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Force and Mom8. Force and Moment Measurement

Measurement of steady and fluctuating forces act-ing on a body in a flow is one of the main tasks inwindtunnel experiments. In aerodynamic testing,strain gauge balances will usually be applied forthis task as, particularly in the past, the main focuswas directed on the measurement of steady forces.In many applications, however, balances basedon piezoelectric multicomponent force transducersare a recommended alternative solution. Contraryto conventional strain gauge balances, a piezobalance features high rigidity and low interfer-ences between the individual force components.High rigidity leads to very high natural frequen-cies of the balance itself, which is a prerequisitefor applications in unsteady aerodynamics, partic-ularly in aeroelasticity. Moreover for measurementof extremely small fluctuations, the possibility ex-ists to exploit the full resolution independentlyfrom the preload.

Concerning the measurement of small, steadyforces, the application of piezo balances is re-stricted due to a drift of the signal at constantload. However, this problem is not as critical asgenerally believed since simple corrections arepossible.

The aim of this chapter is to give an impressionof the possibilities, advantages and limitationsoffered by the use of piezoelectric balances. Sev-eral types of external balances are discussed forwall mounted models, which can be suspendedone-sided or twin-sided. Additionally an inter-nal sting balance is described, which is usuallyapplied inside the model. Reports are given on se-lected measurements performed in very differentwindtunnels, ranging from low-speed to tran-sonic, from short- to continuous running time andencompassing cryogenic and high pressure prin-ciples. The latter indicates that special versions ofour piezo balances were applied down to tem-

8.1 Steady and Quasi-Steady Measurement .. 28.1.1 Basics ......................................... 28.1.2 Basic Terms of Balance Metrology ... 68.1.3 Mounting Variations ..................... 88.1.4 Strain Gauge................................ 108.1.5 Wiring of Wheatstone Bridges ........ 118.1.6 Compensation of Thermal Effects.... 138.1.7 Compensation of Sensitivity Shift ... 148.1.8 Strain Gauge Selection .................. 168.1.9 Strain Gauge Application ............... 168.1.10 Materials..................................... 178.1.11 Single-Force Load Cells ................. 188.1.12 Multi-Component Load

Measurement .............................. 208.1.13 Internal Balances ......................... 208.1.14 External Balances ......................... 248.1.15 Calibration .................................. 28

8.2 Force and Moment Measurementsin Aerodynamics and AeroelasticityUsing Piezoelectric Transducers.............. 328.2.1 Basic Aspects of the Piezoelectric

Force Measuring Technique ........... 348.2.2 Typical Properties ......................... 398.2.3 Examples of Application ................ 438.2.4 Conclusions ................................. 51

References .................................................. 51

peratures of −150 ◦C and at pressures of up to100 bar.

The projects span from a wing/engine combi-nation in a low-speed wind tunnel to flutter testswith a swept-wing performed in a Transonic WindTunnel, and include bluff bodies in a high pres-sure and cryogenic windtunnel, as well. These testsserve as examples for discussing the fundamen-tal aspects that are essential in developing andapplying piezo balances. The principle differencesbetween strain gauge balances and piezo balanceswill also be discussed.

2 Part A Sample Chapter

8.1 Steady and Quasi-Steady Measurement

The key measurement system in a wind tunnel is themulti-component force and moment measurement in-strumentation. More than 70% of the tests in a windtunnel require some kind of force measurements. His-torically the instruments were purely mechanical andtheir mechanism resembled balances for weighing;hence the use of the term balance today. Today thesebalances are often based on transducers or are con-structed out of a single piece of metal, on which straingauges are applied. All balances must have a min-imum of one sensing element for every componentto be measured. The strain sensor usually is a resis-tance foil strain gauge, but also semiconductor gaugesare used. Illustrated in Fig. 8.1 is one of the firstwind tunnel balances built by Gustav Eiffel in 1907.The man on the upper gallery was responsible forbalancing the lift generated by the airfoil in the tun-nel below and simultaneously recording its associatedlift.

Fig. 8.1 Gustav Eiffel’s wind tunnel with lift balance

8.1.1 Basics

Balance TypesBalance types are distinguished by the number offorce/moment components which are measured simul-taneously – one to six are possible – and the locationat which they are placed. If they are placed inside themodel they are referred to as internal balances and ifthey are located outside of the model or the wind tunnel,they are referred to as external balances.

External BalancesTwo types of external balances exist. The first is theone-piece external balance, which is constructed fromone single piece of material and which is equipped withstrain gauges. Such balances are also referred to as side-wall balances as used in half-model tests.

The second type of external balance comprises singleforce transducers which are connected by a framework.Such a design can be built very stiff but needs morespace compared to the one-piece design. However, thereis usually plenty of space available around the windtunnel for such a balance, and so the construction can beoptimized with respect to measurement requirements,such as optimized sensitivity, stiffness and decouplingof load interactions.

Internal BalancesThere is limited space inside the model itself, so internalbalances have to be relatively small in comparison toexternal balances. There are two main types of internalbalances. The monolithic type, in which the balancebody consists of a single piece of material, is designedin a way such that certain areas are primarily stressedby the applied loads. The other internal balance typeuses small transducers which are orientated with theirsensing axes in the direction of the applied loads. Sucha balance is combined into a solid structure. A balancemeasures the total model loads and therefore is placedat the center of gravity of the model and is generallyconstructed from one solid piece of material.

LoadsIn this chapter the word load will be used to describeboth the applied forces and moments. The task of a bal-ance is to measure the aerodynamic loads, which acton the model or on components of the model itself. Intotal there are six different components of aerodynamicloads, three forces in the direction of the coordinate axes

Force and Moment Measurement 8.1 Steady and Quasi-Steady Measurement 3

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Fig. 8.2 Side-wall balance test configuration (left), and typical side-wall balance (right)

Fig. 8.3 External balance and support

and the moments around these axes themselves. Thesecomponents are measured in a certain coordinate systemwhich can be either fixed to the model or to the wind

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Fig. 8.5 Various possible coordinate systems for a windtunnel and model

tunnel. For the measurement of loads on model partssuch as rudders, flaps and missiles, normally less thansix components are required.

Definition of Coordinate SystemsOne possible coordinate system is fixed to the wind tun-nel – the wind axis system – and is aligned to the main

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Fig. 8.6 Definition of wind axis system in the USA

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Fig. 8.7 Definition of model-fixed axis system in Europe

flow direction. The lift force is generally defined as theforce on the model acting vertical to the main flow direc-tion whereas the drag is defined as the force acting in themain flow direction. This definition is common all overthe world. However, the definition of the positive direc-tion of the forces is not universal. Whereas lift (normalforce) and drag (axial force) are defined positive in theUSA (Fig. 8.6), in Europe (Fig. 8.7) weight and thrustare defined as positive in the wind axis system.

To form a right-hand axis system, the side forcein the USA has to be positive in the starboard direc-tion. The definitions of the positive moments do notfollow the sign rules of the right-hand system. The pitch-ing moment is defined as positive turning right aroundthe y-axis, but yawing and rolling moments are definedpositive turning left around their corresponding axes.This makes this system inconsistent in a mathematicalsense.

Table 8.1 Definition of positive axis direction

Balance Name of European USAAxis ComponentSystem

Positive Positive

direction direction

X Axial force In flight In wind

Y Side force To starboard To starboard

Z Normal force Down Up

Mx Rolling Roll to Roll to

moment starboard starboard

My Pitching Turn up Turn up

moment

Mz Yawing Turn to Turn to

moment starboard starboard

The European axis system is a consistent with theright-hand system and the definition is based on a stan-dard given by DIN-EN 9300 or ISO 1151. A balancewhich always stays fixed in the tunnel, and relative tothe wind axis system, always gives the pure aerodynamicloads on the model.

In the case of the model-fixed axis system, the bal-ance does not measure the aerodynamic loads directly.The loads acting on the model are given by the balanceand the pure aerodynamic loads must then be calculatedfrom these components by using the correct yaw andpitch angles. The difference between American and Eu-ropean definitions of the positive direction remains thesame in this case.

Specification of Balance Load RangesBefore a balance can be designed, the specifications ofthe load ranges and the available space for the balanceare required. This is a challenging step prior to the designof a balance since cost and accuracy considerations mustbe made long before the first tests are performed.

The maximum combined loads specify the loadranges for the balance design. The maximum designloads of a balance are defined in various manners. Forexample, if several loads act simultaneously, then theload range must be specified as the maximum combinedload. If the maximum load acts alone, the load rangeis defined then as the maximum single load. Usuallysuch single loads do not exist in wind tunnel tests andcombined loads must be expected. Such combined loadsstress the balance in a much more complicated mannerand therefore deserve very careful attention. The stressanalysis of the balance has to take into account thissituation. Furthermore, the combination of two loads

Table 8.2 Determination of maximum combined loads for an external balance

Wind axis system Model axis system

Test q A Cx Cy C. . . Drag Side F. . ., max Fx Fy Fz Mx My Mz

type Force M. . . α, β, γ

(Pa) (m2) (N) (N) (N), (N m) (deg) (N) (N) (N) (N m) (N m) (N m)

usually requires that the balance carries higher loads.To determine which balance can be used for a givensetup, the balance manufacturer provides the test engi-neer with loading diagrams which define the maximumload combinations for various available models.

In the case of external balances the available space isusually not a limiting factor. External balances are oftenused over several decades in a wind tunnel and thereforespecifications of the design load ranges are orientatedmore to the capabilities of the wind tunnel itself andthe associated model setups such as half-model and full-model tests, or the possibility of aircraft, car and buildingtesting. For the design of an external balance, first loadranges of the principle balance configuration must bedefined. Two different options are possible:

The first option is to mount the turntable inside theweigh bridge. In this case the balance stays in the windaxis system and therefore the balance always measuresthe wind loads. The disadvantage of this option is thatthe whole turntable mechanism has to be mounted onthe metric side of the balance such that the balance ispreloaded by the weight of this mechanism.

The second option is to mount the whole balanceon a turntable. In this case some components stay inthe wind axis system and some stay in the model axissystem, so a calculation of the aerodynamic loads from

Table 8.3 Determination of maximum combined load for an internal balance

Wind axis system Model axis system

Test type q A Cx Cy C. . . Drag Side F. . ., max Fx Fy Fz Mx My Mz

Force M. . . α, β, γ

(Pa) (m2) (N) (N) (N), (deg) (N) (N) (N) (N m) (N m) (N m)

Transporter

Landing

Cruise

Combat

the balance loads is necessary. For example, in the caseof a full model setup, as shown in Fig. 8.9, the balancewill always measure the aerodynamic loads when theangle of attack changes. In a half-model setup, as shownin Fig. 8.11, the balance will move with the model whenthe angle of attack changes and will measure the loadsin the model axis system.

This makes the determination of the balance loadranges rather difficult. Therefore it is useful to fill outa table where first the maximum loads for the differ-ent test setups are calculated in the wind axis system. Inorder to do this some assumptions of the aerodynamiccoefficients and the model size must be made. By as-suming values for the maximum angle of attack or yawangle, the maximum loads in the model axis system canbe calculated.

From such a table the maximum of each componentcan be taken as the maximum load for the balance. Nat-urally this leads to a balance with a rather high loadranges and for some cases the load range could be toohigh to measure with high resolution. However, if a cer-tain test requires a high resolution and this test is mostlyperformed in the tunnel, it is generally better to acceptthe lower load range to obtain higher resolution andhigher accuracy. These considerations must be madefor all components to ensure a balance with the best

fit of the load range for the normal operation of thetunnel.

For an internal balance the available space is a majorconcern. The available space for balances is restrictedby the diameter of the fuselage. As transport aircraftbecome larger, the scale for models also become larger,complicating matters since the cross sections of windtunnels have not grown at the same rate as the aircraft.As a result the available diameter for internal balanceshas become smaller.

For combat aircraft the loads in relation to the avail-able space inside the model are very high. This is thecase since the wind tunnel tests for this type of aircraftare mostly performed in pressurized wind tunnels to ob-tain the correct Mach number. The high static pressureleads to relatively high loads on the model in comparisonto tests at atmospheric pressure.

These two effects lead to higher specific loads on thebalance, making it much more complicated to developa balance with high accuracy. Therefore the definitionof the load ranges and the definition of the availablespace must be performed very carefully to ensure a highquality balance design.

The specification for an internal balance shouldtherefore be made related to the model and the loadson this model during the tests, and not on the tunnelcapabilities themselves. If these specifications are notcarefully performed, the internal balances will provideinsufficient sensitivity and accuracy for the tests.

Unlike an external balance, where some of the com-ponents are always fixed to the wind axis system, theinternal balance always measures the loads in the modelaxis system and therefore the lift and drag are always

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a combination of the axial and normal forces. Becauseof this, the angle of attack at which maximum loadingoccurs must be taken into account. For combat aircraftmaximum loads can act at an angle of attack as high as40◦, whereas the maximum forces for a clean transportaircraft occur in and around an angle of attack of 15◦.

Because an internal balance is mounted inside themodel and does not change in orientation relative tothe model itself, no maximum single load occurs.For different test setups (transporter, combat, high-lift, cruise-condition, etc.) different maximum combinedloads occur, so it is also useful to prepare a table todetermine the maximum combined loads on the balance.

Maximum Combined Load:Maximum Single Load

The definition of the maximum load can differ betweena combined load acting simultaneously, termed maxi-mum combined load, and a maximum load acting alone,defined as the maximum single load. The maximumsingle load forms a load trapeze, which does not au-tomatically cover the test requirements (Fig. 8.8). Themaximum combined load specifies the load range forthe balance design. Usually single loads do not occur inwind tunnel testing. Combined loads stress the balancein a much more complicated way, so the stress analy-sis of the balance has to take this situation into account.With the combination of only two loads the balance usu-ally can carry higher loads than defined by the maximumcombined loading. To estimate which load can be carriedfor a given situation the balance manufacturer providesa loading diagram (load rhombus) which allows the testengineer to judge whether the load combination of theplanned test is within the limits of the balance.

Which one of the above mentioned loads is used asthe “full-scale load” depends on the balance manufactur-er’s philosophy. The user should specify the definitionof the full scale load, because by definition the relativeuncertainty of the balance can vary by a factor of twowithout any difference in the absolute uncertainty. Thisis discussed in detail in the following section.

8.1.2 Basic Terms of Balance Metrology

In this chapter brief definitions are given of the termsused. Most of these terms are defined in some interna-tional standard such as the “Guide of uncertainties inmeasurement (GUM)” [8.1] or in the case of the UnitedStates, the AIAA Standards documented in Assessmentof Experimental Uncertainty with Application to WindTunnel Testing [8.2] and the Calibration and Use of In-

ternal Strain Gauge Balances with Application to WindTunnel Testing [8.3].

Full Scale Load or Output. Full scale load or outputcan be interpreted in several ways. The most obviousdefinition is the maximum combined load or the signalcorresponding to this load. It is also possible to definethe full scale load or output as the maximum of the sin-gle loads. The maximum single loads are usually muchhigher than the maximum combined loads, so uncertain-ties related to these values are much smaller than thoserelated to the maximum combined loads. This has tobe taken into account if balances from different manu-factures are compared. However, for a particular windtunnel test the maximum of the single loads seldom oc-cur and the use of maximum combined loads or signalsas the full scale reference yields much more realisticinformation about the accuracy of the balance.

Systematic Errors or Bias of an Instrument. System-atic errors are repeatable errors which occur at everymeasurement. If the cause of a systematic error can bedetected, it can be eliminated by calibration or compen-sation. If the source of a systematic error can not bedetected under repeatable conditions it is then simplyaccepted as the difference between the measured valueand the true value.

Random Errors. Random errors are defined as the dif-ference between the mean value of an infinite number ofmeasurements under repeatable conditions and a sin-gle measurement. The value of the random error isequal to the difference between the total error minusthe systematic error.

Resolution. Resolution is the smallest value which canbe detected by a balance. Similarly it can be defined asthe smallest detectable difference between two loads.The maximum resolution should be in the range of0.005% of the full scale load. For a normal wire straingauge, resolution in this range is not a problem andthe limits of the resolution are given by the measuringequipment. Good equipment today offers a resolution ofless than 0.0003% of the full scale load. Effectively themore money one spends on the equipment, the better theobtainable resolution.

Repeatability. If a certain balance loading is repeatedafter a certain amount of time, the repeatability is meas-ured as the difference in the two signals. This is a veryimportant characteristic for a balance, since many tests

in a wind tunnel compare different model configurations.Most often wind tunnel tests can not exactly reproduceconditions found in reality. This means that if the test it-self does not represent reality yet the engineers attemptto compare the difference between two designs underwind-tunnel test conditions, the extrapolation of resultsto reality can be very challenging. Repeatability can beas good as the resolution but is usually worse. The re-peatability of a good balance is in the range of 0.005% ofthe full scale load. Repeatability depends also on time,so it is distinguished between short-term repeatability,for example between two wind tunnel runs, and long-term repeatability, which is for example the differencebetween two complete wind tunnel installations. Bothshort- and long-term repeatability are of equal impor-tance since the loads on a new aircraft as well as theloads on an older aircraft design must be measured withthe same accuracy as the differences between the newmodel configurations. The main challenge often is thediscrepancy in the flow parameters between model andreality, especially Reynolds number. Most of the uncer-tainty in the force prediction on the real aircraft is thencaused by this Reynolds number gap, therefore relativemeasurements to the model of an older aircraft designare used to reduce this level of uncertainty.

Interactions and Interference. One of the major sys-tematic errors of a wind tunnel balance is caused by theinteractions or interference of the model with surround-ing components. For example, the sensor measuring theaxial force might also pick-up the loads from other com-ponents. This additional signal can be several percent ofthe measured axial force signal. As mentioned above,such a systematic error can be corrected through propercalibration.

Accuracy. The term accuracy is very broad and generallydescribes the agreement between the measured data, inthis case the wind tunnel test data, and the true valuewhich will be measured in the flight test after wind tunneltesting is complete. There are many influencing factors,such as the measurement of static and dynamic pressure,wall and sting interactions, precision of model geometry,flow quality, angle of attack and balance uncertainty.Since there are so many potential errors, it becomesdifficult to specify the accuracy for a wind tunnel test.Balance uncertainty alone must be taken into accountthrough balance calibration.

Absolute Error and Uncertainty. The absolute error isdefined as the difference between the real load acting on

the model (true value) and the load detected by the bal-ance. Normally the true value is unknown; therefore inpractice a “conventional true value” is used. Besides allthe error sources in the instrumentation and the balance,the error of the load measurement is strongly influencedby the balance calibration, since in this process the re-lation between the signals of the balance and the trueloads are determined. According to the “Guide to the Ex-pression of Uncertainties in Measurement” [8.1], oftenabbreviated as GUM, the absolute error is defined as theuncertainty of the measurement and can be given as theexperimental standard deviation of the whole process.For a given wind tunnel test the uncertainty of the meas-ured data is not only dependent on the measurement ofthe loads, but also influenced by the measurement of theangle of attack, the dynamic pressure, the model geom-etry, the flow quality and all the instrumentation whichare used to determine the aerodynamic performance andassociated derivatives. Regarding the desired precisionof the test result, minimum requirements for the loadmeasurement can be estimated from flight test data ofan existing aircraft.

Accuracy Requirements. The requirement placed onaccuracy is a function of the price of the balance. If a bal-ance is specifically designed and built for one particularset of wind-tunnel tests, it should be only as accurateas those tests require. This is however not usually thecase. The high cost of balance construction usually re-stricts a given tunnel to a small number of balances,which should ideally cover the range of test capabilitiesfor that particular tunnel. An estimate of the maximumrequired accuracy for the development of transport air-craft [8.4,5] can be made by defining which differencesbetween a developed aircraft and the new aircraft areto be investigated. The usual outcome of such an accu-racy requirement study is that the balance must be ableto measure a difference of 1 to 2 drag counts, which isequal to an accuracy requirement of the balance of bet-ter than 0.07% to 0.1% of the full scale load. This valueis a global one yet should be specified for every new testsetup.

8.1.3 Mounting Variations

When using external balances, there are many differ-ent possibilities for mounting the models. For example,a full model aircraft can be supported by a three-stingarrangement (Fig. 8.9) or a central sting (Fig. 8.10).For cars and buildings more than three supports aresometimes necessary. The external balance support

system should provide for as many arrangements aspossible.

The struts on the wing support the model at thequarter-chord positions and carry most of the load, ex-cept for the pitching moment which is balanced by thestrut at the tail of the model. All links to the model arejointed around the y-axis, so that a vertical movement ofthe tail strut allows for easy variation of the angle of at-tack. Yaw angles are set by moving the whole setup onthe turntable.

Using the central-sting mounting the model is fixedinside the fuselage in all directions. The adjustment ofthe angle of attack is done through y-axis mechanisminside the fuselage. All loads must be carried by thissupport and therefore must be very rigid to minimizedynamic movements of the model during testing.

Fig. 8.9 Three-sting mounting on external balance

Fig. 8.10 Centre-sting mounting on external balance

Fig. 8.11 Semi-span models on external balance

Fig. 8.12 Tail sting with fin attachment on lower side

Fig. 8.13 Tail sting through engine nozzle

Semi-span models (Fig. 8.11) are used to increasethe effective Reynolds number of the tests by increasingthe geometry of the model. Besides the higher Reynoldsnumber, the lager model size makes the models withvariable flaps and slats much easier to construct, thus

Fig. 8.14 Twin-sting rig with dummy tail sting

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semi-span models are often used for the testing of take-off and landing configurations.

The most common setup using an internal balanceis the back-sting arrangement (Fig. 8.13), in which the

and the attachment point of the beam. If a force is notapplied at the point where the calibration load is appliedone will produce errors proportional to this misalign-ment. This problem can be overcome by using a differenttransducer design. Some possible designs are shown inFig. 8.27. Their common design principle is that twobending beams should be coupled forming a parallelo-gram. If the coupling element is stiff enough the loadattachment point remains vertical, such that the trans-ducer signal does not depend on the distance betweenthis point and the gauge area.

Load cells which use the shear stress to determineeither an applied force or a torque moment do havethe same principle advantage that within the gauge areaa positive and a negative shear stress is generated withthe same magnitude. Therefore this type also has a linearoutput proportional to the applied load.

Shear-type load cellsThe maximum shear stress on a cantilever beam(Fig. 8.28), produced by force (F), appears at the centerline of the beam at (45±w)◦here the tension of compres-sion stresses are nearly zero. In such a case the maximumstrain also appears at (45±,)◦ therefore to get the max-imum output the gauges must be bonded as is shown inFig. 8.28. The dimensions of the beam can be calculatedby determining the stresses in τmax = Fc/A [N/mm2],where F is the applied force, A = bh [mm2] the beamcross section and c is a form factor which depends onthe shape of the beam cross section. For a rectangularcross section b ≤ h/2 and c = 3/2, whereas for a circularcross section c = 4/3. These formulas are approxima-tions for the centerline. The strain gauge covers a certainarea around the centerline such that the integrated valuemeasured by the strain gauge will be smaller. The signalof the transducer can be determined using the equationΔU/U = kε45◦ for the full bridge output as well as theequation ε45◦ = τmax/2G for the strain under the gauge.

For a torque transducer the shear stress must be cal-culated using τmax = Mt/Wp [N/mm2], where Mt [Nm]is the torque moment and Wp [mm3] is the polar sectionmodulus.

Tension and Compression Load CellsThe main difference between shear- and bending-stresstransducers and load cells using tension and compres-sion stress measurements is that in the case of the latterthere is no positive and negative stress of equal value. Ifthe tension stress σtension = F/A is defined as positive,the negative compression stress becomes σcomp = νF/A,termed the Poisson stress. For metals ν = 0.3 while

Fig. 8.27 Parallelogram-type load cells

the compression stress is only about 1/3 of the ten-sion stress. Using a Wheatstone bridge with four gaugesapplied, as shown in Fig. 8.30, the output of such a trans-ducer related to the force (F) will be nonlinear. This isnot a big disadvantage as long as these nonlinearities aretaken into account through calibration.

For standard load cells a nonlinear characteristic isnot very common, however for applications in wind-tunnel testing they are some times advantageous sincethey do not require much space. Another advantage of

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Fig. 8.29 Torquetransducer

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Fig. 8.30 Tension-type load cell (left) and cage of tensionand compression columns (right)

such a transducer is that the strain gauges are placedvery close to each other, thus remaining at the sametemperature level. This minimizes the zero-drift andtemperature-gradient sensitivity of the transducer. Insome wind-tunnel balances such tension and compres-sion columns can be arranged in a cage. In such a wayit is possible to measure tension and compression aswell as the moments acting on the metric side of thetransducer.

8.1.12 Multi-Component Load Measurement

The fundamental criterion of all multi-component loadmeasurements is that all the loads acting on a model mustbe separated into single components as best as possible.In order to measure each single component at least oneassociated transducer per component must exist. Thiscriterion can be best fulfilled in external wind-tunnelbalances, where plenty of space is available to separatethe load by decoupling rods with flexures. Sting bal-ances are much smaller and so this criterion can be onlypartially fulfilled. Consequently, interactions or interfer-ences in the measurement of the different componentsmust exist.

The interactions inside a balance are systematicerrors which can be determined through calibration.Therefore it is often necessary to measure more compo-nents in order to separate the errors during calibration.Another reason for having more measurement sectionsthan components is to measure the errors caused bytemperature gradients inside the balance. Temperaturegradients cause deflections of the metric part against thenon-metric part which in turn are measured by the straingauges. This is also a systematic error which can be sep-arated through calibration. In order to extract the loads

from the balance signals, the following equation mustbe resolved:

F = ES , (8.25)

where F is the force vector, E is the evaluation matrixand S the signal vector.

Through calibration one obtains an evaluation matrixwhose elements take all the interactions and systematicerrors into consideration. For a balance with no inter-actions, the six sensitivities for each component are thediagonal of the evaluation matrix while all other ele-ments become zero. For a balance where nonlinearitiesup to the third order are considered, the evaluation matrixconsists of 6×33 = 198 elements.

8.1.13 Internal Balances

Two general groups of internal balances exist. The firstgroup consists of the so-called box balance. These canbe constructed from one solid piece of metal or can beassembled out from several parts. Their main character-istic is that their outer shape most often appears cubic,such that the loads are transferred from the top to the bot-tom of the balance. The second type of internal balanceis termed sting balance. These balances have a cylindri-cal shape such that the loads are transferred from oneend of the cylinder to the other in the longitudinal di-rection. Both one-piece and multi-piece sting balancesexist.

Sting BalancesInternal sting balances are divided into two differentgroups. One group is the force-balance type and the othergroup is the moment-balance type. If the bridge output isdirectly proportional to one load component then thesebalances are termed direct read balances. Typically forall groups, the axial force and rolling moment are di-rectly measured with one bridge. The measurements oflift force and pitching moment or for side force and yaw-ing moment are done in different ways characterizingeach group.

Moment-type balances and force-type balances haveone main feature in common, being the lack of a direct

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Fig. 8.31Separation offorce and mo-ment

output proportional to lift/pitch and side force/yaw. Thesignals which are proportional to each of these loadsmust be then calculated by summing or subtracting thesignal from one another, before being fed into the datareduction process. The advantage is that the associ-ated concentrated wiring on each section is much lesssensitive to temperature effects.

Force Balances. This type of balance uses two mea-surement sections placed in both the forward and the aftsection of the balance. In these measurement sectionsa forward and aft force is measured most often throughtension and compression transducers. These forward andaft force components are used to calculate the resultingforce in the plane as well as a moment around the axis(perpendicular to the measurement plane). An exampleof a typical force balance is shown in Fig. 8.32.

Moment-Type Balances. Moment-type balances havea bending moment measuring section in the front aswell as in the aft regions of the balance (S1 and S2 inFig. 8.33).

The measurement of the two bending moments (S1and S2) is used to obtain a signal which is proportionalto the force in the measurement plane and a second onewhich is proportional to the moment around the axis(perpendicular to the measurement plane). The stressdistribution shows that the moment My (Mz) is propor-tional to the sum of S1 and S2. However, the force Fy(Fz) is proportional to the difference in the signals S1and S2.

To measure the rolling moment (Mx) one bendingsection must be applied with shear stress gauges to de-tect the shear stress τ . The most complicated part ofthe balance is the axial force section which consists offlexures and a bending beam to detect axial force. Theseflexures enable axial movement whilst carrying the otherloads.

Direct-Read Balances. A direct-read balance canbe categorized as either a force-balance type or asa moment-balance type. Instead of measuring a forceor a bending moment at each section separately, halfbridges on every section are directly wired to a momentbridge while the other set of half bridges are directlywired to a force bridge. Thus the difference betweendirect-read balances and the other types is only in thewiring of the bridges. The disadvantage of such a wiringis the length of the wires from the front to the aft ends.Temperature changes inside these wires cause errors inthe output signals.

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Box BalancesThe main difference between box balances and stingbalances are the model and sting attachment area(Fig. 8.35). The load transfer in such balances is from

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top to bottom along the vertical z-axis. Therefore thesebalances use a central sting arrangement, as shown inFig. 0.30 for the case of an airplane configuration. Themono-piece balance is constructed from one single pieceof material. The advantage of this relatively expensivemanufacturing process is the low hysteresis and goodcreep behavior, which are basic requirements for goodbalance repeatability. Multi-piece box balances are builtfrom several parts which can in turn be manufacturedseparately. The load transducers can either be integratedin the structure or separate load cells can be used in-stead. This enables a parallel manufacturing processwith a final assembly at the end, in turn making the wholeprocess quicker than that for a mono-piece balance.Box-type balances are considered internal balances, buthave actually more in common with semi-span balances.In particular their temperature-sensitivity behavior issimilar to that of semi-span balances.

Principle Design EquationsAll internal balances measure the moment and the forcein two different sections along the x-axis. The distancebetween the two sections defines the separation of thesignal between force and moment. In the ideal case, halfof the signal should be proportional to the force and theother half should be proportional to the moment.

To obtain the same output for the force and the mo-ment, the distance l = l1 + l2 between the two sectionshas to be calculated. For a moment-type balance theserelations can be described by the following equations

σ1 = MB1

W1= M + Nl1

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σ2 = MB2

W2= M − Nl2

W2, W1 = W2 , l1 = l2 ,

(8.26)

where σ1 and σ2 are the stresses in sections one and two,respectively. These stresses are caused by the moment(M) and the force (N). W1 and W2 are the section moduli.The sum as well as the difference of these two stressesare

σ1 +σ2 = M

− l2W2

W, (8.27)

σ1 −σ2 = M

W1− 1

+ l2W2

W. (8.28)

In (8.27) it can be seen that the sum of the stressesis only proportional to the moment (M) and in (8.28)it can be seen that the difference of the stresses is onlyproportional to the force (N). Consequently the sumof the bridge signals S1 and S2 is proportional to themoment (M) while the difference of the bridge signal S1

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and S2 is proportional to the force (N)

σ1 +σ2 ≈ ΔUM

σ1 −σ2 ≈ ΔUN (8.29)

At this point the ratio of the sum and the differenceof the signals can be calculated

ΔUN= 2M

Nl. (8.30)

For a given moment (M) and a given force (N),the aim is to have the ratio of the signal equal to one.The distance (l) between the measuring sections can becalculated in the following manner:

l = 2M

N. (8.31)

This equation is also valid for force-type balances.Therefore for the same force and moment output, thereexists an optimum distance between the measuring sec-tions; thus the length of the balance can be in this waydetermined. If the required load combination results ina length that does not fit into the model, then the distancebetween the measuring sections must be compromisedin such a way that the signals for the force or the momentare smaller than the other.

Another problem appears when the distance betweenlift and pitch in the x − z plane is different than thedistance between side force and yaw in the y − x plane.One solution is to use different measuring sections, butthis will enlarge the total length of the balance and isusually avoided.

For a single-test setup normally the balance lengthcan be easily optimized for the model. However, the bal-ance load range definition is more often a compromisebetween requirements for different test setups, wherethe maximum loads for all tests form the envelope ofthe combined-load range specification. In such casesvery seldom can a good compromise for the balancedimensions be found.

Specific-Load Parameter. Before designing the bend-ing section it is good to first determine whether thebalance will have high loading or not. Loading in thiscase refers to the ratio between the loads and the avail-able volume for the balance. This ratio expresses themagnitude of the stress level inside the balance beforestarting with the calculation. This ratio is also referredto as the specific-load parameter

Sround = N + L/2+ M

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Srectangular = N + L/2+ M

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where L is the active length of the balance withoutinterfaces, D is the diameter, and B and H the max-imum available width and height of the balance. Thefirst equation is used when the main cross section ofthe balance is circular whereas the second one whenthe main cross section is rectangular. Experience showsthat highly loaded balances have a specific load param-eter greater than 1000 N/cm2. In this case the highlystressed areas occur not only in the area where straingauges are applied, but also in the flexures of the axialforce elements.

Bending Section Design. After the distance of the mea-suring section is fixed, the bending sections must bedesigned such that the output and full scale are on theorder of 0.5 mV/V to 3 mV/V. The design output de-pends on the data acquisition equipment to be used.Some systems have a maximum input and therefore itmust be guaranteed that no overflow occurs. This is thecase even for a single maximum load which can be upto 100% higher than the maximum combined load. Inmost cases, for maximum output of the design load-ing, the sum of the full scale output of the force andthe full scale output of the moment are the limiting fac-tors. Usually the maximum full scale output is around1.5 mV/V.

In order to determine the geometry of the bend-ing section it is sufficient to use handbook formulas.If a careful calculation is made the accuracy of the pre-dicted full scale output will be ±10%. Since the real

Fig. 8.39 Massive rectangular geometry (left), massive cross geometry (center) and cage with five beams (right)

gauge factor at this stage is not yet known, it is good touse k = 2 as default. Normally the real gauge factor issomewhat higher and so the final output of the sectionis usually higher than calculated.

To design the optimum cross section many differentdesigns are used. Some commonly-used geometries areshown in Fig. 8.39.

Possible Geometries for Bending Section Design. Onthe surface of the massive cross sections (cross, rectan-gular or octagonal in shape) the surface stresses causedby the bending moment are measured. In a cage de-sign the tension and compression stresses in the singlebeams are measured. This design is preferable when thespecific load parameter is lower than 300 N/cm2. Dur-ing the bending section calculation the measurement

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sections for five components must be designed. Thesecomponents are: lift, pitch, side force, yaw and roll.

Axial Force Section Design. The axial force mea-surement requires much attention in the design andconstruction stages. Most of the cost for an internalbalance is attributed to the axial force system. Usu-ally the axial force is very small in comparison to theother forces and moments such that the sensitivity ofthis measurement must be extremely high. This in turnmakes the axial force sensitive to interactions of theother components.

In Fig. 8.40 the components of a typical axial forcesection are shown. The left-hand and right-hand sides ofthe balance are connected by the flexures. These flexurescarry the loads of all five components but are relativelyflexible in the axial-force direction. Most of the axialforce (more than 60%) is supported by the cantileverbeam in the middle of the balance.

The axial force measurements are best made in themiddle of the axial force section, since the mechanicalinteractions are minimal in this position. For thermaleffect compensation, in particular temperature gradi-ents, it is better to have four rather than two axial forcemeasuring beams placed near the flexures.

8.1.14 External Balances

Balances have been used since the beginning of aerody-namic testing. One of the first balances ever used wasbuilt by Otto Lilienthal. In Fig. 8.42 Lilienthal’s appara-tus for the measurement of lift can be seen. The apparatus

(ΔFrm) is given as:

ΔFrm =n∑

n. (8.37)

Subsequently the experimental standard deviation canbe calculated from the following equation:

√√√√√n∑

i=1(ΔFri)

n −1. (8.38)

The analysis of the residual loads gives the balance userinformation about the accuracy class of the instrumen-tation under certain environmental conditions. All theconditions which were kept constant during calibration,like temperature and humidity may have another influ-ence on the accuracy of the measurement in the tunnelitself. Thus the effects of temperature must be correctedor calibrated separately. Another source of error not of-ten taken into account is creep. Creep effects in thebalance must be tested separately as well.

All these tests provide information about the accu-racy of the balance. However, a few problems remain.Firstly, how to formulate the requirements for the accu-racy in a specification? Secondly, how to compare theserequirements with the calibration data? One suggestionto solve these problems was made by Ewald and Graewein the early 1980’s and is briefly described in [8.7]. Anequation was formulated that would take into accountthe error influenced by the number and the magnitude

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of the interactions:

δi = AFi max

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∣∣∣∣ Fi

Fi max

∣∣∣∣⎞⎠ , (8.39)

where δi is the allowed residual load, Fi max is the max-imum combined load of component i and Fi the loadsapplied during calibration. The factor A is the generalaccuracy factor and the accuracy factor ai is for the indi-vidual component i. bi is a weighting of the interaction.The customer can specify the factors A, ai and bi andafter calibration the balance manufacturer has to verifyif all the residual loads are below these specifications.A more global verification is to calculate the factors A,ai and bi from the calibration data and to compare themwith the specifications.

All other influences on the accuracy of a balance canbe integrated by using the error propagation law. For theinfluence of the temperature the (8.39) is rewritten as

δi = AFi max

⎡⎢⎣

⎛⎝ai +bi

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∣∣∣∣ Fi

Fi max

∣∣∣∣⎞⎠

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⎤⎥⎦

. (8.40)

Calibration PrinciplesTo obtain the above mentioned data several principlesare used during calibration. The first one most used in

Force and Moment Measurement 8.2 Force and Moment Measurements in Aerodynamics and Aeroelasticity 41

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Fig. 8.67 Demonstration of the high resolution of thepiezo-balance in its range of highest sensitivity. A 1 gweight was hung from the balance, and then the significantjump was caused by unloading the weight

or a platform balance, which are based on four of thelarger transducers (9067). The typical maximum loadfor each component is at least Fi ≈ 10 kN. Thus, themeasuring range extends over six orders of magnitude,since the threshold for dynamic measurements is as lowas 0.01 N. Experience shows, as does the later resultin Fig. 8.71, that quasistatic measurements are possi-ble down to lower than F ≈ 1 N. Consequently, in thequasistatic mode a measuring range of four orders ofmagnitude is attainable.

ReproducibilityIn order to get a measure for the reproducibility, in a timeperiod of a few hours a calibration cycle was repeated10 times under normal laboratory conditions. For thistest, a platform balance for half-span models was used,based on the larger transducer (type 9067). One calibra-tion cycle was performed with calibration weights of 5,10, 20, 35 and 50 kg and they lasted roughly 15 min. Ta-ble 8.5 shows the results of the measurements. The 2ndcolumn displays the sensitivity of the x-component Exin [pC/N], determined from the slope of the calibrationcurves. The 3rd column singles out one measuring pointof the calibration cycle, the voltage Ux corresponding toa load of 50 kg.

Calculating the mean and the standard deviation wefind for the sensitivity of the x-component:

Ex = (7.8634±0.0005) pC/N . (8.42)

Table 8.5 Results of 10 calibration cycles repeated undernormal laboratory conditions

Cycle No Ex (pC/N) Ux (V/50 kg)

1. 7.8637 1.9287

2. 7.8638 1.9287

3. 7.8625 1.9283 min

4. 7.8634 1.9285

5. 7.8630 1.9285

6. 7.8633 1.9284

7. 7.8632 1.9285

8. 7.8631 1.9285

9. 7.8644 1.9288 max

10. 7.8636 1.9285

Mean 7.8634 1.9285

Stand. dev. 0.0005 0.0002

The ratio between the difference of the peak valuesand the full scale range can be seen as a measure ofthe reproducibility. These values can be derived fromthe 2nd column: largest deviation U ′ = Uxmax −Uxmin =0.5 mV, full-scale range (x12 + x34) each 10 V ⇒ UFS =20 V.

Thus the reproducibility has a value of:

UFS= 0.025%0 . (8.43)

These results are also, at least, representative for theother external balances and they demonstrate that it ispossible to attain good accuracy if one is able to holdthe ambient conditions constant.

Behaviour Under Cryogenic ConditionsAs mentioned in the introduction, a piezoelectric balancewas built for the cryogenic Ludwieg tube in Göttingen(KRG) in such a way that the balance itself is totally inthe cryogenic environment. This fact is not self-evidentas such a balance has to withstand a large amount ofthermal stresses when the temperature is changed overthe entire range of the cryogenic facility.

To clear up the question as to the extent the forcemeasurements can be made with piezoelectric transduc-ers at cryogenic conditions was one motivation for thisactivity.

At our request, a special version of transducer type9252 was manufactured by Kistler for application atcryogenic temperatures. The modification concerns theinsulators in the plugs by default made from silicone,which were replaced by ceramic ones such that applica-tion down to cryogenic temperatures (T = −150◦) andpressures up to 10 bar was more feasible. The modifi-

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Fig. 8.68 Determination of the sensitivity of the shearcomponents Fx and Fy of the cryo-balance depending ontemperature

cation mainly ensures that no humidity effects diffusein the transducer case during the unavoidable largetemperature changes.

Before application in the windtunnel, the bal-ance with the modified multicomponent transducers(Sect. 8.2.1) was tested and calibrated in a cryostat downto a temperature of T = −160◦. The low temperaturewas produced by injection of vaporised nitrogen. Forthe connection between the force transducer in the cryo-stat and the charge amplifier outside, the usual cablesfor piezoelectric sensors could be used.

In the pre-tests we found no significant deviationin the behaviour of the balance compared with nor-mal conditions concerning drift or electrical noise ofthe signals.

The calibration was conducted using weights, whichwere appended outside of the cryostat via cables. Con-cerning the axial component Fz , it was found thatthe cool-down from 24◦ to −169◦ led to a con-traction of the prestressing bolts resulting in 1.5 kNincrease of the prestressing force, which is one or-der of magnitude smaller than the standard prestress.This effect was caused by the different thermal expan-sion coefficients of the transducer and the prestressingbolt.

Both shear components Fx and Fy showed goodlinearity compared to that at normal conditions, andthe slopes i. e. the sensitivities, dependent on temper-ature are displayed in Fig. 8.68. It is obvious that thesensitivity slightly changes with temperature. This sen-sitivity shift is caused by the fact that the correspondingpiezoelectric coefficient (d11), which is responsible for

the shear effect, is slightly increasing with decreasingtemperature [8.17].

In this context, it should be mentioned that at normalconditions, arrangements of force transducer are alsosensitive to temperature changes during a measurementcycle. This problem concerns, in particular, the directionof the prestressing bolts. Thus, in any case the bal-ances must be protected against changes in the thermaldistribution, at least while a running measurement.

Measuring Time for Quasistatic MeasurementsAs mentioned, the piezoelectric measuring system is anactive one, which generates an electrical quantity. Hereinlies a fundamental disadvantage, namely that only qua-sistatic measurements are possible. A time constantT = RgCg, characteristic for the exponential decline ofthe charge signal, results from the entire input capac-ity Cg and the finite insulation resistance Rg, posed bythe transducer, cord, plugs and amplifier input etc. Fur-ther fault currents in the charge amplifier, which arefortunately independent from the load, cause the zero-point to drift. Thus the combined error is smaller, thelarger the charge on the quartz, meaning that the ef-fective measuring time increases as the loading and thesensitivity increase. Fortunately, the drift is dominatedby the fault currents in the input devices of the chargeamplifier, which are nearly constant, leading to a lineardrift depending on time at the output. The sign of thedrift can be positive or negative. A simple linear cor-rection for every test point in time can be computed asfollows: For each measurement, the raw data, integratedin time, and the corresponding time are stored. Know-ing the zero point before the measurement (flow speedU = 0) and after the measurement (where the flow speedis zero again), a correction can be computed by linearinterpolation.

In order to give an impression on the drift behaviourunder nearly extreme conditions, the time function ofthe 3 components of the cryo-balance were recorded,while the balance was attached to the calibration setup,i. e. without load and under good environmental lab-oratory conditions. In addition, the cables and plugswere verified to have an overall resistance of at leastR ≈ 1013 Ω. In another (unfavourable) condition, thesystem was switched in the range of highest sensitiv-ity, where the drift effect was maximal. Figure 8.69shows first, that the drift was rather linear for all threecomponents and secondly, that at least at good environ-mental conditions the drift effects are not as extensiveas generally believed. In other words, the results showthe probable lower reachable limit when the compo-

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Fig. 8.70 Measurement of a relatively small dragforce Xon a building model, taken in the boundary layer windtunnel of the University of Florence using the cryo-balance(u = const = 4.3 m/s. wind off at t = 0 and t > 7 m). Xu:uncorrected values i. e., without drift correction

nents such as plugs, cables etc. are selected and the testconditions are nearly optimal.

In order to provide an impression of the drift errorat small loads, an example is presented in Fig. 8.70,taken in the boundary layer windtunnel of the Uni-versity of Florence. A simplified building model wasmounted at the cryo-balance corresponding to the sketchin Fig. 8.58. The figure shows a measurement of a rela-tively small drag force of X = 3.1 N at a low flow speedu = const = 4.3 m/s dependent on time t. The airflowwas started at t = 0 min and switched off for t > 7 min.

The index u (Xu) denotes values without drift correction.Looking at the + symbol(uncorrected) at t = 0 min, wesee a small deviation in negative direction, caused byswitching on to the operate mode. At the end of themeasurement run at t = 8.5 min, there is also a small de-viation but in positive direction. The small difference inthe outputs between start and end is caused by the driftin positive direction. After correction, the correspondingpoints (symbol ∗) lie on the zero line.

Although the windtunnel speed is not exactly con-stant, we can state that the effect of the drift of thezero-point is not as extensive as generally believed.

8.2.3 Examples of Application

Bluff Bodies in a High-Pressure WindtunnelThe flow around a circular cylinder is a classical prob-lem of fluid dynamics, which exhibits strong Reynoldsnumber effects mirrored in drastic variation of the dragcoefficient and Strouhal number. A second classical bluffbody case is the sharp edged, square section cylinder,which has a high drag coefficient nearly independent ofthe Reynolds number.

Thus, both sections were selected as examplesconcerning force measurements performed in the high-pressure windtunnel (HDG). The flow speed rangedfrom 2 m/s to 38 m/s, the pressure could be increasedup to 100 bar and the test section measures 0.6×0.6 m2.Since even steady loads in this low-speed wind tunnelcan vary over four orders of magnitude merely by chang-ing the flow parameters, the results give an impressionof the large dynamic range of a piezo balance. Indeed,this property of the wind tunnel and the deduced require-ment of a large dynamic range motivated the author todesign and built his first piezo balance [8.?].

The principle setup of the balance was describedin Sect. 8.2.1 (Fig. 8.63). We selected the larger 3-component force measuring elements (Kistler, type9067), because of their large load range. A special dif-ficulty when measuring in the high-pressure windtunnelis the fact that the model, the sensors and the balance arelocated in the high pressure section, where it is desirableto have the electronic equipment outside at atmosphericpressure. Since one of the primary prerequisites for qua-sistatic measurements is that an insulation resistanceof R ≈ 1013 Ω is reached for all connections betweenthe force element and charge amplifier, a special solu-tion was necessary for the crossover from the high tothe atmospheric pressure section. Because this require-ment is difficult to satisfy with hermetic connectors, thenecessary cables were inserted into flexible pressure-

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Fig. 8.71 Measurement of drag coefficients of a circular-and a square cylinder in the high-pressure windtunnel. Dueto the large dynamic range of the balance the individual Renumber range could be overlapped by merely changing theflow parameters

resistant hoses, which were pressure sealed connectedat the transducer and then laid out through the windtun-nel wall and connected to the charge amplifier outside of

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Fig. 8.72 Power spectra of the lift- and drag fluctuations on a squarecylinder at an angle of incidence of α = 10◦. Even the very lowintense sub- and superharmonics can be resolved. The distance ofthe peak height is up to 50 dB

the high pressure section. In this way, atmospheric pres-sure was maintained within the element, as well as in thecorrugated hoses, so that an increase of static pressurein the windtunnel acts as a preload on the element. Sincethe zero-point in the sensor/charge-amplifier system canbe chosen arbitrarily by short-circuiting the charge, thepreload in axial direction has no significant influence onthe accuracy of the measurement.

This modification of the force transducer for applica-tion at high pressure up to 100 bar was also manufacturedby Kistler.

Such modified transducers were also applied in sev-eral water tanks in Hamburg to measure the forces onship models and marine structures [HSVA Jochmann].A detailed description of the balance and many resultsconcerning flow around more or less bluff bodies can befound in [8.10, 11, 18–20].

As an example of a quasisteady measurement,Fig. 8.71 shows drag coefficients of a circular cylinderand a square cylinder dependent on the Reynolds num-ber. The flow speed was increased up to 40 m/s and thepressure up to 51 bar. In the case of the circular cylinder,the smallest drag force was 0.8 N at the lowest Reynoldsnumber. The largest drag force was about 2000 N for thesquare cylinder at Re ≈ 5×106. Since only about 20% ofthe range of the balance was used, it was demonstratedthat, in principal, steady measurement over four ordersof magnitude was possible. As for fluctuating forces, thedynamic range is extended to six orders of magnitudebecause the resolution is about 0.01 N.

Figure 8.72 depicts a typical dynamic measurement,which is representative of the ability to resolve and de-tect even very weak nonlinear effects in a global forcemeasurement. The figure shows the power spectra ofthe lift – and drag fluctuations on a square cylinder atan angle of incidence of α = 10◦. In this state, the freeseparated shear layer is probably more or less regularlyattaching to the side wall of the square cylinder pro-ducing sub- and superharmonic peaks. It is surprisingthat this localised effect can be found and resolved ina global, i. e.integrated measurement. In addition, apartfrom the fundamental Strouhal peak and the sub- and su-perharmonics, there are significant peaks at 3/2 and 5/2of the vortex shedding frequency [8.21]. The dynamic isreflected in the distance between the spectral densities,which is up to 50 dB.

Further applications concerning force measurementon a bridge section and an airfoil at high angle of attackcan be found in Schewe [8.19].

Typical Half-Span Modelin a Conventional Low-Speed Windtunnel

The wing/engine combination described in Sect. 8.2.1was tested in the low-speed windtunnel (3 × 3 m2) inGöttingen. The project comprised force and pressuredistribution measurements. The influence of the thrustof the ejector engine on the aeroelastic and aerodynamicbehaviour of the wing/engine combination was of par-ticular interest. For this reason, in the engine model fourmulticomponent force transducer were installed to mea-sure separately the global forces on the engine. Moreabout the motivation for the project, a detailed descrip-tion of the test setup”, and the results of the pressuremeasurements can be found in Triebstein et al. [8.15].

Figure 8.73 shows as an example the steady normalforce and its rms value for angles from −4◦ up to 14◦,taken at a flow speed of 60 m/s. In this case the bal-ance was not fixed to the windtunnel, but rotated withthe model, thus the normal force on the wing and notthe lift was measured. The results demonstrate that themeasurement of steady forces is possible with sufficientaccuracy. The angle α = 0 was measured twice – at the

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Fig. 8.73 Normal force coefficient and corresponding rmsvalue depending on angle of incidence of a wing/enginecombination in a low-speed windtunnel. CN (α) is nota straight line since the balance is rotated with the wing.After the discontinuous drop of the steady normal force at13◦, the rms jumps to nearly double its previous value

beginning and at the end of the test run. Within drawingaccuracy, both measuring points overlap.

Referring to the span of the measurement range, itshould be mentioned that at the maximum normal forceof more than 1000 N, the range of the balance is usedby only about 6%, meaning that this balance can also beapplied at much higher loads (i. e. in the transonic rangewithout any changes being necessary.

As an example for an unsteady measurement, in theupper part of the Fig. 8.73 the rms of the normal forceis presented, which is nearly constant below the onsetof flow separation. After the discontinuous drop of thesteady normal force at 13◦, the rms jumps to nearlydouble its previous value. One has to bear in mind thatinertia forces are included.

The rms of the bending moment was also measured,and it has similar behaviour. All rms values were ob-tained by integrating the corresponding power spectra.Figure 8.74 shows two examples of normal force spectra,immediately before and at the onset of the flow separa-tion. The dotted line represents the spectrum taken atα = 13.2◦, the solid line the spectrum taken at 13◦. Thespectra are dominated by a rather narrow peak at thebending frequency of the wing. The bending frequencyis excited by the noise-like random contributions whichare inherent in the flow. Particularly after the onset ofthe flow separation, the intensity of the fluctuating aero-dynamic loads and, consequently, the bending vibrationof the wing increase drastically. Hence, the rms jumpsto nearly double its previous value in the normal forceand bending moment. When considering these unsteady

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force measurements, it is important to remember thatthe signals contain several components. In addition tothe aerodynamic loadings, contributions of elastic andinertia forces due to the vibration are also present.

Finally, it can be stated that the changes of the flowfield at the onset of separation lead to a small frequencyshift of the bending frequency. This frequency change,Δ f , represents a small contribution to the stiffness,caused by aerodynamic effects.

As for the balance, the spectrum shows that thereare no significant peaks which could be produced by thebalance itself.

Aeroelastic Experiments:Oscillating Models in a Transonic Windtunnel

Aeroelasticity studies the interplay between elasticstructures in an air stream and its aerodynamic forcesand moments. The interaction between aerodynamicand structural forces may lead to complicated nonlinearstatic and dynamic effects, for example the feared flutteroscillations. Thus knowledge of the steady and unsteadyforces and moments is very essential. Therefore threedifferent setups for aeroelastic experiments at airspeedsup to the transonic regime have been developed. Thesesetups are usually applied in the 1 m×1 m adaptive testsection of the transonic windtunnel in Göttingen.

The first setup sketched in Fig. 8.75 is designed forinvestigating flutter phenomena of airfoil models. It issymmetrically built from blade- and cross-springs fora bilateral elastic suspension. To measure the steady andunsteady forces, a piezoelectric balance is installed oneach side between the bending and the torsion spring.Each balance corresponds to the platform balances com-prising four multicomponent elements (type 9252) asdescribed for half models in Sect. 8.2.1. In case of flutteror forced motion the balance is oscillating in heaving di-rection. Therefore the smaller transducers were selecteddue to their lower weight and the advantage gained byreducing the moving masses.

Figure 8.75 also shows a schematic representationof the flutter-control system used to dampen or exciteoscillations of the model. A laser vibrometer was usedto measure heaving motion of the airfoil oscillations.

Fig. 8.76 Artificial initiation of selfexcited flutter oscilla-tions in a hysterisis regime (subcritical bifurcation). Theinitial amplitudes are set for different temporal lengthsvia positive feedback. The limit amplitude of α = 1.2◦acts as a repeller. Depending on whether or not the ini-tial amplitudes lie below or above this threshold value, theoscillations will be damped or excited

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Fig. 8.77 Pitch test setup for forced torsion oscillations. The installation of both optional torsion springs (cross springs)gives the wing a torsion degree of freedom for investigating torsional flutter. The piezoelectric balances are between thehydraulic actuators and cross springs

The heave-speed signals were fed into an operationalamplifier and then into one electrodynamic exciter ateach side. The excitation is acting directly on the bend-ing springs in heave direction, whose connecting boxforms the basis for the piezoelectric balance. Thus theexcitation forces do not act directly on the piezoelectricbalance, but rather appear only indirectly in the balancesignals since the heave motion of the airfoil induces in-ertial forces. Forced heave oscillations can be driven byreplacing the electrodynamic exciters by stronger hy-draulic linear actuators. The exciter force Fex itself canbe measured directly with the one component piezo-electric force sensor (Kistler 9301 A), built into theheave rod.

Figure 8.76 shows an instructive example of a fluttermeasurement using a symmetrical NACA 0012 airfoiltaken at the flutter boundary. The state of the system iscritical i. e. in the transition range between stability andinstability. We will see that it is a hysteretic-encumberedtransition (subcritical bifurcation), which was recordedat a mean angle of attack of α = 1.1◦. The curvesplotted in the Fig. 8.76 are for (a) the angle of attackα(t)−αmean, (b) the lift force L(t), and (c) the heave-rodforce Fex of the excitation, measured with the piezoelec-tric transducer. First we see in the offset that the mean liftis 0.7 kN. Second the time functions demonstrate howthe system reacts to disturbances of different strengths ordurations. Such a disturbance occurred when the controldevice was switched to positive feedback for a shorttime. The period of excitation of the system can beclearly seen in the curve for Fex(t), where the ampli-tudes shoot up at the indicated time points at t ∼= 11.3,

14.2, 16.5, and 20.0 s. It is also obvious that the timespan of the disturbances increases with increasing time.Whereas the flutter oscillations decay after the first threeshort bursts of excitation, they diverge after the fourth,the longest of the excitations. This behaviour indicatesthat we must be in the hysteresis range of a subcriti-cal bifurcation, i. e., the last disturbance was sufficientto lift the system above an unstable limit cycle, whichthen acted as a repeller to cause the increase in the am-plitudes. At this point, we should note that the forcesneeded to influence the system are about two orders ofmagnitude smaller than the lift forces that occur, eventhough Fz(c) still contains inertial forces.

Finally the example shows that it is possible toperform measurement of steady and unsteady forces un-der very difficult conditions, i. e. while the balance isoscillating.

By use of the second test setup (Fig. 8.77), the aero-dynamic effect of forced pitching motions of a modelmay be investigated. In this case, two torsional hy-draulic actuators work with 180◦ phase shift and forcethe pitching motion of a two-side suspended model inthe air stream. It is successfully used for example intesting airfoil models equipped with piezoelectricallydriven flaps for dynamic stall control. The piezo-electric actuators use the inverse piezoelectric effectand are described by Schimke et al. [8.22]. This testsetup can be upgraded with a torsional degree offreedom in order to investigate free pitch oscillationsof the model. To measure the steady and unsteadyforces, the same piezoelectric balances described abovecan be installed on each side between the hydraulic

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Fig. 8.78 Power spectra of moment fluctuations for differ-ent angles of attack for a fixed supercritical airfoil. Withincreasing α a peak at the buffet frequency of ω∗ = 0.56shows up. The corresponding steady lift coefficients cl arealso included

actuators, the model, and the optional crossprings,respectively.

The ability to investigate unsteady phenomena likebuffet oscillations in transonic flow is demonstrated inFig. 8.78 where spectra of the moment fluctuations arepresented. In this case, the crossprings were not in-stalled, the model with supercritical section (NLR 7301)was at rest, and the angle of incidence α was varied usingthe hydraulic actuators.

These spectra show what happens when α is in-creased while the Mach number is held constant atMa = 0.75. Above an angle of attack of α = 1.5◦, thereappear peaks in the spectra that can be traced back toselfexcited shock oscillations (buffet) and, therefore, be-cause of the absence of the necessary degrees of freedomfor oscillations, have purely fluid-dynamical origins.The non-dimensional buffet frequency has a valueof ω∗ = 0.55, which corresponds to a frequency off = 72.7 Hz. Simultaneously, the mean lift was meas-ured and the values are included in the figure. For thistype of measurement, the high stiffness of the twin sidedpiezo-balance is a significant prerequisite. The test se-tups and the experiments are described in more detail bySchewe et al. [8.23].

The third test-setup, sketched in Fig. 8.79, shows thata wing model is mounted on a turntable device such thatthe wing meets the sidewall with a negligible gap. Theturntable device allows adjusting the model’s angle of at-

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Fig. 8.79 Test setup for oscillating half models in the tran-sonic windtunnel. The piezo balance is located at the rootof the wing

Fig. 8.80 Elastic wing models in the adaptive test sectionof the transonic wind tunnel

tack around an axis perpendicular to the sidewall of thetest section. Furthermore, the model can be forced bymeans of a hydraulic rotation actuator to perform pitchoscillations around the spar axis plotted in Fig. 8.79.Laser triangulators are used to measure the pitch accord-ing to the spar axis. Also here, a piezoelectric platformbalance is used to measure the root loads outside of thetest section. The time-averaged signal of the balance al-

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Fig. 8.81 Comparison of the lift-curve slope ∂c1/∂α and ∂cm/∂c1 for the rigid and the elastic model upon the Machnumber

lows determining the global aerodynamic loads, whilethe unsteady part of the balance signal represents thesum of unsteady air loads and inertia forces.

Figure 8.80 shows the half-spanmodel of the project“Aerostabil” [8.24] mounted in the adaptive testsectionof the Transonic Windtunnel Göttingen (TWG). Thereare two models with the same outer geometry, repre-senting the outer part of a transport aircraft wing witha supercritical airfoil section. The first model was de-signed conventional, i. e. as rigid as possible and thesecond was elastically scaled corresponding to the pro-totype. The aim was to study the static aeroelastic effects,

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Fig. 8.82 Half-span model twisted and bended by air loadsin the state of a limit cycle oscillation (LCO). Such mea-surements postulate a rigid balance

which were often ignored in the past. Figure 8.81 showsthe influence of the elasticity of the swept wing forthe dependence of the lift curve slope ∂CL/∂α and thepitching-moment-slope curve upon the Mach number ata constant angle of incidence at the model root and con-stant Reynolds number. Significant differences due toelastic deformation can be seen as the lift curve slopeis reduced up to 16% at Ma = 0.83. For the highestMach numbers, the regions on the wing with flow sepa-ration are probably larger in the case of the rigid modelresulting in smaller values of the lift curve slope.

If the elasticity of a half-span model is designed in anappropriate way, flutter tests can be performed in this testsetup as can be seen in Fig. 8.82. We see a snapshot of thehalf wing twisted and bended by the steady air loads, inaddition the wing is undergoing flutter i. e. a limit-cycleoscillation (LCO) at a Mach No. of Ma = 0.865.

Circular Cylinder in a Cryogenic-Ludwieg-TubeThe flow around a circular cylinder and its dependenceon the Reynolds number is one of the most importantproblems and favourite test cases in fluid dynamics.Thus, this simple geometry was selected for the firstapplication of the piezoelectric balance under cryogenicconditions [8.25].

The measurements were performed in the cryogenicLudwieg tube in Göttingen (KRG), which is a blow-down windtunnel for high Reynolds number researchin transonic flow and is described by Rosemann [8.26].The Mach number range is 0.28 < Ma < 0.95 and highReynolds numbers up to more than 107 are achieved by

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Fig. 8.83 Drag depending on time for a circular cylinder,measured with a piezo-balance in the cryogenic Ludwiegtube at extreme conditions (Re = 5.8×106, Ma = 0.28, T =−150◦◦C, p0 = 10 bar). The drag coefficient is cd = 0.53,taken in the time window Δt between 0.8 and 0.9 s

cooling down the fluid medium to nitrogen temperatureand by pressurizing up to 10 bar. The test section mea-sures 0.4×0.35 m2 and the effective measuring time isroughly 0.5 s.

The test setup is similar to the others using two-dimensional models such as airfoils or cylinders. Behindeach wall of the rectangular test section there is a cryoplatform balance, attached to a solid base at the testsection. Similar to the high pressure windtunnel, thecircular ends of the freely suspended circular cylinderare passed through the windtunnel walls and the endsare clamped in the holes of the force conducting topplate of each balance by a ring locking assembly. In thiscase, both balances can also be connected in parallel,thus electrically they are acting as one balance yieldingthree signals for drag, lift and moment.

Figure 8.83 shows a typical result for the drag forceas a function of time, measured on a smooth circularcylinder (aspect ratio = 11.4) at extreme values of theoperating range of the facility. The intention was to getthe highest possible Reynolds number in nearly incom-pressible flow. Thus the measurement was taken at thelowest temperature of T = −150 ◦C, the highest pres-sure possible p0 = 10 bar and the lowest attainable Machnumber of Ma = 0.28, resulting in a Reynolds numberof Re = 5.8×106. The curve clearly shows that with theonset of flow, the drag increases rapidly up to a cer-tain level, remains there as long as flow continues, thendecreases quickly to zero when flow ceases. The drag co-

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Fig. 8.84 Upper: Power spectrum of the lift fluctuationscorresponding to above measurement. Lower: Power spec-trum of the pressure fluctuations at the shoulder of thecircular cylinder (ϕ = 90◦)

efficient is cd = 0.53, and a narrow peak in the spectrumof the lift fluctuations (Fig. 8.84) generated by the Kar-man vortex street, leads to a Strouhal number St = 0.25.In order to substantiate the force measurements, pressuremeasurements at the shoulder of the cylinder (ϕ = 90◦)were performed with a pressure sensor (Kulite). Thelower spectrum in Fig. 8.84 displays the behaviour ofthe fluctuating pressure and thus confirms that the cor-responding peak in the force spectrum is indeed due tothe Karman vortex street at the same Strouhal number.

The rms-value of the lift fluctuations for this caseamounts to c′

1 = 0.20, which is more than double thevalue as in other measurements [8.10].

The reason is the fact that at the lowest Mach num-ber and with that low flow velocity the also low vortexshedding frequency ( fV = 465 Hz) was quite near thenatural frequency of the cylinder ( fn = 435 Hz) leadingto superelevation due to resonance effects.

Force and Moment Measurement References 51

The measured drag coefficient and the Strouhal num-ber are in good agreement with the result in the highpressure wind tunnel [8.10].

The strong oscillations in the drag signal, in partic-ular after the flow has ceased (t > 1.3 s) can have manycauses. One could be the mentioned proximity to the vor-tex resonance range.. Although the vortex induced dragfluctuations have double the value of fVortex, a higherorder resonance due to nonlinear interaction may beresponsible for the significant oscillations in the dragsignal. In any case the rapid decrease of the flow veloc-ity acts as a transient or jump excitation on the cylinder.This effect was not observed when both frequencies werewell separated.

Nevertheless, it is interesting to note that, in spite ofthe pulse operating mode of the tunnel, the steady andunsteady processes can be measured very well.

8.2.4 Conclusions

Based on the applications described before, the typicalpositive properties of a piezo balance can be summarizedas follows:

• High rigidity, which leads to small static deforma-tions and to high natural frequencies• Low interferences, which are typically lower than1%• High resolution (< 0.01 N), which is independent onthe preload

• A large dynamic range; dynamic: 6 orders of mag-nitude, quasistatic: up to 4 orders of magnitudepossible• Application in difficult ambience possible such ascryogenic conditions, very high pressure and water.

Properties of piezoelectric measuring systems,which can be disadvantageous, when the generatedcharges are small:

• Restricted to quasistatic measurements imposed bythe drift of the zero point, but this is not as exten-sive as generally believed and drift corrections arepossible.• Sensitivity to temperature changes during the mea-surement in particular in direction of the prestressingbolts

Finally, in the field of aircraft aerodynamics, whenthe flow is attached and the interest is focused ondrag measurements with a resolution of drag counts(ΔCd = 0.0001) the application of strain gauge balancesis suggested, since so far a piezoelectric measuring sys-tem cannot guarantee accuracy for very small steadyvalues.

In all problems, where the flow is more or less sep-arated, for example in bluff body flows or situationsaround stall or when the model is oscillating, a highend drag measurement has less significance and thedisadvantages of piezo balances are more than out-weighed by its inherent rigidity with the known positiveconsequences.

References

8.1 ISO: Guide to the Expression of Uncertainties inMeasurements (International Organization for Stan-dardization, Geneva 1995)

8.2 AIAA: Assessment of Experimental Uncertainty withApplication to Wind Tunnel Testing, AIAA S-071A-1999 (AIAA, Reston 1999)

8.3 AIAA: Calibration and Use of Internal Strain GaugeBalances with Application to Wind Tunnel Testing,AIAA R-091-2003 (AIAA, Reston 2003)

8.4 B. Ewald, G. Krenz: The accuracy problem of air-plane development force testing in cryogenic windtunnels, AIAA Paper 86-0776, Aerodynamic TestingConference Palm Beach (AIAA, 1986)

8.5 B. Ewald: Balance Accuracy and Repeatability as aLimiting Parameter in Aircraft Development ForceMeasurements in Conventional and Cryogenic WindTunnels, AGARD FDP Symposium, Neapel, September1987 (, 1987)

8.6 B.C. Carter: Interference Effects of Model SupportSystems, AGARD Rep. R 601 (AGARD, )

8.7 A. Pope, K.L. Goin: High-Speed Wind Tunnel Testing(Krieger, New York 1978)

8.8 G. Bridel: Untersuchung der Kraftschwankungenbei einem querangeströmten Kreiszylinder, Disser-tation, Nr. 6108 (ETH Zürich, Zürich 1978)

8.9 G. Schewe: A multicomponent balance consisting ofpiezoelectric force transducers for a high-pressurewindtunnel, Techn. Messen 12, (1982)

8.10 G. Schewe: On the force fluctuations acting on acircular cylinder in crossflow from subcritical totranscritical Reynolds numbers, J. Fluid. Mech. 133,265 (1983)

8.11 G. Schewe: Force measurements in aerodynamicsusing piezo-electric multicomponent force trans-ducers. Proc. 11th ICIASF ’85 Record, Stanford Univ(, 1985) p. 263

8.12 N.J. Cook: A sensitive 6-component high-frequency-range balance for building Aerodynamics, J. Phys. E.16, (1983)

8.13 H. Psolla-Bress, H. Haselmeyer, A. Hedergott,G. Höhler, H. Holst: High roll experiments on a deltawing in transonic flow, Proc. 19th ICIASF 2001 Record,Cleveland, Ohio, Aug. 27-30 2001 (, 2001) p. 369

8.14 G. Schewe: Beispiele für Kraftmessungen im Wind-kanal mit piezoelektrischen Mehrkomponenten-meßelementen, Z. Flugwiss. Weltraumforsch. 14,32–37 (1990)

8.15 H. Triebstein, G. Schewe, H. Zingel, S. Vogel: Mea-surements of unsteady airloads on an oscillatingengine and a wing/engine combination, J. Aircr.31(1), 97 (1994)

8.16 N. Schaake: Querangeströmte und schiebende Zylin-der bei hohen Reynoldszahlen, Dissertation (Univ.Göttingen, Göttingen 1995)

8.17 G. Gautschi: Piezoelectric Sensorics (Springer, Berlin,Heidelberg 2002)

8.18 G. Schewe: Sensitivity of transition phenomena tosmall perturbations in flow round a circular cylinder,J. Fluid. Mech. 172, 33 (1986)

8.19 G. Schewe: Reynolds-number effects in flow aroundmore-or-less bluff bodies, J. Wind Eng. Ind. Aero-dyn. 89, 1267 (2001)

8.20 G. Schewe: Reynolds-number-effects and their in-fluence on flow induced vibrations, Proc. StructuralDynamics Eurodyn 2005 (Millpress, Paris 2005) p. 337

8.21 G. Schewe: Nonlinear flow-induced resonances ofan H-shaped section, J. Fluid. Struct. 3, 327–348(1989)

8.22 D. Schimke, P. Jänker, V. Wendt, B. Junker: Windtunnel evaluation of a full scale piezoelectric flapcontrol unit, Proc. 24th European Rotorcraft Forum,Marseille, 15-17. Sept. 1998 (, 1998)

8.23 G. Schewe, H. Mai, G. Dietz: Nonlinear effects intransonic flutter with emphasis on manifestationsof limit cycle oscillations, J. Fluid. Struct. 18, 3 (2003)

8.24 G. Dietz, G. Schewe, F. Kießling, M. Sinapius: Limit-Cycle-Oscillation Experiments at a Transport AircraftWing Model, Proc. Int. Forum Aeroelasticity andStructural Dynamics 2003, Amsterdam (, 2003)

8.25 G. Schewe, C. Steinhoff: Force measurements on acircular cylinder in a cryogenic-Ludwieg-tube us-ing piezoelectric transducers, Experiments in Fluids, (2007)

8.26 H. Rosemann: The Cryogenic Ludwieg-Tube-Tunnelat Göttingen, AGARD Special Course. In: Cryogenicwind tunnel technology, ed. by (AGARD, 1997)

8.27 J. Tichy, G. Gautschi: Piezoelektrische Meßtechnik(Springer, Berlin, Heidelberg 1980)

8.28 F.G. Tatnall: Tatnall on Testing (American Society ofMetals, Metals Park 1966)

8.29 K. Hoffmann: An Introduction to Measurement usingStrain Gages (Hottinger Baldwin, Darmstadt 1989)

8.30 Measurement Group: Strain Gage based Transducers(Measurement Group, Raleigh 1988)

8.31 B. Ewald: Multi-component force balances for con-ventional and cryogenic wind tunnels, Meas. Sci.Technol. 11, 81–94 (2000)

8.32 K. Hufnagel, B. Ewald: Force testing with inter-nal strain gage balances, AGARD FDP Special Course,AGARD R-812. In: Advances in Cryogenic Wind TunnelTechnology, ed. by (AGARD, )

8.33 M. Dubois: Feasability Study on Strain GageBalances for Cryogenic Wind Tunnels at ONERA, Cryo-genic Technology Review Meeting, NLR Amsterdam,September 1982 (, )

8.34 K. Hufnagel, : A new Half-Model-Balance for theCologne-Cryogenic-Wind-Tunnel (KKK), The SecondInternational Symposium on Strain Gauge Balances,Mai 1999, Bedford (TU Darmstadt, Darmstadt 1999)

8.35 G. Dietz, G. Schewe, H. Mai: Experiments onheave/pitch limit-cycle oscillations of a supercrit-ical airfoil close to the transonic dip, J. Fluid. Struct.19(1), 1–16 (2004)

8.36 H. Hönlinger, J. Schweiger, G. Schewe: The use ofaeroelastic windtunnel models to prove structuraldesign methods, Proc. No. 403 of the 63rd SMP Meet-ing of AGARD, Athens, Greece (, 1986) pp. 9–1–9–15

8.37 G. Schewe: Force measurements in aeroelasticityusing piezoelectric multicomponent transducers, In-tern. Forum Aeroelasticity and Structural Dynamics1991 Aachen, DGLR-Bericht 91-06 (DGLR, Bonn 1991)

8.38 H. Zingel, : Measurement of steady and unsteadyairloads on a stiffness scaled model of a mod-ern transport aircraft wing. Proc. Int. Forum onAeroelasticity and Structural Dynamics, Aachen,DGLR-Bericht 91-06 (DLRG, Bonn 1991) p. 120

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