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February 27, 2003 19:7

9th AIAA/ISSMO Symposium and Exhibit on Multidisciplinary Analysis and Optimization AIAA-2002-5668

OPTIMIZED UNMANNED AERIAL VEHICLE WITH WING MORPHINGFOR EXTENDED RANGE AND ENDURANCE

Shawn E. Gano ∗ John E. Renaud †

Department of Aerospace and Mechanical EngineeringUniversity of Notre Dame

Notre Dame, IndianaEmail: [email protected]

AbstractDue to their current successes, unmanned aerial

vehicles (UAVs) are becoming a standard means ofcollecting information. However, as their missionsbecome more complex and require them to flyfarther, UAVs can become large and expensivedue to fuel needs. Sidestepping the paradigm of afixed static wing, the variform concept developed inthis paper allows for greater fuel efficiency. Bulkywings could morph into sleeker profiles, reducingdrag, as they burn fuel. The development of suchwings will rely heavily on computational designexploiting state of the art optimization techniquesthat account for uncertainty and insure reliability.

Nomenclature

α Angle of attackη Propeller efficiencyρ∞ Free stream densityc Specific fuel consumption

∗Graduate Research Assistant, Student Member AIAA†Professor, Associate Fellow AIAA.

Copyright 2002 by John E. Renaud. Published by the Amer-ican Institute of Aeronautics and Astronautics, Inc. with per-mission.

CD Drag coefficientCL Lift coefficientD Total dragE EnduranceP Engine powerPA Power availablePR Power requiredR RangeS Planform Areat TimeT ThrustTR Thrust requiredV∞ Free stream velocityW1 Weight of aircraft without fuel

and with full payloadW0 Weight of aircraft with full fuel

and payloadWf Weight of fuel

1 Introduction

Unmanned aerial vehicles (UAVs) are beingused more frequently in all parts of the worldtoday. This type of vehicle can take on manydifferent missions, ranging from the conductingof scientific experiments to intelligence gatheringsurveillance during the day or night. They are

1American Institute of Aeronautics and Astronautics

capable of undertaking missions from 50 hours,like IAI Malat’s Heron, to fractions of an hour.In every case the range and endurance of thecraft is limited by its storage capacity for fuel.In most cases, especially for surveillance mis-sions, an increase of mission range and endurancewithout the addition of heavy fuel is greatly desired.

The problem is that UAVs today have alreadybeen optimized for their current mission objectives.Thus, in order to conduct longer missions, morefuel and, hence, the size of the aircraft wouldneed to be increased. In this proposal, a newparadigm is described that could allow these craftgreater range without requiring them to carry morefuel. Alternatively, they could carry less fuel thancurrent models and still achieve the same objectives.

In order to improve the fuel efficiency ofUAVs, we propose using a wing that changes itsshape during flight to minimize total mission drag.This wing morphing18 approach is referred to asthe variform wing concept. The fuel would bestored in balloon-like bladders inside the wingstructure. These bladders would shrink as the fuelis consumed. A bladder’s size and shape, as wellas the possibility of multiple bladders in a wing,will be determined by optimization techniques.The integrated bladder and elastic structure of thewing provide a truly multidisciplinary problem thatinvolves aerodynamics, structures, and controls.

There are other classes of aircraft that could alsobenefit from the variform concept, such as microaerial vehicles (MAVs). However, in this paper wewill focus on applications and examples involvingUAVs.

The variform concept presented here differsfrom other current research, like that done byNASA’s Aircraft Morphing Program18, which usespiezoelectric to induce shape changes. The useof piezoelectrics has been mostly for control11,17.They are using them to rapidly change the shape ofthe trailing edge of the wings in place of ailerons

(or in some cases to change the shape of the wholewing). The variform concept as presented here isto use the consumption of fuel to slowly changethe shape of the entire wing throughout the flightto lower the drag on the craft over the entire mission.

Research being done at the Naval ResearchLaboratory (NRL) also deals with structure-plus-power concepts19. Their program has three maindesign concepts. Their first concept is replacingsome of the passive structure of smaller MAVs withwith battery material. More simply stated, theyincorporate the battery as a structural member ofthe craft, so the weight of the battery is somewhatoffset by lowering the weight of the structuralcomponents needed. A second NRL idea usesautophagous structure-fuel components. In thiscase the structure itself would be a fuel source, sothe aircraft would self-consume structure over thecourse of the mission. Their last concept is anothertype of variform structure-power idea. In thiscase the structural members of the wing would beinflated with fuel. The first two concepts conserveconstant aerodynamic shapes and thus are not verysimilar to the work presented in this paper. Thethird concept is similar in that the aerodynamicshape is altered via the fuel supply. However, thevariform concept that is presented in this paper doesnot restrict the fuel to be inflated into structuralmembers or in any certain configuration, but allowsfor an optimization process to choose where andhow the structure should deform.

In this paper the variform concept is introducedin more detail, along with a description of theresearch that has been completed and an outlineof future work. Initial efforts have focused onthe development of a computational fluid dy-namics model for predicting aerodynamic forcesand performance. Future efforts will include thedevelopment of a finite element model of thebladder-filled elastic wing structure. The CFDand FEA codes will then be integrated to form amultidisciplinary model of the variform concept.Shape optimization techniques will be used to


optimize the uninflated airfoil geometry and theuninflated bladder geometry. The optimization willseek to maximize the variform UAV’s range whileaccounting for system uncertainties. The modelwill allow users to explore different structuralmaterials and variform design concepts.

2 Typical UAV Description

To provide a better understanding of the UAVclass of aircraft, this section covers the main aspectsof the AAI Corporation’s Shadow.

The Shadow is a small stealthy monoplane pow-ered by a pusher engine. It has two tail booms andan inverted V tail. It is composed of mainly graphiteand Kevlar epoxy composites. The optional tricyclelanding gear is detachable. The Shadow typicallycaries either a video camera, electro-optical camera,or an infra-red sensor. Hence, it is primarily usedfor surveillance and target acquisition. The craftcan be controlled either by pre-programming or viaremote control and can be launched by conventionalmeans or by a hydraulic catapult. It can carry about40 liters of fuel, has a wing span of about 4 m, andcan be up to 149 kg at launch9. AAI’s Shadowis depicted both in flight and during launch inFigure 1.

Figure 1. AAI Shadow UAV launch (left) and in flight (right).

The Shadow exhibits the typical performancecharacteristics of UAVs9. It can cruise at a max-imum speed of 156 km/h and has a flight ceilingresulting from the fuel to air mixture in the engineof 4,575 m. The craft can operate for about 5-6

hours with one tank of fuel and has an operationalradius of about 125 km.

3 The Variform Concept

The variform wing is simply a wing that changesshape as fuel is consumed in order to maximize thelift to drag ratio. Maximizing this ratio leads to agreat increase in the range of the aircraft. It is a wayof making the aircraft go substantially further onthe same amount or less fuel. For example, say westart with a NACA 23015 wing cross-section. Asthe fuel is used up, the wing could morph into theshape of a FX 60-126. This is captured in Figure 2,where the outside line is the larger NACA airfoiland the inner solid section is the sleeker shape.

Figure 2. Variform Wing Concept

This shape changing could be done in a varietyof ways. One way this change could occur wouldbe to store the fuel in balloon like bladders thatinteract with the structure of the wing. When thebladders are filled the shape would look like theouter profile in Figure 2, and when empty theshape would look like the inner solid-filled shape.The simplest bladder configuration, as shown inFigure 3A, would just be an oval or any simplegeometric shape. However, to achieve greatercontrol of how the wing changes over time, anon-symmetric shape could be used as the bladder(Figure 3B), or even possibly multiple bladders ofdifferent size and shape seen in part C of the samefigure.

3.1 MDO Problem Description

The variform wing concept will require anelastic wing structure capable of satisfying con-ventional UAV structural concerns. At the same


(A)

(B)

(C)

Figure 3. Possible Fuel Bladder Configurations.

time the variform wing’s elastic structure mustaccommodate the shape deformations induced bythe pressurized fuel filled bladder. The analysis ofthe variform wing involves a coupled fluid-structureanalysis of the wings’ geometry throughout themission. In addition, one needs to perform aconventional aeroelastic analysis of the wing. Anumber of structural issues such as rigidity andthe integrity of the wing will need to be addressedconcurrently. Additionally, the fuel control, orpressurization of the fuel bladders, needs to betaken into account. This is due to the fact thatthere may be a certain sequence in which the airfoilshould deform to achieve the maximal performance.The design procedure should insure that the designis consistent for this complex coupled system.Figure 4 illustrates the coupled system analysis.

Aero

Structures

Fuel

Figure 4. Variform MDO Problem

The design objective is to maximize the rangeor endurance of the UAV. System constraints mayinclude climb rates and gradients, stability, maxi-mum weights, as well as any other performance orstructural limitations desired. This could easily bewritten in the standard form:

maximize : R(x)x

subject to : l ≤

xAero(x)

Struct(x)Contr(x)

≤ u

Where x are the design variables, l and u are theupper and lower bounds respectively, and Aero(x),Struct(x), and Contr(x) are aerodynamic, struc-tural, and control constraints, respectively.

The full MDO problem would include designvariables for each node that defines the airfoil andbladder shapes (as seen in Figure 5) or the parame-ters needed to describe the shapes of the airfoil andthe bladders20. Additional design variables couldinclude maximum takeoff weight, cruise altitudes,and thrust.

Fuel Bladder

Airfoil

Figure 5. Variform Parametrization

Once the analysis model is completed, opti-mization methods could be employed to search outthe most efficient wing sections and determine howthey evolve throughout the flight. Methods suchas Adaptive Experimental Design14 (AED) couldbe used because of their CPU savings. Further,massively paralleled computers would be used fortheir time savings. One could apply ReliabilityBased Design Optimization8 (RBDO) to find thebest design to account for uncertainties in thesystem.

3.2 Range and Endurance Improvement Esti-mates

For a conceptual qualification of the savings ofthe variform concept, first consider two airfoils.


The first airfoil has a thicker cross-section andthe second has a sleeker profile. The only otherconstraint of these two airfoils is that the smallerairfoil must fit entirely inside the larger one. Next,we find the aerodynamic properties of these twoshapes, either through wind tunnel experiments orCFD simulations (or both). The drag polar for eachairfoil might look like the initial and final airfoillines depicted in Figure 6. The diagram showsthat the initial airfoil has a higher drag coefficientat every corresponding lift coefficient. This maynot be the case everywhere in the drag polars butshould be a general trend.

CL

CDTakeoff

Landing

Initial Airfoil

Final Airfoil

Possible Variform Airfoil

Figure 6. The drag polar of the initial, final, and predicted vari-

form airfoils.

Next, assume that the aircraft only looses weightvia fuel consumption. This is not an essentialassumption, but it is more for convenience toavoid discontinuities. Further, most missions willbe of this type for UAVs. This means that thereare defined takeoff and landing weights, withcorresponding coefficients of lift. These two valuesfor lift are also drawn in Figure 6.

Finally, if our wing started off in the shape of thethicker airfoil and as the craft used up the fuel sup-ply, the wing morphed into the shape of the thinnerairfoil, then the drag polar of this aircraft would bedifferent than each of the other airfoils. Let us as-sume that this wing’s drag polar runs between thetwo airfoils and again, for simplicity, just follows a

straight line between the two. In the example prob-lem at the end of the paper we investigate furtherwhere the actual drag polar lies. Using the Breguetequations2 for propeller powered aircraft that as-sume steady level flight, the range and enduranceequations are:

R =ηc

CL

CDln

(

W0

W1

)

, (1)

E =ηc

C3/2L

CD

√2ρ∞S

√W1 −

√W0

. (2)

Of all the parameters in Equations 1 and 2, theonly values that are not constant are the lift anddrag coefficients. For this qualitative estimate wewill just take the average values of lift and dragcoefficients over the mission. The average lift isabout the same for all the airfoils, but the drag forthe variform wing is significantly less than thatof its non-shape-changing counterpart the thickerairfoil. From looking at experimental data of lowReynolds number airfoils12,15 this savings could bein the range of 15 to 30 percent.

3.2.1 Range and Endurance EquationsThe Breguet equations used in the previous sectionserve well only for very rough estimates for the truerange or endurance of an aircraft and have manyassumptions in their derivations. A few of theseassumptions are valid for typical aircraft but are notas applicable for an aircraft with variform wings.However, they do provide a good reference point.In this section we derive from first principles moreaccurate equations for analyzing the morphingwings so that we can better quantify the range andendurance gain.

The weight of fuel consumed over a time changeof ∆t is defined as c ·P ·∆t. Therefore, the differ-ential change in weight due to fuel consumption isc ·P ·dt. Considering that, the weight of the aircraftis defined as:

W1 = W0 −Wf . (3)


Here we assume that the only changes in weightinvolve the fuel weight change and that the weightdecreases with time. Thus:

dWf = dW = −cPdt. (4)

Rearranging Equation 4 and integrating bothsides, time between 0 and the endurance E, andweight between Wo (full fuel) and W1 (fuel empty),gives:

∫ E

0dt = −

∫ W1

W0

1cP

dW. (5)

From this we get an expression for the en-durance:

E =∫ W0

W1

1cP

dW. (6)

To find the range, we multiply Equation 4 by V∞and note that V∞dt is a differential distance dx. Thisgives:

V∞dt = dx = −V∞dW

cP. (7)

Integrating both sides from x = 0 to the finalrange R and the same weights as before produces:

∫ R

0dx = −

∫ W1

W0

V∞

cPdW. (8)

Therefore an expression for the range is:

R =∫ W0

W1

V∞

cPdW. (9)

At this point, in order to simplify the equationsfor range and endurance, we introduce one assump-tion. We assume that the entire mission is level un-accelerated flight. This would be a good assumptionfor an aircraft that was trying to maximize its rangeor endurance. From this assumption, the thrust re-quired is equal, to the drag of the craft: TR = D.Also, the power required is equal so the trust re-quired times the free stream velocity is: PR = TRV∞.Combining these two equalities yields:

PR = TRV∞ = DV∞. (10)

By definition, the total power of the engine isequal to the power required divided by the efficiencyof the propeller. Combining this fact with Equa-tion 10 gives:

P =PR = PA

η=

DV∞

η. (11)

Substituting the previous result into the rangeequation (Equation 9) simplifies to:

R =∫ W0

W1

ηcD

dW. (12)

Because of our assumption of steady level flightW = L, we can multiply the right hand side of Equa-tion 12 by L

W to get:

R =∫ W0

W1

LD

ηc

dWW

. (13)

Further noting that L/D = CL/CD, we get our fi-nal expression for the range:

R =∫ W0

W1

CL

CD

ηc

dWW

. (14)

Using the same procedure for simplifying the en-durance equation yields:

E =∫ W0

W1

ηc

CL

CDV∞

dWW

. (15)

However, this expression can be simplified onestep further using L = W = 1

2 ρ∞V 2∞SCL, solving for

V∞, and subsituting that into Equation 15 to get thefinal endurance equation:

E =∫ W0

W1

ηc

C3/2L

CD

√

ρ∞S2

dW

W 3/2. (16)

4 Example Case: Flying Wing

To demonstrate the level of range and endurancegained in using the variform concept, we presenthere a simple example. This example is not a bestcase or worst case scenario but rather just a pseudorandom example to see if and how much can begained by using this new approach.


This example considers a flying wing that has alarge aspect ratio and is in steady level flight fromtakeoff to landing. This assumption is made tomake the analysis simpler. Using these assump-tions we can just analyze the airfoil cross-sectionproperties while not worrying about drag from theairframe body or other three dimensional effects.This is a simplification from a real-world UAV;however, it does maintain key aspects which makethis a reasonable model for testing out this newconcept.

For this example the airfoils shown in Figure 2,specifically, the NACA 23015 morphing intothe FX 60-126, are used. The flying wing wasmodelled using parameters of the Shadow UAVwhich was introduced in a previous section. Theflight conditions were established at an altitudeof 3,000 km, Reynolds number of 1 × 106, andat a cruising speed, V∞ = 33.7 m/s. Using thenear maximum takeoff weight for the craft, whichmust equal the lift, we calculate a lift coefficient,CL = 1.1. Likewise at landing, subtracting the fuelweight gives: CL = 0.89.

For the airfoil analysis a computational fluiddynamics code, called CFL3D v6.0, developedat NASA’s Langley Research Center was used.CFL3D is a Reynolds-Averaged thin-layer Navier-Stokes flow solver for structured grids10. Thealgorithms employed within CFL3D solve thetime-dependent conservation law form of theReynolds-averaged Navier-Stokes equations. Asemi-discrete finite-volume approach is used inspatial discretization10. The convective pressureterms use upwind-biasing. Central differencingis employed for the shear stress and heat transferterms. Implicit time advancement is used, allowingfor the solving of both steady and unsteady flows.CFL3D version 6.0 features a new ability to obtaina solution for a specific lift coefficient (CL). Forthis case the angle of attack (α) is not known and isconsidered part of the desired solution. Thereforethe analysis of the airfoil cross-sections will beable to predict drag and allow for runs when the

coefficient of lift is known instead of the angle ofattack (as in the case of the variform wing).

The first step of the analysis varies the angleof attack for the initial and final airfoil shapes toconstruct a drag polar for each. Each drag polar isshown in Figure 7. Also shown in the figure are thetakeoff and landing lift coefficients.

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.30.015

0.02

0.025

0.03

0.035

0.04

0.045

CL

CD

NACA 23015FX 60−126Variform Airfoil Takeoff

Landing

Figure 7. Drag Polars from CFD Simulations

The next step was to linearly morph the shape ofthe larger airfoil to the smaller airfoil. Then, usingeach corresponding intermediate lift coefficient,the variform airfoil’s drag polar was constructed.A linear morph was used purely as a convenience,since no optimization to find the best shape changeover time was done in this example. Thus, the finalresult could be improved by such an optimization.The results are plotted in Figure 7. The streamlineflow solutions for both the takeoff and landing con-ditions are shown in Figures 8 and 9, respectively.

Once all this data was computed and collected,the range and endurance was found for both thevariform and the NACA 23015 airfoils usingthe Equations 14 and 16, which were derived inSection 3.2.1. It is assumed that both the specificfuel consumption and the propeller efficiency wereconstant throughout the flight. The results showed


Figure 8. Takeoff, CL = 1.1

Figure 9. Landing CL = 0.85

that the range of the of the variform wing was22.3% further and the endurance was 22.0% longerthan the initial static NACA airfoil.

5 Conclusions and Future Research

Even with no optimization done on the var-iform wing in this example case, the range andendurance increase was within the expected range.The increase in both distance and time was quitesignificant and would greatly benefit many UAVmissions.

The example case shows that the variformconcept readily extends missions and therefore,a more complete model and analysis should becompleted. The work illustrated in this paper laysthe foundation for further progress on this topic andshows that the concept is worth more investigation.

Further work should be directed towards de-

veloping a structural model and finding suitablematerials that will allow for this deformation withthe needed stiffness. Building the full coupledMDO analysis and parameterizing the outer airfoilshape and inner bladder shape also need furtherstudy.

The majority of the research remaining for thismorphing wing design will be in developing therest of the software model for the complete systemanalysis and then employing optimization methodsthat account for uncertainty8 to produce a robustvariform wing with maximized range.

Once all the systems have been modelled andintegrated, this MDO problem could also serve as atest problem for comparing different optimizationmethods.

Acknowledgments

This multidisciplinary research effort is sup-ported in part by the following grants and con-tracts; NSF grants DMI98-12857 and DMI01-14975, NASA grant NAG1-2240. Thank you Re-bekah Hauch and Jessica Hauch (undergraduate re-search assistants) for helping run the example case.

References

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