Facility. A. W. Burner, R. A. Wahls, and W. K. Goad ... A.W. Burner. R.A. Wahls ......
AUTHORS). Alpheus W. Burner, Richard A. Wahls, and William K. Goad. ;7.
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.--: " ,,. "-"?:" 7 ::., NASA Technical Memorandum
110229
Wing Twist Measurements Transonic Facility
A. W. Burner, R. A. Wahls, and W. K. Goad Langley Research Center, Hampton, Virginia
February
1996
National Aeronautics and Space Administration Langley Research Center Hampton, Virginia 23681-0001
at the National
WING
TWIST
MEASUREMENTS
NATIONAL
TRANSONIC
AT THE
FACILITY
A.W. Burner R.A. Wahls W. K. Goad ABSTRACT A technique
for measuring
described.
of two dimensional The wing
currently
upon
for selection
transformation
Examples
run-to-run
of wing twist
The advantages
of this particular
in cryogenic
third dimensional
coordinate. and wind-off
wind-on
and limitations
mode
is
of the technique
are discussed.
repeatability
nitrogen
Facility
determination
between technique
and test-to-test
Transonic
photogrammetric
with a fixed (and known)
from a conformal
to illustrate
in use at the National
a single camera
in the plane of rotation.
as well as the rationale are presented
is based
coordinates
twist is found
2-D coordinates
mode.
wing twist
The technique
Examples
of the technique
in air
are also presented.
INTRODUCTION Model
deformation
wings
and control
design results
geometry can cause differences between the acquired and expected wind tunnel if the expected results are based upon rigid body assumptions. Differences can also
occur body
between
may be defined surfaces)
acquired
assumptions.
process. years
under
as the change aerodynamic
wind tunnel
These
The measurement
and was identified
data
differences of model as especially
as early as the mid 1970's.
More
measuring
distributions
surface
the importance
pressure
of model
loads,
because
model
has moved
attitude
of requirements and changed
and computational
measurements wind-on
of different
types
photogrammetric incorporation required. options tunnels.
used to measure
video
systems
In some
limited
to the requirement
wind tunnel
(NTF)
for has renewed
aerodynamic
between
which
the
tests (ref.
model
systems system
low contrast
deformation.
because
measurement video
to a number Video
not suitable
of the user and limited systems imagers
imaging,
in low cost
techniques
are generally
targets,
1) 2-dimensional
are used in
low cost electronic
photogrammetric
for custom
to be
imagers
with improvements
including
but these
continues
electronic
of relatively
data acquisition
view ports,
deformation
coupled
of video
problems,
are available,
into a wind tunnel
all contribute
market,
the application
of measurement
In addition,
model
ago, but today
The rapid development
have enabled
rigid
for over 20 Facility
(PSP)
under images
upon
shape.
by the consumer
computing
of interest
paints
in the
design
in the potential
sensitive
and deformation
based
Transonic
interest
to ratio wind-offand
as was the case 20 years
driven
widespread with pressure
technique
of film cameras.
for the National
the
This change
the aircraft
has thus been
desirable
recently,
(particularly
predictions
and degrade
deformation
photogrammetry largely
of a model
load in a wind tunnel.
can lengthen
The fundamental place
in shape
for
interaction illumination for many wind
have been
replacedwith instead
1-dimensional
of passive
active
sources
installation
linear arrays
rub-on or painted
and active infrared
targets.
This combination
more readily enables automation
of active
targets
is acceptable.
made
by Northern
the Optotrak
® system
determining
3-dimensional
locations
sources
are used as targets
of 1-dimensional
of the measurement,
A good Digital
example
arrays
provided
and
the
of this latter type of system
Inc. of Canada.
This system
at up to 600 Hz (for a limited number
is
is capable
of
of markers).
Well-controlled laboratory static calibration tests at Northern Digital have shown that the rms error in angle of attack (AOA) measurements can approach several arcseconds over a range of 180 ° (ref. 2). One disadvantage emitting
diodes
(LED's)
then be activated
in sequence
with the Optotrak
® measurement
which may make
it difficult
MODEL Transonic
pressurized
wind
configuration.
tunnel
(ref.
The wind
140 ° F, normally
provide
length of 9.75 wide range effects
inches.
at constant Reynolds
dynamic
pressure
pressure
environment
The constraints
development,
testing
for a
number effects
effects
imposed Even
number
Reynolds
aeroelastic
number
of temperatures
for the facility.
1984, instrumentation
loads
encountered
for an instrumentation
was identified
early.
Several
modulated
at
at constant
by operation
in a high
have had a significant though
the facility
improvement,
film cameras
techniques
or image
dissector
selected
for initial tests at the NTF
cameras
at the NASA
thought
that there
Langley
would
to measure
model
were considered moir6 contouring
model
has been
and
geometry
cameras. Foot
tunnel
Transonic
Pressure
implementation
Two parallel
successful problems
photogrammetric
approach tunnel
including using was
tests with film
(ref. 6).
It was also
with photogrammetry
efforts
a
heterodyne
techniques
Tunnel
a
at test conditions
(ref. 4), scanning
The photogrammetric
due to earlier
deformations,
for the measurement
(ref. 5), and photogrammetric
largely
Eight
be fewer
techniques.
in the NTF can cause
system
techniques
laser technique,
holographic
than with the other
2
number.
range for the
Reynolds
model
and Math
to
inside the
1.0, based on a chord
are possible:
pressure;
as a coolant,
insulation
and cold test gas can
at Mach full-scale
up to T =
are still underway.
requirement
interferometry,
number;
development
high aerodynamic
microwave
and dynamic
mode
total pressure
of pressure
afford
has a slotted-wall
temperature
using liquid nitrogen
of investigations
over such a wide range
since August
optimization
either
and Reynolds
continuous-flow
-250 ° F. Thermal
of 120,000,000
and Math
on instrumentation
operational
Since
number
number
closed-circuit,
The design
characteristics
Three types
Math
BACKGROUND
The combination
number
These
of aircraft.
constant
impact
Reynolds
problem sensors
FACILITY
mode,
consumption.
15 psia to 130 psia.
a maximum
Another
large size of the image
in an elevated
range down to about energy
must
markers
The 8.2 x 8.2 x 25-fl long test section
using air, and in a cryogenic
shell minimizes
NTF is from
TRANSONIC
is a fan-driven,
3).
light
These
for use in some wind tunnels.
tunnel can operate
obtain a test temperature pressure
is the relatively
DEFORMATION
Facility
is that infrared
real time maker discrimination.
system
to adapt
® system
in the model as markers.
to provide
NATIONAL
The National
of the Optotrak
must be placed
were initiated
for
the NTF.
ITT was selected
to develop
the Stereo
Electro-Optical
Tracking
System
(SETS) for the NTF (ref. 7). This rather large developmental effort to provide an automated model deformation measurement system for the NTF was based upon image dissector cameras which at the time were state of the art. A second, smaller, in-house effort concentrated
on film photogrammetry
tunnel experience.
However,
in order to more rapidly
in just a few years, the image
gain initial lab and
dissector
technology
obsolete due to the rapid advancement in solid state image sensors. made to abandon the SETS and concentrate on the in-house effort.
became
The decision was then For initial tests at the
NTF film cameras were replaced with high resolution, 875 scan line, video tube cameras because of inaccessibility of cameras which must be housed within the cryogenic, high pressure
plenum.
Additional
distortions
introduced
photogrammetric measurement were investigated distortions were evaluated (ref. 8). Initial model video
photogrammetric
technique
in both air and cryogenic
the NTF became
operational
Solid state video vibration-induced
cameras were chosen electronic distortion
severely
degraded
addition, eliminate
into the
modes
were made soon after
(ref. 9).
the video
for subsequent testing at the NTF since tunnel associated with the camera tube construction
data at low temperature
and high pressure
(ref. 10).
In
a personal computer (PC) controlled image acquisition system was employed the manual measurement of targets associated with the previous tube camera
technique. establish
by video tube cameras
and techniques to correct for these deformation tests with the tube-based
Camera
calibration,
the uncertainty
data reduction
of this technique
procedures,
(denoted
and laboratory
the Video
Model
to
tests to
Deformation
or
VMD system) were reported in reference 10 where the accuracy for measuring wing deflection was shown to be about 0.005 inch rms under best case wind-off ambient conditions
over a 26.5 inch semi-span
measurement conditions,
errors
as large
test wing.
It was also determined
as 0.2 ° might be experienced
even with suitable
least-squares
fits to a large
under number
In order to improve the accuracy of the VMD system, laboratory on the calibration and characterization of industrial and scientific cameras
(refs.
techniques
11 and 12).
and cameras,
These
while
studies
helpful
indicated
under
ambient
that state wind-off
that wing twist
best case wind-off of targets. studies were conducted solid state area array
of the art calibration conditions,
were
limiting factors for VMD system performance during wind-on test conditions The harsh environmental conditions at the NTF, which can severely degrade thought
to be the limiting
factors
since temperature-induced
contractions
not
at the NTF. imagery, are
from ambient
to
cryogenic conditions, coupled with the high refractive index in the test section, can lead to bias errors in the photogrammetric measurement which are much larger than the precision error. errors
Attempts to develop suitable correction techniques to reduce or eliminate these bias were unsuccessful. The technique currently used at the NTF to measure wing twist,
however, rationale
has the potential for development
to partially
compensate
of this technique
follows.
for some
of the bias errors.
The
RATIONALE In discussions people
about
involved
aerodynamic
model
FOR
WING
deformation
in aerodynamic
measurement
testing,
load is considered
TWIST
TECHNIQUE requirements
the determination
to be the primary
among a number
of the induced
concern,
of
wing twist under
with wing deflection
(bending)
being of secondary importance. Laboratory investigations, simple error analyses, and preliminary wind tunnel tests at the NTF of wind-on and wind-off conditions indicated flow-induced
wing twist
was decided
to investigate
technique
measurement
in order to provide
The resolution
acceptable
of photogrammetric
the field-of-view.
Thus
uncertainty
ways to increase
was larger than desired.
the resolution
wing twist
generally
to increase
Therefore
it
of the photogrammetric
uncertainties.
measurements
it is possible
that
resolution
is inversely
proportional
to
at the expense
of limited
field-
of-view by using longer focal length lenses to zoom in on the outboard portion of the wing near the tip. However, once this is done the fuselage is no longer in the field of view to serve
as a reference
deflection.
in order
Thus,
semispan
without
locations
to remove
fuselage
will contain
bending.
If wing
a second
camera will be required
bending
Photogrammetric
deflection
is desired,
coordinates
component
data, deflection
this sting deflection calculated
values
are based upon
to the 2-D image
from the wing
measurements
component
to view the fuselage
data reductions
the 3-D object
the sting deflection
at various
as well as the wing
for sting deflection
must be used
in order to measure
sting deflection.
the collinearity
equations
plane coordinates.
which relate
For high accuracy
static
measurements the data reduction procedure of choice in photogrammetry is bundle adjustment with self calibration (ref. 13). In this procedure a single camera is moved number
of locations
of high contrast the test field.
(usually
targets,
8 or more) at which photographs
properly
The 3-dimensional
parameters
associated
adjustment
with the 2-dimensional
unknowns,
and photogrammetric
suitable
for wind tunnel port locations
limit the practicality calibration
disks,
of the targets
along
are computed
image
use because
of multi-camera
applications.
can still be used for pre-test data reductions installation
before
determined
by a space
plane coordinates dimensional
resection
In multi-camera simultaneously
intersection,
photogrammetric optimize
nature
widely
method. of targets
of tests.
or simply
solution
restricted
high contrast
targets
Even so, the bundle method camera
calibrations angles
resection,
For
cameras
of the camera
image
locations
equations
triangulation,
of wing
are
fief.
given
13).
sometimes
twist it is often difficult
for two or more cameras
are
are
the 2-dimensional
of the collinearity
by multi-camera
with self
(ref. 12).
is inappropriate,
is not
intersection.
measurements
the lighting
this method
in the field of view with known
are then found
for the
In addition,
distributed
and pointing
In space
throughout
least-squares
however,
where bundle adjustment
least-squares
coordinates
to as space
laboratory
and the locations
of a number
used as input to a nonlinear
to utilize
distributed
initial guesses
Generally,
to a
of a large number
with calibration
by a nonlinear
plane coordinates,
of the dynamic
and the inability
calibrated
referred
retroreflective
scale as inputs.
photogrammetric
Three
illuminated coordinates
with the camera
viewing
are taken
or
to
the wind tunnel
lighting
restrictions
surface typical photogrammetric point
and the difficult
task of illuminating
for the NTF, at various AOA measurements, computation
is required
along
with precise
targets
on a mirror-like
wing
setpoints. In addition, for multi-camera ofcentroids from each image for each data
time synchronization
in order
to match
corresponding
fields from the cameras. Target identification and matching between the cameras is also required. However, if a single camera photogrammetric technique can be used, which is possible lessened
whenever one of the three target coordinates is known, then these problems considerably. A single camera technique may also be more amenable to
automation.
The major
of the coordinates
limitation
be known.
is known.
than one camera
is required
A single camera
photogrammetric
in the spanwise
in the flow direction coordinates effect
are recorded coordinate
solution
direction
a one second
means
are computed.
Once X, Z coordinates conditions
dimensional
data recording
estimates
transformations of rotation of rotation. A major change
optical
instrumentation
range.
In addition
in temperature
introduce Since
on a pure rotation
been fully successful,
in the wing twist
difference
in wing
pitch angle between
angle at wind-on
and wind-offtest
plane
are a good
dynamic
yaw, since over linear even
angle on the wing
desirable
center
from
of a conformal
location. properties.
of rotation
two-
Least-squares
of the least-squares
The change along
with
reduction.
The
For example, will yield the angle
due simply to the offset
such as window
and non-uniform bias errors
which
to account
to use wind-offpolars
computation.
image
and linear motion.
problems
wall targets
it was decided
reference pitch
measurement
at using test section
fields
from the center
at the NTF has been the wide operational
to operational
can lead to uniform
photogrammetric
attempts
a displaced
in Z coordinates
problem
the
10 video
in X and Z are determined
the angular
about
To reduce
by means
has several
If the Y
exists.
at each semispan
as a byproduct
also separates
only the X coordinate
are very nearly
in pitch
is
the Y
Y to vary,
without
are determined
displacements
since motion
vary with pitch.
plane coordinates
equations
Z coordinates
transformation
on/y, not the change
temperature
conditions
of)(,
sweeps
from which
coordinates
the differences
for each variable
transformation
on
then more
pitch sweeps
solution causes
interval,
object-image
and the corresponding
of precision
conformal
plane
pitch
direction
which
The mean image image
to wind-on
of the conformal
in pitch angle
will then depend
does not change;
in the vertical
at the NTF,
are computed,
transformation
computation
that one
are unknown,
wind-off
then a single camera
typical
to the expected
during
During
of each target
are known
yaw motion
small intervals of Y the collinearity though they are globally nonlinear.
wind-off
is possible
at least for wind-of
over
approximation
solution
In case all coordinates
and the Z coordinate
of all targets
of dynamic
is the requirement
to find a solution.
to the pitch plane,
coordinate
solution
The error in a single camera
how well the third coordinate
confined
of a single camera
are
Wind-on wind-off points
frosting,
contractions.
These
are very difficult
and wind-on
conditions.
had not
condition
wing twist is then computed
may not be equal,
tend to
to quantify.
for these bias errors at each tunnel
the large
as
as the
Since the model
it is necessary
to
subtract out the difference as determined by the primary model pitch angle measurement system, to obtain flow-induced wing twist. Since the wind-on and wind-off data are computed from images at nearly the same temperature and pressure, the effects of these variables are lessened. If the same model pitch angle is used for the wind-on and wind-off images, then the images from each will be at nearly the same image plane location neglecting sting bending. Thus any potential optical and sensor distortion will be comparable and tend to cancel. This error cancellation is only approximated at wind-on test conditions due to sting deflection and wind-on flow structure such as shock waves or boundary layers which can cause refractive index variations. EXPERIMENTAL
PROCEDURE
AND DATA REDUCTION
The optical technique used to determine wing twist data presented herein is based upon the recording and analysis of digitized video images. A video signal from a standard RS170 solid state camera with 752 horizontal by 240 vertical pixels per field is routed to a frame grabber controlled by a 386-33 MI-lz PC which records ten video fields in one second into the frame grabber memory. Ten fields are recorded in order to reduce the effects of dynamic yaw as discussed later. Only ten fields are presently recorded, instead of the desired 60 fields in one second, in order to reduce data storage time and volume. The contents of the grabber memory are stored on a hard disc with the current point number as file name. Once the hard disc is full, currently 144 data points, the digital images are transferred to an optical disc for archiving. The charge-coupled device (CCD) video camera used for wing twist measurements at the NTF has an adjustable field integration time in order to reduce the effects of dynamics on image recording. An 11.5 to 69 mm focal length remote zoom lens is currently used for imaging. Considerations when calibrating zoom lenses for wind tunnel use are discussed in reference 14. The CCD camera is mounted in a protective housing in the test section sidewall. The camera looks over the fuselage at one of the wings of the model (fig. 1). The camera is rotated 90 ° so that the horizontal X axis is vertical on the image plane in order to provide additional viewing flexibility. In addition, the 90 ° rotation more nearly matches the number of pixels vertically and horizontally across a target image since perspective causes the images to be longer in the X (streamwise) direction. The protective housing is equipped with insulation and sheath heaters to maintain camera temperature. The housing is pressure rated to greater than 9 atm. In order to prevent frost, air heated by an inline heater flows to a purge ring with a number of holes to direct the heated air over the inside surface of the one inch thick fused silica window viewport. A purge air vent to atmosphere maintains the camera housing pressure at approximately 1 atm. Circular targets, with an approximate diameter of 5 mm, are applied to the wing surface (fig. 2) with a Sharpie ®marking pen. it should be pointed out that such targets have not been acceptable for all test conditions as discussed later. A template is used to place targets in several rows in the streamwise direction. For the data reported here the target
rows
were located
Initial Xand
at normalized
Y coordinates
reference
locations
drawings
of the wing.
Data
recording
is taken.
with a script
grabber
menu
driven
code
was written
language. control
versions,
and configure the trial code
NASA
the data recording
Langley
on high-contrast
Transonic
In order
Tunnel
during
The initial
data
grabber
frame
acquisition
several
are used to
grabber
images
both wind-off
during
the
in the C programming
first saving the digital
targets
Dynamics
trigger as
and control
to reduce
for the frame
as well to access
without
upon
configure
for initial developments.
4.5.
functions
tap and other
acquisition
of code have been written
C language
can be computed
file for automatic
and 0.922.
from cross-sectional
files to automatically
was convenient
0.778,
from pressure
are estimated
in QuickBASIC
time, trial versions
In these
that centroids using
program
equal to 0.635,
are determined
The Z coordinates
The use of script
data reduction and reduction
locations
of the targets
on the wing.
is programmed
each data point frame
semispan
recent
video
memory
so
as DOS
files.
Tests
and wind-on
tests
at the
semispan
tests were
encouraging. The initial pre-test
calibration
procedure
camera
necessary
for conversion
parameters
coordinates. through
Techniques
for determining
14. The need for extensive
calibration
using the model
temperature
and pressure
The pointing determined
angles
run.
wind-off
points
these parameters
camera
and rotation
determines
calibration
image
are discussed
is lessened
those
plane
in references
somewhat
11
at the tunnel
by on-line total
test conditions. of the camera
set of targets
into a single reference
run temperature
technique
pitch angle for wind-offreference
and location
A known
optical
from pixels to corrected
in the tunnel
at the start of the test by photogrammetric
reference rotation
for the video
angle.
for resection target
over the range
resection
a range
of the center
a wind-off
expected
are
a wind-off
by merging
on knowledge
step requires
of angles
system
during
are established
field based
The final calibration
and pressure
coordinate
during
pitch
of
of
sweep
at
the wind-on
testing. Image
plane coordinates
inverting
The background pixels which from
is found
is slightly
the ten recorded
the photogrammetric coordinates equations
are determined
the gray scale and subtracting
by gray level center-of-mass the background
from the maximum
larger
than the target
gray scale on the border images
fields are then transformed principal
are determined
calculation
plus a few additional
(ref.
11).
and corrected
from a single camera
solution
scales
of a window
The mean (including
point xp, Yv) to give units of length.
after
gray
correction
The X and Z
of the following
of
pixei coordinates
collinearity
for
x = - c [m. (x- Xo)+ ml_(r- to) + m_ (z- zOJ [m31
(X-
X¢)
t- m32 (Y - ]'Pc) + m33
(Z - Z¢)]
(1) y = - c [m21 (X- Xc) + mz_ (Y[m31 (XX¢) + m32 (Y-
Yc) + mz_ (Z - Zc)] Y_)
+ m33
(Z - Zc)]
where x andy are the corrected image plane coordinates, c is the principal distance (or camera constant) which will be slightly larger than the focal length, X, Y, and Z are the object space center,
coordinates
of the target,
and the m terms
are elements
mt]
K"
= cos _cos
Xc, Y¢, and Z_ are the coordinates of the following
rotation
of the perspective
matrix
m_z = sin co sin _ cos t¢ + cos 09 sin ?¢ m_a = -cos cosin _cos
to+ sin co sin I¢
m21 = cos _ sin tc
(2)
m22 =- sin co sin _ sin x + cos co cos x mz_ = cos co sin _ sin ?¢+ sin ca cos ?¢ m31
=
sin
m32 = -sin co cos m33
= COS CO COS #
The pointing
angles
respectively,
are defined
of the camera, as positive
co, 4, and _', which
positive end of their axes. The X and Z coordinates equations (1) for a single camera solution are given X = Xc + (Y-
rotate
about
if they are counterclockwise
the X, Y, and Z axes
when viewed
determined below
fi'om the
from the collinearity
Yc) (Q206 - aj o.O / (a,_ a3 - al f16)
(3)
z = zc - (x- xo) a,/a3 - (r- to) a2/a_
(4)
where
al
= x m31
+ c ml!
a2
= x m32
+ c ml2
as = x mz._ + c
(5)
m13
a4 = y m_t + c m2_ a5 = y m32 + c m_ a6 = y m33 + c m23
Expression
(4) above
that the horizontal the a3 term is nearly
is suitable
for use at the NTF where
X axis is vertical
on the image
plane.
the camera When
zero so that al, a2, and a3 in expression
a4, as, and a6 respectively.
is rotated
the camera
(4) should
90 ° so
is not rotated,
be replaced
with
Thewind-ondataat eachsemispan locationis thenmatchedwith a wind-off pointwith similarmodelpitchangleto determineangleanddisplacement andcorrespondingstandard deviations,usingthe following leastsquaresconformaltransformation X' = X cos 0- Z sin 0 + Tx (6) Z' =Xsin/9+ where
Zcos
Tx and Tz are the translation
coordinates
of the wind-off
for the conformal freedom.
terms
reference
transformation,
one degree
where
in the X and Z directions
point.
If a nonlinear
at least two targets
If a linear least-squares
angle directly,
O+ Tz
technique
least-squares
are required
is used to solve
a = cos 0 and b = sin 0, a minimum
of freedom
since scale is implicit
and X' and Z' are the method
is used
for one degree
for a and b rather of three
in the a and b terms
targets without
of
than the
is needed
for
the constraint
that a 2 plus b 2 be equal to one. In the linear least-squares solution, the standard deviation of the rotation angle is not computed directly, but is instead computed from the standard deviations of the a and b coefficients. However, given three or more targets, nearly identical
results
have been
obtained
with both nonlinear
and linear-least
squares
conformal
transformations. The model reference wing
pitch angle, point,
measured
ao_-, is added
angle at a particular
Ot_st, is then found
with an onboard
to the angle
semispan
by subtracting
0 found
location. the model
accelerometer above
of the wind-off
in (6) to yield the streamwise
The wing twist pitch
package,
due to aerodynamic
angle of the wind-on
point,
load,
ao,, or
(7)
Oiwist= 0 + Otoff- ao. WING Examples
TWIST
of repeated
uncertainty
EXAMPLES
measurements
is expressed
AND
ERROR
of wing twist
as the sum of systematic,
CONSIDERATIONS
are presented or bias error,
below.
The total
and precision,
or
repeatability error. Bias errors are generally very difficult to determine under flow conditions, whereas repeatability can be computed. In addition to laboratory and wind tunnel wind-off determinations of error, run-to-run and test-to-test repeatabilities can be used
to gauge
the adequacy
The uncertainty are unresolved. corresponds
of wing twist measurements
requirements It has been
for measurement of wing twist caused by aerodynamic loads suggested that the desired uncertainty for wing twist which
to an uncertainty
of 0.01 ° for the model
not 0.01%
In other
have
about
the same magnitude
pitch
angle.
Wing
twist
angles
which
words,
measurement
with flow.
an uncertainty effect
on drag
error can occur
are used in equations
of the order
pitch
angle is of the order
of 0.05 ° in wing
measurements
(5) to determine
twist is thought
as 0.01 ° uncertainty
due to errors in the camera
(2) through
of 0.05 °,
position
to
in model
and pointing
the X and Z coordinates.
Pre-test
calibration
lens distortion that errors
errors
or frame
can also contribute grabber
The Y coordinate, well-behaved
assumed
for ambient
measurements under
to be known
contributes
images
image coordinates error
angle,
However,
the expected
error.
solution,
reduces
this error
to the onboard
in the pixel coordinates
that the variations
are typically
of several
pixels.
ceiling
camera.
Note
Wing
transformation
bending
causes
the g coordinate
error in the computation tip deflection
of X and Z. Assuming
bending
would
inboard
of the tip would
experience
be approximately
swept
wings
the wing
rapidly.
locations
are not too far separated,
in bending
under
load.
wing.
to decrease
which
bending
at the tip.
example
would
causes
which
experience
a wing due to wing
The shit_ in Y for targets station
will
Note
that it is this
wing
twist for
produces
in the streamwise
a wing twist
at the tip separated
a bias
dependence, in Yvalue
and shifts in Y value.
fore and aft targets
For two targets
out in the
at the same semispan
fore and ait targets
For instance,
tip of the previous
30 ° swept-back
in both bending
between
cancel
0.
a 2nd order
Targets
by plots
of time which show
equal to 580 mm, the change
0.5 mm for targets
decrease
only slight differences
small difference
angle
of wing targets
of 20 mm, and semispan
also that any
of a pixel even for total
Thus as long as the image
(6) used to determine
in Y
to determine
This is verified
as a function
a fraction
conditions
is as large as :1:3
This variation
in Y by averaging.
of the targets
angle sensor
over one second
the errors in X and Z will also be similar and will tend to partially conformal
and
which typically
during wind-on
Lateral model motion 10 images
equal to within
is constant
inertial
in Y will be nearly the same for all wing targets.
of the variation
to the
in ao_iS much
technique,
Y is not constant
Recording
error
(7)
This is verified by independent
bending.
from a test section
incorrect
ao., will contribute
as well as by the single camera
and wing
to the precision
excursions
sweeps.
if, for instance,
Also note from equation
for the single camera
wind-offpitch
conditions.
mm based on video
are used.
generally
of 0.03 ° or less when compared
wind-offambient
remaining
ao_; and wind-on
8t.z,t, although
due to model yaw dynamics
mean
angle,
in the test section
has an rms error
twist error
corrections
in wind-offreference
error in the wing twist angle, smaller than the error in ao..
to wing
affinity
direction
of almost
at
-2 ° for a
by 50 mm the difference
in
bending would be 1.7 mm out of a total bending of 20 mm with a corresponding difference in the shift of the Yvalue for the two targets of 0.06 mm. A shift in Yvalue of 0.06 mm will cause typical
a difference
object
in angle
in image
distances
caused
scale between
at the NTF
(-1.8
by this small difference
m).
the fore and aft targets For the geometry
in scale will be negligible
of only 1.00003
for
used at the NTF the error compared
to other error
sources.
Wind-off: flow,
Data
compute
apparent
temperature runs differed
possible
error for the video
in Table 1. Two wind-offruns wing
twist,
which ideally
for both runs was nearly considerably
22 °. The mean
10
illustrating
are presented
error
wing twist technique on adjacent
be zero without
deviation
without
days were used to flow.
the same (-105 ° F), but the pressure
(20 and 94 psia).
and standard
should
taken
The for these two
The AOA range for both runs was from 0 ° to of the error for the 13 data points
are
presented
for the three normalized
semispan
stations
(Y/b2)
equal to 0.635,
0.778,
and
0.922. Only three wing targets were used at Y/b/2 = 0.922, whereas four wing targets were used at 0.778 and 0.635. The wing twist error for Y/b/2 = 0.922 is presented in figure 3. The "error bars" in the figure represent the computed standard deviation from the conformal least squares adjustment for each data point and should not be confused with the standard wind-off
deviations
denoted
run used as reference
by cr presented
in determining
wing
in Table 1. Note twist would
that normally
the
be taken within an hour at
the same total temperature and pressure as the wind-on run. Thus the data in Table 1 may be taken to be a conservative estimate of possible wind-off error at non-cryogenic conditions.
Table 1. Error
to-run
0.635
0.778
0.922
mean
-0.001
-0.018
-0.019
o-
0.018
0.026
0.016
in degrees
from the previous Run-to-run
Y/b/2
when
measuring
wing twist without
repeatability: number,
a wind-off
run
day as reference. The repeatabilities
on the same day of a low aspect-ratio
for Mach
flow using
M, of 0.3 and dynamic
of the video research
pressure,
wing twist
model
during
technique
from run-
air runs are presented
Q, of 153 psfin
Table
2 and M = 0.9
and Q = 965 psfin Table 3. The results for 4 runs with 30 data points per run are shown in Table 2. Results for 4 runs with 23 data points per run are shown in Table 3. Wing twist,
O_,t, was computed
equation repeat
(7).
set of four data
AOA sensor accelerometer
at normalized
The mean and maximum points
semispan
stations
of the computed
are denoted
0.635,
sample
0.778,
and 0.922
standard
deviation
as o',,_on and crm_ in the tables.
The
with of each
arcsector
(ARCSEC) is much less affected by test dynamics than the onboard so that o-m,_, for the ARCSEC variable may be taken as an indicator
of
model pitch angle variability for repeat points. These two tables show that the mean standard deviation in 0,_,,, for repeat points was less that 0.02 ° in air mode. In general standard
deviation
of the wing twist,
0, since any real variations are subtracted
out when
the onboard
angle
repeatability
versus
worse
repeatability
the other presented symbol
O_,_t, is less than the standard
in angle-of-attack is computed.
Otwist
of attack
for aon or ao//will
aon are presented at higher
two semispan in figures size) represent
settings
in figures
aon, especially
stations
behaved
6 and 7 where
between
However,
repeat
to the 0,,,,_, value. Mach
number
The corresponding
bars (which
plus and minus one standard
present
are plotted
deviation
in 0
and variability
4 and 5 for Y/b/2 = 0.922
at the higher
of the angle,
points
note that any error
be added
similarly.
the error
deviation
the
in
Plots of the which
and Q. wing
if greater
show Data
twist
for
plots are
than the
of the four repeats
at each
_on-
11
Y/b/2
--
0.635
0.778
...........A_cs_ aato,., a0_,_ ....A0
a0_,_
0.922 A0
a0_,_,t
aO
cr,,,_,
0.010
0.011
0.008
0.009
0.007
0.012
0.006
0.018
or,,,,=
0.015
0.019
0.019
0.018
0.024
0.029
0.017
0.018
Table 2.
Run-to-run
repeatability
in degrees
for four repeat
air runs at M = 0.3 and Q =
153 psf. Y/b/2
=
0.635
0.778
0.922
.......................... _c_c........4._., ........... Aq._,:::. ............... ..4..q. ........... ..a..q._:_ ............... A.q. ........ .....4..q._,.,.:. ............. ..4..q. .......... o',_o,
0.006
0.011
0.016
0.016
0.013
0.015
0.014
0.016
o-,,_
0.012
0.015
0.029
0.032
0.025
0.033
0.037
0.051
Table 3. Run-to-run 965 ps£ Upright
repeatability
and inverted
angularity
by comparison
on the underside
Inverted
reference
due to the inversion.
could
an error check
the wing twist,
between
12
A wind-off
inverted for change
0.3 and Q = 153 psfare
linear interpolation
(extrapolation
in angle signs presented
nearest
0.778
0.922
mean
-0.045
-0.018
-0.013
o"
0.035
0.023
0.032
and standard deviation,
or, in degrees
for the differences
Y/b/2
0.635
0.778
0.922
mean
-0.010
-0.002
0.038
0.030
0.051
0.042
deviation,
o;, in degrees
air runs at M = 0.9 and Q = 965 psfat
semispan
for the differences various
semispan
in
in Table 5. coincide was used
data points.
pitch range of-3 ° to 5 ° were used in the computations
0.635
and standard
twist
run was used as
for end points)
of the pitch angle between
air runs at M = 0.3 and Q = 153 psf at various
5. Mean
and inverted
with flow.
Y/'b/'2
cr
Table
When
to upright runs at the
0.9 and Q = 965 psf are presented
twist values at the midpoint
Mean
and inverted
wing twist.
pitch angle at which the data were taken did not necessarily
Nine data points over a model Tables 4 and 5.
Table 4.
be made to compare
Data from runs made atM=
upright and inverted,
to determine
flow
air runs targets were placed
to determine
making proper allowance
Table 4 and data from runs made atM= Since the model
For two inverted
to determine
180 ° these targets were then in the field of view of the wing
to provide
to compute
air runs at M = 0.9 and Q =
runs are conducted
wing normally viewed
so that wing twist measurements
same conditions
for four repeat
model
to upright runs.
of the opposite
the model was inverted camera
runs:
in degrees
between locations,
between locations,
for
upright Y/b/2.
upright Y/b/'2.
Test-to-testrepeatability: Comparisonsof repeatrunsfrom two five months are presented
in Table 6. Linear interpolation
model pitch angle setpoint standard
deviation,
Mach number, comparisons
varied from
are presented
different
symbols.
pressure.
18 to 26.
are presented
pressures
number and total pressure
M
Q
example
of wing twist, in figure
0.635
,
mean
in
The mean and
of semispan
a plot comparing
12 for Y/b/2 = 0.922. as computed
The error
from the least squares
0.922
.... .a ................ .mean. ....... .a ...........
mean
0.022 -0.013 0.030
a
......... .........
534
-0.004
0.059
0.013
0.071
0.011
0.049
0.3
805
0.022
0.093
0.017
0.109
0.026
0.087
0.9
967
0.001
0.027
-0.016
0.026
-0.005
0.047
in degrees
by
air runs made
dynamic pressure.
0.778
repeatability
location
The Mach
0.6
Table 6. Test-to-test
location,
11. Data from the two tests are represented
is presented
....... .......
for differences
Wing twist data for these runs at a semispan
were varied to give the desired
=
by over
above.
as a function
bars represent plus and minus one standard deviation conformal transformation (6). Y/b/2
separated
The number of data points used for these
in figures 8 through
As an additional
dynamic
to account
the tests was used as described
or, of the differences
and dynamic
of 0.922
at different
between
tests
during air mode.
Units for dynamic
pressure
Q are psf. Wing twist measurements at cryogenic conditions have been limited by frosting on the inside surface of the window of the camera protective housing. In the past, the amount window
frosting
gradually
increased
as the tunnel
causing a degradation in video imagery. run-to-run and test-to-test repeatability Preliminary figures
psf.
of 0.922.
data for two runs under
psf.
For figure
The error
computed
14 the Mach
conformal
are expected
operation
number
increase
number
efforts
are expected
viewing the quality
to include a detailed
predicted
and measured
wing twist,
system
for on-line
data recording
and reduction
grabber
data reduction
board nearly
with dual TMS320C40 simultaneous
the
in
to image
pressure
the standard (6).
conditions of video
Recent
was
was
1795
deviation
improvements
and flexibility data
pressure
during
under
at low temperatures.
WORK
between frame
are presented
was 0.6 and the dynamic
transformation
FUTURE Future
conditions
14 also represent
to improve
and should
cryogenic
was 0.9 and the dynamic
13 through
in the least squares
of
of time
runs at -152 ° F and -250 ° F at a semispan
13 the Mach
bars in figures
a facility upgrade cryogenic
For figure
cold for long periods
Additional wing twist data are needed before under cryogenic conditions can be evaluated.
13 and 14. The data are for nitrogen
location 2670
wing twist
remained
uncertainty
analysis,
and the development to provide
digital capture.
a nearly
signal processors In addition,
comparisons
of a measurement automated is expected innovations
system.
A
to enable are sought
13
to obtainhighcontrast,durablewing targetswhich requirements
at the NTF.
microinches,
resulting
also contain
additional
successfully
automate
needed
which
white
circles
applied
produced
some
uncertainty
about
would
of the targets
a measurable
These
are neither
prefer
on aerodynamic
adverse
effect.
In order
targets
should
contrast.
applied
to are
be fiat-
The nor durable.
the targets
performance;
Targets
may
targets
high contrast
not to apply
l0
surface
high contrast
or the opposite
pen black targets
finish
of a wall or ceiling.
finish requirements.
of the facility
the effects
do not indicate
of the wing
at the NTF
background
the surface
at the NTF can approach images
by reflections
the surface
customers
Thus
measurement
on a fiat-black
Sharpie ® marking
In addition, to date
artifacts
finish of models
like" surface.
the wing twist
do not exceed
solid-filled
currently
The surface
in a "mirror
do not exceed
due to
however,
results
by a chemical
etching
technique would be durable, but of low contrast. Gun bluing could also produce durable targets on at least some of the materials used for models at the NTF, but would still produce
low contrast
rusting
process".
targets
Ideas
and have the additional
for a suitable
target
problem
application
of being
method
a "controlled
at the NTF
are solicited.
SUMMARY The history National camera
of the development
Transonic
Facility
photogrammetric
been presented. given.
It has been speculated technique
at Mach
better
than 0.02 ° . Upright
were
numbers
and equations
of wing twist
for data with error
for wing
and inverted
pressures
runs agreed
than 0.03 ° were also noted.
at tunnel
along
total temperatures
of-152
twist
has
have been
considerations
were
to 0.01 ° model
1-sigma
error
in the
repeatabilities
up to 965 psfwere
Wing
single
reduction
twist equivalent
to within
for the
of wing twist
to be less than 0.03 °. Run-to-run
up to 0.9 and dynamic
of better
presented
for the current
of 0.05 °. The wind-offnon-cryogenic
was shown
mode
capability
on the measurement
that the uncertainty
may be of the order
repeatabilities
procedure
of the measurement
measurement
The rationale
with emphasis
The experimental
Examples
measurement
deformation
has been presented. technique
given.
pitch angle
of a model
in air
shown
to be
0.05 ° . Test-to-test measurement
° F and -250 ° F. Future
examples efforts
include
the use of frame grabbers with onboad digital signal processors and the development of high contrast targets suitable for cryogenic operation which do not exceed the surface finish requirements the measurement.
necessary
at the NTF.
These
efforts
should
aid in the automation
of
REFERENCES 1. Smith, D. G. and Crowder,
J. P.:
The Northern
Digital
OPTOTRAK
Measurement of Model Deflections. Presented at the 71 st Meeting Tunnel Association, Burbank, CA, April 3-4, 1989. 2.
Sherk,
T. and Crouch,
Attack Measurement. Canada, N213V2.
14
D. G.:
Available
Using
the OPTOTRAK®/2010
from Northern
Digital
® for Wind-On
of the Supersonic
System
Inc. 403 Albert
for Angle St., Waterloo,
of
3. Fuller,D. E.
and Williams,
Facility.
AIAA
86-0748-cp.
Beach,
FL, March
M. S.: AIAA
Testing
14th Aerodynamic
Techniques
with the National Testing
Transonic
Conference
West Palm
5-7, 1986.
4. Harding, K. and Harris, J.: Evaluation UDR-TR-81-111, U. of Dayton Research 5. Hildebrand,
Experience
B. P. and Doty,
Applicable
Within
of Moire technique for Wind Tunnel Metrology. Institute, Dayton, OH, Oct 1981.
J. L: A Study of Model the National
Transonic
Deformation
Facility.
Measurement
NASA
CR-165853,
Feb.
1982. 6. Brooks, the Wind
J. D. and Beamish, Tunnel
at Transonic
J. K.:
Measurement
Speeds
Using
of Model
Aeroelastic
Stereophotogrammetry.
Deformations
NASA
in
TP 1010,
Oct. 1977. 7. Hertel, R. J.: Stereo-Electro-Otical Deformation at the National Transonic 8. Burner, Video
A. W., Snow,
Cameras.
published
in proceedings A. W.,
Snow,
a Cryogenic
Wind
Tunnel
May 622.
1985; published
10. Burner, Model
A. W.,
Deformation
published
W. L., and Goad,
presented
9. Burner,
at Annual pp.
W. L., and Goad,
published
of ASPRS,
W. K.:
Using Photogrammetry.
in Instrumentation
Snow,
for the Measurement of Model CR-159146, Oct 1979.
W. K.: Close-Range
meeting
Photogrammetry
Washington,
Mar.
W. L., Goad, presented
'87 RECORD,
Photogrammetry
Deformation Industry
W. K., and Childers, at 12th ICIASF,
IEEE,
Meets
in SPIE Proceedings
Model
with
1985;
pp.
Measurements
at
San Diego,
CA,
31st ISA Symposium,
in the Aerospace
11. Burner, A. W., Snow, W. L., Shortis, Calibration and Characterization of Video Close-Range
System NASA
62-77.
System.
in ICIASF
Tracker Facility.
- vol 31 ISA pp.
B. A.: A Digital
Williamsburg,
615-
Video
VA, June
1987;
210-220.
M. R., and Goad, W. K.: Laboratory Cameras. presented at ISPRS Symposium:
Machine
Vision,
Zurich,
Switzerland,
Sept.
1990;
1395 pp. 664-671.
12. Shortis, M_ R., Burner, A. W., Snow, W. L., Goad, W. K.: Calibration tests of industrial and scientific CCD cameras. Invited paper presented at First Australian Photogrammetry 13. Karara, Photogrammetry
Conference, H. M., ed.:
Sydney,
Non-Topographic
and Remote
14. Burner,
A. W.:
Proceedings
Vol. 2598,
Nov.
Zoom
Sensing,
Lens
7-9, Paper
6, 11 pages,
Photogrammetry. 2nd edition,
Calibration
American
Society
for
1989.
for Wind
pp. 19 - 33, Videometrics
1991.
Tunnel
Measurements.
IV, Philadelphia,
SPIE
PA, Oct. 22-26,
1995.
15
f / f_./¢ d
f f
Figure
1. Wing twist camera
location
at the NTF.
0
Figure 2. Wing
16
twist camera view.
Flow axis is vertical.
2t
.1
Y/b/2
= 0.922
.05
{
c
_
-.05
-5
I
I
I
I
I
I
0
5
10
:15
20
25
ALPHA,
Figure 3. Error previous deviation
in measuring
day as reference.
wing twist
The "error
from the conformal
without
runs
flow using
a wind-offrun
bars" in the figure represent
least squares
.04
deg
adjustment
24,
30,
32,
from the
the computed
standard
for each data point.
34
.03 C_ (D _D
.02 03 0 0 0
tt)
.01 O0
0 000000
0
-5
0 0
,
,%e,%
0
5
dynamic
4. One sigma repeatability pressure
= 153 ps£
0
0
, 15
:10 ALPHA,
Figure
0
Oo
corresponding
0
I
I
20
25
deg
to Table
2 for air runs at Mach
= 0.3 and
Y/b/2 = 0.922.
17
runs
.O4
25,
2g,
.O3 0J "O 0
0
.O2
0
CO I.--4
0
F-
0
0
0
0
0
8
o
.01
O0
o
0
0
0
0 O 0 I
]
I
I
I
I
0
5
10
15
20
25
0
-5
ALPHA.
deg
Figure 5. One sigma repeatability corresponding to Table 3 for air runs at Mach = 0.9 and dynamic pressure = 965 psf. Y/b/2 = 0.922.
• 15
24,
30,
32,
34
Y/b/2
:
0.922
_0 D o
0
O0
o 0
):
c-
-.15
]:
o
-.3 -5
i 0
j 5
i t0 ALPHA,
i _5
t 20
i 25
deg
Figure 6. Mean wing twist corresponding to Table 2 for air runs at Mach = 0.3 and dynamic pressure ffi 153 psf. The standard deviations of the scatter are plotted as error bars if greater than the symbol size. Y/b/2 = 0.922.
18
_
29,
25,
31,
33
Y/b/2
= 0.922
O
.5
O 0
Q) "O
0 0
0
.d
0
0
(/3 .,-4 "a: 0
-.5 O3 C.,-4
000000
°
-1
-I
000000
.5
i 0
-4
I 4 ALPHA,
Figure dynamic
7. Mean pressure
bars if greater
wing twist corresponding = 965 psf
than the symbol
• 15
57-7
I 12
deg
to Table 2 for air runs at Mach
The standard size.
i 8
deviations
of the scatter
= 0.9 and
are plotted
as error
Y/b/2 = 0.922.
g
50-12
Y/b/2
= 0.922
cn 02
xJ
0
.5 O3 .,--_
c_
C .,-4
-.15
-.3
-5
I
I
I
I
I
I
0
5
10
15
20
25
ALPHA,
Figure 8. Wing twist corresponding pressure = 154 psf Y/b/2 = 0.922.
deg
to Table 6 for an air run at M = 0.3 and dynamic
19
57 -8
.5
& 60-14
Y/b/2
= 0.922
Q
o% 0
°°_
-,-4
--.5
_"
C
-_
i 0
-5
E 5
i t0
I
15
ALPHA,
25
deg
to Table 6 for an air run at M = 0.6 and dynamic
Figure 9. Wing twist corresponding pressure = 534 psf. Y/b/2 = 0.922.
•5
I
20
O 57-13
g 60-11
Y/b/2
= 0.922
D []
0
Q.Z
% o%
.j • r-i
--
.
3
)= .iJ
i-
-_ 5 -5
I 0
_ 5
J _0
ALPHA.
Figure pressure
20
10.
Wing twist corresponding
= 804 psi'. Y/b/2
-- 0.922.
i 15
I
I
20
25
deg
to Table 6 for an air run at M = 0.3 and dynamic
1
57-9
6 60-_9
Y/b/2
= 0.922
D .5
rl
E_ GJ "C3
[]
0 tD 4.J
-,5
t2_ t.r.
