ARL-RP-0592 ● Mar 2017

US Army Research Laboratory

A Dynamic Calibration Method for 

Experimental and Analytical Hub Load 

Comparison

by Robert P Thornburgh, Andrew R Kreshock, and 

Matthew L Wilbur

Reprinted from the 71st American Helicopter Society International Annual Forum 2015; 2015 

May 5–7; Virginia Beach, VA. Red Hook (NY): Curran Associates, Inc.; c2015. p. 2641–2654. 

Approved for public release; distribution is unlimited.
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Destroy this report when it is no longer needed. Do not return it to the originator.
ARL-RP-0592 ● Mar 2017

US Army Research Laboratory

A Dynamic Calibration Method for 

Experimental and Analytical Hub Load 

Comparison

by Robert P Thornburgh, Andrew R Kreshock, and 

Matthew L Wilbur

Vehicle Technology Directorate, ARL 

Reprinted from the 71st American Helicopter Society International Annual Forum 2015; 2015 

May 5–7; Virginia Beach, VA. Red Hook (NY): Curran Associates, Inc.; c2015. p. 2641–2654.

Approved for public release; distribution is unlimited.
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A Dynamic Calibration Method for Experimental and Analytical Hub Load 

Comparison

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Robert P Thornburgh, Andrew R Kreshock, and Matthew L Wilbur

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US Army Research Laboratory

Vehicle Technology Directorate 

Mechanics Division (ATTN: RDRL-VTM)

Aberdeen Proving Ground, MD 21005-5066

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14. ABSTRACT

This report presents the results from an ongoing effort to produce improved correlation between analytical hub force and 

moment prediction and those measured during wind-tunnel testing on the Aeroelastic Rotor Experimental System (ARES), a 

conventional rotor testbed commonly used at the Langley Transonic Dynamics Tunnel (TDT). A frequency-dependent 

transformation between loads at the rotor hub and outputs of the testbed balance is produced from frequency response 

functions measured during vibration testing of the system. The resulting transformation is used as a dynamic calibration of the 

balance to transform hub loads predicted by comprehensive analysis into predicted balance outputs. In addition to detailing the 

transformation process, this report also presents a set of wind-tunnel test cases, with comparisons between the measured 

balance outputs and transformed predictions from the comprehensive analysis code CAMRAD II. The modal response of the 

testbed is discussed and compared to a detailed finite-element model. Results reveal that the modal response of the testbed 

exhibits a number of characteristics that make accurate dynamic balance predictions challenging, even with the use of the 

balance transformation.

15. SUBJECT TERMS

dynamic calibration, rotorcraft, wind tunnel testing, dynamic calibration, elastic wind tunnel model 

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Andrew R Kreshock

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1

A Dynamic Calibration Method for Experimental and Analytical Hub Load 

Comparison

Robert P. Thornburgh

Research Aerospace Engineer

Andrew R. Kreshock

Research Aerospace Engineer

U.S. Army Research Laboratory 

Vehicle Technology Directorate 

Hampton, Virginia

Matthew L. Wilbur

Senior Research Engineer

ABSTRACT

This paper presents the results from an ongoing effort to produce improved correlation between analytical hub force 

and moment prediction and those measured during wind-tunnel testing on the Aeroelastic Rotor Experimental System 

(ARES), a conventional rotor testbed commonly used at the Langley Transonic Dynamics Tunnel (TDT). A 

frequency-dependent transformation between loads at the rotor hub and outputs of the testbed balance is produced 

from frequency response functions measured during vibration testing of the system. The resulting transformation is 

used as a dynamic calibration of the balance to transform hub loads predicted by comprehensive analysis into predicted 

balance outputs. In addition to detailing the transformation process, this paper also presents a set of wind-tunnel test 

cases, with comparisons between the measured balance outputs and transformed predictions from the comprehensive 

analysis code CAMRAD II. The modal response of the testbed is discussed and compared to a detailed finite-element 

model. Results reveal that the modal response of the testbed exhibits a number of characteristics that make accurate 

dynamic balance predictions challenging, even with the use of the balance transformation.

INTRODUCTION

As a result of the rising costs for wind-tunnel testing of rotor 

systems, achieving quality experimental data for comparison 

with analysis has become a critical component in the effort to 

validate comprehensive modeling techniques. Traditionally, 

the measurement of dynamic rotor loads transmitted to the 

fixed-system has been a significant challenge, and 

correlations between predicted loads and measured loads have 

historically produced mediocre results. Modern rotor system 

testbeds have strain-gauge balances that are typically used to 

measure the load transmitted from the rotating system to the 

fixed system during wind-tunnel testing. This technique has 

a number of drawbacks that result in differences between the 

balance output and the loads at the hub. First, due to 

imperfections in manufacturing and applying strain gauges to 

the balance, individual output channels tend to be coupled to 

each other. Thus, a single force applied to the balance most 

often results in outputs on all six channels of the balance. This 

is typically compensated for by performing a static calibration 

of the balance to develop a transformation matrix that can be 

used to “back out” the applied forces and moments. Second, 

contrary to its stated intention, a balance does not actually 

measure forces and moments, but instead measures the strain 

at the various flexures in the balance. When loaded statically, 

these strains are easily converted into forces and moments 

using calibration data. In a dynamic system, however, these 

strains are induced not only by external loads, but also by the 

dynamic response of the entire testbed. Further complicating 

matters is the fact that the balance flexures are often flexurally 

soft relative to the rest of the system, and thus contribute to 

system resonances that can result in large balance outputs for 

relatively small loads. Finally, the balance loads are not only 

induced by the rotor hub loads, but also by loads transmitted 

via the pitch links to the swashplate. Thus, it is erroneous to 

equate balance output to hub loads without compensating for 

the pitch link loads in some manner.

A number of wind-tunnel test teams have attempted to use a 

dynamic calibration to overcome these issues (refs. 1–3). 

Using a shaker attached to the hub, these teams applied 

dynamic loads in different directions to compute the 

frequency response of the balance output relative to the 

applied hub loads. Using this data, they then determined 

dynamic amplification factors for the balance at the rotor 

harmonic frequencies. In some cases this work did not 

present the phase relationship between the applied hub loads 

and the balance output, and did not consider the coupling 

between the balance output channels. In addition, there is 

little discussion in the literature regarding the extent to which 

the predictions from comprehensive analysis were improved 

by the dynamic calibration.

Presented at the AHS 71st Annual Forum, Virginia Beach, 

Virginia, May 5–7, 2015. This is a work of the U.S. 

Government and is not subject to copyright protection in the 

U.S.
2

Thus, the objective of the current work is to demonstrate the 

improvement that is achievable through the use of careful 

dynamic measurements of the testbed combined with 

incorporation of the testbed dynamics in the comprehensive 

analysis model of the system. This paper describes the 

dynamic testing of the Aeroelastic Rotor Experimental 

System (ARES), the model-scale conventional rotor system 

testbed in use at the Langley Transonic Dynamics Tunnel, 

including measurements of the balance frequency response 

and the modal response of the hub. In addition, the 

development of a detailed finite-element model of the ARES 

is described, along with its use in understanding the testbed 

dynamics. Finally, examples of the comparison between 

predicted and measured hub loads during wind-tunnel flight 

are presented and discussed. 

OVERVIEW ON UTILIZING DYNAMIC 

MEASUREMENTS 

Prior to presenting the results from the vibration testing of the 

ARES testbed, some discussion is needed to clarify what data 

is being obtained from testing and exactly how it can be 

utilized. The goal of this work is to develop a transformation 

so that analytically predicted dynamic hub loads can be 

transformed into predicted balance outputs for comparison 

with experiment. In its simplest sense, this transformation is 

a six-by-six matrix that relates the hub forces and moments to 

the balance outputs. The static balance calibration is an 

example this type of transformation, but it is not valid for 

dynamic loads. To develop a transformation for dynamic 

loads, the assumption is made that there exists a unique 

transformation matrix for each excitation frequency, and that 

system linearity permits the dynamic balance output to be 

identified by transforming the hub loads at each harmonic 

frequency. This transformation is commonly referred to as a 

“dynamic calibration.” Unlike with a static calibration that 

only corrects amplitude, transformation matrices used in a 

dynamic calibration must be complex valued to account for 

phase changes that occur across the frequency spectrum. To 

develop this transformation, the balance output is measured 

during a series of vibration tests using a shaker to excite the 

ARES at the hub, and this output is used as the basis for the 

creation of an empirical transformation. 

It should be emphasized that the measurements used to create 

the balance transformation are for the ARES testbed without 

most of the hub mass. Thus, the natural frequencies of the 

system will be different from those for the ARES including 

the hub and rotor system. Historically, researchers have 

included the hub mass during vibration testing, but this is not 

necessary, provided that the mass is accounted for in the 

comprehensive analysis. Applying excitation loads to the 

actual rotor hub can be challenging and can require additional 

fixtures that add mass to the system. In the present work, a 

“dummy” hub has been constructed which replaces the rotor 

hub and provides attachment points for the shakers during 

testing. It is assumed that the difference in mass between the 

actual rotor hub and the dummy hub will be accounted for in 

the comprehensive model of the rotor system. Divorcing the 

rotor hub from the testbed during vibration testing also 

implies that the test results are a testbed property that can be 

utilized regardless of the rotor system attached to it. This is 

of particular interest to the authors, since there are multiple 

rotor hubs compatible with the ARES testbed. 

Balance Transformation 

The primary experimental test result that is being sought is a 

transformation relationship between the hub loads and the 

balance output as a function of frequency, but this is a 

synthesized result that must be created from the measured 

data. This transformation relationship is referred to herein as 

the balance transformation. First, a number of vibration tests 

are performed with a shaker connected at multiple points on 

the dummy hub and oriented in multiple directions. Each of 

these tests results in a measured frequency response function 

(FRF) for the six balance outputs relative to the applied load 

at the hub. Depending on the orientation and location of the 

excitation force, a combination of forces and moments are 

produced at the center of the hub. The nomenclature used for 

the balance outputs and the assumed coordinate system for the 

model is presented in Figure 1. The balance transformation 

for each FRF frequency is computed by solving for the 36 

complex-value components of the matrix that satisfies the 

relationship 

{

 

 

N

A

P

R

Y

S}

 

 

i

= [Tbal]

{

 

 

Fx

Fy

Fz

Mx

My

Mz}

 

 

i

where F and M are the force and moment vectors at the hub, 

and N, A, P, R, Y, and S are the Normal force, Axial force, 

Pitch moment, Roll moment, Yaw moment, and Side force 

outputs of the balance for the i

th load case. This can also be 

expressed as 

B

i

(ω) = [Tbal](ω) ∙ Hi

(ω)

Side X

Roll

Yaw

Normal

Axial

Pitch

X

Z

Y

Figure 1. Model coordinate system and directions for 

positive balance outputs.
3

which emphasizes the fact that this transformation must be 

computed for each frequency () in the FRF. If testing 

includes more than exactly six orthogonal excitation loads, 

then it is necessary to perform an averaging process to obtain 

a single balance transformation. This can be accomplished 

through the use of an H1 FRF estimator, just as was used to 

generate the FRF functions during the shake test. In this case, 

the cross-spectrum between the balance output and the 

applied loads is divided by the auto-spectrum of the applied 

loads. Thus, the matrix components of the balance 

transformation can be computed using

[Tbal]j,k

(ω) =

∑ Bj

i

(ω) ∙ Hk

i

(ω)

∗

i

∑ Hk

i

(ω) ∙ Hk

i

(ω)

∗

i

The balance transformation describes the balance output 

induced by the hub loads, but does not account for any loads 

transmitted via the pitch links. A similar process can be used 

to create a swashplate transformation to describe the 

relationship between the loads and moments induced by the 

pitch links and the balance output. Because these two 

separate load paths exist, inverting the balance transformation 

and using it to convert experimentally measured balance loads 

into hub loads is not necessarily valid. However, analysisexperiment comparison is most often done in this manner, and 

pitch link loads are combined with hub loads for comparison 

with transformed balance loads. This approach is only valid 

if the hub can be assumed to be rigidly connected to the 

swashplate such that they move together as a rigid body. A

more mathematically reliable option would be to transform 

analytically predicted hub loads and pitch link loads into a 

predicted balance output that can then be compared to 

experimentally measured balance values, which is the 

approach taken herein.

Hub Modal Response

One issue that is typically ignored in rotor analysis, with the 

exception of stability analysis, is the effect of testbed motion 

and dynamics on the predicted hub loads. A testbed 

resonance that results in a large amplification between the hub 

loads and the balance output will also likely result in hub 

motion that may alter the loads transmitted from the rotor to 

the hub. Thus, the second test result of interest is the modal 

response of the ARES testbed. In particular, if acceleration 

measurements are made on the hub during the shake tests 

discussed above, it is possible to identify the modal response 

of the hub, which describes the motion of the hub induced by 

the applied hub loads. This modal response captures the 

dynamics of the testbed for the frequency range of interest and 

permits them to be incorporated into the comprehensive

analysis of the rotor system.

The computation of the hub modes begins with measurement 

of hub acceleration FRFs during each vibration test. Since 

direct rotational measurements are not practical, 

measurements from tri-axial accelerometers are combined to 

derive the displacement and rotation of the point defined to be 

center of the hub in the comprehensive analysis. If more than 

exactly six orthogonal accelerations are measured during 

testing, then it is necessary to average them at each FRF 

frequency to obtain the six translational and rotational 

components of the hub motion. This averaging assumes that 

the dummy hub is rigid, which was shown to be 

approximately true for the ARES testbed in the frequency 

range of interest. The resulting six FRFs for each vibration 

test describe the six components of the hub acceleration as a 

function of the applied load for each test. There are numerous 

ways to extract modes from these FRFs, but it was decided 

that the most direct method was to use a technique identical 

to the balance transformation to create average FRFs and then 

extract modes from these. Reciprocity was enforced during 

creation of this hub transformation, so the components 

represent the idealized average FRFs of the hub motion for 

the six components of the hub load. A commercial software 

package was used to extract modes from these FRFs using a 

Rational Fraction Polynomial-Z method.

VIBRATION TESTING AND RESULTS

Demonstration of the techniques discussed above was 

performed on the ARES testbed with the goal of developing 

balance transformations and modal data that could be

incorporated into a comprehensive model and used to create 

comparisons with wind-tunnel test results.

Figure 2. The Aeroelastic Rotor Experimental 

System (ARES) model-scale helicopter rotor research 

testbed shown mounted in the test section of the 

Langley Transonic Dynamics Tunnel (TDT).
4

Setup

The ARES testbed, shown in Figure 2, is designed to support 

testing in the Langley Transonic Dynamics Tunnel of 

aeroelastically-scaled model rotor systems of up to 

approximately 10-ft diameter. Rotor systems on the ARES 

are powered by a variable-frequency synchronous motor rated 

at 47-hp output at 12,000 rpm. The motor is connected to the 

rotor shaft through a two-stage, belt-driven, speed reduction 

system. Rotor control is achieved using a conventional, 

hydraulically actuated rise-and-fall swashplate system using 

three independent actuators. The testbed also has a 

hydraulically actuated pitch degree-of-freedom to achieve the 

rotor shaft tilt necessary for rotor system trim in forward 

flight. The shaft tilt range on the ARES is typically +8° (shaft 

back) to -18° (shaft forward). All rotor system drive and 

flight controls are shielded by generic fuselage skin panels. 

Custom hub configurations may be mounted on the ARES, 

however, the primary hub available currently is an articulated 

hub with coincident flap and lag hinges placed at the 3.0 inch 

radial station. Rotor systems tested on the ARES typically 

have a 1/rev rotating speed of 10.5 to 11.5 Hz, which provides 

Mach-scaling in the heavy-gas test medium of the TDT.

During the current vibration testing the hydraulic system was 

at standard operating pressure and the model was maintained 

at 0° shaft tilt. Vibration testing was conducted at other shaft 

tilts to examine the influence of shaft angle on the modal 

response, but minimal differences were noted. 

As discussed above, a “dummy” four-bladed hub was 

fabricated to permit application of shaker loads to the ARES 

testbed, as illustrated in Figure 3. The dummy hub has shaker 

and accelerometer mounting locations at points 

corresponding to the center of each hinge on the ARES 

articulated hub. Nonrotating radial, vertical, and lateral 

shaker loads were applied at each location, thereby inducing 

hub forces and moments in a manner similar to the actual 

rotor. The shaker was mounted to a reaction mass and 

suspended above the testbed. A variety of excitation modes 

were investigated, but the majority of measurements used a 

burst-random excitation with 0-200Hz frequency content and 

an 80-percent duration over an 8-second frame. Peak 

excitation was typically about ±10 lbf, although loads from 2

lbf to 15 lbf were tested to investigate system nonlinearity. 

Although ±10 lbf was smaller than harmonic loads often 

observed during wind-tunnel testing, system resonances 

resulted in peak balance outputs in the mid to upper portion 

of their ranges.

In addition to the six balance outputs and the four tri-axial 

accelerometers on the dummy hub, a number of other 

accelerometers were mounted on both the metric and 

nonmetric side of the ARES to permit quantification of the 

ARES mode shapes. These additional measurements were 

critical to identifying the modes for comparison with the 

developed finite-element model. Measured FRFs were 

computed from the average of forty frames to minimize noise, 

and were measured from 0-400Hz with a 0.125Hz interval.

Balance Output

Shaker loads were sequentially applied at all four rotor hinge 

positions along the three principal axes of the ARES. Since 

the shaker forces were applied at the hinge positions, each 

Figure 3. The “dummy” hub used during vibration 

testing of the ARES testbed to provide connectivity for 

shakers and accelerometers.

Figure 4. Balance transformation: Normal and Axial 

balance outputs to a hub force in the Z direction 

(Normal).

Frequency (Hz)

Balance Output (lb/lb)

0 20 40 60 80 100

10

-2

10

-1

10

0

10

1

Normal Force

Axial Force

Frequency (Hz)

Phase (deg)

0 20 40 60 80 100

-180

-90

0

90

180
5

excitation typically induced both a force and moment about 

the hub center, except when the force was in the radial 

direction. The balance output from the resulting twelve sets 

of FRFs was used to form the balance transformation using 

the process presented above, which is not adversely affected 

by the fact that each set did not possess a pure hub force or 

moment. A sample of balance transformations is presented in 

Figures 4–6.

The response of the Normal and Axial balance outputs for hub 

excitation in the Z direction (vertical) is presented in Figure 

4. These responses are what one would typically expect for a 

testbed. The magnitude of the Normal response is relatively 

flat and close to unity, with the exception of two peaks and a 

valley created by modes at 21 Hz and 41 Hz. The peak 

amplification value is 2.4, at the 21 Hz mode. The phase 

angle between the excitation and output is also close to zero, 

except in the vicinity of those two modes. The Axial balance 

output is largely unresponsive to the vertical excitation, 

except near the 41 Hz mode. One could almost make the 

case, based on these results, that the dynamic transformation 

is unnecessary, were it not for the fact that the mode at 41 Hz 

is close to the typical ARES 4/rev frequencies of 42–46 Hz. 

The response of the Normal and Axial balance outputs for hub 

excitation in the X direction (axial), presented in Figure 5, 

tells a very different story. It is immediately clear that the 

response is highly dependent on the excitation frequency and 

that use of the static calibration values would result in loads 

being incorrect by as much as one order of magnitude. The 

Axial balance output has a magnitude that varies from 0.04 to 

7.3 times the axial excitation load, and exhibits a phase angle 

that is approximately 180° for much of the frequency range. 

The dynamic response of the model also results in much 

greater coupling between the balance outputs, depending on 

the modes being excited at a given excitation frequency. For 

example, Normal output produced by the axial force at the 

hub is actually greater than the Axial output between 37 and 

68 Hz. The complex nature of these results was more typical 

across the other balance outputs than the relatively simple 

response presented in Figure 4.

Figure 6 presents the Pitch balance output for excitation in 

both the X and Z directions. Since the center of the balance 

is 1.75ft below the center of the hub, in-plane force at the hub 

results in significant Pitch and Roll outputs. The 

amplification of the Pitch output from an axial force varies 

between 0.03 and 11, relative to the static value. It is also 

interesting to note that above 41 Hz the phase of the Pitch 

output switches. Ideally, a vertical force should not excite and 

Pitch output, but on the ARES the normal force induces 

significant Pitch output between approximately 20 and 50 Hz. 

Modal Response

The objectives of the modal test data acquired during hub 

excitation were to create a modal representation of the 

translational and rotational response of the hub, and to acquire 

sufficient accelerometer measurements over the ARES to be 

able to characterize the global nature of the measured modes.

Using the data from four tri-axial accelerometers located on 

the dummy hub, the modal hub response was computed as 

described above. The first twenty primary hub modes are 

listed in Table 1. There were a number of other local modes 

that did not exhibit significant response at the hub, and were 

Figure 5. Balance transformation: Normal and Axial 

balance outputs to a hub force in the X direction 

(Axial).

Frequency (Hz)

Balance Output (lb/lb)

0 20 40 60 80 100

10

-2

10

-1

10

0

10

1

Normal Force

Axial Force

Frequency (Hz)

Phase (deg)

0 20 40 60 80 100

-180

-90

0

90

180

Figure 6. Balance transformation: Pitch balance output 

for hub forces in the X and Z directions (Axial and 

Normal).

Frequency (Hz)

Pitch (in-lb/lb)

0 20 40 60 80 100

10

-2

10

-1

10

0

10

1

10

2

FZ Excitation

FX Excitation

Frequency (Hz)

Phase (deg)

0 20 40 60 80 100

-180

-90

0

90

180
6

subsequently ignored. Note that the names listed for each 

mode are approximate descriptions for the overall character 

of the testbed deformation, and do not refer to any classical 

mode-shape definitions.

A comparison of the measured hub modes and the balance 

outputs presented in Figures 4–6 illustrates that not all modes 

contribute equally to the balance transformation. Although 

deformation at the balance flexure is a significant contributor 

to the modal response, it is not the only significant source of 

flexibility in the ARES. Thus, although the modes can 

generally be observed in the peaks of the balance 

transformation, there is minimal correlation between the 

transformation amplitudes and the magnitudes of the modal 

components. The magnitude of the peaks in the balance 

transformation are influenced not only by the amount of strain 

occurring in the balance flexures for a particular mode, but 

also by the degree to which that mode is excited by the 

dynamic load at the hub.

FINITE-ELEMENT MODELING

In addition to performing a GVT to identify the dynamic 

response of the ARES, an ABAQUS finite-element model 

(FEM) was developed for use in predicting the modal 

behavior of the ARES. The objective for this model was to 

study ARES configuration changes to determine their effect 

on the rotor response. Also, if the model were of sufficient 

accuracy, it could be used to generate the modal hub motion 

for use in the comprehensive analysis, and possibly the 

balance transformation as well. In addition, the development 

of a finite-element model was used to provide insight into the 

sources of flexibility within the testbed and their effect on the 

dynamic response. The FEM was developed in stages using 

substructure models of individual components. This 

permitted verification of the model in stages using measured 

component masses and shake tests of sections of the ARES. 

In addition, this approach permits a library to be developed so 

that different model configurations can be studied. This 

section will describe how the model was developed, discuss 

results from the testing of each section, and present lessons 

learned during this process. 

The development of the FEM began with modeling the lower 

portion of the stand, shown in Figure 7a. The ARES stand is 

mounted on foam-rubber pads to add flexibility and damping 

to prevent ground-resonance instabilities. The stiffness and 

damping of the foam rubber was unknown prior to 

experimental testing, but it was known that the stiffness was

dependent on the torque applied to the mounting bolts during 

testbed installation. Modal testing demonstrated that the solid 

steel stand could be modeled very accurately using a 

combination of solid and shell elements. This provided a set 

of stiffness and damping values for the pads that were used in 

subsequent models. The resulting model predicted the first 

14 natural frequencies to within 3 percent.

Table 1. Measured modal response at the hub (normalized by modal mass).

Mode

Frequency

(Hz)

Damping

(%)

Modal 

Mass (slug) X (ft) Y (ft) Z (ft) RX (rad) RY (rad) RZ (rad)

1 5.787 3.26 0.06852 -7.54E-2 -1.05E-2 1.27E-3 -1.03E-3 1.65E-2 -1.34E-3

2 5.805 5.06 0.06852 8.90E-3 8.60E-2 8.33E-4 1.26E-2 -7.50E-3 -2.86E-3

3 15.92 2.87 0.06852 -4.21E-2 -4.21E-3 -8.92E-3 2.22E-4 4.59E-2 -1.04E-3

4 21.26 5.92 0.06852 -1.16E-2 8.00E-4 -5.11E-2 3.72E-4 4.99E-3 5.09E-4

5 25.54 2.79 0.06852 0.0 -4.80E-2 0.0 -2.91E-2 3.29E-3 1.24E-2

6 40.70 1.68 0.06852 -1.05E-1 -6.72E-4 1.89E-2 3.04E-3 9.73E-2 -7.83E-4

7 44.85 3.92 0.06852 -7.36E-2 -3.91E-2 1.02E-2 -6.45E-3 6.58E-2 -6.01E-3

8 48.85 1.43 0.06852 1.50E-4 -3.11E-2 3.70E-4 -3.58E-2 1.61E-3 -3.39E-2

9 56.05 2.44 0.06852 7.17E-3 2.44E-1 -1.11E-3 1.92E-1 -2.15E-2 -4.69E-3

10 57.57 1.81 0.06852 5.28E-4 -7.25E-3 -8.24E-4 -1.83E-1 1.94E-2 1.38E-2

11 74.87 3.96 0.06852 -1.52E-1 -8.10E-3 -7.03E-3 -1.24E-3 1.13E-1 -2.22E-2

12 77.17 4.30 0.06852 -1.01E-1 -2.07E-2 -7.69E-4 7.54E-3 1.34E-1 -3.77E-3

13 79.06 2.13 0.06852 -5.22E-2 -4.61E-2 7.52E-4 -5.20E-2 4.15E-2 3.20E-2

14 88.41 1.68 0.06852 -9.17E-2 -1.45E-2 -2.64E-3 7.02E-3 1.05E-1 -3.40E-3

15 91.21 5.71 0.06852 1.86E-2 -6.70E-2 -5.50E-3 -1.09E-1 -1.40E-2 2.26E-2

16 107.6 1.53 0.06852 -1.23E-1 -4.12E-2 -1.20E-2 -5.39E-2 4.60E-2 -9.20E-2

17 107.8 2.34 0.06852 -4.28E-2 -1.20E-1 2.42E-3 -1.90E-1 4.64E-2 2.31E-2

18 119.1 3.68 0.06852 1.16E-1 2.85E-1 -8.77E-3 4.22E-1 -2.01E-1 -2.15E-2

19 128.3 4.00 0.06852 2.27E-1 -3.02E-2 -6.00E-2 -5.35E-2 -5.99E-1 1.92E-3

20 158.0 1.59 0.06852 2.20E-2 1.25E-3 7.73E-2 -1.20E-2 -5.18E-2 -2.51E-3
7

Next, the full stand was modeled, including all of the 

components below the pivot about which the ARES pitches

(Figure 7b). This part of the ARES consists largely of solid 

sections with robust bolted joints (except for the foam-rubber 

pads). Consequently the FEM was able to accurately predict 

most of the first 16 natural frequencies to within 4 percent. 

The exception was the first two torsion modes. The first 

torsion mode is characterized by rigid-body rotation of the 

stand on the pads, and the second is characterized by elastic 

torsion of the stand coupled with rotation on the pads. The 

predicted natural frequencies for these modes were 

approximately 15 percent higher than observed. The source 

of this error seems to be that torsional response of the pads is

nonlinearly dependent on the weight of the test stand. The 

Figure 7. Finite-element models of the sections of the ARES investigated during vibration testing and 

development of the dynamic testbed model.

(a)

(b)

(c)

(d)

(e)

(f)
8

response of the pads continued to vary slightly as other 

components were added to the ARES, and remained a source 

of error in all subsequent models.

A FEM of the balance was developed, with careful attention 

to accurately capturing the stiffness. The balance is a solid 

stainless steel component, which made solid modeling using 

CAD geometry relatively easy (Figure 7c). The thin flexures 

required a very fine mesh for the stiffness of the model to 

converge, and the final mesh had more than 3 million degrees 

of freedom. The predicted mass of the balance agreed with 

the measured mass to approximately 0.1 percent. The 

predicted natural frequencies were found to be highly 

dependent on the boundary conditions. Experimentally, 

frequencies were measured for the balance bolted to a heavy 

backstop, but predicted frequencies were found to vary 

depending on the area assumed to be in contact with the 

backstop. This result is similar to a conclusion found in prior 

work with bolted joints (ref. 4). Overall, the predicted 

frequencies agreed to within four percent. When one 

considers the uncertainty in material properties and the 

machining tolerances on the thin flexures, then these results 

are within the accuracy that is possible for this balance. One 

might consider replacing the detailed FEM with a simplified 

empirical representation of the balance, but based on the 

sensitivity to boundary conditions that was observed, this is 

something that would require great care to do accurately.

The components on metric side of the balance were modeled 

as a single group and compared to modal testing of this 

section mounted to a heavy backstop rather than the balance. 

This section included the rotor-shaft housing, rotor shaft, 

dummy hub, swashplate, motor, drive sheaves, and belts. The 

FEM for this section is shown in Figure 7d, minus some 

components which are modeled as lumped masses, beams or 

springs, such as the swashplate, actuators and belts. The 

masses of individual components were computed and 

validated against measured values. Some components, such 

as the motor and bearings, required modeling using 

homogenized properties based on the measured mass. Drive 

belt stiffness was derived from the empirically measured 

drive system natural frequencies. This was necessary because 

the belt stiffness varied depending on the belt tension, which 

was controlled by turning locking nuts that adjust the length 

of threaded rods connecting the motor to an intermediate 

driveshaft housing and the intermediate driveshaft housing to 

the rotor-shaft housing. In addition to the threaded rods, there 

are also guide rods that travel through bronze bushings that

keep the components aligned. This complex connectivity 

between the drive components was found to be very difficult 

to model using traditional finite-element methods. Estimating 

the bending stiffness of a threaded rod is always a tricky 

process, and the guide rods seemed to impose an intermediate 

constraint that was difficult to estimate empirically. As a 

result, predicted natural frequencies for the complete section 

were as much as 15 percent high for some modes and 15 

percent low for others.

The fuselage was modeled using solid elements for the frame 

and shell elements for the skins. The FEMs of the skins were 

validated using mass measurements and measured free-free 

natural frequencies for each section. This fuselage model and 

the balance FEM were combined with the stand model and 

compared to modal testing of the ARES with nothing attached 

to the metric side of the balance (Figure 7e). The pitch pivot 

was modeled using a solid model of each pivot bolt connected 

to the stand and fuselage frame using distributed constraints. 

The pitch actuator was modeled using beams based on 

actuator geometry connected by a linear spring. One of the 

beams was assigned a coefficient of thermal expansion that 

permitted actuation to be simulated by prescribing a 

temperature change during analysis. Thus, the modal 

response of the ARES could be computed at various pitch 

angles through changes in actuator length. The linear spring 

stiffness was estimated by using the internal volume of the 

actuator and the bulk modulus of hydraulic oil (assumed to be 

250 ksi). This was intended to be an initial guess before an 

empirical value could be derived, but modal testing revealed 

this to be a very reasonable approximation. The modal testing 

showed that the primary source of error was the modeling of 

the pitch pivot. The ideal model that was initially used was 

found to be too stiff, resulting in over-prediction of most of 

the natural frequencies. Addition of translation and rotation 

springs at the connection between the pivot bolt and the stand 

permitted some tuning of the model, but behavior seemed to 

Table 2. Measured and predicted ARES natural 

frequencies.

Mode

Experimental 

(Hz)

FEM 

(Hz) Mode

1 5.823 5.868 Rigid-body Axial

2 6.068 5.970 Rigid-body Side

3 12.44 14.17 Rigid-body Yaw

4 15.96 16.62 Model Pitch - actuator

5 21.22 19.34 Rigid-body Normal

6 25.39 20.38 Rigid-body Roll

7 27.60 24.01 Rigid-body Pitch

8 33.95 39.75 Fuselage-stand Yaw

9 40.77 45.61 Balance Pitch

10 44 52.79 Fairings

11 48.89 57.26 Fuselage Roll

12 56.05 53.86 Balance Side/Yaw

13 65.63 67.70 Balance Roll

14 74.73 84.00 Stand bending Axial

15 78.40 88.20 Stand bending Axial

16 88.51 85.58 Balance Normal

17 93.75 98.14 Fuselage Roll + skin

18 108.0 114.5 Fuselage Normal

19 118.1 124.2 Drivetrain

20 120.5 120.9 Fuselage Axial
9

be nonlinear and no single set of spring stiffnesses was able 

to capture the entire modal response accurately. The overall 

response of the FEM was reasonable and all observed modes 

were captured, but some natural frequencies were mispredicted by as much as 20 percent, particularly yawing of the 

fuselage relative to the stand.

The issues with modeling the pivot connection and the 

connectivity of the metric-side components resulted in a final 

FEM that captures the general behavior of the ARES, but has 

significant errors in the predicted natural frequencies (Figure 

7f). The measured and predicted frequencies for the full 

model are presented in Table 2. The FEM predicts the number 

and sequence of the modes quite well, but there are 

differences in natural frequencies of almost 20 percent for 

some modes. Although these errors in the frequencies may 

not seem large, the location of these modes greatly affects the 

balance transformation. Because of the sharp peaks that can 

be observed in the balance transformations, a small shift in 

frequency may result in large changes in both the 

amplification and phase between the loads at the hub and 

output of the balance. Consequently, the resulting FEM is 

considered useful for studying the effect of configuration 

changes, but not of sufficient accuracy to replace vibration 

testing.

COMPARISON BETWEEN ANALYSIS AND 

EXPERIMENT

Finally, a study was conducted to determine the impact of 

using the balance transformation on predicted balance 

harmonics in comparison with experimentally measured 

results obtained during a wind-tunnel test. The experimental 

data used for comparison was from wind-tunnel testing of a 

set of Active-Twist Rotor (ATR) blades, which had 

undergone extensive bench testing to validate the structural 

model used in the comprehensive analysis (ref. 5). This rotor 

system was tested in heavy gas in the Langley Transonic 

Dynamics Tunnel. Two forward-flight test cases, presented 

in Table 3, were chosen for comparison of the comprehensive 

analysis and the experimental measurements, one low-speed 

and the other high-speed. Although these blades are capable 

of actively twisting during flight, in both of these test cases

the blades were unactuated.

The tested ATR has a radius of 63.36 in. and was operated at 

604 RPM to achieve a tip Mach number of 0.63. The blades 

have a constant 4.64-in chord, a built-in -9deg/R linear twist, 

and the outer 0.07R span of the blades are swept aft by 20 deg. 

Further details regarding the design of the blades can be found 

in reference 5. The rotor blade beam properties were 

computed using UM/VABS, a finite element analysis that

computes beam properties for arbitrary cross-sectional 

configurations (ref. 6). The beam properties were used within

the comprehensive analysis CAMRAD II, and verified 

through a series of cantilevered and free-free vibration tests 

(ref. 5). 

CAMRAD II is a rotorcraft aeromechanics analysis tool that 

combines non-linear finite element solution with multi-body 

dynamics (ref. 7). A lifting line model is employed with 

varying complexities of wake models. To supplement the 

aerodynamic model within CAMRAD II (CSD analysis), the 

solution was coupled with a CFD analysis, FUN3D. The CFD 

mesh includes 4.6 million nodes for the rotor and 2.1 million 

nodes for the overset mesh, which includes the rigid fuselage 

geometry (ref. 8). For hub load calculation, CAMRAD II uses 

a harmonic balance method. The predicted hub forces and 

moments were converted into predicted balance outputs using 

the empirical balance transformation developed above. The 

complex valued transformations at the first 10 harmonic 

frequencies were interpolated from the empirical balance 

transformation function, which had a 0.125Hz interval. The 

comparisons were made between the predicted and measured 

balance harmonics, and in addition, these were used to 

generate synthesized waveforms over the rotor azimuth. 

Figure 8 presents hub loads for the low-speed forward flight

results for CFD/CSD coupling in the time domain for one 

rotor revolution. The case was run using a single blade 

analysis with no fixed system modes. The red line shows the 

traditional method of predicting the balance output, by taking 

the predicted hub loads and applying only the moment arm 

induced by the height of the hub above the balance. The blue 

line shows the balance output after the dynamic calibration 

has been applied to the predicted hub loads, and the black line 

represents the experimental data. In general, the traditional 

balance output predictions are significantly smaller in 

magnitude than the measured values. Since the dynamic 

balance response is dominated by the 4/Rev harmonics, the 

large amplification created by the modes near this frequency 

results in a dramatic increase in the predicted balance outputs. 

However, the use of the balance transformation over-predicts 

the experimental loads by more than double in some cases. 

The only case which appears reasonably accurate is the Side 

force, which was only slightly increased by the balance 

transformation.

As discussed above, the large balance amplification likely 

implies that the testbed will exhibit sufficient motion to alter 

the rotor loads transmitted to the hub. Flexibility of the fixed 

frame can be modeled in CAMRAD II using mode shapes. Of 

the ARES hub modes identified in Table 1, the 16 dominant

Table 3. Wind-tunnel test cases used for balance output 

comparison.

Mode

LowSpeedHighSpeed

Advance Ratio 0.127 0.335

Shaft Angle (deg) -1.5 -9.5

Rotor Speed (RPM) 604 604

Coefficient of lift / 

solidity 0.0715 0.0715
10

Figure 8. Balance output for the low-speed test case with CFD/CSD coupling, single blade analysis, and no fixed 

system modes.

Figure 9. Balance output for the low-speed test case with CFD/CSD coupling, multi-blade analysis, and with fixed 

system modes.
11

Figure 10. Balance output for the high-speed test case with CFD/CSD coupling, single blade analysis, and no fixed 

system modes.

Figure 11. Balance output for the high-speed test case with CFD/CSD coupling, multi-blade analysis, and with fixed 

system modes.
12

modes were used to simulate airframe flexibility through 

8/Rev. For purposes of reduced complexity, the CFD/CSD 

coupling was trimmed and converged without fuselage 

modes, which resulted in significant computational savings. 

The modes where then introduced as a final CSD cycle using 

CFD airloads and multi-blade analysis. The hub loads, in 

particular their phase angles, were found to be very sensitive 

to the convergence tolerances used in the comprehensive 

analysis computational loops that control airframe response, 

rotor trim, and the motion coupling the airframe and the rotor.

The results for the low-speed case using multi-blade analysis 

coupled with fixed system modes, are presented in Figure 9. 

The most significant result from the use of the fuselage modes 

was the reduction in the Normal, Axial and Pitch outputs for 

the predictions using the balance transformation, which

results in better correlation with the experimental data. The 

4/Rev predicted load magnitudes for each output are

reasonably close to the experimental levels observed during 

the test. However, there is relatively poor agreement for the 

Roll and Yaw outputs, and there are still differences in the 

phase between the predicted and measured outputs.

The effect that the balance transformation has on the 4/Rev 

balance outputs can be better understood by examining the 

contributions from each hub component, as detailed in Table 

4. Each row represents the contribution of each component 

of the hub force and moment to a specific balance output, and 

the complex sum of these components is the net balance 

output at 4/Rev. The coupling between the axial force and the 

pitch moment at the hub and the Normal and Axial balance 

outputs is particularly noteworthy. Not only does the 2.04-lb 

4/Rev axial force at the hub get amplified to a 12.3-lb Axial 

output, but it also contributes 17.9 lb to the Normal output. In 

addition, the 6.43-ft-lb 4/Rev pitching moment at the hub 

contributes 29.0 lb to the Axial output and 44.8 lb to the 

Normal output. Thus, the 4/Rev Normal output from the 

balance exhibits very little correlation to the 7.51-lb 4/Rev 

vertical force at the hub. Since the net balance output is a 

complex-valued sum, it is clear that accurate accounting of 

the phase angles in both the predicted hub loads and the 

balance transformation is required to accurately predict these 

balance outputs. 

The results from the high-speed case are very similar to those 

from the low speed case. The CFD/CSD coupled results

presented in Figure 10 over-predict the response when the 

dynamic calibration is applied to the single blade analysis 

with no fixed system modes. When fuselage modes are 

introduced into the model, the predicted 4P balance load 

correlates reasonably well with the test data, as presented in 

Figure 11. The 8/Rev harmonic evident in the experimental 

Axial and Normal outputs was not captured by the 

comprehensive analysis for either the low-speed or highspeed case. 

Based on the results from the two comparison cases, the 

dynamic calibration method appears very promising, but there 

are a number of issues limiting the accuracy of the predicted 

balance outputs. The apparent sensitivity of the

comprehensive analysis to convergence and trim tolerances, 

particularly with regard to the CFD/CSD coupling and the 

inclusion of fuselage modes, limits the authors’ confidence in 

the repeatability of the results until a broader array of test 

cases can be assessed. Additional CFD coupling cycles may 

be required, since best practices have not yet been established 

for CFD/CSD coupling with fixed frame modes.

Table 4. Component-level breakdown of the 4/Rev predicted balance output for the low-speed test case.

Analytical 

4/Rev Hub 

Load

Fx Fy Fz Mx My Mz

2.04 lb

-23.2°

19.3 lb

-18.0°

7.51 lb

-1.9°

7.88 ft-lb

28.7°

6.43 ft-lb

-58.1°

4.39 ft-lb

78.2°

Hub Load Contribution (Magnitude and Phase) Net Experiment

4/Rev Balance Output

Normal

(lb)

17.9

-84.2°

3.4

23.0°

8.3

125.3°

0.5

125.3°

44.8

-167.4°

2.8

171.0°

50.1

-158.1°

31.5

-57.9°

Axial

(lb)

12.3

-82.6°

3.2

27.2°

7.4

143.0°

0.4

-145.4°

29.0

-167.7°

1.8

-168.7°

34.3

158.5°

19.3

-70.9°

Pitch

(ft-lb)

37.4

-81.2°

8.3

28.5°

24.6

147.4°

1.3

140.9°

94.4

-164.0°

5.4

175.4°

114.3

156.7°

61.5

-74.0°

Roll

(ft-lb)

0.7

-102.7°

55.2

-164.2°

0.3

121.6°

13.2

-149.6°

1.1

140.5°

1.1

109.4°

66.4

173.8°

32.2

-64.3°

Yaw

(ft-lb)

2.2

68.4°

13.4

12.3°

1.1

-58.8°

1.1

-18.2°

4.8

-5.0°

13.7

94.0°

25.7

-40.8°

9.2

-117.6°

Side

(lb)

0.5

-64.7°

22.9

-164.7°

0.2

160.5°

1.9

142.9°

0.6

-156.2°

4.5

95.0°

24.7

177.6°

16.2

-95.8°
13

Another source of error in the predicted balance output comes 

from the limitation of the modal approximation used to 

simulate testbed motion at the hub. First, the modes are 

derived from a synthesis of twelve separate shake tests, and 

the nonlinear aspects of the response are effectively averaged 

out. In addition, modes extracted from the average response 

are assumed to be linear, and smaller local modes are ignored. 

The net result of this is that the response simulated by the 

modal representation can only be described as an 

approximation of the actual testbed response. This can be 

observed in Figure 12, which presents the frequency response 

of the hub acceleration in the axial direction due to an axial 

force at the hub. The experimental response from the shake 

tests is compared to the acceleration predicted by CAMRAD 

II using the synthesized modes. Not only does the 

experimental result show a number of small variations 

induced by local modes not included in the analysis, but at 

high frequencies the testbed begins to exhibit a response that 

is beyond what the modal approximation can simulate.

Also, the frequencies of modes in the vicinity of 4/Rev were 

observed to be highly influenced by the addition of mass 

above the balance. The effect of adding the rotor mass is 

shown in Figures 13 and 14, which present the frequency 

response of the hub acceleration in the axial direction due to 

an axial force at the hub and the acceleration in the side 

direction due to a side force, respectively. The addition of the 

rotor mass results in the axial mode at 41Hz being reduced to 

37 Hz, significantly altering its influence at 4/Rev. Also, the 

side mode at 56 Hz without the rotor shifts to almost exactly 

the 4/Rev frequency, indicating that this mode is extremely 

sensitive to changes in the mass. The testbed with a spinning 

rotor will, of course, exhibit different natural frequencies, but 

it is clear that this modal activity in the vicinity of the 4/Rev 

harmonic frequency greatly impacts the accuracy of any 

predicted loads.

Frequency (Hz)

aX

/FX Magnitude (ft/s

2

/lb)

0 20 40 60 80 100

10

-2

10

-1

10

0

10

1

CAMRAD II

Experiment

Frequency (Hz)

Phase (deg)

0 20 40 60 80 100

-180

-90

0

90

180

Figure 12. Measured and simulated hub acceleration in 

the axial direction induced by an axial force at the hub.

Figure 13. Effect of rotor mass on the simulated hub 

acceleration in the axial direction induced by an axial 

force at the hub.

Frequency (Hz)

aX

/FX Magnitude (ft/s

2

/lb)

0 20 40 60 80 100

10

-2

10

-1

10

0

10

1

With Rotor Without Rotor

Frequency (Hz)

Phase (deg)

0 20 40 60 80 100

-180

-90

0

90

180

Figure 14. Effect of rotor mass on the simulated hub 

acceleration in the side direction induced by a side force 

at the hub.

Frequency (Hz)

aY

/FY Magnitude (ft/s

2

/lb)

0 20 40 60 80 100

10

-2

10

-1

10

0

10

1

10

2

With Rotor Without Rotor

Frequency (Hz)

Phase (deg)

0 20 40 60 80 100

-180

-90

0

90

180
14

CONCLUSIONS

This work presented results from an effort to develop a 

dynamic calibration of the Aeroelastic Rotor Experimental 

System (ARES) model-scale rotor system testbed. The 

mathematical development of the balance transformation was 

described, along with the experimental testing used as the 

basis for this transformation. In addition, a detailed finiteelement model of the ARES was developed and compared to 

modal measurements for the testbed. Finally, examples of the 

comparison between predicted and measured hub loads 

during wind-tunnel flight were presented and discussed. 

Based on the work presented herein, the following 

conclusions were made.

 Based on the two wind-tunnel test cases examined, the use 

of the balance transformation has the ability to 

significantly improve the correlation between predicted 

and measured balance outputs.

 Incorporation of the fuselage modes into the 

comprehensive analysis appears to be necessary for 

effective use of the balance transformation.

 The ARES testbed exhibits several natural frequencies 

near the 4/Rev rotor frequency, resulting in a balance 

transformation that has large amplification and is very 

sensitive to model changes. This greatly limits the 

accuracy of the developed dynamic calibration.

 Although most of the components of the ARES could be 

accurately modeled using finite-elements, modeling the 

connectivity between the components was found to be 

significantly challenging. This resulted in the final FEM 

having insufficient accuracy to replace vibration testing, 

but still being useful for studying the effect of 

configuration changes.

Based on the behavior exhibited by the ARES testbed, future 

work will center on verification of the modal response and 

accuracy of the balance transformation at the 4/Rev 

frequency. The use of tuned-mass dampers and the addition 

of mass will be investigated to mitigate the testbed vibration 

mode near the 4/Rev frequency, which could help reduce the 

amplification of balance loads at this frequency. Also, since 

the modal response of the testbed near this frequency appears 

to be highly dependent on the mass attached to the metric side 

of the balance, sensitivity to swashplate position and blade 

mass requires further investigation to ensure the accuracy of 

the balance transformation.

Author contact: 

Robert Thornburgh Robert.P.Thornburgh.civ@mail.mil

Andrew Kreshock Andrew.R.Kreshock.civ@mail.mil

Matthew Wilbur Matthew.L.Wilbur.civ@mail.mil

ACKNOWLEDGEMENTS

The authors would like to acknowledge the NASA Rotary 

Wing program and Steve Massey for the CFD support they

provided.

REFERENCES 

1Russell, C. R., “Shake Test Results and Dynamic 

Calibration Efforts for the Large Rotor Test Apparatus,” Fifth 

Decennial Specialists’ Meeting on Aeromechanics, San 

Francisco, California, January 22-23, 2014.

2Nguyen, K., and Lau, B., “Dynamics of the McDonnell 

Douglas Large Scale Dynamic Rig and Dynamic Calibration 

of the Rotor Balance,” NASA TM 108855, October 1994.

3Peterson, R. L., and van Aken, J. M., “Dynamic 

Calibration of the NASA Ames Rotor Test Apparatus 

Steady/Dynamic Rotor Balance,” NASA TM 110393, April 

1996.

4Thornburgh, R. P., Floersheim, R. B., and Hou, G. J. -W., 

“An Analytical and Experimental Study of a Scaled 

Helicopter Tailcone,” 49th AIAA/ASME/ASCE/AHS/ASC 

Structures, Structural Dynamics, and Materials Conference, 

Schaumburg, Illinois, April 7-10, 2008.

5Kreshock, A. R., Thornburgh, R. P., Wilbur, M. W., and 

Langston, C. W., “Experimental Bench Testing of an ActiveTwist Rotor Blade,” 53rd AIAA/ASME/ASCE/AHS/ASC 

Structures, Structural Dynamics, and Materials Conference, 

Honolulu, Hawaii, April 23-26, 2012.

6Palacios, R. and Cesnik, C., “Cross-Sectional Analysis of 

Nonhomogeneous Anisotropic Active Slender Structures,” 

AIAA Journal, Vol. 43, No. 12, 2005, pp. 2624-2638.

7

Johnson, W., Comprehensive Analytical Model of 

Rotorcraft Aerodynamics and Dynamics II v4.6, Palo Alto, 

CA, 2007.

8Massey, S. J., Kreshock, A. R., and Sekula, M. K., 

“Coupled CFD/CSD Analysis of Rotor Blade Structural 

Loads with Experimental Validation,” Paper 2013–3158, 31st 

AIAA Applied Aerodynamics Conference Proceedings, June 

2013.
15

1 DEFENSE TECHNICAL

(PDF) INFORMATION CTR

DTIC OCA

2 DIRECTOR

(PDF) US ARMY RSRCH LAB

RDRL CIO L

IMAL HRA MAIL & RECORDS

MGMT

1 GOVT PRINTG OFC

(PDF) A MALHOTRA

3 US ARMY RSRCH LAB

(PDF) RDRL VTM

A R KRESHOCK

R P THORNBURGH

M L WILBUR
16

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