A Correlation Between Flight Determined Lateral Derivatives and Ground-Based Data for the Pilatus PC9A Training Aircraft in Cruise Configuration

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C I E N C E T E C H N O L O G Y R G A N I S A T I O N D S T O

A Correlation between Flight- determined Lateral Derivatives and Ground-based Data for the Pilatus PC 9/A Training A ircraft in Cruise

Configuration Hilary A . Keating, Nick van Bronswijk, Andrew D . Snowden and Jan S. Drobik DSTO-TR-0988

DISTRIBUTION STATEMENT A Approved fo r Public Release

D istribution Unlimited



A Correlation

between

Flight-determined

Lateral

Derivatives and Ground-based Data for the Pilatus PC 9/A Training Aircraft n Cruise

Configuration Hilary A. Keating, Nick van Bronswijk, Andrew D.

Snowden and Jan S. Drobik

Air Operations Division Aeronautical and Maritime Research Laboratory

DSTO-TR-0988

ABSTRACT A series of flight ests were conducted on the PC 9/A aircraft, A23-045,

at the Royal Australian A ir Force's Aircraft Research and Development Unit.

System identification techniques were applied to the data obtained from these

flight ests o determine the stability and control derivatives of the aircraft. The lateral results for the aircraft in cruise configuration are presented in this report and comparisons ar e made with empirical and ground based estimates.

APPROVED FOR PUBLIC RELEASE DEPARTMENT OF DEFENCE

IEFERCE CIENCE t TECIROLOGT O ICM I SHT ION D S T O flQfOOll-3VW



DSTO-TR-0988

Published by DSTO Aeronautical and Maritime Research Laboratory 506 Lorimer St , Fishermans Bend, Victoria, Australia 3207

Telephone: (03) 9626 7000 Facsimile: (03) 9626 7999 © Commonwealth of Australia 2000 AR No. AR-011-475 June, 2000

APPROVED FOR PUBLIC RELEASE



DSTO-TR-0988

A Correlation between Flight-determined Lateral Derivatives and Ground-based Data for the Pilatus PC 9/A

Training Aircraft n Cruise Configuration

EXECUTIVE SUMMARY A ir Operations Division A O D ) has developed, or acquired, a number of fixed-wing

flight dynamic models and is also responsible for providing advice to the Australian De-

fence Organisation A D O ) on flight simulator flight dynamic m ode l requirements. he

models generally make us e of extensive static and dynamic stability and control derivative

databases, in addition to engine and flight control models. The static model data m ay be

obtained from wind tunnel testing, whilst the dynamic data is traditionally obtained from

flight tests using system identification techniques.

T he system identification techniques used to estimate aerodynamic derivatives of con-

ventional aircraft ar e well established. The major requirement of these techniques is high fidelity measurements of manoeuvre input i.e. control surface deflections), and aircraft

response (i.e. angular rates and linear accelerations), as well as air data including airspeed,

altitude, angle-of-attack and angle-of-sideslip.

Following the completion of the A O D PC 9/A wind tunnel tests, the requirement ex -

isted fo r a dedicated flight dynamic modelling flight est program to both validate the flight dynamic model of the PC 9/A and to provide dynamic derivative estimates which

were unobtainable in the A M R L wind tunnel. A n instrumentation suite, including an air

data probe for the direct and accurate measurement of angle-of-attack, ngle-of-sideslip,

temperature, and static and dynamic pressure, w as fitted to the aircraft and a test ma-

noeuvre matrix w as designed specifically fo r the purpose of gathering flight dynamic data.

This flight test program w as conducted at the Aircraft Research and Development Unit (A RDU) during 1998/99.

This report details the analysis of the lateral manoeuvres carried out with the aircraft

in th e cruise configuration. he static and dynamic derivatives thus obtained ar e com-

pared with wind tunnel estimates s well as a number of empirical estimates obtained

from alternative sources. discussion of some of the difficulties encountered during the estimation process is also included. he data obtained from these tests will be used in th e development of the PC 9/A flight dynamic model fo r the purpose of enhancing A OD

support fo r the PC 9/A fleet, including possible upgrades to the part-task trainer.

1 1 1



DSTO-TR-0988

IV



DSTO-TR-0988

Authors Hilary Keating Air Operations Division Hilary Keating graduated ro m he University of Sydney n

1998, having obtained a Bachelor of Engineering in Aeronauti-

ca l Engineering with first class honours. he commenced em - ployment at A M R L in 1999, and has been involved in perfor-

mance modelling and parameter dentification of the Pilatus PC 9/A.

Nick van Bronswijk Air Operations Division Nick va n Bronswijk graduated from the University of Sydney

with first class honours in Aeronautical Engineering in 1995. He

is currently completing his P hD in the area of propeller power

effects. Since joining A M R L in 1998 he has been involved with a

range of projects including flight and w ind tunnel test programs

of the Pilatus PC 9/A.

Andrew Snowden Air Operations Division Andrew Snowden graduated from the Royal Melbourne Insti-

tute of Technology in 1991, having obtained a Bachelor of Engi-

neering in Aerospace Engineering with first class honours. Be -

fore com m encing work at A M R L he served a short term attach- m e nt with McDonnell Douglas in St. ouis, Missouri, s he recipient of the McDonnell Aircraft Company Aerospace Engi-

neering Prize fo r 1991. e commenced employment at A M R L

in 1992 and participated in several experimental investigations

in a number of different fields during his rotation. ow a full

time member of the flight dynamics and performance area of

the A ir Operations Division, hi s most recent work includes the organisation of flight testing for parameter identification of the Pilatus PC 9/A as well as performance estimation of modern jet fighters.



DSTO-TR-0988

Jan Drobik Air Operations Division Jan Drobik eads a eam hat s esponsible or he mple- mentation of solutions to flight dynamic problems which arise

throughout the ADF' s fleet of aircraft. ince joining the then A R L in 1978, he has acquired broad experience in the areas of

flight dynamics and experimental aerodynamics. e has been

responsible fo r the development of aircraft flight dynamic mod-

els and aerodynamic parameter estimation echniques within

A M R L , and has managed it s successful application to a wide

range of practical problems. e has been involved n TTCP activities in A ER Technical Panel A E R TP-5 for many years,

becoming Australian National Leader in 1998.

VI



DSTO-TR-0988

Contents

Glossary i Notation i 1 ntroduction

2 C 9/A Test Aircraft

2.1 ircraft Description

2.2 light Control System

2.3 eight, Centre-of-Gravity and Mass Moments-of-Inertia 3

nstrumentation

4 ethods of Analysis

4.1 tepwise Regression

4.1.1 Error Band

4.2 aximum Likelihood

4.2.1 Cramer-Rao Bounds

5 esults and Discussion

5.1 ngle-of-Sideslip Derivatives

5.2 aw Rate Derivatives

5.3 oll Rate Derivatives

5.4 ontrol Derivative

5.5 ariation of Lateral Derivatives with Rate of Climb and Angle-of-Attack

5.6 anoeuvre Type an d Altitude Dependancy

6 onclusions

References 0 Appendices

A Weight, Centre-of-Gravity and Mass Moments-of-Inertia 4

vn



DSTO-TR-0988

B ide Force, Rolling Moment and Yawing Moment Coefficients 6 B.l ide Force Coefficient 6

B.2 awing Moment Coefficient 6

B.3 olling Moment Coefficent 6

Figures

1 ir data boom installation 2

2 C 9/A angle-of-sideslip derivatives, 3-2-1-1 manoeuvres at 5000 ft 3 3 C 9/A angle-of-sideslip derivatives, 3-2-1-1 manoeuvres at 10 00 0 ft 4 4 C 9/A angle-of-sidslip derivatives, 3-2-1-1 manoeuvres at 15 00 0 ft 5 5 C 9/A angle-of-sidslip derivatives, doublet manoeuvres at 5000 ft 6 6 C 9/A angle-of-sideslip derivatives, doublet manoeuvres at 15 00 0 ft 7 7 C 9/A ya w rate derivatives, 3-2-1-1 manoeuvres at 5000 ft 8 8 C 9/A ya w rate derivatives, 3-2-1-1 manoeuvres at 10 00 0 ft 9 9 C 9/A ya w rate derivatives, 3-2-1-1 manoeuvres at 15 00 0 ft 0 10 C 9/A ya w rate derivatives, doublet manoeuvres at 5000 ft 1 11 C 9/A ya w rate derivatives, doublet manoeuvres at 15 00 0 ft 2 12 C 9/A roll rate derivatives, 3-2-1-1 manoeuvres at 5000 ft 3

13 C 9/A roll rate derivatives, 3-2-1-1 manoeuvres at 10 00 0 ft 4 14 C 9/A roll rate derivatives, 3-2-1-1 manoeuvres at 15 00 0 ft 5 15 C 9/A roll rate derivatives, doublet manoeuvres at 5000 ft 6 16 C 9/A roll rate derivatives, doublet manoeuvres at 15 00 0 ft 7 17 C 9/A control derivatives, 3-2-1-1 manoeuvres at 5000 ft 8

18 C 9/A control derivatives, 3-2-1-1 manoeuvres at 10 00 0 ft 9 19 C 9/A control derivatives, 3-2-1-1 manoeuvres at 15 00 0 ft 0 2 0 C 9/A control derivatives, doublet manoeuvres at 5000 ft 1

21 C 9/A control derivatives, doublet manoeuvres at 15 00 0 ft 2 22 ariation of lateral derivatives with nominal rate of climb 3

Bl elative magnitudes of Cy equation components 7

B 2 elative magnitudes of C „ equation components 8

B 3 elative magnitudes of dequation components 8

vm



DSTO-TR-0988

Tables 1 ateral derivatives estimated

2 ummary of derivatives estimated using max imum likelihood 3 ummary of derivatives estimated by stepwise regression Al light test aircraft m a ss distribution 3 , 4 ] 4

IX



DSTO-TR-0988



DSTO-TR-0988

Glossary

AHRS rtificial Horizon Reference System

A M R L eronautical and Marit ime Research Laboratory

A OD ir Operations Division

A R D U ircraft Research and Development Unit

D S T O efence Science and Technology Organisation

GDA S eneral Data Acquisition System

IA S ndicated Airspeed

ITT nlet Turbine Temperature

KIA S nots Indicated Airspeed

M A C ea n Aerodynamic Chord

N A SA ational Aeronautics and Space Administration

N G as generator speed

OA T utside A ir Temperature PA P rimary Analysis Processor

R A A F oyal Australian A ir Force

SHP haft Horse Power

XI





DSTO-TR-0988

c Reference chord (1.65 m )

F Ratio of the regression mean square to the residual mean square

9 Gravitational acceleration (9.81 m/s2)

Ixx Roll moment of inertia (kg.m2)

IYY Pitch moment of inertia (kg.m 2) Izz Y aw moment of inertia (kg.m

2)

IxY Cross product of moment of inertia (kg.m2)

Ixz Cross product of moment of inertia (kg.m2)

IYZ Cross product of m om e nt of inertia (kg.m2)

I Rolling m om e nt N.m)

M Mass of aircraft kg )

n Yawing m om e nt N.m)

P Roll rate rad/s)

q Pitch rate (rad/s)

Q Dyna m i c pressure (N/m2)

R2 Squared multiple correlation coefficient

r Y aw rate (rad/s) S Reference area (16.29 m 2) V True velocity (m/s)

X Longitudinal force (N ) xc.g. Longitudinal eg. position (m )

Y Side force (N )

Vc.g. Lateral e.g. position (m )

z Vertical force (N )

c.g. Vertical e.g. position (m )

a Angle-of-attack °)

ß Angle-of-sideslip (° )

S a Aileron deflection (6a = SaL — SaR) °)

6 e Elevator deflection (° ) 5 r Rudder deflection (° )

e Pitch angle (° )

Roll angle (° )

* Y aw angle (° )

Subscripts

b Body axes

eg. Centre of gravity

F Fuel

L Left port) R R i ght starboad)

XUl



DSTO-TR-0988

Control surface

Aircraft sign convention and flow angle definitions (body axes).

XI V



DSTO-TR-0988

Wing Reference Area (S) 16.29 m2

Wing Span £ > ) 10.124 m

Mean Aerodynamic Chord (? ) 1.65 m

Datum

Forward Fueslage

Reference Plane

Aircraft Principle Dimensions. (Numeric data sourced from Pilatus Structural Configuration Drawing 506.00.09.220F)

XV



DSTO-TR-0988

xvi



DSTO-TR-0988

1 Introduction

T he Pilatus PC 9/A is on e of a number of high performance turbo-prop aircraft currently

operated by the Royal Australian A ir Force (R AAF).

Work currently

underway in

the A ir

Operations Division (A OD) of the Defence Science and Technology Organisation (DSTO)

includes investigations into the propeller power effects of such aircraft, and the PC 9/A

w as considerd a suitable platform for study. A si x degree-of-freedom flight dynamic model

of the PC 9/A has been developed by A O D for us e in these investigations, as well as for

pilot-in-the-loop imulations in the A ir Operations Simulation Centre and incident an d

accident investigations.

The development of a flight dynamic model requires information on the static and dynamic

stability an d control derivatives of the aircraft, as well as flight control laws and physical

properties. The static data for the PC 9/A were collected during both power-off and power-

on testing of a scaled aircraft model in the Aeronautical and Marit ime Research Laboratory

( A M RL) ow-speed wind tunnel. dditional power-off static data were obtained from a

computational fluid dynamic model fo r a limited number of aircraft configurations.

Flight test data for the PC 9/A w as required to both validate the flight dynamic model

and o provide dynamic derivative estimates of the aircraft. flight est program w as

conducted on a PC 9/A aircraft, serial number A23-045, by the R A A F Aircraft Research

and Development Unit A R D U ) between November 1998 an d February 1999. T he details

of this flight test program and the aircraft nstrumentation ar e reported in reference 1 ] .

The estimation of the stability and control derivatives from the flight test data involved the

us e of system identification techniques, and required control input, aircraft response and

flight condition data, measured using a high fidelity instrumentation system. aximum

likelihood an d stepwise regression techniques were employed for the system identification.

The longitudinal derivatives for the PC 9/A aircraft in the cruise configuration determined

using system identification techniques ar e reported in reference 2 ] .

This report presents the lateral stability and control derivatives of the PC 9/A extracted

from flight test data for the cruise configuration, including a comparision with A M R L wind

tunnel test data an d empirical results. Sections 2 and 3 present details of the test aircraft

and instrumentation system. Section 4 presents the system identification techniques, while

section 5 discusses the results.

2 PC 9/A Test Aircraft

2 .1 Aircraft Description

The flight test aircraft, A23-045 is a Pilatus PC 9/A operated by A R D U . The PC 9/A is a single-engine, metal-skinned, low-wing, tandem two-seat training aircraft. he aircraft

is powered by a Pratt and Whitney P T 6 A - 6 2 turbo-prop engine flat rated to 95 0 SHP 3 ] ,

which drives a Hartzell HC-D4N-2A four-blade variable pitch propeller. The aircraft was

instrumented as outlined in section 3.



DSTO-TR-0988

2.2 light Control System

T he aircraft primary flight controls consist of the ailerons, rudder and elevator. The control

surfaces are manually operated from a conventional dual control column and rudder pedal

arrangement. he stick and rudder pedals are connected to the control surfaces through a system of control rods, bellcranks, cables and levers. rimming control is provided on

al l three axes.

2.3 eight, Centre-of-Gravity and Mass Moments-of-Inertia

T he test aircraft, A23-045, w as weighed by A R D U prior to th e flight tests and had a basic

mass of 1784.5 kg and a longitudinal centre-of-gravity position of 26.25% M A C 4 ] . During the flight test program, the aircraft weight, centre-of-gravity and mass moments-of-inertia

varied with fuel usage. hese parameters were calculated fo r each test manoeuvre using

the equations in Appendix A.

3 Instrumentation

Aircraft A23-045 w as fitted with an instrumentation system designed specifically fo r th e

gathering of flight dynamic data. summary of the instrumentation used in the flight test program is included below and a more comprehensive description of the design re -

quirements and calibration is included in references 1 ] and 5 ] . The A R D U General Data Acquisition System (GDAS) w as fitted in place of the rear ejection seat. he data were

encoded by a 16-bit pulse code modulation system and were ecorded onboard the air-

craft using a MARS-2000 14-track tape. Real-t ime flight test monitoring w as provided by

telemetry data transmitted to the A R D U Primary Analysis Processor (PAP) hut. T he angular rates (p,q,r) and linear accelerations axaY,az were measured using the A R D U KAISG1134-1 Motion Platform. This consisted of three Smith Industries 95 0 RGS

angular rate gyros and three SunStrand QA 1 40 0 servo accelerometers. he aircraft roU,

pitch and yaw attitude angles < £ , 0, j > were obtained by tapping output from the existing

LISA 2000A Artificial Horizon Reference System (AHRS).

Static outside air temperature O A T) , ndicated airspeed (IAS), angle-of-attack a) and

angle-of-sideslip ß) were obtained from the Rosemount Model 9 2A N flight test air data boom, mounted on the outboard hardpoint on the starboard wing (see figure 1). Aileron

and elevator deflections were measured using Space A ge Control nc . eries 16 0 cable position transducers. Rudder deflection w as measured using a type 26V-11CX4C position

transducer. A ll sensors were calibrated prior to commencement of the flight test program.

The aircraft w as also instrumented to measure engine torque, propeller speed, inlet turbine

temperature ITT), gas generator peed NG), ue l flow and fuel quantity. he torque,

propeller speed, altitude and true airspeed, w h e n used in conjunction with a performance

m ap for the HartzeU HC-D4N-2A propeUer [6], allowed the calculation of engine thrust.



DSTO-TR-0988

4 Methods of Analysis

During the flight est program, doublet and 3-2-1-1 manoeuvres were performed about

steady flight conditions at airspeeds between 90 and 20 0 KIAS. Reference 1 ] describes

these manoeuvres in detail. The 26 lateral doublet and 12 9 lateral 3-2-1-1 manoeuvres were

analysed using stepwise regression 7 ] and maximum ikelihood estimation techniques 8 ]

to determine the lateral stability and control derivatives of the aircraft.

A range of independant aircraft derivative data were used for comparision purposes and, for

the max imum liklihood analysis, as a priori estimates to increase the rate of convergence

of the system identification. his data w as ouced ro m A M R L power-off wind tunnel

tests 9 ] and empirical data estimated by the University of Sydney [10] using Datcom 1 1 ]

and Pilatus [12] using both Digital Datcom [13] 14] and other long-hand' methods.

A right handed orthogonal axes system was adopted for the analysis of the flight test data.

Positive control urface deflections were defined as elevator railing edge down, udder

trailing edge to port, and starboard aileron trailing edge down, port aileron trailing edge

up .

4.1 Stepwise Regression

Stepwise regression is an unbiased least squares estimator in which ne w independent vari-

ables ar e nserted into a model, on e at a time, until the regression equation is deemed

acceptable. he appropriateness of the model ca n be determined by examining a num-

ber of quantities including the squared multiple correlation coefficient and the F statistic.

The squared multiple correlation coefficient, R2, gives a measure of the mportance of

each variable as it is inserted into the equation 7 ] ; however, the improvement in R2 du e

to the addition of ne w terms must have some real significance besides simply reflecting th e

inclusion of more terms. This ca n be determined by monitoring the F statistic, th e ratio of

the regression mean square to the residual mean square. The inclusion of an y significant

terms is generally accompanied by an increase in the F statistic and the best fit with th e

least number of parameters m ay be obtained by maximising F. A ny variable which does

not make a significant contribution is removed from the model, with the selection process

continuing until no ne w variables remain to be inserted into the equation. Whilst stepwise

regression gives estimates of the derivatives ncluded in the regression equation, t lso

permits a suitable structure fo r the model to be determined. n addition, it provides an

independent check on the data estimated using the maximum likelihood technique.

The tepwise egression echnique w as applied using code available n he M A T L A B©

Statistics Toolbox [15]. The following model equations were identified during th e analysis.

CY = CY 0 + C Y ßß + CYs8 1)

Cn — Cno + Cn ß + Cnv — + CnT —+ CnSr 5 T (2 )



DSTO-TR-0988

C i = c l0 + ßß + h + cw + S asa (3 )

4.1.1 Error Band Included in he tepwise egression analysis s he calculation of an error band on he estimated derivatives. Fo r a confidence interval of 95%, this error band is approximately

equal to tw o standard deviations. Figures 2 to 21 show the stepwise regression derivative

estimates, including the calculated error band.

4.2 Maximum Likelihood

The m a xi m um likelihood estimation technique w as applied using the computer program,

pEst, developed at N A SA Dryden Flight Research Center 16]. pEst is an interactive pa - rameter estimation program which solves a vector se t of time-varying, ordinary differential

equations of motion.

Prior to he application of the maximum likelihood technique, tepwise regression w as used to determine a suitable structure fo r the lateral model equations. Those derivatives

that were found to be statistically insignificant were not estimated using pEst. However, unlike stepwise regression, these derivatives were no t removed from th e model equations

but were nstead fixed at heir a priori values. Yp w as ixed at a value of -0.16 per

radian), Cy at 0.34 (per radian), CyS a at 0.0 (per degree), CnSa at -0.000035 pe r degree) and C ig ixed at 0.00035 (per degree). These a priori values were obtained from em pirical

data of references 1 0 ] and 12]. he lateral derivatives which were identified using the

maximum likelihood technique are given in table 1.

Side Force Yawing M om e nt Rolling Moment

Aerodynamic CY0 Cnp Crir

Qß Cir

Control

CYS, C n Sm Clsa

Table 1: Lateral derivatives estimated The resulting total force and m om e nt coefficient equations used in the state and response

equations fo r the maximum likelihood analysis of the PC 9/A are given in equations 4, 5 and 6. he differences between equations 1, and 3, and 4, 5 and 6 ar e important, and arise from the inclusion of the a priori values in the max imum likelihood technique.

pb rb CY = CYo + CYßß 0.16 + 0.34— + CYsr5

2V 2V (4 )



DSTO-TR-0988

Cn = Cno + Cnßß + Cnp + Cnr 0.000035£a + Cngr6r 5)

Ci = Ch + Chß + Ch + Ci T + ClSa Sa + 0.00035£r 6)

4.2.1 Cramer-Rao Bounds Fo r the estimated parameters, pEst calculates a measure of the estimation certainty known

as the Cramer-Rao bound. A detailed interpretation of this quantity is given in [17]. The

Cramer-Rao bounds ar e shown fo r each derivative estimated by pEst in figures 2 to 21 .

T he Cramer- Rao bounds have been factored in accordance with the procedures described

in 1 7 ] o account fo r the presence of band-limited noise.

5 Results and Discussion

Lateral derivatives estimated via maximum likelihood parameter estimation, stepwise re -

gression, empirical methods and power-off wind unnel experiments are ummarised in figures 2 to 21 .

5 .1 Angle-of-Sideslip Derivatives

Figures 2 o ho w he angle-of-sideslip derivatives Cye, Cn0 and Q0 plotted against a. he light est estimates of the ide force du e o ngle-of-sideslip derivative, Cy, generally fall between the empirical and wind tunnel estimates with the results showing

a small degree of scatter at angles-of-attack bove 6°. he estimates of Cy ro m he

stepwise regression method are slightly smaller in magnitude than those from the maximum

likelihood technique.

Estimates of the directional stability derivative, Cn , show good agreement between results

from stepwise regression and maximum likelihood techniquess for both3-2-1-1 and doublet

manoeuvres. owever, at low angles-of-attack, he flight test estimates ar e smaller than the wind unnel and empirical estimates, which are both power-off. his difference s

du e to the imbalance between tw o competing effects acting on the portion of the vertical

tail within the propeller slipstream, hese being the increased dynamic pressure and the decreased angle of incidence. The reduction in angle of incidence dominates, resulting in an

overall reduction in the directional stability of the aircraft. The flight test results show less

variation with angle-of-attack than the wind tunnel results because the natural reduction

in directional stability with angle-of-attack is partially balanced by the increasing portion

of the vertical tail which is subject to increased dynamic pressure within the slipstream.

In general, the Cramer-Rao bounds and stepwise regression error bands for Cn estimates

ar e small.



DSTO-TR-0988

The m a xi m um likelihood and stepwise regression estimates of the rolling moment du e to

angle-of-sideslip derivative, Ch, show good agreement with the empirical and wind tunnel estimates fo r both the 3-2-1-1 and doublet manoeuvres. he flight test estimates of Clß show little variation with angle-of-attack, as predicted by the wind tunnel results. Similarly

to CY estimates, Clß estimates from the stepwise regression technique ar e slightly smaller in magnitude than those obtained by the m a xi m um likelihood technique.

5.2 aw Rate Derivatives

Figures 7 to 11 ho w the ya w rate derivatives, C„r and Qr, plotted against a. ngular

rates were not measured during th e wind tunnel test program and hence no wind tunnel

ya w ate derivatives ar e vailable or comparision. s mentioned previously, CYr w as

constrained to its a priori value for the maximum likelihood analysis, and not estimated

in the stepwise regression analysis. nvestigations were undertaken to assess the relative

contribution of each derivative to the aircraft's forces and moments to ensure that those

set o their a priori values were small contributors. his analysis, which is detailed in Appendix B, showed the ya w rate contribution to side force to be small.

The flight test estimates of the yawing moment du e to ya w rate, CUr, agree well with th e

empirical estimate fo r both the 3-2-1-1 and doublet manoeuvres A high degree of scatter is hown n the derivative estimates bove 6° ngle-of-attack. he tepwise egression

technique gives estimates of C„r which are slightly larger in magnitude than the estimates

from the max imum likelihood technique.

The olling moment du e o ya w ate, lr, whilst being mall s an mportant ateral-

directional cross-coupling derivative. The flight test anaylsis results show Qr estimates to be g enerally larger than the empirical estimate for both 3-2-1-1 and doublet manoeuvres at all angles-of-attack. The flight test estimates of QT show an increase with angle-of-attack.

This is an expected result caused by the increase in lift coefficient with increasing angle- of-attack, which results in a greater rolling m om e nt as the aircraft yaws refer [18]). T he flight test results show a small degree of scatter, particularly fo r the estimates obtained

by the max imum likelihood technique.

5.3 oll Rate Derivatives

The roll rate derivative estimates, Cnp and Ch, ar e plotted against a in figures 12 to 16 .

The side force du e to roll rate, C y p , s a small derivative, not estimated in the stepwise

regression or maximum likelihood analysis.

The yawing m om e nt du e o ol l rate s an mportant ateral-directional cross-coupling

derivative. The max imum likelihood estimates of Cnp agree well with the stepwise regression estimates, and estimates from both techniques have small uncertainty levels. However,

the flight test estimates are larger in magnitude than the empirical estimate. Similarly to CiT, Cn s influenced by the angle-of-attack and lift coefficient and it s value is expected to vary with angle-of-attack 18]. This trend is seen in the flight test estimates, which show

the value of C„p to decrease with angle-of-attack. The results also show a small degree of



DSTO-TR-0988

scatter at angles-of-attack above 6° .

The roll damping derivative, Cip, estimates from both the stepwise regression and maxi-

m um likelihood techniques show good agreement with the empirical estimate. A s expect-

ed 18], he Ci

p estimates

do not

ho w any variation

with

angle-of-attack.

he results display little scatter with small error bands, ndicating a high level of confidence in the

results.

5.4 Control Derivative

The control derivatives estimates, CyS r, CnSr and QSa, are plotted against a in figures 17

to 21 . he yawing moment du e to aileron derivative, Cng and rolling moment du e to rudder derivative, Cig are both small derivatives, which were not estimated in either th e

stepwise regression or maximum likehood analysis.

Estimates of the side force due to rudder deflection derivative, CYS T are scattered about

the empirical and wind tunnel estimates. T he maximum likelihood estimates of Cy av e large Cramer-Rao bounds indicating a higher level of uncertainty in the estimates than

other derivatives. owever, CYS T as only a small contribution to the total aircraft side

force coefficient (refer Appendix B) and hence, the increased uncertainty in this derivative

will not significantly affect the overall aircraft model characteristics.

Estimates of the rudder control effectiveness, CnSr, show good agreement with the empir-

ical and wind tunnel estimates and small uncertainty levels, particularly at low angles-of-

attack. he flight test estimates of the aileron control effectiveness derivative, Cts al l

between the empirical and wind tunnel estimates fo r the 3-2-1-1 and doublet manoeuvres.

These results exhibit only a small degree of scatter and show a good correlation between

the stepwise regression and m a xi m um likelihood estimation techniques.

5.5 Variation of Lateral Derivatives with Rate of Climb and Angle-of-Attack

The variation of lateral derivatives with angle-of-attack and nominal rate of climb fo r a selection of 3-2-1-1 manoeuvres is shown in figure 22 . linear curve fi t w as applied to each rate of climb data se t to highlight the trends shown by the data. The influence of rate of climb with increasing angle-of-attack is seen in figure 22 , with CnSr, Cy and Cnß ll

increasing in magnitude. These trends ar e due to increases in the aircraft thrust coefficient

and the dynamic pressure in the propeller slipstream as the rate of climb increases fo r a given angle-of-attack. These trends ar e supported by previous theoretical and experimen-

tal studies detailed in references 1 9 ] and 20]. or the manoeuvres in figure 22 , hrust coefficient varies from approximately 0.02 to approximately 0.12.



DSTO-TR-0988

5.6 Manoeuvre Type and Altitude Dependancy

Tables 2 and 3 show the mean values across the linear angle-of-attack range (0° - 6°) of the aerodynamic derivatives estimated by both max imum likelihood and stepwise regression

techniques, fo r each manoeuvre type and altitude band.

3-2-1-1 3-2-1-1 3-2-1-1 Doublet Doublet

5000 ft 10 00 0 ft 15 000 ft 5000 ft 15 000 ft

Cy -1.35E-02 -1.35E-02 -1.40E-02 -1.40E-02 -1.38E-02

3.29E-03 3.00E-03 3.26E-03 3.27E-03 3.63E-03

1.41E-03 1.39E-03 1.33E-03 1.44E-03 1.42E-03

-6.32E-02 -6.29E-02 -5.28E-02 -5.40E-02 -6.06E-02

(^7lr -2.01E-01 -1.97E-01 -2.03E-01 -1.80E-01 -1.91E-01

-2.02E-03 -1.91E-03 -1.89E-03 -1.73E-03 -1.86E-03

Qo -1.52E-03 -1.55E-03 -1.49E-03 -1.37E-03 -1.36E-03

-5.08E-01 -5.04E-01 -4.94E-01 -4.64E-01 -4.77E-01

1.14E-01 1.20E-01 0.962E-01 1.31E-01 1.52E-01

Clsn -1.89E-03 -1.91E-03 -1.79E-03 -1.48E-03 -1.71E-03

Table 2: Summary of derivatives estimated using maximum likelihood 3-2-1-1 3-2-1-1 3-2-1-1 Doublet Doublet

5000 ft 10 00 0 ft 15 00 0 ft 5000 ft 15 000 ft

Cy CY

-1.26E-02 -1.32E-02 -1.24E-02 -1.25E-02 -1.27E-02

3.41E-03 3.50E-03 3.34E-03 3.45E-03 3.68E-03

1.45E-03 1.47E-03 1.45E-03 1.52E-03 1.50E-03

-5.54E-02 -5.21E-02 -5.19E-02 -4.72E-02 -5.55E-02

-2.43E-01 -2.23E-01 -2.24E-01 -2.19E-01 -2.28E-01

Cns T -1.99E-03 -1.91E-03 -1.91E-03 -1.87E-03 -1.88E-03

-1.38E-03 -1.28E-03 -1.37E-03 -1.34E-03 -1.30E-03

-4.89E-01 -4.44E-01 -4.66E-01 -4.38E-01 -4.61E-01

Qr 1.43E-01 1.43E-01 1.57E-01 1.47E-01 1.63E-01

CK -1.82E-03 -1.65E-03 -1.73E-03 -1.61E-03 -1.70E-03

Table 3: Summary of derivatives estimated by stepwise regression The flight test derivative estimates from the 3-2-1-1 and doublet manoeuvres show similar

trends or al l ateral derivatives. n general, here w as no ignificant change n uncer-

tainty levels, derivative values or degree of scatter in the results fo r the tw o manoeuvre

types at angles-of-attack below 6°. A s no doublet manoeuvres were performed above this angle-of-attack, o conclusions ca n be draw s o he nfluence of manoeuvre ype on

derivative estimates at higher angles-of-attack. s expected, figures 2 to 21 do no t show an y ignificant altitude dependancy as he esults are non-dimensionalised by dynamic

pressure.



DSTO-TR-0988

6 Conclusions

T he ateral stability and control derivatives of the PC 9/A n he cruise configuration

have been determined from flight test data measurements using max imum likelihood an d

stepwise regression estimation techniques. Comparisions have been m a de with derivative

estimates from empirical methods and wind-tunnel experiments.

T he ideslip derivatives, Cy nd Q , howed good agreement between he light est

and ground-based estimates, while the results fo r Cn0 howed small differences due to th e

exclusion o f po w er effects in the wind tunnel and empirical estimates. Flight test estimates

of the ya w rate derivatives, CU r and Cir, showed good results whe n compared to empirical

estimates, and displayed the expected trends with angle-of-attack. Estimates of CUp were

slightly larger in magnitude than the empirical estimate, while flight est and empirical

estimates of Cip compared well.

T he control derivatives, CyS r, CnSr and QSa, were also estimated from the PC 9/A flight

test measurements. ng nd Ci

s erivative estimates compared well with results esti-

mated from empirical methods and wind tunnel experiments, while Cy stimates showed

a higher level of uncertainty than other derivatives.

Trends were ound n he CnSr, Cyß nd Cn estimates w h e n plotted s a function of

airspeed and rate of climb that agree with predictions from previous theoretical and ex-

perimental studies. n general, the flight test results did not show an y significant variation

with altitude or manoeuvre type.



DSTO-TR-0988

References

1. A . D. Snowden. PC 9/A flight tests summary. Client Report A O D 99/01, Aeronautical

and Maritime Research Laboratory, 1999. 2. A . D. Snowden, H. A. Keating, N. va n Bronswijk, and J. S. Drobik. A correlation be -

tween flight-determined longitudinal derivatives and ground-based data fo r the Pilatus

PC 9/A training aircraft in cruise configuration. Technical Report 0937, DSTO Aero-

nautical and Marit ime Research Laboratory, Melbourne, Victoria, Australia, 2000.

3. Royal Australian A ir Force. Flight Manual PC 9/A. Defence Instruction Air Force) AAP 7212.007-1, June 1989.

4. M.C. Sciberras. Aircraft weigh record - A23-045. A R D U 2501/60/TechPtl(5), Novem-

ber 1998.

5. B. A . Woodyatt, A. D. Snowden, and K . E. Lillingston. The development of a PC 9/A

flight dynamic model validation flight test program. Client Report A O D 98/07, Aero- nautical and Maritime Research Laboratory, 1998.

6. British Aerospace. ilatus PC 9/A performance maps. echnical memorandum,

British Aerospace Aerodynamics, Brough.

7. . Klein. stimation of aircraft aerodynamic parameters from flight data. rogress in Aerospace Sciences, 26:1-77, 1989.

8 .E . Maine and K . W . Iliff. pplication of parameter estimation to aircraft stability and control, he output error approach. eference Publication 1168, NA S A Dryden

Flight Research Facility, Edwards, California, U S A , June 1986.

9 armichael and B. A. Woodyatt . stimates of the power-off aerodynamic

characteristics of the Pilatus PC 9/A. lient Report A O D 96/29, Aeronautical and

Maritime Research Laboratory, February 1997.

10. N . van Bronswijk. nvestigation of th e Effects of Propeller Power on th e Stability and Control of a Propeller Powered, Single-Engined, Low-Wing Monoplane. hD thesis,

University of Sydney, In Preparation.

11. R. D. Finck, editor. .S.A.F. Stability an d Control DATCOM. ngineering Docu-

ments, A Division of Information Handling Services, 1978.

12. PEI Aerodynamics. Evaluation of stability derivatives fo r the PC 9/A turbo-trainer.

Technical report, Pilatus Aircraft Limited, 30 July 1983.

13

E illiams and Vukelich. The U S A F stability and control digital D A T C O M - vol- um e I, users manual. Technical Report AFFDL-TR -76 -45, Vol I, McDonnell Douglas

Astronautics Company - East, St Louis, Missouri, USA , November 1976.

14. .E. Williams and Vukelich. he U S A F stability and control digital D A T C O M

volume II, implementation of D A T C O M methods. Technical Report AFFDL-TR -76 -

45, Vo l II , McDonnell Douglas Astronautics Company - East, St Louis, Missouri, USA,

November 1976.

1 0



DSTO-TR-0988

15 . he MathWorks, Statistics Toolbox User s Guide, nc, Natick, M A , January 1997.

16 . J.E. Murray and R.E. Maine. pEst version 2.1 user's manual. Technical Memorandum

8828, N A SA A me s Research Center, Dryden Flight Research Facility, Edwards, CA ,

USA, September 1987.

17 . R.E. Maine and K . W . Iliff. User's manual fo r M M LE3 , a general F O R T R A N program

for maximum likelihood parameter estimation. echnical Paper 1563, Dryden Flight

Research Center, Edwards, California, USA , 1980.

18. . Etkin. Dynamics of Atmospheric Flight. John Wiley & Sons Inc., 1972.

19. . P. Shivers, M. P. Fink, and G. M . Ware. Full-scale wind tunnel investigation of the static longitudinal and lateral characteristics of a light single-engine low-wing airplane.

TN D-5857, National Aeronautics and Space Administration, June 1970.

20 . N . va n Bronswijk, P. W . Gibbens, D. M . N e wm a n, and K . C. Wong. nvestigation

of the ffects of propeller po w er on he stability and control of a ractor-propeller

powered ingle-engined ow-wing monoplane. echnical Report 9801, University of

Sydney, January 1998.

1 1



DSTO-TR-0988

fSSSr^ r i Z~i t^-M .-try- •• «*£.-WS

Figure 1: Air data boom nstallation.

12



DSTO-TR-0988

T3

^o

o . o o o -0.005

-0.010

-0.015

-0.020

-0.025

-0.030

O Flight Test (pEst estimates) □ Flight Test (swr estimates)

-- Empirical estimate - Wind tunnel estimates (Power off)

J§TJ

I .

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 Angle-of-Attack (degrees)

0 . 0 0 4 0 1 L >

T3 0 . 0 0 3 5 0 . 0 0 3 0

S 3 a 0 . 0 0 2 5

C O . 0 . 0 0 2 0 C o 0 . 0 0 1 5

0 . 0 0 1 0 0 . 0 0 0 5 0.0000

0 . 0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0

Angle-of-Attack (degrees)

0 - 0

T3 - I I

D a - 0

C O . - 0 u - 0

- 0 - 0 - 0

. 0 0 0 0

. 0 0 0 5

. 0 0 1 0

. 0 0 1 5

. 0 0 2 0

. 0 0 2 5

. 0 0 3 0

. 0 0 3 5 0040

i

i

0 . 0 . 0 . 0 . 0 4 . 0 . 0 . 0 . 0 . 0 . 0 0 . 0 1 . 0 2 . 0 3 . 0 4 . 0 5 . 0 Angle-of-Attack (degrees)

Figure 2: PC 9/A angle-of-sideslip derivatives, 3-2-1-1 manoeuvres at 5000 ft.

13



DSTO-TR-0988

a ca.

0.000

-0.005

-o.oio ..

-0.015 _

-0.020

-0.025

-0.030

O Flight Test (pEst estimates) 2 Flight Test (swr estimates)


0.0 1.0 2. 0 3.0 4.0 5.0 6.0 7. 0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 Angle-of-Attack (degrees)

1?

- 8 0.0040

0.0035

0.0030 Ö Ä 0.0025

CO. 0.0020

0.0015

0.0010

0.0005

0.0000 .0 1.0 2.0 3.0 4.0 5.0 6.0 7. 0 8.0 9.0 10.0 11.0 12.0 13.0

Angle-of-Attack (degrees) 14.0 15.0

2 0.0000 f e b

S 5 a

-0.0005

-0.0010

-0.0015

eo. -0.0020

u -0.0025

-0.0030

-0.0035

-0.0040 0 1.0 2.0 3.0 4.0 5.0 6.0 7. 0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


Figure 3: PC 9/A angle-of-sideslip derivatives, 3-2-1-1 manoeuvres at 10 00 0 ft.

14



DSTO-TR-0988

^ 0 . 0 0 0 o

~ a b

0.005 0.010 0.015 0.020 0.025

O Flight Test (pEst estimates) = Flight Test (swr estimates)

mpirical estimate ind tunnel estimates (Power off)

-0.030

.0 1.0 2.0 3.0 4.0 5.0 6.0 7. 0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 Angle-of-Attack (degrees)

0.0040 & 0.0035

0.0030 a 0.0025

e n . 0.0020 0.0015 0.0010 0.0005 0.0000

... ,,..,..,. ... •-

i. O 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


).0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


Figure 4:

PC 9/A angle-of-sidslip derivatives, 3-2-1-1 manoeuvres at 15 00 0 ft.

15



DSTO-TR-0988

U

O Flight Test (pEst estimates) - Flight Test (swr estimates)

-- Empirical estimate - Wind tunnel estimate (Power off)

0 . 0 0 0 . > 1

0 . 0 0 5 - 0 . 0 1 0 - e - - 0 . 0 1 5 .^g£ B S~

. IC

0 . 0 2 0 0 . 0 2 5

i 1 .0 1.0 2.0 3.0 4. 0 5.0 6.0 7. 0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


I T 1

C O .

0.0040 0.0035 0.0030 0.0025 0.0020

s 0.0015 0.0010 0.0005 0.0000

0.0 1.0 2. 0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


o . o 1.0 2.0 3.0 4.0 5.0 6.0 7. 0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


Figure 5: PC 9/A angle-of-sidslip derivatives, doublet manoeuvres at 5000 ft.

16



DSTO-TR-0988

f l T 0 . 0 0 0 0.005

T 3 1 5 0.010 C u /o 0.015

> - u 0.020

0.025

O Flight Test (pEst estimates) c Flight Test (swr estimates)


-0.030

ifc c e


0.0040 0.0035 0.0030

C O . 0.0025 0.0020

c o 0.0015

0.0010 0.0005 0.0000

' I r ' l

- • ^ m i i, t....

i. O 1.0 2. 0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


8 o . o o o o -0.0005

2 -0.0010

A -0.0015

ex -0.0020 j -0.0025

-0.0030

-0.0035

-0.0040 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


Figure : PC 9/A angle-of-sideslip

derivatives, doublet manoeuvres at 15 000

ft .

1 7



DSTO-TR-0988


-- Empirical estimate

s 0.2

' S 0.1 2 \ 0.0 u 3 -0.1

w -0.2

-0.3

-0.4

-0.5

-0.6

i I M i i

ra n

0 1.0 2. 0 3. 0 4. 0 5.0 6 .0 7. 0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


'S 2

1. 2 1. 0 0 .8 0 .6

u 0.4 Ü 0.2

0.0 -0.2 -0.4

.0 1.0 2. 0 3. 0 4. 0 5.0 6. 0 7. 0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


Figure 7: PC 9/A aw rate derivatives, 3-2-1-1 manoeuvres at 5000 ft.

18



DSTO-TR-0988

O Flight Test (pEst estimates)

- Flight Test (swr estimates)


'S 2

U

o 0 1.0 2.0 3. 0 4. 0 5. 0 6. 0 7. 0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


3

2

1.2

1.0

CD

3 0.8

0.6

u. 0.4

U 0.2

0.0

-0.2

-0.4 .0 1.0 2. 0 3. 0 4. 0 5.0 6. 0 7. 0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


Figure 8: PC 9/A aw rate derivatives, 3-2-1-1 manoeuvres at 10 00 0 ft.

19



DSTO-TR-0988

O Flight Test (pEst estimates) = Flight Test (swr estimates)


T3 e G u

0.2

0.1

0.0

-0.1

-0.2

-0.3

-0.4

-0.5

-0.6 0.0 1.0 2. 0 3. 0 4 .0 5. 0 6 .0 7. 0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


S 3 1.2

2 1.0

0.8

0.6

« - 0.4

u 0.2

0.0

-0.2

-0.4 0.0 1.0 2. 0 3. 0 4. 0 5.0 6. 0 7. 0 8.0 9. 0 10.0 11.0 12.0 13.0 14.0 15.0


Figure 9: C 9/A yaw rate derivatives, 3-2-1-1 manoeuvres at 15 000 ft.

20



DSTO-TR-0988


ü Flight Test (swr estimates)


2 u a e U

0.0 1.0 2. 0 3. 0 4. 0 5.0 6. 0 7. 0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


'S S u 0 ) 3 O

0.0 1.0 2.0 3.0 4. 0 5. 0 6. 0 7. 0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


Figure 10 : PC 9/A aw rate derivatives, doublet manoeuvres at 5000 ft.

21



DSTO-TR-0988

O Flight Test (pEst estimates) D Flight Test (swr estimates)


e U

0. 0 1.0 2. 0 3. 0 4 .0 5. 0 6. 0 7. 0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


' S ' •6 2

1.2

1.0 u u 3

0.8

0.6

l-t 0.4

u 0.2

0. 0

-0.2

-0.4 0. 0 1.0 2. 0 3. 0 4. 0 5. 0 6. 0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


Figure 11: PC 9/A aw rate derivatives, doublet manoeuvres at 15 00 0 ft.

22



DSTO-TR-0988


2 Flight Test (swr estimates)


'S ' 0.4 'S 2 0.3 u 0.2 V

a 0 .1 Q. 0.0 c u -0.1

-0.2 -0.3 -0.4

0 1.0 2. 0 3. 0 4. 0 5.0 6. 0 7. 0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


T3 2

U

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0 -

-1.2

-1.4

i

u r c

.... ....

0.0 1.0 2. 0 3. 0 4. 0 5.0 6. 0 7. 0 8.0 9. 0 10.0 11.0 12.0 13.0 14.0 15.0


Figure 12 : PC 9/A ol l rate derivatives, 3-2-1-1 manoeuvres at 5000 ft.

23



DSTO-TR-0988



2 u

3.

0.4

0.3

0.2

0.1

a. 0.0 c

-0.1

-0.2

-0.3

-0.4 .0 1.0 2. 0 3. 0 4. 0 5. 0 6 .0 7 .0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


U

0.4

0.2

0.0

-0.2 \ -0.4

-0.6

-0.8

-1.0

-1.2

-1.4

1111 1

.

0.0 1.0 2. 0 3.0 4. 0 5.0 6. 0 7. 0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


Figure IS: PC 9/A ol l rate derivatives, 3-2-1-1 manoeuvres at 10 000 ft.

24



DSTO-TR-0988

O Flight Test (pEst estimates) ü Flight Test (swr estimates)


c 0.4 'S 2 0.3 u. 0.2 l> 3 0 .1

o . 0. 0 c Ü -0.1

-0.2 -0.3 -0.4

** j L S ?i|ä

= JäSS 0.0 1.0 2. 0 3. 0 4. 0 5. 0 6. 0 7 .0 8.0 9. 0 10.0 11.0 12.0 13.0 14.0 15.0


'S 2 u 3

U

0.4

0.2

0.0

-0.2

-0.4

-0.6 -0.8

-1.0

-1.2

-1.4

i i '

0.0 1.0 2. 0 3. 0 4. 0 5.0 6. 0 7 .0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


Figure 14: PC 9/A ol l rate derivatives, 3-2-1-1 manoeuvres at 15 00 0 ft.

25



DSTO-TR-0988



'9 0.4 'S 0.3 2 u

0.2

< D a 0 .1 0.0

c u -0.1

-0.2 -0.3 -0.4

0.0 1.0 2. 0 3. 0 4. 0 5.0 6. 0 7. 0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


Ü

0.0 1.0 2. 0 3. 0 4. 0 5. 0 6. 0 7. 0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


Figure 15: C 9/A roll rate derivatives, doublet manoeuvres at 5000 ft.

26



DSTO-TR-0988


2 Flight Test (swr estimates)

- - Empirical estimate

e c U

1 .0 1.0 2. 0 3.0 4. 0 5. 0 6. 0 7. 0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


U

0.0 1.0 2. 0 3.0 4. 0 5. 0 6. 0 7. 0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


Figure 16 : PC 9/A ol l rate derivatives, doublet manoeuvres at 15 00 0 ft.

27



DSTO-TR-0988

o o fe i u

•a 0.015 0.010 0.005

u 0.000



-0.005 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


fe i

u -0.006

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


) .0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0

Angle-of-Attack (degrees) 14.0 15.0

Figure 17: PC 9/A ontrol derivatives, 3-2-1-1 manoeuvres at 5000 ft.

28



DSTO-TR-0988

0.015

0.010 a .

to 0.005

o 0.000

-0.005

. T.,rT„,--r 1

, ...

0 Flight Test (pEst estimates) - Flight Test (swr estimates)



•a

to G u

-0.006 ). 0 1.0 2.0 3.0 4. 0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


8 o . o o o o j j jb -0.0005 a -0.0010 f e -0.0015

M-0.0020 « 5 0.0025 rj -0.0030

-0.0035 -0.0040

1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


control derivatives, 3-2-1-1 manoeuvres at 10 000 ft.

29



DSTO-TR-0988

0.015 b ) u •o b ft 0.010

t. IO 0.005 *

Ü 0.000



- Wind tunnel estimates (Power off)

-0.005 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 Angle-of-Attack (degrees)

u T3

C O

-0.006 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


8 o g - ° •« -0. Ö -0 to 0et

-0. -0. -0.

. 0 0 0 0

. 0 0 0 5

. 0 0 1 0 0015 0020 0025 0030 0035 0040 0045 0050

.

. .. S ^ ® ^ . . 0 . 0 1 . 0 2 . 0 3 . 0 4 . 0 . 0 6 . 0 7 . 0 8 . 0 . 0 0 . 0 1 . 0 2 . 0 3 . 0 4 . 0 5 . 0 Angle-of-Attack (degrees)

Figure 19: PC 9/A ontrol derivatives, 3-2-1-1 manoeuvres at 15 000 ft.

30



DSTO-TR-0988

1 * o

0.015

0.010

0.005

0.000 -0.005

O Flight Test (pEst estimates) n Flight Test (swr estimates)


0.0 1.0 2.0 3.0 4.0 5.0 6.0 7. 0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 Angle-of-Attack (degrees)

B Ü

0.002

0.001

0.000

-0.001

-0.002

-0.003

-0.004

-0.005

-0.006 0. 0 1.0 2. 0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


u

O

0.0000 -0.0005 -0.0010 -0.0015 -0.0020 -0.0025 -0.0030 -0.0035 |-0.0040 -0.0045 -0.0050

0.0

1P « 1.0 2.0 3.0 4.0 5.0 6. 0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


Figure 20. ierivatives, doublet manoeuvres at 5000 ft.

3 1



DSTO-TR-0988

T3

US

0.015

0.010

0.005

0.000

-0.005

O Flight Test (pEst estimates) a Flight Test (swr estimates)

mpirical estimate — Wind tunnel estimates (Power off)

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7. 0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 Angle-of-Attack (degrees)

U U o

0.002 0.001

b 3

0.000 -0.001

tO -0.002 3 u -0.003

-0.004 -0.005 -0.006

.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


0 T 3 -0

-o b -0 C L

HI UO -0 c -0

-0 -0 -0 -0

. 0 0 0 0

. 0 0 0 5 -

. 0 0 1 0 r

. 0 0 1 5 T , 0 0 2 0

. 0 0 2 5

. 0 0 3 0

. 0 0 3 5

0 0 4 0 - 0 0 4 5 0 0 5 0 •

0 . 0 1 . 0 2 . 0 3 . 0 4 . 0 5 . 0 6 . 0 7 . 0 8 . 0 9 . 0 0 . 0 1 . 0 1 2 . 0 1 3 . 0 1 4 . 0 1 5 . 0 Angle-of-Attack (degrees)

Figure 21 : PC 9/A ontrol derivatives, doublet manoeuvres at 15 00 0 ft.

32



DSTO-TR-0988

I •a

Ö &

u

Nominal Climb Rate 5 00 fpm 2 50 m

Ofpm 25 0 fpm 50 0 fjjm 75 0 fym

-0.0030 0.0 1.0 2.0 3.0 4. 0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


I 13

-0.010

-0.012 t-i u

-0.014

-0.016

-0.018

-0.020 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7. 0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


0.0020

3 0.0016 CO. j .0014

0.0012 0.0010

I üg£ jr

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0


Figure 22 : ariation of lateral derivatives with nominal rate of climb.

33



DSTO-TR-0988

Appendix A: Weight, Centre-of-Gravity and Mass Moments-of-Inertia

The aircraft mass, centre-of-gravity and mass moments-of-inertia were determined for each

test manoeuvre based on the aircraft fuel mass. The basic aircraft, pilot and fuel masses

and m om e nt arms from references 3 ] and 4 ] ar e given in table Al. The m om e nt arms ar e

measured relative to the aircraft datum, ocated 3m forward of the engine firewall, and

2 m below the forward fuselage reference plane.

Mass (kg) Moment A rm (m )

Basic Aircraft

Pilot

Fuel

1784.5

81.6

Variable

4.306

4.061

4.178

Table Al: Flight test aircraft mass distribution [3 , 4 ] - The mass of the aircraft is calculated as the su m of the basic aircraft, pilot and remaining

fuel masses, by the following equation.

M = 1866.1 +MF (kg) (Al)

The longitudinal centre-of-gravity position of the flight test aircraft was determined from

the following equation.

lc.g. _ 015.5+4.178Aff /„N

1866.1+MF (A2)

During the flight test program, the aircraft longitudinal centre-of-gravity position varied between 4.27 m 24.2%M A C) and 4.30 m (25.6 %M A C). The lateral and vertical centre- of-gravity positions were assumed to be invariant with fuel usage, and were fixed at values

of 0.024 m and -2.2 m , respectively, relative to the aircraft datum.

The m a ss moments-of-inertia of the aircraft ar e given by the following equations.

Ixx = 2505.9 +6.177 (M-1866.1) (kg.m2) (A3)

IYY = 6622.2 + 0.033 (M -1866.1) (kg.m2) (A4)

Izz = 8467.1 +6.188 (M-1866.1) (kg.m2) (A5)

34



DSTO-TR-0988

IXY = 49.0 + 0.0057 M- 1866.1) (kg.m2) A6)

Ixz = 196.9 + 0.0041 (M -1866.1) (kg.m2) A7)

IYZ = 3.0 + 0.0007 M- 1866.1) (kg.m2) A8 )

35



DSTO-TR-0988

Appendix B: Side Force, Rolling Moment and Yawing Moment Coefficients

A n analysis w as carried out on he PC 9/A light est data o determine he elative

contribution of each lateral derivative to the aircraft's force and moment coefficients, Cy, Cn and Ci . his analysis w as undertaken to confirm that contributions from derivatives

se t to their a priori values in the max imum likelihood analysis were no t significant in the total force and moment equations of the aircraft. This analysis also confirmed the stepwise

regression results, which showed several derivatives to be insignificant to he regression

equation.

B.l Side Force Coefficient

The side force coefficient m ay be represented by :

Cy = Cy + Cyßß + Cy ()+ Cy Q) + CyS a S a + CyS r Sr B l)

A comparison of the relative size of each component of the above equation is shown in figure Bl for a 3-2-1-1 manoeuvre. The results show that changes in side force are mainly

du e to the change in the aircraft's angle-of-sideslip. he roll rate and rudder deflection

contributions to side force are small, while ya w rate and aileron deflection contributions

ar e negligible.

B.2 Yawing Moment Coefficient

T he yawing m om e nt coefficient m ay be represented by :

Cn = Cno + Cn ß + Cnp Q) + Cnr ()+ CnS a 6 a + Cnsr 5r B2 )

A comparison of the relative size of each component of the above equation is shown in figure B2 fo r a 3-2-1-1 manoeuvre. The results show that the ya w stiffness derivative, Cnß, and the ya w control derivative, CnSr, are important, while the remaining derivatives are

less significant to the total yawing m om e nt coefficient of the aircraft.

B.3 Rolling Moment Coefficent

The rolling moment coefficient m ay be represented by :

36



DSTO-TR-0988

= Clo+C0ß + Ch m + Cl

r 2V J +

C

' ' « 6a +

^ (B3)

^nsion of L i : elative size of each component of the above equation is shown in -2-1-1 manoeuvre. With the exception of Qs each of the rolling m oment

' - . a n t to the total rolling moment coefficient of the aircraft.

0.08

0.06

0.04

0.02

-0.02 -

-0.04-

-0.06

-0.08

CY = CY o

+ V + V*

b/2V)+ V»+ CY * . *S

a CY5r'Sr

—Y0 —

-ß _ 'p'(b/2V) _C YrT'(b/2V) —

CYSa*8a

20 5 Time (s)

Figure Bl: Relative magnitudes of Cy quation components.

37



DSTO-TR-0988

xi<r

c„ = Cn o + V + V <V<b/2V + C n6a *8 a + C rör -8 r

—Cno

— Cnp P _C p (b/2V)

v<b/2V)

15 0 5 0 5 0 Time (s)

Figure B2: Relative magnitudes of Cn quation components.

0.02

0.01 C = Cto + V + Clp* P*

b/2V)+ Glr l*<W2V

> + CBa 'Sa + Vr

-0.01

— ct o — c ,-P _ *p * (W ZV )

|r*r '(b/2V)

— efc*«. *r*8r l TOTAL

W v 20 5

Time (s) 30

Figure B3: Relative magnitudes of Ci quation components.

38



DISTRIBUTION LIST

A Correlation between Flight-determined Lateral Derivatives and Ground-based Data for

the Pilatus PC 9/A Training Aircraft in Cruise Configuration

Hilary A . Keating, Nick va n Bronswijk, Andrew D. Snowden and Jan S. Drobik

Number of Copies

DEFENCE ORGANISATION Task Sponsor

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Aeronautical and Maritime Research Laboratory Director, Aeronautical and Maritime Research Laboratory

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Research Leader, Avionics and Flight Mechanics

Head, Flight Mechanics Applications

Task Manager - G. J . Brian

Author - H. A. Keating

Author - N . van Bronswijk

Author - A. D. Snowden

Author - J. S. Drobik

B. A . Woodyatt

K . L. Bramley

DSTO Research Library and Archives Library Fishermans Bend

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SPARES H. A . Keating

Total number of copies: 5



Page classification: UN C LASSIFIED

DEFENCE SCIENCE AND TECHNOLOGY ORGANISATION DOCUMENT CONTROL DATA

2. TITLE

A Correlation between Flight-determined Later-

al erivatives nd round-based ata or he Pilatus C /A raining ircraft n ruise

Configuration

4 . AUTHORS

Hilary A. Keating, Nick va n Bronswijk, Andrew

D. Snowden and Jan S. Drobik

6 a. DSTO NUMBER

DSTO-TR-0988

6b. AR NUMBER

AR-011-475

1. AVEAT/PRIVACY MARKING

3. SECURITY CI ASSIFI

Document (U ) Title (U ) Abstract (U )

5. CORPORATE AUTHOR

Aeronautical and Marit ime Research Laboratory

50 6 Lorimer S t,

Fishermans Bend, Victoria, Australia 3207 6c . TYPE OF REPORT

Technical Report 7. DOCUMENT DATE

June, 2000

8. FILE NUMBER

Ml/9/746 9. TASK NUMBER

A IR 97/135

10 . PONSOR

COPS H Q A C

11 . N o OF PAGES

38 12 . N o OF REFS

20 13 . URL OF ELECTRONIC VERSION

http://www.dsto.defence.gov.au/corporate/ reports/DSTO-TR-0988.pdf

14 . RELEASE AUTHORITY

Chief, A ir Operations Division

15 . SECONDARY RELEASE STATEMENT OF THIS DOCUMENT

Approved Fo r Public Release OVERSEAS NQUIRIES OUTSIDE TATED IMITATIONS HOULD E EFERRED HROUGH OCUMENT XCHANGE, O OX 500, SALISBURY, SOUTH AUSTRALIA 5108

16 . DELIBERATE ANNOUNCEMENT

N o Limitations

17 . CITATION IN OTHER DOCUMENTS

No Limitations

18 . DEFTEST DESCRIPTORS

Aerodynamics

Aerodynamic stability

Lateral stability System identification

Aerodynamic configurations

Flight tests PC 9/A aircraft

19 . ABSTRACT

A series of flight tests were conducted on the PC 9/A aircraft, A23-045, at the Royal Australian A ir

Force's Aircraft Research and Development Unit. System identification techniques were applied to the data obtained from these flight tests to determine the stability and control derivatives of the aircraft.

The lateral results fo r the aircraft in cruise configuration are presented in this report and comparisons