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

1997

CONTENTS

ABSTRACT .............................................................................. 1

NOMENCLATURE ........................................................................ 1

INTRODUCTION .......................................................................... 3

VEHICLE DESCRIPTION ................................................................... 4

INSTRUMENTATION AND DATA ACQUISITION ............................................. 5

PARAMETER IDENTIFICATION METHODOLOGY ............................................ 6

RESULTS AND DISCUSSION ............................................................... 9

Parameter Identification Maneuvers ......................................................... 9

Extracted Stability and Control Derivatives .................................................. 11

CONCLUDING REMARKS ................................................................ 12

REFERENCES ........................................................................... 14

TABLE

F-18 aerodynamic control surface position and rate limits ........................................... 5

FIGURES

1. NASA F- 18 High Angle-of-Attack Research Vehicle .......................................... 16

2. Three-view of the F- 18 with major dimensions shown ........................................ 17

3. Maximum likelihood estimation concept with state and measurement noise ........................ 18

4. Time-history data from a typical lateral-directional PID maneuver at low AOA ..................... 19

5. Differential control surface deflection schedule due to aileron input (with ARI) ..................... 23

6. Differential control surface deflection schedule due to rudder input (with RAI) ..................... 23

7. Time-history data from a typical lateral-directional PID maneuver at high AOA .................... 24

8. Sideslip derivatives as functions of AOA ................................................... 29

9. Equivalent lateral control derivatives as functions of AOA ..................................... 30

10. Rudder derivatives as functions of AOA .................................................... 32

11. Rotary derivations as functions of AOA .................................................... 33

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 windtunnel 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

ARI

DFRC

FADS

FCS

HARV

HATP

LEF

LEX

NACA

PCM

PID

PROM

RAI

TEF

Symbols

ay

A, B, C, D, F, G

Clp

Clr

angle of attack, deg

aileron-to-rudder interconnect

NASA Dryden Flight Research Center, Edwards, California

flush airdata system

flight control system

High Angle-of-Attack Research Vehicle

High Angle-of-Attack Technology Program

leading-edge flap

leading-edge extension (wing-body strake)

National Advisory Committee for Aeronautics

pulse code modulation

parameter identification

Programmable Read-Only Memory

rudder-to-aileron interconnect

trailing-edge flap

lateral acceleration, g

system matrices

coefficient of rolling moment due to roll rate, rad -t

coefficient of rolling moment due to yaw rate, rad -1
C I[_

ClSa

Cl_dh

Cl_ L

Clsr

Cn r

C

n_

CnSdh

Cn_ L

C

118 r

Cy_

Cy_

CYsdh

CY8 L

CY8

f

g

GG*

H

J

N

n

P

R

U

X

coefficient of rolling

coefficient of rolling

coefficient of rolling

moment due to sideslip, deg -1

moment due to aileron deflection, deg -1

moment due to differential horizontal stabilator deflection, deg -I

coefficient of rolling moment due to lateral deflection, deg -1

coefficient of rolling moment due to rudder deflection, deg -1

coefficient of yawing moment due to roll rate, rad -!

coefficient of yawing moment due to yaw rate, rad -1

coefficient of yawmg moment due to sideslip, deg -1

coefficient of yawing moment due to aileron deflection, deg -1

coefficient of yawing moment due to differential horizontal stabilator deflection, deg -1

coefficient of yawing moment due to lateral deflection, deg -1

coefficient of yawing moment due to rudder deflection, deg -1

coefficient of lateral force due to sideslip, deg -1

coefficient of lateral force due to aileron deflection, deg -l

coefficient of lateral force due to differential horizontal stabilator deflection, deg -1

coefficient of lateral force due to lateral deflection, deg -1

coefficient of lateral force due to rudder deflection, deg -1

system state function

system observation function

measurement noise covariance matrix

approximation to the information matrix

cost function

number of time points

state noise vector

roll rate, deg/sec

innovation covariance matrix

yaw rate, deg/sec

time, sec

known control input vector

state vector

time derivative of state vector
z

_a

Sap

5dh

_LEF

r

_rp

_TEF

v¢

Subscripts

predicted state estimate

observation vector

predicted Kalman filter estimate

angle of attack, deg

angle of sideslip, deg

aileron deflection, deg

pilot aileron input, arc-in

differential horizontal stabilator deflection, deg

equivalent combined lateral deflection of aileron and stabilator, deg

leading-edge flap deflection, deg

rudder deflection, deg

pilot rudder input, in

trailing-edge flap deflection, deg

measurement noise vector

unknown parameter vector

estimate of

gradient with respect to

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 HighAngle-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 phaseI, whichbeganin mid-1987andcontinuedthrough1989,theHARVflew 101researchmissions,

investigatinghigh-AOAflight up to 55°. PhaseI examineddevelopmental issuesof the HARV research

instrumentationsuite and establishedinitial aerodynamiccorrelationsbetweenpredictionsand in-flight

measurements(e.g.,of tail buffetandvortexburstlocationfor thewing-body-strakevortices).PhaseII involved

majorhardwareandsoftwaremodificationstotheHARV,incorporatingamulti-axisthrust-vectoringcontrolsystem

andresearchflightcontrolsystem(FCS).Thisphase,frommid-1991tolate1994,aggressivelyexpandedtheHARV

flightenvelope.Demonstratedcapabilitiesincludestabilizedflightat70°AOAandrollingathighratesat65°AOA.

PhaseIII flightsbeganin 1995andwerecompletedbyMay 1996.Thesetestsfocusedontheimplementationof

actuatedforebodystrakesmountedonthenoseof theHARVtoenhancedirectionalcontrolathighAOA.

A continuingobjectiveoftheflightprogramwasthestudyofthestabilityandcontrolcharacteristicsoftheF-18

aircraftduringlow-speed,high-AOAflight(refs.2and3).Thispaperaddressestheanalysisandresultsofparameter

identification(PID)conductedatDFRCto extractlateral-directional stabilityandcontrolderivativesof thebasic

F-18configurationfromdynamicflightdata.Theresults,basedon42maneuversfromphaseI flights11through38

(flownbetweenJune1987andMarch1988),wereusedtoinitiallyassessstabilityandcontrolderivativesobtained

fromwind-tunneltestsandearlyflighttestbythemanufacturer andU.S.Navy.Thederivativeswereextractedusing

a DFRC-developedcomputerprogram,whichusesthelinearizedaircraftequationsof motionanda maximum

likelihoodestimatorthataccountsforstateandmeasurement noise.Themaneuversanalyzedrangedfrom3° to47°

AOA.Inthispaper,thederivativesareestimated, plotted,anddiscussedrelativetowind-tunnelpredictionsandflight

maneuverquality.

VEHICLE DESCRIPTION

The aircraft testbed was the sixth full-scale developmental F-18 (fig. 1), a single place, twin-engine, fighterattack 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 highAOA 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 (_ia), differential horizontal stabilators (_dh), and asymmetric

LEFs (_LEF) and TEFs (_TEF). Directional control is provided by symmetric rudder deflection (_ir) and a rudder-toaileron interconnect (RAI) between _r and both 8a 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.

4
Thecomputer-basedFCSfeaturesdigitalinputsfromredundantproductionsensorsetsandairdata.Thepilot

commandsprovideautomaticmodelogic,gainscheduling, input-outputmanagement, andsurfacemanagement. The

FCSis adigitally-mechanizedfly-by-wirecontrolaugmentationsystem.ThestandardF-18versionV8.3.3flight

controlawis implementedonfour701B(GeneralElectric,Lynn,Massachusetts) digitalflightcontrolcomputers,

alongwith surfaceactuatorsandanalogsensors,to providea dual-failureoperationalcapability.TheFCSwas

developedwithcompletefailuredetection,failuremanagement, andappropriatemodeswitchingin theeventof

certainfailures.Adigitaldirectelectricalcontrolmodeprovidesafly-by-wireopen-loopcontrollawincasecertain

motionsensorsfail.In addition,amechanical controlmodeisprovidedincasethefly-by-wirecontrolsystemsfail.

Thissystemprovidesadirectmechanical link fromthepilot'ssticktothelongitudinaltrimandstabilatoractuators.

Themechanical modeprovidespitchandrollcontrolfromthepilot'ssticktothestabilators.

F-18aerodynamiccontrolsurfacepositionandratelimits.

Positionlimit, Ratelimit,

Surface deg deg/sec

Stabilator:

Trailing-edgeup 24 40

Trailing-edgedown 10.5 40

Aileron:

Trailing-edgeup 24 100

Trailing-edgedown 45 100

Rudder:

Trailing-edgeleft 30 82

Trailing-edgeright 30 82

TEF:

Up 8 18

Down 45 18

LEF:

Up 3 15

Down 33 15

Speedbrake:

Trailing-edgeup 60 20to 30

ThemissioncomputerprovidesMIL-STD-1553multiplexbuscontrol.Thisdatabusprovidesanintegrated

controlsystemandastandardinterfacefor allequipmentconnectedtothebus.

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
AOAandsideslipvanes.(Althoughtherightwingtipprobewasinstalled 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, highfrequency 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

6
in thenextsection.Tobetteranalyzetheexistingmaneuvers, it wasnecessaryto accountfortheuncommanded

portionsoftheaircraftmotion.

Theprocedureimplementedin thisanalysisusesstatenoiseto modeltheuncommandedforcingfunction.

References12,13,and14completelydescribethetechnique.ThetechniqueappliedtotheF-18dataalsorequired

thatthenormalaircraftequationsof motionbelinearin theaerodynamiccoefficients;thispresentednoparticular

difficultybecausethe normalstabilityandcontrolderivativeswerealreadylocally linearapproximationsof

nonlinearaircraftaerodynamics.

Toperformtheanalysispresentedhere,anexistingparameterestimationcomputerprogramwasmodifiedto

properlyaccountfortheadditionalcomplexityrequiredtoincludetheeffectsof thestatenoise(commandsdueto

separatedand vorticalflows)on thestabilityandcontrolmaneuvers.A brief descriptionof the statenoise

algorithmfollows.

It ispossibletomakeaprecise,mathematicallyprobabilisticstatement oftheparameterestimationproblem.The

first stepis to definethegeneralsystemmodel(aircraftequationsof motion).Thismodelcanbewrittenin the

continuous/discreteformas

x(t0) = x 0

x(t) = f[x(t), u(t), _] + F(_)n(t)

z(ti) = g[x(ti), u(ti), _] + G(_)_i

(1)

(2)

(3)

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"1is 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

1

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 Kalmanfiltered 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) ]

If R is assumed fixed, the first and second gradients are defined as

(8)

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

N .

i=1

The Gauss-Newton approximation to the second gradient is

(10)

N ,

i=1

(11)

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 8a 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 8a 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 8a and 8dh resulted in very poor estimates for _a

9
and _dh effectiveness; so the PID results for 8a and 8dh given here are for an equivalent combined lateral control

defined as 5L. 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:

CIsL = Q_a + 0.42 Q6ah (12)

Crtts L -_ Cn_ a "at-0.42 Cn_dh (13)

CYSL = CYsa + 0.42 CYsdh (14)

The wind-tunnel predictions of C/_L, CnaL, 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 8a, 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 8a, 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 8a, 8dh, and 8r. 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 8a, 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 8r deflection. Near 17 sec, the pilot lateral stick input can be seen along with the resulting deflections of 8a, _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, 8a is highly correlated with 0.42 _dh' and 8r is seen to be about

10
four times-_5a. Fortunately, the rate limit in the _r surface, seen in figure 7(d), should result in some linear

independence between _a and _5r, which will allow, however marginally, an estimate of 5a and 5dh effects (through

_5L ) independent from 5r 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 _5a and _dh call be seen. The rate limit saturation of i_r here shows limited independence

between _5a 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.

11
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:

C18L = 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 C16L 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

12
andMarch1988initsbasichardwareandsoftwareconfiguration. Thelateral-directional maneuverswerelessthan

idealfor parameteridentificationbecauseof highcorrelationsbetweendifferentcontrolsurfacesandbecauseof

control systeminputsby the rate feedbackcontrolsystem,hinderingthe assessment of individualcontrol

effectiveness. In addition,uncommandedaircraftmotionswereinvolvedabove20° angleof attackbecauseof

unsteadyaerodynamics, suchasseparatedandvorticalflows,overtheaircraft.Statenoisewasusedto modelthis

uncommandedforcingfunction.

Twomaneuvers, onenear10° andtheothernear32° angleofattack,wereexaminedindetail,underscoringthe

difficultiesintroducedbytheF-18controlsystem(e.g.,theaileron-to-rudder andrudder-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-ofattack 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

13
REFERENCES

1. Gilbert, William P. and Donald H. Gatlin, "Review of the NASA High-Alpha Technology Program," HighAngle-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-ofAttack 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.

14
17.Moran,W.A., "OperationalandDevelopmental ExperiencewiththeF/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.

15
Figure1.NASAF-18HighAngle-of-AttackResearchVehicle.

EC89096-215

16
Leading-edge

flaps

Leading-edge /

extension

(wing-body strake)

Airdata

boom --_

flaps

brake

21.6 ft

L

_._ 56 ft _-

10.5 ft

_I

15.3 ft

L

Wing area = 400 ft 2

MAC = 11.52 ft

Aspect ratio = 3.5

Stabilator area : 88.26 ft 2

Weight = 31,980 Ib

(includes 60 percent

fuel condition of

6,480 Ib)

_ 37 4 ft _i

960825

Figure 2. Three-view of the F-18 with major dimensions shown.

17
Control input

State noise I Measurement

I T.,, I _ noise

j MathematiCalof aircraftm°del I

] (state estimator)

Gluli-Nlwlon I

computational

algorithm

Maximum likelihood

estimate of

aircraft parameters

Measured

response

Estimated

response

Maximum ]

likelihood _._

cost functional

r\

Response

error

96O578

Figure 3. Maximum likelihood estimation concept with state and measurement noise.

18
AOA,

deg

15

10

Altitude,

ft

40 x 103

Z

30 .......................................................

20

!

i i !

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

: i

; L

I

0

Mech

number

Dynamic

pressure,

Iblft 2

.5.................................................................!.......................................!..............................._......................

.2

.1

0

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

100 ............................................................................................................................................................................................................. '................................................... :.......................................... :

80 ........................................................................................................................... _ ................................................ _............................................ i

60

40 ............................................... ' ................................................................................................................................................................................................................

20

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.

19
deg

-2

-4

Angular

rates,

deg/sec

30

20

10

0

-10

- 20

- 30

ay,

g

Control

deflections,

deg

.3

.2

.I

0

_o2

_°3

3O

20

10

0

-10

- 20

- 30

................................... _............................. T........................................................................ T...............................................................................

[ ........................................................................... I

0 2 4 6 8 10 12

Time, sec

960e27

(b)

Figure 4. Continued.

20
Pilot

0

inputs

Control

deflections,

deg

30

20

10

0

-10

- 20

- 30

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

Control

deflections,

deg

15

10

5

0

-5

-10

-15

0

i i i

2 4 6 8 10 12

Time, eec 960828

(c)

Figure 4. Continued.

21
Pilot

inputs 0

-1

-2

Control

deflections,

deg

15 ................................... _........................... .

10

5

0

-5

-10

- 20

Control

deflections,

deg

15

10

5

0

-5

-10

-15

8dh/(0.42)

.5 1.0 1.5 2.0

Time, sec

960629

(d)

Figure 4. Concluded.

22
Differential

control

surface

deflection,

deg

3O

25

2O

15

10

5

0

\

\

5 10 15 20 25 30 35

AOA, deg 9sos3o

O 8a

[] 5dh

O (_r

A _LEF

4 _I'EF

3.0-in. lateral

stick step

Figure 5. Differential ct,ntrol surface deflection schedule due to aileron input (with ARI).

Differentia I

control

surface

deflection,

deg

30

25

20

15

10

5

0 5 10 15 20 25 30 35

AOA, deg 960831

0 8a

[] (_dh

0 8 r

100-1b rudder

step

Figure 6. Differential control surface deflection schedule due to rudder input (with RAI).

23
AOA,

deg

2O

10

Altitude,

ft

Mach

number

.5

.4

.3

.2

.I

0

50 ............................................. _ ....................... _

40 _-.: ............. '.7.:............................. _ ......... i

Dynamic 30

pressure,

Ib/_ 2o

10

.............................................................................................. i................................................... i.............................................. i................................................. i..........................................i

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.

24
deg

1

0

-1

Angular

rates,

deg/sec

10

-5

-10

ay,

g

Control

deflections,

deg

0

_,2

-- .3

.3 ............................................................................................. :................................................................................................. _......................................................................................

i i i i

: 1

I

!

-10

- 20

- 30

30 [ ....................................................................................................... r .................................................. •.................................................. z .................................................. _ .................................................

20 ' [ _; : i

• dt :

10 =, = _, _

' 'it " /"t =

t ! :

............ _'!'_................ " ; i , vI #_ i ' -, a •

_ o i , ! '

0 5 10 15 20 25 30

Time, sec 960833

(b)

Figure 7. Continued.

25
Pilot

inputs

arc-in.

'-' r , in. i ',:

-2 P .... :.................................... i.........................................................

-4 ;

Control

deflections,

deg

30

20

10

0

-10

- 20

- 30

....J, ............................... ] ........................................... X,'........................ :L /--50 _: ......... ..................................... .............................

J ii i u : ....... T._ ................... i................. i _ ....................... i • .................................. s "°'-- '"' ''_

....... _............................................................................. _..._ ............................. :_.........,,".......... ',,

;J _ l, ........... ,i

! ',1 ,,1

10

Control

deflections,

deg

-5

-10

....................................................................................................................................................................................................................................................................................... i

0

5 10 15 20 25 30

Time, sec

960834

(c)

Figure 7. Continued.

26
Pilot

inputs

-1

-2

Control

deflections,

deg

10

-5

-I0

..................... Ge............................... ............................................... _.i .................................. ,._;:_.. ............. i............................................................ '

Control

deflections,

deg

........................................................................ _ ......................................................... _............................................................................. r ..................................... lO i i )

o_' !

-5

-10 i i i

0 .5 1.0 1.5 2.0

Time, sec 96o835

(d)

Figure 7. Continued.

27
Pilot

inputs

-2

-4

Control

deflections,

deg

10 .....

-5

-I0

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

Control

deflections,

deg

10

-5

-10

17.0 17.5 18.0 18.5 19.0

Time, sec

960836

(e)

Figure 7. Concluded.

28
Cll3

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

0 5 10 15 20 25 30 35 40 45 50

AOA, deg 960837

(a) Clp as a function of AOA.

Cnl_

6

4

2

0

-2

-4

-6

-8

8x10 -3

i _ i !!114-,- i ;

................... ..___-_.[._ "[iT t.................... _.............. Ii.................... -_,............ i................... .-.. _11][I t........................... _..........................................i.................... T.................... _.................. !

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.

29
CYl3

.O4

.03

.02

.01

0

- .01

- .02

- .03

- .04

I --r ...............................

i

J

., _

i

5 10 15 20 25 30

AOA, deg

....i................. i................. i.................... i

i

0 35 40 45 50

960839

(c) Cyf_ as a function of AOA.

Figure 8. Concluded.

Cl8 L

5

4

3

2

1

0

-1

-2

6x 10 -3

.................................r...-j., .........

............. i-:........ jI r-- --d-..... L ........

_-.-<

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.

30
1

Cn_ L 0

-I

-2

-3

-4

0

4 10 -3

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

...................................................

i ........ i

i -- i i

.......... i ..... i

......... I............. _..'

' i i i

............ ____.................... i.i i_

-i i

5 10 15 20 25 30 35 40 45 50

AOA, deg _0_I

(b) Cn6L as a function of AOA.

CY8 L

.O4

.O3 .......................................................... i..................... i......................................... r............................................................. f ...................

.02 ................... i......................................... : ................. i....................................... i.................. _................. !.....

i ! _ ' i i

I '

o i_ LT _- T '. :=-

- .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.

31
Cl(_ r

3

2

1

0

-1

-2

-3

-4

4 x 10-3

i !

i

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

AOA, deg

40 45 50

96O844

(b) Cn6r as a function of AOA.

Figure 10. Rudder derivatives as functions of AOA.

32
CY_r

.03

.02

.01

0

- .01

- .02

- .03

- .04

0

....................................... i................... i..........................................!.................................

................. T.................... i.................... i.................... t.................... T.................... _........................................... _.................... t.................... i

.......... ............. _.................... ,.......................... _ ............. _.7._.=.T_l:_t:.-

i

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.

CIp

2.0

1.5

1.0

.5

0

=.5

- 1.0

- 1.5

- 2.0

i : i

I

=

i

25

I

i

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.

33
Cl r

2.o ..............................i........................................................ .............. -

1.5

1.0 .......... i ...... i..............................T

-r

_B-- _--

5l i

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

--,5

-1.0 ...... i ..........

-1.s i

-2.0 i

0 5 10

., _rL

I

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

15 20 25 30

AOA, deg

_ .._......_

_ (

i'

35 40 45 50

_0_7

(b) fir as a function of AOA.

2.0

1.5

1.0

.5

Cnp 0

--,5

- 1.0

- 1.5

- 2.0

i

. .

0 5 10 15 20 25 30 35

AOA, deg

J

....ii ii

40 45 50

(c) Cnp as a function of AOA.

Figure 11. Continued.

960848

34
Cn r

2.0

1.5

1.0

.5

0

m.5

- 1.0

- 1.5

-2.0

0

i - -

...._i

m

................... i..................... i ......

C

ob.-

........... _4..........................

........... _t ........................

i .

10

) ..........

15 20 25 30

AOA, deg

I

I

s •

! i

! i

t

i

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

35 40

(d) Cn_ as a function of AOA.

Figure 11. Concluded.

960849

35
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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

6. AUTHOR(S)

Kenneth W. Iliff and Kon-Sheng Charles Wang

7.PERFORMINGORGANIZATIONNAME(S)ANDADDRESS(ES)

NASA Dryden Flight Research Center

P.O. Box 273

Edwards, California 93523-0273

9. SPONSORING/MONiTOrING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

11. SUPPLEMENTARY NOTES

WU505-68-50

8. PERFORMING ORGANIZATION

REPORT NUMBER

H-2143

10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

NASA TM-4786

12e. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified--Unlimited

Subject Category 08

13. ABSTRACT (Maximum 200 words)

12b. DISTRIBUTION CODE

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

Aerodynamics, Flight-to-wind-tunnel comparisons, F-I8 aircraft, High angle of attack,

Maximum likelihood estimation, Parameter identification, Stability and control derivatives

17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION

OF REPORT OF THIS PAGE OF ABSTRACT

Unclassified Unclassified Unclassified

NSN 7540-01-280-5500 Available from the NASA Center for AeroSpace Information, 800 Elkridge Landing Road,

Linthicum Heights, MD 21090; (301)621-0390

15. NUMBER OF PAGES

40

16. PRICE CODE

A03

20. LIMITATION OF ABSTRACT

Unlimited

Standard Form 298 (Rev. 2-89)

Pructtbed by ANSI Std. Z39-18

298-102