Comparison of wind-tunnel data repeatability with ...

Copyright© 1998, American Institute of Aeronautics and Astronautics, Inc.

AIAA Paper No. 98-2714 COMPARISON OF WIND-TUNNEL DATA REPEATABILITY WITH UNCERTAINTY ANALYSIS ESTIMATES Dale L. Belter* Boeing Commercial Airplane Group Aero/Noise/Propulsion Laboratory Seattle, Washington

Downloaded by Dale Belter on October 30, 2015 | http://arc.aiaa.org | DOI: 10.2514/6.1998-2714

ABSTRACT When assessing the quality of the wind-tunnel data being acquired at the Boeing Aerodynamics Laboratory, data repeatability is a first concern. Baseline configurations from previous tests, and multiple repeats of a baseline configuration within a test are used by the customer and test personnel to obtain confidence in the test data. One piece missing from the repeatability analysis is the estimated repeatability obtainable from the current test setup. This paper explores some of the tools being used to estimate data repeatability and compares these estimates to test data. INTRODUCTION The market for commercial jetliners has been changing, as airplane performance is no longer the prime consideration. Price and delivery time have become equally, if not more, important. With increasing pressure to reduce cost and cycle time, the Product Development group at Boeing is re-evaluating the airplane development process. Wind tunnel testing dominates the early product-definition phase of this process, which typically includes three wind-tunnel-test cycles. A natural reaction to reduce cost and cycle time is to cut the number of wind tunnel test cycles to two (for new configurations) and one (for derivative configurations). Aerodynamics engineers analyzing wind-tunnel data typically look at the precision of the data for a specified configuration as an indication of the accuracy (actually the variability) of the data. Baseline configurations from previous tests and multiple repeats of a baseline configuration within a test are used by the customer to obtain the required confidence in the test data. Current test planning does not include an uncertainty estimate to determine the amount of repeat testing required to achieve the accuracy requirements. * Lead Engineer, Member AIAA Copyright © 1998 by The Boeing Company. Published by the American Institute of Aeronautics and Astronautics, Inc. With permission.

An engineering approach to wind-tunnel data quality assessment has been developed and accepted as a standard by both the Advisory Group for Aerospace Research and Development (AGARD) and the American Institute of Aeronautics and Astronautics (AIAA)1'2. This paper gives a summary of how these methods are being used at the Boeing Aerodynamics Laboratory to estimate the repeatability of test data. Results are also presented comparing wind-tunnel data repeatability with pre-test estimates. UNCERTAINTY ANALYSIS The result of an uncertainty analysis is the determination of an interval about the measured variable Xt within which the experimenter can state with a specified level of confidence that the true value of the variable lies. That is,

X,±U,

(1)

where Xj is usually the mean value of the sample measurements and f/, is the uncertainty in the measurements of X stated with a specified confidence level. Consistent with the AIAA Standard1, all estimates in this document are made at a 95-percent confidence level. The uncertainty [/,- is a combination of both bias and precision error estimates (B; and />,-, respectively) as shown below: (2)

Estimation of the absolute uncertainty including biases is difficult at best, and is not included in this document. In general, large biases are assumed to be eliminated in a well-controlled experiment by some means, such as by instrument calibration. Small biases, however, typically remain and form the bias error. The precision error is the random component of the uncertainty estimate and is referred to as the repeatability error (or repeatability). The repeatability error represents the difference between a measured value and the mean of a population of measured values. The random nature of the repeatability error lends itself

1 American Institute of Aeronautics and Astronautics


to estimation by statistical analysis and is easier to quantify mathematically than the bias error.


This section describes the approach taken to estimate data repeatability using statistical methods. The approach builds on the use of simple statistics for the analysis of individual sample data, and extends it to the multivariable regression analysis problem. This approach is referred to as curve fit statistical analysis (CFSA). The approach is based on estimating the data mean (polynomial least-squares curve) and then representing the data scatter about the estimated mean (confidence and prediction intervals). Estimation of the Data Mean The polynomial least-squares equation of order K can

be written as: C2X2 + C3X3+...+CKXK

(3)

where X is the independent variable, Y is the resulting best estimate of the independent variable, and C0, C1; ... , CK are the least-squares constant coefficients. Measures of Repeatability

When an estimate of the data mean Y(X) is determined, a measure of the data scatter about the mean is applied. The fundamental measure of the scatter about an estimated mean in the CFSA approach is the standard error SE, which is defined as:

SMf 1=1 N-K-l

(5)

The prediction interval is defined as a band about the estimated mean within which, in the absence of bias, the next acquired point falls. The prediction interval PI is defined as:

STATISTICAL CHARACTERIZATION OF DATA: METHOD OF REPEATABILITY ANALYSIS

Y(X) = C0

= ±t95-SE-Q(X0)

(6) As with single sample statistics, t95 is the value of the Student t distribution for a 95% confidence level and v degrees of freedom (v = N - K - 1), with N samples, and polynomial-least-squares curve fit of order K. The term Q(Xo) is a measure of data density in the area of the independent variable of interest X0. It accounts for data density so that highly populated regions of the data sample have narrower confidence and prediction intervals than sparsely populated areas. Time Scales for Repeatability Analysis

Three time scales are defined to classify a given repeatability sample: short, near and long term. The time

scales relate to both the period and the circumstances in which data are collected. A short-term repeatability sample describes data variability over a relatively short period with minimal change in circumstance. Repeat Mach number polars within a Mach number series is an example of short-term repeatability. A near-term repeatability sample describes data variability when a given configuration is retested during a single tunnel entry and at least one other configuration is tested in between. A long-term repeatability sample describes data variability from tunnel entry to tunnel entry for a given model configuration. Obviously, the potential for the introduction of bias errors, particularly modelrelated biases, increases when going from short- to longterm comparisons.

(4)

PROPAGATION OF REPEATABILITY UNCERTAINTIES TO CALCULATED RESULTS

where Yf is the estimated value of Y that corresponds to the dependent variable X, of the ith data point. In effect, the standard error is an extension of the sample standard deviation defined in single sample statistical analysis.

The propagation of the individual repeatabilities into the final result is accomplished using a Taylor series expansion. (7)

The confidence and prediction intervals, both of which

depend on the standard error, are two additional measures of repeatability that can be extended as well. The confidence interval is defined as a band about the estimated mean within which, in the absence of bias, the "true" mean lies. The confidence interval CI is defined as:

The partial derivatives quantify the sensitivity of the result to each measured input jc,-. A computer program3 has been developed that computes influence coefficients and uses them with specified measurement uncertainties to calculate the uncertainty in a parameter. The program is known as a "jitter" program in which each

American Institute of Aeronautics and Astronautics


independent variable is perturbed by the same percent, and the resulting change in the parameter of interest is observed. At this time, this program does not account for correlated bias or precision errors.

Drag Coefficient When determining wind-tunnel data repeatability, the

one parameter that gets the most attention is the stability axis drag coefficient (CDSA). In simple terms, CDS A is defined as follows: CDSA =

DRAGSA

,2

PTCORR

(11)

Individual parameters and their associated repeatability

estimates are defined in the following sections. Propagation Equations for an Internal-BalanceMounted Model

For an internal-balance mounted model, pre-test CDSA estimates include the following repeatability estimates:

CDSA

(12)

DRAGSA — '

(13)

(8)

}

REF


r

where:

DRAGSA 1 SREF

= =

model drag, Ib dynamic pressure, psf wing reference area, ft2

pSCORR

r

PTCORR

(14)

BOEING TRANSONIC WIND TUNNEL (BTWT)

Prior experience with uncertainty estimates at the Boeing Transonic Wind Tunnel have shown that the balance measurements have the largest influence on the

CDSA uncertainty. Corrections to Drag Coefficient

For most tests, the basic drag coefficient has many corrections applied to determine the final, corrected drag coefficient. These corrections may include, but are not limited to tunnel flow angularity, buoyancy, mounting system tare and interference, and wall interference. When doing an uncertainty analysis, the errors associated with these corrections are handled as bias errors. Even if there were precision errors

associated with these corrections, it would be impractical to include them in pre-test estimates. The next sections examine estimates of the CDSA repeatability for an external-balance mounted model and an internal-balance mounted model in the Boeing Transonic Wind Tunnel. For these estimates, repeatabilities for dynamic pressure and angle of attack are shown, but the main focus is on the balance repeatabilities.

Facility Description The Boeing Transonic Wind Tunnel is a closed circuit, atmospheric, single return facility with an 8 x 12 ft slotted wall test section. Models are plate or floor mounted on the six-component main external force and

moment balance, or sting or swept-strut mounted on an internal balance. The slotted test section and variable reentry door design permit testing at transonic velocities. Two test sections, with an 11% porosity slotted or a nonporous solid wall are available. Variable fillet flaps and re-entry doors provide adjustment for test section longitudinal pressure gradient and thereby minimize clear tunnel buoyancy effects. The maximum attainable Mach number with the standard test section and empty tunnel is 1.12.

Boeing Transonic Wind Tunnel (BTWT) Fan & Fan Struct!

Propagation Equations for an External-BalanceMounted Model

For an external-balance mounted model, pre-test CDSA estimates include the following repeatability estimates: r

CDSA

r

-f-

DRAGSA

DRAGSA = P, DRAG

(9)

(10)

Figure 1. Boeing Transonic Wind Tunnel (BTWT)



TUNNEL PARAMETERS Mach Number Measurement and Calibration


The Mach number measurement system in BTWT is a static pressure and differential pressure system. Tunnel

static pressure (PS) is measured in the test section plenum (cap static) and then corrected to tunnel centerline (tunnel station 1000, tunnel waterline 48 and tunnel buttline 0) by means of calibration probe results (PSCORR). The difference between tunnel total and static pressure (PT-PS) is measured by a total pressure probe at the beginning of the test section. The tunnel total pressure (PT) is then calculated. This measurement is then referenced to tunnel centerline by means of calibration probe results (PTCORR). The corrected tunnel Mach number (MACHC) is computed from these pressure measurements, and the corrected tunnel dynamic pressure (QPSFC) is then calculated from the Mach number.

CORRECTION

CONFIDENCE INTERVAL

PREDICTION INTERVAL

PSCORR

0.0025 %Rdg.

0.0300 %Rdg.

PTCORR

0.0005 %Rdg.

0.0075 %Rdg.

Table 2. BTWT Tunnel Static and Total Pressure Correction Uncertainties

BTWT C e n t e r l i n e S t a t i c P r e s s u r e C o r r e c t i o n (PSCORR) S u p e r P r o b e + IF t DRH

Mach Number Pressure Transducers

The tunnel static pressure transducer (Rosemount Serial No. 2543) and the tunnel differential pressure transducer (Rosemount Serial No. 1499) are calibrated in place at least once a year. The five latest calibrations are combined into one data set and fit with a third order least-squares curve fit. The 95% confidence level, confidence and prediction intervals are computed for each transducer as shown in Table 1. 0.0

TRANSDUCER

CONFIDENCE INTERVAL

PREDICTION INTERVAL

PS

0.0012 psi

0.0076 psi

PT-PS

0.0003 psi

0.00 18 psi

0.2

0.4

i

0.6

0.8

1.0

1.2

:

95% P r e d i c t i o n I n t e r v a l

Table 1. BTWT Mach Number Pressure Transucer Uncertainties

Tunnel Static and Total Pressure Corrections

The static pressure correction to tunnel centerline (PSCORR) is computed from static pressure probe data acquired during a tunnel calibration test. For each Mach number calibrated, 50 data points are collected, then the entire data set is combined and fit with a leastsquares curve fit (figure 2). Similarly, the total pressure correction to tunnel centerline (PTCORR) is computed from total pressure probe data (figure 3). The 95% confidence level, confidence and prediction intervals are computed for each correction. The computed uncertainties are summarized in Table 2.

95% Confidence I n t e r v a l _

0.00 0.2

0.4

0.6

0.8

1.0

MACH Number

Figure 2. BTWT Centerline Static Pressure Correction



Table 3 shows the maximum component limits of the balance.

BTWT C e n t e r l l n e Totil Pretitire C o r r e c t i o n (PTCORR) T o t i l P r o b t * IF + DRH BT2190

Component DRAG LIFT PM SF YM RM

Maximum Load 1000 10,000 100,000 5000 75,000 25,000

Ib Ib in-lb Ib in-lb in-lb

Table 3. BTWT Main Balance Load Limits


Model Drag Calculations .

|

1

| 95% P r d l c t l o n Inltrval

1

Since the Main Balance is a wind-axes balance and does not move with the model, when computing pre-test repeatability estimates, the measured balance drag is a

good measure of the model stability-axes drag: |

DRAGSA = DRAG

(15)

I

Main External Balance Calibration Residuals 1 [

*~

;

-

:

__

—"

!

Figure 3. BTWT Centerline Total Pressure Correction

FORCE AND MOMENT MEASUREMENTS

Six-component force and moment measurements in BTWT can be made using either the BTWT Main External Balance or an internal-strain-gage balance, depending on the type of model mount. Although there are many contributions to balance uncertainty and much effort is being expended nationwide to understand and

estimate them, no one method has become a standard. Consequently, the following sections explore four different methods of estimating balance repeatability: balance calibration residuals, balance end zeros (EWOZ's), generalized balance curves, and balance interaction matrix repeatability.

BTWT MAIN EXTERNAL BALANCE The BTWT Main External Balance is a six-component force and moment balance which is permanently installed below the BTWT test section floor. The balance is considered a wind axes balance with the force sensing cage being fixed in wind axes. The moment sensing cage sits on top of a turntable which remains fixed during full-model testing, but rotates with the model during half-model testing.

The BTWT Main Balance is calibrated in place with the calibration being referenced to gravity, this permits

dead-weight loading for a majority of the calibration runs (load codes). Since the Main Balance is a fixed installation, the horizontal loads are applied over adjustable pulleys, while the vertical loads are applied using an adjustable jack-loadcell push-rod combination. Any misalignment of the cable line of action or push-rod will cause residual balance loads. These residual loads, in turn, cause interactions to be generated that do not reflect the true balance characteristics. Balance calibration uncertainty is evaluated by examining the calibration residuals. For the Main Balance calibration, 33 different load codes define the complete calibration. In addition, certain primary loads (DRAG, LIFT and PM) are repeated periodically throughout the calibration. The individual calibration loads are reduced through the interaction matrix and calibration residuals are computed. For this study, the residuals from the last two Main Balance calibrations are combined into one data set for analysis. Main Balance DRAG residuals are plotted (figures 4) along with the corresponding 95% confidence-level prediction intervals. These prediction intervals are used as an estimate of the long term Main Balance calibration repeatability.



BTWT M a i n Balance C a l i b r a t i o n R e s i d u a l s Long Term Hi s t o r y

BTWT Main Balanca End Zeroes

Long Term History

« -sn

il%2^

»0

NO

WO

MO


Figure 5. BTWT Main Balance Drag EWOZ's G e n e r a l i z e d Balance U n c e r t a i n t y E s t i m a t e s EXTERNAL BALANCE -120000

-80000

-4000I

IOOOO

120000

160000

A p p l i e d C a l i b r a t i o n Load (Ibs. or in-lbs.)

Figure 4. BTWT Main Balance DRAG Calibration Residuals

Main Balance End Zeroes

Balance end zeroes (EWOZ) are recorded in BTWT after every series of wind on running. While these end zeroes are not used to correct the balance data, they are used to monitor balance performance. The variation of the balance end zeros. are a good indication of data repeatability. For this study, the end zeros from the last three BTWT tests with the same plate-mounted model are combined into one data set for analysis. Main Balance DRAG ends zeroes are plotted (figure 5) along with the corresponding 95% confidence-level prediction intervals. These prediction intervals are used as an estimate of the long term Main Balance end zero repeatability. Generalized Balance Uncertainty Estimates

Figure 6 shows a set of generalized uncertainty estimate curves that have been used at the Boeing Aerodynamic Laboratories for external balance uncertainty estimates. The figure shows curves for balance component repeatability and absolute uncertainty as a percentage of maximum balance component range. Use of these curves apply only to the individual component being loaded and do not take into account balance interactions.

-1.0

-0.6

DECIMAL PORTION OF MAXIMUM BALANCE COMPONENT RANGE

Figure 6. BTWT Main Balance Generalized Uncertainty Curves Main Balance Calibration Matrix Repeatability Estimates

The BTWT Main Balance is calibrated every one to two years. This provides a set of repeat calibration data for analysis. A method is being developed to analyze these repeat calibrations by determining the repeatability of each sensitivity and interaction (6 x 27 interaction



matrix) individually. The last five Main Balance

from the last two 6226E Balance calibrations are

calibrations are analyzed together, and the variability of

combined into one data set for analysis. 6226E Balance AF and NF residuals are plotted (figure 7) along with the corresponding 95% confidence-level prediction intervals. These prediction intervals are used as an estimate of the long term 6226E Balance calibration repeatability.

the individual interactions are determined over that time frame. Thus, the repeatability of the individual interactions (and their influence on the balance component readings) are used as an estimate of the

balance repeatability.


Internal-Strain-Gage Balances

6226E B a l a n c e C a l i b r a t i o n R e s i d u a l s Long Term H i s t o r y

Boeing internal-strain-gage balances are one-piece, sixcomponent force and moment balances which are used in models mounted on either a swept strut or straight sting. The balance is considered a body-axes balance which rotates with the model when it is pitched. Measurement of the pitch angle of the balance relative to the freestream velocity vector (angle of attack) is critical in resolving the balance force components into the model stability axes.

95% P r e d i c t i o n I n t e r v a l

The 6226E balance is a high-capacity balance used regularly in BTWT. Table 4 shows the maximum component limits of the balance: -ISO

Component AF NF PM SF YM RM

Maximum. Load 360 4,750 21,000 2,400 8,400 8,400

-100

-50

0

50

100

150

Percent of Maximum Primary C a l i b r a t i o n Load

Ib Ib in-lb Ib in-lb in-lb

Table 4. Balance 6226E Load Limits

Model Drag Calculations For an internal-strain-gage balance which rotates with the model, the following is assumed when computing

pre-test repeatability estimates:

DRAGSA = AF • COSa + NF • SINa

(16)

6226E Balance Calibration Residuals The 6226E Internal Balance is calibrated in the Boeing

Balance Calibration Laboratory with the calibration being referenced to gravity. This permits dead-weight loading for all of the calibration runs (load codes). Balance calibration uncertainty is evaluated by looking at the calibration residuals. For an internal balance calibration, 41 different load codes define the complete calibration. In addition, certain primary loads (AF, NF and PM) are repeated periodically throughout the calibration. The individual calibration loads are reduced through the interaction matrix and calibration residuals are computed. For this study, the residuals

-150

-100

-50

0

50

100

150

P e r c e n t o f Maximum P r i m a r y C a l i b r a t i o n Load

Figure 7. Balance 6226EAF & NF Calibration Residuals

6226E Balance End Zeroes

Balance end zeroes (EWOZ) are recorded in BTWT after every series of testing. While these end zeroes are not used to correct the balance data, they are used to monitor balance performance. Experience has shown that temperature gradients across internal balances are among the largest contributors to balance nonrepeatability. The variation of the balance end zeros is a good indication of data repeatability. For this study, the end zeros from the last three BTWT tests using the 6226E are combined into one data set for analysis. 6226E Balance AF and NF end zeroes from one of these



tests are plotted (figure 8) along with the corresponding 95% confidence-level prediction intervals. These prediction intervals are used as an estimate of the long term 6226E Balance end zero repeatability.

Generalized Balance U n c e r t a i n t y Estimates INTERNAL BALANCE

USEFUL WRKING

USEFUL TORKING

RANGE

6226E Balance End Zeroes Short Term H i s t o r y (Single Test)

0.3727

\^_

0.3-

!

! !

i

j

--.^

^ 8

___/

0.2236

0.1667

0.1000

|

95% Pred i ct i on

.. L.J. . o *>m


RANGE

0

3 m

" i " -1° p

s

~i

nterval i NON-REP EATABI LITY

j

-0.1000

0

O ~"

0

„

JJ_

! T'T~~

ABSOLUTE UNCE ?TAINTY

o -0.3-

I

- 0.2236

- 0.1667 \,

/

- 0.3727

-1.0

- 0 . 6 -0.2 0.2

0.6

1.0

DECIMAL PORTION OF MAXIMUM BALANCE COMPONENT RANGE

Figure 9. Internal Balance Generalized Uncertainty Curves

6226E Balance Calibration Matrix Repeatability Estimates

Figure 8. Balance 6226EEWOZ's Generalized Balance Uncertainty Estimates Figure 9 shows a set of generalized uncertainty estimate curves that have been used at the Boeing Aerodynamic Laboratories for internal balance uncertainty estimates. The figure shows curves for balance component repeatability and absolute uncertainty as a percentage of maximum component range. These curves apply only to the individual component being loaded and do not take into account balance interactions.

Similar to the Boeing Main External Balance, the 6226E Balance is calibrated every one to two years, providing a complete set of repeat calibration data for analysis. These calibrations are analyzed together, and the variability of the individual interactions are determined over that time frame. Thus, the repeatabilities of the individual interactions (and their influence on the balance component readings) are used as an estimate of the balance repeatability. MODEL ANGLE OF ATTACK MEASUREMENT The primary angle of attack device in BTWT is the Sundstrand Data Control, Inc. QA-2000 servo accelerometer4. The accelerometer is mounted on a bracket installed on the forward face of the internalbalance adapter, which permits a reliable measurement of the balance attitude (angle of attack). By measuring the balance attitude directly with the accelerometer, uncertainties associated with balance and mounting system deflections are eliminated. The initial level of the accelerometer is set by using a standard leveling fixture and a precision 10 arc-sec bubble. The error associated with the initial model level is considered a test bias and is not used in this analysis. Estimates of accelerometer



repeatability are made from a laboratory calibration of the accelerometer. The calibration uses a precision sine plate, gage blocks, and a digital voltmeter which produces a 95% prediction interval of ±0.005 deg over an angle range of ±20 deg.

BTWT PLATE MOUNT MODEL - MAIN BALANCE CONFIDENCE I PREDICTION INTERVALS ON THE DRAG COEFFICIENT BUCKET 5 MACH SERIES, 16 REPEAT RUNS

REPEATABILITY ESTIMATES AND EXPERIMENTAL RESULTS BTWT Data Repeatability

Figure 10 shows near term repeatability results from a


recent test of a plate-mounted model (using the Main External Balance) in the BTWT. Sixteen repeat polars from five separate repeat configurations are combined into one data set. Figure 11 shows data from an upperswept-strut mounted model using the 6226E internal

balance. Nine repeat polars from two repeat configurations are combined into one data set. Each combined data set is fit with a least-squares polynomial curve and the confidence and prediction intervals are computed. The prediction interval is used as a measure of data repeatability when comparing to pre-test

ALPBODY

estimates.

Pre-test Estimates vs. Test Data

Figure 12 summarizes the pre-test CDS A estimates for the plate-mounted model and figure 13 shows similar estimates for the internal-balance-mounted model. Each bar represents a method of estimating the balance repeatability. Also shown are the actual test data repeatability prediction and confidence intervals. For comparison purposes, the test data repeatability was computed using single-sample-statistical methods (two standard deviations) and is shown as data points on the graph. Balance Calibration Residuals

For each test case, using the balance calibration residuals to estimate the balance repeatability provided the worst estimate of CDS A repeatability. The probable cause is that the large calibration residuals are being driven by the maximum balance loads being applied during the balance calibration. When the balance is used during a test, actual measured balance loads are much less than the balance capacity.

ALPBODY

Figure 10. BTWT Main Balance Mounted Model Test Data Repeatability

Balance End Zeros

Using balance EWOZ's as an estimate of balance

repeatability also leads to poor estimates of CDSA repeatability. Such an approach assumes that any shift in balance end zeros is due to balance repeatability. In actuality, the specific causes of balance zero shifts are not known. Changing test conditions, long wind-on run times, and temperature fluctuations are all potential causes of balance zero shifts. For a complete uncertainty analysis, balance EWOZ's should be considered as a

source of bias error in the final data, but they are not recommended for use in estimating data repeatability.



BTWT USS MOUNT MODEL - 6226E BALANCE CONFIDENCE 4 PREDICTION INTERVALS ON THE DRAG COEFFICIENT BUCKE 2 MACH SERIES, 9 REPEAT RUNS

Calibration Matrix Repeatability Using balance repeatability estimates from the calibration matrix analysis did the best job when

comparing the pre-test CDSA estimates with the actual test data. In all cases the estimates were within one drag

count of the prediction intervals and matched the single sample data in most cases. The advantages of using this method for estimating balance repeatabilities is that it takes into account all of the balance interactions. The


one case that stands out as an exception is the first Main Balance case (ALPBODY = 0.0 degrees). In this case, balance DRAG is only loaded to 76 Ib so other factors

are probably driving the CDSA repeatability.

BTWT Main Balance Data Repeatability

ALPBODY

Figure 11. BTWT Internal Balance Mounted Model Test Data Repeatability Generalized Balance Curves

Using the generalized balance curves as an estimate of balance repeatability consistently underpredicted CDSA repeatability for both the Main Balance and internal-balance cases (although the estimates in both cases matched the curve fit confidence interval suprisingly well). Use of the generalized curves has two drawbacks:

1. The curves assume that each balance component

Figure 12. BTWT Pre-Test CDSA Repeatability Estimates, Main Balance

behaves the same way (has the same repeatability characteristics as a function of load).

2. Estimates of each component uncertainty is made independently of the other components (balance interactions are not evaluated). This is especially apparent in the BTWT Main Balance data, which has some large interactions due to the balance calibration process. Nevertheless, when calibration data is not available, use of the generalized curves is recommended in lieu of either balance calibration residuals or balance EWOZ's.



REFERENCES

1.

"Quality Assessment for Wind Tunnel Testing," AGARD-AR-304, July 1994.

2.

"Assessment of Wind-tunnel Data Uncertainty," AIAAS-071-1995, 1995.

3.

Belter, Dale L., "Application of Uncertainty Methodology at the Boeing Aerodynamics Laboratory," AIAA 96-2215, 19th AIAA Advanced Measurement and Ground Testing Technology Conference, June 17-20, 1996, New Orleans, Louisiana.

BTWT Internal Balance Data Repeatability


4. Watzlavick, Robert L., Crowder, James P., and Wright, Frank L., "Comparison of Model Attitude Systems: Active Target Photogrammetry, Precision Accelerometer, and Laser Interferometer," AIAA

96-225, 19* AIAA Advanced Measurement and Ground Testing Technology Conference, June IT20, 1996, New Orleans, Louisiana.

Figure 13. BTWT Pre-test CDSA Repeatability Estimates, Internal Balance

CONCLUSIONS

Pre-test estimates of CDSA can be made if care is taken to properly estimate balance component uncertainties. Cases were shown using four different methods to estimate balance repeatabilities: calibration residuals, balance end zeros, generalized curves and calibration matrix analysis. Balance-calibration residuals or balance EWOZ's should never be used in pre-test CDSA estimates as they consistently overpredict the data repeatability. Using the generalized-balance curves consistently underestimated the balance repeatability since they do not take into account balance interactions. It was shown to get proper balance repeatability estimates, the balance interactions must be taken into account. A new method being developed at the Boeing Aerodynamics Laboratory estimates balance repeatability by analyzing balance calibration matrix repeatability from repeat calibrations. The use of these estimates of balance repeatability leads to pre-test estimates of CDSA that matched actual test data within two drag counts. Nevertheless, when calibration data is not available, use of the generalized curves is recommended in lieu of either balance calibration residuals or balance EWOZ's ACKNOWLEDGEMENTS The author would like to thank Dave Holler of the Boeing Aerodynamics/Noise/Propulsion Laboratories for his work in developing the method for analyzing calibration matrix repeatability.


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