AIAA 2003-42 12

PUTTING TEN POUNDS IN A FIVE-POUND SACK: CONFIGURATION TESTING WITH MDOE

Richard DeLoach* NASA Langley Research Center, Hampton, VA 2368 1-2 199

Abstract

A configuration aerodynamics test recently conducted in the Transonic Dynamics Tunnel at NASA Langley Research Center featured a total of 14 configuration variables with suspected non-linear force and moment responses. Resource constraints would prohibit the exploration of all main effects and potential interactions using conventional one factor at a time (OFAT) methods. This paper describes a Modem Design of Experiments (MDOE) approach used to achieve test objectives within resource constraints.

Introduction

A new approach to experimental aerospace research has been under development at NASA Langley Research Center, known as the Modem Design of Experiments (MDOE). This technique addresses certain shortcomings in conventional testing, including wind tunnel testing, that contribute to reproducibility problems and limit productivity, as well as masking certain important insights as will be summarized in the next section.’-’ MDOE methods have been successfully applied at Langley Research Center in a wind range of applications, including wind tunnel testing,8-” facility process im r o ~ m e n t , l ~ - ~ ~ measurement system devel~pment,”~ and hypersonic propulsion technology d e ~ e l o p m e n t , ~ ~ ~ ’ ~ to cite but a few examples.

This paper reports on the application of the MDOE method in a wind tunnel test conducted in the Langley Transonic Dynamics Tunnel (TDT) as part of the Stingray technology development program. The objective of this program is to develop enhanced aerodynamic vehicle control for the Stingray Unpiloted Aeronautical Vehicle (UAV) through fluidic effectors with closed-loop feedback. The Stingray UAV can be seen in Fig. 1 . It features a pair of skin-hinged trailing- edge flaps on both the port and starhard wings, with an array of rero-mass-flux synthetic jets on the leading edge of each wing. Figure 2 illustrates this schematically. The interactions among these leading-

* Senior Research Scientist Copyright 0 2003 by the American Institute of Aeronautics and Astronautics, Inc. No copyright is asserted by the United States under Title 17, U. S. Code. The U. S. Government has a royalty-free license to exercise all rights under the copyright claimed herein for Government Purpow. All other rights are reserved by the copyright holder.

Fig. 1. Stingray UAV.

edge jets with each other and with the vehicle’s trailing edge control surfaces were of particular interest.

As Fig. 2 illustrates, there are four banks of jets on each wing, or eight independent variables associated with jet amplitude (quantified in terms of percent of maximum jet velocity). There are likewise three control surface variables for each wing, consisting of mean deflection angles for the inboard and outboard flaps plus a differential angle between the upper and lower surfaces of the outboard flap, which was tested in this experiment in a “clamshell” mode as well as the conventional flap deflection mode. There were thus a total of 14 configuration variables in this test. (Note that Fig. 2 is a schematic diagram for general illustration, and is not a scale drawing of the actual vehicle tested.) Figure 3 illustrates the clamshell mode of the outbaard flap

Starboard Jet k n k g 4

SJ3 - ‘\

Starboard Flam SJ2 SJ1

\ Outboard (Mean + Dm I-- Inboard

Pun Flaps lnbaard Outbuard (Mean + Dm)

Fig. 2. Fourteen configuration variables in Stingray Icading-edgc synthetic jet flow study (not to scale).

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21st Applied Aerodynamics Conference23-26 June 2003, Orlando, Florida

AIAA 2003-4212

This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.

Fig. 3. Upper and lower surface deflections for all four Stingray outboard flap MDOE factor-level combinations. Note: Red is upper surface, blue is lower. Positive flap deflection implies trailing edge down.

The specific objective of this wind tunnel test was to quantify the performance of the synthetic jets in the Stingray configuration. The intent was to quantify the effects of the jets and to compare these effects to control surface (flap) effects. The intent was also to quantify the interaction effects involving jets and flaps, as well as flap-flap and jet-jet interaction effects.

Expected benefits of a successful technology development program include expanded aerodynamic performance through leading-edge control (more lift, milder stall, and hysteresis prevention), lower cost (less complexity, lighter weight, less volume than conventional flaps and slats), higher maneuverability (increased instantaneous turn rate, increased sustained turn rate, distributed control, fast response) and improved survivability. These objectives are believed to be attainable through the application of leading-edge zero-mass flux excitation and its interaction with trailing edge flaps. One specific objective was to quantify the potential for leading-edge synthetic jets of this kind to prolong upper-surface flow attachment, extending the pre-stall angle of attack range (Fig. 4).

Changes in the forces and moments associated with changes in each of the 14 configuration variables were assumed to be more complex than a simple first order or linear dependence on these variables. Preliminary data suggested that a model featuring a second-order dependence on each of the variables would account for most of the curvature in the anticipated response; that is, a second-order model in 14 independent variables would be expected to explain a sufficient amount of the total variance in an ensemble of data acquired while changing the configuration variables over relevant ranges. This implies that a minimum of three levels would have to be set for each of the 14 factors. To fully characterize this vehicle by physically setting every factor-level combination would require 314 = 4,782,969 separate configuration settings, each of which might be

expected to generate a different and potentially interesting combination of forces and moments. In this test, jet amplitude and control surface deflection could both be set from the control room, with the schedule of configuration changes fully automated so that points could be acquired at the rate of about two per minute. Even at this high data acquisition rate, and assuming two eight-hour shifts per day, it would require almost 10 years to set every jet-flap combination in a three- level full factorial design in 14 variables. Two weeks were allocated for the test.

Wind tunnel researchers are routinely faced with this dilemma: a situation in which there are too few resources to examine every unique configuration in a given test. A frequently-invoked solution is for the principal investigator to employ his engineering judgment and intuition to rank order the various combinations of configuration variables by their assumed relative importance, and to specify as many configurations as resources permit. Such a strategy may appear to be the only practical possibility, but it suffers from at least one major weakness in that it assumes the researcher already understands the system well enough to make this decision. Unfortunately, the reason for conducting the experiment in the first place is that our understanding of system response is imperfect. This could lead to what in hindsight might come to be regarded as poor decisions about which factor combinations to study and which to ignore as we attempt to conserve limited resources. It is difficult to forecast in advance which configuration variables truly are influential and which are not, especially since some variables will exert their influence also through subtle interactions with other variables. These interaction effects are generally too numerous, and in many cases may also be too subtle, to forecast reliably on the basis of intuition alone.

This paper describes an alternative approach to satisfling resource constraints in a configuration study involving a substantial number of variables, using the

Fig. 4. Impact of synthetic jet flow control on lift.

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synthetic jet flow control test as an example. Fortunately, formal experiment design methods that are applied routinely in a wide range of other scientific, engineering, and industrial applications to minimize resource requirements are directly applicable to wind tunnel configuration testing. It was possible to acquire the minimum volume of data required to achieve test objectives well within the allocated test time. MDOE testing techniques also ensure higher quality results by employing tactics that defend against systematic variation (randomization, blocking, and replication). These methods are also able to quantify complex, subtle interaction effects among jets and flaps, in addition to all of the main factor effects to which conventional testing methods are typically limited. These factor interactions provide additional insights into the underlying physics of flight, and improve our ability to predict future system performance

Overview of MDOE

In 1997, NASA Langley Research Center began examining the costs and benefits of applying formal experiment design methods to wind tunnel testing. These techniques, described collectively at Langley as the Modem Design of Experiments (MDOE), differ in fundamental ways from classical wind tunnel test methods referred to in the literature of experiment design as One Factor at a Time (OFAT) testing. The OFAT method places a high premium on data volume and the quality of individual data points, stressing quality assurance measures that rely upon efforts to improve the measurement environment by reducing variance. MDOE methods assume that real-world measurement environments are inherently imperfect, and rely instead upon tactical measures in the design of their test matrices to achieve high quality results even in the presence of systematic and random variation in the mmsiirement environment, which are assumed to be inevitable. While high data volume is a measure of productivity in conventional wind tunnel testing, MDOE practitioners tend to view data volume more as a measure of cost, recognizing that increases in data volume are generally realized only through increases in cycle time, direct operating expenses, and direct and indirect labor costs. In an MDOE test, data volume requirements are defined from an inference error risk management perspective, in t e r n of precision requirements and inference error risk tolerance levels. Ample data are specified to meet precision and inference error risk requirements defined in the experiment design process. Resources that would otherwise be expended by acquiring additional data beyond this are preserved.

Design of StinPrav MDOE ExDeriment

The design of any MDOE experiment begins with a specific description of the objectives. The criterion is that the objectives be stated in a way that enables the researcher to know unambiguously when the test is completed. That is, the statement of test objectives constitutes an important element of the exit criteria by which a successful end of the experiment is identified. Note that general statements of the objectives such as, “To study the aerodynamics of the Stingray vehicle” are not satisfactory because they fail the criterion that the researcher must know when the objective has been achieved. Simply knowing when to stop is a powehl cycle-time reduction tool.

For the Stingray MDOE experiment, the specific objectives were as follows:

I. To rank-order main effects and selected interactions among the Stingray jets and control surfaces.

11. To identify factors with relatively small effects that might be eliminated from effects models.

111. To test the null hypothesis that there are no significant interactions between the leading-edge jets and the trailing edge control surfaces. If this hypothesis cannot be rejected, that is, if one can conclude with sufficiently high confidence from the experimental evidence that there are no significant jet-flap interactions, then independent experiments involving the jets without the flaps and the flaps without the jets would be justified, simplifjmg follow-on studies.

The original experiment design specified all eight jets and all six control surface variables, for a total of 14 variables, each at two levels. Ideally, one would like to execute a “full factorial” design - one involving every combination of every level for every variable. Unfortunately, that would require 214 = 16,384 configuration changes, which would take about a month of two-shift testing at one configuration change per minute facilitated by remote control of the flaps and jets. This would assume almost no tunnel down time or other delays.

The full factorial design would enable one to quantify all 14 main effects and all the n-way interactions, where n ranges from 2 to 14. An interaction occurs when a change in one variable causes a different effect when a second variable is at one level than when it is at another. For example, if the ef’fect of a unit change in the port-side inboard flap is different when port-side jet one is on than when it is off, we say thert. 15 a two-way inleraciion ~ C I N L T L ‘ H t h c x I N U

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variables. If the strength of this interaction depends on the mean deflection of the outboard port flap, say, then there is a three-way interaction among the two flaps and the jet, and so on.

There are 91 possible two-way interactions among the 14 factors, 364 three-way interactions, 1001 four- way interactions, 2002 five-way interactions, 3003 six- way interactions, 3432 seven-way interactions, and so on - a total of 16,383 main effects and interactions. One needs at least one degree of freedom (one data point) for every effect one wishes to quantify.

It is instructive to consider the value of quantifying all 16,383 of these effects. Do we really want to allocate 3,432 configuration changes (57+ hours) to a determination of all the seven-way interactions, for example? We might, if seven-way interactions were likely to be important. But in practice, the “sparsity of effects principle” says that in most physical systems only the main effects and low-order interactions tend to be large enough to be important. Most of the time, not many effects higher than about third-order are large enough to concern us. If we were only interested in the 14 main effects and the 91 two-way interactions, say, then we would only need 106 data points, theoretically. (We always need one more than the sum of all effects, because one degree of fieedom is lost to the mean of the data. The effects simply define changes from the mean.) In truth we would want some additional data to estimate the uncertainty in the results and for other reasons, so we would not cut it that close. But if 106 points is roughly all we need, then it makes little sense to acquire over 16,000 points in a full-factorial experiment. MDOE exploits these discrepancies to achieve reliable insights with relatively parsimonious data sets through a type of design known as a fractional factorial, described in some detail elsewhere.”

The original proposed screening design featured 256 combinations of factor levels - a 1/64th fraction of the full factorial design. It is a “Resolution V” design, meaning that if one can ignore interactions of order 3 and higher, then one will have reliable estimates of all 14 main effects and all 91 two-way interactions. If there are some significant three-way interactions, this design would also provide some indication of that. In that case, the design provides an efficient path for “augmentation,” or the addition of data points to allow higher-order effects to be examined without throwing away the data acquired to that point.

The original design was modified after preliminary runs revealed a significant asymmetry in the port and starboard flap and jet effects. This may be attributable to manufacturing effects in the machining of the model, or to some difference in how the port and starboard jet actuators operated. The full travel on one of the starboard f l a p wm slso nhscrved to he rcdrictcd rel,iiivt+ tti I IK p i t sick. f r r i t l i c ~ ICN~UI~S, tliu

experiment design was altered to focus on each wing independently, with the other wing featuring no flap deflections and jets off. This eliminated problems of interpreting interaction effects between non-symmetric cross-wing elements and reduced the design to seven variables that facilitated a full factorial design for each wing. Twelve “center points” - 50% jet amplitude and half deflection of flaps - were replicated to provide a model-independent measure of pure error - the error due just to chance variations in the data.

Table I is the test matrix for the port-side full- factorial experiment design with replicated center- points. The test matrix in Table I was executed a total of eight times, once with the leading-edge jets operating at a frequency of 30.5 Hz, and once with a frequency of 76.25 Hz, each at two angles of attack (6 and 16 degrees) for both the port and starboard wings.

Execution

Pure error measurements were acquired that facilitated estimates of “block effects,” to be described below. The replicated measurements also facilitated an objective estimate of curvature - non-linear dependence of forces and moments on the flap deflections and jet amplitudes. If there is curvature, this will suggest a certain kind of augmentation to the design to quantify it for each of the variables displaying such curvature. Most importantly, the replicated center-points served as a “meter stick” by which to gauge the magnitude of main effects and interactions. Any main effect or interaction not large enough to be distinguished from the noise levels defined by the replicates with at least 99% confidence was considered too small to be reliably detected. (We say that such effects are not statistically significant.) Note that in a high-precision experiment, it might be possible that certain effects are statistically significant and yet too small to be of practical consequence. As always, judgment is needed to interpret the results of any experimental investigation.

The set-point order was randomized with respect to $lap deflection and jet amplitude set points to defend against persisting effects such as instrumentation drift, changes in flow angularity, shifts in the data system, etc. Randomizing the order of the configuration changes ensures that the ‘Ijet-off runs for a particular jet are just as likely to occur late as early in the point sequence, and likewise for the “jet-on” runs. So if there is a systematic variation occurring that biases early lift measurements low and later lift measurements high, 1 his will have minimal effect on our estimate of the jet effect. (If we took all the “jet o f f data early and all the “jet-on” data later, then any systematic variation would Lc: erroneously attributed to the jd effect.) The virttirs uf irliidLmiz3tiQn RTC discuswd in gTcatter detail

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Fig. 5. Stingray block effects for lift as a multiple of pure random error.

elsewhere in the literature, including for wind-tunnel application^.^. 5*

The design was “orthogonally blocked” into two sets of points for each of the eight wing/frequency/ angle-of-attack combinations tested. Orthogonal blocking confounds between-block effects with high- order interaction effects not likely to be of interest, thus freeing low-order interactions plus all main effects from this type of bias error. All changes to the instrumentation and tunnel state were performed on block boundaries to eliminate these changes as sources of error for the effects likely to be of most interest.

Block Effects

The unexplained variance in an ensemble of wind tunnel data falls into two broad categories. There are random, chance variations in the data that cause individual measurements to differ somewhat from ostensibly identical measurements made even within a short time interval. The general assumption of wind tunnel testing today is that tunnels are in a state of “statistical control” - that these chance variations occur about a mean value that is stable with time. Unfortunately, this is seldom the case in a facility as complex and energetic as a modem wind tunnel. Persisting effects such as temperature changes, flow angularity changes, instrumentation and data system drift, and countless other effects can conspire to create systematic variations in the data so that measurements

made later are biased higher or lower than measurements made earlier. The fact that MDOE Octics defend against these hard-todetect effects is one of the three major advantages of this testing method over conventional OFAT testing. (The other two advantages are that MDOE acquires no more data than necessary to meet minimum requirements and thus reduces cost, and that MDOE reveals interaction effects that OFAT testing does not routinely quantify.)

We define a “block” to be a relatively short segment of tunnel time - typically no more than a few minutes - within which we feel justified in assuming that any systematic variation is small. We can compare the mean of replicates acquired in one block with the mean of ostensibly identical replicates acquired in another block separated from the first by a larger time interval, to see if the difference is large enough to detect unambiguously in the presence of ordinary chance variations in the data. If so, we call this difference a “block effect.”

Block effects were estimated for the eight combinations of wing, jet frequency, and angle of attack that were investigated in this test. In all eight combinations, replicates were acquired in a pair of blocks, with an intervening interval typically of about an hour. The block effects for lift observed between block pairs is reported in Fig. 5, normalized by the standard deviation of pure error for lift. Block effects exceeding the heavy dashed line at a normalized level of “1” in this figure were greater than the chance

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I met

Fig. 6. Stingray flap effects for lift.

variations that are the only error source considered in a typical wind tunnel experiment. Note that this was true in six of the eight cases. It was not uncommon for the block effects to exceed ordinary chance variations by a factor two, and in one case the systematic component of the unexplained variance was almost five times greater than the random component.

Factor Effects

Table I1 assigns a letter to each of the flap and jet factors tested, to make it convenient to specify main effects and interactions effects. For example, “ A refers to the port inboard flap main effect. The A effect for lift, for example, would be the change in lift due to a flap deflection change from -13” to +13”, and similarly for the other forces and moments. Likewise, “C” is the differential port outboard flap effect, which for lift is the change in lift when the outboard flap is changed from no differential deflection to a differential deflection of 26 degrees. See Fig. 3. The “AC” interaction is the difference in the “C” effect between the case when the port inboard flap is at -13” and +13”, and so on.

Figure 6 compares the main flap lift effects for two jet excitation frequencies, 30.5 Hz and 76.25 Hz for the port-side wing at an angle of attack of 16”. Effects are normalized by the smallest effect that was statistically significant at the 0.01 level (large enough that there is a 99% probability the estimate of the effect is not due simply to noise). This figure clearly reveals the rank- ordering of flap effects, and shows that changes in the inboard flap had a larger effect on changes in lift than the outboard flap in either its conventional or differential mode. The main flap effects are also seen

to be virtually independent of synthetic jet excitation frequency.

Figure 7 presents the significant jet main effects for lift, and also the jet-jet and jet-flap interaction effects for port-side wing at an angle of attack of 16”. These are normalized to the same level as the flap effects in Fig. 6 to facilitate a direct comparison. Note that even the largest jet lift effects are small compared to the flap effects, a result which is not unanticipated since the intent of the jets is simply to modify the lift performance of the flaps. These results suggest that the third bank of synthetic jets has the greatest positive effect on lift, and that interactions of other jets with themselves and with the flaps may have a negative effect ob lift. This M e r suggests that in flight regimes for which maximum lift is a priority, it might be advantageous to minimize banks 1, 2, and 4, which may be more usefbl when other performance augmentations are desirable, such as rolling and possibly even yawing.

Concluding Remarks

The block effects reported in Fig. 5 are consistent with observations made in over six years of MDOE testing at Langley Research Center, and apply across all facilities and Mach ranges. The general result is that the systematic component of the unexplained variance dominates the random component. It is the author’s considered opinion that the failure of conventional OFAT testing methods to defend against (or even to recognize the existence of) block effects is a leading cause of reproducibility problems in wind tunnel testing. It is also a major reason for what has come to be called “between facility effects,” in recognition of the fact that good reproducibility from one tunnel to

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f 6 #

Fig. 7. Stingray jet main effects, and jet-jet and jet-flap interaction effects for lift at 16” angle of attack.

another is so rare. Formal experimental techniques make good use of tactical quality assurance measures such as blocking, randomization, and replication, to defend against the dominant systematic component of unexplained variance. As these techniques become more widespread within the experimental aeronautics community, they will begin to ameliorate elements of the ubiquitous “between fhcility effects” so common in conventional OFAT wind tunnel testing.

The factorial experiment design method employed in this test facilitated an efficient and objective examination of all main effects and interactions among seven independent variables of interest. Each of the eight executions of the test matrix in Table I required only on the order of an hour and a half of testing, so that the entire investigation was completed in less than two shifts of testing time, well within allocated resources.

Subsequent experiments can be more highly focnscd mad smaller in scale now that the dominant !lap and jet effects have been identified, providing further opportunities to optimize the deployment of limited test resources. Such variables as Mach number and synthetic jet waveform can be added to the study using a design that can deemphasize effects now known to be relatively small. The MDOE methods illustrated in this test facilitate an approach to wind tunnel operations known at Langley Research Center as “agile testing,” in which experimental investigations are organized into a series of small, sequential experiments, with the result of each one informing the design of the next. Efforts are underway to automate the analytical operations required to do this, with a view to improving both quality and productivity in wind tunnel testing.

Acknowledeements

This work was supported by the Langley Research Center Wind Tunnel Enterprise. The contributions of Barton J. Bacon and Irene M. Gregory of the Dynamics and Control Branch, and of Anthony E. Washburn of Ihe Flow Physics and Control Branch are gratefully acknowledged, as are those of the Langley Transonic Dynamics Tunnel facility staff, who provided outstanding technical support during the experiment reported in this paper. The contributions of Rob Scott, Dave Piatak, James Florance, and Tom Ivanco of the Langley Aeroelasticity Branch are especially noted.

References

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DeLoach, R. “Applications of Modem Experiment Design to Wind Tunnel Testing at NASA Langley Research Center” AIAA-0713 36th AIAA Aerospace Scieiiccs Meeting and Exhibit. Reno, NV, Jan 1998.

DeLoach, R. “Tailoring Wind Tunnel Data Volume Requirements Through the Formal Design Of Experiments” AIAA-98-2884 20th Advanced Measurement and Ground Testing Conference. Albuquerque, NM. Jun 1998.

DeLoach, R. “Improved Quality in Aerospace Testing Through the Modem Design of Experiments (invited)”. AIAA 2000-0825. 38th AIAA Aerospace Sciences Meeting and Exhibit. Reno, NV. Jan 2000. DeLoach, R. “The Modem Design of Experiments: A Technical and Marketing Framework (invited)” AlAA 2000-2691. 21st AIAA Aerodynamic

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Measurement Technology and Ground Testing Conference. Denver, CO. Jun 19-22,2000.

DeLoach, R. “Tactical Defenses Against Systematic Variation in Wind Tunnel Testing” AIAA 2002-0885. 40th AIAA Aerospace Sciences Meeting & Exhibit. Reno, NV. January 14-17, 2002

DeLoach, R. “MDOE Perspectives on Wind Tunnel Testing Objectives” AIAA 2002-2796. 22nd AIAA Aerodynamic Measurement Technology and Ground Testing Conference. St. Louis, MO. Jun 24-26,2002.

DeLoach, R. “Applications of the Modem Design of Experiments at NASA Langley Research Center (Invited)” 46th Annual Fall Technical Conference. Valley Forge, PA. October 2002.

DeLoach, R., Hill, J. S., and Tomek, W. G. “Practical Applications of Blocking and Randomization in a Test in the National Transonic Facility” (invited) AIAA 2001-0167. 39th AIAA Aerospace Sciences Meeting and Exhibit. Reno, NV. Jan 2001.

Morelli, E.A., and DeLoach, R. “Response Surface Modeling Using Multivariate Orthogonal Functions” (invited) AIAA 2001-0168. 39th AIAA Aerospace Sciences Meeting and Exhibit. Reno, NV. Jan 2001.

10. DeLoach, R., Cler, D., Graham, B. “Fractional Factorial Experiment Designs to Minimize Configuration Changes in Wind Tunnel Testing” AIAA 2002-0746. 40th AIAA Aerospace Sciences Meeting & Exhibit. Reno, NV. January 14-17, 2002

11. DeLoach, R. “A Factorial Data-Rate and Dwell- Time Experiment in the National Transonic Facility”. AIAA 2000-0828. 38th AIAA Aerospace Sciences Meeting and Exhibit. Reno, NV. Jan 2000.

12. Dominguez, K. Graham, B., DeLoach, R. “Implementation of an MDOE Compliant Control System in the VfGYAN Low Speed Wind Tunnel” (invited) AIAA 2001-0169. 39th AIAA Aerospace Sciences Mcrting and Exhibit. Reno, NV. Jan 2001.

13. Underwood, P., Everhart, J., DeLoach, R. “National Transonic Facility Wall Pressure Calibration Usin? Modem Desiq Of Experiments”

(invited) AIAA 2001-0171. 39th AIAA Aerospace Sciences Meeting and Exhibit. Reno, NV. Jan 2001.

14. Erickson, G. E., Burner, A. W., and DeLoach, R. “Pressure-Sensitive Paint and Video Model Deformation Systems at the NASA Langley Unitary Plan Wind Tunnel” High-speed Research Aerodynamic Perfonnance Workshop, Hampton, Virginia, February 25-28, 1997.

15. Parker, P. and DeLoach, R. “Response Surface Methods for Force Balance Calibration Modeling” 19th International Congress on Instrumentation in Aerospace Simulation Facilities, Cleveland OH, August 200 1.

16. Parker, P. and DeLoach, R. “Structural Optimization of a Force Balance using a Computational Experiment Design (Invited)” AIAA 2002-0540. 40th AIAA Aerospace Sciences Meeting & Exhibit. Reno, NV. January 14-17, 2002

17. Burner, A.W., Liu, T. and DeLoach, R. “Uncertainty of Videogrammetric Techniques used for Aerodynamic Testing” AIAA 2002-2794.22nd AIAA Aerodynamic Measurement Technology and Ground Testing Conference. St. Louis, MO. Jun 2426,2002.

18. Cutler, A., Danehy, P., Springer, R,, DeLoach, R., and Capriotti, D. P.:”CARS Thermometry in a Supersonic Combustor for CFD Code Validation” AIAA 2002-0743. 40th AIAA Aerospace Sciences Meeting & Exhibit. Reno, NV. January 14-17, 2002

19. Danehy, P.M., DeLoach, R., and Cutler, A.D. “Application of Modem Design of Experiments to CARS Thermometry in a Model Scramjet Engine” AIAA 2002-2914. 22nd AIAA Aerodynamic Measurement Technology and Ground Testing Conference. St. Louis, MO. Jun 24-26,2002.

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Table 1. Full Factorial One-Wing MDOE Test Matrix

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Table 11. Flap and Jet Variables

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