Document
tI/J.#l 7/Jl- f'77//
NASA-TM-87711 19860015232
NASA Technical Memorandum 877 11
LATERAL AND LONGITUDINAL
AERODYNAMIC STABILITY AND CONTROL
PARAMETERS OF THE BASIC VORTEX FLAP
RESEARCH AIRCRAFT AS DETERMINED
FROM FLIGHT TEST DATA
WiUiam T. Suit and
James G. Batterson
April 1986
IJ'\NGLEY RESEARCH CENTER . - LIBRARY, NASA H,I\~,'PTO~, VIRGINIA
NI\SI\
National Aeronautics and Space Administration Langley Research Center 111111/111111 1111 11111 1111111111 11111 11111111 Hampton, Virginia 23665 NF01277 INTRODUCTION Wind tunnel investigations have indicated that for swept wings a leading edge flap can improve the LID of the wing by as much as 30 to 40 percent in the .6 to .9 Mach range. The flap causes the leading edge vortex of the swept wing to keep the flow at the leading edge attached at higher angles-of-attack, increasing the lift from the wing while not significantly increasing the drag.
The FI06B aircraft was selected as a test bed for flight testing the leading edge vortex flap. There were three primary reasons for using this aircraft. First, the delta wing was simple, and modifying the leading edge should not be extremely difficult. Second, the speed envelope of the aircraft covered the speed range where the vortex flap should be effective. Third, the 60° leading edge sweep fell in the sweep range where the flap was effective.
So that the improvement from the vortex flap could be assessed, the basic air- craft must be documented. To do this, all available information on the aerodynamics of the FI06B is being assembled. One part of this collection of aerodynamic charac- teristics is the flight-determined stability and control derivatives. These param- eters can be correlated with the results obtained from wind tunnels and used to determine aerodynamics for areas in the flight envelope where wind tunnel tests were not run. Flight tests can also be used to estimate rotary derivatives that cannot be obtained from many tunnels. Finally, agreement between wind tunnel and flight-determined aerodynamic parameters for the basic airplane will be an important factor in determining how the flight data from the modified aircraft can be used.
An important step in the assessment of the possible effect of the flap on the handling of the basic FI06B is the development of a realistic simulation of the vehicle. Flight test results will be used in conjunction with the wind tunnel data to develop a realistic simulation of the basic aircraft. This basic simulation will then be modified to reflect the expected impact on the performance and handling qualities of the aircraft of adding a leading edge flap. Flight data from the modified aircraft will then be used to refine the simulation.
The purpose of this paper is to present the aerodynamics of the basic FI06B as determined at selected points in the flight envelope. In this paper, the test aircraft and the flight test procedure will be presented. Thus, the aircraft instrumentation and the data system will be discussed. This will be followed by a presentation of the parameter extraction procedure and a discussion of flight test results. These results will then be used to predict the aircraft motions for maneuvers that were not used to determine the vehicle aerodynamics. The control inputs used to maneuver the aircraft to get data for the determination of the aerodynamic parameters will be discussed in the Flight Test Procedure section. The results from the current flight tests will be compared with the results from wind tunnel tests of the basic FI06B, where comparisons can be made, and based on these comparisons, the need for additional data was concluded.
TEST AIRCRAFT The aircraft used in this investigation was a slightly altered FI06B. The configuration tested had a nose boom for measuring angle-of-attack and angle-of- sideslip. Also, a light source was mounted in the left side of the aircraft to illuminate the vortices on the wing. A photograph of the test aircraft is shown as figure 1. The physical characteristics that affect the parameter identification procedure are given as table I. The inertias for the subject aircraft as tested are not known. The inertias used are from manufacturer's data for a similar configuration and their accuracy is not known.
FLIGHT TEST PROCEDURE Maneuvers were made from steady conditions, either from 1 "g" flight or from a higher "g" coordinated turn. Since the aircraft could not maintain altitude in these steady turns, the maneuvers were actually perturbations from a descending spiral. In this maneuver, the greatest rate of descent was approximatly 300 ft/sec. The assumption of a constant density for each run could result in an error of up to 3 percent at the final part of a run. Elevon doublets were used to perturb the vehicle for the identification of longitudinal parameters. The amount of elevon deflection used was determined by the variation in normal acceleration.
The maneuvers used for determining the lateral parameters consisted of a rudder doublet followed by an aileron doublet. The critical parameters during the lateral maneuvers were sideslip angle due to danger of departure and roll rate due to instrument limits. In practice, roll rate usually was the variable that established the limits on the magnitude of the inputs since the range of roll rate instrument was ±1 radian per second and moderate rudder or aileron inputs could easily cause responses that would exceed these limits. In most runs, the sideslip angle did not become excessive. Also, the yaw rate tended to be small and in some early runs, was marginal for good identification of the yaw rate and yaw moment derivatives.
For runs designated as flight 13, the input design was to put in the first half of the rudder doublet at a magnitude that would result in a 60 deg/sec roll rate in hopes of getting a 100-150 per second yaw rate. Then, on the second part of the rudder doublet, start the aileron doublet early to try to keep the roll rate from exceeding 60 per second after the rudder switch. Then the second part of the aileron doublet would be large enough to give at least a 30° per second roll rate.
This design generally kept the roll rate in limits and did not result in excessive sideslip, but the yaw rate still did not exceed 100 per second and was still marginal for good identification.
INSTRUKENTATION AND DATA PROCESSING On the F106B aircraft the instrument channels were accessed using a pulse code modulation (PCM) system that processed the data at 82 samples per second (sps).
This data was then recorded on magnetic tape for processing. The data on this tape were converted to engineering units, and quantities such as true airspeed were calculated. Selected channels that are required for parameter identification were recorded at a rate of 41 sps (one-half the original data rate) and corrections for instrument location relative to the vehicle center-of-gravity and instrument alignment were made. This process resulted in a data tape that was suitable for use with the parameter identification program. The quantities recorded and their ranges are given in table II. The assumed accuracy of these measurements was 1 percent of full scale of the measuring instrument.
PARAMETER EXTRACTION PROCEDURE Maximum Likelihood and Linear Regression Parameter Extraction Programs were used to examine the flight test data. These programs are described in references 1 and 2. For both extraction programs, a linear aerodynamic model describing a rigid airplane was assumed. The parameter values obtained using the extraction programs are given in tables that include the parameter value and the estimated sensitivity for each parameter. The estimated standard deviation and sensitivity are indicators of the identifiability of the different parameters. If the estimated standard devi- ation is less than 10 percent of the extracted value for the parameter, then the parameter is identified, less the 5 percent well identified. The larger the sensi- tivity, the more identifiable the parameter and the greater the influence of the parameter value on the vehicle motion.
RESULTS AND DISCUSSION Maneuvers were made to independently excite the longitudinal and lateral modes of the test vehicle. The parameters determined from the longitudinal modes will be discussed first. The longitudinal parameter values for the assumed longitudinal mathematical model are given as table III. Selected longitudinal parameters are plotted versus trim angle-of-attack (Fig. 2). In addition to the runs that resulted in the parameter values shown in figure 2 and referred to as "surface" in table III, runs were made in earlier flights before the actual control surface deflections were instrumented. During these flights, stick position was measured and the correspond- ing control surface position calculated. The results of these maneuvers are referred to as "stick" in table III. Since the parameters plotted account for over 90 percent of the vehicle's response to pilot's inputs, the discussion will center on these parameters.
There were maneuvers performed at four different Mach numbers. At Mach numbers of .6 and .9 maneuvers were performed at several different trim angles-of-attack.
Each maneuver was examined using the two parameter extraction methods mentioned in the Parameter Extraction Procedure Section. The results for the four parameters shown in figure 2 will now be discussed.
C - The values determined by both extraction methods agreed well, za indicating confidence in these results. Also, the values obtained showed trends that were similar to those of other investigators, and their magnitudes seemed reasonable. An examination of table III showed C to be well identified for Za most runs, but in general, it was not the longitudinal parameter that was most identifiable.
C - The values obtained for both extraction methods agreed well, and for rna Mach numbers to .6, the values were close to those predicted by other investi- gators. For the Mach .9 cases, the values of C became more negative as ma expected. There were no data to check the magnitude of the increase; however, the estimated standard deviations and sensitivities implied that the parameter was generally well determined (table III) and had a significant effect on the vehicle motion. A repeat run at an angle-of-attack around 15.5 degrees gave a more negative value for the parameter. When assessing the C values from the two runs, the ma maximum likelihood, regression and estimated standard deviations were all considered, and for the Mach equals .9 case, a value of aproximately -.27 seemed reasonable.
em - The values obtained for both extraction methods agreed for most
q runs. The values extracted generally were close to those predicted by other inves- tigators for the Mach .6 case. The trends of the data were reasonable except for two points at the highest angles-of-attack. These two points both have larger mag- nitudes than might be expected from the other runs examined. A trend to more damping such as that seen in the regression results is reasonable, but the large jump seen in the maximum likelihood results is questionable. The values of esti- mated standard deviation and sensitivity shown in table III indicate that the param- eter is not as well identified as the past two and does not have a great influence on the vehicle motion for many of the runs examined.
Cm~e - As with C , the values obtained for both extraction methods mq agreed for most of the runs. The values for Cm~e determined by other investi- gators varied widely and the values for the Mach .6 runs generally fell between the extremes. The values showed a definite Mach effect between Mach .6 and Mach .9.
Also, a trend toward greater effectiveness with angle-of-attack was seen. Both trends are reasonable, although the amount of variation seen at the largest angles-of-attack for the Mach .9 data was greater than expected. Based on the estimated standard deviation and sensitivity values, C was considered to be moe well identified and to have a significant influence on the vehicle motions.
A comparison of the results of longitudinal runs using actual and calculated surface positions for Mach .6 are given in figure 3. Also shown in the figure are the Mach .6 results from a run where only calculated control position was available. The results from the actual and calculated control surface position runs agree reasonably well for all parameters. The results from Mach .6 runs from the flight where only calculated surface deflection was available show the same trends and magnitudes as the runs where the actual surface positions were measured. For the longitudinal aerodynamics, these additional runs definitely add to the definition of the parameters identified.
As an additional test of the model determined using flight tests, a run at Mach .6 that was not used for determining values for the parameters was used for prediction. In this case, values for the various parameters in the mathematical model describing the vehicle were picked from figure 2 for the specific Mach number and trim angle-of-attack of the prediction run. This model was then perturbed by the actual input time history from the flight test and the resulting motions compared with the motions measured in flight. The results of this prediction are shown as figure 4a and b. The assumed model is seen to do a good job of predicting the vehicle motions.
LATERAL PARAMETERS Next we will discuss the lateral parameters. Parameter values for the assumed lateral model are given in table IV. As was the case with table III, the designation "surface" or "stick" indicated how the control input was determined.
The lateral parameters that have the greatest effect on the vehicle motion and which describe approximately 90 percent of the vehicle's response motion are shown as figure 5. The estimated standard deviations and sensitivities of the parameters that had the most effect on the vehicle motion are given in table IV. An examina- tion of these values indicated that C , Cna' and C are very well ta ncSr identified; the parameters C and Ct~ are well identified; and that these p ua five parameters describe most of the vehicle's motion. The parameters C ' 1cSr C and C are not as well identified and do not have much influence on ya ncSa the vehicle motion. The parameters shown in this figure will now be discussed individually as to their trends with angle-of-attack and actual parameter values extracted.
C - The parameter showed consistent trends with angle-of-attack for all ta Mach numbers. These trends were similar to those of other investigations. The magnitudes of the extracted parameters fell within the range of the values predicted by other investigators, but in general, were less negative then expected. However, since both the Regression and Maximum Likelihood extraction programs gave similar results, the values seem reasonable.
C - The parameter showed similar trends as indicated by the results from na other investigators. The trend to larger C values with increased Mach number n in the Mach .6 to Mach .9 range is also seen~ The agreement between the values determined by the two extraction methods was poor, which reduced the confidence in the values determined. However, in general, the values seemed to fall in a reasonable range when compared to other results.
C - The trends of the parameter values with angle-of-attack and Mach ya number were reasonable. The magnitude of the change appeared to be greater than anticipated. Also, the agreement between the values determined using the two extraction methods was not good for most maneuvers. The values for the parameter were also reasonable, but possibly were not negative enough in most cases.
C - The magnitudes of the extracted parameters seemed reasonable, but the p scatter in the parameters precluded establishing any definite trends with angle-of- attack on Mach number. At the largest angles of attack the two extraction methods agreed fairly well giving some confidence in the values obtained.
C - The magnitudes determined for the parameter seemed reasonable.
tcSa However, the parameter values for the Mach .9 runs seemed to show a trend with angle-of-attack which was not predicted by other investigators. There also appeared to be a trend toward more effectiveness with increasing Mach number which was greater than expected. The two extraction methods did not agree well, but the trends noted were clearly defined. The scatter in the Mach .6 results prevented any definite comments on the trend of that data.
C - There was considerable scatter in the extracted parameter values, so 1cSr no trends were obvious. The parameter showed less effectiveness than was predicted by other investigators. Since the two extraction methods gave different values in most cases, the confidence in the values for this parameter was reduced.
C - The values for this parameter were generally reasonable but showed ncSa considerable scatter. The trend of the parameter values was to be less effective than predicted by other investigators. However, the scatter in the values and the lack of agreement between the two extraction methods imply a reduced confidence in the parameter values obtained.
C - The values determined for this parameter had magnitudes and trends nor as expected, and the agreement with the predictions of other investigators was good. ,Both extraction methods gave similar results, increasing the confidence in the values extracted.
Figure 6 shows the results of comparing runs where the actual surface deflec- tion was measured with runs where the surface deflection was calculated based on stick position or rudder pedal position. Also shown are runs where only stick posi- tiori and rudder pedal position were measured. The figure shows that the trends for ali the calculated deflections seen are the same as those seen in figure 5. Also, where the scatter was such that trends were not detectable, the same was true for the runs using calculated deflections. In general, with one exception, the addi- tional runs where surface deflections were calculated were a reasonable addition to the parameter data base.
The orie exception is the rudder deflection. The rudder pedal position to surface deflection calibration was done at 0 Mach. The results indicate that for a giveri pedal positiori, the deflections of the rudder decrease above Mach .5. At Mach .6 the deflections are about two-thirds of the Mach 0 deflection, and at
Mach .9 the rudder deflection is about one half to Mach 0 deflection. The parameter
values extracted for C and C reflect this reduced rudder deflection in tor nor
that a greater or ~s calculated than actually existed, so the parameter values
showed less effectiveness by about two-thirds.
The predictive capability of the lateral model was also checked and the results are shown as figures 7a and b. As with the longitudinal model check, a run that was not used for extraction was used for prediction. As can be seen in figures 7a and b, two mathematical models were used for prediction. The first used values determined from extraction runs made at similar ang1es-of-attack and Mach number, and the second used parameter values determined by wind tunnel tests where values were available and extracted values where wind tunnel values were not available.
The actual values used for the parameters are shown on the figure. The prediction using extracted values was fairly good (Fig. 7a). However, the response to input using the wind tunnel parameters had a different phase than that of the actual vehicle (Fig. 7b). Figure 8 shows the fit and parameter values obtained when the predictIon data set was used with the Maximum Likelihood program to estimate parameter values.
CONCLUSIONS Flight tests were conducted using the F106B that will be used for a leading edge vortex flap study. These flight tests used the basic aircraft and were run at several conditions with emphaSis on Mach numbers of .6 and .9 and at ang1es-of- attack greater than 10°. The trends of the parameters that describe up to 90 percent of the vehicle motion were established and were reasonable. For the majority of the runs, the magnitudes of parameters were reasonable as evidenced by the fact that when these values were used in a mathematical description of the vehicle, that mathematical model had good prediction capability. Additional runs should be made to get more data points at ang1es-of-attack above 12° at Mach numbers of .6 and .9. Three additional points at each Mach number should be sufficient to document the basic aircraft in the high angle-of-attack region. This documentation will then serve as a basis for evaluation of the modified aircraft.
TABLE 1.- PHYSICAL CHARACTERISTICS OF THE FI06B Mass Range During Test: 1050 slug to 900 slug Assumed Inertias 19,000 slug-ft Ix 185,000 slug-it Iy I 200,000 slug-it Z 60,000 slug-it IXZ Dimensional Characteristics: Wing Area (S) 695.0 it Chord (C) 23.76 it Span (b) 38.13 ft TABLE 11.- FI06B INSTRUMENTATION SYSTEK Variables Range (Time, Sec) ft/sec 0.0 V, to 1300 .00 ± 13 , rad 0.52 rad ± n, 0.52 rad/sec ± p, 1.0 rad/sec ± q, 1.0 r, rad/sec ± 1.0 9, rad/sec ± 0.52 rad/sec ± 1.4 <I> , "G" A , units ± 1.0 x "G" units ± A , 1.0 y "G" units A + 1.0 to - 7.0 z' ± <5 , rad 0.122 a <5 rad + 0.28 to .42
-
e' ±
<5 , rad 0.42
r Estimated accuracy 1 percent of full scale I-' o TABLE III. - LONGITUDINAL PARAKETKR. IDENTIFICATION RESULTS ML; Surface ML; Stick Regression; Surface 0 0 aT = 8.7 ~ = 8.7 ~ = 8.]0 M = .4 M = .4 M = .4 Parameter Value Standard Sensitivity Value Standard Sensitivity Value Standard Sensitivity Deviation Deviation· Deviation Cx .53 .093 .16E3 .65 .040 .9E3 .275 .0021 a C -.23 .0037 .17E6 -.22 .00055 .46E6 .224 .001 zO C .31E4 .021 -2.11 .113 -2.32 .30E5 -2.15 .009 Za C z -6.61 2.25 .29E3 .69 .37 7.3 -3.27 .17 q C -.66 .24 .21E2 -.34 .029 .25E3 -.663 .015 Zt5e -.131 .0039 .32E5 -.12 .00057 .IE6 -.127 .0023
Cma
,
Cm
-.87 .235 .nE3 -.73 .018 .85E4 -.60 .043 q .021 .114E5 -.31 .0019 .IE6 -.35 .004 -.36 <1n&e * (1) Surface denotes runs where 3ctual control surface position was measured.
(2) Stick denotes runs where stick position was measured and corresponding surface position calculated.
(3) Regression denotes runs examined using the regression program of reference 2.
ML denotes runs examined using the maximum likelihood program of reference 1.
TABLE III. - LONGITUDINAL PARAMETER IDENTIFICATION RESULTS (CONTINUED) ML; Surface MLj Stick Re~ression; Surface 0 0 0 aT = 8.5 ~ = 8.5 ~ = 8.5
M = .4 M = .4 M = .4
Parameter Value Standard Sensitivity Value Standard Sensitivity Value Standard Sensitivity Deviation Deviation Deviation
Cx .404 .087 .29E2 .426 .04 .17E3 .29 .0017
a C -.226 .0073 .17E5 -.217 .0015 .2E6 -.215 .003 ZO C -2.22 .215 .19E3 -2.49 .03 .14E7 -2.22 .013 Za C 7.67 .95 z -3.6 3.9 1.7 .34E4 -3.38 .25 q C -.30 .36 1.2 .118 .056 .55E2 -5.8 .02 Zoe Cma -.14 .0062 .105E4 -.135 .00096 .9E6 -.133 .0025
Cm .12E3 -.64 .034 .25E4 -.65 .049
-1.0 .20 q -.35 .02 .104E4 -.28 .0032 .92E6 -.33 .0043 <1no e ML; Stick Regression; Surface ML; Surface 0 0 aT = 11.5 ~ = 11.5 ~= 1l.5°
M = .6 M = .6 M = .6
Standard Sensitivity Parameter Value Standard Sensitivity Value Standard Sensitivity Value Deviation Deviation Deviation C .004 .61 .052 .3E3 .48 .036 .7E6 .2 Xa C -.34 .002 -.34 .0046 .11E6 -.34 .0057 .13E8 zO C -2.46 .12 .19E4 -2.32 .13 .17E6 -2.5 .013 Za C .35 z -13.1 3.7 .86E2 -8.8 3.9 .27E5 -6.0 q C .15E2 -.33 .26 .68E4 -.6 .026 -.56 .29 Zoe .0023 Cma -.15 .0016 .23E5 -.147 .0024 .21E6 -.15 C .062 m -1.31 .15 .28E3 -.6 .17 .79E5 -.96 q ......
Cm -.41 .014 .62E4 -.32 .015 .25E5 -.37 .0046
...... oe _._- ~--- --- f-' TABLE III. - LONGITUDINAL PARAMETER IDENTIFICATION RESULTS (CONTINUED) N ML; Surface ML; Stick Regression' Surface
aT = 14.3° aT = 14.3° 0.1' = 14.3°
M = .6 M = .Il M ". .6
Sensitivity Parameter Value Standard Value Standard Sensitivity Value Standard Sensitivity Deviation Deviation Deviation .08 .17E5 .40 .88 .3E2 .85 .134 .0041
Cxa
C -.46 .0023 .72E6 -.51 .027 .7E4 -.45 .003 zO C -2.88 .041 .34E5 -3.52 .54 .6E3 -2.74 .0096 Za C z -1.28 .87 9.0 14.2 11.4 .14E2 -7.15 .21 q C -.51 .056 .25E3 1.5 .58 .25E2 -.73 .014 zoe .0011 .16E6 -.20 .012 .28E4 .0034 -.205 -.193
<1na
Cm -1.04 .03 .58E4 -.21 .31 4.6 -1.03 .075 q .13E4 .0048 -.39 .0026 .92E5 -.31 .02 -.38 Croce Regression; Surface ML; Surface ML; Stick
aT = 13.r aT == 13.r ~ = 13.r
M = .32 M = .32 M = .32
Parameter Value Standard Sensitivity Value Standard Sensitivity Value Standard Sensitivity Deviation Deviation Deviation C .445 .31 3.1 .47 .32 .23E2 .309 .0038 lCa C -.375 .0044 .25E6 .002 -.373 .0043 .44E5 -.38 zO C -2.32 .23 .18E3 -2.42 .19 .28E5 -2.26 .016 Za Cz -2.7 3.2 1.4 1.47 3.18 .71E2 -4.48 .26 q C -.67 .22 .18E2 -.453 .18 .25E3 -.71 .018 Zoe .22E4 -.144 .0038 -.16 .009 .84E3 -.149 .0085
<1na
.64E2 -.744 .062 Cm -1.01 .22 .98E2 -.57 .22 q -.355 .019 .12E4 -.29 .016 .49E5 -.35 .0042 Croce L _____ ~ - - - --------- '------- --- TABLE III. - LONGITUDINAL PARAMETER IDENTIFICATION RESULTS (CONTINUED) ML; Surface ML; Stick Regression; Surface aT = 5.7
aT = 5.7 ~ ... 5.r
M = .9 M = .9 M = .9 Parameter Value ~tancfal"cl Sensitivity Value Standard Sensitivity Value Standard Sensitivity Deviation Deviation Deviation .45 .048 .98E2 .55 .12 .26E2 .195 .0023 I
Cxa
C .0054 -.134 .0005 .22E6 -1.33 .18E5 -.135 .0008 ZO C -2.7 .027 .15E5 -2.80 .32 .19E3 -2.70 .011 Za C z -2.66 .64 .28E2 1.90 6.3 .21 -8.05 .25 q C .054 .26E3 .225 .44 .41 -.674 .022 -.65 Zoe -.254 .0008 .14E6 -.246 .0077 .24E4 -.262 .0044
Cma
Cm -1.42 .032 .76E4 -.75 .31 .25E2 -1.14 .096
q I C .58E5 -.34 .027 .65E3 -.443 .0084 -.456 .0035 moe , ML; Surface ML; Stick Regression; Surface 0 0
aT = 17 aT = 1r
~ = 17 M = .6 M :0 .6 M = .6 Sensitivity Value Standard Sensitivity Value Standard Sensitivity I Parameter Value Standard Deviation Deviation Deviation C -.97 .094 .22E4 -.55 .076 .17E4 .052 .009 Xa C I .19E6 -.69 .0064 .21E6 -.604 .003 -.638 .012 zO C -2.93 .097 .29E4 -3.4 .084 .73E4 -2.84 .032 Za C I z 3.45 3.8 .37E2 18.7 1.98 .68E4 -9.16 .85 q C -.72 .043 -.501 .165 .31E2 -.083 .083 2.4 I Zoe !
.0037 .18E5 -.157 .0014 .43E8 -.19 .0055 -.194
Cma
Cm .14 .14E5 -2.59 .10 .23E5 -1.25 .145
-2.95 q .007 .0073 Cm -.458 .011 .24E5 -.43 .52E5 -.40 oe ......
Vol f-' TABLE III. - LONGITUDINAL PARAMETER IDENTIFICATION RESULTS (CONTINUED) ~ ML; Surface ML; Stick Regression; Surface I
aT = lS.r aT = lS.r nr = lS.r
I M = .9
M = .9 M = .9
Parameter Value Standard Sensitivity Value Standard Sensitivity Value Standard Sensitivity I Deviation Deviation Deviation I C:xa 1.38 .1SES .12 1.6 .4 .6E6 -.03 .00S7 I C -.S78 .34E6 .004S -.64 .06 .31ES -.S73 .003 ZO !
I C -2.92 .049 .29E5 -2.84 .48 Za .13E6 -2.86 .026 C I z -14.6 .78 .3SE4 7.4 26.8 .13E4 -11.5 .66 q C -.637 .072 .38E3 .83 1.4 .15E3 -.836 .042 Zoe I -.31 .0028 .14E6 -.23 .024 .13E7 -.287 .008
Cma
Cm -.77 .056 .64E3 -.46 .81 .3ES -1.22 .20 q I I Cm -.61 .0065 .12E6 -.47 .081 .12E5 -.51 .013 oe I M.L; ::lurrace M.L; ::lt1CK. Kegress1on; ::lurrace aT = 15.So aT = 15.5°
nr = lS.5°
I
M = .9 M = .9 M = .9
Parameter Value Standard Sensitivity Value Standard Sensitivity Value Standard Sensitivity Deviation Deviation Deviation C:xa .69 .33 .25E3 .67 .069 .S2E4 .013 .0036 C -.SS .05 .79E4 -.54 .009 .17E6 .504 .003 zO I C -2.91 .7 .41E3 -2.97 .095 .87E4 -2.8 .019 Za I Cz -1.41 15.3 .18 -1.31 2.4 2.7 -8.7 .44 q C 1.2 .88 23.6 .43 .19 68.4 -.69 .033 Zoe -.2S .016 .21E4 -.24 .0028 .21ES -.24 .006
Cma
Cm
-2.42 .S3 .3SE3 -2.08 .10 .29E4 -1.27 .13 q .01 Cmoe -.S8 .046 .27E4 -.S5 .0093 .24ES -.4S i - ---- TABLE IV. - LATERAL PARAMETER IDENTIFICATION RESULTS ML;Surface ML' Stick Regression; Surface 0 0 aT := 8.7 aT = 8.7
a.r = 8.r
M = .4 M = .4 M = .4 Parameter Value Standard Sensitivity Value Standard Sensitivity Value Standard Sensitivity Deviation Deviation Deviation CYP. -.468 .02 .75E3 -.49 .01 .37E4 -.50 .006 ,)
CyP 0 --- 0 .021 .023
-- -- ---
C
0 --- 0 .27 .105
-- --- ---
Yr C .19 .049 .17E2 .16 .02 .7E2 .164 .014 yc.a C .064 .37E2 .028 .011 .0033 .9E2 .056 .0032 Y')r C, -.053 .0009 .15E5 -.054 .0006 .14E8 -.054 -[3 .0006 Gt -.124 .0061 .41E4 -.116 .0018 .12E8 -.107 .0024 p CZ .17E3 .009 7.3 .194 .106 .026 -.006 .011 r C9..
-.086 -.072 .004 .11E5 .0017 .25E5 -.088 .0014 oa C .015 .0007 .92E3 .007 .0002 .11E5 .012 .0003 '~or C .08 .0015 .2E5 .082 .001 .17E6 .090 .0019 ne Cnp -.027 .0097 .lIE3 .068 .004 .12E5 .018 .007 Cn -.20 .033 .33E3 .29 .014 .12E5 -.107 .032 r C -.057 -.068 .0065 .36E3 .0052 .14E5 -.046 .0043 noa C -.054 .0005 .24E6 -.037 .0003 .14E6 -.051 .001 nlSr (1) Surface denotes runs where actual control surface position was measured.
'"
(2) Stick denotes runs where stick position was measured and corresponding surface position calculated.
lj) Regressiondenotes runs examined using the regression program of refecence 2.
ML denotes runs examined using the maximum likelihood program of reference 1.
I-' V1 t-' 0\ TABLE IV. - LATERAL PARAMETER IDENTIFICATION RESULTS (CONTINUED) HL; Surface ML; Stick Regression; Surface 0 0 0
ar = 8.5 ar = 8.5 or = 8.5
M = .4 M = .4 M = .4 Parameter Value Standard Sensitivity Value Standard Sensitivity Value Standard Sensitivity Deviation Deviation Deviation C -.486 .0046 .16E5 -.51 .009 . .6E4 -.51 .0032 ya 0 0
CyP -- --- -- --- 0
--
C 0 0
--- --- -- --- .225 .055
Yr C .182 .0089 .45E3 .17 .015 .15E3 .16 .0067 YcSa C .056 .0022 .77E3 .023 .0025 .95E2 .055 .0016 YcSr CR,a -.054 .0003 .2E6 -.056 .00002 .12E7 -.054 .0006 CR, -.143 .0008 .25E6 -.135 .0006 .7ES -.12 .0021 P CR, .045 .0071 .18E3 -.138 .0027 .7E4 .15 .Oll r C~cSa -.09S .0009 .32E5 -.080 .Oll .12E6 -.089 .0014 .014 .0002 .0018 C~6r .16E5 .006 .18ES .012 .0003 C .080 .OOOS .24E6 .080 .0008 .14E7 .093 .0016 , ns Cn .016 .0033 .48E3 .113 .005 .26ES .043 .00Sl P C i n -.302 .013 .51E4 .36 .018 .36ES -.025 .027 r Cn - -.040 .0023 .28E4 -.001 .0038 .27E2 -.04S .0033 CIa C -.OS9 .13E6 -.042 .0004 .0004 .SE6 -.051 .0008 nor TABLE IV. - LATERAL PARAMETER IDENTIFICATION RESULTS (CONTINUED) MI..' Surface MI.- Stick Regression; Surface 0 0
aT = 13.7 aT = 13.7 ar = 13.7
M = .32 M = .32 M = .32 Parameter Value Standard Sensitivity Value Standard Sensitivity Value Standard Sensitivity Deviation Deviation Deviation C -.51 .016 .3E4 -.48 .021 .21E4 -.436 .009 Yf3
CyP 0 --- --- 0 .151 .018
-- ---
C
0 --- --- 0 --- 1.08 .14
--
Yr C .19 .013 .36E3 .16 .017 .18E3 .138 .008 Y8a Cy " .05 .26 .003 .40E3 .0031 .12E3 .039 .002 ')r Co, -.067 .0015 .81E6 -.066 .0023 .33E6 -.058 .0014 ''';J C.!p -.111 .0013 .6E5 -.062 .0021 .19E5 -.117 .0027 CZ -.013 .02 .45E2 -.263 .028 .16E5 .139 .02 r C -.090 .0008 .17E6 -.095 .0011 .llE6 -.095 .0012 lSa C9.S .009 .0002 .2SES .004 .0003 .64E4 .009 .0003 r C nR .11 .00Sl .53E6 .067 .0082 .98E5 .062 .004 I-' Cn .006 .0061 .41E2 -.063 .008S .36E4 .01 .0076 p C .114 nr .072 • 136E4 .109 .091 .96E3 -.133 .060 r -.09 "n6a .0016 .72ES -.070 .0026 .31E5 -.030 .003S " -.[,3 '-'nor .0013 .96ES -.023 .001S .43ES -.036 .0009 .- t-' '-I f-' co TABLE IV. - LATERAL PARAMETER IDENTIFICATION RESULTS (CONTINUED) .-- HI." Surface ML· Stick Regression· Surface ':(T = S.7° aT = S.7° aT = S.7° M = .9 M = .9 M = .9 Parameter Value Standard Sensitivity Value Standard Sensitivity Value Standard Sensitivity Deviation Deviation Deviation C -.S2 .003S .4ES -.Sl .0069 .89E4 -.S9 .002 Ya CyP 0 0 .16
-- --- -- --- .008
C
0 -- 0
--- --- --- .70 .047
Yr C .23 .013 .SE3 .117 .022 .4E2 .19 .0077 Yoa C .067 .0024 .9E3 .036 .002S .2SE3 .046 .0017 Yor -.053 .OOOS .S4E6 -.OS4 .0006 .27E6 -.OSl .OOOS Cg'B C],p -.147 .0032 .8ES -.142 .0021 .17ES -.124 .0019 C Q -.123 .019 .47ES .10
--- --- .37 .011
-r CQ.
-.094 .001S .8ES -.072 .0024 .3ES -.108 .0018 oa .020 .0002 CQ.or .47ES .013 .0002 .44ES .017 .0004 C .0007 .42E6 .098 .9SE6 .099 .OOOS .14 .0009 na C n -.089 .004S .3ES -.047 .002 .27E4 .123 .0036 p C
n .657 .027 .41ES -.40 --- -.022 .022
---
r C -.092 .0026 .26E5 -.09 -.039 .003S
-- ---
nca C -.061 -.027 .7ES -.054 .0004 .22E6 .00034 .0008 ncr ------- TABLE IV. - LATERAL PARAMETER IDENTIFICATION RESULTS (CONTINUED) --- ML; Surface ML; ,Stick Regression; Surface 0 0 uT - 11.5 aT = 11.5 aT = 11.5 M = .6 M = .6 M = .6 Parameter Value Standard Sensi tivity Value Standard Sensitivity Value Standard Sensitivity Deviation Deviation Deviation CY (1 -.53 .0064 .72E6 -.48 .04 .4E6 -.5 .0024 C
y 0 --- --- 0 ---
--- .087 .010
-p C
0 --- --- 0 --- 1.32 .061
---
Yr C .173 .016 .20E3 .35 .12 .2E4 .2 .0078 Yea .0026 .19E5 .055 .015 .2E4 .064 .0012 CYer .067\ C -.064 .0011 .21E7 -.074 .006 .96E6 -.071 .0005 te C -.17 .0041 .26E6 -.18 .019 .19E7 -.145 .002 t P C -.32 .01.3 .98E4 -.089 .082 .35E5 .227 .012 tr C -.086 .0037 .12E7 -.075 .017 .46E6 -.115 .0015 tea Ct .019 .0005 .18E6 .013 .0017 .37E6 .015 .00023 er C .0021 • 8E (j .064 .012 .16E5 .083 .0012 .069 ne Cn -.007 .0063 .24E2 -.006 .044 .51E2 .002 .005 p C n -.503 .9E5 -.017 .042 .22 .5 -.34 .030 r C -.131 .0076 .7E6 -.096 .031 .15E5 -.045 .0038 nea C -.038 -.055 -.056 .0009 .18E7 .0035 .87E5 .00057 ner t-'
'"
N o TABLE IV. - LATERAL PARAMETER IDENTIFICATION RESULTS (CONTINUED) ML; Surface ML- Stick Reeression- Surface aT = 14.3° aT = 14.3° aT = 14.3° M = .6 M = .6 M = .6 Parameter Value Standard Sensitivity Value Standard Sensitivity Value Standard Sensitivity Deviation Deviation Deviation C .42 .31 .44E2 -.43 .0095 .34E4 -.45 .0055 YB C
--- --- 0 --- --- -.024 .019
Yp C
0 --- --- 0
--- --- -.84 .134
Yr C 1.98 .48 .61E2 .24 .014 .57E3 .24 .011 Yoa -.49 .10 .11E3 .061 .0031 .47E3 .066 .0026 CYor -.107 .0029 .22E5 -.108 .0015 .58E5 CR.a -.11 .0009 CR, -.18 .0092 .51E4 -.17 .0043 .8E4 -.176 .003 p CR, _19 .072 .15E3 -.41 .038 .23E4 .287 .022 r -.118 .0042 .28E4 -.083 CR,oa .0026 .6E4 -.127 .0017 CR.
.017 .0010 .15E4 .008 .00042 .15E4 .015 .0004 or C .051 .0057 .19E4 .062 .0026 .19E5 .067 .0018 na Cn .034 .020 .37E2 .032 .0065 .12E3 .0062 .037 p C n -.5 .113 .79E3 .19 .057 .11E4 .043 -.013 r C -.035 .0079 .22E3 .0022 .0025 .lE2 -.035 .0034 noa C -.059 .0030 .45E4 -.040 .00074 .27E5 -.055 .0008 nor -- -- - ------ - - - ------ TABLE IV. - LATERAL PARAMETER IDENTIFICATION RESULTS (CONTINUED) Regression; Surface ML; Surface MI.; Stick ClT 14.5° ClT 14.5° ClT 14.5° M .6 M = .6 M .6 ParameterlValuelStandard ISensitivitylValuelStandard ISensitivitylValuelStandard ISensitivity Deviation Deviation Deviation C -.43 I .014 .12E4 -.38 .01 .2E4 -.38 .0054 YB C
o o .12 .02
Yp C
o o 1.4 .107
Yr C .21 .019 .14E3 .23 .Oll .7E3 .186 .0075 Yoa .07 .0058 .23E3 .054 .0028 .54E3 .07 .0024 CYor -.098 .001 CtB .9E5 -.085 .0009 .23E6 -.105 .0009 Ctp -.16 .0048 .IE5 -.103 .0037 .15E5 -.145 .0035 C .27 .015 .46E4 .57 .013 .8E6 .29 .019 tr C -.11 .0011 .4E5 -.097 .0008 .9E6 -.13 .0013 toa C .019 .0004 .31E5 .015 .0003 .25E6 .015 .0004 tor C .0821 .0014 .25E5 .065 .0013 .46E5 .08 .0016 nB Cnp .00571 .0075 6.8 -.019 .0054 .54E3 .015 .006 Cnr .24E3 .25 .017 .36E6 .14 .032 -.0341 .02 C -.04R .0016 .4E4 -.05 .0012 .7E6 -.035 .0023 noa -.0521 .00067 .24E6 -.033 .0004 .23E7 -.054 .0007 Cnor N ~ 1-..)
N TABLE IV. - LATERAl. PARAMETER IDENTIFICATION RESIJLTS (CONTINURD) ML; Sur race ML; Stick Regression; Surface aT = 15.7° aT = 15.7° aT = 15,i° M = .9 M = .9 M = .9 Parameter Value' Stancl<lrd Sensitivi ty Value Stanr\(lrd Sensitivity Value Standard Sensit i vity Deviation Ilevi(ltion Deviation C -.2h .27 3.(, -./~h .0 I I~ .11E4 -.5 .009 YB C
0 --- --- 0 ---
--- -.08 .022
Yp C
--- --- 0 --- ---
.19 .18 Yr C .71 .221Q .18 .1 :3 .01(, .91-:2 .17 .012 Yoa C -.08(' .11(, 7. I .22 .0041 .31Q .03 .005 Yor CIa -.107 .0092 .151<:4 -.086 .001') • 9/~ E 5 -.116 .002 CR.
-.18 .023 • I ')1-:5 -.08 .O(n5 .411':4 -.164 .005 p I CR.
.4 '3 • I 7 .26E.l .55 .011 .62E5 .38 .04 r I I C -.14 .OOR9 -. 114 .0012 • 5') 1-:4 .15E6 -.146 .0025 16a C .024 .0027 .4hE/~ .012 .0005 .99E4 .017 .001 10r CnB .082 .0 1 I .089 .0024 .73E5 .098 .0026 • 111':4 en -.01 .025 -. nOli .00n 3.0 .031 .00(, · Ion p C -.48 .22 .151-:3 nr .19 .053 .74E4 -.1 I, .050 C -.Onl • (ll ] .4//1-:1 -.()5h noa .0021 .31-:5 -.035 .0032 I C n .0Ohh -.058 ./I/IES -.024 .OO()8 • 14K') -.05/1 .001.1 or - TABLE IV. - LATERAL PARAMETER IDENTIFICATION RESULTS (CONTINUED) MI." Snrface MI.; Stick Regression" Surface (IT = 15.5° (IT = 15.5° (IT = 15.5° M = .9 M = .9 M = .9 Parameter Value Standard Sensitivity Value Standard Sensitivity Value Standard Sensitivity Deviation Deviation Deviation C -.51 .016 .13E4 -.57 .27 9.4 -.56 .0064 YB
CyP 0 --- --- 0 -.12 .02
-- ---
C
0 --- --- --- --- .OOS .11
Yr .26 .024 .15E3 .45 .38 11.6 .19 CYOa .0093 C .068 .0071 .11E3 -.OS6 .077 13.4 .053 .0027 Yor -.11 .0009 .lE6 -.17 .011 .27E4 -.11 .002 C~B CR. -.17 -.OS .002S .22E5 .032 .15E3 -.18 .006 p C~ .34 .018 .15E5 .1S .21 41.0 .034 .61 r -.15 .001 .84E5 -.13 .011 .41E4 -.17 .0028 CR.oa CR.
.018 .0035 .13E5 .013 .0026 .38E3 .017 .OOOS or C .076 .0019 .46E4 .08 .024 .3E3 .093 .0019 ns Cn .011 20.0 .OS3 .0016 .0071 .072 lS.0 .0059 P C -.61 .029 .42E5 .37 .42 54.7 -.2S .033 nr C -.10 -.057 .0027 .002 .17E5 -.073 .026 .28E3 noa C -.064 .0007 .54E5 -.031 .005 .38E3 -.060 .0008 n6r N (.,.)
REFERENCES
1. Murphy, Patrick c.: An Algorithm for Maximum Likelihood Estimation Using an
Efficient Method for Approximating Sensitivities. NASA TP-2311, June 1984.
2. Klein, V.; Batterson, J. G.; and Murphy, P. c.: Determination of Airplane Model
Structure from Flight Data by Using Modified Stepwise Regression. NASA TP-1916, October 1981.
3. Eulrich, B. J.; Govindaraj, K. S.; and Harrington, W. W.: Estimation of the Aerodynamic Stability and Control Parameters for the FI06A Aircraft from Flight Data: Maneuver Design and Flight Data Analysis. AIAA Paper 78-1326.
4. Frostman, David L.: An Investigation of the Tracking Performance of the Fire Fly Manual Director Gunsight for Air-to-Air Gunnery. AFIT/GGC/EE/77-5, December 1977.
5. Hallissy, J. B.; Frink, N. T.; and Huffman, J. K.: Aerodynamic Testing and Analysis of Vortex Flap Configurations for the Five Percent Scale F-I06B.
Vortex Flow Aerodynamics Conference, Volume 2. NASA CP-2417, 1986.
u ~ jr-; /} ~ jr·, '/.. -X.'
!
b..
.32 Mach .4 Mach
<>
0 .6 Mach N 0 .9 Mach Flag for Regression Results
'"
Wind Tunnel Results (Unpublished) - - - Reference 3 - - - - Reference 4
o
o ; '; ~! i i -. -~_~~~_-~.;;.~-~~--i ".- .6 -t.ir-_:; . oJ .<!}' 0.hf6 . : . : -1.0 -1.0 ~ : r!/I6> i 13 G>: i ,.
C ' z C a -2.0 m -2.0 q Per Rad.
~ it. ____ _
III .... _ .... ; Per Rad.
~ ; - --t-.--~-~- $
l..... ·.0.· -3.0 -3.0 ,.
-4.0 -4.0 ~ e ., -.35 -.1 -.3
~-----~---
, - - 4- -f ~ - - - - ----.,.---~ 0 8 0
--~-. 8 8
C ' -.2 m -.4
o
C ' a m
-------- -
oe
It
Per Rad.
ri 0
8'
8" Per Rad.
rf -.3 9 r:f -.5 -.4 -.6 [!]
!
L...... _._ c ...
-- _ .. ------- _ ..
20 20 12 16 4 8 12 16
o 4 8 o
a, deg a, deg Figure 2. Longitudinal Aerodynamic Parameters plotted against trim angle-of-attack for several Mach Numbers.
Maximum Likelihood (Surface) FIt 13 Maximum Likelihood (Stick) FIt 13 FIt 53 Maximum Likelihood (Stick)
<>
0 r o .
[!J ~ B -1.0 -1.0 ~ ~ CD
C z '
Cm ' q a -2.0 -2.0 , ~ Per Rad.
0, Per Rad.
-_. g
G ~ 0 <;> •.. ..;,L .• "' '.e. ; .. --_ ; -3.0 ~ -3.0
~
a .- -0 -4.0
L
-4.0 .L ___ .l._ •• __ _~ ___ ~_. __ ---L-_. . ... _ .......
-.35 -.3
-.1 r B
B 8 B-
<>
(> ~ <:> CD -.4 -.2 @} em ' C ' m (> a -[3 oe Per Rad.
Per Rad. <:> ~ -.3 -.5 -.4 -.6 .........
4 B 12 16 40 0 B 12 16 0 4 a, deg a, deg Figure 3. Longitudinal Aerodynamic Parameters for Mach .6 runs using both N stick motion and actual surface motion time histories as control
"
effectors.
.3
+ + + + Flight Data
Fit Alpha, .2 Rad.
.1 .1 q, 0 rad/sec -.1
o
az, -1. 0 "G" Units -2.0 0 2 4 6 8 10 12 Time, Sec C .61 C - -.316 C -2.46 x z z
-
a 0 a C C eo -.56 - -13.10 C - -,15 z ma zlSe q C C
= -1.13 - -.41
m mISe q (a) Values obtained from other parameter extraction runs.
M=.6, ar- ll •5 ° • Figure 4. Longitudinal Predictions Runs
+ -+- + + Flight Data
.3 Fit Alpha, .2 Rad.
.1 .1 q, 0 rad/sec ~
-.1 ~'IIIIIIIIHi~ ,,,,,1,,,,,,,,11,1,,,,,,,1,,,11,1111,,111,,1,1
o
-LO a z' "G" Units -2.0 4 6 8
o 2
Time, Sec
C = .61 ML
C = -.316 ML C .. -2.80 WT
xa Zo za
C .. -.56 HI.
C - -13.10 ML
C - -.16 wr
z m z6e q a C - -.70 REFS.
C - -.30 WT m m6e q ML-Maximum Likelihood WT-Wind Tunnel (b) Values obtained from wind tunnel data where available and from parameter extraction when wind tunnel values were not available. M=.6, a~11.5°.
Figure 4 (Concluded) 11 .32 Mach
<>.4 Mach
w 0.6 Mach .,:) 0.9 Mach Flag for Regression Results - - - Reference 3 - - - -:- Reference 4 ---- Reference 5
o
-.30 t!l
--
--
- -------- ..
I C ' i
B e· ;---: .. --!
-.40 Per Rad.
8' A-
_ .. _"
._. -,- .. - I .. ~
•
.. lA
<> -.10 C , -.50 y
g o Ad
~
B a . ~.
(1) Per Rad.
Gf - ." ~ ., -.15
,,/
-.60 -;- .-.,...~.--- :.-;:.;.....;.:.J...:...:... •• 1.::"':;.0"J .... _ J.
~. I I -- .: .. ,.- .
-.04 .15 d
~, --
(I} c -.10 ¢
-
C , .10 t
ri ¢ nS ¢ Per Rad. C '
/<:>
i 6 6
p
/"
0r:f (;) - e- -A6'"
.,...--- .... -
Per Rad.
.". ~ a1J .r- . __ -1._._ .02 .. _ •• ...I_. ____ ~ •. 1 -.20 8 12 16
d 4
o 4 8
12 16 20 a, deg a, deg Figure 5. Lateral Aerodynamic Parameters plotted against trim angle-of-attack for several Mach Numbers.
) ~ A .32 Mach
o .4 Mach
o .6 Mach
o .9 Mach
Flag for Regression Results - - - Reference 3 - - - - - Reference 4
- ---
o
[;l.---- -----~ .02 .
....
" (j) <:> c- - - I --
"
d 0r#
"
, CR, ,
"
CR, ,
oa
or 6. - ~
o
Per Rad.
o
Per Rad.
<6
G) i ---
o B-
ff
t
.01 -- -.10
'" , ---- - ~
< 0 6
~
...J_
"'--- ------
I & I.
.005 r1 -.02 -.02
~r=1
t
ri C , 6
$
.0 C ' n nor _0
~ -- -t-~~ fit oa
~ Per Rad.
Per Rad.
..- .... ---- - - ....
-~ "... B --A' -.10 Ill- -.10 - 1 0- 8 12 16 20 12 16 20
o 4 o 4 8
a, deg a, - deg Figure 5. (Concluded) W f-' W
N o Maximum Likelihood (Surface) FIt 13
C Maximum Likelihood (Stick) FIt 13
<> Maximum Likelihood (Stick) FIt 53
o . 1-- --I -.30 I _ ....... I --I c , ,m I R.8 -.40 Per Rad. ~; ·1
0 ~- -s -1-'
~ m !
~ m, ~ -.10 Cy, -.50
~ o
it' I - .1-- ._. -- - i .-I- .. ~i· '-1 Per Rad.
!
-.15 -.60 -t-::.··; ·····t -.04 .15 ~, -.10 r a ~ .10 C , 0, nS CR. ' Per Rad.
r
p 9 @ a 0 0 ~ 0
Per Rad. l
____ .1-. _ ... ,- ...
-.20 ' ~ . 02 0 8 12 16 20 0 4 R 12 16 20 a, deg a, deg Figure 6. Lateral Aerodynamic Parameters for Mach .6 runs using both stick motion and actual surface motion time histories as control effectors.
o Maximum Likelihood (Surface) FIt 13
o Maximum Likelihood (Stick) FIt 13
<> Maximum Likelihood (Stick) FIt 53
o -, .02
G ,(3 I
" .
. 1 ,.
.;- -'1 "l· I !,., I .
C ' t -~- ~ "I . I
-~-.--:- ,,--+._-!
C ,
oa I
, .. , I R.
'Gil .
or ___ . t_ Per Rad.
.-.-. ;----1·- - - "_.-,-. ,--
-~- L -1 i--·
•• ~ . I
Per Rad.
~ I, 10)' GJ • _ I 0- em Q i ~ [jJ .... ,. - .....
-.10 .01 ~ <:> iii () .005 OJ ~ ~ -.02 -.02 [jJ Q 0, : I!J . , [jJ C , ~ ~ .1 nor <:> cfo C ' n (j)
'oa
Per Rad.
Per Rad.
I!J -.10 -.10 <:> 16 20
8 12
o 4
4 16 20
o 8 12
a, deg a, deg Figure 6 (Concluded) w w .1
+ + + + 4- Flight Data
Fit Beta, 0 Rad.
-.1 C - -.53 Y
B
.17 C
-
Y c5a 1.0 .067 C
-
Y 6r :II -.064 p, CR, rad/sec
a
• -.17 CR, p -1.0
= 0.0
CR, r • -.086 CR, c5a .2 ..
.014 CR, tSr r, ..
.069 C rad/sec n
B
0.0 C
=
-.2 n p a -.50 C n r C -.113 "" ... + 0 nc5a .. -.056 C nc5r a y ' Units -.5 "G" -1.0,~~~~~~~~~~~~~~~~~~~~~ 2 4 6 8 10 12 o Time, Sec 34 (a) 1 f h I Va ues or ot er parameter extract on runs.
M"".6, ll
ar • 5 ° •
Figure 7. Lateral PredictIon Runs .1
+ + + + Flight Data
Fit Beta, 0 Rad.
-.1 C - .17 ML Yc5a 1.0
p, o
rad/sec Ct. - -.17 ML p -1.0 C - 0.0 t r .2 r,
o
rad/sec C III 0.0 -.2 n p C - -.50 ML n r ... ++
o
C - -.05-S WT nc5r -.5
4ay
"G" Units L..I...J...L..LJL.LL.L.L.Ju...L.L.L.Ju..L...L.L..1~.l..I..L"""""'L...L.L-'-'-'-"-,-' W.tllU I I II I rill I I I I wJ -1.0
o
2 4 6 8 10 12 Time, Sec (b) Values obtained from wind tunnel data (as given in Fig. 5) where wind tunnel values were available and from parameter extraction where wind tunnel values were not available.
M=.6, a "'1l.5°.
T Fi::;ure 7 (r.onrl11npn) .1
+ + + + Flight Data
----Fit Beta, 0 Rad.
-.1 C - -.50 Y e C .23
-
Y lSa 1.0 .068 C
-
Y lSr C .. -.079 p, 0 t rad/sec e C - -.178 t
,,,,,,,1,,,,,,,1,1,,,,,,,,,1,,,,,, ;.UJ
P -1.0
C = -.084
t r .087 C - tlSa .2 C ..
.015 tlSr r, 0 rad/sec .069 C
-
ne .0079 C
I III! II I! I! 1111 d I II II 1 II I I, 1 I I I I II II III I 1\ : 1 t!
-
-.2 n p .. -.39 C n r
C = -.055
nlSa o 8y .. -.057 C "G" Units ncSr -.5 -1.0 4 6
o
36 Time, Sec Figure 8. Lateral Aerodynamic Parameters extracted from the prediction T1In. M= .6. ex '1'= 11 .5 • 1. Report No.
I 2. Government Accession No. 3. Recipient's Catalog No.
NASA TM-S7711 4. Title and Subtitle 5. Report Date LATERAL AND LONGITUDINAL AERODYNAMIC STABILITY AND April 1986 CONTROL PARAMETERS OF THE BASIC VORTEX FLAP RESEARCH 6. Performing Organization Code AIRCRAFT AS DETERMINED FROM FLIGHT TEST DATA 506-46-21-01 7. Author(s) 8. Performing Organization Report No.
William T. Suit James G. Batterson ~--------------------------------1 10. Work Unit No.
9. Performing Organization Name and Address NASA Langley Research Center 11. Contract or Grant No.
Hampton, VA 23665 ~--------------------------------1 13. Ty~of Repo"~d P~iod Cov~~ 12. Sponsoring Agency Name and Address Technical Memorandum National Aeronautics and Space Administration 14. Sponsoring Agency Code Washington, DC 20546 15. Supplementary Notes 16. Abstract Longitudinal and lateral stability and control parameters were estimated from flight data for an F106B aircraft. Parameters were estimated from test maneuvers performed at selected points in the flight envelope. Since the subject aircraft is to be fitted with a leading edge flap, the data obtained will serve as a documentation of the basic aircraft. The parameter values estimated were compared with values from other sources to obtain as complete a documentation of the basic airplane as possible at selected flight conditions.
17. Key Words (Suggested by Author(s)) 18. Distribution Statement Unclassified--Unlimited Parameter Estimation Stability and Control Parameters Subject Category--OS Maximum Likelihood 19. Security Classif. (of this report) 20. Security Classif. (of this page) 21. No. of Pages 22. Price 37 A03 Unclassified Unclassified N-30S For sale by the National Technical Information Service. Springfield. Virginia 22161