April 2013 

NASA/TM–2013-217977

Experimental Investigation of Aeroelastic 

Deformation of Slender Wings at Supersonic 

Speeds Using a Video Model Deformation 

Measurement Technique 

Gary E. Erickson 

Langley Research Center, Hampton, Virginia 
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April 2013 

NASA/TM–2013-217977

Experimental Investigation of Aeroelastic 

Deformation of Slender Wings at Supersonic 

Speeds Using a Video Model Deformation 

Measurement Technique 

Gary E. Erickson 

Langley Research Center, Hampton, Virginia 
Available from: 

NASA Center for AeroSpace Information 

7115 Standard Drive 

Hanover, MD 21076-1320 

443-757-5802 

Acknowledgments 

The following individuals at NASA Langley Research Center are acknowledged for their 

helpful discussions and contributions to this paper: Alpheus W. Burner, Kenneth H. Cate, 

Harriet R. Dismond, John R. Micol, Floyd J. Wilcox, and Ricky L. Hall. 

The use of trademarks or names of manufacturers in this report is for accurate reporting and does not 

constitute an official endorsement, either expressed or implied, of such products or manufacturers by the 

National Aeronautics and Space Administration. 
Table of Contents

Table of Contents .......................................................................................................................................... v

Abstract ......................................................................................................................................................... 1

Introduction ................................................................................................................................................... 1

Nomenclature ................................................................................................................................................ 2

Wind Tunnel Facility .................................................................................................................................... 2

Wind Tunnel Models .................................................................................................................................... 3

Wind Tunnel Test Conditions ....................................................................................................................... 4

VMD System Description, Calibration, and Wind-On Image Processing .................................................... 4

VMD System Components ....................................................................................................................... 4

VMD System Calibration ......................................................................................................................... 5

Wind-On Image Acquisition and Processing ............................................................................................ 6

Discussion of Results .................................................................................................................................... 7

Flapped Wing ............................................................................................................................................ 7

Span Station Sweeps ............................................................................................................................. 7

Mach Number Sweeps .......................................................................................................................... 7

Reynolds Number/Dynamic Pressure Sweeps ...................................................................................... 7

Data Repeatability ................................................................................................................................. 8

Solid Wing ................................................................................................................................................ 8

Span Station Sweeps ............................................................................................................................. 8

Mach Number Sweeps .......................................................................................................................... 8

Comparison of Flapped and Solid Wings ................................................................................................. 8

Summary ....................................................................................................................................................... 9

References ..................................................................................................................................................... 9

Table.......................................................................................................................10 

Figures....................................................................................................................11 

Y
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vi
1

Abstract

A video-based photogrammetric model deformation system was 

established as a dedicated optical measurement technique at supersonic 

speeds in the NASA Langley Research Center Unitary Plan Wind Tunnel. 

This system was used to measure the wing twist due to aerodynamic 

loads of two supersonic commercial transport airplane models with 

identical outer mold lines but different aeroelastic properties. One 

model featured wings with deflectable leading- and trailing-edge flaps 

and internal channels to accommodate static pressure tube 

instrumentation. The wings of the second model were of single-piece 

construction without flaps or internal channels. The testing was 

performed at Mach numbers from 1.6 to 2.7, unit Reynolds numbers of 

1.0 x 106 to 5.0 x 106

, and angles of attack from -4 degrees to 

+10 degrees. The video model deformation system quantified the wing 

aeroelastic response to changes in the Mach number, Reynolds number

concurrent with dynamic pressure, and angle of attack and effectively 

captured the differences in the wing twist characteristics between the two 

test articles. 

Introduction

Model deformation may be defined as the 

change in shape of a model, particularly the 

wings and control surfaces, under aerodynamic 

load in a wind tunnel (references 1-6). The 

aerodynamic characteristics obtained in wind 

tunnel testing of a flexible model may differ 

from expected results or from computational 

fluid dynamics (CFD) predictions based on rigid

body assumptions. Reference 7 compares three 

optical techniques that have been assessed at the 

National Aeronautics and Space 

Administration’s Langley Research Center 

(NASA LaRC) for measuring model 

deformation, which include video 

photogrammetry, projection moiré 

interferometry (PMI), and the commerciallyavailable OptotrakTM system. The fundamental 

technique used at the NASA LaRC Unitary Plan 

Wind Tunnel (UPWT) to measure model 

deformation is photogrammetry, and the 

evolution of a video-based photogrammetry 

technique at NASA LaRC is summarized in 

reference 8. The primary application of the 

video model deformation (VMD) system at 

UPWT is wing twist measurements on 

supersonic transport airplane configurations.

The basic hardware of the VMD system at 

UPWT is a charge-coupled device (CCD) 

camera, computer with frame grabber, diffuse 

light source, and array of retroreflective tape 

targets on the model. The VMD technique 

consists of a single-camera, single-view, 

photogrammetric solution from digital images of 

targets placed on the wing at known semi-span 

locations. A photograph of a supersonic 

transport airplane model with wing targets 

installed for model deformation testing in 

UPWT is shown in figure 1. The 

videogrammetric system determines the spatial 

coordinates of the targets from the target 

centroids in the images, and then computes the 

model twist and bending (deflection) produced 

by the aerodynamic loads. The initial 

application of a VMD system at UPWT was in 

1996 as part of a unified optical measurement 

technique development program at NASA

(reference 9). An outcome of this work was the 

implementation of a dedicated UPWT VMD 

system described herein. The current report 

provides an overview of the UPWT VMD 

hardware, setup, calibration, and operational

procedures and representative results from a

specific application to two supersonic 

commercial transport airplane models with 

identical outer mold lines but different 

aeroelastic properties. 
2

Nomenclature

b local wing span, inches (in.)

bref reference wing span, 26.383 in. 

B. L. butt line, in.

cref reference length, 19.085 in. 

CAD computer-aided design

CCD charge coupled device

CFD computational fluid dynamics

DESL data engineering scripting language 

Ho stagnation pressure, psfa 

Mach free stream Mach number

Mf free stream Mach number

Mode tunnel operating mode 

M. S. model station, in. 

OML outer mold line

psfa pounds per square foot absolute 

psia pounds per square inch absolute 

PC personal computer 

PMI projection moiré interferometry

PSP pressure sensitive paint

q free stream dynamic pressure, psfa

Re/ft unit Reynolds number 

Sref reference area, 2.385 square feet 

 (sq. ft.) 

T0 stagnation temperature, degrees 

Fahrenheit (o F) 

T. S. test section

UPWT Unitary Plan Wind Tunnel

VMD video model deformation 

X retrotarget chordwise location in 

wind tunnel coordinate system, 

positive in free stream direction, in. 

y distance along wing local 

semi-span measured from wing 

centerline, in. 

Y retrotarget spanwise location in 

wind tunnel coordinate system, 

positive in direction of right wing 

tip, in. 

Z retrotarget vertical location in wind 

tunnel coordinate system, positive 

up, in. 

D angle of attack, deg

K nondimensional semi-span location

T wing twist angle, degrees (negative 

 leading edge down) 

' denotes delta value;

in data repeatability analysis, '’s 

are obtained by interpolating in 

each run to the nominal values of 

the independent variable, then 

averaging and subtracting the 

averages from the interpolated data

Wind Tunnel Facility

UPWT is a closed-circuit pressure tunnel 

with two test sections that are nominally 4 feet 

by 4 feet in cross section and 7 feet long.

Detailed descriptions of UPWT are provided in 

reference 10 and reference 11. An aerial view of 

the facility is shown in figure 2. The primary 

elements of UPWT are a 100,000-horsepower 

compressor drive system, a dry air supply and 

evacuating system, a cooling system, and the 

necessary interconnecting ducting to produce the 

proper air flow through either of the two test 

sections. The Mach number range is 

approximately 1.47 to 2.86 in Test Section 1 and 

2.30 to 4.63 in Test Section 2. The stagnation 

pressure can be varied up to a maximum of 

approximately 50 psia in Test Section 1 and 

approximately 100 psia in Test Section 2. The

nozzle throat-to-test section area ratio is varied 

by a lower asymmetric sliding nozzle block that 

provides continuous variation of the Mach 

number. A cross-sectional illustration of the 

nozzle block is presented in figure 3. The 

second-minimum area is controlled by moving 

hinged sidewalls to provide the proper 

constriction to stabilize the normal shock 

downstream of the test section at the various 

operating Mach numbers. In order to cover the 

entire Mach number range for each test section, 

the tunnel duct configurations must be altered to 

provide the proper compression ratio. Six 

centrifugal compressors are used in five tunnel 

configurations or modes, and the tunnel 

operating modes are available for only one test 

section at a time. Test Section 1 has two modes 

within which the Mach number is varied from 

1.47 to 2.16 in Mode 1-IA and 2.36 to 2.86 in 

Mode 1-II, respectively. Three modes exist in 

Test Section 2 within which the Mach number is 

varied from 2.30 to 2.96 in Mode 2-II, 3.00 to 

3.71 in Mode 2-III, and 3.82 to 4.63 in 
3

Mode 2-IV, respectively. The tunnel stagnation 

temperatures are typically 125o F and 150o F, 

depending on the mode of operation. Typical

unit Reynolds numbers, Re/ft, for testing at 

UPWT are 2.0 x 106

 to 4.0 x 106, although a 

range of unit Reynolds numbers from 1.0 x 106

to 5.0 x 106 can be easily accommodated. A unit 

Reynolds number of 6. 0 x 106 is possible on a 

selected basis only because of tunnel drive 

system operational limits.

Several methods to support the model have 

been used, but the basic mechanism is a 

horizontal wall-mounted strut which is capable 

of forward and aft travel of over 3 feet in the 

streamwise direction. A main sting support is 

attached to the strut and has lateral traverse and 

sideslip motion of +/-20 inches and 

+/-12 degrees, respectively. Forward of the 

main sting support is the angle-of-attack 

mechanism which provides pitch motion from 

-15 degrees to +30 degrees. A roll mechanism 

can be installed ahead of the pitch mechanism to 

provide continuous roll motion with a range of 

360 degrees. The model is mounted to the roll 

mechanism or the pitch mechanism by means of 

a wide assortment of available stings. Figure 4

illustrates the overall test section layout with the 

major support system components. Upgrades to 

the facility include a Tunnel Flow Control 

System for automated control of the tunnel 

stagnation pressure, stagnation temperature, and 

dewpoint and Model Attitude Control Systems 

for Test Sections 1 and 2 providing automated 

test sequencing for pitch, yaw, and roll angles, 

axial and lateral positions, and data acquisition. 

Wind Tunnel Models

Two precision metal models of supersonic 

transport airplane configurations were used 

during this test. The models featured identical 

outer mold lines (OMLs) and had an overall 

length of 52.740 inches and wing span of 26.383 

inches. A sketch of the model configuration is 

shown in figure 5. One model featured leadingand trailing-edge flap segments that could be 

deflected to prescribed angles using bolt-on 

brackets. This model was also instrumented 

with surface static pressure orifices on the wings 

and fuselage, which required machined channels 

within the wings to accommodate the stainless 

steel pressure tubing. A second model featured 

wings of single-piece construction with no flaps 

or pressure instrumentation. The two models are 

designated in this report at the “flapped wing” 

and “solid wing,” respectively. Both models 

featured two flow-through engine nacelles (per 

side) mounted to the left and right wings. The 

flapped wing and solid wing models without 

engine nacelles are shown installed in UPWT 

Test Section 1 in figure 6 and figure 7, 

respectively. It is noted that the wings-vertical 

orientation of each model without engine 

nacelles is for illustrative purposes only. The 

models were tested in a wings-level position 

with nacelles on throughout the VMD 

investigation.

Each model was instrumented with an 

internal strain-gage balance for six-component 

force and moment measurements. Balance data 

were acquired during the VMD image 

acquisition but are not included in this report. 

The balance measurements were used, however, 

to correct the model attitude for balance and 

sting deflections caused by the aerodynamic 

loads and to estimate the flow angle corrections 

at each Mach number and Reynolds number. 

The balance was installed on a custom sting 

mounted to the UPWT main pitch support 

system in Test Section 1. 

Five streamwise rows of adhesive

retroreflective tape targets (retrotargets) for 

VMD measurements were installed on the right 

wing upper surface of each model as shown in 

figure 8 and figure 9. The targets are to be 

distinguished from several smaller fastener holes 

for the wing nacelles and flap brackets that are 

filled with dental plaster and boundary layer 

transition “trip dots” that also appear as white 

circles in the photographs. The retrotargets were 

approximately 0.004-in. thickness and had 

excellent adhesion to the metal model surface. 

Test results described in reference 8 indicated 

the targets were aerodynamically non-intrusive 

at supersonic speeds. The target row span
4

locations were previously shown in figure 5 and 

corresponded to 22.6%, 41.1%, 54.1%, 76.0%, 

and 99.1% of the local semi-span distance 

measured from the fuselage centerline, or 

K y/(b/2) values of 0.226, 0.411, 0.541, 0.760, 

and 0.991. These span locations were selected 

based on the wing trailing-edge flap breaks, 

which served as quantifiable and repeatable 

reference locations. Each of the first four target 

rows at K 0.226, 0.411, 0.541, and 0.760 

featured four retrotargets having 0.375-inch 

diameter with 1.00-inch spacing. The target row 

near the wing tip, or K 0.991, featured three 

retrotargets having 0.25-inch diameter with 

0.875-inch spacing. 

Boundary layer transition trip dots with 

0.010-inch height were applied to the wing 

leading edges, nacelle leading edges (inside and 

outside nacelle surfaces), and fuselage nose tip 

on both models. The trip dots were located 0.60 

inches aft of the wing and nacelle leading edges 

measured in a streamwise direction and 1.00 

inch from the nose measured along the model 

surface. The trip dot location, height, and size 

were based on extensive prior testing of similar 

models in UPWT as described in reference 12. 

Wind Tunnel Test Conditions

All testing was performed in UPWT Test 

Section 1. The flapped wing model was tested 

at free-stream Mach numbers of 1.6, 1.8, 2.1, 

2.4, and 2.7 at a unit Reynolds number of 

4.0 x 106 or a Reynolds number of 6.36 x 106

based on the reference wing chord. The flapped 

model was also tested at unit Reynolds numbers 

of 1.0, 2.0, 3.0, and 5.0 x 106

 (or 1.59, 3.18, 

4.77, and 7.95 x 106 based on the reference wing 

chord) at M= 2.1. Test data were obtained on 

the solid wing model at free-stream Mach 

numbers of 1.6, 1.8, 2.1, 2.4, and 2.7 at a unit 

Reynolds number of 4.0 x 106 or a Reynolds 

number of 6.36 x 106 based on the reference 

wing chord. The stagnation temperature was 

maintained at 125 degrees Fahrenheit for all 

Mach numbers and Reynolds numbers. Table I

summarizes the tunnel operating conditions 

during the VMD investigation.

Testing was conducted in both operating 

modes (Mode 1-IA and Model 1-II) in Test 

Section 1 in order to obtain Mach numbers from 

1.6 to 2.7. This represented a significant time

savings, since it eliminated full installations of 

both models in Test Section 2, where Mach 

numbers of 2.4 and 2.7 would typically be 

obtained (reference 10). The compromise to 

running at M = 2.4 and 2.7 in Mode 1-II in 

Test Section 1 was increased test section 

turbulence (reference 10). This did not affect 

the successful pursuit of the primary objective of 

this investigation, which was to demonstrate the 

utility of the UPWT VMD system as a viable 

model deformation measurement tool at 

supersonic speeds. 

Angle of attack sweeps were conducted in 

pause mode in 0.5-degree increments from 

-4 degrees to +10 degrees. Angle of sideslip 

was 0 degrees throughout the testing. The 

model angle of attack was corrected for balance 

and sting deflections caused by the aerodynamic 

loads and for flow angularity in the test section 

for all Mach numbers and Reynolds numbers. 

VMD System Description,

Calibration, and Wind-On Image 

Processing

VMD System Components

In the UPWT VMD system, a video signal 

from a standard RS-170 solid state camera with 

752 horizontal by 240 vertical pixels per field 

was routed to a frame grabber controlled by a

personal computer (PC) workstation which 

recorded a predetermined number of video fields 

into the frame grabber memory. The adjustable 

field integration time of the CCD video camera 

was set to 1/250 second in order to reduce the 

effects of dynamics on image recording. A 10 to 

100 millimeter (mm) focal length remote zoom 

lens was used for imaging. Both models were 

swept through a range of angle of attack at the 

outset of the installation in the wind tunnel, and 

adjustments were made to the focal length in 

order to bracket the targeted region on the right 
5

wing through the desired range of angle of 

attack. Once the focal length providing the 

desired field of view was established, the lens 

remote control module was powered down to 

prevent inadvertent focal length changes. The 

illumination source was a fiber optic-based ring 

light mounted to the front of the camera lens. 

The intensity of this diffuse white light was

adjustable and was tailored to the specific test 

setup and to each model. Figure 10 shows the 

primary components of the UPWT VMD system 

used in the current investigation.

The VMD system software described in 

reference 13 and reference 14 controlled the

video capture hardware and automatically 

reduced and analyzed the sequence of raw 

images. Uncorrected values of the wing local 

angle of attack at all target rows were displayed

real-time as each data point was acquired. The 

PC received selected test conditions from the 

wind tunnel host computer via an RS-232 

communications link. In addition, image 

acquisition was coordinated with the wind 

tunnel data acquisition using a contact closure 

activation system.

Retrotargets were placed on the right wing 

upper surface at predetermined span locations 

and were uniformly distributed within a 

chordwise row. The target installations on the 

flapped and solid wing models in UPWT Test 

Section 1 were previously shown in figure 8 and 

figure 9, respectively. The chordwise and 

spanwise locations of the targets in the tunnel 

coordinate system were known from the 

reference locations on the flapped and solid

wings. A template for target installation on both 

models was created from the wind tunnel model 

computer-aided design (CAD) drawing. The 

template installed on the model in the UPWT 

test section is shown in figure 11. 

The camera and light source were positioned 

slightly above the model (resulting in an oblique 

view of the model) and clamped inside the 

webbing of the UPWT test section side wall 

adjacent to the targeted wing (figure 10). This 

provided excellent optical access to the model 

through the 1.5-inch thick optical-quality 

window. The proximity of the light source to 

the wing (about 1 to 2 feet depending on the 

target row) resulted in very high contrast 

images. Previous experience (reference 8)

showed that automatic target location was faster 

and more reliable if the gray levels of the wing 

targets were significantly greater than the 

background. Glints from the highly-polished 

metal surface of the model were potential 

sources of error in the acquisition of the target 

centroids. As a result, regions of the wing that

were susceptible to this undesired effect were 

identified on both models in the current 

investigation. A thin layer of flat black paint, 

aerodynamically non-intrusive at supersonic 

speeds (reference 8 and reference 15), was

applied to eliminate the unwanted reflections. 

This caused the wing surface to appear dark 

after simple threshold removal, making it easier 

to automatically locate the retrotargets on the 

wing surface.

VMD System Calibration 

Calibration of the VMD system yielded 

camera parameters consisting of the pointing 

angles, spatial location, and photogrammetric 

principal point (an effective camera focal length)

in the tunnel coordinate system. A key element 

of the calibration process was the application of 

a photogrammetric resection method 

(references 1-6) applied to a target plate that was

aligned to the coordinate system of the tunnel.

The target plate was positioned just above the 

right wing surface at a precisely known 

spanwise position with respect to the fuselage 

centerline. The plate was painted flat black and 

featured a 7x7 array of retrotargets with known 

locations, as shown in figure 12. In addition to 

the target plate, the calibration setup featured

lateral and vertical translation stages, dial 

gauges, and laboratory jacks. Figure 13 shows 

the calibration setup used in the current 

investigation. The target plate was translated to 

several known spanwise locations along an 

optical rail. The 49 targets or “blobs” in each 

image were digitized, and the centroids of the 

targets were estimated using a blob analysis 
6

technique (references 1-6). Estimates of the 

blob centroid spatial locations were derived 

from photogrammetric resection. A

commercially-available software package 

(reference 16) was used in conjunction with the 

VMD software (reference 13 and reference 14) 

to derive the camera parameters. The calibration 

was an iterative procedure featuring the 

determination of initial camera parameters 

followed by successive re-computations of the 

blob centroid files until the camera pointing 

angle, spatial location, and principal point values 

had converged. Additional measurements were 

made on the target plate for an in-situ check of 

the final calibration constants. The plate was

translated to different vertical positions while 

maintaining a constant spanwise position, and 

the measured and known vertical positions were

compared. 

The calibration hardware was moved away 

from the model, and a final calibration step was

conducted featuring the acquisition of model 

target images. An initial image was acquired 

with the model angle of attack set to 0 degrees.

The VMD-computed mean angles of attack (or 

local slope angles in the vertical plane of 

symmetry) were recorded at each target row and 

inserted as zero-offset values to an input file that

was read by the setup portion of the VMD 

software (reference 13 and reference 14). Image 

acquisition was repeated with the modified input 

file to confirm that the computed mean angles of 

attack at each target row were essentially zero. 

This process was analogous to the acquisition of 

balance wind-off zeroes (reference 8). A static 

pitch sweep of the targeted model was

conducted next, and images were acquired over 

the same angle-of-attack range as the scheduled 

wind-on runs. This static sweep was similar to 

the required wind-on reference images for 

pressure-sensitive paint (PSP) testing

(reference 8) and to a model weight tare run

(reference 8), since the computed wind-off local 

angles of attack at each target row were applied 

as tares to the corresponding wind-on data. The 

static pitch sweep was repeated at the middle 

and end of the testing of each model as a check 

of the system stability. In addition, the entire 

in-situ VMD calibration process was performed 

for both the flapped and solid wing models to 

ensure the reproducibility of the camera 

parameters and the wind-off tares. 

Wind-On Image Acquisition and 

Processing

VMD image acquisition and preliminary 

processing of the raw images were automated 

during the wind-on runs. Ninety video frames 

were acquired over a 1.5-second time period, 

and every third frame was used for image 

processing (30 frames total). The real-time 

display on the VMD PC workstation featured the 

uncorrected local slopes at each target row, and 

this information was updated as each data point 

was acquired. Final reduction and plotting of 

the model deformation results occurred off-line.

The wind-off and wind-on image files created by 

the VMD software were processed using the 

computational software in reference 16. The 

local slopes with wind-on were corrected using 

the wind-off curve-fitted data. A procedure was 

incorporated into the UPWT VMD image 

processing to provide a better spatial mapping of 

the wind-on and wind-off images in a manner 

similar to the image registration process used in 

the PSP technique (reference 8). For example, 

the wind-on model angle of attack computed by 

the wind tunnel data system consisted of the 

main support system accelerometer 

measurement, the deflections of the model, 

balance, and sting caused by aerodynamic loads, 

and the tunnel flow angle. However, to achieve 

the same angle of attack during wind-off 

conditions required the main support system to 

be set to a higher angle such that the model 

spatial location differed relative to the wind-on 

case. Consequently, the wind-off tare that was

applied was determined at an angle of attack that 

did not include the sting deflection angles or the 

tunnel flow angle, which significantly improved 

the spatial alignment with the corresponding 

wind-on image. 

The final wind-on VMD local angle of attack

at each target row was subsequently computed 

as the uncorrected wind-on angle of attack 
7

minus the static tare plus the flow angle at a 

given Mach number and Reynolds number. The 

local twist was computed as the difference 

between the VMD-measured angle of attack at a

given target row and the model angle of attack

computed by the wind tunnel data system. The 

resultant data file was then transferred to a 

separate computer workstation for conversion to 

binary format suitable for use in a Data 

Engineering Scripting Language (DESL)

software package for final plotting and analysis

(reference 17). 

Discussion of Results

The primary application of the UPWT VMD 

system in the current investigation was to 

determine local wing twist. Secondary 

measurements included wing deflections or 

bending, which are not presented in this report. 

Flapped Wing

Span Station Sweeps

Figures 14-18 are composite plots of the 

variation of the measured wing twist angle, T,

versus the model angle of attack, D, at all span 

stations (K = 0.226, 0.411, 0.541, 0.760, and 

0.991) corresponding to a unit Reynolds number 

of 4.0 x 106

 and Mach numbers of 1.6, 1.8, 2.1, 

2.4, and 2.7, respectively. Negative values of 

the wing twist correspond to leading edge down.

Error bars are superimposed on each data point 

corresponding to the 95 percent confidence 

limits based on the Student’s t distribution 

(reference 18) and a sample size of 30. The 

wing twist at K = 0.226 is negligible at any 

Mach number, since this measurement station is 

within an essentially rigid region near the wingfuselage junction. The wing twist measurements 

at K = 0.411 exhibit a systematic trend with the 

angle of attack but are typically small, since this 

station is also within a thicker region of the 

wing. The wing twist consistently increases at 

K = 0.541, 0.760, and 0.991, where the reduced 

section thickness and presence of flap breaks 

and pressure tubing channels increase the wing 

flexibility and sensitivity to the aerodynamic 

loading. The trends are similar at all Mach 

numbers, although the magnitude of the wing 

twist diminishes with increasing Mach number. 

The latter effect is shown in more detail in the 

next section.

Mach Number Sweeps

Figures 19-23 show the effect of the Mach 

number on the wing twist at K = 0.226, 0.411, 

0.541, 0.760, and 0.991, respectively. The unit 

Reynolds number is constant at 4.0 x 106

. The 

wing twist is insensitive to the Mach number at 

K = 0.226 because of the rigid properties of the 

wing at this station. Similarly, the Mach number 

effect on the wing twist at K = 0.411 is small. 

The negative slopes of the wing twist curves at 

K = 0.541, 0.760, and 0.991 are less pronounced

as the Mach number increases. At K = 0.991 

(figure 23), for example, the wing twist angle 

decreases from a maximum of approximately 

-2.6 degrees at M = 1.60 to approximately 

-1.2 degrees at M= 2.70. Part of this effect is 

attributed to the decreased free-stream dynamic 

pressure at the higher Mach numbers 

(M = 2.4 and 2.7, for example). However, the 

majority of the effect is caused by the reduced 

aerodynamic loads as the Mach number 

increases from the lower to higher supersonic 

conditions (reference 19).

Reynolds Number/Dynamic Pressure Sweeps

Figures 24-28 show the wing twist at 

K = 0.226, 0.411, 0.541, 0.760, and 0.991, 

respectively, at a Mach number of 2.1 and unit 

Reynolds numbers of 1.0, 2.0, 3.0, 4.0 and 

5.0 x 106

. The Reynolds number effect is 

confounded with the free-stream dynamic 

pressure, q, since UPWT cannot conduct 

Reynolds number sweeps at constant q. The 

most significant effects are observed at 

K = 0.541, 0.760, and 0.991, where a five-fold 

increase in the Reynolds number and dynamic 

pressure generally promotes a five-fold increase 

in the wing twist angle at a given angle of attack.
8

Data Repeatability

Figures 29-33 compare the wing twist angles 

obtained at K = 0.226, 0.411, 0.541, 0.760, and 

0.991, respectively, in three repeat runs at a 

Mach number of 2.1 and a unit Reynolds 

number of 4.0 x 106

. The repeat runs were 

obtained within the same wind-on run series. 

The lower plot in each figure compares the wing 

twist angle versus the angle of attack obtained in 

the three repeat runs. The upper plot in each 

figure shows the differences in the twist angles, 

where the delta-twist values ('T) were obtained

by applying a third-order polynomial curve fit to 

the original data, interpolating in each run to the 

nominal values of the independent variable, then 

averaging and subtracting the averages from the 

interpolated data. The results suggest good 

short-term repeatability of the wing twist 

measurements, and the 'T values are typically 

bounded by upper and lower limits 

corresponding to +/-0.02 degrees or less. These 

results are consistent with previous VMD testing 

cited in references 1-6. 

Solid Wing

For completeness, the wing twist 

measurements obtained on the solid wing model 

are presented in the following sections. 

Reynolds number/dynamic pressure sweeps and 

data repeatability runs were not performed on 

the solid wing model. 

Span Station Sweeps

Figures 34-38 are composite plots of the 

variation of the measured wing twist angle

versus the model angle of attack at all span 

stations (K = 0.226, 0.411, 0.541, 0.760, and 

0.991) corresponding to a unit Reynolds number 

of 4.0 x 106 and Mach numbers of 1.6, 1.8, 2.1, 

2.4, and 2.7, respectively. The wing twist angles 

are negligible at K = 0.226 and very small (less 

than 0.2 degrees) at K = 0.411 and 0.541 at any 

Mach number. These results are indicative of 

the more rigid wing construction compared to 

the flapped wing model. The more significant 

wing twist angles are confined to the outer span 

stations, K = 0.760 and 0.991, where the wing is 

sufficiently thin to render it sensitive to 

deformation due to aerodynamic loads. Similar 

to the results obtained on the flapped wing, the 

wing twist trends with the angle of attack at a 

given span station are insensitive to the Mach 

number, although the magnitude of the wing 

twist diminishes with increasing Mach number.

Mach Number Sweeps

Figures 39-43 show the effect of the Mach 

number on the wing twist at K = 0.226, 0.411, 

0.541, 0.760, and 0.991, respectively. The unit 

Reynolds number is constant at 4.0 x 106

. The 

wing twist is insensitive to the Mach number at 

K = 0.226, 0.441, and 0.541 because of the rigid 

properties of the solid wing at these three 

stations. The slopes of the wing twist versus 

angle of attack curves at K = 0.760 and 0.991

exhibit a consistent decrease as the Mach 

number increases. At K = 0.991 (figure 43), for 

example, the wing twist angle decreases from a

maximum of approximately -1.9 degrees at 

M = 1.60 to approximately -0.9 degrees at 

M= 2.70. 

Comparison of Flapped and Solid Wings

Figures 44-48 compare the measured wing 

twist angles obtained on the flapped and solid 

wing models at M= 1.6, 1.8, 2.1, 2.4, and 2.7, 

respectively, and a unit Reynolds number of 

4.0 x 106

. Each figure contains comparison 

plots at K = 0.226, 0.411, 0.541, 0.760, and

0.991. The differences are small at K = 0.226 

and 0.441 at any Mach number. At the outer 

span stations, however, the VMD measurements 

clearly show the more flexible response of the 

flapped wing compared to the solid wing. 

Figures 49-53 show composite plots of the 

computed differences between the flapped wing 

and the solid wing, 'T, at all span stations and at

M = 1.6, 1.8, 2.1, 2.4, and 2.7, respectively. 

The unit Reynolds number is constant at 

4.0 x 106

. Third-order polynomial curve fits 

were applied to the original wing twist data, and 

the differences between the interpolated values 
9

of the wing twist were calculated in 0.5-degree 

increments in the model angle of attack. Each 

figure reveals two distinct subsets consisting of 

small differences in the wing twist angle at 

K = 0.226 and 0.411 and much larger differences 

at K = 0.541, 0.760, and 0.991. The largest 

differences in the wing twist angles between the 

flapped and solid wings typically occur at 

K = 0.760 at a given Mach number. The wing 

tip regions of both wings are quite thin and 

flexible, which accounts for the diminished 'T

values at K = 0.991. The increased variability of 

the 'T curves at M= 2.4 and 2.7 in figure 52

and figure 53, respectively, are attributed to a 

higher turbulence level in operating mode 1-II in 

Test Section 1 (reference 10). However, the 'T

trends are consistent with the results obtained at 

the lower supersonic Mach numbers in operating 

mode 1-IA. 

Summary

A dedicated video model deformation system 

was established at the NASA LaRC UPWT to 

measure wing twist at supersonic speeds. The 

VMD system was successfully applied to the 

measurement of wing twist on two precision 

metal models of a supersonic transport airplane 

configuration. The models featured identical 

outer mold lines. However, the wings of one 

model were more flexible because of the 

presence of multiple leading- and trailing-edge 

flap segments and internal machined channels to 

accommodate surface static pressure 

instrumentation. The second model featured 

single-piece, solid-construction wings. The 

VMD system effectively quantified the 

sensitivity of the local wing twist to the freestream Mach number and a combined effect of 

the Reynolds number and free-stream dynamic 

pressure in a repeatable manner. In addition, the 

wing twist measurements clearly illustrated the 

more significant aeroelastic deformation of the 

flapped wing at the mid- and outer-span 

measurement stations which were most affected 

by the presence of the segmented flaps and the 

internal pressure tubing channels. The VMD 

system was demonstrated to be an effective, 

end-to-end optical measurement tool featuring 

the installation, in-situ calibration, and image 

acquisition, processing, and analysis by resident 

wind tunnel facility personnel. 

References

1. Burner, A. W. and Martinson, S. D., 

“Automated Wing Twist and Bending 

Measurements Under Aerodynamic Load,” 

AIAA-1996-2253, June 1996. 

2. Burner, A. W., Wahls, R. A., and Goad, W. 

K., “Wing Twist Measurements at the 

National Transonic Facility,” NASA TM 

110229, February 1996. 

3. Burner, A. W., “Model Deformation 

Measurements at NASA Langley Research 

Center.” AGARD 81st Fluid Dynamics Panel 

Symposium on Advanced Aerodynamic 

Measurement Technology, September 1997.

4. Burner, A. W., Radeztsky, R. H., and Liu,

T., “Videometric Applications in Wind 

Tunnels,” Videometrics V, Proceedings of 

the International Society for Optical 

Engineering (SPIE), Vol. 3174, pp 234-247, 

July 1997. 

5. Burner, A. W. and Liu, T., 

“Videogrammetric Model Deformation 

Measurement Technique,” Journal of 

Aircraft, Vol. 38. No. 4, pp 745-754, 

July-August 2001. 

6. Burner, A. W., Liu, T., Garg, S., Ghee, T. 

A., and Taylor, N. J., “Aeroelastic 

Deformation Measurements of Flap, Gap, 

and Overhang on a Semispan Model,” 

AIAA-2000-2386, June 2000.

7. Burner, A. W., Fleming, G. A., and Hoppe, 

J. C., “Comparison of Three Optical 

Methods for Measuring Model 

Deformation,” AIAA-2000-0835, January 

2000. 

8. Erickson, G. E., “Overview of Selected 

Measurement Techniques for Aerodynamics 

Testing in the NASA Langley Unitary Plan 

Wind Tunnel,” AIAA-2000-2396, June 

2000. 
10

9. Bell, J. H. and Burner, A.W., “Data Fusion 

in Wind Tunnel Testing: Combined Pressure 

Paint and Model Deformation 

Measurements,” AIAA-1998-2500, June 

1998. 

10. Jackson, C. M. Jr., Corlett, W. A., and 

Monta, W. J., “Description and Calibration 

of the Langley Unitary Plan Wind Tunnel,”

NASA TP 1905, November 1981. 

11. Wassum, D. L. and Hyman, C. E. Jr., 

“Procedures and Requirements for Testing 

in the Langley Research Center Unitary Plan 

Wind Tunnel,” NASA TM 100529, 

February 1988. 

12. Kennelly, R. A. and Goodsell, A., “Skin 

Friction and Transition Location 

Measurements on Supersonic Transport 

Models,” Paper No. 160, 9th Millennium 

International Symposium on Flow 

Visualization, August 2000. 

13. Cate, K. H., “Videogrammetric Model 

Deformation Measurement Software 

Package, Reference Manual for MDef.exe,”

NASA TM-2001-210554, March 2001. 

14. Dismond, H. R., “Videogrammetric Model 

Deformation Measurement System User 

Manual,” NASA TM-2002-211641, April 

2002. 

15. Amer, T. R., Liu, T., and Oglesby, D. M.,

“Characterization of Pressure Sensitive Paint 

Intrusiveness on Aerodynamic Data,”

AIAA-2001-0556, January 2001.

16. Using MATLAB - Version 5, The 

MathWorks, Inc., Natick, MA, December 

1996.

17. Graham, A. B., “The Data Analysis System, 

System Description and User’s Guide,”

NASA Langley Research Center, April 

1993.

18. Montgomery, D. C., Design and Analysis of 

Experiments, 7th Edition. John Wiley & 

Sons, Inc., New York, 2009.

19. Küchemann, D., The Aerodynamic Design 

of Aircraft, Pergamon Press, June 1978.

Table I. Tunnel operating conditions for VMD testing in UPWT Test Section 1. 

M Mode Ho

(psfa)

To

(

o

F) Re/ft q (psfa)

1.6 1-IA 2157 125 4.0 x 106 909.6

1.8 1-IA 2308 125 4.0 x 106 911.0

2.1 1-IA 656 125 1.0 x 106 221.4

2.1 1-IA 1312 125 2.0 x 106 442.8

2.1 1-IA 1968 125 3.0 x 106 664.2

2.1 1-IA 2623 125 4.0 x 106 885.6

2.1 1-IA 3279 125 5.0 x 106 1107.0

2.4 1-II 3039 125 4.0 x 106 838.2

2.7 1-II 3554 125 4.0 x 106 778.8
11 

Figure 1. Supersonic transport airplane model with retroreflective targets on right wing 

 upper surface for video model deformation testing in the NASA LaRC UPWT. 

Figure 2. Aerial view of the NASA LaRC UPWT. 
12 

Figure 3. Illustration of UPWT asymmetric sliding nozzle block arrangement. 

Figure 4. Overall UPWT test section layout. 

 Test Section 7.00 ft. 

0.625 in. 

8.00 in. 

Door 69.375 in. 

 Model Support System 8.50 ft. 

8.75 in.

 

Top View 

Side View 
13 

Figure 5. Planview of supersonic transport airplane configuration. (Flapped wing is shown. 

 Retroreflective targets on right wing upper surface are denoted by solid red circles.) 

Figure 6. Photograph of flapped wing model installed in UPWT Test Section 1. 

B. L. 13.073 

B. L. 10.026 

B. L. 7.137 

B. L. 5.422

B. L. 2.981

M. S. 0.000 M. S. 52.740 

B. L. -13.192 
14 

Figure 7. Photograph of solid wing model installed in UPWT Test Section 1. 

Figure 8. Retrotarget installation on flapped wing model. 
15 

Figure 9. Retrotarget installation on solid wing model. 

(a) VMD camera installation in webbing of UPWT test section sidewall. 

Figure 10. Major components of the UPWT VMD system. 

video camera 

ring light controller 

test section 

sidewall webbing 
16 

(b) VMD PC workstation in UPWT control room. 

Figure 10. Major components of the UPWT VMD system. 

Figure 11. Template for application of retrotargets on right wing upper surface. 
17 

Figure 12. Target plate with 7x7 array of retrotargets for VMD system calibration. 

Figure 13. VMD system calibration setup in UPWT Test Section 1. 

dial gage target plate 

optical rail lab jack 

target plate 

ring light 
18 

Figure 14. Variation of wing twist with angle of attack at all five measurement 

 stations and M = 1.6; flapped wing. 

Figure 15. Variation of wing twist with angle of attack at all five measurement

 stations and M = 1.8 ; flapped wing. 
19 

Figure 16. Variation of wing twist with angle of attack at all five measurement 

 stations and M = 2.1; flapped wing. 

Figure 17. Variation of wing twist with angle of attack at all five measurement 

 stations and M = 2.4; flapped wing. 
20 

Figure 18. Variation of wing twist with angle of attack at all five measurement 

 stations and M = 2.7; flapped wing. 

Figure 19. Effect of Mach number on wing twist at Re/ft = 4.0 x106

 and K = 0.226; flapped wing. 
21 

Figure 20. Effect of Mach number on wing twist at Re/ft = 4.0 x106 and K = 0.411; flapped wing. 

Figure 21. Effect of Mach number on wing twist at Re/ft = 4.0 x106

 and K = 0.541; flapped wing. 
22 

Figure 22. Effect of Mach number on wing twist at Re/ft = 4.0 x106 and K = 0.760; flapped wing. 

Figure 23. Effect of Mach number on wing twist at Re/ft = 4.0 x106

 and K = 0.991; flapped wing. 
23 

Figure 24. Effect of Reynolds number/dynamic pressure on wing twist 

 at M = 2.1 and K = 0.226; flapped wing. 

Figure 25. Effect of Reynolds number/dynamic pressure on wing twist 

 at M = 2.1 and K = 0.411; flapped wing. 
24 

Figure 26. Effect of Reynolds number/dynamic pressure on wing twist 

 at M = 2.1 and K = 0.541; flapped wing. 

Figure 27. Effect of Reynolds number/dynamic pressure on wing twist 

 at M = 2.1 and K = 0.760; flapped wing. 
25 

Figure 28. Effect of Reynolds number/dynamic pressure on wing twist 

 at M = 2.1 and K = 0.991; flapped wing. 
26 

Figure 29. Repeatability of wing twist measurements at M = 2.1 and Re/ft = 4.0 x 106

; 

 K = 0.226; flapped wing. 
27 

Figure 30. Repeatability of wing twist measurements at M = 2.1 and Re/ft = 4.0 x 106

; 

 K = 0.411; flapped wing. 
28 

Figure 31. Repeatability of wing twist measurements at M = 2.1 and Re/ft = 4.0 x 106

; 

 K = 0.541; flapped wing. 
29 

Figure 32. Repeatability of wing twist measurements at M = 2.1 and Re/ft = 4.0 x 106

; 

 K = 0.760; flapped wing. 
30 

Figure 33. Repeatability of wing twist measurements at M = 2.1 and Re/ft = 4.0 x 106

; 

 K = 0.991; flapped wing. 
31 

Figure 34. Variation of wing twist with angle of attack at all five measurement 

 stations and M = 1.6 ; solid wing. 

Figure 35. Variation of wing twist with angle of attack at all five measurement 

 stations and M = 1.8; solid wing. 
32 

Figure 36. Variation of wing twist with angle of attack at all five measurement 

 stations and M = 2.1; solid wing. 

Figure 37. Variation of wing twist with angle of attack at all five measurement 

 stations and M = 2.4; solid wing. 
33 

Figure 38. Variation of wing twist with angle of attack at all five measurement 

 stations and M = 2.7; solid wing. 

Figure 39. Effect of Mach number on wing twist at Re/ft = 4.0 x106

 and K = 0.226; solid wing. 
34 

Figure 40. Effect of Mach number on wing twist at Re/ft = 4.0 x106 and K = 0.411; solid wing. 

Figure 41. Effect of Mach number on wing twist at Re/ft = 4.0 x106

 and K = 0.541; solid wing. 
35 

Figure 42. Effect of Mach number on wing twist at Re/ft = 4.0 x106 and K = 0.760; solid wing. 

Figure 43. Effect of Mach number on wing twist at Re/ft = 4.0 x106

 and K = 0.991; solid wing. 
36 

(a) K = 0.226 

Figure 44. Comparison of flapped wing and solid wing twist at M = 1.6 and Re/ft = 4.0 x106

. 

(b) K = 0.411 

Figure 44. Comparison of flapped wing and solid wing twist at M = 1.6 and Re/ft = 4.0 x106

. 
37 

(c) K = 0.541 

Figure 44. Comparison of flapped wing and solid wing twist at M = 1.6 and Re/ft = 4.0 x106

. 

(d) K = 0.760 

Figure 44. Comparison of flapped wing and solid wing twist at M = 1.6 and Re/ft = 4.0 x106

. 
38 

(e) K = 0.991 

Figure 44. Comparison of flapped wing and solid wing twist at M = 1.6 and Re/ft = 4.0 x106

. 

(a) K = 0.226 

Figure 45. Comparison of flapped wing and solid wing twist at M = 1.8 and Re/ft = 4.0 x106

. 
39 

(b) K = 0.411 

Figure 45. Comparison of flapped wing and solid wing twist at M = 1.8 and Re/ft = 4.0 x106

. 

(c) K = 0.541 

Figure 45. Comparison of flapped wing and solid wing twist at M = 1.8 and Re/ft = 4.0 x106

. 
40 

(d) K = 0.760 

 Figure 45. Comparison of flapped wing and solid wing twist at M = 1.8 and Re/ft = 4.0 x106

. 

(e) K= 0.991 

Figure 45. Comparison of flapped wing and solid wing twist at M = 1.8 and Re/ft = 4.0 x 106

. 
41 

(a) K= 0.226 

Figure 46. Comparison of flapped wing and solid wing twist at M = 2.1 and Re/ft = 4.0 x 106

. 

(b) K= 0.411 

Figure 46. Comparison of flapped wing and solid wing twist at M = 2.1 and Re/ft = 4.0 x 106

. 
42 

(c) K= 0.541 

Figure 46. Comparison of flapped wing and solid wing twist at M = 2.1 and Re/ft = 4.0 x 106

. 

(d) K= 0.760 

Figure 46. Comparison of flapped wing and solid wing twist at M = 2.1 and Re/ft = 4.0 x 106

. 
43 

(e) K= 0.991 

Figure 46. Comparison of flapped wing and solid wing twist at M = 2.1 and Re/ft = 4.0 x 106

. 

(a) K= 0.226 

Figure 47. Comparison of flapped wing and solid wing twist at M = 2.4 and Re/ft = 4.0 x 106

. 
44 

(b) K= 0.411 

Figure 47. Comparison of flapped wing and solid wing twist at M = 2.4 and Re/ft = 4.0 x 106

. 

(c) K = 0.541 

Figure 47. Comparison of flapped wing and solid wing twist at M = 2.4 and Re/ft = 4.0 x 106

. 
45 

(d) K = 0.760 

Figure 47. Comparison of flapped wing and solid wing twist at M = 2.4 and Re/ft = 4.0 x 106

. 

(e) K = 0.991 

Figure 47. Comparison of flapped wing and solid wing twist at M = 2.4 and Re/ft = 4.0 x 106

. 
46 

(a) K = 0.226 

Figure 48. Comparison of flapped wing and solid wing twist at M = 2.7 and Re/ft = 4.0 x 106

. 

(b) K = 0.411 

Figure 48. Comparison of flapped wing and solid wing twist at M = 2.7 and Re/ft = 4.0 x 106

. 
47 

(c) K = 0.541 

Figure 48. Comparison of flapped wing and solid wing twist at M = 2.7 and Re/ft = 4.0 x 106

. 

(d) K = 0.760 

Figure 48. Comparison of flapped wing and solid wing twist at M = 2.7 and Re/ft = 4.0 x 106

. 
48 

(e) K = 0.991 

Figure 48. Comparison of flapped wing and solid wing twist at M = 2.7 and Re/ft = 4.0 x 106

. 

Figure 49. Differences between flapped wing and solid wing twist angles 

 at all five measurement stations; M = 1.6, Re/ft = 4.0 x 106

. 
49 

Figure 50. Differences between flapped wing and solid wing twist angles 

 at all five measurement stations; M = 1.8, Re/ft = 4.0 x 106

. 

Figure 51. Differences between flapped wing and solid wing twist angles 

 at all five measurement stations; M = 2.1, Re/ft = 4.0 x 106

. 
50 

Figure 52. Differences between flapped wing and solid wing twist angles 

 at all five measurement stations; M = 2.4, Re/ft = 4.0 x 106

. 

Figure 53. Differences between flapped wing and solid wing twist angles 

 at all five measurement stations; M = 2.7, Re/ft = 4.0 x 106

. 
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