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\, NASA TM-81361 CORRELATION OF PREDICTED AND FLIGHT DERIVED STABILITY AND CONTROL DERIVATIVES - WITH PARTICULAR APPLICATION TO TAILLESS DELTA WING CONFIGURATIONS Joseph Weil and Bruce G. Powers C'.._ c • July 1981 NASA TM-81_1 CORRELATION OF PREDICTED AND FLIGHT DERIVED STABILITY AND CONTROL DERIVATIVES - WITH PARTICULAR APPLICATION TO TAILLESS DELTA WING CONFIGURATIONS Joseph Weft and Bruce G. Powers Dryden Flight Research Center Edwards. Calif.
NASA
"_at,On8: "_e"cr'3u_,c$ 3_c _cace .:,ar_,r',s:ra_or' .'8 CORRELATION OF PREDICTED AND FLIGHT DERIVED STABILITY AND CONTROL DERIVATIVES - WITH PARTICULAR APPLICATION TO TAILLESS DELTA WING CONFIGURATIONS Joseph weil and Bruce G. Powers Dryden Flight Research Center INTRODUCTION During the Inltlal development of the space shuttle orblter It was fcund that the flight control system performance was sensltlve to uncertainties In a number of stability and control derlvatlves. Differences between predlcted and flight experienced characterlstlcs were of partlcular concern, Inasmuch as the orD1ter test program does not allow the flexlbillty of the Incremental flight envelope bulldup available to conventional _irplanes.
The Dryden Fllght Research Center had performed numerous Investlgatlons In whlch wlnd tunnel data were correlated wlth full scale fllght test results and at the request of Johnson Space Center agreed to examine pertinent correlations to deter- mlne what maxlmum uncertalnties mlght be encountered in the flrst shuttle entry from orbit - at least in the Mach range below 3, where the great majorlty of data existed.
Inasmuch as designers In the aerospace communlty might be able to apply the results of the correlations herein, it was declded to make the Informatlon orlglnally assembled in 19:U avallaDie for general use.
SYMBOLS ALT approach and land'.ng test roll_ng moment coefflclent C, = bC, _8 = _C_,./_5r C_ pitching moment coefficient C m C = _Cm/BC M mc N C = _Cm/36 e m_ e normal force coeffzcient CN yawing moment coefficient n : ,_C n 3_ = _C 3,% n a t.
a = ,_ C 3,5 n r n A r lateral force coefflclent = _Cy 0k D FLT _¢'lght Math numDer FRED predlcted d'='namlc pressure tra_ilng edge angle of attack, deg sldesilp angle, deg ° _ncrement (filght predlcted) 5 -,5 • L e R , deg _:lercn deflectzon. 2 6eL + 8eR , deg elevator deflection, 2
6e
rudder deflection, deg
6r
wing sweep angle, deg Subscripts : L left MAX maximum R rlght APPROACH Task The task consisted of the examination of all available and applicable flight versus predicted correlation data to determine a reasonable estimate of the extreme uncertainties from the nominal predicted derivative values. Nominal values as defined herein are derivatives obtained from rigid wind-tunnel tests corrected for aeroelasticity.
Applicable Configurations The orbiter, with its thick double delta wing and large blunt fuselage, is a rather unusual vehicle (fig. i).
Furthermore, sources of good flight test versus predicted cor- relatlons are limited. Figure 2 presents a summary of the geo- metric characteristics sought and those possessed by the air- craft selected for inclusion in the analysis together with some clarlfying remarks.
The desired geometric characteristics were a classic tail- less delta design where trailing-edge wing flaps provide the re- quired longitudinal and lateral control. The presence of a single vertical tail and a large fuselage relative to wingspan would also have been desirable. Unfortunately there was no single airplane that provided such geometry.
The XB-V0 airplane (fig. 3) had the requisite wing flap con- trols but a relatively thin (2 to 2.5 percent thick) delta wing, a rather slender fuselage, twin vertical talls, and a canard.
The delta wing YF-12 airplane (fig. 4) had large engine nacelles at midspan and twin vertical tails.
The X-15 configuration (fig. 5) was dissimilar to the orbiter, but because it was one of the few sources of hyper- sonic data it could not be totally ignored.
Very limited data were use_ ,om the transonic aircraft tecbmology (TACT) airplane (wing _wept 58") and from the British HP-I15 programs.
The B-58 (fig. 6) and Concorde (fig. 7) airplanes had generally acceptaDle geometry and a good predictive base and Mach coverage.
The YF-16 and F-8 supercritical wing ($CW) airplanes were used only as a source of rudder control data.
The lifting bodies (figs. 8 and 9) had (by a stretch of the imagination) a delta platform as well as trailing edge longitudinal and lateral controls. However, it is believed that the flow phenomena were not similar to those for the orbiter, particularly in view of the multi-tailed aft body.
The lifting bodies were considered a unique class of rather extremely shaped vehicles. Therefore the considerable store of infnrmation available for these shapes was judged to provide a measure of the extreme variations of flight and predicted characteristics that would not be exceeded by the orbiter; thus, the data were included.
Scope of Correlations The specific parameters correlated in the investigation are noted in figure i0 for each of the applicable vehicles.
There were several reasons that certain data were not utilized in the studies. The XB-70, YF-12 and X-15 airplanes incorporated all-moving vertical tails, and hence rudder data were not available. The X-15 and TACT airplanes were equipped with slab horlzontal tails for longitudinal and lateral control, so the aileron and elevator control derivatives were not con- sldered meaningful. As mentioned previously, the YF-16 and F-8 SCW airplanes were included only to provide badly needed rudder effectlveness data.
In a few other instances data were not correlated because they were unavailable or because serious questions existed relative to quality. Although it is known that much effort was spent on Concorde wind-tunnel versus flight correlations, the
only data available to the authors were the liaited results
presented in reference 1.
The data used in this study were obtained from references 1 to 11 and from unpublished sources.
FACTORS AFFECT ! NO CORRELAT ION CRED I B IL ITY Inasmuch as the data used in this study were acquired from many sources and over a significant time span, it was felt that some means was required to assess the quality or credibility of the individual correlations. In order to accomplish this, the correlation credibility index shown in figure Ii was established.
Wind-Tunnel Test Factors Model fidelity. - Because the bulk of wind-tunnel testing is usually done before a design is completely frozen, there may be important differences between the model and the full scale airplane. In such instances it is necessary to estimate the effects of the discrepancies.
Test coveraqe. - Although systematic wind-tunnel data are certainly easier to come by than similarly complete flight data, it is often impractical to obtain a sufficient matrix of data for newer configurations having many moving surfaces.
Particular care must be taken tc provide information near trimmed flight conditions. Of special importance is the avail- abllity of control effectiveness at small surface deflections and sideslip characteristics at small angles of sideslip.
Tunnel suitability. - This factor pertains to the general suitability of the wind-tunnel and model support system to the particular type of test being conducted. There are numerous instances of too large a model being used in a facility, par- ticularly near sonic speed.
Measurement accurac and sco e. - Some of the items in .
this _ are availability of accurate tare data and supple mental information such as pressure distributions, strain gage measurements, oil flow studles, and Schlieren pictures, which mlght enhance the basic force and moment data.
Flight Test Factors Test coverage. - Optimum coverage would provide data at several Nach numbers over a reasonable angle-of-attack range wlun an emphasis on small increments in regions of rapid change.
This permits spurious data points to be "faired out." It is also desirable, where feasible, to test at several altitudes with overlapping Mach numbers and angles of attack to provide a check on aeroelastic effects. Too often test coverage is sparse, which makes it difficult to provide a rational fairing of data points where nonlinearities may occur.
Data acquisition system. - Some of the earlier programs have suffered from inadequacies in the analog instrumentation systems - zero shifts, poor resolution, and nonoptimum scallng.
Frequently, contractor sponsored programs have not had suf- ficient resources to maintain current calibration.
For situations where a high temperature environment is encountered, insensitivity to heat soak is requlred for per- tinent instrumentation.
The inherent accuracy and adaptability of modern digital acquisition systems has the potential of fulfilling the require- ments of most correlation programs.
Data analysis methods. - Prior to the period from 1965 to 1970, the Dryden Flight Research Center used several analog methods to derive stability and control deriJatives from flight maneuvers. Although the results were usually reasonably accept- able, the techniques left much to be desired. In the 1960's Dryden developed a versatile method for determining derivatives that had many advantages and is now accepted internationally.
A good discussion of this preferred method (referred to as the modlfied maximum likelihood estimator, or MMLE) can be found in references 12 and 13.
Mass and inertia accuracy.. Accurate knowledge of weight, the moments of inertia, and the principal axis inclination are required. Moments of inertia and principal axis inclination are usually calculated by the welght and balance department of the manufacturer. Where possible, experimental checks obtained by "swinglng the airplane" improves confidence in these values (ref. 14).
Other Considerations
Match%n_ t_t conditions. - This factor assesses how well the flight and wiRd-tunnel test conditions match. The test conditions include Mach number, leading and trailing edge flap settings, speed brake deflection, and so forth. In the most serious correlation efforts the wind-tunnel tests are performed after the flight tests to insure maximma compliance.
Basis for full-scale extrapolations Wind-tulmel data are a_most always obtained with essentially rigid models, where- as the full scale airplane can experience significant aero- elastic effects in the higher dynamic pressure regimes that can drastically affect correlation. Accurate aeroelastic correc- tions are not always readily available, and the analytical base must be carefully examined, particularly where large corrections are predicted.
Another factor in this category is the derivation of any Reynolds number correction that may be required.
Experience and motlvation of correlators. - This last factor, namely, the experience and motivation of the individual responsible for a particular correlation effort, is certainly one of the most important elements. In fact, the better efforts usually involve representatives of both the flight test and wind- tunnel disciplines as active members of the test team to achieve the requlred depth of background.
Correlation Credibility Index The index in figure Ii has not been applied to each of the separate correlations that were used in this paper. However, it does allow us to make some general categorizations of the da_a used.
There were relatlvely few truly high quality "A" rating correlatlons, and they will be referred to later in the dis- cusslon. In all cases a major effort was required to achieve the excellence attained. This generally involved fabricatlon of a carefully scaled model of the actual alrplane flown, with the wlnd-tunnel testing of the model accomplished after the flight tests were completed. Correlation was the primary program objective.
Most of the data used would fall in the "B" rating cate- gory. Reasonable care was exercised in the conduct of the
overall effort, but flight-to-wind-tunnel correlation was but
one of four or five major program objectives. The NASA/Air Force Flight Test Center (AFFTC) lifting-body investigation would De assigned this designation.
Several programs exhibited definite shortcomings that would require certain elements to be rated marginal at best.
These will be identified where appropriate.
METHOD OF ANALYSIS Typical Procedure The M2-F3 results will be used to illustrate the procedure followed in analyzing the flight derivative data. The angle-of- attack/Mach number envelope over which flight derivatives were obtained is shown in figure 12. The nominal angle of attack was somewhat arbitrary but was close to a ig value for the altitude profile used in the testing. It was decided to concentrate the analysis In a Z5 ° angle-of-attack range about the nomlnal value.
A typical crossplot of a derivative (Cn_) showing the variation with angle of attack is presented in figure 13 for a Mach number of approximately i.i. Note that there is a small variation in Mach number with angle of attack (figs. 12 and 13) and that care must be exercised to limit this variation in regions of rapidly changlng characteristics. The data points shown allow a reason- able fairing, with a single point clearly out of line. The pre- dicted line was rigid wind-tunnel data. In this instance no correction was required for aeroelastic effects because of the rigidity built into the research airplane. The maximum devi- ation between flight and predicted results was 0.0006 for Cn at M = I.i.
Format of Correlated Parameters For many derivatives, a percentage deviation from the pre- dicted value seemed to provide a logical correlating base that would not be affected by wing reference geometry. Thus the ratio of FLT - PI_ED PRED was used for correlating the primary con- trol power parameters C_ , C n , and , as well as for 6 a 6 r Cm6 e C_6r and Cys. For other parameters, such as Cn6 a, Cn , and C 18, where the predicted value might be near zero at tine$, the data were correlated in terms of FLT - PRED. This quantity is more sensitive to wing reference geometry, but the impact should be relatively minor for the data used in the present study, inas- much as the wing geometry used for the aforementioned correla- tion parameters was generally similar. Other comments on this subject will be included in the discussion of results.
DISCUSSION OF BASIC CORRELATIONS Lateral-Directional Parameters C n . - Flight measured C n has always been one of the most 8 a 8a difficult parameters to correlate with wind-tunnel predictions.
Moreover, experience has shown that Cn8 can drastically affect a lateral controllab_lity, and therefore the ability to predict that particular derivative is often of considerable importance.
The correlation of flight and predicted Cn8 is presented in a figure 14 for conventional air_lanes and in figure 15 for lift- ing bodies. Note that aileron derivatives are based on average aileron deflection rather than total aileron deflection.
For the conventional aircraft the largest discrepancy oc- curred at Mach 0.95 and was in a negative direction. Above Mach 1.5 there is definite evidence of a decrease in the magni- tude of the difference between flight values and predictions.
At Mach numbers greater than 2.0 only B-70 and YF-12 data were available and the correlations were very good.
It should be noted that particular pains were taken to verify the maxlmum deviations for the B-70 at Mach 0.95, which included supplemental wind-tunnel tests.
The lifting body data (fig. 15) encompass a smaller Mach number range than was available for the conventional airplanes.
with the exception of the extreme posltive points for the HL-10 correlation at Mach numbers of 1.2 and 1.5, the maximum flight determined is more negative than predicted.
Cn 6 a All of the data were considered in the formulation of reasonable maximum uncertainty limits. Below: Mach 0.7 a value of z0.0004 was selected. At transonlc speeds the maximum uncer- tainty level was increased to ±0.0008. Above Mach 1.5 it appeared appropriate to reduce the uncertainty as shown, although the data on which the supersonic boundaries are based are admittedly meager.
Note that the uncertainty limits shown are based on engineering judgment rather than on a statistical weighting of the points.
C_5 - The correlations of the aileron effectiveness deriv- a ative, C_ , are presented in figures 16 and 17 for conventional 6 a aircraft and lifting bodies, respectively. There appears to be little variation with Mach number. For both sets of data the flight determined derivative showed more extreme values in the Maximum uncertainty limits of higher-than-predicted direction.
40 percent and -25 percent of the predicted values appeared to be reasonable choices. The higher value would be used for sys- tem limit cycle checks, and the lower value to determine adequa_ system gain to avoid stability problems.
C n . - The correlation of the rudder effectiveness deriv- 6 r ative is presented in figure 18 for conventional aircraft Cn 6 r and in figure 19 for lifting bodies. Considerably more data were available from the liftlng body programs than for the more conventional airplanes, and the lifting body data showed greater differences from the predicted results. Levels of 50 uercent greater than predicted and 25 percent less than predicted are felt to represent reasonable maximum uncertainty values.
It ls evident that the Concorde data fall outside the selec- ted limits at low supersonic speed (fig. 18). However, the resolution of the plot from whlch the information was derived (ref. i) was very low. Furthermore, the aeroelastic correction applled was at tlmes greater than 60 percent of the rigld wind- tunnel data. Thus, 1_ is likely that a _ood measure of the dis- crepancy is of aeroelastic rather than aerodynamic orlgin.
C - The correlatlon of the rolling moment due to rudder r Is presented in flgures 20 and 21.
deflectmon parameter, C_ , 5 r Data were very llmlted for conventional alrplanes, and the lift- ing body informatlon was needed to determine maxlmum uncertainty llmits. The llmlt values selected were 60 percent uncertalnty I0 in the more-effective-than-predicted direction and 30 percent uncertainty in the less-effective-than-predicted direction. The fact that these limits were slightly greater than those proposed for C n may be due in part to the greater difficulty of measuring 6 r accurate values for C_ 6 r " " A correlation of the directional stability parameter Cn8 is presented in flgure 22 for conventional aircraft and in figure 23 for lifting bodies. For the conventional aircraft it would appear that somewhat greater discrepancies between flight measured and wind-tunnel C are indicated near Mach I, with nB most of the flight values showing greater stability than pre- dicted. At Mach numbers above 1.5 a maxim_a discrepancy of 0.0005 is indicated, with the flight values generally less than predicted.
The llfting body data fall mostly between Mach 0.6 and Mach i. _ (fig. 23). For these configurations, unlike the conventional . :._nes, there is a pronounced tendency for decreased fllght _ :.lity relative to predictions, with the value of FLT - PRED as large as -0.0016 to -0.0017.
A conservative approach was followed in formulating the re- commended limits at transonic speed, wlth a possible -0.0014 in the dezreased stability direction and 0.0009 in the increased stability direction.
C . - The rolling moment due to sideslip derivative, Cl , correlated for conventlonal airplanes and lifting bodies in figures 24 and 25, respectively. Note the very good correlation for the X-15 at hypersonic speeds. The recommended uncertainty limits were z0.0005 at subsonic speeds, ±0.0008 at transonic speeds and ±0.0003 above Mach 1.6.
C_ys. - The lateral force coefficient, Cys, is correlated for conventional alrcraft in figure 26 and for llfting bodles mn figure 27. Most of the points fall within a z25 percent band.
Longitudinal Parameters 6eTRI M. - As mentioned earlier, there are relatively few high quality thoroughly coordinated wind-tunnel-to-flight correlations.
One effort worthy of note was made for the XB-70-1 airplane.
A program was undertaken by NASA to evaluate the accuracy of a method for predicting the aerodynamic characteristics of large supersonic cruise airplanes. This program compared pre- dicted and flight measured lift, drag, angle of attack, and con- trol surface deflection for the XB-70-1 airplane for 14 flight conditions with a Mach number range from 0.76 to 2.56. The pre- dictions were derived from the wind-tunnel test data for a 0.03- scale model of the XB-70-1 airplane that was fabricated to close- ly represent the aeroelastically deformed shape at a Mach 2.5 cruise condition. Corrections for shape variations at the other Mach numbers were included in the prediction. The results of the study were described in references 3 and 4.
A correlation of flight and predicted trim 5 e is shown in figure 28 for the XB-70-1, YF-12, and two lifting body configur- ations. If the XB-70-1 point at Mach 1.06 that was derived from interpolated wind-tunnel data is disregarded, lines of ±4 ° vari- ation bound all of the points except one.
:1C m. - Inasmuch as the trim surfaces of the aircraft used in figure 28 were of different size, it would appear that pitch- ing moment coefficient uncertainties (ACm) would provide a better correlation parameter than elevator deflection. Therefore the data in figure 28 were transformed into an equivalent AC m using an appropriate value of Cm6 e The lifting body data were originally reduced to coefficient form by usin9 body length as the reference chord instead of the normal practice of using the mean aerodynamic chord (MAC). Ac- cordingly, an MAC was calculated for each lifting body, and the elevator effectiveness was increased by the ratio of body length to MAC.
The results of the correlation of flight and predicted IC m are presented in figure 29. There is a fairly rapid decrease in IC m above Mach 1 due to the expected reduction in Cm . If the 6 e Mach 1.06 XB-_0 polnt is disregarded, the HL-10 lifting body ex- hibits the largest change in lC m from s_bsonic speed to Mach 1.6, having a magnitude 2 to 3 times that for the other three aircraft shown. It is felt that the proposed limit shown (AC m = 0.022 up to Mach 1.1, decreasing to a value of AC m = 0.005 above Math 1.8} is a reasonable and conservative maximum uncertainty guideline.
C m . - A correlation of flight and predicted C m is shown in 8e 8 e m figure 30 for conventional aircraft and in figure 31 for lifting bodies. Most of the very sparse conventional airplane data are from the XB-70 data base. Much better coverage was available from the lifting bodies, and these latter data were used to arrive at the recommended uncertainty criteria of 40 percent over prediction and 20 percent less than prediction.
C . - A comparison of predicted and flight derived C m mc N variation with C N is shown in figure 32. The overall stability in flight is considerably greater than predicted. However, there are very large differences in local slope due to the presence of nonlinearities. These nonlinear tendencies are often found in C m data of low aspect ratio swept wing configurations, and for that reason it was decided not to specify a longitudinal stability uncertainty value.
APPLICATION OF RESULTS As mentioned earlier, the prime motivation for the corre- lations presented in figures 14 to 31 was to provide a frame of reference that would be useful when assessing the critical aero- dynamic uncertainties that would be required to produce either un- acceptable flight control characteristics or total loss of control during the orbiter entry.
Probability of Exceeding Derivative Uncertainty Boundaries Single uncertainties. - An examination of the data in figures 14 to 31 for a number of aerospace configurations in the transonic and low supersonic Mach number range led to the conclusion that the probability of occurrence of a single uncertainty of the magnitude specified by the boundaries might be as high as 10 -2 . In most instances the chance of encountering such a magnitude deviation would be considerabl_ more remote than 10 "2, but for the purposes of this study the greater probability was assumed.
Uncertainty pairs. - If a single uncertalnty has an occur- rence probability of 10 -2 it follows that the simultaneous occurrence of two derivative uncertainties would have a proba- bility of 10 -4 assuming no aerodynamic interaction between the t two derlvatives.
In the case of the rudder parameters C_ and Cn6 r, one might 6 r assume an almost complete interdependence. In order to determine the actual degree of cross-correlation, the two parameters were compared for a series of lifting body configurations (fig. 33).
If the coefficient of correlation was near unity, all of the points would fall along a 45 ° line. However, quite a bit of scatter is in evidence. For sensitivity studies it is recom- mended that when extreme uncertainties are being studied in either Cn6 or C_ , the other parameter be maintained at zero _) r r uncertainty.
Uncertainty sets. - The overall lateral-directional behavior Is affected by more than a score of indlvldual derivatives. The probablllty of all of these derlvatlves simultaneously experienc- Lng a limiting uncertainty in a degrading direction would be truly infinitesimal. Hewever, the basic flight behavior of an airplane can be shown to be primarily a functlon of a handful of the most s_gnlf_cant terms. If a value of 50 percent of the nominal uncer- talnty is applied to the four most significant terms of each set, the estimated probabLllty ef occurrence is about 10 -4.
Criteria for Flight Control System Capability in Degraded Aero-S_tuations Based on flight test experience of highly augmented aircraft and _ntultlve reasonlng, the following criteria were adopted.
The flight control system {FCS) shall be able to cope wlth situ- ations hav_ng an occurrence of probability greater than 10 -4.
Thus (assumlng a Gausslan dlstr_bution of the uncertainties) the FCS should be able to provlde acceptable characterlst_cs wlth: la) Any single derlvatlve at 1.6 tlmes the nominal uncer- tainty.
(b) Any two derlvat_ves at the nomlnai uncertalnty value.
_c) Sets wlth _.5 Df the nominal uncertalnty applied to all terms.
Shuttle Orbiter Estimates It is beyond the scope and purpose of this report to present in-depth results of the orbiter entry flight control character- istics wlth degraded aerodynamics. However, a brief summary of the study will indicate how the derivative uncertainties described here were applied to flight test planning for a particular program.
Single derivative uncertainties. - The single derivative un- certainties were evaluated by making simulated entries in the auto Mode with progressively increasing values of the uncertainty. The most significant single uncertalnty was a reduction In C_ How- a ever, in order to achieve a signzficant degradation in control characteristics, an uncertainty factor of between 2 and 3 times nomlnal was required, whlch is about 50 percent above the assumed criterla boundary of 1.6 times nominal and Is estimated to have a probability of occurrence of about i0 Uncertainty palrs. - In studying the uncertainty palrs a progressively increasing factor was applied to beth terms in the palr. As might be expected, the most critical pairs included the C, uncertainty, which was the most critical single factor. All a of the critical uncertainty factors were well above the DFRC crl- terla value of 1.0. The crltical uncertalnties were approxlmatelv twice the nominal uncertainties, and the probability of occurrence -14.
was estlmated to be about 10 Uncertalnt[ sets. - Based on engineering ]udgment and simpli- fied analytical techniques a serles of lateral-dlrectzonal uncer- talnty sets was formulated. The same Increasing uncertainty factor was applied to all terms in the set until a critical degradation in control was observed. All of the uncertainty sets had crltical factors weli above the criteria value of 0.5. The loss of control _oundarles were all above a value of 1.0. A divergent loss of control occurrence would correspond to a probability of occurrence of a_cut i_ "13 Comparison of Orbiter Subsonic Derivative Uncertalntles With Maxlmum Variation Crlterla The derlvat_ve data obtained during the subsonic approach and landing _ALT) tests (ref. 15) were assessed In terms of the pred-ctea _ -e,'_vatlves and then compared to the maximum uncertain- tles cr'_ter_a shown In figures 14 to 3!. The results are pre- sented •_n f_gure 34 and :ndlcate much better agreement between
flight and predicted results than have been observed in previous
programs. Note, however, that the test envelope investigated was
below the transonic Mach regime, where some of the largest differ-
ences are often experienced. Because of the quality and quantity of orbiter wlnd-tunnel data and the care exercised In analyzing the flight data an "A" rating In the correlation credibility in- dex would appear warranted.
CONCLUDING REMARKS Fllght test and predicted derivatives for many airplanes have been correlated over a wide Mach number range. The results of the study would appear to offer a valuable source of standard uncertalntles with which to test the sensitlvity of modern command control systems, particularly for tailless delta wing configuratlons.
Dryden Fllght Research Center Natlonal Aeronautics and Space Admlnlstration Edwards, Callfornla 93523 June 8, 1981 _6 REFERENCES .
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Kirsten, Paul W.: W_nd Tunnel and Flight Test Stability and Control Derivatives for the X-24A Lifting Body. FTC-TD- 71-7, Air Force Flight Test Center, Edwards AFB, April 1972.
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Nagy, Chrlstopher J.: and Kirsten, Pau! w.: Handling Qualities and Stability Derivatives of the X-Z4B Re- search Aircraft. AFFTC-TR-76-8, Air Force Flight Test Center, Edwards AFB, March 1976.
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Ma_ne, Richard E.; and Iliff, Kenneth W.: User's Manual for _LE3, a General FORTRAN Program for Maximum L1kellhood Parameter Estlmation. NASA TP-156_, 1980.
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Boucher, Robert W.: Rich, Drexel A.: Crane, Harold L.: and Matheny, Cloyce E.: A Method for Measuring the Product of Inertia and the Incl_natlon of the Prlnczpal Longi- tudlnal Axis of Inertia of an Airplane. NACA TN 3084, 1954.
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Hoey, Robert G., et al.: AFFTC Evaluation of the Space Shuttle Orbiter and Carrier Aircraft - NASA Approach and Landing Test. AFFTC-TR-'3-14, Air Force Flight Test Center, Edwards AFB, May 19_8.
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( "owzcorde ail'p hJne.
'" ,-- " 1'I_ _" p' _ _:. _,., ._,.
Figure 8. Sketch of M2-F3, HL-IO, and X-24A lifting bodies showinj control surfaces.
Fi_iure 9. T_,wee-vie:v drawing of X-2.1B '_i;'ting body.
|
P_UI_TI[RS ¢OlUlLATI[D At gtCP,ArY r C_ C Cn Cn C. Cv C_ TIll Iq C _l • r Q • i i IIIII I I II II1- 7'0 v_-12 1.015 TACT.: COmCOROE 9-_S vlr-16 :" j _2._'?
FiguJ'e 10. CoPn'elation scope.
,_'.._." ".._. - .... :..
-" I _ ' _ _ _, ?._o 0 L m I i ii , _:'2;::_ "''* " , 'z:_2"_ - . "_:_"_'." -.
ml t !
t - I .... ""
, ' I
ii
I
_ !
i i ,:..:. _ L "" ., : ..,... .... .:... . , • --..
._,:..._,.. _ - _ -- _,, -.- : _-...-.- I_ .- ., o.. .... ....
i
F'igut'e I i. ¢op'_'elat_on ¢p'edibil_ly index.
-"6 J2 O0 0 o OQ
"!o
_) ¢ 0000U OD
--o O ____
+S e 0 _ _ _ , _, i _ i i i L , i I • ¥ _ .8 rO /.Z /._ l_.
Figure 12. M2-F3 envelope.
_-'-_¢7. c,ey _,,_.
Z06 r "_'_-_ ..... ,_z'- 2d4 t i
r
* , I .='_ -- • , I F_gw'e I3.
Typical basic data used ;b_" correlation summap3'.
._12-F3:._1 _ I. 1.
_- /_-..,. - i.=1 :. ,._;,,-- _,,\, t ..___ _ \ ,_ - _.._ o-- ._ .......
.d ,,_ _ -:" _ ,.,_.,._ d _--....-._ _ _. .-:, ,.
\ _" ,," ._ ,,.
/ \ ,> . / ; ___, .....
f Conventional aircraft.
Corr'elation of/'light and predicted C Fi!]ure 14 n 5 a • Irt P __ x._._
/ \
I
/
....... _ • -" /," oO ' "_ _al , \ : ,' Lifting bodies.
Com'elation of f[icTht and predicted C n .
FiguD'e 13.
5 a ,_v.IGINAb P#.GB ll_ OP 1Pt_)P. QUALIT_
r
l "_ i_'J= _7 C _ ,_'.,i£ - _i__- 8 li .tO ._C a.
.Z¢ _" ,0 .'2.
N'_ t _ __ _ t C i i i | , l -.'._ l__. '_,e_. - Figure 16.
Conx, en tional aircraft.
Coi,'_latwn of ,,'light and pi'edicted C_8 a • _'_ i l l ll Figu_'e _, 7 Corm'elation of flight and m'edicted " Liftinc/ bodie$.
• C_8 ¢ HP, I£ 0 r_-_5 "2_ Y_'-I6 .4C %.
C v_ :'3D t, it • I ! L I I ,, _ I | I %.
Figm'e 18. Co_'p'elation of flight and predicted C Conven tional aircraft.
n 8 p, ii i '_'-- _'K . " • . '" A -" .a ;'_/.a7"_ ' " .a£. ," ' al , -_ _ 5B J J i i ! ii I I | I i I Figm'e 1,3. Co_'_'_i¢_t_on af ;light and pt'edicted C Li"ting bodies.
n 8 #, ,_,, _ _-',._ _,_, -t.., /° "-'_,U'J w -£ •. .. ".:. , _'_ Figure _0. Con_,entionol aircraft.
Corl'elation of ;7 ight and predicted C_8 i° • #- ".-,, ,t.,,i./l ,4 -.' '_ • _#. " ,_"1 _l _. #.
• . • .4L-_ • ..t W °° _ r.
._ • .- ..,, g . ,.b_,i_ ..- C,,p'_'_l_l/Ion or" ,'_,ight and pr@dicled C _,_ Lit'ring bodies.
t • 31, 7 .'-.. _.¢._e i I
F
L t . . _.,=.,,==,PgWb t x • ..,-¢.. _,.....-..
Figup.e 22. Co,'_'elation of ;light and ppedicted C Conventional aircraft.
n_ F:gtu'e 23. Cop_'elatwn o" "_igt;t and ._pedicted Cn . Lifting bodie_.
"L X _ -7 ''_ ', y_r./_. 937 ,-g 7"-,e_"£p . C_'_I - -" 0 _a ..._.e__¢e_ -: e z_. ___ -..."_b - ; i I - JCZ _ , i , i , , i j S ._ E : Conventional aircraft.
Fi_lui'e 24. Co_'i'elation of/'light and pi'edicted Ct Ip-_ • • _" "'-_, .. . ,,._ ..... ;4,'7" - _ ._ X- ,_ -F3 - X- 24_ '_ - £-I,.B .'JL, r". _ ",,L.
t ..........
i ............. il--_ _l- i LI LId !
I i °o " ._ • .,_ _. ,.- ,,4. _,-'.#£,_ Fi,qure 25. Co_'i'elatton ot':'light and predicted C£ Li;_tng bodies, ORIC/_AL PAGE I_1 _li _' i":.,ll)li (,_(t:%l.fl_" .... ___ .... _ .... _L -.0 ,) ] _ l I l _ _ Figm'e 26.
Co_'_'elation of "light and pt'edicted Cl. _. Conventional air'or'aft.
" ," ,l#*.
i _ _'_i i J, I ii _ -_A C | ._._ c
i
I i | ,,. , o .
o--:..
F_gui'e 27 Covrelatlon o;" :'light and p_'edicted Cy . Li"t',n_ bodies.
v IP.
r ,. j o ..-- __ &
% -, ,>
i -!r | I • ",6' / ., . " Figure 2S. Correlation of flight and predicted trim 8 e" a,, o, * # "3, \,, • / b • - - ,, | ---- t" Fi_3ure 29. Co_'.elation of flight and predicted -_C m 3S ,+P+ A+ • ,'t_ +._- _ _- t ..... ++'+ + ; I 7,, ",+,.., .., .),+,+'.+ =£ ._ Fi,:ure 30. Correlation of ;Ti_-ht _znd predicted C Conven tional aircraft.
m 8 e -->"F _ "" "+ ",'+ A '_E t+- T,,= ,.. Z:. _ _ ]+ . _.
.-L - ",t'%.l+ • d - ¢m .A ---- + +" , ' I i I -." C..c +.
•"._,_., 'v'+.,t+=E_ Lifting bodies.
Fi+]ure 31. Co)')'elation o/'.rTtgltt and predicted Cm8 e i I i I !
I I I?_. ,, !
l I I.O - !
_J I I I I I ,o i / .4.
_ L
- l I L i ; 1 _ i 0 -.I ".2 -.3 -.+ -.5 Fi_3ure 32. Illustration of nonlinear C m characteristics.
ORIGINAL PAGE I,_, OF POOR QI'._,' ' 3?
._ Nz°IO • X-24A I x -2.4_ ZO
F
I I I i !
I .J i /, i .4 / ,L / / 3 I I (z 0 i + _i ".' ! I I I
I
+i :;' i I
".6 I • , I i i • i .Z ._ .6 .8 zo uncertain ties.
Figure 33 Relation of Lifting bodies.
• Cn5 },
b
.-0.6 M ,, 0._ ORBI TER YARI AT tON ORBI TER VARI ATI ON (TAI LCONE OFF) CRITERIA (TAI LCONE OFF) CRITERIA
i
0.00012 t,O. 0005 ,_Cn_ 0.00015 -+0"0005 0.0oo3 _.ooo6s _C _. O. 0004 4.0.0005 -0.13 +0.25 _,cv_ -o. 15 _.z5 : RATI 0_'_ -0.05 -0.25 :C .: -0. !0 -0.25 • a RAT I 0 -0.16 -0.30 .:C. -0.06 -0.30 "RATI 0 -0. 00015 +0. 0004 :.Cn: 0 +_0. 000h -0.16 -0.25 LC n . -0. I 7 -0.25 rRATI 0 0 -0.20 -Cm: -0.05 +0.40 eRATI 0 -0.20 0.008 C). 022 'C_TRI M ::RATI0 - FLT-PRED PREO derix'ati've variations with (ALT F'i!Ture J4. Comparison or" orbiter ,subsonic DFRC "nc,_:imum variation cr_,teria.