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An Investigation into the Aerodynamic Efficiency of TaillessAircraft

Aliya Valiyff1 and Maziar Arjomandi2

The University of Adelaide, Adelaide, South Australia, 5005

From the perspective of aerodynamics, tailless aircraft are defended by many aspotentially the most efficient aircraft configuration. The supporting argument being that thereduced surface area resulting from the tailless configuration directly results in reductionsin drag. However, the efficiency of such configuration is realized through the utilization ofactive control systems. Without active control, the expected aerodynamic efficiency gains arepartially or wholly negated by design compromises required to provide stability and control.The magnitude of washout required to stabilize such aircraft are usually quiet high, in theorder of 8 to 10 degrees depending on the wing loading, airfoil type and controlrequirements of the aircraft. This high magnitude of wash out required dictates the liftdistribution, such that only limited locations on the wing are flown at the design liftcoefficient, thus increasing the associated induced drag. This paper discusses the efficiencyof tailless configuration without active control and through the presentation of a case studyundertaken with the use of both theoretical and empirical methods available proposes an allmoving wing tip configuration as the design configuration of choice when considering taillessaircraft.

NomenclatureA = aspect ratioS = wing planform areab = wing spanc = chord lengthCD0 = zero angle of attack drag coefficientCDinduced = induced drag coefficient of main wingCL = main wing lift coefficientCl = airfoil sectional lift coefficientClα = lift curve slopeCM = main wing moment coefficient (quarter chord)Cm = aerofoil section moment coefficient (quarter chord)D = drag forceα = angle of attack of main wingγ = climb angleε = geometric twist of the wingλ = taper ratio of the wingSM = aircraft static marginΛ1/4 = quarter chord sweepΛ1/2 = mid chord sweepXnp = position of neutral pointXcg = position of centre of gravityE = Jones edge velocity factore = Oswald efficiency factorq = dynamic pressure

1 Undergraduate Student, School of Mechanical Engineering, The University of Adelaide, AIAA Student Member.2 Lecturer, School of Mechanical Engineering, The University of Adelaide, AIAA Member.

47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition5 - 8 January 2009, Orlando, Florida

AIAA 2009-1436

Copyright © 2009 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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CG = centre of gravityX1 = distance between CG and wing aerodynamic centreX2 = distance between CG and tail aerodynamic centreY1 = wing mean aerodynamic chord positionY2 = horizontal tail mean aerodynamic chord position

I. Introductionor the last century, there have been countless patents, projects and concepts regarding tailless aircraft, rangingfrom multi-wing aircraft to flying planks, from the early works of Horten to Northrop’s YB49 advanced

bomber1. Since then, following the significant growth in military aviation and the associated technology in the areasof propulsion, material sciences and control systems, there has been a resurgence of interest in tailless aircraft withproposals of one hundred seat delta wing2 to blended wing body passenger aircraft from industries such as Boeing3-8.

In their design, tailless aircraft present interesting challenges. The exclusion of a horizontal stabilizer is the mainfeature of tailless aircraft distinguishing it from the other classes of aircraft. With tailless aircraft the pitch controlsurfaces are located on the main wing. With a significant portion of an aircraft’s flight envelope under steady flightconditions such as cruise, climb or glide, the principle of static equilibrium is thus important in the assessment ofaircraft stability. Static stability is concerned with the initial response of the aircraft to a disturbance and therebyonly aerodynamic loads and the associated moments are considered. Due to the symmetry of aircraft along itscentre-line, longitudinal stability is treated independently of roll or yaw, as small changes in angle of attack do notinfluence the directional or lateral components of stability.

Static margin is a concept used in the assessment of longitudinal stability, and is defined to be the distancebetween the neutral point and centre of gravity (CG) position. A positive static margin corresponds to a negative(positive) pitching moment if the angle of attack increases (decreases), hence aircraft tends to return to its originalstate. Static Margin is expressed by

Χ−Χ=−−

cgnpSM (1)

In an aircraft of conventional configuration, longitudinal stability is achieved through the horizontal tail plane. Insuch an aircraft, the aerodynamic centre of the wing with a symmetric or positively cambered airfoil is ahead of theaircraft centre of gravity hence wing produces a pitch up moment about the CG. This is then trimmed by thepresence of the horizontal tail, via the lift produced at the tail plane acting through the corresponding moment arm,which moves the aerodynamic centre behind the CG.

In a tailless aircraft, however, due to the lack of a horizontal tail plane, longitudinal stability is achieved throughthe use of an aerofoil with reflex camber for low aspect ratio wings while for high aspect ratio planforms thecombined effects of sweep and twist are implemented. The use of twist alters the lift distribution along the span ofthe wing, such that the inner sections of the wing produce more lift than the tip section. By using sweep, a lever armcorresponding to the lift generated at the tip section of the wing is generated. This lever arm combined with thecorresponding lift force means that the tip section can create enough moment to counteract the moment from theroot section of the wing. In this manner the combined effects are enough to trim the aircraft in longitudinal motion.

Tailless aircraft are most often linked to high aerodynamic efficiency and almost always are considered to bemore efficient than conventional configuration aircraft. This belief is evident specially in many of the earlier worksconducted into tailless aircraft9,10. Furthermore, the studies presented on BWB design, also suggest the superioraerodynamic efficiency of tailless configuration over conventional aircraft3.

In this manner, it seems where the efficiency of tailless aircraft is considered, mostly the reductions in aircraftparasitic drag due to the lack of a horizontal tail is noted. However, compared to a conventionally configured aircrafta heavily twisted wing requires a larger wing area for a similar wing loading hence the wing parasitic drag increases.The magnitude of twist utilized for stability purposes in turn reduces the effective lifting area. A properly twistedwing has favorable effect on reduction of the induced drag; however, in the case of a tailless aircraft with large twist,part of the wing near the tip produces negative lift with the mixed effect on induced drag in different flightconfiguration.

This paper investigates the efficiency of tailless aircraft and their efficiency comparing to the other existingconfigurations in particular, conventional configuration. For a given set of design requirements, the case studyutilizes both theoretical as well as empirical methods11-13 available to estimate the required twist and its effect ondrag. In addition, the limitations of the empirical methods will be discussed. Finally, through a case study, the use of

F

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all moving wing tips will be proposed, as a favorable configuration when considering tailless aircraft without theutilization of any active control system.

II. Case StudyThe case study presented below is an excerpt from a design project conducted at the University of Adelaide into

tailless fuel cell powered remotely piloted vehicles. The aim of this project was to develop a platform utilizing ahydrogen-oxygen fuel cell as its chief power source. The intention was for the platform to be suitably designed foradaptation into civil surveillance applications and, as such, was to be designed, developed and manufactured usingexisting techniques and readily available materials and components. The project consisted of the design andmanufacture of the airframe and control systems together with the introduction and integration of the fuel cell powersource. The current fuel cells available on the market are still heavier and with less power output than their electricand piston engine counterparts. Thus, the design required high wing loading to meet the specific powerrequirements. The combination of tailless configuration and high wing loading in addition to the problem oflongitudinal stability of the vehicle required the implementation of innovative approaches. The high wing loadingnature of the design, posed a challenge in determining the twist required to stabilize the aircraft which could besuccessfully implemented without degrading its performance. At first available empirical methods were utilized toestimate the required twist, however, it was realized that these methods were limited in their applications thus anapproach from first principles was employed to determine the twist required. The methodology presents thetheoretical approach used and compares the result to that obtained form the empirical approaches. The aircraftconfiguration and its technical specifications are presented in figure 1 and table 1.

Figure 1. The remotely piloted aircraft designed and built at the University of Adelaidewith the tailless configuration and all-moving wing tips

Takeoff Weight 10 kgCruise Speed 70 kphEndurance 1 hrWing Loading 14.23 kg/m2

Total Wing Area 0.843 m2

Span 2.9 mAspect Ratio 8Airfoil MH78

Table 1. The technical specification of the tailless remotely piloted aircraft

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III. MethodologyAssume a wing with linear distribution of twist, in order to estimate the incidence angles of the root and tip

sections, the wing tips were approximated partially as horizontal stabilizers, displaced back from the centre ofgravity through the use of wing sweep. The outboard wing sections generate a downward lift and thus providing amechanism to stabilize the aircraft. Figure 2 demonstrates the aerodynamic forces acting at the root and tip sections.

During steady level flight the combined lift from the wings must be equal to the weight of the aircraft. Byplacing the aerodynamic centre of the wing at 25% of the MAC, and assuming a trapezoidal planform areaapproximation, the following set of relationships between the parameters were established. Each portion of the wing(1 - root section) and (2 - tip section)) were treated to be separate wings with associated taper and aspect ratios.

( )( )2114/1

12

21

tan Υ+Υ−Λ==−

=−

bC

CXX

WLL(2)

After establishing the above relationships between the parameters, moments around the cg position wereestimated. By taking X1 as a percentage of the MAC and equating the moments about the cg, the required lifts wereobtained.

( )

2,1,2211,

2

0,

0

cos2

cos

wingwingcgm

mwingm

MMXLXLM

A

ACC

+++−==

Λ+

Λ= (3)

The required twist was then estimated by determining the angle of attack of the wing root and tip sections. Theangles of attack of the wing sections were estimated by dividing the respective lift coefficients by their respectivelift curve slopes.

Figure 2. Graphical Representation of Wing

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α

β

α α

ββ

πβ Lw

LLw C

C

AkA

C =

+

Λ+

= .2

)(cos

12

212

22

(4)

The result of the above theoretical method was compared to empirical methods consisting of the Panknin twistdistribution and the two methods presented in the references 11 and 12 provided. The Panknin twist distribution wasbased on Helmut Schenk’s13 research. The Panknin formula presented a relationship between static margin and therequired twist using sweep angle, zero lift angles and moment due to aerofoil profile, as detailed in the equationsbelow. The equation only considers wing moment and lift, and claimed to provide an accurate model for sweepangles of up to and including 30 degrees13. This formula has been used by model aircraft designers over the last twodecades13.

( )

( )( )

)(

1

1

23

4

1

54.1

00

12

2

2

1

43.1

,2,1

LtipLroottotalgeo

Ltipmrootmtotal

KK

K

Ae

SMCCKCK

εεεε

λλλλ

ε

−−=−=

++++=

Λ−

−+=

(5)

Another approach presented by Torenbeek12 estimates the overall static margin, while taking into account boththe fuselage and wing contributions. The method is limited to constant aerofoil section wings, with linear twistdistribution and sweep angles less than 30 degrees. A summary of the approach has been outlined below.Torenbeek’s method separates the moment contributions from the wing body into individual contributions based onthe angle of attack dependency of the terms.

( ) ( )

( ) ( )

( ) ( ) ( )

( ) 4/1

0

tan

4

5.218.1

Λ

−=∆

∆+=

−−=∆

∆+=

Χ−Χ

+=

−

−

−

−−

AE

C

c

cGC

CCC

C

C

cS

lhb

l

bfC

fCCCc

CCC

ltgmac

macbasicmacwingmac

l

Lfff

f

fmac

macwingmacwbmac

npcg

wbLwbmacwbm

α

α

εε

ε

π(6)

While the third method analyzed, accounted for the twist and sweep effects in the wing pitching moment11. Thewing pitching moment is derived by adjusting the airfoil pitching moment for a given wing geometry through theuse of aspect ratio and sweep angle. Raymer11 states that the effects of twist on the overall wing pitching momentcan be approximated to be -0.01 multiplied by the twist angle in degrees.

( ) ε01.0cos2

cos2

0−

Λ+Λ=

A

ACC

airfoilmwingmac

(7)

With the exception of the Panknin twist distribution, for the empirical methods described above, the requiredtwist was estimated by solving the above equations for trim. Given the aircraft profile outlined as per case study thethree empirical methods outlined were used to estimate the required twist to achieve a given static margin. In thiscase, the analysis was limited to contributions from the wing as the magnitudes of the moment contributions fromthe propeller and the fuselage were negligible in comparison. Table 2 summarizes the magnitude of washoutrequired estimated from the three empirical and the theoretical approaches presented.

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Method Twist Required for SM=6% Twist Required for SM=10%Reference 13 -0.15o -3o

Reference 12 0o -2.85o

Reference 11 -0.55o -3.6o

Theoretical Approach -6o -8.5o

Table 2. Comparison of Washout

As can be seen the results vary between the three empirical methods, however, this variation is minor incomparison to the theoretical approach. The magnitude of the twists obtained from the empirical methods translatesinto an upward lift being generated across the wing. In this case there is no stabilizing mechanism as moments aboutthe CG do not equate. The results obtained from the empirical methods do not provide an accurate representation ofthe dynamics of the model. It is hypothesized that the empirical methods are sensitive to wing loading and aspectratio. Aircraft which have utilized the above approaches normally have wing loadings of approximately 7 kg/sqm.Furthermore, Panknin’s formulation was specific to model aircraft with low wing loading (Panknin’s flying wingwhich was designed based on the above distribution has the wing loading of only 3.3kg/sqm13) and for a specificairfoil.

A sensitivity analysis of the static margin derived from the three methods to sweep angle was conducted andresults compared. Figure 3 shows the variation in static margin with sweep angle for the three empirical approachespreviously discussed for the aircraft profile per the case study with washout of -2 degrees.

Although the values obtained for the static margin using the empirical twist approaches were limited, the generaltrends exhibited between the static margin and taper ratio, sweep and twist angles were as expected for the twistapproximations given by Panknin12 and Torenbeek13. The analysis of longitudinal stability via Raymer11 resulted instatic margins within the vicinity of the results obtained from the Panknin distribution for sweep angles of 20-25degrees. However, the approximation of twist distribution obtained from Raymer11, did not demonstrate this trend.With increasing sweep angle a decrease in static margin was observed, which shows the limited application of thismethod.

IV. DiscussionIn this case, as the design parameters were outside the range recommended by the empirical methods described

above, the result of the theoretical approach was used. Having obtained the twist angle required for longitudinalstability, the incidence angles for the root and tip sections were estimated for a range of tip to wing section arearatios, as shown in figure 4.

Figure 3 Comparison of Empirical Methods

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The combination of high wing loading and low power loading nature of the design required an airfoil with highlifting capacity with neutral or positive moment coefficient for stability. The reflex airfoils available could notprovide the lift required and thus a slightly cambered airfoil with positive moment coefficient was used. Due to thesteep lift curve slope of the aerofoil (MH78), the angle of attack of the root section of the wing was in the order ofsix degrees. By extending the analysis for a wide range of area ratios (wing tip and root section) and sweep angle,the optimum area ratio and sweep angle resulting in the minimum angle of attack of the wing root and tip sections,were derived. This resulted in the required twist of approximately six degrees and therefore an incidence angle of 12degrees for the wing root. Given the aerofoil stall angle of 20 degrees, this incidence angle was deemed too high.The high incidence angle would have further increased the overall drag of the vehicle. For a well designed airfoil,the drag at the design lift coefficient is approximately equivalent to skin friction drag. Thus aircraft are designed toachieve at cruise a coefficient of lift in the vicinity of the design lift coefficient. With the optimum lift coefficient ofthe MH78 airfoil at 0.694 corresponding to an angle of attack of 6 degrees, the additional twist of 6 degrees linearlydistributed meant that only one wing section of the aircraft was at the optimum angle of attack.

As a result of the increased drag associated with linear distribution of twist, the use of an all moving wing tipwas proposed, where the wing tip rotates to produce the required moment to trim the aircraft outside level flightconditions. There have been several British tailless aircraft on which the all-moving elevator has been realized.Examples of these include the experimental aircraft ‘Sherpa’, and the Granger Archaeopetrix1. Further analysis wasundertaken to determine the degree of rotation required by the wingtips in order to trim the vehicle during takeoff. Itwas determined that the wingtips needed to rotate 6 degrees clockwise, bringing the aerofoil to a final angle ofattack of 12 degrees. However, since the MH78 aerofoil is cambered with some reflex, its performance at negativeangles of attack was greatly limited, with stall angle of attack of 12 degrees. Thus the aerofoil was inverted at thewing tips to attain the same performance exhibited at positive angles of attack.

Figure 4. Incidence Angle - Cruise (St=6%)

Figure 5 Aircraft during Flight

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The associated drag of a vehicle consists of parasitic and induced drags. At subsonic speeds the parasitic drag inturn is dominated to a large extent by skin friction drag and to a lesser degree by pressure drag11. This parasitic dragcontribution is approximated through the product of the equivalent skin friction coefficient which accounts for theeffects of skin and separation drag and the ratio of wetted surface area to the wing reference area. Most often, whenthe efficiency of tailless aircraft are discussed and compared to aircraft of differing configurations, the reductions inthe wetted surface area of tailless aircraft are immediately noted and directly linked to superior performance andaerodynamic efficiency. It is claimed that the lift over drag ratio of flying wings is 20-25% larger than for jettransport aircraft. 3

However, the quoted percentage increases in lift to drag ratios are only feasible through the use of active control.As illustrated above, without the use of active control, the magnitudes of washout required to stabilize the aircraftcould overcome any reductions observed in the vehicle’s wetted surface area. One aspect which is often overlookedwhen considering the aerodynamic performance of tailless aircraft is the affect of twist on induced drag. Forinstance, the early Horten flying wings exhibited losses of and up to 40% in induced drag1.

The optimum lift distribution which results in the minimum induced drag is the elliptical lift distribution. Withtailless aircraft, in order to minimize the induced drag, the lift distribution is optimized through the appropriateselection of twist and wing planform. However, the lift distribution cannot be optimized through twist at multiple liftcoefficients. Optimization of the lift distribution at the design lift coefficient means that at other coefficients of liftthe performance of the vehicle is reduced. Thus, magnitudes of twist above 5 degrees are not recommended11.However, without the use of any active control, achievement of reasonable stability margins is reliant on theutilization of large magnitudes of twist.

The use of all moving wing tips meant that with the exception of the wing tips, the wing during cruise is at thedesired design lift coefficient corresponding to the highest lift to drag ratio. The increase in drag is localized to thesmall wing tips only and thus the overall associated drag of the vehicle would be smaller than that observed for thedistribution of linear twist. In addition, in tailless aircraft due to the configuration’s sensitivity to changes in theoperating environment such as gust, the elevons are not in neutral position for most of the flight. Thus, with theconventional control surfaces the leading edges of the elevons do not sit flush with the leading edge of the wing,acquiring extra drag.

Although, similar behavior is observed in conventional aircraft, due to the presence of the horizontal stabilizerthe aircraft is less sensitive and the aileron and elevator control surfaces are separate, thus the associated drag issmall in comparison. Nickel and Wolfhart1 attribute two factors for this loss; the airfoil bend in the wing section andthe end gaps, the laminar boundary behind the bend due to the presence of the bend becomes turbulent. With the allmoving tips, the end gap is minimized and any bending of the airfoil is eliminated, eliminating with it theaccompanying losses.

As discussed above, it can be seen that the aerodynamic efficiency of a tailless aircraft without active controlsystem could be comparable with the aerodynamic efficiency of a conventional configuration due to the requirementof large twist angle for longitudinal balance. It’s also suggested that the use of all moving tip could be considered analternative option with similar or better aerodynamic efficiency than a highly twisted wing due to more efficientdistribution of the airfoil angle of attack along the wing span. For better understanding of the behavior of all movingwing tips, however, further theoretical and experimental investigations are required.

V. ConclusionThe aerodynamic efficiency of tailless aircraft is often claimed to be high in comparison to the conventional

configuration. This belief is usually based upon the supposition that the reduced wetted surface area provided by thetailless configurations directly leads to reductions in drag. However, without the use of active control system, thelarge magnitudes of twist required to stabilize the aircraft means that most of the wing section is operated at liftcoefficient values above or below the desired lift coefficient, negating the affects of the above mentioned benefits.Thus, in applications where the use of active control systems is not viable the use of all moving wing tips canoptimize the lift distribution and may lead to increased efficiency. Wind tunnel experiments of this configurationand those which utilize linear twist distribution are required to quantify the differences in the performances of thetwo configurations. This would provide the means to verify the theoretically predicted performance values.Furthermore, the application of currently available empirical methods is limited in their estimation of the twist anglefor longitudinal stability and don’t seem to encompass high aspect ratio and high wing loading designs.

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AcknowledgmentsThe authors would like to acknowledge the financial support received from the School of Mechanical

Engineering, the University of Adelaide and the Sir Ross and Sir Keith Smith Fund for the University of AdelaideFuel Cell UAV project as well as the individual group members of the project team Christopher French, CraigCollins, Elizabeth Pham and Rebecca Baylis.

DisclaimerResearch undertaken for this report has been assisted with a grant from the Smith Fund (www.smithfund.org.au).

The support is acknowledges and greatly appreciated. The Smith Fund by providing for this project does not verifythe accuracy of any findings or any representation contained in it. Any reliance in any written report or informationprovided to you should be based solely on your own assessment and conclusions.The Smith Fund does not acceptany responsibility or liability from any persons, company or entity that may have relied on any written report orrepresentations contained in this report if that person, company or entity suffers any loss (financial or otherwise) as aresult.

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