Document
I
NASA Technical Paper 1350
the F-111 Tact Research Aircraft
Alex G. Sim and Robert E. Curry OCTOBER 1978
NASA
TECH LIBRARY KAFB, NM
NASA Technical Paper 1350
Flight-Determined Stability
and Control Derivatives for
the F-111 Tact Research Aircraft
Alex G . Sirn and Robert E . Curry DrydenFlight. Reseurch Center Edwurds, Culiforniu National Aeronautics and Space Administration Scientific and Technical Information Office I FLIGHT-DETERMINEDSTABILITY AND CONTROLDERIVATIVES FORTHE F-111 TACTRESEARCHAIRCRAFT
Alex G . Sim and Robert E . Curry
Dryden Flight Research Center INTRODUCTION The F-111 transonic aircraft technology (TACT) aircraft is the latest of a series of research aircraft to incorporate supercritical wing technology. Unlike previous supercritical wing designs, the TACT wing was designed to provide improvements in transonic maneuver capability without degrading the F-111A aircraft's cruise and supersonic performance.
A research program was conducted jointly by the National Aeronautics and
Space Administration (NASA) and the U . S . A i r Force. During the envelope-expansion
phase of the flight program, the flight-determined derivatives were used to update the analysis of the vehicle dynamics to insure safety of flight. One goal of the TACT program was to provide stability and control derivatives to establish a data base with which experimental and analytical prediction techniques could be improved for this class of aircraft. To lend credence to the flight-determined derivatives and to indicate the deviation from potential theory, some of the major derivatives were calculated based on computer models of the aircraft's geometry. These are referred to in this report as analytical model derivatives.
This report presents the flight derivative data base for the F-111 TACT research aircraft. The flight derivatives are correlated with the analytical model derivatives for specific flight conditions and aircraft configurations.
SYMBOLS The stability and control derivatives, as presented, are partial derivatives representing standard NASA coefficients of forces and moments. A right-hand sign convention is used to determine the direction of forces, moments, angular displacements, and velocities. Except for angle of attack, the data are referenced to the vehicle body axis. Angle of attack is referenced to the wing reference plane for consistency with wind tunnel data and other TACT flight data, and thus, it is lo higher than it would b e if it were referenced to the vehicle body axis.
Physical quantities are given in the International Systemof Units and parenthet- ically in U . S , Customary Units.
CLB rolling moment coefficient with respect to angle of sideslip, per degree CLDA rolling moment coefficient with respect to aileron deflection, per degree CLDR rolling moment coefficient with respect to rudder deflection, per degree CLDS rolling moment coefficient with respect to spoiler deflection, per degree CLP rolling moment coefficient with respect to rolling rate, per radian CLR rolling moment coefficient with respect to yawing rate, per radian pitching moment coefficient with respect to angle of attack , CMA per degree CMDE pitching moment coefficient with respect to elevator deflection, per degree pitching moment coefficient with respect to pitching rate, per radian CNA untrimmed normal-force coefficient with respect to angle of attack, per degree yawing moment coefficient with respect to angle of sideslip , CNB per degree CNDA yawing moment coefficient with respect to aileron deflection, per degree CNDE untrimmed normal-force coefficient with respect to elevator
deflection , per degree
CNDR yawing moment coefficient with respect to rudder deflection, per degree CNDS yawing moment coefficient with respect to spoiler deflection, per degree CNP yawing moment coefficient with respect to rolling rate, per radian CNR yawing moment coefficient with respect to yawing rate, per radian C Y B side-force coefficient with respect to angle of sideslip, per degree I I I C YDA side-force coefficient with respect to aileron deflection, per degree CYDR side-force coefficient with respect to rudder deflection, per degree CYDS side-force coefficient with respect to spoiler deflection, per degree C section normal-force slope, per degree n a M Mach number a angle of attack with respect to wing reference plane, degrees h angle of wing leading-edge sweep, degrees AIRCRAFTDESCRIPTION The TACT modifications to the F-111A baseline vehicle included a new wing planform with a supercritical airfoil and a new high-lift system, a modified wing seal, a modified overwing fairing, and a fixed-structure glove. The general arrangement of the F-111 TACT aircraft is shown in figure 1, and the aircraft's physical characteristics are given in table 1. Additional description of the TACT aircraft, as well as a comparison with the F-111A baseline vehicle, is given in references 1 and 2 .
The TACT aircraft's control surfaces were controlled by an irreversible hydraulic system. The pilot controlled the aircraft through a conventional center stick and rudder pedals. For pitch control, the horizontal stabilizer was deflected symmetrically by either the pilot or the rate command augmentation system. A similar arrangement with the rudder was used for yaw control. However, for roll control, the pilot's inputs activated both the differential horizontal stabilizer and the spoilers, while the rate command augmentation system activated only the differential stabilizer.
INSTRUMENTATION Data were obtained at 20 samples per second through a 10-bit pulse code modulation system. All the data were calibrated and analyzed after the flight using a ground-based computer.
Angle of attack and angle of sideslip were measured using a vane flow angu- larity sensor system. This system and its calibration are described in reference 3 .
I,,.. . ..,, In addition, angle of attack was estimated along with the flight derivatives for correlation with the measured angle of attack. Angular positions were measured with a stable platform, angular rates were measured using rate gyros , and linear accelerations were determined from linear accelerometers. Control positions were measured using control position transducers.
Corrections were appliedto the airspeed data to obtain true velocity, Mach
number , and dynamic pressure. Linear accelerations , angle of attack, and angle
of sideslip were corrected for displacementfrom the center of gravity.
FLIGHTCONDUCT Before each flight, a detailed flight plan (checklist) specifying particular maneuvers was prepared. The flight was then monitored by chase aircraft pilots and control room personnel. This procedure not only insured safety of flight but also allowed the research engineer to monitor the flight data in real time, thus giving him insight into the adequacy of the maneuvers and the instrumentation data quality. The flight plan flexibility was sufficient to allow a maneuver to be repeated if necessary.
Longitudinal and lateral-directional maneuvers from which aircraft data were obtained were performed throughout the flight envelope. Data were obtained for angles of attack from approximately 3 O to 1 4 O for a Mach number range from approx- 0.25 to 1 . 7 0 . The data for the higher angles of attack were obtained at imately elevated load factors. The longitudinal maneuver consisted of a horizontal stabilizer doublet , followed by 2 to 3 seconds of no pilot input , followed by a second horizontal stabilizer doublet. Because the vehicle normally exhibited an over-
damped longitudinal response , the second doublet was necessary to increase the
amount of statistically significant transient response information.
One of the objectives in the lateral-directional mode analysis was to obtain independent derivatives with respect to spoiler and aileron (rolling tail) .
However, i t was difficult to separate the aileron and spoiler derivatives with the roll augmentation off because the two control surfaces operated nearly in phase.
Because the roll augmentation acted only through the aileron, out-of-phase aileron and spoiler motion could be obtained with the roll augmentation on. With both roll and yaw augmentation on, the resulting airplane motion was heavily damped.
The maneuver finally selected (fig. 2 ) was performed with the roll augmentation on and the yaw augmentation off. It consisted of two pilot-initiated roll doublets followed by a rudder doublet. This maneuver proved to be adequate for the derivative extraction process.
One flight was made without the use of the spoilers during maneuvers to evaluate the possibility of obtaining more consistent sets of derivatives with lower uncertainties. Better results were obtained from these maneuvers.
Some of the maneuvers analyzed were not performedto obtain derivatives.
Examples of these include structural excitation (using stick raps) and handling quality evaluations. Although specific derivatives could be obtained from these maneuvers, a consistent, complete set of high-quality derivatives could not.
DERIVATIVEANALYSIS Flight Data A digital computer program employing a maximum likelihood estimator method was used to determine sets of derivatives and uncertainty levels for the longitudinal and lateral-directional modes from flight data. This computer program and its theory, mathematical model, and practical application are documented in references 4 to 6 .
The derivative analysis was usually performed within a week of the flight using a "best estimate'? set of moments of inertia. After the completion of the derivative-extraction flights, the moments of inertia were experimentally determined using the A i r Force Flight Test Center's Moment of Inertia Facility. The derivatives for presentation in this report were adjusted to reflect the experimentally determined moments of inertia. In addition, the derivatives were adjusted to a reference longitudinal center of gravity. The reference center of gravity varied as a function of wing sweep, and the variation is documented in table 2 . A variable reference was used to provide a derivative data set consistent with the performance flight data. These reference values represent an average flight center of gravity for each wing sweep.
Geometric Models Analytical model derivatives were obtained from two large computer programs based on a grid determined by dividing the aircraft geometry into constant pressure panels. Integration of these pressures yielded the forces and moments. Both programs assume inviscid, incompressible (with Prandtl-Glauert corrections), attached flow. They differ in the way they represent the aircraft geometry and in the solution for the constant pressure panels.
The first program, referred to as the WING-BODY program, models both lifting surfaces (wings) and a body. It is a potential-doublet panel program in which the wing-body combination is represented by a large number of distributed singularities which are used to satisfy the linearized potential equations. It can be used for both supersonic and subsonic analysis. Further information on the theory and use of the program is given in references 7 and 8 , respectively.
For the second program, referred to as the VORTEX-LATTICE program, the lifting surface planforms are represented with a lattice of horseshoe vortexes.
By solving the flow boundary condition of each horseshoe vortex, the elemental lift of each panel can be determined. The program is used for subsonic analysis.
It can be used to compute the potential a s well as the vortex leading- and side- edge components of forces and moments; however, only the potential solution was used for these studies. Further information on the theory and use of similar programs is given in references 9 to 11.
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In using the above programs , an attempt was made to model the geometry
in a basic , conceptual manner. This was done to best represent the manner
in which these programs are mechanized to minimize computer time. A WING-BODY panel model that was used to obtain rolling tail control effectiveness is shown in figure 3 . Only the right half of this model was used for the typical case where vehicle symmetry is assumed. The panel coordinates are the basic inputs to the program.
A typical VORTEX-LATTICE planform model is shown in figure 4. The panels are not shown since paneling is an internal process of the program. Only the planform view is shown since, for this case the wings are coplanar. It was not necessary to model wing camber in either program.
DATAPRESENTATION The majority of the flight data were obtained over'the airplane's Mach number and angle of attack ranges, predominantly at wing sweep angles of 2 6 O , 35O, and 5 8 O with the airplane in a clean configuration (that is, landing gear and flaps retracted) Additional flight data were obtained at low speeds (Mach numbers from 0.25 to 0 . 4 5 ) with various combinations of landing gear and flap positions for wing sweep angles of 1 6 O , 20°, and 26O. A l l the data are presented as a function of angle of attack for specific Mach number ranges. Where possible, a recommended fairing is given to aid in the interpretation of the flight derivatives. In addition certain derivatives that are strong functions of Mach number as well as angle of attack are presented as functions of Mach number for a given angle of attack.
Uncertainty levels are shown for all flight data. These uncertainty levels are proportional to the Cram&-Rao bounds described in reference 5 and were obtained by multiplying the Cram&-Rao bounds of reference 5 by a simple scale factor of 5 . The factor is justified in reference 6 . In a more general sense , the uncertainty level can be interpreted as a measure of the relative accuracy of each derivative value.
The analytical model derivatives were computed for the clean configuration at a Mach number of 0 . 6 0 for wing sweep angles of 2 6 O , 3 5 O , and 58O and at a Mach number of 1 . 2 0 for a wing sweep angle of 58O. These derivatives are only presented where the assumptions used to compute them are considered valid. Thus due to the assumption of attached flow , the analytical model data are only valid , and hence only presented for low angles of attack.
RESULTS AND DISCUSSION Since a primary purpose of this report is to provide a stability and control data base, many of the results are presented without discussion.
Longitudinal Derivatives The clean-configuration longitudinal derivatives for a wing sweep angle of 2 6 O are shown in figure 5 as a function of angle of attack and in figure 6 as a function of Mach number. For angles of attack less than 7 O , the flight and analytical model values for CNA are in good agreement. Above an angle of attack of approx- imately 8O, the magnitude of the flight CNA decreases significantly as compared to the analytical model values obtained from linearized potential theory. The trend exhibited in the flight-determined CNA values is substantiated by figure 7 , which shows a reduction in the section normal-force slope, cn , with increasing angle of a attack for four wingspan locations. These section data were obtained independently by integrating the flight-determined wing pressure coefficients.
Even though CNA has been shown to decrease with angle of attack, the actual angle of attack at which the break in the slope occurs can be easily misinterpreted from the data in figure 5(a). The maximum likelihood estimator used to obtain the flight derivatives provides a linearized derivative from the transient motion of the aircraft. For longitudinal derivatives, the average angle of attack is used as the independent variable; the actual angle of attack, being a state variable, will typically vary ? 2 O from trim. The resulting linearized derivative (in this case, C N A ) tends to acquire an average slope over the angle of attack range for the maneuver.
This, in effect, filters any sharp breaks in the coefficient. Thus, even though the first indications of a break in the data of figure 5(a) occur at an angleof attack of approximately 7 O , the actual break occurs at an angle of attack between 8 O and g o , as shown in figure 8 , which was taken from reference 1 2 . Note that in this reference, the normal-force slope break is correlated with buffet intensity rise, which is an indication of flow separation.
The flight-determined CMA values (fig. 5 (a)) decrease with angle of attack while the analytical model values do not. This lack of linearity for the flight values is related to the similar reduction in C N A . The apparent scatter in CMA is a Mach number effect, as shown in figure 6 ( a ) .
CNDE and CMDE are presented in figure 5 (b) . The flight values for CMDE a r e
significantly lower than the analytical model values. The analytical model predictions for CMDE can be considered the theoretical upper limit for this planform configuration because they do not account for the reduction in dynamic pressure on the horizontal tail, which is caused by the wing wake.
Although the flight values of CMQ appear to contain considerable scatter (fig. 5 (c)) , much of this apparent scatter is a Mach number effect, as shown in figure 6 ( b ) . The correlation between the flight and analytical model derivatives is considered to be good even though the flight values are higher, because CMQ is historically difficult to estimate theoretically.
The clean-configuration longitudinal derivatives for a wing sweep angle of 35O a r e shown in figure 9 a s a function of angle of attack and in figure 1 0 as a function of Mach number. In general, the previous discussion for a wing leading- edge sweep angle of 26O also applies to the 35O wing sweep data.
Figures 11 and 1 2 present the clean-configuration longitudinal derivatives for a wing sweep angle of 58O as a function of angle of attack and as a function of Mach number, respectively. A s shown in figure 11 ( a ) , CNA increases slightly with angle I of attack. This is due to the formation of a leading-edge vortex , which is character- istic of aircraft with highly swept wings.
The subsonic flight values of CMDE included in figure ll(b) are slightly lower than the prediction. However , the analytical model greatly overpredicts CMDE at Mach 1 . 2 0 , which is a result of the overestimation of the aft movement of the center of pressure on the horizontal stabilizer due to an assumption of established super- sonic flow. This discrepancy may indicate that the flow over the horizontal tail of the flight vehicle is not established supersonic flow.
The longitudinal derivatives obtained with various combinations of landing gear and flap positions at wing sweep angles of 16O, 20°, and 26O are shown in figure 1 3 .
All these data were obtained at Mach numbers less than 0.45. The flaps-deflected configuration consisted of having the Krueger leading-edge flaps deployed and the Fowler trailing-edge flaps deflected 3 0 ° . Of particular significance is the increase in CMA due to flap deflection at a wing sweep angle of 26O.
Lateral-Directional Derivatives The clean-configuration lateral-directional derivatives for a wing sweep angle of 26O are shown in figure 1 4 as a function of angle of attack and in figure 15 as a function of Mach number. These flight derivatives exhibit more scatter and higher uncertainty levels than the clean-configuration lateral-directional derivatives at other wing sweeps. For a low-sweep configuration , greater uncertainty would be expected at higher angles of attack where buffet and flow separation exist. However , figure 1 5 shows that the scatter in these derivatives exists at an angle of attack of 4 O and increases with increasing Mach number. The pilot's comments indicate that a low level of buffet exists at these low angles of attack , beginning at a Mach number a s low a s 0.85. This slight indication of flow separation on the wing was not of sufficient magnitude to affect the flying qualities. Its primary effect appears to be an increase in the uncertainty in the flight derivative analysis for a wing sweep angle of 26O.
The VORTEX-LATTICE program was used to compute analytical model values for CNB and C Y B by representing the side view of the body and the vertical tail as wing planforms and disregarding the wing. A s shown in figures 14(a) and 14(g) , these analytical model derivatives are reasonably close to the flight values. A similar analysis could have been conducted using the WING-BODY program , but the imple- mentation would have been more complex because of the input requirements.
Analytical model values for CNDA and CLDA were computed using both programs.
Using the VORTEX-LATTICE program, CLDA was computed based on the horizontal tail lift and center of pressure. To compute CNDA, it was assumed that CNDA is a result of the differential drag from the horizontal stabilizer. Assuming the far field solution for drag due to the incremental horizontal stabilizer lift, the following expression was obtained: CNDA = (CLDA ) (tan a ) TO compute the two derivatives using the WING-BODY program, the airplane was modeled a s shown in figure 2 . The resulting rolling and yawing moments were
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direct outputs from the program. The analytical model and flight derivatives are shown in figure 14(d). This figure shows that the WING-BODY program computed a value for CLDA close to the flight value and that the value for CNDA based on the results from the VORTEX-LATTICE program is a good estimate.
The flight and analytical model values for CNDR and CLDR a r e shown in figure 14(e). For the VORTEX-LATTICE analysis, the rudder was modeled a s aft camber in the side views of the vertical tail. When modeling a control surface of the aft camber type with the WING-BODY program, it is common procedure to scale down the resulting control derivatives to compensate for the WING-BODY program's historical tendency to overpredict the effects of aft camber. For this report, a scale factor of one-half was selected; however, an analysis of the results indicates that a scale factor of about two-thirds would have been more appropriate.
The flight derivatives are generally within the boundaries of the predicted values.
The clean-configuration lateral-directional derivatives for wing sweep angles of 35O and 58O a r e shown in figures 16 to 1 9 . The analytical model derivatives were computed using the same techniques discussed for the 26O wing sweep data.
The correlations between the flight and analyticalmodel derivatives follow the same trends. Of particular interest in these data are the nonlinearities in CLB , C L P , and
CLDS with respect to angle of attack (figs. 16 to 1 8 , parts (a), (b) , and (f)) . A l l
three of these derivatives have primary effects on the handling qualities.
The lateral-directional derivatives obtained with either the landing gear extended or the flaps deflected at a wing sweep angle of 1 6 O or 26O are shown in figure 2 0 . The Mach number range and the flaps-deflected configuration were the same a s those for the longitudinal derivatives of figure 13. To determine the in- cremental effects of the landing gear and flap configurations as compared with the clean configuration, the data of figure 2 0 should be compared with those of figure 14.
Of the derivatives presented, CNB , C L P , CLDS , and CNDS show the most significant
effects. A definite, and expected, decrease in CNB results from the extension of the landing gear. CLP increases when the flaps are deflected as a result of the increase in the actual wing area. CLDS and CNDS also increase when the flaps are deflected as a result of having higher levels of lift to decrease.
To check the validity of the angle of attack measurement, angle of attack was calculated based on the value of sin a . The value and uncertainty of sin c1 were obtained from the maximum likelihood estimator used to compute the flight deriv- tives. The calculated angle of attack includes the lo angle between the angle of attack reference axis and the vehiclebody axis.
In figure 2 1 , calculated angle of attack is correlated with reference angle of attack for Mach numbers near 0 . 7 0 . These data indicate that the reference angle
of attack is correct from 3 O to l o o . At higher angles of attack, the results are
inconclusive because the uncertainties are high and the values were obtained from high load factor maneuvers, which undoubtedly induced aeroelastic effects.
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CONCLUDING REMARKS A flight investigation was conducted to provide a stability and control derivative data base for the F-111 transonic aircraft technology (TACT) research aircraft.
Both longitudinal and lateral-directional derivatives were obtained for the clean configuration (that is, landing gear and flaps retracted) at wing sweep angles of 2 6 O , 3 5 O , and 5 8 O . In addition, the effects of landing gear extension and flap deflection were obtained for several low speed and low wing sweep conditions.
Data were obtained for angles of attack from approximately 3 O to 1 4 O for a Mach number range from approximately 0 . 2 5 to 1 . 7 0 .
The VORTEX-LATTICE and WING-BODY analysis programs were used to predict selected derivatives based on vehicle geometry. These derivatives, referred to as the analytical model derivatives, were obtained for wing sweep angles of 2 6 O , 3 5 O , and 58O at a Mach number of 0.60 and for a wing sweep angle of 58O at a Mach number of 1 . 2 0 .
A correlation between the flight-determined and analytical model derivatives indicated both the strengths of the prediction methods and the variation of the Of particular significance was the break flight derivatives from potential theory.
in the flight normal-force slope which occurred at a relatively low angle of attack.
This break was correlated with data from two independent sources.
The validity of the angle of attack measurement was verified independently at a Mach number of 0 . 7 0 for angles of attack from 3 O to loo.
D r y d e n FZight R e s e a r c h C e n t e r National Aeronautics and Space Administration E d w a r d s , C a l i f . , N o v e m b e r 17, 1977 1 0 REFERENCES
1. Marquardt, R . F .: Transonic Aircraft Technology - TACT Aircraft Geometric
Characteristics. MAIR 595-19 GeneralDynamics,April 16 1973.
2 . Hallissy , James B .; and Ayers , Theodore G . : Transonic Wind-Tunnel Investi-
gations of the Maneuver Potential of the NASA Supercritical Wing Concept.
Phase I . NASA TM X-3534, 1977.
3. SakamotoGlennM.: AerodynamicCharacteristics of aVane Flow Angularity Sensor System Capable of Measuring Flightpath Accelerations for the Mach Number Range From 0 . 4 0 to 2 . 5 4 . NASA TN D-8242 1976.
4 . Maine Richard E . ; and Iliff Kenneth W .: A FORTRAN Program for Determining
Aircraft Stability and Control Derivatives From Flight Data. NASATN D-7831 1975.
5 . I l i f f , Kenneth W . ; and Taylor Lawrence W . , Jr . : Determination of Stability
Derivatives From Flight Data Using a Newton-Raphson Minimization Technique.
NASATN D-6579, 1 9 7 2 .
6 . I l i f f , Kenneth W . ; and Maine Richard E . : Further Observations on Maximum
Likelihood Estimates of Stability and Control Characteristics Obtained From Flight Data. AIAA Paper 77-1133, Aug. 1 9 7 7 .
7 . Woodward, Frank A .: Analysis and Design of Wing-Body Combinations at
Subsonic and Supersonic Speeds. J . Aircraft, vol. 5 no. 6 , Nov. -Dec . 1968
pp . 528-534.
8 . Gustavsson S . Anders L .: A Computer Program for the Prediction of Aero-
dynamic characteristics of Wing-Body-Tail Combinations at Subsonic and SupersonicSpeeds.Part 2 . Report AU-635 FlygtekniskaForsoksanstalten (The Aeronautical Research Institute of Sweden) 1 9 7 2 .
9 . MargasonRichard J .; and Lamar, John E.: Vortex-Lattice FORTRAN Program
for Estimating Subsonic Aerodynamic Characteristics of Complex Planforms.
NASATN D-6142, 1 9 7 1 .
1 0 . Lamar John E . ; andGlossBlair B . : SubsonicAerodynamicCharacteristics
of Interacting Lifting Surfaces With Separated Flow Around Sharp Edges Predicted by a Vortex-Lattice Method. NASA TN D-7921 1975.
11. Luckring, James M . : Some Recent Applications of the Suction Analogy to
Asymmetric Flow Situations.Vortex-LatticeUtilization NASA SP-405 1 9 7 6 , pp. 219-236.
1 2 . Monaghan, Richard C .: Flight-Measured Buffet Characteristics of a Super-
critical-Wing and a Conventional Wing on a Variable-Sweep Airplane.
NASA TP-1244, 1978.
1 1 1 1 1 1 TABLE 1. -PHYSICAL CHARACTERISTICS OF F-111 TACT RESEARCH AIRCRAFT
Fuselage length, m (ft) . . 22.39 (73.47)
Wing- 2 2
Reference planform area, m (ft ) . 56.1 (603.9)
Reference iongitudinal length, m (ft) . 3.65 ( I O . 4875)
Reference span, m (ft) . 1 8 . 1 (59.3)
h , deg . . 1 0 to 58
Taper ratio at h = 1 6 O . 0.542
Aspect ratio at h = 1 6 O . 5 . 8 2
Dihedral, . . . 0
Horizontal tail- 2 2
Area (movable), m (ft ) . 1 4 . 2 (153)
Span, m (ft) . 8 . 9 4 ( 2 9 . 3 )
h , deg . . 5 7 . 5
Deflection, elevator is average symmetric deflection where trailing edge up is negative and aileron is right (movable
area) minus left (movable area), deg . 15 to -30
Vertical tail-
Area, m 2 (ft2) . 1 0 . 4 (112)
Span, m (ft) . 2 . 7 1 (8.90) A , d e g . . 55 Rudder- 2 . 7 2 ( 2 9 . 3 ) Area, m 2 (ft ) .
Span, m (ft) . 2 . 4 3 ( 7 . 9 8 )
Deflection, trailing edge left positive, deg . +30 Spoilers (two per side)- Type . Flap Total area, rn2 (ft ) . 2 . 4 7 ( 2 6 . 6 ) Deflection (maximum), average right minus average left where trailing edge up is negative, deg . 45 Leading-edge flaps (three sections per wing)- Type * Krueger 2 2
Total area, m (ft ) . 5 . 1 1 ( 5 5 . 0 )
Deflection (maximum), deg . 45
Trailing-edge flaps (four per side)-
Type . . Fowler, single slotted
Total area, m 2 (ft ) . 1 2 . 5 4 (135)
Deflection (maximum), deg . 30
TABLE2.-REFERENCECENTER OF GRAVITY A S A FUNCTIONOF WING S'WEEP R e f e r e n c e center of gravity 0.245 0.255 0 . 2 7 5 30 0 . 2 8 0 0 . 2 9 0 0.305 45 0.310 50 0.320 58 Figure 1 . F-111 TACT aircraft.
L Spoiler deflection, deg -20 1 1 I
-4 I r l 1 I I I I
lo r
Aileron deflection, ;v?vl
deg
-10 1 I I
- Yaw rate, 0 u- rc- deglsec -10 - 1 I I I 1 J R o l l rate,
4:bnT
deglsec -40 I I 4 r - Angle of sideslip, "" deg -A I I 0 4 8 12 16 20 24 28 Time, sec Figure 2 . Typicallateral-directionalmaneuverused for derivative extraction.
Figure 3 . W I N G - B O D Y modeZ of F - 1 1 1 TACT aircraft. h = 26O.
Figure 4 . TypicalVORTEX-LATTICEpZanform model.
1 5 Flight data- M 0 0.45 to 0.75 0 0.75 to 0.84 0 0.84 t o 0.90 a 0.90to 0.94 X 0.94 to 1.00
I Uncertainty level
Analytical model data- 0 . 1 6 ~ VORTEX-LATTICE model, M = 0.60 _" WING-BODY model, 0 . 1 2 M = 0.60 Flight fairing- CNA* 0 . 0 8 M per deg -" 0.60 ". - 0.85 0.04 0.90 0.95 0 .oo -0 - 0 8 - 0 . 0 6 X " _ \ .
-0.04 per deg -0.02 0 . o o ( a ) C N A , C M A .
Figure 5 . Longitudinal derivatives obtained from flight data as a function of angle of attack and comparison with analytical model r e s u l t s . h = 26O; clean configuration.
Flight data- M 0 0.45 to 0.75 0.75 to 0.84 0 0.84 to 0.90 A 0.90 to 0.96 X 0.96to 1.00
I Uncertainty level
0.08 Analytical model data- __ VORTEX-LATTICE model, M = 0.60 "_ WING-BODY model, 0.04 M = 0.60 CNDE* 0 .oo per deg M 0.60 " . -
1 0.85
- -0.04 0.90 " _ 0.95 I -0 -08 - I - -0.03 CMDE, - - 0 . 0 2 per deg
-0.01 I
0 .OD 2 4 6 8 10 12 4 deg ( b ) CNDE, CMDE.
F i g u r e 5. Continued.
I Flight data- M 0 0.45 to 0.75 0 0.75 t o 0.84 0 0.84 to 0.90 0.90tO 0.96 X 0.96to 1.00
1 Uncertainty level
Analytical modeldata- __ VORTEX-LATTICE model, M = 0.60
I
-60 1 Flight fairing-
M I T _" 0.60 "" 0.85 C*Ql - 4 0 per rad " " - 0.90 ".
0.95 -20 Figure 5. Concluded.
. . " " . . . . . . .
o a = 4 " % 1 "
1 Uncertainty level
.16 .12 .08 per deg .04 -.08 -.06 CMA, per deg Q -.02 CNA,CMA.
Figure 6 . Longitudinal derivatives obtained from flight data as a function of Mach number. h = 26O; clean configuration.
o a = 4 " * l o
I Uncertainty level
-.04 I
I J
0 L
-80 -60 CMQ, -40
T dJ
per rad -20
.4 I - 1 J
.5 .6 .7 .a .9 1.0 M ( b ) CMDE, CMQ I Figure 6 . Concluded.
2 0 Row o A O B o c A D D C B A Row
-"8 0" 0
.08 ' a 0 8 0
deg . 0 4
Figure 7 . Section normal-force slope as a function of angle of attack. M = 0.60; h = 26O.
M - 0.71 -" 0.82
1.2 r
F i g u r e 8 . Normal-force coefficient as a f u n c t i o n of angle of attack (from ref. 1 2 ) .
2 1 Flight data- M 0 0.55 t o 0.75 0 0.75 t o 0.84 0 0.84 to 0.90 a 0.90 to 0.96
I Uncertainty level
Analytical modeldata- ~ VORTEX-LATTICE model, M = 0.60 "_ WING-BODY model, M = 0.60 Flight fairing- M "_ 0.60 "" 0.85 0.90
0 - 0 4 1
- 0 . 0 3 1
1 -1 2 J
0.00 L " ~-
4 6 2 F : 10 12 1 4 1 6 a, deg ( a ) CNA, CMA.
Figure 9 . Longitudinal derivatives obtained from flight data as a function of angle of attack and comparison with analytical model results. h = 35O; clean configuration.
Flight data- M 0 0.55 t o 0.75 0.75 t o 0.84 0 0.84 t o 0.90 A 0.90 t o 0.96
I Uncertainty level
Analytical model data- - VORTEX-LATTICE model, M = 0.60 0.08 I _" WING-BODY model, M = 0.60
0.04 t
9 Flight fairing-
M "_ 0.60 "" 0.85 -0 - 0 4 0.90
I
-0.06 1 -0.01
0 .oo t 1 I 4 I I I I
2 4 6 8 10 12 1 4 16 a, deg ( b ) C N D E , C M D E .
Figure 9 . Continued.
I Flight data- M 0 0.55 to 0.75 0 0.75 to 0.84 0 0.84 to 0.90 A 0.90 t o 0.96
I Uncertainty level
Analytical model data- - VORTEX-LATTICE model, M = 0.60 Flight fairing- M "_ 0.60 0.85 0.90 ____"
4-F
J 10 12 14 16 a, deg Figure 9 . Concluded.
0 a = 4 " .16
I Uncertainty level
-12 CNA, Per deg .OB . 0 4 -.06 --OB
-.02 I
-1 I O .5 . 6 .7 .8 - 9 1.0 M ( a ) C N A , C M A .
Figure 10. Longitudinal derivatives obtained from flight dataas a functionofMachnumber. = 35O; clean configuration.
o a=4O * l o -.04 1 Uncertainty level -.03 CMDE, "02 per deg -.01 _1 .5 .6 .7 .8 .9 1.0 M ( b ) CMDE, CMQ.
Figure 10. Concluded.
Flight data- M 0 0.50to 0.88 0 0.88 to 0.96 0 0.96to 1.10 A 1.10 to 1.35 X 1.35 to 1.72
I Uncertainty level
Analytical modeldata- - VORTEX-LATTICE model, 0.12 M = 0.60 "_
O.l6 I
WING-BODY model, M = 0.60 "_ CNA, 0 . 0 8 WING-BODY model, per deg M = 1.20 " Flight fairing- 0.04 M "" 0.60 0.90 "_ 1.20
- @ - 0 8 r
- 0 . 0 6 ( a ) CNA, CMA.
Figure 11. Longitudinal derivatives obtained from fZight data as a function of angle of attack and comparison with analytical model results. h = 58O; clean configuration.
Flight data- M 0 0.50to 0.88 0.88 to 0.96 0 0.96 to 1.10 A 1.lOto 1.35 X 1.35tO 1.72
1 Uncertainty level
0 . 0 8 0.04 1
Analytical modeldata- - VORTEX-LATTICE model, CNDE, M = 0.60 _" per deg O m o 0 WING-BODY model, M = 0.60 _" WING-BODY model, -0.04 M = 1.20
t
Flight fairing-
-0.08 L A 1 1
M "" 0.60 0.90 " _ -0 - 0 4 1.20 L""
-0.01 1
I ( b ) CNDE, CMDE.
F i g u r e 1 1 . Continued.
I
Flight data- M 0 0.50 to 0.88 0 0.88 to 0.96 0 0.96to 1.10 A 1.10 to 1.35 X 1.35 to 1.72
I Uncertainty level
Analytical model data- ~ VORTEX-LATTICE model, M = 0.60
s
Flight fairing- M
"-1
"" 0.60 0.90 -" 1.20 $ 2 4 4 6 8 10 12 1 4 a, deg Figure 1 1 . Concluded.
2 9 I I o a = 4 " * 1 "
I Uncertainty level
0.12
0.16 1
CNA, - per deg
- *
0 . 0 4
-
-0.08 -0 - 0 6 -0.04 per deg ' -0.02 2 2 2 0.00 I-~ 0 . 4 0 . 6 0 . 8 1.0 1 . 2 1 . 4 1 . 6 1.8 M ( a )C N A ,C M A .
Figure 12. Longitudinal derivatives obtained from flight data as a function of Mach number. h = 58O; clean configuration.
-0 - 0 4 0 a = 4 " * I o
1 Uncertainty level
-0.03 CMDE, per deg " O .02 -0.01 0 .oo - 4 0 -30 CMQ, per rad -20 -10 M ( b ) C M D E , C M Q .
Figure 1 2 . Concluded.
Flagged symbol denotes 0.12 flaps deflected
I
Solid symbol denotes landing gear extended CNA, 0.08 per deg
I *
J 0 . 0 0 L 6 8 10 12 14 4 deg ( a ) CNA, CMA .
Figure 13. Longitudinal derivatives obtained from flight data for various combinations of landing gear and flap positions. Low s p e e d .
A , deg
I Uncertaintylevel
Flagged symbol denotes flaps deflected Solid symbol denotes landing gear extended o - 0 8 ! 0.04 CNDE, 0.00 per deg - 0 -04 I
-0.08 i
-0 -04
I
-0 -03
t
-0.01
0 .oo i
( b ) CNDE, CMDE.
Figure 1 3 . Continued.
A , deg
I Uncertaintylevel
Flagged symbol denotes
-30 -401
flaps deflected Solid symbol denotes landing gear extended
- I 0 t
"J 1 4 Figure 13. Concluded.
Flight data- M 0 0.55 to 0.75 0 0.75 to 0.84 0 0.84 to 0.90 A 0.90 to 0.94
I Uncertainty level
Analytical modeldata- - VORTEX-LATTICE model, M = 0.60 Flight fairing- M "_ 0.60 "" 0.90 - 0.0004 " ".L "A 0.0000 -
-0 SO03 c
CLB, -
per deg -' . O o 2
-0.001 - ( a )C N B ,C L B Figure 14. Lateral-directional derivatives obtained from flight data as a function of angle of attack and comparison with analytical model r e s u l t s . h = 26O; cleanconfiguration.
Flight data- M 0 0.55 to 0.15 0 0.75to 0.84 0 0.84 to 0.90 a 0.90 to 0.94
I Uncertainty level
Analytical model data- ~ VORTEX-LATTICE model, M = 0.60 Flight fairing- 0 .o M "_ 0.60 "" 0.90 CNP, -0.1 per rad -0.2 -0 - 3 ( b ) C N P , C L P .
Figure 14. Continued.
.. _. . .... . .-..... .
e Flight data- M 0 0.55 t o 0.75 0 0.75to 0.84 0 0.84 to 0.90 a 0.90 t o 0.94
I Uncertainty level
Analytical modeldata- __ VORTEX-LATTICE model, M = 0.60 0.4 O - 1 Flight f a i r i n g - -" M = 0.60, 0.90 1 -
CNR* 0.0 L
per rad -0.4 - 0 -5 CLR, per rad Figure 1 4 . Continued.
I.
Flight data- M 0 0.55 to 0.75 0 0.75tO 0.84 0 0.84 to 0.90 A 0.90 to 0.94
I Uncertainty level
Analytical modeldata- ~ VORTEX-LATTICE model,
0 ' 0 0 0 4 1 T - M = 0.60
"_ WING-BODY model,
"_""
M = 0.60 CNDAl 0 .oooo per deg
+
-$= Flight fairing-
M -0 -0004 "- 0.60 "" 0.90
I
( d ) C N D A , CLDA.
Figure 14. Continued.
Flight data- M 0 0.55 to 0.75 0 0.75 to 0.84 0 0.84 t o 0.90 A 0.90 to 0.94
1 Uncertainty level
-0.0020 r
I Analytical model data-
- VORTEX-LATTI CE model, -0.0015 M = 0.60 "_ WING-BODY model, M = 0.60 CNDR* -0.0010 per deg Flight fairing- M "_ -0.0005 0.60 "" 0.90
I
0.0000 L - I
0.0005 CLDR,
per deg o'oooo I I--
I - - 0 . 0 0 0 5 A -0.0010 - - " 2 4 6 8 10 12 a, de9 ( e ) CNDR, CLDR.
Figure 1 4 . Continued.
Flight data- M 0 0.55 to 0.15 0.15 to 0.84 0 0.84 to 0.90 A 0.90 to 0.94
I Uncertainty level
Flight fairing- M --- 0.60 0.0002 0.90 L
0.0000 I
CNDS, - " per deg -O 'ooo2
@
1 1 -0 -0004
t
-0.0006 -0.0016 - - -0.0012 -0 -0004
i
-
0 .oooo - '
2 4 6 8 1 0 12 4 deg ( f ) CNDS, CLDS.
Figure 14. Continued.
....... ".
Flight data- M 0 0.55 to 0.75 0 0.75 to 0.84 0 0.84 to 0.90
* 0.90 to 0.94
I Uncertainty level
Analytical modeldata- - VORTEX-LATTICE model, M = 0.60 Flight fairing- - 0 . 0 2 0
r
M "_ 0.60 - "_ 0.90 -0.015
!
-0 -005
0 .ooo t
0.006 r - 0.004 CYDR, per deg * O o 2 .
0.000 L
-0.002 I
(9) C Y B ,C Y D R .
Figure 14. Continued.
Flight data- M 0 0.55 to 0.75 0.75 to 0.84 0 0.84 to 0.90 a 0.90 to 0.94
0.008 I Uncertainty level
Flight fairing- "- M = 0.60, 0.90 0.004 I T
-0 - 004
-0 .OOB CYDS, 0.001 Per deg 0 .ooo
- 0 . 0 0 1 '
2 4 6 8 10 1 2 a, deg ( h ) C Y D A ,C Y D S .
Figure 1 4 . C o n c l u d e d .
0 a=4O f 1"
I Uncertainty level
0.0016
0 . 0 0 1 2 I
CN B f 0 . 0 0 0 8 per deg
I
0 - 0 0 0 4
0 .oooo I
-0 SO032 -0 - 0 0 2 4 T CLB, per deg -o.oo16
t
I - 0 . 0 0 0 8 1 - 1
0 .oooo t
0 . 4 0.5 0.6 0 . 7 0.8 0.9 1.0 M ( a )C N B , C L B .
Figure 15. Lateral-directionalderivativesobtained from flight data as a function of Mach number.
h = 26O; clean configuration.
0 a = 4 " * 1 "
1 Uncertainty level
- 0 . 0 0 2 0 -0.0015 C N D R f -0.0010 per deg -0 moo05 0 .oooo
-
- 0 . 0 2 0 .
-0.015 CY B, per deg - o ' o l o - 0 . 0 0 5 . I J
0 .ooo -
0.6 0.7 0 . 8 0.9 1 . 0 0 . 4 0 . 5 M ( b ) CNDR, C Y B .
Figure 1 5 . Continued.
o a = 4 " * l o
I Uncertainty level
- O m O ' I O 4 - .
- 0 . 0 0 0 3 I CNDS, -0.0002 .
per deg -0.0001
t
0 . 0 0 0 0 1- 1
-0.0016
I
-0.0012
t
CLDS, -0.0008 - per deg - 0 -0004
0 .oooo 0.4 1 . 0.5 d.6 d.7 i.8 d.9 I'.O
M ( c ) CNDS, CLDS, Figure 15. Concluded.
Flight data- M 0 0.68 t o 0.79 0 0.79 to 0.90 0 0.90 to 0.93 0.0016 0.98
r
I I Uncertainty level
0.0012 Analytical modeldata- T P A " $ - VORTEX-LATTICE model,
CN R t "
T - L m -..- M = 0.60
- - per dhg 0 - 0 0 0 8 Flight fairing- M 0.0004 _" 0.60 "" 0.90
I
-0.004
- 0 - 0 0 3 I
I T
( a ) C N B , C L B .
Figure 16. Lateral-directional derivatives obtained from flight data as a f u n c t i o n of angle of attack and comparison with analytical model results.
h = 3 5 O ; clean configuration.
Flight data- M 0 0.68 to 0.79 0.79 to 0.90 0 0.90 to 0.93 a 0.98
I Uncertainty level
I Analytical model data- - ~ VORTEX-LATTICE model, 0 . 1 M = 0.60 CN P , Flight fairing- . .
perrad o.o M "_ 0.60 "" 0.90 - -0.1 ~~ - 0 . 2 - - 0 . 8 - - 0 . 6
CLP, -
per rad - - - 0 . 2
a'
( b ) CNP. CLP.
Figure 16. Continued.
Flight data- M 0 0.68 to 0.79 0 0.79 to 0.90 0 0.90 t o 0.93 A 0.98
I Uncertainty level
Analytical model data- __ VORTEX-LATTICE model, M = 0.60 Flight fairing- "_ M = 0.60, 0.90 CNR, - per rad - 0 . 4 - 0 . 4 CLR, per rad
'I
- O a 4 I
( c ) C N R , C L R .
Figure 16. Continued.
Flight data- M 0 0.68 to 0.79 0 0.79 to 0.90 0 0.90 t o 0.93 A 0.98
I Uncertainty level
0 . 0 0 0 8 Analytical modeldata- __ VORTEX-LAlllCE model, M = 0.60 "_ 0 . 0 0 0 4 WING-BODY model, M = 0.60 Flight fairing- M " _ 0.60 "" 0.90 - 0 . 0 0 0 8 _I- -0.0016
-0.0012 1 1 -~
I 1
0 .oooo 1
2 4 6 10 12 1 4 ( d ) C N D A , CLDA.
Figure 16. Continued . . . .."
I I II I Flight data- M 0 0.68 to 0.79 0 0.79 to 0.90 0 0.90 to 0.93 A 0.98
I Uncertainty level
Analytical model data- - 0 . 0 0 2 0 - VORTEX-LATTICE model, M = 0.60 _" __ WING-BODY model, -0.0015 ""$~"p-"+ @ M = 0.60 Flight fairing- "_ M = 0.60, 0.90 - 0 . 0 0 0 5 L . -~ 1 0 . 0 0 0 0 0.0010
i
0 . 0 0 0 5 CLDR, ~ - ~" per deg o.oooo - 0 . 0 0 0 5 ( e ) CNDR, CLDR.
Figure 1 6 . Continued.
Flight data- M 0 0.68to 0.79 0 0.79 t o 0.90 0 0.90 t o 0.93 a 0.98 0.0004
I Uncertainty level
Flight fairing- 0 . 0 0 0 2 M "_ 0.60 "" 0.90 CNDS* 0 .oooo per deg - 0 . 0 0 0 2 - 0 - 0 0 0 4 -0.0016 -0.0012 CLDS, per deg-o'oooE -0.0004
-
10 12 1 4 C f ) CNDS, CLDS.
F i g u r e 16. Continued.
I
Flight data- M 0 0.68 to 0.79 0 0.79 to 0.90 0 0.90 to 0.93 A 0.98
I Uncertainty level
Analytical model data- ~ VORTEX-LATTICE model, M = 0.60 -0.020 Flight fairing- M -0.015 " - 0.60 "" 0.90 cyB* -0.010 per deg 0.006
I
(8) C Y B ,C Y D R .
Figure 16. Continued.
Flight data- M 0 0.68 t o 0.79 0.79 t o 0.90 0 0.90 t o 0.93 A 0.98
I Uncertainty level
0 . 0 0 6 Flight fairing- "_ M = 0.60, 0.90
I
O - O o 4 t
- 0 . 0 0 4 - 0 . 0 0 8 0 . 0 0 2
!
per CYDS* deg O - O o l 1
0 .ooo
-0.001 I
(h) C Y D A , C Y D S .
Figure 16. C o n c l u d e d .
0 a = 4 " * 1 "
I Uncertainty level
0.0016 0.0012 CNB' 0.0008 per deg 0.0004
I
-0.0032 I -0 -0024 CL B, per deg - o m o o 1 6 -0 - 0 0 0 8 0 . 0 0 0 0 L - L -1 - 1 . "L - "-_1 0.4 0.5 0.6 0.7 0.8 0.9 1.0 M ( a ) C N B , CLB d Figure 1 7 . Lateral-directional derivatives obtained from h = 3 5 O ; clean flight data as a function of Mach number.
configuration.
0 a = 4 " * 1 " - 0 . 0 0 2 0
I Uncertainty level
-0.0015 CNDR, (9 p e r deg -o'oolo -0 - 0 0 0 5 0 . 0 0 0 0 - 0 . 0 2 0 -0 mol5 C Y B, p e r deg - O . O 1 ' - 0 a005 0 . 0 0 0 1 L 0 . 4 0.5 0 . 6 0 . 7 0.8 0.9 1.0 M ( b ) C N D R , C Y B .
Figure 1 7 . Continued.
I 111111111111111111 . I . 1 ” ” 1 1 . 1 1 1 1 1 1 1 . 1 1 1 1 . . . ” ” 1 ” . “ . -.- 0.0004 0 a = 4 O f 1”
1 Uncertainty level
0.0002 I T T
-0.0002 1 T T
-0.0016 - - -0.0012 CLDS, .0°08 per deg -0.0004 ( c ) CNDS, CLDS.
Figure 17. Concluded.
Flight data- M 0 0.55 to 0.88 0.88 to 0.96 0 0.96 to 1.10 6 l . l O t o 1.35 X 1.35to 1.70
I Uncertainty level
- 0.0016 Analytical model data- __ VORTEX-LATTICE model, - 0 . 0 0 1 2 M = 0.60 Flight fairing- - CNB* 0 . 0 0 0 8 M per deg
I -
"" 0.60 0.90 - " _ 0.0004 1.20 - 0 . 0 0 0 0 - 0 . 0 0 4 - - -0.003 CLB* - 0 . 0 0 2 - per deg I - 0 . 0 0 1 - ( a ) C N B , C L B .
Figure 18. Lateral-directional derivatives obtained from flight data as a f u n c t i o n of angle of attack and comparison with analytical model r e s u l t s . h = 58O; cleanconfiguration.
Flight data- M 0 0.55 to 0.88 CI 0.88 to 0.96 0 0.96to 1.10 A 1.10 to 1.35 X 1.35 to 1.70
I Uncertainty level
Analytical model data- - VORTEX-LATTICE model, M = 0.60 Flight fairing- M "" 0.60 CNP, 0 . 0 0.90 per " _ 1.20 -0.1
-0.2 I(I"
-0.3 1
T ( b ) C N P , C L P .
Figure 18. Continued 5 8 Flight data- M 0 0.55 to 0.88 0 0.88 to 0.96 0 0.96 to 1.10 A 1.10 to 1.35 X 1.35to 1.70
I Uncertainty level
- 0 . 0 Analytical modeldata- - ~ VORTEX-LATTICE model, CNR, - M = 0.60 per rad Flight fairing- M - - 0 . 4 "" 0.60, 0.90 "_ 1.20 "" I 1 " 0.60, 0.90, 1.20 -0.6 0 . 4 - CLR,
per rad .'
J "I 2 -0.8 2 4 6 8 10 12 a, de9 ( c ) C N R , CLR Figure 18. Continued.
Flight data- M 0 0.55 t o 0.88 0 0.88 t o 0.96 0 0.96 t o 1.10 1.lOto 1.35 x 1.35 to 1.70
I Uncertainty level
0 . 0 0 0 8 Analytical modeldata- __ VORTEX-LATTICE model, M = 0.60 "" WING-BODY model, 0.0004 M = 0.60 : "- WING-BODY model, ~ CNDA* 0 .oooo M = 1.20 per deg
+
-+-%&%$i Flight fairing-
-0.0004 M "" 0.60 0.90 _" 1 2 1.20 - 0 . 0 0 0 8 - 0 . 0 0 1 2 k T ..
-0.0°04 t
-1 1 J 0 . 0 0 0 0 " -1 - - 2 4 6 10 12 8 a, de9 ( d ) CNDA, CLDA .
Figure 18. Continued.
Flight data- M 0 0.55 to 0.88 0 0.88 t o 0.96 0 0 . 9 6 t o 1.10 A l.lOto 1.35 X 1.35 to 1.70
I Uncertainty level
Analytical modeldata- -0.0020 .- VORTEX-LATTICE model, M = 0.60 """ WING-BODY model,
+
M = 0.60 -0.0015 " - WING-BODY model, - "_ M = 1.20 CNOR, ~ _ _ _ "-4" per deg -o.oolo " Flight fairing-
--*-;--
M . " - 0.60 -0.0005 z - - 0.90 ~" 1.20 "" I 0.60, 0.90, 1.20 0 .oooo 0.0010 0 . 0 0 0 5 CLDRJ 0 .oooo per deg -0 -0005 -0.0010, ( e ) CNDR, CLDR.
Figure 18. Continued.
Flight data- M 0 0.55 to 0.88 0 0.88tO 0.96 0 0.96 to 1.10 A l . l O t o 1.35 X 1.35to 1.70
1 Uncertainty level
O . O o o 4 1
Flight fairing -
M 0.0002 "" 0.60
i
I 0.90
CNDS, 1.20 0 .oooo ziJq+ per deg
-0.0002 +
- 0 - 0 0 0 6 -0.0004 ( f ) C N D S , C L D S .
Figure 1 8 . Continued.
Flight data- M 0 0.55 to 0.88 0 0.88 to 0.96 0 0 . 9 6 t o 1.10 A 1.1OtO 1.35 x 1.35 to 1.70 -0.020
I Uncertainty level
i
Analytical model data- -0.015 VORTEX-LATTICE model.
"L T M = 0.60 CY 6, per deg - o ' o l o
+!--#-- Flight f a i r i n g -
M "" 0.60
1 1
-0 - 0 0 5 " 0.90 .~ "" 1.20 -- 0.60, 0.90 1 -I 0 .ooo I - 0 . 0 0 2 CYDR, ~- per deg o . O o o - 0 . 0 0 2
t
( 8 ) C Y B , C Y D R .
Figure 18. Continued.
I
Flight data- M o 0.55 to 0.88 0.88 to 0.96 0 0.96 to 1.10 n 1.lOto 1.35 x 1.35to 1.70
I Uncertainty level
0.008 Flight fairing- " "" M=0.60, 0.90, 1.20 0 . 0 0 4
m- -&
CYDA, 0 .ooo per deg -0 - 0 0 4 r 0 . 0 0 3 - 0.002 C Y D S * 0.001 per deg 0 .ooo 11 4 1 1. .,
-0.001 h- -
10 12 2 4 6 8 Q, deg ( h ) C Y D A ,C Y D S .
F i g u r e 18. Concluded.
6 4 .
o a=5.0°i 1.5" 0.0016
I Uncertainty level
0.0012 a,
per CNB, deg 0.0008 - t f i
0 - 0 0 0 4 t
0.0000 1
- 0 . 0 0 3 2 - 0 - 0 0 2 4 1 r 0 . 0 0 0 0 1 I J 0 . 6 0 . 8 1.0 1.2 1 . 4 1.6 1.8 M ( a ) C N B . C L B .
Figure 19. Lateral-directional derivatives obtained from flight data as a function of Mach number. h = 5 8 O ; clean configuration.
o a = 5.0" f 1.5" - -0.0020
I Uncertainty level
- -0.0015 CNDR, -0.0010 per deg (D -0 -0005
I
- 0 - 0 2 0 -0.015 C Y B, per deg - o * o l o
if#
( b ) CNDR, C Y B .
Figure 19. Continued.
I 0 a = 5.0" f 1.5" 0 -0004
I Uncertainty level
0.0002 CNDS, per deg o'oooo -0.0002 -0 -0004 -0 - 0 0 0 6 -0 -0004 T CLDS, per deg - o * o o o 2 0 .oooo 0 . 0 0 0 2 0.6 0 . 8 1.0 1 . 2 1.4 1.6 1.8 M ( c ) C N D S , C L D S .
Figure 19. Concluded.
A , ] p 3 0 26 I Uncertainty level
0.0016 - Flagged symbol denotes
flaps deflected Solid symbol denotes landing gear extended CN B, 0.0008 per deg 0.0004 -0 - 0 0 4
i
( a ) CNB, C L B .
F i g u r e 20. Lateral-directionalderivativesobtained from flight data for various combinations of landing gear and flap positions. Low s p e e d .
A , deg 0 16 I Uncertainty level 0.1 r Flagged symbol denotes flaps deflected Solid symbol denotes landing gear extended 0 .o T T -0.2 -0.3
- O e 8 I
Figure 2 0 . Continued.
A , deg 0 16
I Uncertainty level
0.0 1 - Flagged symbol denotes flapsdeflected Solid symbol denotes CNR, landing gear extended
- \+
per rad -0.2
- 0 ' 4 i
- 0 . 6 LL 1.5 - - 1.0 per rad 0 .o ( c ) CNR, C L R .
Figure 2 0 . Continued.
A , deg 0 16 1 Uncertainty level Flagged symbol denotes 0.0002 r flaps deflected Solid symbol denotes landing gear extended 0 .oooo CNDAJ -0.oooiI - per deg - -0.0004 -0.0006 1 - -0.0008 - 0 -0006
- 0 . 0 0 0 2 1 1
0.0000 L 1 6 8 10 12 1 4 a, de9 ( d ) CNDA, CLDA.
Figure 2 0 . Continued.
A , deg 0 16
I Uncertainty level
-0.0020 r Flagged symbol denotes flaos deflected -0.0015
- 8
- CNDR, -0.0010 per deg - -0.0005 0 . 0 0 0 0 - 0.0008 - 0.0006 - CLDR9 0.0004 per deg 0.0002
- 1
0.0000 6 8 CNDR,CLDR.
Figure 20. Continued.
7 2 -0.0008 Flagged symbol denotes
r
flaps deflected Solid symbol denotes -0 -0006 landing gear extended
T
CNDS' -0.0004 per deg
-0.000;1 *
J I 1 . I
0.0000 I
-0 -0032
r
- -0.0024 CLDS, -0.0016 per deg
I
-0.0008 w w
0.0000 I
( f ) C N D S , CLDS.
Figure 20. Continued.
A , deg o 16
I Uncertainty level
Flagged symbol denotes flaps deflected Solid symbol denotes
-0.020 -
landing gear extended -0.015 -
I '
- 0 - 0 0 5 1 _1 "I 0 . 0 0 6 0.004
I
I T
CYDR,
per deg ' - O o 2 1 1
'i ' 1 ; I
0 . 0 0 0 1 -
- 0 . 0 0 2 6 L A - 8
(8) C Y B ,C Y D R .
Figure 20. C o n t i n u e d .
A , deg 0 16
I Uncertainty level
Flagged symbol denotes flaps deflected Solid svmbol denotes
O m 0 0 4 1
-0.002 1
t
I - I
- 0 . 0 0 4 ‘
0.003
I
0 . 0 0 2 1
T 1
o * o o o I
-0.001 6 8 10 1 2 1 4 4 deg (h) CYDA, CYDS.
Figure 20. Concluded.
7 5 Calculated angle of attack, deg F i g u r e 21. Correlation of calculated and reference angle of attack. M = 0.70.
- - . . ~ 3. Recipient's Catalog No.
1. Report No. 2. Government Accession No.
I
NASA TP-J.350- I .. . . 1 ~
Report Date 4. Title and Subtitle 1 5.
I October 1978
FLIGHT-DETERMINEDSTABILITY AND CONTROLDERIVATIVES 6. PerformingOrganization Code FORTHE F-111 TACT RESEARCHAIRCRAFT
1 H-1004
-. . " .. - ~~ 8. PerformingOrganization Report NO.
7. Author(4 Alex G . Sim and Robert E . Curry 10. Work Unit No.
. .
-~ ~ 9. PerformingOrganization NameandAddress
I 505-11-24
NASA Dryden Flight Research Center 11, Contract or Grant No P .O. Box 273 Edwards,California 93523 " 13. Typeof Report and Period Covere( . -.
2. SponsoringAgencyNameandAddress Technical Paper National Aeronautics and Space Administration 14. SponsoringAgencyCode Washington, D . C . 20546 ~ . . - .. - " ~~ 5. Supplementary Notes 6. Abstract A flight investigation was conducted to provide a stability and control derivative data base for the F-111 transonic aircraft technology (TACT) research aircraft. Longitudinal and lateral-directional data were obtained as functions ofMach number, angle of attack, and wing sweep. For selected derivatives, the flight results were correlated with derivatives calculated based on vehicle geometry. The validity of the angle of attack measurement was independently verified at a Mach number of 0 . 7 0 for angles of attack between 3 O and l o o .
. "- - - 18. Distribution Statement 7. Key Words(Suggested by A u t h o r k ) ) Transonic aircraft technology, supercritical wing, maximum likelihood, derivative extraction, computational aerodynamics, Woodward panel Unclassified-Unlimited method, vortex-lattice method
STAR Category: ( 18 J
. . . ~ " "" --
9. Security Classif. (of this report) 1 2 0 : Security Classif. (of this page)
Unclassified Unclassified J .. ..
~ ~- ~ " - *For sale by the National Technical Information Service, Springfield, Virginia 22161 NASA-Langley, 1978 THIRD-CLASSBULKRATE Postage and Fees Paid National Aeronautics and National Aeronautics and Space Administration Space Administration NASA451 Washington, D.C.
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