Extraction of Lateral-Directional Stability and Control Derivatives for the Basic F-18 Aircraft at High Angles of Attack

NASA Technical Memorandum 4786

Extraction of Lateral-Directional

Stability and Control Derivatives

for the Basic F-18 Aircraft at High

Angles of Attack

Kenneth W. Iliff and Kon-Sheng Charles Wang February 1997 NASA Technical Memorandum 4786

Extraction of Lateral-Directional

Stability and Control Derivatives

for the Basic F-18 Aircraft at High

Angles of Attack

Kenneth W. Iliff Dryden Flight Research Center Edwards, California Kon-Sheng Charles Wang SPARTA, Inc.

Lancaster, California National Aeronautics and Space Administration Office of Management Scientific and Technical Information Program CONTENTS TABLE FIGURES iii ABSTRACT The results of parameter identification to determine the lateral-directional stability and control derivatives of an F-18 research aircraft in its basic hardware and software configuration are presented. The derivatives are estimated from dynamic flight data using a specialized identification program developed at NASA Dryden Flight Research Center. The formulation uses the linearized aircraft equations of motions in their continuous/discrete form and a maximum likelihood estimator that accounts for both state and measurement noise. State noise is used to model the uncommanded forcing function caused by unsteady aerodynamics, such as separated and vortical flows, over the aircraft. The derivatives are plotted as functions of angle of attack between 3° and 47 ° and compared with wind- tunnel predictions. The quality of the derivative estimates obtained by parameter identification is somewhat degraded because the maneuvers were flown with the aircraft's control augmentation system engaged, which introduced relatively high correlations between the control variables and response variables as a result of control motions from the feedback control system.

NOMENCLATURE Abbreviations and Acronyms AOA angle of attack, deg ARI aileron-to-rudder interconnect DFRC NASA Dryden Flight Research Center, Edwards, California FADS flush airdata system FCS flight control system HARV High Angle-of-Attack Research Vehicle HATP High Angle-of-Attack Technology Program LEF leading-edge flap LEX leading-edge extension (wing-body strake) NACA National Advisory Committee for Aeronautics PCM pulse code modulation PID parameter identification PROM Programmable Read-Only Memory RAI rudder-to-aileron interconnect TEF trailing-edge flap Symbols lateral acceleration, g ay A, B, C, D, F, G system matrices coefficient of rolling moment due to roll rate, rad -t Clp coefficient of rolling moment due to yaw rate, rad -1 Clr coefficient of rolling moment due to sideslip, deg -1 C I[_ coefficient of rolling moment due to aileron deflection, deg -1 ClSa coefficient of rolling moment due to differential horizontal stabilator deflection, deg -I Cl_dh coefficient of rolling moment due to lateral deflection, deg -1 Cl_ L coefficient of rolling moment due to rudder deflection, deg -1 Clsr coefficient of yawing moment due to roll rate, rad -!

coefficient of yawing moment due to yaw rate, rad -1 Cn r C coefficient of yawmg moment due to sideslip, deg -1 n_ coefficient of yawing moment due to aileron deflection, deg -1 coefficient of yawing moment due to differential horizontal stabilator deflection, deg -1 CnSdh coefficient of yawing moment due to lateral deflection, deg -1 Cn_ L C coefficient of yawing moment due to rudder deflection, deg -1 118 r coefficient of lateral force due to sideslip, deg -1 Cy_ coefficient of lateral force due to aileron deflection, deg -l Cy_ coefficient of lateral force due to differential horizontal stabilator deflection, deg -1 CYsdh coefficient of lateral force due to lateral deflection, deg -1 CY8 L coefficient of lateral force due to rudder deflection, deg -1 CY8 f system state function g system observation function GG* measurement noise covariance matrix H approximation to the information matrix J cost function N number of time points n state noise vector P roll rate, deg/sec R innovation covariance matrix yaw rate, deg/sec time, sec U known control input vector X state vector time derivative of state vector predicted state estimate observation vector z predicted Kalman filter estimate angle of attack, deg angle of sideslip, deg aileron deflection, deg _a pilot aileron input, arc-in Sap differential horizontal stabilator deflection, deg 5dh equivalent combined lateral deflection of aileron and stabilator, deg leading-edge flap deflection, deg _LEF rudder deflection, deg r pilot rudder input, in _rp trailing-edge flap deflection, deg _TEF measurement noise vector unknown parameter vector estimate of gradient with respect to

v¢

Subscripts i general index INTRODUCTION The NASA High-Angle-of-Attack Technology Program (HATP) was established in the mid-1980s to develop and validate some of the key technologies required for safe, predictable, and usable high-angle-of-attack (AOA) flight. The two prime objectives of the HATP were (1) to provide a flight-validated design methodology through experimental and computational methods that simulate and predict high-AOA aerodynamics, flight dynamics, and flying qualities; and (2) to improve aircraft agility at high AOA while expanding the usable high-AOA envelope. The HATP used a close integration of ground-based and flight activity, including wind-tunnel experiments, computational fluid dynamics models, piloted simulations, and flight tests to focus on three key areas: high-AOA aerodynamics, advanced high-AOA control concepts, and maneuver management (ref. 1).

To provide the critical flight validation element, an F-18 aircraft was loaned to NASA by the U.S. Navy.

Extensive instrumentation was subsequently added for flight research purposes. The airplane was named the High- Angle-of-Attack Research Vehicle (HARV) (fig. 1). Access to full-scale flight conditions was deemed essential to address inherent shortcomings of subscale ground-testing techniques and to provide the confidence afforded through flight validation of new analytical methods and design concepts. Research flight testing was performed in three phases beginning in 1987 at NASA Dryden Flight Research Center (DFRC), Edwards, California. Flight testing was completed by the spring of 1996, meeting the three-phase program schedule of the HATP.

In phase I, whichbegan in mid-1987 andcontinued through1989, the HARVflew 101research missions, investigating high-AOAflight up to 55°. PhaseI examined developmental issuesof the HARV research instrumentation suite and established initial aerodynamic correlations betweenpredictionsand in-flight measurements (e.g.,of tail buffetandvortexburstlocation for thewing-body-strake vortices). Phase II involved majorhardware andsoftware modifications totheHARV, incorporating amulti-axis thrust-vectoring controlsystem andresearch flightcontrolsystem (FCS). Thisphase, frommid-1991 tolate1994, aggressively expanded theHARV flightenvelope. Demonstrated capabilities include stabilized flightat70°AOAandrollingathighrates at65°AOA.

Phase III flightsbegan in 1995 andwerecompleted by May 1996. These testsfocused on theimplementation of actuated forebody strakes mounted onthenose of theHARVtoenhance directional controlathighAOA.

A continuing objective oftheflightprogram wasthestudy ofthestability andcontrol characteristics oftheF-18 aircraft duringlow-speed, high-AOA flight(refs.2and3).Thispaper addresses theanalysis andresults ofparameter identification (PID)conducted atDFRCto extract lateral-directional stabilityandcontrolderivatives of thebasic F-18configuration fromdynamic flightdata. Theresults, based on42maneuvers fromphase I flights11through 38 (flownbetween June1987 andMarch1988), wereused toinitiallyassess stabilityandcontrol derivatives obtained fromwind-tunnel tests andearlyflighttestbythemanufacturer andU.S.Navy. Thederivatives wereextracted using a DFRC-developed computer program, whichusesthelinearized aircraftequations of motionanda maximum likelihood estimator thataccounts forstate andmeasurement noise. Themaneuvers analyzed ranged from3° to47° AOA.Inthispaper, thederivatives areestimated, plotted, anddiscussed relative towind-tunnel predictions andflight maneuver quality.

VEHICLE DESCRIPTION The aircraft testbed was the sixth full-scale developmental F-18 (fig. 1), a single place, twin-engine, fighter- attack aircraft built by McDonnell Douglas Corp. (St. Louis, Missouri) and Northrop Grumman Corp. (Los Angeles, California) for the U.S. Navy. The Navy previously used this particular aircraft (serial number 160780) for high- AOA and spin testing. The aircraft is powered by two General Electric (Lynn, Massachusetts) F404-GE-400 afterburning engines, each rated at approximately 16,000 lb static thrust at sea level. The F-18 features a midwing configuration with a wing-root leading-edge extension (LEX) that extends from the forward portion of the fuselage and blends into the wing. The configuration under study, (dating from 1987 to 1988) did not carry the LEX fence modification, introduced in late 1988, nor any of the thrust-vectoring enhancements used during phases II and III of the HATP flight program. The F-18 as flown carried no external stores and was highly instrumented for research purposes. The wingtip missile launch rails and missiles were replaced with specially designed airdata sensors and camera pods (explained later in the "Instrumentation and Data Acquisition" section). The in-flight refueling capability and tail-arresting hook were retained. Figure 2 shows a three-view drawing of the F-18, along with major physical characteristics.

The F-18 has five pairs of aerodynamic control surfaces: stabilators, rudders, ailerons, leading-edge flaps (LEFs), and trailing-edge flaps (TEFs). The twin vertical stabilizers, with trailing-edge rudders, are canted outboard at approximately 20 ° from the vertical. Pitch control is provided by the collective operation of the all-movable horizontal stabilators and the symmetric LEFs and TEFs. For flight above 25 ° AOA, symmetric LEFs are fixed to 33 ° full down. Though symmetric TEFs are scheduled with AOA below 25 °, they are fixed to 0° deflection above 25 ° AOA. Roll control uses deflections of the ailerons (_i a), differential horizontal stabilators (_dh), and asymmetric LEFs (_LEF) and TEFs (_TEF). Directional control is provided by symmetric rudder deflection (_ir) and a rudder-to- aileron interconnect (RAI) between _r and both 8 a and 8dh. In addition, the FCS augments lateral-directional control with an aileron-to-rudder interconnect (ARI), to be discussed with the RAI in the "Results and Discussion" section.

Symmetric aileron droop and rudder toe-in are employed in the power approach configuration. A speed brake is on the upper aft fuselage, between the vertical stabilizers. The table provides maximum control surface positions and rate limits.

Thecomputer-based FCSfeatures digitalinputsfromredundant production sensor setsandairdata. Thepilot commands provide automatic mode logic,gainscheduling, input-output management, andsurface management. The FCSis a digitally-mechanized fly-by-wirecontrolaugmentation system. The standard F-18version V8.3.3flight controllawis implemented onfour701B(General Electric, Lynn,Massachusetts) digitalflightcontrolcomputers, alongwith surface actuators andanalog sensors, to providea dual-failure operational capability. The FCSwas developed with complete failuredetection, failuremanagement, andappropriate modeswitching in theeventof certain failures. A digitaldirectelectrical control mode provides a fly-by-wire open-loop controllawin case certain motionsensors fail. In addition, a mechanical controlmode isprovided in case thefly-by-wire controlsystems fail.

Thissystem provides a directmechanical link fromthepilot'ssticktothelongitudinal trimandstabilator actuators.

Themechanical modeprovides pitchandrollcontrolfromthepilot'ssticktothestabilators.

F-18aerodynamic control surface position andratelimits.

Position limit, Ratelimit,

Surface deg deg/sec

Stabilator:

Trailing-edge up 24 40

Trailing-edge down 10.5 40

Aileron:

Trailing-edge up 24 100

Trailing-edge down 45 100

Rudder:

Trailing-edge left 30 82

Trailing-edge right 30 82

TEF:

Up 8 18

Down 45 18

LEF:

Up 3 15

Down 33 15

Speed brake:

Trailing-edge up 60 20to 30

Themission computer provides MIL-STD-1553 multiplexbuscontrol.Thisdatabusprovides anintegrated controlsystem anda standard interface for allequipment connected tothebus.

INSTRUMENTATION AND DATA ACQUISITION Onboard data acquisition included standard parameters from the production F-18 MIL-STD-1553 data bus and from specialized research instrumentation such as accelerometers, rate gyros, control surface position transducers, and airdata sensors. Early in phase I, which included the flights studied here, airdata measurement was investigated with several techniques. Up to flight 16, a standard NACA noseboom-mounted probe was used for airdata. From flights 17 to 31, noseboom airdata were complemented with airdata from a right-wingtip-mounted NACA probe with AOAandsideslip vanes. (Although therightwingtipprobe was installed on flight 4, an acceptable calibration was not available until flight 17.) From flight 32 on, a swiveling (self-aligning) pitot probe with conventional AOA and sideslip vanes was mounted on the left wingtip (ref. 4). After flight 38, the noseboom probe was removed because it affected the forebody flow and thus the high-AOA stability and control of the aircraft. Shortly thereafter, a flush airdata system (FADS) was installed in the tip of the nose cone (ref. 5). Given the several airdata systems----each with different calibrations, calculated functions, and function revisions implemented over a relatively short time span--an assessment of true airdata early in phase I proved somewhat complicated. However, sufficiently accurate airdata were obtained for the PID analysis presented here.

For purposes of in-flight aircraft flow visualization, the airplane was equipped with a smoker system (refs. 6 and 7) and a surface flow visualization system (refs. 8 and 9). Flow visualization and associated pressure data have been used to validate computational fluid dynamics models and wind-tunnel results. Video data were obtained with two forward-facing, black-and-white video cameras mounted on the inboard side of the vertical tails; a color video camera on the left wingtip pod; a still 35-mm camera on the right wingtip pod; and another color video camera behind the cockpit, on the turtleback, looking aft. Data measurements, including video signals from any two of the onboard video cameras, were sent by telemetry to the ground for real-time monitoring and recording.

The telemetry system consisted of two independent, asynchronous pulse code modulation (PCM) data encoders, each with a basic PCM word size of 10 bits. The output of the encoders was sent by telemetry to the ground; no onboard recording of the PCM data was provided in the airplane. Special provisions were incorporated in the data acquisition system for higher resolution signals of certain types of data. For example, data collected from rate gyros, linear accelerometers, and the inertial measuring system were encoded into 14-bit words. The 16-bit words from the MIL-STD-1553B bus were inserted in two 10-bit PCM words to obtain the parameters involving the digital FCS.

Flight data used in the present analysis were thinned to a final sample rate of 40 Hz from ground-recorded data received via telemetry from the aircraft. Airdata used in the present analysis were taken from either the noseboom or right wingtip boom, depending on the flight number as mentioned previously. Measurements of AOA and sideslip were corrected for center-of-gravity offset. Wind-vane data were also corrected for upwash, sidewash, and boom-bending effects. Linear accelerometer data were corrected for instrument offsets from the center of gravity in the PID program. Transducers were also available for measuring closed-loop and open-loop input variables, response variables, engine operation, and fuel consumption, from which instantaneous mass and inertia characteristics were calculated.

Furthermore, before the maneuvers were analyzed, the data were corrected for time lags introduced by sensor dynamics and signal filtering. Making these corrections is critical to adequately estimate the stability and control derivatives (ref. 10).

PARAMETER IDENTIFICATION METHODOLOGY A primary purpose of the HARV flight program was to evaluate the aircraft configuration flying at high AOA.

It is well known that while flying at high AOA where there is significant flow separation and vortical flow over the aircraft that the vehicle will exhibit uncommanded motions. Reference 11 presents a discussion of maneuver difficulties and related analysis issues under these conditions for the 3/8-scale F- 15 Remotely Piloted Vehicle aircraft at AOA from -20 ° to 53 °. At high AOA, the uncommanded motions vary from relatively small amplitude, high- frequency disturbances to very large wing rocking motions to complete roll-off from the flight condition. In addition to being bothersome to the pilot, the motions also complicate the extraction of stability and control derivatives from the planned stability and control maneuvers (ref. 11). The present analysis was also made difficult by the F-18 flight control system necessarily interconnecting certain control surfaces together, an important issue to be expanded upon in thenextsection. Tobetteranalyze theexisting maneuvers, it wasnecessary to account for theuncommanded portions oftheaircraftmotion.

The procedure implemented in this analysis usesstatenoiseto modelthe uncommanded forcingfunction.

References 12,13,and14completely describe thetechnique. Thetechnique applied totheF-18dataalsorequired thatthenormal aircraftequations of motionbelinearin theaerodynamic coefficients; thispresented noparticular difficulty because the normalstabilityandcontrolderivatives werealreadylocally linearapproximations of nonlinear aircraft aerodynamics.

Toperformtheanalysis presented here,anexisting parameter estimation computer program wasmodifiedto properlyaccount for theadditional complexity required toinclude theeffects of thestate noise (commands dueto separated and vorticalflows)on the stabilityandcontrolmaneuvers. A brief description of the statenoise algorithm follows.

It is possible tomake aprecise, mathematically probabilistic statement oftheparameter estimation problem. The first stepis to define the general system model(aircraftequations of motion).Thismodelcanbe writtenin the

continuous/discrete formas

(1) x(t0) = x 0 x(t) = f[x(t), u(t), _] + F(_)n(t) (2) (3) z(ti) = g[x(ti), u(ti), _] + G(_)_i where x is the state vector, z is the observation vector, f and g are system state and observation functions, u is the known control input vector, _ is the unknown parameter vector, n is the state noise vector, q is the measurement noise vector, F and G are system matrices, and t is time. The state noise vector n is assumed to be zero-mean white Gaussian and stationary, and the measurement noise vector 1"1 is assumed to be a sequence of independent Gaussian random variables with zero-mean and identity covariance. For each possible estimate of the unknown parameters, a probability that the aircraft response time histories attain values near the observed values can then be defined. The maximum likelihood estimates are defined as those that maximize this probability. Maximum likelihood estimation has many desirable statistical characteristics; for example, it yields asymptotically unbiased, consistent, and efficient estimates.

If equations (2) and (3) are linearized (as is the case for the stability and control derivatives in the aircraft problem), then x(/0) = x0 (4) :_(t) = Ax(t) + Bu(t) + Fn(t) (5) z(ti) = Cx(ti) + Du(ti) + Glqi (6) where A, B, C, and D are system matrices.

When state noise is important, the nonlinear form of equations (1) through (3) is intractable. For the linear model defined by equations (4) through (6), the cost function that accounts for state noise is N J(_) = _ _ [z(ti)- i=1 where R is the innovation covariance matrix and N is the number of time points. The _(ti) term is the Kalman- filtered estimate of z. (The cost function is the function of the difference between the measured and computed time histories.)

To minimize the cost function J(_), we can apply the Newton-Raphson algorithm, which chooses successive estimates of the vector of unknown coefficients _. Let L be the iteration number. The L + I estimate of _ is then obtained from the L estimate as follows: = [V_ J(_L) ] (8) If R is assumed fixed, the first and second gradients are defined as N , V_ J(_)=-Z [z(ti)-z_(ti)] (GG*)-IIv _ 7._(ti)] (9) i=1 N , 7_ J(_) = Z [7_ 7-_(ti)] (GG*)-I[v_ z_(ti) ] i=1 (10) N .

i=1 The Gauss-Newton approximation to the second gradient is N , (11) i=1 The Gauss-Newton approximation, which in past reports by the first author was sometimes referred to as modified Newton-Raphson, is computationally much easier than the Newton-Raphson approximation because the second gradient of the innovation never needs to be calculated.

Figure 3 illustrates the maximum likelihood estimation concept. The measured response is compared with the estimated response, and the difference between these responses is called the response error. The cost function of equation (7) includes this response error. The minimization algorithm is used to find the coefficient values that minimize the cost function. Each iteration of this algorithm provides a new estimate of the unknown coefficients on the basis of the response error. These new estimates are then used to update values of the coefficients of the mathematical model, providing a new estimated response, and therefore, a new response error. Updating of the mathematical model continues iteratively until a convergence criterion is satisfied. The estimates resulting from this procedure are the maximum likelihood estimates.

The maximum likelihood estimator also provides a measure of the reliability of each estimate based on the information from each dynamic maneuver. This measure of the reliability, analogous to the standard deviation, is called the Cramrr-Rao bound (refs. 13 and 15). The Cram&-Rao bound, as computed by current programs, should generally be used as a measure of relative, rather than absolute, accuracy. The bound is obtained from the approximation to the information matrix, H, which is based on equation (11); the actual information matrix is defined when evaluated at the correct values (not the maximum likelihood estimates) of all the coefficients. The bound for each unknown is the square root of the corresponding diagonal element of H-I; that is, for the ith unknown, the Cramrr-Rao bound is _). The stability and control derivatives presented and discussed in the next section were analyzed assuming that state noise was present in all cases.

RESULTS AND DISCUSSION To accurately interpret the stability and control derivative results obtained here for the F-18, a careful examination of the quality and characteristics of the PID maneuvers themselves is necessary.

Parameter Identification Maneuvers As mentioned in the previous section, two main difficulties affected the PID maneuvers and their analysis. The first issue was one of aerodynamics, resulting from unsteady separated and vortical flows over the aircraft above 20 ° AOA, which caused the aircraft to exhibit uncommanded motions of varying amplitude and frequency. The effect of the uncommanded responses was accounted for by considering state noise in the analysis.

The other difficulty arose because the PID maneuvers were performed with the basic F-18 control system engaged. The resulting maneuvers were less than ideal for derivative extraction because of the near linearly dependent (ref. 10) motions of all of the controls (especially above 25 ° AOA) and the relatively high correlation between the response variables and the resulting control motions due to the feedback control system.

The near linearly dependent control motions not only made it difficult to obtain control derivatives of individual control surfaces but also degraded attempts to determine an equivalent combined control derivative. In other words, the control deflections were too closely correlated to obtain good independent estimates of the correlated control deflections. Furthermore, this correlation made the attempt to estimate an equivalent control derivative--that is, a combination of two or more controls--also less than completely satisfactory. Correlations between response and control motions also made it difficult to obtain high-quality rate derivatives. These important issues will now be discussed more fully in connection with figures 4 through 7.

Figure 4 shows a typical maneuver obtained between 9 ° and 12 ° AOA. The altitude was about 31,000 ft at a Mach number of 0.46 to 0.41, with a dynamic pressure that varied between 88 and 72 lb/ft 2, as shown in figure 4(a).

Figure 4(b) shows most of the responses and control inputs used for PID analysis. Figure 4(c) shows the pilot inputs made for the PID maneuver, along with the resulting control deflections. The control deflections are a result of the pilot input and the control command from the feedback control system. References 16 through 18 provide a more complete description of the control system. The lateral stick input _ap, during the first 2 sec of the maneuver, directly causes deflections of 8 a, 8dh, and _r in this portion of the maneuver. Fortunately in this maneuver, the pilot rudder input observed between 4 and 9 sec caused no deflection of the aileron and differential stabilator. (The aileron deflection between 7 and 9 sec is from pilot aileron input.) The result of this independent control surface motion is that a useful estimate of a combined 8 a and 8dh effectiveness can be obtained independent of the _r effectiveness.

The first 2 sec of the maneuver are repeated in figure 4(d) on a finer scale. The response of the rudder and aileron shows that although both rudder and aileron respond to the pilot lateral stick input, the rate limiting of the rudder surface makes separation of 8 a and _r control effectiveness probable, which enhances the information from the rudder-pedal-pulse portion of the maneuver last discussed for figure 4(c). The difficulty of separating _a from _dh effectiveness can be seen by observing the high correlation (a multiple of 0.42) between 8 a and _)dh"These control signals are essentially the same, except for a time lag of about 35 msec for the _dh signal compared with the/5 a signal.

The high correlation (or near linear dependence (ref. 10)) between 8 a and 8dh resulted in very poor estimates for _a and _dh effectiveness; so the PID results for 8 a and 8dh given here are for an equivalent combined lateral control defined as 5 L. Above 15 ° AOA, the coefficients of rolling moment due to lateral control, yawing moment due to lateral control, and lateral force due to lateral control are, respectively: (12) CIsL = Q_a + 0.42 Q6ah (13) Crtts L -_ Cn_ a "at-0.42 Cn_dh (14) CYSL = CYsa + 0.42 CYsdh The wind-tunnel predictions of C/_L, Cna L, and CYsL, tO be used for comparison with flight-estimated values, are calculated with the same preceding equations. Between 2 ° and 15 ° AOA, the coefficients ClsL, Cn_, and Cy8 are • ¢ nonlinear functions of _a' _dh' and _)TEF controls. Figures 5 and 6 highlight the issues of correlation and linear dependency between differential control surface deflections. Figure 5 shows the relationship between pilot input and the resulting control surface deflections for full lateral stick input 5% as a function of AOA; figure 6 shows them for full rudder input _rp as a function of AOA.

For the maneuver shown in figure 4 at about 10 ° AOA, the resulting response to full Sap, as given in figure 5, involves no deflection of differential trailing-edge flaps or differential leading-edge flaps. For the same maneuver, however, full _ap results in about 23 ° of aileron deflection, 30 ° of rudder deflection, and 9 ° of differential stabilator deflection. Above 2 ° AOA, the differential leading-edge flap does not respond to Sap, and above 10 ° AOA, differential trailing-edge flaps do not respond to 8%. All maneuvers analyzed in this report are above 2 ° AOA, so no effect of differential leading-edge flap resulted. For the maneuvers below 10% however, _ap resulted in effects of trailing-edge flaps in addition to the effect of 8 a, 8dh, and 8r, as previously observed and discussed for figure 4.

Figure 6 shows the control deflections resulting from full rudder pedal deflection 8rp. Below 10 ° AOA, only the rudder deflects, but above 10 ° AOA, rudder, aileron, and differential stabilator all respond to pilot rudder pedal command. By comparing figures 5 and 6 above 25 ° AOA, one can see that rudder, aileron, and differential stabilator all respond to _ag and 8rp with exactly the same proportions, making accurate estimation of the control effectiveness for 8 a, 8dh, and o r difficult. The following discussion will examine a PID maneuver at a higher AOA. Not only are there differences in control deflections for given stick and rudder inputs (i.e., different control laws and scheduling), but there are also differences in flight dynamics due to unsteady aerodynamics.

Figure 7 shows a typical maneuver flown at AOA between 31° and 33 °. For this maneuver, the altitude is between 16,000 and 15,300 ft, the Mach number is from 0.23 to 0.22, and the dynamic pressure varies from 42 to 40 lb/ft 2. Figure 7(b) shows the response variables and control inputs used for PID. Figure 7(c) shows the pilot inputs 8% and 8rp, along with the resulting deflections of 8 a, 8dh, and 8 r. During the first 2 sec, the pilot rudder pedal input 8rp can be seen with very little pilot lateral stick input. The resulting deflections for 8 a, 8dh, and _r can be seen.

These deflections are different from those for the lower AOA maneuver that figure 4 shows where 8rp only results in 8 r deflection. Near 17 sec, the pilot lateral stick input can be seen along with the resulting deflections of 8 a, _dh, and 8 r. The amount of control surface deflection due to Sap and 8rp is the same in this AOA range as would be expected by comparing figures 5 and 6.

The correlation of 8 a, 8dh, and _r with _rp is more apparent in figure 7(d), where the first 2 sec of the maneuver are shown on a more sensitive scale• Once again, 8 a is highly correlated with 0.42 _dh' and 8 r is seen to be about four times-_5 a. Fortunately, the rate limit in the _r surface, seen in figure 7(d), should result in some linear independence between _a and _5 r, which will allow, however marginally, an estimate of 5 a and 5dh effects (through _5 L ) independent from 5 r effects, in the PID analysis.

Figure 7(e) shows the high-AOA maneuver at an increased time sensitivity between 17 and 19 sec. Here the deflection of the controls _a' _dh' and _r are shown for the pilot lateral stick input Sap. Once again, the previously observed correlation between _5 a and _dh call be seen. The rate limit saturation of i_ r here shows limited independence between _5 a and 8 r for PID purposes.

With this discussion considered, the PID results that follow will estimate rudder derivatives independent of the equivalent lateral control variable _L as previously defined.

Extracted Stability and Control Derivatives All lateral-directional maneuvers were analyzed using the maximum likelihood method with state noise as described in the "Parameter Identification Methodology" section. State noise was assumed for all maneuvers regardless of AOA, although the uncommanded responses warranting use of state noise were only significant above 20 ° AOA. The lateral-directional derivative estimates are presented as functions of AOA in figures 8 through 11, along with corresponding wind-tunnel predictions. The circle indicates the estimate of each derivative from a given flight maneuver, with the vertical bar indicating the uncertainty level for the estimate. The uncertainty level used in this analysis is five times the Cramrr-Rao bound. The solid line is a fairing of the estimates without any consideration of the wind-tunnel values and represents the authors' interpretation of the estimate, which includes a combined assessment of the uncertainty levels, the scatter in the estimates, and the quality of the individual maneuver. In addition to the issues of near-linear dependence discussed previously, the authors also assessed the maneuvers on the basis of the duration of the maneuver, the amount of control input, and the level of excitation of the vehicle (response variables 13, p, r, and ay). Theoretically, these considerations are also contained in the values of the uncertainty levels, where a large uncertainty level indicates low information on that derivative, and a small value indicates high information. The dashed line shown on the figure represents the wind-tunnel prediction of the derivatives as a function of AOA. The predictions are from the aerodynamic model and database used in the DFRC flight simulator of the F- 18 aircraft. The aeromodel was acquired from the U.S. Navy Naval Air Test Center, Patuxent River, Maryland, and based on the McDonnell Douglas F-18 basic aerodynamic database (refs. 19 and 20). Although the flight estimated stability and control derivatives are plotted as functions of AOA, other variables, such as altitude (and thus Reynolds number) and horizontal stabilator position, account for some of the scatter in the flight estimates seen in these figures.

Figure 8 shows the sideslip derivatives Cl_, Cn_, and Cyl_ as functions of AOA. The comparison between flight estimate and wind-tunnel prediction of Cl_ (dihedral) in figure 8(a) is very good below 20 ° AOA. The flight fairing is up to 0.001 more positive than the wind-tunnel prediction between 20 ° and 25 ° AOA and up to 0.0015 more negative between 25 ° and 42 ° AOA. The flight and wind-tunnel values are in very good agreement above 42 ° AOA.

To assess the agreement between 33 ° and 42 ° AOA is difficult, as only two maneuvers are in this interval, both with fairly large uncertainty levels. More flight maneuvers in this interval would be required to make a definitive statement about the correlation of flight estimates and wind-tunnel predictions of Ct_ between 33 ° and 42" AOA.

Flight-estimated and wind-tunnel trends of C% (directional stability) with AOA are very similar, as figure 8(b) shows. In general, the flight trend is somewhat lower below an AOA of 10 °. At 20 ° AOA and above, the wind-tunnel prediction is a very valid fairing of the flight estimates, indicating excellent agreement between flight estimate and wind-tunnel predictions.

Figure8(c) shows Cyf_ as a function of AOA for both flight estimates and wind-tunnel predictions where the flight values are consistently higher below an AOA of 25 ° and between 35 ° and 45 °. The paucity of maneuvers between AOA of 33 ° and 42 ° makes derivative assessment in this region difficult.

Figure /9 shows flight estimates, and wind-tunnel predictions for the equivalent combined lateral control derivatives _CI_ L, CnsL, and Cy_L) as functions of AOA. Above 15 ° AOA, both extracted and predicted lateral control derivatives are as previously defined: C18 L = CI_ _ + 0.42 Cl_dh Cn_ L = Cn_,, + 0.42 C%dh Cy8 L = Cy8 _ + 0.42 CY_dh Below 15 ° AOA, flight estimates and fairings are given, but wind-tunnel predictions are not assumed in this range because of more complicated control surface correlations and dependencies. The trend of the lateral control effectiveness C16 L for both flight estimates and wind-tunnel predictions in figure 9(a) is the same. The agreement varies, with the flight estimate showing 10 to 30 percent more effectiveness. In figure 9(b), the decreasing trend of Cn_ L as a function of AOA is seen for both flight and prediction up to an AOA of 35 °. The flight values are more proverse (more positive CnsL ) than prediction for all AOA, with the flight values showing a trend toward even more proverse values above 30 ° AOA. Figure 9(c) shows that the Cy8 L is very small for both flight and prediction.

Figure 10 shows the rudder derivatives as functions of AOA. Figure 10(a) shows C/_ r as a function of AOA for flight and predicted values. Flight and predicted values agree below an AOA of 25 °, and then flight values increase up to 0.0005 more positive than the wind-tunnel prediction above 25 ° AOA. The rudder effectiveness Cn_ r (fig.

10(b)), shows good agreement throughout the AOA range, but the flight values indicate somewhat more effectiveness below 25 ° AOA than the predicted values. The agreement between flight and predicted values for Cr6 r for all AOA is excellent (fig. 10(c)).

Figure 11 compares flight and predicted values of the rotary derivatives Clp , Cnp , CI , and Cnr as functions of AOA. The flight values of Clp (fig. 11 (a)) are closer to zero than predicted near 20 ° AOA and between 30 ° and 45 ° AOA. The flight values of Ct, (fig. 11 (b)) are near zero for most of the AOA range, dipping negatively near 32 ° AOA, while the predicted values remain positive over the entire AOA range. Figure 11 (c) compares Cnp flight values and prediction with AOA, and the prediction is near zero throughout. Figure 11(d) compares flight and predicted values for Cn/ with good agreement below 20 ° AOA. Above 20 ° AOA, the flight values are more positive than the predicted values. It is always difficult to obtain linear rate derivatives at high AOA, but it is especially so for the maneuvers analyzed here. These maneuvers were obtained with the rate feedback control system engaged, and they also suffered because of the high correlation (discussed earlier) of the control surfaces used in the feedback control system.

CONCLUDING REMARKS The lateral-directional stability and control derivatives of an F-18 research aircraft were extracted from flight data over an angle-of-attack range of 3 ° to 47 ° using a maximum likelihood estimator accounting for state and measurement noise. The F-18 testbed performed these parameter identification flight maneuvers between June 1987 andMarch1988 in itsbasichardware andsoftware configuration. Thelateral-directional maneuvers werelessthan idealfor parameter identification because of highcorrelations between differentcontrolsurfaces andbecause of control systeminputsby the rate feedback controlsystem,hinderingthe assessment of individualcontrol effectiveness. In addition,uncommanded aircraftmotionswereinvolvedabove 20° angleof attackbecause of unsteady aerodynamics, suchasseparated andvorticalflows,overtheaircraft. Statenoisewasusedto modelthis uncommanded forcingfunction.

Twomaneuvers, onenear10 ° andtheothernear 32° angleofattack, wereexamined in detail,underscoring the difficulties introduced bytheF-18controlsystem (e.g.,theaileron-to-rudder and rudder-to-aileron interconnects) in response to lateral stick inputs and rudder inputs. Because of near linear dependency problems between the aileron and differential stabilator control surfaces, an equivalent lateral control _L was defined to denote a combined aileron and differential stabilator control.

Despite the degraded maneuvers, lateral-directional stability and control derivatives (Clf_,Cnf_,Cyf_, CI_L, Cn_L, CysL, Cl_r, Cn_ r, Cy 6 ,.Ctr. CI , Cn , and Cnr ) were estimated, plotted, and compared with wind-tunnel predictions. The coefficients of }av, ing moment due to sideslip (C%) and lateral force due to sideslip (Cyf_) exhibited good comparison with w rod-tunnel prediction, capturing predominant trends over the entire angle-of- attack range. Estimated derivatixc, lot the equivalent lateral control were fair. The rudder derivatives showed fair comparison as well. The rotaD dcn_ atl_ e, exhibited largely poor correlation between flight estimate and prediction.

Dryden Flight Research Center National Aeronautics and Space Admtm._tration Edwards, California, November. /996 REFERENCES 1. Gilbert, William P. and Donald H. Gatlin, "Review of the NASA High-Alpha Technology Program," High- Angle-of-Attack Technology - Volume 1, NASA CP-3149, Part 1, Joseph R. Chambers, William P. Gilbert, and Luat T. Nguyen, editors, Langley Research Center, Hampton, Virginia, May, 1992, pp. 23-59.

2. Klein, Vladislav, Thomas P. Ratvasky, and Brent R. Cobleigh, Aerodynamic Parameters of High-Angle-of- Attack Research Vehicle (HARV) Estimated From Flight Data, NASA TM- 102692, Aug. 1990.

3. Klein, Vladislav, "Aerodynamic Characteristics of High-Angle-of-Attack Research Vehicle (HARV) Determined From Flight Data," High-Angle-of-Attack Technology - Volume 1, NASA CP-3149, Part 1, Joseph R. Chambers, William P. Gilbert, and Luat T. Nguyen, editors, Langley Research Center, Hampton, Virginia, Oct. 30 to Nov. 1, 1990, pp. 265-278.

4. Moes, Timothy R. and Stephen A. Whitmore, A Preliminary Look at Techniques Used to Obtain Airdata From Flight at High Angles of Attack, NASA TM-101729, Dec. 1990.

5. Whitmore, Stephen A., Timothy R. Moes, and Terry J. Larson, Preliminary Results From a Subsonic High Angle-of-Attack Flush Airdata Sensing (HI-FADS) System: Design, Calibration, and Flight Test Evaluation, NASA TM-101713, 1990 (also available as AIAA 90-0232, Jan. 1990).

6. Richwine, David M., Robert E. Curry, and Gene V. Tracy, A Smoke Generator System for Aerodynamic Flight Research, NASA TM-4137, Sept. 1989.

7. Fisher, David E, John H. Del Frate, and David M. Richwine, In-Flight Flow Visualization Characteristics of the NASA F-18 High Alpha Research Vehicle at High Angles of Attack, NASA TM-4193, May 1990.

8. Fisher, David E, David M. Richwine, and Daniel W. Banks, Surface Flow Visualization of Separated Flows on the Forebody of an F-18 Aircraft and Wind-Tunnel Model, NASA TM-100436, May 1988.

9. Fisher, David E and Robert R. Meyer, Jr., Flow V_sualization Techniques for Flight Research, NASA TM-100455, Oct. 1988.

10. Iliff, Kenneth W. and Richard E. Maine, Practical Aspects of Using a Maximum Likelihood Estimation Method to Extract Stability and Control Derivatives From Flight Data, NASA TN D-8209, Apr. 1976.

11. Iliff, Kenneth W., Richard E. Maine, and Mary E Shafer, Subsonic Stability and Control Derivatives for an Unpowered, Remotely Piloted 3/8-Scale F-15 Airplane Model Obtained From Flight Test, NASA TN D-8136, Jan. 1976.

12. Iliff, Kenneth W., "Identification and Stochastic Control with Application to Flight Control in Turbulence," UCLA-ENG-7430, Ph.D. Dissertation, University of California, Los Angeles, California, May 1973.

13. Maine, R. E. and K. W. Iliff, Identification of Dynamic Systems, AGARD-AG-300-Vol. 2, Jan. 1985 (also available as NASA RP-1138, Feb. 1985).

14. Iliff, Kenneth W., "Identification and Stochastic Control of an Aircraft Flying in Turbulence," Journal of Guidance and Control, vol. 1, no. 2, March-April, 1978, pp. 101-108.

15. Iliff, Kenneth W. and Lawrence W. Taylor, Jr., Determination of Stability Derivatives From Flight Data Using a Newton-Raphson Minimization Technique, NASA TN D-6579, Mar. 1972.

16. Groll, D. B., R. K. Hess, W. D. Hodges, and R. E Moomaw, "F/A-18A Flight Control System Design Report," Vols. I, II, and III, MDC A7813, rev. A, McDonnell Aircraft Co., McDonnell Douglas Corp., St. Louis, Missouri, Sept. 1984.

17.Moran, W.A., "Operational andDevelopmental Experience withtheF/A-18ADigitalFlightControlSystem;' Active Control Systems - Review, Evaluation and Projections, AGARD Conference Proceedings No. 384, Flight Mechanics Panel Symposium, Toronto, Canada, October 15-18, 1984, pp. 12A 1-13.

18. Burton, R. A., B. T. Kneeland, U. H. Rabin, and R. S. Hansen, "Flight Testing and Development of the F/A-18A Digital Flight Control System," Active Control Systems - Review, Evaluation and Projections, AGARD Conference Proceedings No. 384, Flight Mechanics Panel Symposium, Toronto, Canada, October 15-18, 1984, pp. 12B 1-18.

19. Anon., "F/A-18 Basic Aerodynamic Data," MDC A8575, McDonnell Aircraft Co., McDonnell Douglas Corp., St. Louis, Missouri, 1984.

20. Pelikan, R. J. and R. L. Swingle, "F/A- 18 Stability and Control Data Report," Vols. I and II, MDC A7247, rev. B, McDonnell Aircraft Co., McDonnell Douglas Corp., St. Louis, Missouri, Aug. 1981.

EC89096-215

Figure1.NASAF-18HighAngle-of-Attack Research Vehicle.

Leading-edge flaps flaps 21.6 ft extension Leading-edge /

L

(wing-body strake) brake Airdata boom --_ _._ 56 ft _- 15.3 ft 10.5 ft

L

_I

Wing area = 400 ft 2 MAC = 11.52 ft _ 37 4 ft _i Aspect ratio = 3.5 Stabilator area : 88.26 ft 2 Weight = 31,980 Ib (includes 60 percent fuel condition of 6,480 Ib) 960825 Figure 2. Three-view of the F-18 with major dimensions shown.

State noise I Measurement Measured

I T.,, I _ noise

Control input response Estimated response r\ j MathematiCalof aircraftm°del I ] (state estimator) Response error computational likelihood _._ Gluli-Nlwlon I algorithm cost functional Maximum ] estimate of Maximum likelihood aircraft parameters 96O578 Figure 3. Maximum likelihood estimation concept with state and measurement noise.

AOA, deg 40 x 103 Z 30 .......................................................

Altitude, ft !

i i !

10 ......................................... ,................................................. + .......................................................................................... ' ............................................................................................

: i ; L I .5 .................................................................. ! ........................................ !............................... _ .......................

.3 ............................................................................................... _ ............................................. i............................................ _ ......................................................................................

Mech number .2 .1 100 ............................................................................................................................................................................................................. '................................................... : .......................................... : 80 ........................................................................................................................... _ ................................................ _ ............................................ i Dynamic pressure, Iblft 2 40 ............................................... ' ................................................................................................................................................................................................................

i 0 2 4 6 8 10 12 Time, eec 960826 (a) Figure 4. Time-history data from a typical lateral-directional PID maneuver at low AOA.

deg -2 -4 Angular rates, 0 deg/sec -10 - 20 - 30 .3 ................................... _ ............................. T ........................................................................ T ...............................................................................

.2 [ ...........................................................................

I .I ay, g _o2 _°3 3O Control deflections, 0 deg -10 - 20 - 30 0 2 4 6 8 10 12 Time, sec 960e27 (b) Figure 4. Continued.

Pilot inputs Control deflections, deg

--k/'. _T _ .... _ ...... --"-----_"- ', ,,- _

-10 - 20 - 30 Control deflections, 0 deg -5 -10 i i i -15 2 4 6 8 10 12 Time, eec 960828 (c) Figure 4. Continued.

Pilot inputs -1 -2 15 ................................... _ ........................... .

Control deflections, deg -5 -10 - 20 Control 8dh/(0.42) deflections, deg -5 -10 -15 .5 1.0 1.5 2.0 Time, sec 960629 (d) Figure 4. Concluded.

3O O 8a [] 5dh O (_r A _LEF 4 _I'EF 3.0-in. lateral 2O stick step Differential control surface deflection, deg

\

\

0 5 10 15 20 25 30 35 AOA, deg 9sos3o Figure 5. Differential ct,ntrol surface deflection schedule due to aileron input (with ARI).

0 8 a [] (_dh 0 8 r 100-1b rudder step Differentia I control surface deflection, deg 0 5 10 15 20 25 30 35 AOA, deg 960831 Figure 6. Differential control surface deflection schedule due to rudder input (with RAI).

AOA, 2O deg Altitude, ft .5 .4 .3 Mach number .2 .I 50 ............................................. _ ....................... _ 40 _-.: ............. '.7.: ............................. _ ......... i .............................................................................................. i................................................... i.............................................. i................................................. i.......................................... i Dynamic 30 pressure, Ib/_ 2o

J J

0 5 10 15 20 25 30 Tlme, sec _0_2 (a) Figure 7. Time-history data from a typical lateral-directional PID maneuver at high AOA.

deg -1 Angular rates, deg/sec -5 -10 .3 ............................................................................................. :................................................................................................. _ ......................................................................................

i i i i : 1 ay, g I _,2

!

-- .3 30 [ ....................................................................................................... r .................................................. • .................................................. z .................................................. _ .................................................

20 ' [ _; : i • dt : 10 =, = _, _ ' 'it " /"t = t ! : Control deflections, deg -10 ............ _'!'_ ................ " ; i , v I #_ i ' -, a • _ o i , ! ' - 20 - 30 0 5 10 15 20 25 30 Time, sec 960833

(b)

Figure 7. Continued.

arc-in.

Pilot inputs '-' r , in. i ',: -2 P .... : .................................... i ............................................................

-4 ; 10 ....J, ............................... ] ........................................... X,' ........................

:L /--50 _: ......... ..................................... .............................

Control deflections, 0 deg -10 J i u : s "°'-- '"' ''_ i i ....... T._ ................... i ................. i _ ....................... i • ..................................

- 20 ....... _ ............................................................................. _..._ ............................. :_ ......... ,," .......... ',, ;J _ l, ........... , i ! ',1 ,,1 - 30 Control deflections, deg -5 ....................................................................................................................................................................................................................................................................................... i -10 5 10 15 20 25 30 Time, sec 960834 (c) Figure 7. Continued.

Pilot inputs -1 -2 ..................... G e ............................... ............................................... _.i .................................. ,._;:_.. ............. i............................................................ ' Control deflections, deg -5 -I0 ........................................................................ _ ......................................................... _............................................................................. r .....................................

lO i i ) Control deflections, deg o_' !

-5 -10 i i i 0 .5 1.0 1.5 2.0 Time, sec 96o835 (d) Figure 7. Continued.

Pilot inputs -2 -4 10 .....

-_ ....---....

Control deflections, deg -5 -I0 Control deflections, deg -5 -10 17.0 17.5 18.0 18.5 19.0 Time, sec 960836 (e) Figure 7. Concluded.

6 x ...................................... 10 -3 ............................................................. _ .................... _ ................... _ ................. ,..................... _ ...............

Cll3 0 5 10 15 20 25 30 35 40 45 50 AOA, deg 960837 (a) Clp as a function of AOA.

8x10 -3 i _ i !!114-,- i ; ................... "[iT I - t .................... _ .............. i .................... i ................... _11][I t ........................... i .................... T .................... _ .................. !

..___-_.[._ _,. ............ .-.. _ ..........................................

Cnl_ -2 -4 -6 -8 0 5 I 0 15 20 25 30 35 40 45 50 AOA, deg 960838 (b) Cnp as a function of AOA.

Figure 8. Sideslip derivatives as functions of AOA.

.O4 .03 I --r ...............................

.02 i .01 CYl3 .... i................. i................. i.................... i - .01 - .02 - .03 J i ., _ i - .04 5 10 15 20 25 30 0 35 40 45 50 AOA, deg 960839 (c) Cyf_ as a function of AOA.

Figure 8. Concluded.

6x 10 -3

............. i-: ........ j-

I r-- --d-..... L ........

Cl8 L _-.-< ................................. r...-j., ..........

-1 -2 0 S I 0 15 20 25 30 35 40 45 50 AOA, deg 9sos4o (a) C16L as a function of AOA.

Figure 9. Equivalent lateral control derivatives as functions of AOA.

4 10 -3 i ........ i i -- i i .......... i ..... i 1 ......... I............. _..'

:_

." ."..'.." ( I : '..........

' i i i Cn_ L 0 ............ ___ i.i i _ _ ....................

-I -2 ...................................... ........... .......

-i i

-3 -4 40 45 50 5 10 15 20 25 30 35 AOA, deg _0_I (b) Cn6 L as a function of AOA.

.O4 .......................................................... i..................... i......................................... r............................................................. f ................... .O3 .02 ................... i......................................... : ................. i ......................................... i.................. _ .................... !.....

i ! _ ' i i

I '

o i_ LT _- T '. :=-

CY8 L - .01 i ff -i : i --, -.02 i - : _ --_ --_ ..........

!

/

i k i _ E

- .03 ...................................... i.................... _ .................... _ .................... !................................................................................ _ .....................

-.o4 i ! i I i ! :_

0 5 10 15 20 25 30 35 40 45 50 AOA, deg 96o842 (c) Cr_. as a function of AOA.

Figure 9. Concluded.

4 x 10-3 Cl(_ r -1 -2 i !

i -3 -4 0 5 10 15 20 25 30 35 40 45 50 AOA, deg 96o843 (a) CI_ r as a function of AOA.

0 5 10 15 20 25 30 35 40 45 50 AOA, deg 96O844 (b) Cn6 r as a function of AOA.

Figure 10. Rudder derivatives as functions of AOA.

.03 .02 ....................................... i................... i.......................................... ! .................................

.01 ................. T .................... i.................... i.................... t.................... T .................... _ ........................................... _ .................... t.................... i CY_r .......... ............. _ .................... ,. ......................... _ ............. _.7._.=.T_l:_t:.- i - .01 - .02 - .03 - .04 0 5 10 15 20 25 30 35 40 45 50 AOA, deg 9eo_s (c) Cy8 r as a function of AOA.

Figure 10. Concluded.

2.0 I 1.5 1.0 .5 CIp =.5 i : i - 1.0 I - 1.5 = i i - 2.0 5 10 15 20 30 35 40 45 50 AOA, deg 96o846 (a) Clp as a function of AOA.

Figure 11. Rotary derivations as functions of AOA.

2.o ..............................i ........................................................ .............. - 1.5 1.0 .......... i ...... i ..............................

T -r L

5 l i

I _B-- _-- ., _r- Cl r _ .._......_

o ......... _!

--,5 _ ( -1.0 ...... i ..........

-1.s i

....... -i ...... i

i'

-2.0 i 0 5 10 15 20 25 30 35 40 45 50 AOA, deg _0_7 (b) fir as a function of AOA.

2.0

J

1.5 i 1.0 . .

.5 Cnp 0 --,5 - 1.0

....ii ii

- 1.5 - 2.0 0 5 10 15 20 25 30 35 40 45 50 AOA, deg 960848 (c) Cnp as a function of AOA.

Figure 11. Continued.

2.0 i - - 1.5 I I 1.0 s •

i

...._ m .5 C ob.- ! i ........... _4 ..........................

Cn r ........... _t ........................ ) ..........

m.5 ! i t - 1.0 i - 1.5 ................... i..................... i ......

i .

...... !I........... i......

-2.0 0 10 15 20 25 30 35 40 AOA, deg 960849 (d) Cn_ as a function of AOA.

Figure 11. Concluded.

REPORT DOCUMENTATION PAGE Form Approved OMB No. 0704-0188 Public reporting burden for this collection of informatio_ is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway. Suite 1204, Arlington.

VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503 1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORTTYPE AND DATES COVERED February 1997 Technical Memorandum 4.TITLE AND SUbTiTLE 5. FUNDING NUMBERS Extraction of Lateral-Directional Stability and Control Derivatives for the Basic F- 18 Aircraft at High Angles of Attack WU505-68-50 6. AUTHOR(S) Kenneth W. Iliff and Kon-Sheng Charles Wang 7.PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION REPORT NUMBER NASA Dryden Flight Research Center P.O. Box 273 H-2143 Edwards, California 93523-0273 9. SPONSORING/MONiTOrING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING/MONITORING AGENCY REPORT NUMBER National Aeronautics and Space Administration NASA TM-4786 Washington, DC 20546-0001 11. SUPPLEMENTARY NOTES 12e. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE Unclassified--Unlimited Subject Category 08 13. ABSTRACT (Maximum 200 words) The results of parameter identification to determine the lateral-directional stability and control derivatives of an F-18 research aircraft in its basic hardware and software configuration are presented. The derivatives are estimated from dynamic flight data using a specialized identification program developed at NASA Dryden Flight Research Center. The formulation uses the linearized aircraft equations of motions in their continuous/discrete form and a maximum likelihood estimator that accounts for both state and measurement noise. State noise is used to model the uncommanded forcing function caused by unsteady aerodynamics, such as separated and vortical flows, over the aircraft. The derivatives are plotted as functions of angle of attack between 3 ° and 47 ° and compared with wind-tunnel predictions. The quality of the derivative estimates obtained by parameter identification is somewhat degraded because the maneuvers were flown with the aircraft's control augmentation system engaged, which introduced relatively high correlations between the control variables and response variables as a result of control motions from the feedback control system.

14. SUBJECTTERMS 15. NUMBER OF PAGES Aerodynamics, Flight-to-wind-tunnel comparisons, F-I8 aircraft, High angle of attack, 16. PRICE CODE Maximum likelihood estimation, Parameter identification, Stability and control derivatives A03 17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATION OF ABSTRACT OF REPORT OF THIS PAGE OF ABSTRACT Unclassified Unclassified Unclassified Unlimited NSN 7540-01-280-5500 Available from the NASA Center for AeroSpace Information, 800 Elkridge Landing Road, Standard Form 298 (Rev. 2-89) Linthicum Heights, MD 21090; (301)621-0390 Pructtbed by ANSI Std. Z39-18 298-102