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TOWARDS COMPUTATIONAL FLIGHT DYNAMICS OF APASSENGER JET AIRCRAFT

Cristofaro, M.∗ , Wang, Y.∗∗ , Da Ronch, A.∗∗University of Southampton, Southampton, S017 1BJ, United Kingdom∗∗China Academy of Aerospace Aerodynamics, Beijing, 100074, China

Keywords: aerodynamic tables, flight simulation, aircraft design, computational fluid dynamics.

Abstract

This paper investigates the efficient generationof an aerodynamic database for flight simulationof a regional jet aircraft. A hierarchy of aero-dynamic models is used, from semi–empiricalapproaches up to computational fluid dynamicsanalyses. The prediction tools are first validatedat both low and high speeds against wind tun-nel measurements. To reduce the number andcosts of computational fluid dynamics calcula-tions, Kriging interpolation is exploited to gen-erate the aerodynamic tables. Data fusion al-lows combining different aerodynamic sourcesinto one single database that is more accuratethan each single database. The longitudinal andlateral handling qualities are first investigated forthe regional jet aircraft. Then, the impact of ge-ometry changes on the aircraft dynamic charac-teristics is investigated. It is found that improvedaircraft characteristics could be achieved for rel-atively small changes relative to the baseline ge-ometry.

1 Introduction

The aircraft design process is very expensive andthe largest part of the life–cycle cost is directlydependent on decisions taken during the concep-tual design phase. Obtaining accurate and reli-able information about aircraft stability and per-formance characteristics during the first steps ofthe design is then highly critical. The engineeringtools for aircraft design are generally based onempirical handbook methods or linear fluid me-

chanics hypothesis [1]. These provide low–costaerodynamic data predictions reliable for benignflow conditions, e.g. ruling out the most criticalpoints of the flight envelope. The data points atthe borders of the flight envelope do not considerthe nonlinear flight dynamic behaviour of the air-craft. As discussed in Ref. [2], a solution maybe found in using computational fluid dynam-ics (CFD) techniques in the conceptual designphase in order to predict the nonlinear effects.However the computation of the complete aero-dynamic database over the whole flight envelopewith CFD is very expensive and requires a longcomputation time. High–fidelity simulations arestill expensive despite today high performancecomputing facilities are available Ref. [3]. In air-craft design where the geometry changes, the useof CFD is prohibitively expensive and unrealisticfor computing the entire aerodynamic database.The computation of dynamic derivatives requiresan unsteady time accurate CFD analysis, whichneeds a very long computational time [4, 5, 6].Hence, acceleration techniques based on CFD al-lows retain the fidelity at a reduced cost. An ef-ficient way to produce a good full aerodynamicdatabase with a fewer computations is to usea Kriging–based surrogate model and fusion oftwo available databases as described in Ref. [7].In the following work these methods are effi-ciently used to study the effect of some design pa-rameters over aircraft stability and performancecharacteristics. For every considered configura-tion a full–order CFD aerodynamic model wascomputed with a few computations, maintainingthe high–fidelity characteristics of CFD over the

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CRISTOFARO, WANG, DA RONCH

whole flight envelope. The handling qualitiesare then evaluated and the influence of the newconfiguration design parameters over the perfor-mances and stability are presented. The papercontinues in Sec. 2 where the passenger aircraftmodel is presented. Section 3 discusses the gen-eration of the aerodynamic tables, presenting thedifferences between the results obtained from dif-ferent methods and the acceleration techniquesthat were adopted. Then the results of a trim anal-ysis and the handling qualities, both longitudi-nal and lateral–directional, are presented for themodel and for some modified configurations inSec. 4. Finally, conclusions are given in Sec. 5.

2 Passenger jet aircraft model

The aircraft model used in this work is a concep-tual design of a regional jet originally designedusing traditional hand–book methods. The air-craft model belongs to the 100–120 passengersclass. The existing similar models consideredduring the design process were the new Bom-bardier CS100, the Embraer E–190, the Boe-ing 737–600 and the Airbus A318–100. Table 1presents the mission specifications and the maindimensions 1.

Table 1 Mission specifications and dimensions ofthe regional jet aircraft

Parameter ValueRange 2,600 kmCruise Mach 0.78Cruise altitude 10,668–11,887 mNumber of engines 2Number of passengers 110Landing field length 1,450 mTake off field length 1,550 mLong. ref. length 3.6 mLat. ref. length 30 mWing area 105 m2

For flight simulation, a model of the aerody-

1The presented model that is stored in a CEASIOM–compatible format is open source and can be requested toAndrea Da Ronch [email protected].

namic forces and moments is required through-out the entire flight envelope. Figure 1 presentsthe model in scale 1:23 used in the German–Dutch Wind Tunnels (DNW) at Reynolds number4 ·106.

Fig. 1 Wind tunnel model of the regional jet air-craft in scale 1:23

Fig. 2 Surface grid with the control surfaces inred and pressure coefficient distribution resultingfrom Euler solution at M = 0.78 and α = 3 deg

The analysis presented in this work is ob-tained using the Computerised Environment forAircraft Synthesis and Integrated OptimisationMethods (CEASIOM 2) software. Inside CEA-SIOM, AcBuilder is a customized geometry con-struction system to define the aircraft configura-tion. It requires only ∼100 geometrical parame-ters because the design is still considered in theconceptual phase. With a simplified set of pa-rameters, the CEASIOM model approximates thenose geometry and the tail. Once the geometry is

2http://www.ceasiom.com/ [retrieved 14 July,2014]

2

mailto:[email protected]

http://www.ceasiom.com/

Towards Computational Flight Dynamics of a Passenger Jet Aircraft

built, an automated grid generator is used to cre-ate within few seconds an initial mesh for CFDcalculations. The Surface Modeller (SUMO 3)was used. SUMO is a graphical tool for a rapidaircraft geometry creation coupled to high effi-cient unstructured surface and volume grid gen-erators. It takes as input the AcBuilder basic pa-rameterization and uses it to produce surface andvolume grids for Euler CFD simulations. Thesurface unstructured grid with the control sur-faces and the Euler CFD result about the pressurecoefficient distribution for a Mach number (M) of0.78 and an angle of attack (α) of 3 deg is shownin Fig. 2. This reference geometry is referred asbaseline geometry in the remaining of the paper.

3 Generation of Aerodynamic Tables

In this work the stability characteristics are in-vestigated. Aerodynamic tables are needed tostudy the aircraft static and dynamic properties.The following sections illustrate the models usedfor the aerodynamic predictions, their validationagainst wind tunnel measurements, and the ap-proaches used to reduce the number of CFD cal-culations to a manageable computational cost.

3.1 Validation

The methods used for the aerodynamic predic-tions are an empirical method (Stability and Con-trol Digital Data Compendium – Datcom [8]),a linear panel method based on Vortex LatticeMethod (VLM) (Tornado 4) and an unstructuredCFD solver (Edge 5).

The lift, drag and pitch moment coefficients(CL, CD, and Cm) with the angle of attack atMach number of 0.5 are shown in Fig. 3. Thegood agreement with wind tunnel data found forDATCOM is not unexpected since it relies on adatabase of similar aircraft configurations to theone presented herein. Tornado provides the cor-rect global trends but the quantitative differences

3http://www.larosterna.com/sumo.html[retrieved 14 July, 2014]

4http://www.redhammer.se/tornado/[retrieved 14 July, 2014]

5http://www.foi.se/edge/ [retrieved 14 July,2014]

are due to the limiting underlying assumptions(linear panel method) and the neglect of non–lifting surfaces that contribute significantly to thepitch moment. The flow solver Edge is used inEuler mode in this work. For this reason it doesnot consider the viscous term and so the result-ing drag values appear smaller than the coeffi-cients computed during the wind tunnel test. Forhigh angles of attack Edge shows the most sim-ilar behaviour to the wind tunnel data. At thecruise Mach number of 0.78, similar consider-ations were found, with Edge showing a bettercorrelation to experimental data. The results arenot shown for brevity.

3.2 Aerodynamic Tables

The aerodynamic table is divided in static, con-trol and dynamic derivatives. The static partof the table is based on a (α,M,β) three–dimensional domain. The α values were consid-ered between -5 and 12 deg with a 1 deg step,M between 0.1 and 0.9 with 0.1 step and β val-ues between -10 and 10 deg with a 1 deg step.The total number of static flight points is 3,402.The control derivatives part of the table considersthe elevator, rudder and ailerons deflections sep-arately. The elevator deflection was studied forvalues between -20 and 20 deg with 5 deg stepsand the rudder and ailerons deflections for valuesbetween -15 and 15 deg with 5 deg steps. Aboutthe dynamic derivatives, the yaw, pitch and rollangular velocities are considered. They are takenfrom -80 to 80 deg/s with a step of 20 deg/s. Ev-ery considered control surface deflection and an-gular speed was studied singularly for any com-bination of α,M, so adding a total of 7,128 moreentries to the table. The total size of the aero-dynamic table was 10,530 points. The referencepoint considered for computing the moments andthe angular velocities was the approximated cen-tre of gravity position.

The CFD was not used to compute the dy-namic derivatives because of the very high costfor computing an unsteady time accurate CFD so-lution. Datcom results were used for both thecontrol and dynamic derivatives. Furthermore,for any geometry modification a new table needs

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http://www.larosterna.com/sumo.html

http://www.redhammer.se/tornado/

http://www.foi.se/edge/


α [deg]

CL

5 0 5 10

0.4

0

0.4

0.8

1.2

Datcom

Tornado

Edge

WT data

α [deg]

CD

5 0 5 10

0

0.05

0.1

0.15

0.2

Datcom

Tornado

Edge

WT Data

α [deg]

Cm

5 0 5 100.6

0.3

0

0.3

0.6

Datcom

Tornado

Edge

WT Data

Fig. 3 Lift, drag and pitch moment coefficientsat Mach number 0.5 and Reynolds number 2.2 ·107; the reference point is taken at the centre ofgravity

to be generated, and so an efficient method to re-duce the computational time is highly required.In order to fill in the aerodynamic table, the datawere taken from the three aerodynamic modelsand experimental results. Figure 4 shows theflight states that were computed for each aerody-namic model. The semi–empirical method Dat-com was used all over the domain to provide aquick overview of the aerodynamic data sinceit has good accuracy for traditional aircraft andvery low computational cost. Tornado was usedto compute the results for Mach number from 0.1to 0.5, which is the appropriate range for the vor-tex lattice method. Tornado computational costis relative low and it does not consider any com-pressibility correction. Edge was used for higherMach numbers, from 0.5 to 0.9, in order to cap-ture the nonlinear aerodynamic characteristics.For Mach numbers from 0.1 to 0.3 only 5 sam-ples from Edge were computed on the edges ofthe domain to calibrate the low fidelity results.For all the combinations of these parameters, theresults of different sideslip angle (β) were inves-tigated for angles of 0, 5 and 10 deg apart fromDatcom that does not provide a sideslip angle in-put option.

Fig. 4 Samples distribution over the α−M domain

Full tables were obtained for both Datcomand Tornado. About the table computed usingCFD, Kriging interpolation and data fusion ap-proaches were used to reduce the cost to a man-

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ageable requirement. A total of 97 non–viscousCFD calculations using Edge were performed inthe (α,M,β) parameters space.

3.3 Kriging Interpolation

Kriging interpolation is an interpolation methodfor nonlinear and multi–dimensional determinis-tic functions. In Ref. [9, 10] the Kriging inter-polation is efficiently used to reduce the compu-tational cost for generating a full aerodynamicmodel. Once the Kriging model is created, itbecomes a computationally cheap model for pre-diction of the function at untried locations. Theavailable samples that were computed by Edgecovered Mach numbers from 0.5 to 0.9, anglesof attack from -5 to 12 deg and beta of 0, 5and 10 deg. In Fig. 5 the pitching moment re-sulting surface in the (α,M) domain, obtainedwith the Kriging interpolation of the Edge datais compared with the experimental results fromthe wind tunnel testing. The linear trend showsa smaller slope for the wind tunnel results andfor high Mach number the Edge pitch momentslope is much higher. This nonlinearity doesnot appear from the wind tunnel tests, for whichthe pitch moment slope is very similar for everyMach number. Only the pitch moment coeffi-cient results are presented for brevity. The Krig-ing interpolating surface have the same trendswith wind tunnel results for all the computedforce and moment coefficients. The lift coeffi-cient at low Mach numbers is very close to ex-perimental results from every angle of attack.Close to the transonic field, for high Mach num-bers, the values of lift coefficient are higher thanthe wind tunnel results. This also results in thedifferences between pitch moment coefficientson Cm Kriging surface and experimental results.About the drag coefficient predicted by Krigingmodel, it shows a good correlation with exper-iment results. The values are lower than windtunnel because the solutions are achieved solvingthe Euler equations. In conclusion the Krigingmodel shows very efficient prediction capabilityand could considerably reduce the computationalcost. In this study only the 5.45% of the totalnumber of flight states of the full table were com-

puted by CFD. This method extends a few calcu-lations fidelity to the entire flight envelope at areduced cost, enabling the use of CFD for aero-dynamic predictions. Hence, the aerodynamictable accuracy is improved for a more accurateflight simulation. Furthermore Kriging interpola-tion allows studying different configurations witha good level of accuracy and without an exces-sively high computational cost as shown in thecontinuation of this study.

Fig. 5 Dependency of pitch moment coefficienton angle of attack and Mach number; the surfacerepresents the Kriging interpolation of Edge sam-ples (red cubes)

3.4 Data Fusion

The aerodynamic force and moment coefficientscan be obtained from test or computed by us-ing various methods predictions. Data fusion cancombine different aerodynamic predictions intoa more accurate database. Considering the avail-able data coming from the empirical method Dat-com (cheap and low–fidelity) and a CFD solverEdge (expensive and high–fidelity), it is possi-ble to fuse them considering the new functionwith the same trend as the cheap samples butwith quantitative values given by the expensivesamples. Usually the cheap estimates are moredensely distributed over the domain compared tothe expensive ones. The method extensively em-ploys the Kriging interpolation function, and it

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is based on the creation of an interpolated func-tion whose domain is increased by one dimensionwith the values of the cheap computation at theexpensive locations. The function is then evalu-ated over the entire domain as explained in Ref-erence [7]. About this study Datcom was con-sidered to be the low fidelity method, which wasused to compute all the domain points. Expen-sive high fidelity samples were taken from Edge,and they were densely computed only in tran-sonic field. Furthermore 5 samples were takenon the border at low speed (Mach 0.1) to avoidextrapolation problems. The data fusion resultsabout the pitch moment are shown in Fig. 6. The

Fig. 6 Dependency of pitch moment coefficienton angle of attack and Mach number; the surfacerepresents data fusion between Datcom and Edge

trend of data fusion model was influenced by theDatcom samples, but the values were correctedby the Edge samples. The data fusion modelexhibits good capabilities at high Mach numberand high angle of attack. Nonlinear aerodynamiceffects can be still seen for the contributions ofEdge samples. Data fusion, combined with Krig-ing interpolation, allows computing a full aerody-namic model with an overall low computationalcost. The contribution of Datcom is not very ev-ident because of the linear trend, but if a nonlin-earity appeared in it, it would be transposed inthe fused data, adding important information tothe new model. During this study different fi-

delity aerodynamic methods, Kriging interpola-tions and data fusion models were used here to in-vestigate their impacts on aircraft trim properties.The models that will be used in the following sec-tion are shown in Table 2. In the next section thetrim and handling qualities resulting from the ta-bles are compared. The proximity of the Krig-ing interpolation of the Edge samples databasecompared to the one using the wind tunnel datais assessed. During the conceptual design phasewind tunnel tests are usually too expensive to beintegrated into the design cycle and so the T3database can be a cheaper but well representativealternative.

Table 2 Generated full tables and reference numbers

Source of data TableDATCOM T1Tornado T2Edge with Kriging interpolation T3Data fusion of T3 and wind tunnel data T4

4 Results

4.1 Baseline Geometry

The equations of motion, governing the static anddynamic behaviour of the aircraft, are composedby the aerodynamic forces and moments actingon the aircraft, geometrical and mass features, thecommand variables, notably throttle and elevator,rudder and aileron deflections and the state vari-ables [11].

During the conceptual design phase, usuallythere is no accurate mass and inertia propertiesand so some approximated empirical methods areadopted. In this paper, weight and balance datawere predicted by Howe’s empirical method inte-grated in the CEASIOM Weight & Balance mod-ule. It is important to consider that the mass prop-erties heavily influence the trim and stability re-sults, and so these must be only considered astrend indications. Table 3 shows the main massand inertia values of the baseline configuration.The resulting maximum take–off weight is sim-

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ilar to the values of the existing aircraft used asreference for this work.

Table 3 Baseline mass and inertia computed prop-erties

Parameter ValueMTOW 4.97·104 kgCG location (16.13, 0, 0.0236) mIxx 1.11·106 kg·m2

Iyy 1.90·106 kg·m2

Izz 2.87·106 kg·m2

Ixz 6.72·104 kg·m2

Ixy, Iyz 0 kg·m2

4.1.1 Trim and Stability

In order to longitudinally trim the aircraft in thewhole flight envelope, e.g. for different valuesof angle of attack, the traditional way to obtainthat is by a variation in pitching moment valuesby regulating the incidence angle of the horizon-tal tail plane. This may be achieved by use of thecontrol surface or by rotating the whole horizon-tal tail.

The Mach number was fixed at 0.78 and theflight altitude was varied between 10,668 and11,887 m, which is the step cruise height. Fig-ure 7 shows the trim angles of attack and de-flection of elevator, respectively, at different alti-tudes during the cruise mission phase. The aero-dynamic model considering the wind tunnel ex-perimental data (T4), which is expected to havethe highest fidelity, is taken as reference solutionfor all methods. Tornado model (T2) is the onlyone with a positive elevator deflection for trim-ming the aircraft. Datcom table (T1) identifies alarger slope of the trim angle of attack increas-ing the altitude. The results obtained from theEdge database (T3) are very similar to the valuescomputed with wind tunnel data (T4), obtainingan almost identical trimming angle of attack anda slightly smaller elevator deflection but with thesame trend.

h [ft]

α [

de

g]

35000 36000 37000 38000 39000

2

3

4

T1

T2

T3

T4

(a) Trim angle of attack

h [ft]

Ele

va

tor

[de

g]

35000 36000 37000 38000 39000

4

2

0

2

4

T1

T2

T3

T4

(b) Trim elevator deflection

Fig. 7 Trim conditions at different cruise alti-tudes; see Table 2 for tables definition

4.1.2 Longitudinal handling qualities

Aircraft handling qualities at Mach cruise of 0.78and altitude of 11,887 m were evaluated using theresulting aerodynamic force and moment coef-ficients given by different aerodynamic models.Figures 8 and 9 show the phugoid and short pe-riod characteristics, respectively, according to In-ternational Civil Aviation Organization (ICAO)criteria. About the phugoid longitudinal dynamicmode, the models show similar results, with thelowest rating and the farthest being Tornado (witha smaller damping).

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2 ζ ωn [rad/s]

Pe

rio

d, T

[s

]

0.015 0 0.015 0.030

20

40

60

80

100

T1

T2

T3

T4

SATISFACTORYfor normal operation

UNACCEPTABLE

ACCEPTABLEfor emergency conditions

Fig. 8 Phugoid characteristics according toICAO criteria at Mach number of 0.78 and alti-tude of 11,887 m; see Table 2 for definition

The short period mode for the 4 consideredmethods has almost the same period, but differenttimes to half amplitude. The worst rating case isTornado and the best is Datcom, with the othertwo in the middle. According to ICAO, both thephugoid and short period are acceptable for allthe tables.

Period, T [s]

Tim

e t

o h

alf

am

plitu

de

[s

]

0 4 80

0.5

1

1.5

2

T1

T2

T3

T4


UNACCEPTABLE

Pilot rating 6.5


Pilot rating 3.5

Fig. 9 Short period characteristics according toICAO criteria at Mach number of 0.78 and alti-tude of 11,887 m; see Table 2 for definition

As for trim, linear panel method is sus-pected in transonic regime, unless corrections are

made. However, corrections require experienceand database of existing aircraft and are inade-quate to support engineers to design innovativeconfigurations.

4.1.3 Lateral–directional handling qualities

As previously done with the longitudinal han-dling qualities of aircraft, in this section thelateral–directional handling qualities are inves-tigated. The flight conditions are Mach cruiseof 0.78 and altitude of 11,887 m. Figures 10and 11 show the dutch roll and spiral modes char-acteristics, respectively, according to the UnitedStates military standards MIL–F–8785C criteriaat Phase B. The dutch roll mode shows differ-ent results for every considered table. The lessdamped mode is obtained using Edge database(T3) that may be caused by the neglected viscos-ity term in the fluid dynamic equations. The Tor-nado database (T2) is the only one to present anunstable nonconservative behaviour in damping.The natural frequency does not change consis-tently. According to MIL–F–8785C, the resultsare acceptable for all the tables.

Undamped natural frequency [rad/s]

Da

mp

ing

ra

tio

[]

0 1 2 30.05

0

0.05

0.1

0.15

0.2

T1

T2

T3

T4

ζ=0

Level 1ζ ω

n=0.15

Level 2ζ ω

n=0.05

Min. damp.Level 2

ωn=

0.4

Min. damp.Level 1

Level 3

Fig. 10 Dutch roll characteristics according toMIL–F–8785C criteria at Phase B at Mach num-ber of 0.78 and altitude of 11,887 m; see Table 2for definition

For the spiral mode, Tornado (T2) is the onlyone to lead to an unstable mode. This means thatfor Tornado the static directional stability has a

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relatively higher level compared to lateral stabil-ity and dihedral effect [11].

TAS [m/s]

T2

[s

]

230 2326000

4000

2000

0

2000

T1

T2

T3

T4Level 1

Stable

Fig. 11 Spiral characteristics according to MIL–F–8785C criteria at Phase B at Mach number of0.78 and altitude of 11,887 m; see Table 2 fordefinition

The roll characteristics according to Cooper-Harper criterion are then showed in Fig. 12. Ac-cording to Cooper–Harper criterion the rating ofthe roll mode characteristics are good (Cooper–Harper pilot assessment rating under 3.5). All theresults are almost coincident apart from Tornado(T2).

The presented trim and handling qualitiesanalysis show that the Kriging interpolation ofthe Edge computed samples (T3) are a good ap-proximation of the table based on the wind tun-nel test data (T4). The trend is very similar, andthe off–set is always small. For some analysis,e.g. short period or phugoid mode, the result-ing values are almost identical. For this reasonthe table obtained with Kriging interpolation ofthe CFD samples can be considered a good alter-native to wind tunnel tests during the conceptualdesign phase.

4.2 New Wing Geometry

Having investigated the stability characteristicsof the baseline geometry and the influence ofaerodynamic models on the predicted static anddynamic behaviour, the next step is to explore

Fig. 12 Roll characteristics according to Cooper–Harper criterion at Mach number of 0.78 and al-titude of 11,887 m; see Table 2 for definition

whether aircraft characteristics may be improvedby a better geometry design. For every new con-figuration a new aerodynamic table needs to begenerated With the tools and methods describedabove, the cost of this task is manageable evenusing CFD as source of the aerodynamic data.Using Kriging interpolation and data fusion waspossible to compute a high–fidelity aerodynamicfull–database with a few high–fidelity computa-tion for every case. To study the geometry im-pact on aerodynamics and handling qualities, 8configurations shown in Table 4 were consideredstarting from the baseline. The parameters in-

Table 4 Configurations with different leadingedge sweep angle (ΛLE) and aspect ratio (AR)

Configuration ΛLE [deg] AR [–]Baseline 27 9.4Configuration 1 20 9.0Configuration 2 20 9.4Configuration 3 20 10.0Configuration 4 27 9.0Configuration 5 27 10.0Configuration 6 33 9.0Configuration 7 33 9.4Configuration 8 33 10.0

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clude leading edge sweep angle (ΛLE) and aspectratio (AR). For every configuration the mass andinertia properties were computed with Howe’smethod and a new aerodynamic table was com-puted. Since the differences between new con-figurations and baseline are not large, the sameflow topology assumption was used here. Only18 CFD samples at the border of the flight enve-lope were computed for every new configuration.Using data fusion between the baseline configu-ration table obtained with the Kriging interpola-tion of the Edge data (T3), and the new samplesat the border, a full table was computed for everynew considered configuration.

The aim of such modifications was to simu-late a real design cycle, where different geome-tries are screened to find the best one. Figure 13show the configuration geometry differences be-tween baseline and Configuration 1 and Configu-ration 8 respectively.

Fig. 13 Configurations 1 and 8 geometry com-pared with the baseline

4.2.1 Aerodynamic characteristics

The considered databases are now based onthe Edge predictions for all the configurations.About the baseline the table is generated by usingKriging interpolation of the 97 computed sam-ples (T3), while for the new configurations it isgenerated by data fusion between the baseline ta-ble (T3) and the 18 samples computed for each

geometry. Since all the results are located be-tween the values obtained for Configuration 1and 8, in this section only the results of thesetwo configurations are shown and compared withthe baseline. Figure 14 shows the pitch momentcoefficient trends comparison between baselineand new configurations. The lift coefficient, dragcoefficient and pitch moment coefficient of newconfigurations are close to the baseline results.The most influencing parameter is the sweep an-gle, increasing it the pitching moment decreasesat lower angle of attack and increases faster whenclose to the stall.

α [deg]

Cm

5 0 5 100.6

0.3

0

0.3

0.6

Baseline

Config 1

Config 8

Increasing ΛIncreasing Λ

Fig. 14 Pitching moment coefficient comparisonat Mach number of 0.78 and altitude of 11,887m; see Table 4 for definition; arrows indicate in-creasing values of wing sweep angle

4.2.2 Trim and Handling Qualities

After computing a full–order aerodynamic modelfor all the configurations with the aerodynamictables previously presented, it was possible tocarry out an analysis on the impact of the mod-ified design parameters over the handling quali-ties.

The trim angle of attack and elevator deflec-tion results at step cruise stage for all the config-urations and baseline are shown in Fig. 15. Themost influencing parameter over the trim condi-tions is the sweep angle. Increasing it with re-spect to the baseline configuration, both the an-

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gle of attack and elevator deflection to trim theaircraft increase.

h [ft]

α [

de

g]

35000 36000 37000 38000 39000

2

3

4

Baseline

Config 1

Config 8

Increasing Λ

(a) Trim angle of attack

h [ft]

Ele

va

tor

[de

g]

35000 36000 37000 38000 39000

6

4

2

0

Baseline

Config 1

Config 8

Increasing Λ

(b) Trim elevator deflection

Fig. 15 Trim conditions at different cruise alti-tudes; see Table 4 for definition; arrows indicateincreasing values of wing sweep angle

For the 8 configurations presented in Table 4,the phugoid characteristics do not change consid-erably with respect to the baseline configuration.The period T is 90 ± 2 seconds and the dampingratio 2ζωs is 0.045 ± 0.01 rad/s. The short pe-riod characteristics improve to some extent whenincreasing the sweep angle (ΛLE). The trendof short period characteristics between baselineand 8 configurations are shown in Fig. 16. In-creasing the sweep angle, the short period mode

shows better characteristics increasing the timeto half amplitude. At the same time the angleof attack and elevator deflection to trim the air-craft increase in module, causing an higher drag.So increasing the baseline sweep angle seems tolead to better handling qualities but decreases theaerodynamic efficiency.

Period, T [s]

Tim

e t

o h

alf

am

plitu

de

[s

]

0 4 80

0.5

1

1.5

2

Baseline


UNACCEPTABLE

Pilot rating 6.5


Pilot rating 3.5

Increasing Λ

Fig. 16 Short period characteristics according toICAO criteria at Mach number of 0.78 and alti-tude of 11,887 m; arrows indicate increasing val-ues of wing sweep angle

4.3 New Horizontal Tail Geometry

Other four configurations were created modify-ing the horizontal tail. The difference is the hor-izontal tail area (Sht) and position on the fuse-lage (xht). The horizontal tail of configuration11 was moved forward by 3%, while configura-tion 12 was moved backward by the same value.The horizontal tail area of configuration 13 wasincreased by 10%, while configuration 14 de-creased by the same value. Table 5 shows theposition and area of horizontal tail for these fourconfigurations compared to the baseline. Thevalue of the horizontal tail position in table wasdivided by the length of fuselage (l f us). Data fu-sion was also used to get the aerodynamic dataand Edge Euler solver was used to compute addi-tional data for these four configurations.

The phugoid characteristics do not changemuch by comparing with the baseline. The pe-

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Table 5 Configuration with different horizontal tailConfiguration xht/l f us [–] Sht [m2]Baseline 0.8364 23.78Configuration 11 0.8664 23.78Configuration 12 0.8064 23.78Configuration 13 0.8364 26.16Configuration 14 0.8364 21.40

riod T is 89.5 ± 1.5 seconds and the damp-ing ratio 2ζωs is 0.049 ± 0.025 rad/s. Theshort period characteristics were improved by in-creasing the horizontal tail dimensional volumexht Sht . The trend of short period characteristicsbetween baseline and 8 configurations are shownin Fig. 17.

Period, T [s]

Tim

e t

o h

alf

am

plitu

de

[s

]

0 4 80

0.5

1

1.5

2

Baseline


UNACCEPTABLE

Pilot rating 6.5


Pilot rating 3.5

Increasing xht

Sht

Fig. 17 Short period characteristics according toICAO criteria at Mach number of 0.78 and alti-tude of 11,887 m; arrows indicate increasing val-ues of horizontal tail volume

As for the wing sweep angle analysis, thesame considerations may be done for the hori-zontal tail position. Increasing the horizontal tailvolume, the phugoid mode increases the time tohalf amplitude but a longer fuselage or a biggerhorizontal tail cause an higher drag. So increas-ing the baseline horizontal tail surface or posi-tion, better handling qualities were obtained butaerodynamic efficiency was reduced.

5 Conclusions

The performance and stability characteristics ofa regional jet design are presented. The base-line configuration is studied with different aero-dynamic models. Datcom results are very closeto computational fluid dynamics (CFD) and windtunnel experimental data, underlining the effec-tiveness of the empirical method Datcom for atraditional configuration. Some differences werefound between the vortex lattice method Tornadobecause of linear assumptions. The CFD methodEdge is the only one to capture the nonlinearityobserved during the wind tunnel tests. The stallangles of attack predicted by Edge and measuredin the wind tunnel are very similar but the CFDcomputation obtained a smaller effect from thenonlinear aerodynamics. The Kriging and datafusion methods are used to fill the aerodynamictables with a reduced computational cost. Thegenerated aerodynamic models are then com-pared and performance and stability character-istics computed. Among the computed models,Tornado is the only one to predict a positive ele-vator deflection to trim the aircraft during cruiseand an unstable behaviour for the spiral mode.The impact of geometry changes on the aircraftdynamic characteristics is then investigated. Thewing sweep angle is found to have a larger in-fluence than the wing aspect ratio on the perfor-mance and stability characteristics. Increasingthe wing sweep leads to a higher angle of attackand a less negative elevator deflection to trim theaircraft. Furthermore a more damped short pe-riod mode is obtained for higher sweep angle ofthe wing. The short period mode is influenced bythe horizontal tail size and position. A higher tailvolume coefficient causes a more damped shortperiod.

The future work will include the applicationof the presented framework in an optimizationenvironment to refine the aircraft geometry usinghigher fidelity aerodynamic tools than currentlyused in industrial practice and demonstrate thatCFD techniques can be used in a routine mannerfor aircraft design.

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6 Acknowledgment

The authors are grateful for the computing re-sources provided by the University of Southamp-ton. Marco Cristofaro thanks Politecnico diTorino for the exchange period at the Universityof Southampton. Yongzhi Wang acknowledgesthe financial support provided by China Scholar-ship Council (CSC).

References

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7 Contact Author Email Address

Cristofaro, M. [email protected], Y. [email protected] Ronch, A. [email protected]

Copyright Statement

The authors confirm that they, and/or their company or or-ganization, hold copyright on all of the original materialincluded in this paper. The authors also confirm that theyhave obtained permission, from the copyright holder of anythird party material included in this paper, to publish it aspart of their paper. The authors confirm that they give per-mission, or have obtained permission from the copyrightholder of this paper, for the publication and distribution ofthis paper as part of the ICAS 2014 proceedings or as indi-vidual off–prints from the proceedings.

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