Progress in Aerospace Sciences 47 (2011) 647–659

Contents lists available at SciVerse ScienceDirect

Progress in Aerospace Sciences

0376-04

doi:10.1

n Corr

E-m

journal homepage: www.elsevier.com/locate/paerosci

Analysis of conventional and asymmetric aircraft configurationsusing CEASIOM

Thomas S. Richardson a,n, Cormac McFarlane a, Askin Isikveren a, Ken Badcock b, Andrea Da Ronch b

a Faculty of Engineering, University of Bristol, University Walk, Bristol BS8 1TR, UKb School of Engineering, University of Liverpool, Liverpool L69 3BX, UK

a r t i c l e i n f o

Available online 14 October 2011

Keywords:

CEASIOM

SimSAC

Flight Control

Z-wing

Asymmetric Aircraft

Eigenstructure Assignment

21/$ - see front matter & 2011 Elsevier Ltd. A

016/j.paerosci.2011.08.008

esponding author.

ail address: thomas.richardson@bristol.ac.uk

a b s t r a c t

One of the main drivers behind the SimSAC project and the CEASIOM software is to bring stability

analysis and control system design earlier into the aircraft conceptual design process. Within this paper

two very different aircraft are considered, a conventional T-tail based on the existing EA500 Very Light

Jet and the second, a novel Z-wing configuration known as the GAV or general aviation vehicle. The first

aircraft serves as a baseline comparison for the second, and the cruise case is considered as a

benchmark for identifying potential drag reductions and aircraft stability characteristics. CEASIOM, the

Computerised Environment for Aircraft Synthesis and Integrated Optimisation Methods, is used to

generate aerodynamic data sets for both aircraft, create trim conditions and the associated linear

models for classical stability analysis. The open-loop Z-wing configuration is shown to display both

highly unstable and coupled modes before a multivariable Stability Augmentation System (SAS) is

applied both to decouple and stabilise the aircraft. Within this paper, these two aircraft provide a test

case with which to demonstrate the capabilities of the CEASIOM environment and the tools which have

been developed during the SimSAC project. This new software suite is shown to allow conceptual

development of unconventional novel configurations from mass properties through adaptive-fidelity

aerodynamics to linear analysis and control system design.

& 2011 Elsevier Ltd. All rights reserved.

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 648

2. Aircraft models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 648

2.1. Eclipse Aerospace EA500 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 648

2.1.1. EA500 wing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 649

2.1.2. EA500 horizontal tail . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 650

2.1.3. EA500 vertical tail . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 650

2.1.4. EA500 engines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 650

2.1.5. EA500 weights and balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 650

2.2. General aviation vehicle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 651

2.2.1. GAV wings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 652

2.2.2. GAV canted vertical tail . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 652

2.2.3. GAV control surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 652

3. Aerodynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 652

3.1. EA500 aerodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 652

3.2. General aviation vehicle aerodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653

4. Linear trim analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654

4.1. Eclipse Aerospace EA500 straight and level trims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654

4.2. EA500 modal analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654

4.3. GAV linear trim analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655

4.4. GAV modal analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655

ll rights reserved.

(T.S. Richardson).

T.S. Richardson et al. / Progress in Aerospace Sciences 47 (2011) 647–659648

5. GAV stability augmentation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656

5.1. Eigenstructure assignment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656

5.2. GAV eigenstructure assignment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656

5.3. GAV simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657

6. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 659

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 659

1. Introduction

Complex control system design is usually not consideredduring the initial conceptual phases of an aircraft design and isoften only used to augment or address deficiencies that arise at alater stage in the design cycle. One of the primary driving forcesbehind SimSAC and the development of the CEASIOM [1] (Com-puterised Environment for Aircraft Synthesis and IntegratedOptimisation Methods) environment is to allow linear analysisand control system design to be used as tools at a very early stageand offer the potential for design optimisation, and the ability tobe able to consider highly novel aircraft concepts.

The purpose of this paper is to demonstrate the potential of theCEASIOM tools when applied to an example of both conventionaland unconventional aircraft design. CEASIOM was developed withinSimSAC (Simulating Aircraft Stability And Control Characteristics forUse in Conceptual Design) by a partnership of European academicand industrial contributors. Funding was provided for this work bythe European Commission 6th Framework Programme. With theinitial project at an end, the software is now available online forindustry and academia with optional support available.

CEASIOM consists of a set of tools that allow the user togenerate a wide range of aircraft concepts from initial templatesand then use these to work through the design process generatingthe required aircraft parameters as they proceed. Aerodynamicmodules, DATCOM, Tornado and Edge, are available which allowsimple aerodynamic predictions utilising empirical methodsthrough to an inviscid Euler solver. The AcBuilder module is usedto define simplified aircraft geometry using approximately onehundred parameters and which also includes algorithms which canbe used to predict the required weights and balance parameters.

Once the aircraft aerodynamics and mass properties have beenpredicted the Stability and Control Analyser and Assessor (SCAA)and Flight Control System Design Toolkit (FCSDT) modules can beused to provide classical linear analysis and control systemdesigns for the concept aircraft. The ability to be able to easilygenerate aircraft models and design control systems for novelconcepts allows the designer to exploit the potential benefitsassociated with bringing stability analysis and control systemdesign earlier into the aircraft conceptual design process.

In order to demonstrate the full potential of CEASIOM, twoaircraft have been selected and the process followed through tothe initial control system design stage. The first of these aircraft isthe Eclipse Aerospace EA500 which is a conventional T-tail VeryLight Jet (VLJ). Results are presented for this aircraft, and thefuselage is also taken as the basis for a novel asymmetric design,General Aviation Vehicle (GAV), which demonstrates highlycoupled asymmetric behaviour. It has been suggested that thisasymmetric VLJ configuration proposed by Isikveren [2] has thepotential to reduce drag and so improve fuel economy.

CEASIOM is used to assess the performance of both aircraft,generating aerodynamic and mass properties for linear analysis ofthe trimmed cruise condition. These results are used to suggestwhether a drag reduction is possible and secondly to assess themodal dynamic response of both aircraft. Finally it is demon-strated that the addition of a multi-input, multi-output Stability

Augmentation System (SAS) may be employed to both decoupleand stabilise the asymmetric GAV design. The same aerodynamicprediction methods have been used for both the conventional andunconventional Z-configuration aircraft.

It is intended that the results within this paper demonstrateboth the power and the flexibility of the CEASIOM environmentwhich allows the user to create a full 6DoF aircraft model basedon simple initial design concepts. Although the process is highlyautomated, the software allows the user to edit the aircraft files atany point, and as is done with the case studies provided here,update parameters for which additional information is available.These results also demonstrate that it is possible to considerhighly unconventional designs, the full benefits and feasibility ofwhich cannot be exploited without integrated complex controlsystem design within the design process.

In Section 2 the two aircraft models are presented, theconventional EA500 and unconventional GAV Z-wing design.The configurations for both are given together with the weightsand balance parameters used to build up the 6DoF models.Section 3 describes the aerodynamic models and provides sam-ples of the aerodynamic data sets generated. These are then usedin Section 4 to generate trimmed linear models for whichperformances parameters are considered and the associateddynamic response given for both aircraft. Within this sectionthe requirement is demonstrated for stability augmentation of theZ-wing GAV aircraft which is subsequently addressed in Section 5.Within Section 5 a short outline of the theory behind Eigenstruc-ture Assignment (EA) is presented together with the applicationof this method to the GAV. Conclusions are given in Section 6.

2. Aircraft models

Within this section the two aircraft models are described. Thebaseline aircraft selected was the Eclipse Aerospace EA500, anddetails of the implementation of this aircraft within the AcBuildermodule is given in Section 2.1. Where differences between theEA500 and the actual aircraft occur the reasons for these differ-ences and justifications for them are given. In Section 2.2 the GAVZ-wing configuration [3] is presented whilst highlighting thedifferences between the two models.

2.1. Eclipse Aerospace EA500

Dimensions for the EA500 were taken from detailed 3-viewdrawings obtained from the Eclipse Aerospace website [4], and theside and top views used are shown in Figs. 1 and 3. For use withinCEASIOM the model geometry is split up into 5 sub-components:fuselage, wing, horizontal tail, vertical tail and engines. These aredefined within model XML files consisting of a limited number ofparameter values that are used to approximate each of thecomponents. This allows a large degree of flexibility in the designwhilst keeping the model complexity relatively low.

Each component is defined by a set of fields for whichvalues must be given. The first component of the EA500 implemen-ted in CEASIOM was the fuselage, which was split into three

Nomenclature

Symbols

A state matrixAcl closed-loop state matrixB input matrixIxx moment of inertia about x-body axisIyy moment of inertia about y-body axisIzz moment of inertia about z-body axisIxz product of inertiaK feedback (static) gain matrixL rolling momentm aircraft massM pitching momentN yawing momentp roll rateq pitch rater yaw rateu control inputVt total translational velocityV achievable closed-loop eigenvaluesx state vector

Abbreviations

CEASIOM Computerised Environment for Aircraft Synthesisand Integrated Optimisation Methods

CG Centre of GravityFCSDT Flight Control System Design ToolkitGUI Graphical User InterfaceMAC Mean Aerodynamic ChordSAS Stability Augmentation SystemSCAA Stability and Control Analyser and AssessorSimSAC Simulating Aircraft Stability And Control Character-

istics for Use in Conceptual Design

Greek letters

a angle of attackK desired closed-loop eigenvaluesf roll angley pitch anglec yaw angle

T.S. Richardson et al. / Progress in Aerospace Sciences 47 (2011) 647–659 649

subcomponents: the nose, the central fuselage, and the tail. Fig. 2shows the divisions that were chosen for the EA500 fuselage with atotal fuselage length of 9.2 m.

Sizing for each of these fields within CEASIOM for the fuselagecomponent was completed by hand based on the informationextracted from the 3-view drawings. Detailed information onthese and the remaining components described below can befound in [4].

2.1.1. EA500 wing

As with the fuselage, the wing is split into subsections withinCEASIOM, allowing the geometric characteristics of the wing to bevaried along its span. These divisions are shown in Fig. 4 and can becompared against the original plan view shown in Fig. 3.

Fig. 1. EA500 side view [4].

Fig. 2. EA500 CEASIOM side view components.

The incidence angle relative to the longitudinal axis of theaircraft and the aerofoil section for each of the cross-sections waschosen to be the same for the EA500 within CEASIOM. These were01 for the incidence angle, and the MS313 aerofoil for the cross-section. For the purposes of this paper the twist angle of the wingfor both the EA500 and the GAV was therefore assumed to be 01.Additional parameters required included the leading-edge sweep,the taper ratio and the dihedral angle. The thickness to chord ratiowas also considered to be constant along the span.

The inboard subsection of the EA500 wing is contained withinthe fuselage and was modelled as a rectangular wing section with

Fig. 3. EA500 top view [4].

T.S. Richardson et al. / Progress in Aerospace Sciences 47 (2011) 647–659650

the portion of the wing outside the fuselage exhibiting a constantdihedral angle of 5.41, covering the midboard and outboard sections.CEASIOM uses the values of the wing subsection fields along withthe wingspan and area to determine the root wing chord.

2.1.2. EA500 horizontal tail

The EA500 horizontal tail was modelled in a similar way to thewing, but with only two subsections (inboard and outboard), andwith one kink. The fields concerning the horizontal tail as a wholewere the same as the wing, namely its span and area, and itsvertical and horizontal location in relation to the fuselage. Theincidence angle and aerofoil sections at the root and tip (andhence at the kink) remain the same, with a 01 incidence and inthis case a NACA 0012 aerofoil for the cross-section. As with thewing CEASIOM calculated the root chord of the horizontal tailfrom the other fields.

Fig. 4. EA500 CEASIOM top view components.

Fig. 5. EA500 vertical tail model.

Fig. 6. EA500 within the CEA

2.1.3. EA500 vertical tail

The EA500 vertical tail was modelled as shown in Fig. 5. Onecurrent issue with modelling the vertical tail in CEASIOM is thatthe root edge is assumed to be horizontal; however, this is not thecase for the EA500, as can be seen in Fig. 1. When using the Edgeaerodynamic module within CEASIOM the mesh generation soft-ware models this intersection, whereas the Tornado module usesthe horizontal root edge. It is possible therefore to overestimatethe influence of the vertical tail when using the lower fidelityaerodynamic modules.

The EA500 vertical tail also has a kink in it located 1.05 mbelow the tip (0.45 m above the modelled root). The incidenceangle and aerofoil sections at the root, kink and tip remain thesame, however, with a 01 incidence and a NACA 0012 aerofoil.

2.1.4. EA500 engines

The final components of the EA500 implemented withinCEASIOM were the two engines mounted on the rear of thefuselage. The central point of the EA500 engine inlets are located6.16 m aft of the nose tip, 0.13 m above the fuselage centreline,and 0.89 m laterally from the fuselage centreline. The engines arealso pitched down by 0.81.

Fig. 6 shows the final assembled EA500 in the AcBuildermodule within CEASIOM. On the left is the viewer and on theright, a list of the components outlined above. It is possible toeither edit these within AcBuilder or to edit the XML files directly.This module also gives direct access to the weights and balancecalculations.

2.1.5. EA500 weights and balance

CEASIOM has a set of tools for estimating the weights andbalance (W&B) data for aircraft models. As the EA500 model isbased on an existing aircraft rather than a concept there wassome additional data available in the public domain which wasused to update the estimates produced by CEASIOM. One sourceof information concerning the W&B of the EA500 is the FAA typecertificate data sheet[5]. The Centre of Gravity (CG) range fromthis sheet is summarised in Table 1. The mass of the emptyaircraft taken from [5] is 1648 kg (3634 lbs) with a maximum fuelcapacity of 254.4 US gallons located 4.44 m aft of the nose tip.

SIOM AcBuilder module.

Table 1EA500 CG limits.

Condition Mass (kg) Fore CGlimit (m)

Aft CGlimit (m)

Max ramp weight 2734.7 4.438 4.473

Max takeoff weight 2719.3 4.436 4.483

Max landing weight 2540.1 4.415 4.600

Max zero fuel weight 2232.6 4.379 4.600

Table 2Estimated mass breakdown for the EA500.

Component Mass (kg) % Empty aircraft

Fuselage 250.0 15.2

Wing 290.0 17.6

Empennage 65.0 4.0

Landing gear 106.0 6.4

Nacelles 41.0 2.5

Power plant 367.5 22.3

Systems 457.0 27.7

Other 71.5 4.3

Table 3Estimated component CG locations for the EA500.

Component CG fromnose(m)

Weight(kg)

Fuselage 4.14 250.0

Wing 4.72 290.0

Empennage 9.06 65.0

Landing gear 3.47 106.0

Engines and

nacelles

6.73 408.5

Systems 4.21 457.0

Other 4.71 71.5

Fig. 7. Estimated component CG locations for the EA500.

Table 4Estimated EA500 mass properties.

Ixx 2670 kg m2

Iyy 6020 kg m2

Izz 8155 kg m2

Ixz 535 kg m2

Fig. 8. EA500 GAV comparison.

T.S. Richardson et al. / Progress in Aerospace Sciences 47 (2011) 647–659 651

Table 2 gives the breakdown of all the EA500 componentmasses as generated by CEASIOM. The last component labelled‘Other’ represents the difference between the estimates fromCEASIOM and the actual EA500 figure with an error of just 4.3%.

Table 3 lists the CG locations for each of these componentsalong with their masses and Fig. 7 shows the estimated compo-nent CG locations for the EA500

The EA500 type certificate [5] also provides the moment arms (CGlocations) for the fuel and baggage, which are 4.44 and 4.94 m aft ofthe aircraft nose, respectively. The seats for the pilots and passengersare distributed through the cabin, and an estimated CG of 2.6 m aft ofthe aircraft nose was taken for the pilot, together with a CG range of3.5–4.35 m aft of the aircraft nose taken for the passengers.

The Moments of Inertia (MoIs) were estimated for the emptyEA500 by KTH using the USAF Stability and Control DATCOMsoftware [6], and are given in Table 4. The MoIs of an aircraft willchange depending on the loading configuration as extra massesare added or removed from different locations on the aircraft.Simple models were used to within CEASIOM in order to includethe effect of these on the MoIs.

2.2. General aviation vehicle

In this section the General Aviation Vehicle (GAV) configurationis presented. This GAV model is based on the EA500 aircraft modelwhich is modified to create a novel asymmetric design. The ‘‘Z-wing’’ morphology GAV has a low starboard wing mounted on theforward fuselage and a high port wing mounted on the aft fuselage,enabling direct lift control and the removal of the horizontal tail. The

vertical tail is also canted over providing a third lifting surface. Thesuggested benefits of this design include [2]:

�

a reduction in total drag due to absence of dedicated horizontal tail, � configured direct lift promotes all-positive lift, � vortex-induced drag benefits due to discrete load tailoring.

Fig. 8 is a plan view of the EA500 and GAV aircraft forcomparison. As with the EA500, the GAV was created inAcBuilder. The purpose of the GAV is to fulfil the same role as

T.S. Richardson et al. / Progress in Aerospace Sciences 47 (2011) 647–659652

the EA500 with the same payload in terms of passengers andbaggage. Because of this, the fuselage was designed to be similarin shape and size to that of the EA500. There would be somestructural differences due to changes to the mounts for the wingsegments and tail; however, for the purpose of this study anidentical fuselage was used for both configurations.

Fig. 10. Approximate GAV control surface layout.

2.2.1. GAV wings

The starboard wing for the GAV was mounted forward of theEA500 wing, just behind the main cockpit window, to provide amoment arm for controlling pitch. As with the EA500 wing it waslocated low on the fuselage. The port wing was mounted aft of theEA500 wing, where the fuselage narrows and was located high onthe fuselage. This horizontal separation between the two wingsmeans that varying the lift distribution between the two wingswill enable the pitching moment to be controlled. The dihedral ofthe starboard wing is the same as that of the EA500; however, thehigh port wing is mounted with anhedral equal to the samemagnitude as the dihedral of the starboard wing.

A simple tapered design with no kinks was chosen and the forewing was swept forward slightly so that its leading edge wasperpendicular to the aircraft centre line, whilst the aft wing wasswept back slightly so that its trailing edge was perpendicular tothe aircraft centre line. As with the EA500 model the MS313aerofoil section was used for both wings.

2.2.2. GAV canted vertical tail

The GAV has no horizontal tail, so the next component of theaircraft implemented in CEASIOM was the vertical tail. Thevertical tail is canted over 551 to provide a third lifting surface.As with the wings a simple tapered design with no kinks waschosen with a leading edge sweep of 47.51 and the MS313 aerofoilsection. Fig. 9 is the SUMO visualisation of the GAV Z-wing inwhich the two main wings and canted vertical tail can be clearlyseen together with a single, fuselage mounted engine.

Fig. 11. SUMO EA500 model.

2.2.3. GAV control surfaces

Five control surfaces were chosen for the GAV, two on each ofthe main wings and a single control surface on the canted verticaltail. The approximate size and locations of these are shown inFig. 10. Nominally the two inner surfaces are referred to aselevators and can be used to generate a desired pitching moment,and the two outer surfaces are referred to as ailerons and can beused to generate a desired rolling moment. Yaw control isachieved via the single control surface on the canted tail. Becauseof the configuration, however, each control channel will result in

Fig. 9. SUMO GAV model.

coupling between longitudinal and lateral-directional motion,resulting in a challenging control problem.

3. Aerodynamics

3.1. EA500 aerodynamics

Before any investigation of the EA500 can be carried outaerodynamic tables for the model needed to be generated. CEA-SIOM can generate aerodynamic tables using a range of differentaerodynamic prediction codes and for the work presented in thispaper, the relatively high fidelity Euler Edge code was used. Thefirst step in this process is to create a mesh representation of theEA500 based on the initial AcBuilder aircraft model (Fig. 11).

The SUMO module of CEASIOM converts AcBuilder aircraftmodels to a mesh that can be used in the Edge aerodynamiccalculations. For simplicity and to allow a direct comparison, theengines on both aircraft were removed at this step to create a cleanaircraft model. The second step was to specify the control surfaces,

Fig. 13. EA500 Cm vs. AoA (deg).

T.S. Richardson et al. / Progress in Aerospace Sciences 47 (2011) 647–659 653

which can be done both in AcBuilder and SUMO. These were addedand a mesh was generated for the EA500. This mesh was importedinto the AMB module of CEASIOM from which the Edge predictioncode could be run. The reference wing area, wing span andaerodynamic chord used in these calculations are given in Table 5.

The aerodynamic force and moment coefficients were calcu-lated across a selected flight envelope. For each table the aero-dynamic coefficients were generated for a range of values of angleof attack, Mach number and one other variable. The othervariables included sideslip angle and control surface deflections.Table 6 gives the range of values for each of the variables thatmake up the aerodynamic tables and Figs. 12 and 13 show the liftand pitching moment coefficients for a range of Mach numbersand angles of attack. It can be seen that both the lift-curve slopeand pitch stiffness increase as the Mach number increases.

Fig. 14 shows how the static margin of the EA500 varies withMach number, going from 28.8%MAC at Mach 0.2 down to25.5%MAC at Mach 0.65. This puts the Neutral Point (NP) forthe aircraft at 50.8%MAC at Mach 0.65. The minimum staticmargin for the EA500 within the flight envelope can thereforebe calculated to be 13.9%MAC and therefore the aircraft is alwaysstatically stable longitudinally.

3.2. General aviation vehicle aerodynamics

As with the EA500, aerodynamic tables were generated for theGAV Z-wing using CEASIOM. The same Edge prediction code was

Table 5EA500 reference values.

Wing area 13.92 m2

Wing span 11.00 m

MAC 1.385 m

Table 6EA500 aerodynamic table variables.

Variable Variable range Units

AoA [�4 �2 y 8 10] deg

Mach [0.2 0.35 0.5 0.65] –

AoS [�6 �3 0 3 6] deg

Elevator [�15 –7 0 7 15] deg

Rudder [�20 �10 0 10 20] deg

Aileron [�15 –7 0 7 15] deg

Fig. 12. EA500 CLift vs. AoA (deg).

Fig. 14. EA500 static margin (%MAC) vs. Mach number.

Table 7GAV aerodynamic table variables.

Variable Variable range Units

AoA [�4 �2 0 2 4] deg

Mach [0.20 0.65] –

AoS [�4 �1.33 0 1.33 4] deg

Elevator [�5 0 5] deg

Rudder [�5 0 5] deg

Aileron [�5 0 5] deg

used to generate this data to ensure the results were comparable.The aerodynamic force and moment coefficients were againcalculated across a selected flight envelope. Table 7 gives therange of values for each of the variables that make up theaerodynamic tables for the GAV. For this aircraft, the effect ofeach control surface was considered individually to provide fiveindependent control surfaces. As with the EA500, the engine wasalso removed to provide a clean aircraft and comparable results.

Figs. 15 and 16 show how the lift and pitching momentcoefficients, respectively, of the GAV Z-wing vary with angle ofattack. It can be seen that the lift coefficient curve slope for theGAV is similar to that of the EA500 seen in Fig. 12. The pitchingmoment slope for the GAV is also similar to that of the EA500

Fig. 15. GAV Z-wing CLift vs. AoA (deg).

Fig. 16. GAV Z-wing Cm vs. AoA (deg).

Table 8Flight parameters selected for trim.

Parameter Value Units

Mass 2700 kg

CGx 4.44 m (aft)

Mach 0.50 –

Fig. 17. EA500 trim AoA (deg) vs. altitude (km).

Fig. 18. EA500 trim elevator deflection (deg) vs. altitude (km).

T.S. Richardson et al. / Progress in Aerospace Sciences 47 (2011) 647–659654

seen in Fig. 13; however they are offset, with the EA500 pitchingmoment being zero at an angle of attack of approximately zerowhilst the Z-config pitching moment is zero at an angle of attackbelow �41.

The static margin was also calculated for the GAV and was foundto be greater than that of the EA500 which would affect the trimdrag of the aircraft. In order to reduce the static margin on the GAVto the same as that for the EA500 at cruise speed the associated CGwas subsequently moved 5.5 cm further aft. The SCAA softwareenables the user to move the CG and accounts for the effect of thiswhen modelling the equations of motion of the aircraft.

4. Linear trim analysis

In this section the results of trimming and linear analysis inthe cruise for both the EA500 and GAV are presented. A widerange of classical analysis results are available within CEASIOM;however, for the purposes of this paper only the aircraft modalcharacteristics will be given for the trimmed cruise condition.

4.1. Eclipse Aerospace EA500 straight and level trims

The EA500 was trimmed across a range of altitudes todemonstrate the influence that altitude has on the trim values

of the elevator and angle of attack. Table 8 lists the otherassociated flight condition parameters. Trims were calculatedfor altitudes between 10,000 and 40,000 ft, with Figs. 17 and 18showing the trimmed angle of attack and elevator deflectionagainst altitude. As the altitude increases, the required angle ofattack also increases, and this is matched by an increasinglynegative trimmed elevator deflection. It is interesting to note thatboth the required elevator deflection and the angle of attack areclose to a minimum at the expected cruise altitude.

4.2. EA500 modal analysis

In this section the dynamic modes of the EA500 are calculated.For these purposes, a flight condition consisting of a speed of160 m/s and an altitude of 8000 m was selected and a state space

Table 11GAV Z-wing control authority.

Control surface Normalised effect of deflection

CL CY Cl Cm Cn

Left elevator 0.53 �0.07 �0.10 �0.84 �0.02

Right elevator 0.56 0.13 0.08 0.81 0.03

Left aileron 0.53 �0.06 �0.21 �0.82 �0.01

Right aileron 0.65 �0.03 0.23 0.72 0.01

Rudder 0.25 �0.17 0.05 �0.95 �0.08

Table 12

T.S. Richardson et al. / Progress in Aerospace Sciences 47 (2011) 647–659 655

representation was then obtained by linearising the trimmedaircraft model at this point. This model was reduced to the statesthat dictate the classical modes of an aircraft as given in Eq. (4.1).The SDSA and FCSDT modules within CEASIOM contain all thetools required to provide a wide range of trims and linearisations:

States¼ a b Vt p q r f yh i

ð4:1Þ

The eigenvalues of the linearised system are given in Table 9and they can be seen to exhibit the five classical aircraft modes.The fast modes, Short Period, Dutch Roll and Roll Subsidence, areall shown to be stable, together with a stable Phugoid andmarginally unstable Spiral mode. Although not shown here, theassociated eigenvectors demonstrate that the longitudinal andlateral-directional modes are decoupled, as would be expectedwith a classical aircraft configuration of this type.

4.3. GAV linear trim analysis

Following on from the EA500, the GAV was also trimmed andlinearised within CEASIOM in the cruise condition. As with theEA500, the aircraft was trimmed to be flying straight and level;however, for this asymmetric configuration the problem is morecomplex. The requirements are the same, namely that the summa-tion of all the independent forces and moments acting on theaircraft must be zero. The aerodynamic forces and momentsgenerated on the aircraft however will not necessarily be symmetricand the calculation of the trim point is therefore more difficult.

With the five control surface deflections, engine thrust, angleof attack and angle of sideslip as variables available to meet theserequirements it is also possible to explore different trim config-urations. For the purposes of this paper zero sideslip was main-tained and the angle of attack varied in order to produce thesmallest associated control surface deflections and associateddrag. Although not guaranteed to be the minimal drag case, itwas considered sufficiently representative for the purposes of thispaper. The resultant trimmed control surface deflections for thistrim are given in Table 10.

The last value given in Table 10 is the trimmed thrust require-ment. At 1.4 kN this was found to be higher than for the EA500 atthe same flight condition which was calculated to be 1.2 kN. Aninitial conclusion therefore that could be drawn is that the GAVwill not realise the potential drag reduction that was initiallysuggested. One reason for this could be the relatively large control

Table 9EA500 eigenvalues.

Mode Eigenvalues

Short Period �1.876.5i

Phugoid �0.003570.1i

Dutch Roll �0.1175.6i

Roll Subsidence �7.8

Spiral 0.0037

Table 10GAV Z-wing trimmed control deflections.

Control Value Units

Left elevator deflection �9.4 deg

Right elevator deflection �11.5 deg

Left aileron deflection 8.3 deg

Right aileron deflection 3.3 deg

Rudder deflection �8.9 deg

Thrust 1.4 kN

surface deflections required to trim the aircraft at this point in theflight envelope. It would be possible to revisit the initial GAVdesign in order to minimise these however for the purposes of thispaper, the modal analysis will now be presented to demonstratethe scope for control system design. It should also be noted thatonly inviscid aerodynamic results have been used for this study.Table 11 demonstrates the effect that each of the control effectorshas on each of the force and moment coefficients.

4.4. GAV modal analysis

In this section the dynamic modes of the GAV Z-wing areanalysed and compared to those of the EA500. Due to theasymmetry of the aircraft it does not exhibit the classical aircraftmodes; however, the modes have been named after the closestclassical mode, with their values listed in Table 12.

It can be seen that there are only two complex modes insteadof the usual three for conventional aircraft, and there is a highlevel of instability with two positive real, and one complex pairwith positive real parts. This is in stark contrast to the EA500modes which exhibit classical modes with a marginally unstableSpiral mode. Note that for the GAV Z-wing configuration themodes have been labelled using ‘’ because the GAV modes are notpure classical modes but are highly coupled between longitudinaland lateral directional motion. An example of this can be seenwith the ‘Short Period’ mode, the eigenvector of which is shownin Table 13. Note also that there are two real roots labelled ‘DutchRoll (1)’ and ‘Dutch Roll (2)’. Essentially these are two real; onestable, one unstable; both predominantly lateral-directional

Table 13GAV Z-wing ’Short Period’ eigenvector.

State Component

a �0.0170.1i

b 0.0470.04i

P �0.4670.39i

Q 0.6870.00i

R 0.370.22i

VT 0.0770.07i

j �0.0370.08i

y �0.0370.09i

GAV Z-wing eigenvalues.

Mode Eigenvalue

Short Period �2.176.6i

Phugoid 0.00270.087i

Dutch Roll (1) �0.65

Dutch Roll (2) 1.14

Roll Subsidence �5.0

Spiral 0.21

Table 14Eigenvector Element Specification.

Element Required effect of the state

0 No effect in the mode

1 Dominant in the mode

x Left unspecified: allows the unconstrained

influence of the element in the mode

Table 15GAV Z-wing specified eigenvectors for the classical

modes.

T.S. Richardson et al. / Progress in Aerospace Sciences 47 (2011) 647–659656

modes whose eigenvectors are most like those of the classicalDutch Roll mode although they also display longitudinal coupling.

The dominant component of the Short Period eigenvector isthe pitch rate term, which agrees with the classical mode;however, it can be seen that there is a great deal of couplingwith both the lateral and the directional terms. The roll ratecomponent is nearly the same magnitude as the pitch rate and theyaw rate component is more than half the size. This crosscoupling between longitudinal, lateral and directional motionsin the various modes would make it impossible to fly the GAVmanually without incorporating at a minimum a Stability Aug-mentation System (SAS). An example of an SAS generated inCEASIOM is given in Section 5.

Mode Eigenvalue

[a b p q r VT j y]

Short Period [x x 0 1 0 x x x ]

Phugoid [x x 0 x x 1 0 x ]

Dutch Roll [0 x 1 0 x x x x ]

Roll Subsidence [x x 1 0 0 x x x ]

Spiral [x x 1 0 x 0 x x ]

5. GAV stability augmentation

The open-loop response of the GAV Z-wing is unsuitable formanual flight due to inherent instability and the highly crosscoupled nature of the longitudinal, lateral and directional dynamics.In this section eigenstructure assignment (EA) is used to specifydesired eigenvalues and decouple the aircraft modes. eigenstructureassignment allows the control system designer to specify thelocations of the aircraft dynamic modes and to influence how thesemodes affect each of the aircraft states. For each of the desired modelocations a desired eigenvector can be created.

5.1. Eigenstructure assignment

The following is a short description of eigenstructure assign-ment as it has been implemented in the CEASIOM environment.For additional information, please see [7–10]. The linearisation ofa system where x and u are perturbations from the linearisationpoint can be written as

_x¼ AxþBu ð5:1Þ

If a state feedback scheme is considered then the input u canbe expressed in terms of the states x and an appropriate feedbackgain matrix K. This will results in the closed-loop system:

_x¼ AxþBKx¼ Aclx ð5:2Þ

Using this linearisation, the gain matrix can be calculatedusing a linear design method such as eigenstructure assignment[7–10]. Alternative methods are available within CEASIOM forcontrol system design such as H-infinity and LQR; however,eigenstructure assignment is used here as an example. Addressingthe eigenstructure directly allows the user to specify which statesto try and decouple, an ideal approach to the problem ofdecoupling the response of the GAV. The eigenvalues and eigen-vectors are related to the closed-loop matrix via

AclV ¼LV ð5:3Þ

where K is a matrix that has the closed-loop eigenvalues on theprincipal diagonal and the achievable closed-loop eigenvectorsare given in the modal matrix, V.

It is not possible to simply specify and achieve any set ofeigenvalues and eigenvectors—this is dependent on the number offeedback states that are available and the number of control inputs.The number of inputs tends to be much less than the number ofstates; hence it is usually only possible to define a desiredeigenvector which consists of the elements given in Table 14.These are then used to calculate a set of achievable eigenvectors, V.

The feedback gain matrix is calculated via Eq. (5.4) whosederivation is given in [9]:

K ¼ Z�1B UT

0 ðVL�AVÞV�1ð5:4Þ

where ZB and U0 are obtained via a QR decomposition of thecontrol matrix, B. Hence the parameters that are required in orderto calculate K are the state matrix A, the input matrix B (and henceZB and U0), desired eigenvalues K and the achievable eigenvectorsin the modal matrix V. In multi-degree-of-freedom systems withmultiple inputs, it is possible to use eigenstructure assignment toachieve not only desired pole placement, but also to shape theresponse of each mode and achieve, for example, decoupling oflongitudinal and lateral aircraft modes as required for the GAV.

Note that only a single trim point and gain calculation iscarried out here for the GAV. It is possible, however, for highlynonlinear systems to do this at a number of trim points and createa series of parameterised gain matrices. The required gains mayvary considerably over the state-space region of interest and soscheduling of the gain matrices may be necessary to maintain anacceptable closed-loop response.

In the presence of state variations, gain scheduling againstcoupled, rapidly changing system states introduces unwantedadditional dynamics or ‘hidden coupling terms’. Further informa-tion on gain scheduling for highly nonlinear systems can be canbe found in [10–14]. In the following section, eigenstructureassignment is used for a single trim point in order to decouplethe GAV response.

5.2. GAV eigenstructure assignment

Table 15 lists the desired eigenvectors used to design the SASfor the GAV Z-wing. The feedback controller generated by the EAalgorithm is a gain matrix dictating the effect that each state hason each of the inputs. The complexity of the feedback matrix forthe GAV was reduced by only using 4 control inputs: the throttle,the rudder, linked elevators with symmetric deflection, and linkedailerons with conventional opposite deflection.

The magnitude of the gains of the feedback controller indicatethe level of control effort required to achieve the desired level ofstability and control augmentation. Table 16 shows the resultinggains for the GAV calculated using eigenstructure assignmentwithin CEASIOM.

The majority of the gains given in Table 16 are low with somenotable exceptions. It is also clear that the vast majority of theelements within the gain matrix K are nonzero. This is asexpected given the highly coupled nature of the open-loop GAVdynamics and the coupled response that GAV control surfacesprovide.

T.S. Richardson et al. / Progress in Aerospace Sciences 47 (2011) 647–659 657

What can be seen from Table 16 and the control surfaceauthority presented previously in Table 11 is that the GAV lackssufficient yaw authority. Further work could be carried out at thispoint using CEASIOM in terms of providing additional controlpower through split ailerons and possibly thrust vectoring. Thiswould enable alternative solutions to be found with lower overallcontrol surface demands.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1000

-500

0

500

1000

Time (seconds)

p (d

eg/s

)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-200-100

0100200300400500600700

Time (seconds)

Phi

(deg

)

Fig. 19. Open-loop GAV roll ra

Table 17GAV Z-wing closed-loop Short Period eigenvector.

State Component

a 0.370.43i

b 70.01i

p 0

q 0.81

r 0

VT 0

j 0

y �0.270.2i

Table 16GAV Z-wing stability augmentation gain matrix K.

Input Gains

a b p q r VT j y

Ailerons �1.4 �2.0 �0.04 0.3 �0.5 0.0 0.04 �0.5

Elevators 3.2 3.9 0.1 �0.5 �0.1 0.0 �0.03 1.4

Rudder �1.5 1.1 0.0 �0.02 0.2 0.0 �0.02 0.07

Throttle �0.03 �8.7 �0.6 0.1 �8.9 0.03 �0.6 �0.3

This is a viable solution however, and the eigenvalues wereplaced as desired. Table 17 shows the resulting eigenvector forthe closed-loop Short Period mode. It can be seen that theresponse is almost completely decoupled from the lateral-direc-tional states, with the only nonzero value associated with theangle of sideslip. As mentioned previously, this response could beimproved further with additional directional control authority.

5.3. GAV simulations

Fig. 19 shows the open-loop response of the GAV to a 51/s rollrate perturbation. This response exceeds the data limits; however,it is clearly unstable and although not shown here, highly coupledinvolving both longitudinal and lateral-directional states. This tiesin directly with the example eigenvector shown in Table 13.

Fig. 20 shows the closed-loop response of the GAV to a 51/s rollrate perturbation. In this case the aircraft is well behaved anddemonstrated a well damped response in terms of the roll rate,settling out to a small nonzero roll angle. Associated with thissimulation are the longitudinal states shown in Fig. 21. With theexception of a small increase in VT the remaining longitudinalstates remain relatively constant, demonstrating that the multi-variable SAS employed has successfully decoupled the system, asindicated by the eigenvector given Table 17.

6. Conclusions

The objective of the work presented in this paper is todemonstrate how the CEASIOM environment can be applied toboth conventional and unconventional aircraft designs. The mod-ules available within CEASIOM allow aircraft concepts to be

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-400

-300

-200

-100

0

100

200

300

400

Time (seconds)

r (de

g/s)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-100

-50

0

50

100

Time (seconds)

Bet

a (d

eg)

te perturbation response.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-10

-5

0

5

10

Time (seconds)

p (d

eg/s

)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-10

-5

0

5

10

Time (seconds)

Phi

(deg

)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-10

-5

0

5

10

Time (seconds)

Bet

a (d

eg)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-10

-5

0

5

10

Time (seconds)

r (de

g/s)

Fig. 20. Lateral-directional closed-loop GAV roll rate perturbation response.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-10

-5

0

5

10

Time (seconds)

Alp

ha (d

eg)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-10

-5

0

5

10

Time (seconds)

q (d

eg/s

)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5150

200

250

Time (seconds)

Vt (

m/s

)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-10

-5

0

5

10

Time (seconds)

Thet

a (d

eg)

Fig. 21. Longitudinal closed-loop GAV roll rate perturbation response.

T.S. Richardson et al. / Progress in Aerospace Sciences 47 (2011) 647–659658

T.S. Richardson et al. / Progress in Aerospace Sciences 47 (2011) 647–659 659

created and rapidly taken through to simulation and analysis.Furthermore multivariable control methods can be applied inorder to augment the open-loop aircraft behaviour.

Analysis of the Eclipse Aviation EA500 has shown that theweights and balance and aerodynamic predictions from CEASOIMmodules are sufficiently accurate to provide useful feedback onthe response of classical aircraft concepts. Sample results havealso been given for the aircraft modal analysis, taken from thesuite of metrics available within CEASIOM.

A novel asymmetric aircraft configuration has been presentedwith initial trimmed results indicating that the proposed perfor-mance benefits have not been realised. It should be noted that thepurpose of including these results is to demonstrate the capabilitythat CEASIOM has for modelling asymmetric aircraft. It is possibleif this initial GAV design were revisited that the potentialperformance benefits could be realised.

Linear analysis of the asymmetric GAV demonstrated a highdegree of coupling between the longitudinal and lateral-direc-tional aircraft dynamics. This is clearly highly undesirable andcombined with the associated positive real eigenvalues requiredthe application of a Stability Augmentation System. Whilst thereare several control system design methods available withinCEASIOM, one, eigenstructure assignment was selected and amultivariable SAS created in order to successfully decouple thelongitudinal and lateral-directional modes.

The CEASIOM environment has therefore been shown to be notonly flexible enough to deal with highly unconventional asym-metric aircraft, but results have been shown that demonstratethat with these tools it is now possible to bring stability analysisand control system design earlier into the aircraft conceptualdesign process.

Acknowledgements

The financial support by the European Commission throughco-funding of the FP6 project SimSAC is gratefully acknowledged.

SimSAC was supported under contract number AST5-CT-2006-030838. This paper is edited and reprinted with permission of theAmerican Institute of Aeronautics and Astronautics [15].

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[6] Martin J. Further development and testing of CEASIOM for weight, balanceand structural design of aircraft. Master thesis, Royal Institute of Technology(KTH), Stockholm, March 2010.

[7] Liu GP, Patton RJ. Eigenstructure assignment for control system design. JohnWiley and Sons; 1998.

[8] Andry AN, Shapiro EY, Chung JC. Eigenstructure assignment of linear systems.IEEE Transactions on Aerospace and Electronic Systems 1983;19(5):711–28.

[9] Sobel KM, Shapiro EY, Andry AN. Eigenstructure assignment. InternationalJournal of Control 1994;59(1):13–37.

[10] Jones CDC. Dynamic gain-scheduled control of a nonlinear UCAV model. PhDthesis. University of Bristol, 2006.

[11] Richardson T, Davison P, Lowenberg M, di Bernardo M. Control of nonlinearaircraft models using dynamic state-feedback gain scheduling. NumberAIAA-2003-5503. AIAA Paper, August 2003.

[12] Jones CDC, Richardson TS, Lowenberg MH. Dynamic gain-scheduled controlof the ICE 101-TV. The Aeronautical Journal, December 2005.

[13] Jones CDC, Richardson TS, Lowenberg MH. Dynamic state-feedback gainscheduled control of the ICE 101-TV. AIAA-2004-4754, 2004.

[14] Jones CDC, Lowenberg MH, Richardson TS. Tailored dynamic gain-scheduledcontrol. Journal of Guidance, Control, and Dynamics 2006;29(6):1271–81.

[15] McFarlane C, Richardson TS, Ronch A, Badcock K. Comparison of conventionaland asymmetric aircraft configurations using CEASIOM. AIAA-2010-8243,AIAA atmospheric flight mechanics conference, Toronto, Ontario, August 2–5,2010.