ARTICLE IN PRESS

0376-0421/$ - se

doi:10.1016/j.pa

�CorrespondE-mail addr

andreas.huebne

(T. Loeser).

Progress in Aerospace Sciences 44 (2008) 121–137

www.elsevier.com/locate/paerosci

Experimental and numerical research on the aerodynamics of unsteadymoving aircraft

Andreas Bergmanna,�, Andreas Huebnerb, Thomas Loesera

aGerman–Dutch Wind Tunnels, Lilienthalplatz 7, 38108 Braunschweig, GermanybGerman Aerospace Center, Lilienthalplatz 7, 38108 Braunschweig, Germany

Abstract

For the experimental determination of the dynamic wind tunnel data, a new combined motion test capability was developed at the

German–Dutch Wind Tunnels DNW for their 3m Low Speed Wind Tunnel NWB in Braunschweig, Germany, using a unique six degree-

of-freedom test rig called ‘Model Positioning Mechanism’ (MPM) as an improved successor to the older systems. With that cutting-edge

device, several transport aircraft configurations including a blended wing body configuration were tested in different modes of oscillatory

motions roll, pitch and yaw as well as delta-wing geometries like X-31 equipped with remote controlled rudders and flaps to be able to

simulate realistic flight maneuvers, e.g., a Dutch Roll. This paper describes the motivation behind these tests and the test setup and in

addition gives a short introduction into time accurate maneuver-testing capabilities incorporating models with remote controlled control

surfaces. Furthermore, the adaptation of numerical methods for the prediction of dynamic derivatives is described and some examples

with the DLR-F12 configuration will be given. The calculations are based on RANS-solution using the finite volume parallel solution

algorithm with an unstructured discretization concept (DLR TAU-code).

r 2007 Elsevier Ltd. All rights reserved.

Contents

1. Overview, current situation and motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

2. Facility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

3. Rotary-balance apparatus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

4. Oscillatory motion apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

5. Data evaluation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

6. Measurement of model position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

7. Requirements against wind tunnel models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

8. Numerical approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

9. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

10. Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

e front matter r 2007 Elsevier Ltd. All rights reserved.

erosci.2007.10.006

ing author. Tel.: +49 531 295 2450; fax: +49 531 295 2829.

esses: andreas.bergmann@dnw.aero (A. Bergmann),

r@dlr.de (A. Huebner), thomas.loeser@dnw.aero

1. Overview, current situation and motivation

During the expensive process of aircraft development, itis highly desirable to obtain information about the futureflight mechanics behavior of an aircraft already at a veryearly stage. The reliability of the predicted data is ofeminent importance with regard to cost effectiveness within

ARTICLE IN PRESSA. Bergmann et al. / Progress in Aerospace Sciences 44 (2008) 121–137122

the design process. For the upcoming new airplaneconfigurations (e.g., wide body, green aircraft, blendedwing body) the approach up to now using semi-empiricalmethods as standard prediction tools is not as accurate asrequired. Hence, the DLR Institute of Aerodynamics andFlow Technology in Braunschweig, Germany, started todevelop a new method for the reliable determination of thedynamic derivatives to be able to describe the handlingqualities sufficiently and to be able to predict the dynamicloads of a new aircraft reliably. Of particular importancefor the success of that project was a distinct improvementof the state-of-the-art measuring techniques to experimen-tally determine the derivatives as it was felt to bemandatory to validate the numerical method with a reliableexperimental database. But during the development phase,it turned out that just with close interaction between CFDand the wind tunnel test environment, considerableprogress could be achieved.

Dynamic wind tunnel testing has been performed for 30years in the Low Speed Wind Tunnel DNW-NWB inBraunschweig. The two relevant model supports and thecorresponding data acquisition equipment suitable fordynamic wind tunnel measurements will be described insome detail.

One model support is a classical Rolling and SpinningDerivative Support (RTD) which enables the model toperform a continuous rolling and spinning motion aboutthe wind axis.

The other dynamic model support is the ‘ModelPositioning Mechanism’ (MPM) that complements theabove-mentioned RTD. The development and the perfor-mance of the MPM will be described as well as theinstrumentation necessary for dynamic tests that includesthe stereo pattern recognition technique with CMOScameras. This system is used for determining the time-dependent model position and for measuring the appearingwing shape during a 3Hz forced sinusoidal oscillation aswell as during combined motions to simulate realistic flightmaneuvers. The quality and performance of the dynamicinstrumentation is of special importance as the quality ofthe results of dynamic measurements depends stronglyupon the quality of the measurement of the model’sinstantaneous position with respect to the simultaneous-ness of the position signal and balance and pressure signals.This especially holds true when separate measurementsystems are used for force/pressure and position measure-ment as is the case at DNW-NWB.

A first general survey about the determination ofdynamic stability derivatives, necessary for the identifica-tion of the dynamic characteristic of aircrafts and for thecalculation of the structural loads on individual compo-nents, is given in Ref. [1] in which an article by K.J. Orlik-Rueckemann, giving an overview of different techniquesfor the experimental determination of dynamic derivatives,can be found; see also Ref. [2]. Furthermore, in Ref. [3], thechanging interest in the determination of dynamic deriva-tives regarding the requirements of increasing angles of

attack during the 1970s is described. At extreme flightattitudes and on slender configurations with non-linearaerodynamic characteristics, e.g., by means of highangles of attack, strakes, transonic effects, it is up tonowadays very difficult to predict the airflow and therewiththe aircraft’s behavior correctly. This of course especiallyheld true in the 70s. Of particular importance is, at thattime as today, the determination of confidence levels andstandard deviations which have to be taken into accountin the correlation between theory, wind tunnel test andflight test.Aerodynamic tests on maneuvers with high amplitudes

and high velocities of highly agile combat aircraft were ofinterest at that time and furthermore in the 60s and 70s, theslender configurations like, e.g., Space Shuttle, Saenger andConcorde were the motivation for very comprehensiveactivities to investigate the relevant flow regime. From this,the demand for extensive dynamic wind tunnel tests in thewestern world can be derived, cp. thereto the aerodynamicflight mechanical Conference Proceedings, besides Ref. [1]also Refs. [4,5]. The latter is in close association withRef. [6] in which the rolling and spinning experiments arediscussed in some detail. The essential conclusion here wasthat all achievements show good correlation as long as theairflow is clear and without ambiguity. But if the flow isable to reach different states under same constraints,however, the results rather depend on the wind tunnel inwhich the tests were performed. From this, it was alwaystried to define boundaries inside of which safe flow statesexist and within which an airplane control system can workreliably. But with the requirements for predictions of rapidhigh angle-of-attack maneuvers, it was found out thatmore studies about rather complex and unorthodoxconfigurations were necessary with the extension of thespeed range and with including data of time history effects,scale effects and aerodynamic interference effects. As theexperimental data gained so far seemed to be insufficient todraw conclusions regarding these points, a new AGARDactivity was started in the 90s, see Ref. [7], which for thefirst time provides a comprehensive database for rotary andoscillatory characteristics of a generic WG16 fighter typemodel configuration over a large range of angles of attack,with the objective to examine the reliability of testtechniques. A further objective was to obtain comprehen-sive results on surface pressures, forces and moments forvalidation of reliable numerical codes which have so far notexisted in this field. More validation experiments on simplegeneric shapes designed to provide detailed measured datafor the verification of results from CFD codes are given inRef. [8]. Here, the results for oscillating and transientmovement patterns of complete configurations and foroscillating flaps can be found, including calculations ofdynamic force and pressure measurements on an oscillating651 Delta Wing by DaimlerChrysler Aerospace as well asmeasurements by DLR at DNW-NWB. That can be seenas one of the first examples of a fruitful interaction betweenexperimental and numerical work as the data evaluation

ARTICLE IN PRESSA. Bergmann et al. / Progress in Aerospace Sciences 44 (2008) 121–137 123

could be well improved by the experience from thecalculations, see also Ref. [9].

The determination of the dynamic derivatives in DNW-NWB in Braunschweig, Germany, started in the 70s withthe Mobile Oscillatory Balance MOD [8,10,11], and withthe rolling and spinning device RTD [6,7,10,11], with theconfigurations Alpha-Jet and MRCA Tornado being themost prominent test objects. This kind of testing has beenresumed after two decades of decommission in collabora-tion with the Institute of Aerodynamics and FlowTechnology of DLR within the German MEGAFLUGproject. This project was started to improve the assessmentof the aerodynamic properties of the planned AirbusMegaliner. In particular, the contributions of the indivi-dual components of the airplane should be quantified moreprecisely compared to the industrial handbook methods sofar commonly used, see Ref. [12]. The investigationsproceeded with the development of a numerical predictiontool for aerospace applications. This method is described inRef. [13] in some detail, where in a first step for moredetailed understanding of the unsteady aerodynamic andflight mechanical behavior of an airplane, schematicinvestigations on basic configurations with a NACA0012airfoil have been used. In Ref. [14], more results fromcalculations of the dynamic derivatives of a moderntransport aircraft configuration DLR-F12 are presented,compared with results from corresponding experiments inDNW-NWB. The focus here is not only put upon theevaluation of flight properties and to obtain data for theestimation of the dynamic structural loads on individualcomponents but also on gaining a database for validationof newly developed CFD tools. A complex time accuratemaneuver on a detailed X31-canard configuration withtime accurate remote controlled rudders and flaps isdescribed in Ref. [15]. This can be seen as a first step toprovide a database for validation of recently developedmultidisciplinary time accurate CFD-codes for calculatinga free-flying aeroelastic maneuvering combat aircraft.Here, the computational aerodynamic, structural and flightmechanic codes are embedded into a simulation environ-ment. Hence, it is nowadays the goal of a proper validationto get corresponding results from wind tunnel tests,implying not only time accurate force measurements butalso pressure distribution, model movement and determi-nation of the corresponding change of the wing’s twist andbending.

There is no denying that with the upcoming availablecalculation tools and with the ever advancing calculationpower, the recent trend of the development in aerodynamicresearch shows a fruitful interaction between CFD andexperimental work that is not only much closer today thanin the past but also very efficient and progressive. One ofthe major outcomes of this project is that only thecombination of theory and experiment is sufficient to getproper insight into the flow physics and a better under-standing of the relevant relating facts. It will be shown thatjust the interaction between CFD and the wind tunnel has

led to a proper aerodynamic investigation of the field ofdynamic flight behavior, mandatory for the development offuture prediction tools.

2. Facility

The DNW-NWB is operated by the foundation Ger-man–Dutch Wind Tunnels DNW. It is an atmosphericwind tunnel of closed-circuit type and has a test section sizeof 2.8� 3.25m2 with a maximum free stream velocity ofabout 85m/s (280 ft/s). It can be operated optionally with aclosed, a slotted or an open test section. The DNW-NWBhas recently been considerably upgraded regarding itscontrol systems, measuring techniques and heat exchanger.One important field of business is the dynamic testing.

For this topic, two special devices are available: (a) therotary-balance apparatus and (b) the oscillatory motionapparatus. These two devices are described in some detail.

3. Rotary-balance apparatus

The rotary-balance test technique, developed to provideinformation on the effects of angular rates on theaerodynamic forces and moments on a flying aircraft, isdescribed comprehensively in Ref. [6]. The correspondingRTD apparatus at DNW-NWB has remained unchangedsince the first measurements in 1977. The model is mountedon a support system that can be rotated at constant ratesabout the free stream velocity vector of the wind tunnel.Thus, the attitude of the model remains constant withrespect to the airstream throughout a rotational cycle. Theflow can be considered as steady-state. The forces andmoments are determined by a six-component internalstrain-gauge balance. It can be taken from Figs. 1 and 2that the RTD can be operated both in the closed and in theopen test section of the DNW-NWB. The apparatus isdriven by a servo-controlled hydraulic motor. The rotationrate can be varied up to 300 rpm. While rotating the model,its angle of attack can be changed over a range of 301. Byusing different existing cranked stings, the adjustable angleof attack ranges from 01 to +901. The angle of sideslip canbe changed between7901 by adjusting the front part of thesting manually. The RTD can be operated in the riggingbay beneath the test section while another test is running.After completion of the model instrumentation and allrelevant test preparations, the RTD can be lifted by spindledrives from the rigging bay into the test section to continuewith wind tunnel operation without time delay. Fordescription of a typical test procedure and data reductionplease refer to Ref. [6].

4. Oscillatory motion apparatus

As mentioned before, the first oscillatory balance ofDNW-NWB known as MOD, see Fig. 3, has been replacedsince the end of the 90s successively, starting within theMEGAFLUG project, by improved elements.

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Fig. 1. Rotary-balance RTD of DNW-NWB (sketch).

Fig. 2. Photograph of RTD in the closed test section of DNW-NWB.

A. Bergmann et al. / Progress in Aerospace Sciences 44 (2008) 121–137124

In a first step, a new support called the OscillatoryModel Support (OMS) of DNW-NWB was developed [16].With serial kinematic structures, as depicted in Figs. 1–3,the number of DoF is achieved by serial arrangement of thecorresponding number of linear and rotative axes. So thebottom-most axis of movement has to carry the weight ofall those lying above it and this results in a contradictionbetween the requirement for high stiffness (high mass) and

high dynamics (low mass). In addition to that, all errors(thermal, geometric, caused by loads, y) of movement ofall axes are added. As parallel kinematics get rid of theseproblems, it was decided to choose a kinematics ofHexapod type (Stewart platform) for the OMS. Thismotion apparatus excites the forced sinusoidal modeloscillations in the modes pitch, roll, yaw, heave and lateraloscillation about arbitrary oscillation axes but usually

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Fig. 3. The MOD test setup in the DNW-NWB with an A380 configuration.

A. Bergmann et al. / Progress in Aerospace Sciences 44 (2008) 121–137 125

oscillations are performed about model-fixed or wind-fixedoscillation axes.

Fig. 4 shows the model mounted on a belly sting which isfixed to the movable frame of a hydraulic platform havingsix degrees of freedom. The platform incorporates sixhydraulic jacks. An additional hydraulic actuator which islocated on the Stewart platform is used to excite the pitchand roll oscillation of the model (Fig. 5) via suitablemechanism inside the model’s fuselage that transform thetranslatory motion of the additional actuator into therequired rotatory motions. Larger amplitudes and higheroscillation frequencies are possible this way because it savesthe Hexapod’s upper frame from moving along a circularpath with a radius of approximately 6 ft which doubtlesslyis also possible but which creates large unfavorable inertiaeffects. For more information about the OMS and aboutthe applied test procedures please see Ref. [12].

The idea to use the Stewart platform and utilizing itsvariability as a great advantage in a wind tunnel is not new.A first analysis for using a parallel kinematics as a test rigin a wind tunnel has been made in Ref. [17], but to theauthors’ knowledge, the inherent large number of singularpositions (i.e., locations in the workspace at which thestiffness at the tool disappears in specific directions. In thevicinity of such singularities the stiffness is at least verylow.) of the proposed kinematics restricted the availableworkspace too much. Besides that, the large number ofjoints were challenging for stiffness and precision. Notwithstanding a novel configuration based on the Stewartplatform mechanism was developed. An analysis of themechanism kinematics is presented in Ref. [18].

Nevertheless, the selection of this kind of six degree-of-freedom dynamic test rig as parallel kinematics for theDNW-NWB gives several advantages compared to aconventional multi-axis test rig in serial arrangement.

�

Higher dynamics despite identical input power becauselower weights are being moved. � Higher accuracy because errors of single axes are not

added.

� Higher stiffness regarding the weight of the components

because only forces in axial direction of the legs areacting.

Of course, the inherent disadvantages are serious andmight be the reason why this type of apparatus is not socommonly used as test rig in wind tunnel facilities. Besidethe singularity problems, the available working space isrelatively small compared to the size of the machine. Thatmeans that enlarging the working space leads to anexceedingly large and heavy machine counteracting theadvantage of a proper dynamic behavior.To overcome these difficulties, a new six degree-of-

freedom model support called MPM was developed byDLR and DNW in 2004 as an improved successor to MODand OMS.This novel and so-far-unique MPM is also based on a

parallel kinematic concept. The principle of the kinematicis depicted in Fig. 6. It is based on an idea of Wiegand [19],see also Ref. [20], from ETH Zurich with the intention torealize a parallel manipulator to be used as a high-speedmilling machine. It consists of a movable platform which is

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Fig. 5. Schematic view of the OMS test setup.

Fig. 4. The OMS test setup in the DNW-NWB with an A380 configuration.

A. Bergmann et al. / Progress in Aerospace Sciences 44 (2008) 121–137126

linked to the wind tunnel fixed base by six constant lengthlegs—joined with the platform as well as with six carriageswhich can move along parallel guiding rails so that theposition and orientation of the platform can be adjusted.The six carriages run independently from each other oneach guiding rail, allowing a displacement within sixdegrees of freedom. The test rig can be used for oscillatingthe wind tunnel model about one body axis through asinusoidal motion as well as for combined motions to

simulate realistic flight maneuvers, e.g., a Dutch Roll. It islocated above the test section, so that it can be used notonly for dynamic measurements but also for ground effectsimulation. The realized design as a result of an optimiza-tion against stiffness can be seen in Fig. 7. Because eachguiding rail is shared by three carriages, the design issimplified and has fewer components than previousversions [21]. The major characteristic of the MPM is itshigh dynamic capability combined with high and nearly

ARTICLE IN PRESSA. Bergmann et al. / Progress in Aerospace Sciences 44 (2008) 121–137 127

constant stiffness over the whole workspace which spans1100mm in flow direction, 300mm in lateral direction and500mm in heave direction, without singular positions. Toavoid a conventional ballscrew drive with all its elasticity inthe drive chain, the axes are brought into motion byapplication of the linear direct drive technology. Theaccuracy of the system in pivoting angles is better than0.0051. The first Eigen frequency at the sting’s end is above20Hz. The MPM can be operated in the open test sectionas well as in the closed one.

Fig. 7. Implemented MPM kinematic

Fig. 6. Principle of the MPM parallel kinematic machine.

5. Data evaluation

For the evaluation of the derivatives, it is assumed thatthe aerodynamic force and moments are linear functions ofmodel position and angular speed or, in case of heave andlateral oscillation, to be linear functions of translatoryspeed and acceleration. For configurations on whichvertical and/or separated flow cause non-linear character-istics, more sophisticated mathematical models are re-quired. Furthermore, the wind tunnel model is assumed tobe ideally stiff. Because the wind-on balance signalscontain both aerodynamic and inertial forces, the latterhave to be subtracted from the wind-on data. This is,therefore, possible if model weight, center of gravity andmoments of inertia are known. Another more practicalsolution is to determine the inertial forces by measuring theforces acting on an oscillating model in wind-off condition.For more details please see Ref. [12].

6. Measurement of model position

On the MOD, the measurement of the unsteady modelposition was done by means of a strain gauge on a spring-loaded lever located far away from the model below thetest-section floor. This system had the disadvantage of notrecording deviations of the model position due to elasticityof the mechanical setup or due to play in the bearingsbetween the strain gauge position and the model itself. Asimilar technique is the suitable application of an electriclongimetry sensor in the vicinity of the moving frame of theOMS. From Fig. 8, one can see how the position of the

design in DNW-NWB with X-31.

ARTICLE IN PRESSA. Bergmann et al. / Progress in Aerospace Sciences 44 (2008) 121–137128

model’s fuselage interacts with the sensor to get informa-tion about the unsteady position of the model within oneoscillation mode.

Another applied method is the use of an optical positionmeasuring system. A high speed digital video cameramanufactured by Pulnix, recording the position of distinctmarkers on the model, provides the values of translatorydisplacement and angular deflection in real time with afrequency up to 300Hz at a resolution of 648� 100 pixels.Image acquisition and real-time processing are done with adual P-III personal computer which is equipped with a

Fig. 8. Application of the electric sensor for information on the model’s

attitude.

Fig. 9. Optical position measuremen

Viper frame grabber card and a specifically adoptedversion of the PicColor software [22].This method has the advantage of achieving the

amplitudes of the model correctly but extraordinarydiligence has to be taken on the triggering of the videocamera as it is shown below that the phase relationshipbetween the model position signals and the balance signalsis of great importance for the accuracy of the deriveddynamic derivative coefficients.Fig. 9 shows the installation of the camera on the test

section side-wall protected against the flow to minimizevibrations and the installation of the mercury vapor lampwhich is necessary to illuminate markers implemented onthe model. Fig. 10 shows the markers on the fuselage,among holes and screwheads in their vicinity, which arereliably ignored by the software’s rejection criteria.

7. Requirements against wind tunnel models

The mass of an unsteady moving model as well as themoments of inertia must be as low as possible to achieve afavorable ratio between the interesting aerodynamic forcesand the additional acting inertial forces. On the other hand,the elastic deformation has to be as small as possible.Furthermore, the first Eigen frequency of the model shouldbe one order of magnitude above the excitation frequency,at least 15Hz, to avoid excitation of the model by possiblehigher harmonic rates, see also the comments given belowaccording to Fig. 14c. The best material to meet all theserequirements proves to be suitable carbon fiber reinforcedplastic (CFRP). Using CFRP sandwich constructionmethods, as used in building full-size gliders, masses aslow as 8 kg for models with wingspans of 2m can beachieved. Most of the models tested in NWB weremanufactured by the plastics workshop of DLR inBraunschweig from CFRP in molds. Fig. 11 shows a

t with camera and light source.

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Fig. 10. Applied markers to be detected by the optical system.

Fig. 11. Typical wing cross-section.

A. Bergmann et al. / Progress in Aerospace Sciences 44 (2008) 121–137 129

schematic view of the cross-section wing. In order toevaluate the influence of individual components of thetested airplane configuration, such as winglets, vertical orhorizontal stabilizers, nacelles, the models are designed in amodular way so that every component of interest can beadded to the model, Fig. 12.

8. Numerical approach

The first calculations are based on the panel methodVSAERO, a code calculating the non-linear aerodynamiccharacteristics of arbitrary configurations in subsonic flow[23,24]. In an iterative loop with an applied integralboundary layer calculation, some viscosity effects can beconsidered. With this program effects from quasi-steadymotions about the body-fixed axis can be calculated.Results from these calculations are discussed in Ref. [14].

Recent calculations are based on the solution of theReynolds-averaged Navier–Stokes solution equations. Thisis accomplished by adopting a finite volume flow solutionmethod, the DLR TAU code [24,25], which is characterizedby an unstructured mesh concept. The solver is part ofthe MEGAFLOW project and is presented in detail in

Ref. [26]. In addition to quasi-steady solutions, time-accurate computations are possible. For a brief introduc-tion into the numerical environment please see Ref. [14].Generally, there are different approaches to obtain the

parts of the dynamic derivatives. Fig. 13 describes as anexample, the pitching moment due to the pitching motionand the resulting derivative.The pitching motion about the mean value a0 with an

amplitude Da generates a ‘hysteresis’ loop in the aero-dynamic response. The bulging out of this hysteresis looprepresents the dynamic derivative. In this case, the pitchingmoment is negative (damping) and the direction of thesignal is anti-clockwise. The derivative is the sum of twoterms

cm_a ¼@cm

@ð@a=@tÞand cmq ¼

@cm

@q,

where cmq is the quasi-steady term and represents the pitchmoment cm due to constant pitching rates q. After sometransient effects at the beginning of the process, theresulting forces and moments converge to a steady statecondition. Calculated motions with different ratios ofpitching rate q and lever arm r (see Fig. 13) by constant

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Fig. 12. Typical model setup example DLR-F12.

Cm

Cmα + Cmq

Cmα + Cmq unsteady pitching motion

Cmq quasi-steady motion

+ Cmα unsteady heave OSC.

=

α0 α /°

ΔαΔα

steady measurementunsteady measurement

My +

R

X

U

Δα

Δα

Δz

Δzz

α0

q

w

A

Vα

.

Z

X

Fig. 13. Dynamic derivative of the unsteady pitching motion.

A. Bergmann et al. / Progress in Aerospace Sciences 44 (2008) 121–137130

onflow condition give the cmq term. cm_a is an unsteadyterm. It describes, e.g., the influence of a wing-tip vortexwhich reaches the horizontal tailplane after a time delay.The unsteady terms can be obtained by simulating pureheave oscillations.

9. Results

To illustrate the improvement of the kinematic regardingthe quality of motion and its applicability as test rig for

dynamic wind tunnel tests, Fig. 14a shows for comparisonbetween the OMS and the new MPM in its upperpart the measured positions of the wind tunnel model overthe time and the corresponding frequency spectrum from aFourier analysis during a forced sinusoidal yawing motion.In the right part of Fig. 14a, the corresponding measuredyawing moment and likewise its derived frequencyspectrum are depicted. For an assessment of the fidelityof the motion, the forces and moments relevant for thechoice of the balance are much more meaningful. As the

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f [Hz]

Am

plit

ud

e

Am

plit

ud

e

0 5 10 15 20 25 30 35

100

10-1

10-2

10-3

Am

plit

ud

e

100

10-1

10-2

10-3

10-1

10-2

10-3

10-4

OMS

MPM

t [s]

Φ [°

]

1 1.2 1.4 1.6 1.8 2-6

-4

-2

0

2

4

6

t [s]

Mz [N

m]

1 1.2 1.4 1.6 1.8-80

-60

-40

-20

0

20

40

60

80

f [Hz]

0 5 10 15 20 25 30 35

Am

plit

ud

e

10-1

10-2

10-3

10-4

f [Hz]

0 5 10 15 20 25 30 35

f [Hz]

0 5 10 15 20 25 30 35

My [

Nm

]

-150

-100

-50

0

50

100

150

OMS

MPM

OMS

MPM

OMS

MPM

OMS

MPM

OMS

MPM

OMS

MPM

OMS

MPM

2

t [s]

1 1.2 1.4 1.6 1.8 2

t [s]

1 1.2 1.4 1.6 1.8 2

Φ [°

]

-6

-4

-2

0

2

4

6

Fig. 14. (a) Yawing motion OMS and MPM, f ¼ 2.1Hz. (b). Pitching motion OMS and MPM, f ¼ 2.8Hz. (c). Pitching motion MPM, f ¼ 3Hz.

A. Bergmann et al. / Progress in Aerospace Sciences 44 (2008) 121–137 131

force and hence the moments involved are directlyproportional to the acceleration, the moments curvehistory can be regarded as the second derivative of theposition’s curve history.

The position signals of MPM and OMS show a rathergood sinusoidal shape and the frequency spectrum of theposition shows only minor differences between thebehavior of OMS and MPM. However, the OMS hassome higher harmonics of the excited frequency of 2.1Hzand this is a disadvantage because the acting forces areproportional to the square of the motion’s frequency. Onthe other hand, the comparison of the correspondingmeasured moments gives distinct differences between thetwo kinematics. From the frequency spectra, the higherharmonics of the MPM are up to one order of magnitudeless than that from the OMS, a result of the increasedstiffness of the new apparatus.

Since the yawing motion results from the six actuatorsarranged in parallel manner on the hexapod mechanism,

the pitching motion is performed by the single seventh axisas a coupled kinematic. Fig. 14b gives an insight into theperformance at that pattern of movement and the samegood improvement can be recognized. All results shown sofar are obtained in wind-off condition.To give an impression of the importance of considering the

Eigen frequencies of the complete system, a similar test withanother model was repeated with 3Hz forced sinusoidalexcitation. The results are shown in Fig. 14c for wind-off andwind-on conditions. The Eigen frequency of 15Hz of theDLR-F12 wind tunnel model is considerably visible in thenormal force FN as well as in the pitching moment My,admittedly much more in wind-off condition due to favorabledamping effects at wind-on condition. Nevertheless, thisexample makes abundantly clear that the specification of theEigen frequency of the model should be carefully reconciledwith the requirements of the test program.A comparison between unsteady numerical and experi-

mental results is depicted in Fig. 15. It can be taken from

ARTICLE IN PRESS

t [s]

Δα

Δα

Δt

[°]

FN

[N

]/A

mpl (E

xp)

[N]

My [N

m]/

Am

pl (E

xp)

[Nm

]

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65

-5

-4

-3

-2

-1

0

1

2

3

4

5

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

.

DLR-F12, pitching oscillation, = 0°, U = 70 m/s, f = 3 Hz

My

FN

α

FN, Exp.

My, Exp.

Δα, Exp.

FN, Euler

FN, Na-St.

My, Na-St.

Δα, Na-St.

My, Euler

Δα, Euler

Fig. 15. DLR-F12. Pitching oscillation, a ¼ 01, U ¼ 70m/s, f ¼ 3Hz.

t [s]

FN

[N

]

1 1.2 1.4 1.6 1.8 2-400

-200

0

200

400

600

800

1000

without windwith wind

without wind

with wind

f [1/s]

Am

plit

ud

e

0 5 10 15 20 25 30

f [1/s]

0 5 10 15 20 25 30

103

101

10-1

10-2

10-3

100

102

Am

plit

ud

e

103

101

10-1

10-2

10-3

100

102without wind

with wind

DLR-F12, pitching motion, α = 0°, f = 3.0 Hz

U = 70 m/s, MPM, close test section

sting modification

without wind

with wind

t [s]

My [

Nm

]

1 1.2 1.4 1.6 1.8 2-100

-50

0

50

100

without wind

with wind

without wind

with wind

without windwith wind

DLR-F12, pitching motion, α = 0°, f = 3.0 Hz

U = 70 m/s, MPM, close test section

sting modification

without wind

with wind

Fig. 14. (Continued)

A. Bergmann et al. / Progress in Aerospace Sciences 44 (2008) 121–137132

the position curve that at the wind tunnel test, thecommanded amplitude of Da ¼ 4.51 was only shortlyachieved, hence the difference between the amplitude fromcalculation and experiment. This situation can be seen asindicative of the importance of a proper position measure-ment. At first glance, the numerical results meet theexperimental results of time-dependent lift and pitchingmoment rather well, the Navier–Stokes solution does it forthe pitching moment even slightly better than the Eulersolution, and the small gap between the input amplitudesmight be the reason for the remaining slight differences.But surveying the calculated and the experimental phase

between position and force/moment, a phase shift ofDtE2ms can be recognized and that leads to the questionabout the sensitivity of the phase and its impact on thequality of the results.Fig. 16 gives the determined phase for the derivatives for

lift and moment coefficients due to a pitching motion. It iseasy to shift the phase in the result records to get someinsight regarding the sensitivity. It turns out that evenminor changes in the phase lead to considerable changes inthe coefficients. For example 11 phase shift leads to achange in the lift derivative cLq þ cL_a of about 1.5% orabout 15%, respectively. It can also be derived that the

ARTICLE IN PRESS

16

12

8

4

0-178 -177 -176 -175 -174 -173 -172 -171 -170 -169

phase of FL [°]

-20

-22

-24

Cm

q +

Cm

α.

CLq +

CL

α.

-26

-28

-91 -90 -89 -88 -87 -86 -85 -84 -83 -82

phase of My [°]

determined phase(from calc. and exper.)

Y = A + B*XA = -7.37 E+1B = -5.79 E-1

R2 = 0.999822

Y = A + B*XA = 2.62 E+2B = 1.46 E+0

R2 = 0.999996

CLq + CLα.

Cmq + Cmα.

Fig. 16. Effect of phase error.

12

11

10

9

897 98 99 100 101 102 103

Ampl / [%]

CLq +

CL

α.

Cm

q +

Cm

α.

-22

-23

-24

-25

-26

Y = A + B*XA = -4.76 E+1B = 2.38 E-1

R2 = 0.999857

Y = A + B*XA = 1.84 E+1B = -9.21 E-2

R2 = 0.999857

CLq + CLα.

Cmq + Cmα.

Fig. 17. Effect of amplitude error.

A. Bergmann et al. / Progress in Aerospace Sciences 44 (2008) 121–137 133

sensitivity to the pitch-damping coefficient is three timessmaller. This interrelation holds true for numerical as wellas for experimental results and makes clear that great carehas to be taken with regard to the estimation of the phaserelationships. Corresponding to the previous procedure,the influence of the amplitude can also be evaluated.However, it can be taken from the example in Fig. 17 that afalse determination of the amplitude leads to only minoreffects in the evaluation of the derivatives.

Fig. 18 gives for comparison, the impact of two differentposition measurement techniques on the evaluated deriva-tives again for the pitching motion. One technique is theafore-mentioned video system that detects the attitude ofthe model directly and the other is the described electricalsensor that determines the position of the model, aspreviously described in Fig. 8, in indirect manner. Bothtechniques were applied simultaneously during one and thesame test run. In the results, a clear difference of 30% isvisible in the lift coefficient and here the influence of thedetected phase and amplitude, respectively, is visible. Thearguments for the optical system are the more reliableprediction of the amplitude as all deformation effects fromthe test rig can be neglected. That is not the case for the

electric sensor as here all deformations between the sensorand the model have to be known. Concerning the phaserelationships, laboratory tests showed an uncertainty ofless than 1ms for both techniques, nevertheless with slightadvantages for the electrical sensor as this device can bemeasured with the identical amplifiers as used for thebalance signals while the video camera can be regarded as acomplete separate system. At 3Hz, 1ms is equivalent to anerror of 11. Again, the difference between the results for thelift due to the pitch oscillation and for the pitch damping isabout three times higher.In Fig. 19a, the comparison of various Euler results for

the DLR-F12 configuration is shown and the influence ofthe quasi-steady contribution cLq and cmq as well as of theunsteady contribution from heave oscillation cL_a and cm_acan be taken. The effects from the unsteady heaveoscillation show only minor influence upon the lift due topitch oscillation while the quasi-steady part is thedominant one. This is typical for the DLR-F12 configura-tion and is not always the case, as shown in Ref. [14], withcalculations on a generic wing/tail combination.The pitch-damping behavior, however, on the right hand

side of Fig. 19a shows an evident influence of the unsteady

ARTICLE IN PRESS

Fig. 19. (a) Different contributions of derivatives for Euler results, DLR-

F12. (b) Comparison of numerical and experimental results at the

DLR-F12.

12

11

10

9

8

7

6

5

4

3

2

1

0

-1 0 1 2 3 4 5 6 7 8

α [°]-1 0 1 2 3 4 5 6 7 8

α [°]

5

0

-5

-10

-15

-20

-25

-30

MPM, electrical sensor

MPM, optical system

MPM, electrical sensor

MPM, optical system

CLq + CLα Cmq + Cmα

Fig. 18. Impact of different position measurement techniques on the evaluated derivatives, pitching motion.

A. Bergmann et al. / Progress in Aerospace Sciences 44 (2008) 121–137134

(heave) cm_a term of about 20% which is not negligible.Adding the quasi-steady solutions and the coefficients dueto the heave oscillation results gives a sum that is in verygood agreement with the full unsteady pitching motionsimulation results.Fig. 19b shows unsteady Euler and Navier–Stokes

solutions to get information about the viscous effects.The plot reveals some minor effects and a comparison withexperimental data still gives deviations of about 20% in liftcoefficient while the results for the pitch damping correlatespretty well. Here, again the deviation is about three timessmaller than for the lift coefficient and the reason for theremaining discrepancies might again be uncertainties in theprediction of the phase in the magnitude of 1–2ms.Fig. 20 gives a comparison of results with the same

model from the positioning mechanism MPM and itspredecessor OMS, again exemplarily for the pitchingmotion. Due to the improvements regarding stiffness andprecision of the apparatus, the experimental data is shiftedslightly closer to the calculated predictions (see Fig. 19b),nevertheless still with a small gap.

10. Outlook

All numerical investigations and experimental dataevaluations so far were based on the assumption of anideal rigid model without deformation. First, work wasconducted to evaluate the error due to effects caused bytwist and bending of the model’s wing. For this purpose, a3D video system with two Mikrotron CMOS videocameras was used for stereo pattern recognition of distinctapplied markers on the wing, see Fig. 21.The accuracy obtained at that test is about 0.1mm. The

system is described in Ref. [27] in more detail. The result is

ARTICLE IN PRESS

12

11

10

9

8

7

6

5

4

3

2

1

0

-1 0 1 2 3 4 5 6 7 8 -1 0 1 2 3 4 5 6 7 8

α [°] α [°]

5

0

-5

-10

-15

-20

-25

-30

OMS, optical system

MPM, optical systemOMS, optical system

MPM, optical system

CLq + CLα Cmq + Cmα

Fig. 20. Experimental results from OMS and MPM on the DLR-F12.

Fig. 21. Applied markers for stereo pattern recognition.

A. Bergmann et al. / Progress in Aerospace Sciences 44 (2008) 121–137 135

illustrated in Fig. 22. The maximum deflection is 7mm andtwist is 0.41 at the wing tip. These experimental results meetthe predicted values rather well. Very first numerical resultsfrom quasi-steady VSAERO calculations with a genericrigid ‘flight’ shape with a bended wing without twist aredepicted in Fig. 23 for the pitch again. The outcome is aconsiderable shift of the results into the expected direction.From previous experiences, it can be assumed that withmore complex and accurate calculations, the predictedresults will fit again closer to the experimental results.

The next step will be an investigation of a new elasticwind tunnel model and the determination of the unsteadywing shape during the motion. On the other hand, thenumerical investigations have to proceed with multidisci-plinary codes with coupled aerodynamic-structural solversto address all parameters necessary for a proper predictionof the unsteady aerodynamics of maneuvering aircraft.In addition, measurements of the steady and unsteady

pressure distributions using the pressure taps of the DLR-F12full configuration are necessary for the validation process.

ARTICLE IN PRESS

Fig. 22. Measured wing deformation of DLR-F12 at constant a ¼ 101, UN ¼ 56m/s.

8.0

7.8

7.6

7.4

7.2

7.0

6.8

6.6

6.4

6.2

6.0

-1 0 1 2 3 4 5 6 7

α [°]-1 0 1 2 3 4 5 6 7

α [°]

-13.0

-14.0

-15.0

-16.0

-17.0

-18.0

-19.0

-20.0

-21.0

-22.0

-23.0

CAq Cmq

wing without bending

wing with bendingwing without bending

wing with bending

Fig. 23. DLR-F12 geometry, VSAERO, inviscid solutions.

A. Bergmann et al. / Progress in Aerospace Sciences 44 (2008) 121–137136

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