size and shape of the Area of wings (mn2)baseline body has been pre-determined. The design ofwings has a large effect on the performance of glider. Eq. Fig. 7 Wing aspect ratios that corresponds to the least18 can be used to calculate Me/v2. amountmof Me/V2 at =14o.

V=0.4 m/sme p Sref (-CD sin4+CL cosD (19)2V2 2.g

=1.5a)

Horizontal wings with a rectangular form areconsidered. Using Eq. 19 , the wing design that is best in E

terms of gliding energy is determined. For example, at 0 rwl =-0 (cm)the glide angle of 140, the location ofthe wing is placed 30 rwl=-60 (cm)

abs net vol. changecm behind the center of body coordinate, the best wing that °10 20 30 40 50 60 70 80causes the least amount of me / V2 can be found in Fig. 6. glide angle (degrees)Fig. 7 plots the apex of the curve defined by each aspect Fig. 8 Total volume change at three different wingratio. It is clearly seen in Fig. 7 that a unique wing design locations.is found that is the best in the performance of the energyconsumption by specifying the wing's area and aspect ratio. V. CONCLUSIONSThe location of the wing relative to the center ofcoordinateonalsoaffectthe pingrermane to the glider. As Design issues of a glider equipped with fore and aft

buoyancy engines are considered. Force equations are usedshown in Fig. 8, the total volume change necessary to to determine ballast masses of buoyancy engines in orderperform gliding at a specific angle is reduced as the wing is to achieve desired glide angle and the forward velocity.installed at a location backwardly away from the center of The tank capacity of the buoyancy engine is determined bycoordinate. specifying the glide angle envelope. Energy expenditure of

the buoyancy changes are estimated with a simplifiedmodel. Glide angle that corresponds to the least amount ofenergy in operating the buoyancy engines are specified.Design with fixed rectangular wings for minimizing energy

-2.5 = 140 cost and enlarging the working envelop using the fore andCN r 1 aft buoyancy engines configuration is discussed. The gliderE> < =< will be constructed and the performance evaluation will be

conducted. Motion control and underwater communicationcm ~experiments using the glider will be studied.

cN -3,X

0 lil AR=5 ACKNOWLEDGEMENTSE ~~~~~~_AR=10

a) _AR=15 The authors would like to thank the National Sciencexi, AR=20 Council of the Republic of China for financially supporting-55 0.1 0.15 0.2 0...25 this research under Contract No. NSC94-2611-E-002-011.

Area of wings (m2

Fig. 6 me / V2 for different wing sizes and aspect REFERENCESratios at4=140.

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Underwater Vehicles. G.. Griffiths, ed., Taylor andFrancis, London, 2002.

[2] C. C. Eriksen, T. J. Osse, R. D. Light, T. Wen, T. W.Lehman, P. L. Sabin, J. W. Ballard, and A. M. Chiodi,"Seaglider: A Long-Range Autonomous UnderwaterVehicle for Oceanographic Research," IEEE Journal ofOceanic Engineering Vol. 26, No. 4, pp.424-436,2001.

[3] N. E. Leonard and J. G. Graver, "Model-BasedFeedback Control of Autonomous UnderwaterGliders," IEEE Journal of Oceanic Engineering, Vol.26, No. 4, pp.633-645, 2001.

[4] P. Bhatta and N. E. Leonard, "Stabilization andCoordination of Underwater Gliders," Proc 41st IEEEConf Decision and Control, Vol. 2, pp. 2081-2086,2002.

[5] A. M. Galea. Optimal Path Planning and High LevelControl ofan Autonomous Gliding Underwater Vehicle,Master's Thesis, Massachusetts Institute of Technology,1999.

[6] J. G. Graver, Underwater Gliders. Dynamics, Controland Design, Ph.D. Thesis, Princeton University, 2005

[7] J. D. Anderson, JR. Aircraft Performance and Design,McGraw-Hill, 1999

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