Final Technical Report

(According to NASA Handbook NHB 5800.IC)

A LOW COST SIMULATION SYSTEM

TO DEMONSTRATE _5-] J

PILOT INDUCED OSCILLATION PHENOMENON

Syed Firasat Ali

Principal Investigator

Aerospace Science Engineering Department

Tuskegee University, Tuskegee, AL 36088

NASA Dryden Flight Research Center

Research Grant No. NAG 2-4006

April 1, 1994 to January 15, 1997

https://ntrs.nasa.gov/search.jsp?R=19970026582 2019-06-13T21:55:00+00:00Z

ABSTRACT

A flight simulation system with graphics and software on Silicon Graphics computer

workstations has been installed in the Flight Vehicle Design Laboratory at Tuskegee

University. The system has F-15E flight simulation software from NASA Dryden which uses

the graphics of SGI flight simulation demos. On the system, thus installed, a study of pilot

induced oscillations is planned for future work. Preliminary research is conducted by

obtaining two sets of straight level flights with pilot in the loop. In one set of flights no

additional delay is used between the stick input and the appearance of airplane response on

the computer monitor. In another set of flights, a 500 ms additional delay is used. The

flight data is analyzed to find cross correlations between deflections of control surfaces and

response of the airplane. The pilot dynamics features depicted from cross correlations of

straight level flights are discussed in this report. The correlations presented here will serve as

reference material for the corresponding correlations in a future study of pitch attitude

tracking tasks involving pilot induced oscillations.

ACKNOWLEDGMENTS

The research project covered by this report was sponsored by the NASA Dryden Flight Research Center under grant number

NAG2-4006. Mr. Larry Shilling's support and encouragement and Mr. Ken Norlin's expertise on simulation software were

vital to the completion of this work.

Dr. Amnon Katz from the University of Alabama and Dr. Vascar G. Harris from Tuskegee University, who are both pilots

and aerospace engineering professors, contributed greatly by providing their invaluable support and insights on such

issues as experimental design, statistical data processing, and most importantly, relating the data to a pilot's performance.

Jason Williams, an aerospace engineering student at Tuskegee University, enthusiastically participated in all aspects of

the research project including alterations in the software, system trouble shooting, and developing C++ codes to aid in

calculating and graphing of the cross correlations. Together with Yusef Johnson, a fellow aerospace engineering student,

Jason coordinated the conduct of the test flights performed by the volunteer pilots and even participated as one of the

simulator pilots in the study. It should also be noted that Yusef demonstrated keen interest in obtaining and understanding

the cross correlations.

Despite their professional commitments, Dr. Larry Koons, Mr. Nathaniel Glover, and Glen Morean devoted their valuable

time as volunteer pilots to conduct all of the required test flights.

Special appreciation is expressed to Dr. C. L. Chert, Abraham George, and Ernest Kashiri who are faculty and staff members

of Tuskegee University for providing substantial advice on software related issues.

Ronald Jones and Dennis Ezell, Tuskegee University aerospace engineering students, deserve special recognition for their

efforts in helping to initiate flight simulation research at Tuskegee University. It was during their tenure as Co-op students

at the NASA Dryden Flight Research Center that they developed this desire and their continued interest in that regard was

well received by Mr. Chuck Brown and Mr. Larry Schilling of NASA Dryden as well as by Dr. Shaik Jeelani of Tuskegee

University. In part, their desire has materialized into the research project covered by this report. Dennis has continued to

show exemplary devotion to the flight simulation program and has given noteworthy help in editing this report.

I extend my sincere gratitude to all those whose guidance, support, help, and good wishes have resulted in the completion

of a phase of research work that is reported here.

Syed Firasat Ali,

Principal Investigator

ii

TABLE OF CONTENTS

Abstract

Acknowledgments

List of Figures and Tables

ii

iv

Introduction

The Simulation System

Flight Data Processing

The Pilots and the Test Flights

Flight Test Results

Conclusions 17

Nomenclature

References

Appendix A: The Graphs of the Raw Data for the Five Selected Flights.

Appendix B: Copy of the paper; "Pilot Input and Airplane Response Cross Correlations

On a Flight Simulator With and Without Transport Delay."

18

19

A1

B1

iii

LIST OF FIGURES AND TABLES

Figures:

-- Figure 1 : Correlation Between Elevator Deflection and Time Derivative of Altitude.

Figure 2: Correlation Between Elevator Deflection and Airplane Altitude. 10

Figure 3: Correlation Between Elevator Deflection and Airplane Heading.

Figure 4: Correlation Between Aileron Deflection and Airplane Heading.

Figure 5: Correlation Between Rudder Deflection and Airplane Heading.

Figure 6: Correlation Between Deflections of Elevator and Ailerons.

11

12

13

14

-- Figure 7: Correlation Between Deflections of Elevator and Rudder. 15

Figure 8: Correlation Between Deflections of Rudder and Ailerons. 16

Tables:

-- Table I: Comparison of Pilots' Performance in Their Best Flights. 8

iv

INTRODUCTION

McRuer and Graham (1981) have presented a survey of eighty years of flight control, and Ashkenaz

(1984) has presented a survey of twenty five years of handling qualities research. From both survey

presentations, it appears that prior to 1984, the cross correlations between pilot inputs and airplane

response on a real time simulator had not been studied, but transfer functions representing human

pilots had been proposed (see, for example, Washizu and Miyajima, 1965, and Smith, 1965), and the

pilot induced oscillation (PIO) theory and resulting prediction technique had been developed (see

Smith, 1977). The prediction techniques were tested on eighteen aircraft/flight control system landing

configurations by Bjorkman (1986). Bjorkman indicated the need of more data and simulator studies

to gain physical insights into PIO mechanization. From more recent works on PIO including the

paper by Hess and Kalteis (1990), the need of more data is further desired. Cardullo et al, and

Middendorf et al are some of the recent studies on the effect of simulator transport delay on pilot's

performance. In the present work a low cost flight simulator system with graphics and software on

computer workstations has been installed. On the simulation system, a future study of PIO is

proposed. As prepatory work for a future PIO study, the flight data has been obtained for two sets of

flights with pilot in the loop. For conducting their flights, the pilots utilized the heads-up display on

the computer monitor and operated a joystick to maintain a given altitude and a given heading. One

set of flights is obtained without any additional delay between the stick input and the appearance of

airplane response on the computer monitor. In another set of flights, a 500 ms additional delay is

used. The flight data has been processed to find cross correlations between deflections of control

surfaces and response of the airplane. It is anticipated that these cross correlations for straight level

flights would serve as reference material to compare the respective cross correlations for future

simulator studies of PIO. A portion of the work of this report was presented at an AIAA Southeastern

Student Conference By Williams and Johnson (1997), and their paper is included as Appendix B in

this report. While the test flights for the present study were being conducted, the raw data on some of

them were displayed on the internet at http://silicon.tusk.edu/-jpwill.

THE SIMULATION SYSTEM

The simulation system is comprised of two SGI workstations and a BG System Joystick called a

FlyBox. The two workstations are SGI IRIS with 2 CPUs and SGI Indigo 2 with one CPU; they are

connected through ethernet. The simulation software, which represents the dynamics of flight of an

F-15E jet fighter has been provided by NASA Dryden Flight Research Center. For the graphics of the

system, the graphics of the SGI flight simulation demos has been integrated with the software of the

airplane dynamics. Norlin (1995) has provided a description of the design of software, and its

simulationcapabilities.According to Norlin, the F-15E real-timesimulationis coded with aFORTRAN77 shell and C supportroutinesand it operateson a UNIX-basedmultiprocessorcomputer.TheFORTRANcodeincludestheaircraftmodels,equationsof motion,integrationtablelook-ups,initializationand displaygenerationroutines.The C supportroutinesare usedfor thegraphicaluserinterface,memorymapping,priority boosting,andinterrupthandlers.In addition,C isusedfor thegraphicsanddistributedsystemfunctions.Theintegrationschemeis optimizedfor real-timeoperation.In thismethod,thederivativesareonly calculatedoncefor eachframe,a weightedaverageof themidpointandpreviousframederivativeisusedto predictthederivativeat theendoftheframe.Theequationsof motionassumeflat earthandsix degreesof freedom.The airplaneisassumedsymmetricalaboutits ownx-z plane.The simulationmodelcalculationsandintegrationoftheequationsareperformedin thereal-timeloop. Forpilot in the loop or hardwarein the loop,themainreal-timetaskis interruptdrivenat thehighestallowablesystempriority. The useof 3 CPUsensuresthattimingconstraintsareadequatelymet.For their simulators,NASA Drydenpreferto usethe name engineeringsimulatorsinsteadof production training simulators.The engineeringsimulatorsprovidehighfidelity simulationthatis responsiveto theneedsof theresearchers.TheF-15Esimulatorusedin thepresentwork is anengineeringsimulator.It is calledthe F-15 ACTIVEwhichimpliesthatit incorporatesAdvancedControlTechnologyfor IntegratedVehicles.Thecodehasthe flexibility to programa desiredtransportdelaybetweenthe stick input and the airplaneresponseon themonitor. Theuseof UNIX "makefiles" to compilethe simulationallowsminorupdateswithin about 5 minutes.Thejoystickhasthreedifferentmovementsto deflect the threecontrolsurfaces:forward-rearwardmovementfor elevatordeflection,right-leftmovementfor aileron,andclockwise-counterclockwiserotationaboutits ownaxisto simulatepedalmovementfor rudder

deflection.It maybenotedthattheexperiencedpilots wouldprefer theuseof rudderpedalsinstead

of theexistingstickmovementsto simulatethepedalmovements,therefore,the absenceof pedalsmay causea lack of coordinationbetweenthe rudder and aileronsin their test flights duringsimulation.In a simulatedflight, the digital dataon forty two different flight parameterscanberecordedat every25mstimeintervals.Theflightparametersincludealtitude(H), timerateof changeof altitude(HDOT),andheading(PSI)aswellasstickdeflectionfor elevator(DEP),stickdeflection

for aileron(DAP),andpedalmovementfor rudder(DRP).A pull on thestickor a positivevalueofDEPdeflectstheelevatorupwardwhichraisesthenoseof theairplaneandincreasesits altitude(see,for example,Roskam1995,p. 241).In thepresentreporttheDEP,DAP,andDRPdataareessentiallyusedto find crosscorrelations.It isunderstoodthatthedeflectionsof elevator,aileron,andrudderare

proportionalto the valuesof DEP,DAP, and DRP,respectively.Therefore,for computing thedimensionlesscrosscorrelationcoefficients,thevaluesof DEP,DAP,andDRParetreatedasrelativevaluesof deflectionsof elevator,ailerons,andrudderalthoughthedimensionalvaluesof DEP,DAP,andDRParenot thedimensionalvaluesof deflectionsof therespectivecontrolsurfaces.

FLIGHT DATA PROCESSING

In the present study, all flights conducted on the simulator were straight level flights of three minute

duration. For any flight conducted, the simulator can provide digital data for 42 flight parameters at

every 25 ms time interval. For the present work, however, the digital data was obtained for only

altitude (ft.), heading (deg.), time derivative of altitude (ft./sec.), and the deflections of elevator,

rudder, and aileron. For the altitude, H represents its instantaneous value and h represents the

fluctuating part of its instantaneous value. Therefore,

h(t) = H(t) - avg. H

where the avg. H is the average altitude of the three minute flight and t represents time.

For the heading, ud represents its instantaneous value and _ represents the fluctuating part of its

instantaneous value. Therefore,

_(t) = W(t) - avg.q _

Similar relations are used between instantaneous values, fluctuating values and average values of the

control surface deflections. A is used for instantaneous value of control surface deflection, and 8 for

the fluctuating part of the instantaneous value. For distinction between the three control surface

deflections, the subscripts a and r represent aileron and rudder, respectively. No subscript is used on A

or 8 to indicate elevator. The rms values of the above signals are denoted by, 8 ', h', and x_'. The

coefficient of cross correlations between 8 and h for an arbitrary time gap x is denoted as CORR (x)

and it is defined as:

t=T

1jCORR(x) - T 8' h' 8(0 h(t + '_) dtt=0

The simulator provides data at every 25 ms interval, thus a 3 minute flight has 7201 points for each

signal. The coefficient of cross correlation is therefore calculated as follows:

3

CORR(j) =

( -')

(7200-j) _5'h' h i+ji=l

To cover a time gap, x of 20 seconds, CORR(j) is calculated for j -- 1, 2 ..... 801. For 100 second time

gap j ranges from 1 to 4001. It is suggested that care be exercised in interpreting the long time gap

correlations. For the correlation with zero time gap, the averaging is based on 7200 pts, with 20

second time gap the averaging is based on 6400 points, and with 100 second time gap the averaging

is based on 3200 points. The cross correlation coefficients between any other two signals are defined

and calculated in the same manner. In the above formulas 6 and h may be replaced by any other two

signals between which the cross correlation is desired. In the present work, the cross correlations are

considered between 8 and h, 8 and dh/dt, 8r and _, 8a and % 8r and 8, 8a and 8, 8r and 6a.

THE PILOTS AND THE TEST FLIGHTS

Four volunteer pilots conducted the required flights on the F-15E real-time simulation. Three of

them were experienced licensed pilots and one had no prior experience of flying. In this report, the

volunteer pilots are named P1, P2, P3, and P4. The ages, flying hours, and the license status of the

pilots were P1 : 69 yrs, 3200 hrs, SEL, MEL, INST; P2:48 yrs, 100 hrs, SEL, MEL,/NST; I:'3:'23 yrs,

830 hrs, SEL, MEL, INST; and P4:26 yrs, no flying experience.

In every test flight, a pilot was required to maintain straight level flight for three minutes duration

heading due North, with preadjusted throttle for flying at 450 knots indicated at 10,000 ft. altitude

with autotrim OFF. During the flight, the pilot inputs were limited to the joystick movements only.

The volunteer pilots were provided with the facility to train themselves on the simulator by

conducting several three minute flights until they reached their own asymptotic performance in terms

of (h' + 10_g') a weighted sum of the rms values of fluctuations in altitude and heading in ft. and

deg. respectively. Every pilot conducted two sets of straight level flights. One set of flights was

obtained without any additional delay between the stick input and the appearance of airplane

response on the computer monitor. In another set of flights, a 500 ms additional delay was used.

Including the flights with the asymptotic performance, the pilot P1 conducted 15 flights without

delay and 15 flights with delay; P2 conducted 16 flights without delay and 21 flights with delay; P3

conducted 22 flights without delay and 17 flights with delay; and P4 conducted 40 flights without

delay and 25 flights with delay. From amongst the asymptotic performance flights, for each of the

two kinds of flights, and for each pilot, based on the value of (h' + 10_g'), the best flight, the average

flight, and the worst flight were picked up for further analysis. For all twenty four of these flights,

4

WilliamsandJohnson(1997)havereportedaveragevaluesandrmsvaluesof altitudeand headingand_i-hcorrelationversustimegapgraphs.

A comparisonof theaverageandrmsvaluesof altitudeandheadingfor thefourpilotsindicatedthatthepilotsP3 and P4 had remarkablysmalldeviations,whereaspilots PI and P2 had ratherlargedeviationsfromthedesiredvalues.It is believedthatthecrosscorrelationsbetweenanytwo randomly

changingbutrelatedvariableswouldbebetterrepresentativeof theirmutualinterdependenceif theirdeviationsfrom thedesiredquantitiesarerathersmall.Thereforethecorrelationsfor the flights of

pilotsP1andP2arenotreportedheredueto their largedeviationsin _ andh. Theymayinsteadbeseenin WilliamsandJohnson'spaperprovidedin AppendixB. In themainreport,thediscussionsoncorrelationsdwell uponfive differentflightsandthosearethebestflightsof pilotsP3andP4without

delay,thebestflights of pilotsP3andP4withdelay,andtheaverageflight of pilot P3with delay.Theaverageflight of pilot P3withdelayis includedin thediscussionbecausethebestflight of P3showedanunusualcorrelationfeaturewhencomparedwith theotherflightsof pilotsP3and P4.The

graphsof therawdatafor theseselectedfive flightsareprovidedin AppendixA.

FLIGHT TEST RESULTS

For comparison of pilot's performance in flights without transport delay and those with 500 ms

delay, the rms values of altitude and elevator deflections for the best flights of the four pilots are

shown in Table I. For both kinds of flights, pilots P3 and P4 have achieved better performance

compared with pilots P1 and P2. For the flights of pilots P3 and P4, the rms values of altitude and

elevator deflection for flights with delay are approximately twice their respective values for flights

without delay. It is obvious that the 500 ms transport delay has resulted in deteriorated pilot's

performance. With the existing related publications in view, this is not surprising. For example,

Middendorf et al (1991) have noted that 300 ms transport delay resulted in significant deterioration

of pilot's performance.

In a study of pilot dynamics and pilot's choices of feedback alternatives for controlling altitude, the

frequency response functions of pitch angle and altitude have been obtained and used by Goto and

Matsuo (1988). In the present work, the cross correlations between the control surface deflections and

airplane reponses are obtained to understand some aspects of the pilot dynamics. Let us start with the

consideration of cross correlations between elevator deflection, 5 and airplane altitude, h. An upward

instantaneous deflection of elevator from its average deflection is positive _5 and a downward

deflection is negative 5, although the convention is to take downward elevator deflection as positive,

for example Etkin and Reid (1996, p. 33). A higher instantaneous altitude compared with the average

altitude of the three minute flight is positive h, and a lower than average is negative h. It is understood

thata positivechangein 5 resultsin a positivechangein h anda negativechangein _5resultsin anegativechangein h. Allowingfor a timelag betweenelevatordeflectionand altituderesponse,thetwo signals_5andh shouldhaveapositivecorrelation.

Figure1presents5-hcorrelationsfor pilotsP3andP4for a rangeof timegapsbetweenzeroand20seconds.Figure 1 hasthe graphsfor the five selectedflights, their selectionis indicatedin the

previoussection.All theflightsof Figure1 havea commonfeature- that they do not havelargedeviationsfrom therequiredaltitudeof 10,000ft; themaximumdeviationin averagealtitudeis 6 ft.in the best flight of pilot P4. All the flights showan appreciablemagnitudeof negative5-hcorrelationfor zerotimegap.Thisis expectedbecauseupon noticingpositiveh, thepilot movesthestickto deflecttheelevatordownwardandviceversa.

Letusconsiderthebestflight withouttransportdelayfor pilot P3asa typicaloneamongstthefive

flights of Figure1. In this flight the largestmagnitudeof negativecorrelationis reachedwhenthetimegapis 400ms;to talk aboutit, let uscall it thefirst timegapon thegraph.Thefirst timegap,perhaps,includesthreestagesof airplanealtitudecontrol: the pilot's reactiontime,the time gapbetweenstick movementand the resultingelevatordeflection,and the time gap betweenelevatordeflectionandaffectedaltitudechange.Thisconsiderationappearsreasonablewhenit is seenwithRoskam's(1995,p.765) assumptionsof 100 ms reactiontimefor testpilots and 120 to 200 msreactiontimefor otherpilots.Thecorrelationstaysnegativeup to 2700ms.Let thesecondtimegapon thecorrelationgraphbe thetimegapbetweenthelargestnegativemagnitudeof correlationandzero correlation,here it is 2700 400 = 2300 ms.The secondtime gap,perhaps,representslimitationson theratesof climbanddescent;higherrateswouldleadto lowervalueof the second

timegap.With transportdelay,thebestflight of pilot P3hasanexceptionalfeaturethatits' first timegapis zero;thisexceptionalfeatureisnot exploredfurther.Therawdatain AppendixA, however,showsnosignificantdifferencesin thebestandaverageflightsof pilot P3withdelay;but theelevatordeflectionsfor thefirst 30secondsin theflightswithdelayaredifferentfrom therespectivevaluesin

theflight withoutdelay.Dueto theexceptionalnatureof the bestflight of pilot P3withdelay,theaverageflight of P3is includedin Figure1to bediscussedasanothertypicalflight withdelay.Fourof thefive flights in Figure 1 maybe treatedastypicalstraightlevelflights; for themthefirst timegaprangesfrom 350msto 600msandthesecondtime gaprangesfrom 2300msto 5700ms.Oneof thereasonsfor largedifferencesin thefirst andsecondtimegapvaluesfor different flightsmay

be thatpilot's observationsandactionsarecontinuousratherthandiscretein nature;the pilot doesnot needto wait until elevatordeflectionor airplaneresponsecorrespondswith certain stick

movement.Thelargestmagnitudesof correlationcoefficientsandthefirst andsecondtimegapsarenot significantlyaffectedby the500 mstransportdelay.This is surprising,especiallywhenwenotethatthermsvaluesof fluctuationsof altitudeandelevatordeflectionin flightswith transportdelayare

approximatelytwicethecorrespondingvaluesin flightswithno delay.Therespectivermsvaluesare

6

providedin Figure1.It is understoodthata changein elevatordeflectioncausesapitchingmomentthatbringsabouta rateof changeof airplanealtitude.Therefore,for a moreclear viewof certainfeaturesof thesameflights,to substantiatethe_5-hcorrelationsof Figure1,the 5-hdot(hdot= dh/dt)

correlationsareprovidedin Figure2.

In Figure 2, all the flights, exceptthe best flight with transportdelay for pilot P3, show anappreciablenegative_5-hdotcorrelationat zero time gap.This is expectedbecauseupon noticingpositivehdotabovetherequired10,000ft. altitude,thepilot movesthestickto deflectthe elevatordownward,and upon noticingnegativehdot below10,000ft. he movesthe stick to deflect theelevatorupward.Thenegativevaluesof _5-hdotcorrelationsat zerotimegapin Figure2 arelessinmagnitudethanthecorresponding_-h correlationsin Figure 1. This is understoodbecauseuponnoticingpositive hdot for altitudebelow10,000ft. andnegativehdot for altitudeabove10,000ft.,thepilot doesnotneedto changetheelevatordeflection.

In thebestflight of P3 withouttransportdelay,pickedup hereasa typical flight, the correlationreacheszerowhenthetimegapis 400ms.Forthesameflight, thisreinforcestheobservationthatthelargestmagnitudeof negative_5-hcorrelationoccurredatthesametimegapasseenin Figure1.In allthegraphsof Figure 1 andFigure2, it isnoticeablethatthe_i-hdotcorrelationbecomeszeroat the

sametimegapsatwhichthe_5-hcorrelationshavelocalmaximumor minimumvalues.

In Figure2, letusconsiderthetwoflightsof pilot P4.Forthe_-hdotcorrelationsthenumberof zerocrossingsin20secondsfor theflight with transportdelayis twicethatfor theflight withouttransportdelay.A similarfeatureis not foundin thetwokindsof flightsfor pilotP3.It maybereiteratedherethatpilot P3is acertifiedandexperiencedpilot whereastheexperienceof pilot P4 is limitedto flightsimulatorsonly.FromFigureI, werecallthatthefirst timegapgoesfrom zeroto a valuewherethemagnitudeof negativecorrelationis largestandthesecondtimegapgoesfrom theend of thefirstgapto a valuewherethe correlationiszero.Let thesubsequenttimegapsrepresentthe subsequentzerocrossingsof thecorrelationstartingfrom thefirst zerocrossing.Perhapsthetimegapsbetweentheconsecutivezerocrossingswouldprovidean indicatorof the pilot's performance,largergapsrepresentingbetteror moresteadyperformanceprovidedthatthe deviationin altitudestayssmall.Suchan indicationis jeopardizedto acertaindegreebecausesticksignalin theflightsunderstudyiscontaminatedby electronicnoise.Forelevatorandailerondeflections,thenoisesignalis estimatedat

3%of a typicalstickmovement.Forrudderdeflection,thesignalis significantlylargerthan3%.Noattemptis madeto suppressor filter outthisnoisebecauseit requiresthepilot to remainvigilantif hewishesto maintainthe straightlevel flight. To find the subsequentzero crossingsof the _5-hcorrelations,thegraphsareobtainedfor timegapsfrom0 to 100seconds.Forthe sameflightswhichareincludedin Figure1,the100secondgraphsareshownin Figure3. As suggestedin thesectiononFlightDataProcessing,careis neededin interpretingthelongtimegapcorrelations.In Figure3, for

7

thetime gaprangefrom zeroto 100seconds,for pilot P3,a flight with transportdelayhas5 zerocrossingsandaflight withoutdelayhas16zerocrossings.Onthecontrary,for pilot P4,a flight withtransportdelay has 24 zero crossingsand a flight without delay has 7 zero crossings.UsingLanchaster'sestimate(referenceEtkin and Reid 1996, p. 172), the time period for phugoidoscillationsat450kts.or 760ft./sis 104sec.whichimpliesnearly2 zerocrossingsin 100seconds.Itis notclearif thephugoidoscillationshavea role here.Basedon rmsvaluesof h and8 fluctuationsonly,theperformanceof bothpilotsisnearlythesame.Havingfewerzerocrossingsin flightswithoutdelay as comparedwith the ones with delay is intuitively more acceptable.Therefore, theperformanceof pilot P4is somewhatpredictablebut thatof P3is surprising.It maybe interestingtoreiteratethatpilot P3is a licensedandexperiencedpilot but theexperienceof P4is limited to flightsimulatorsonly.

Figure4 showsthecoefficientof crosscorrelationbetweenailerondeflectionsandairplaneheadingversustimegapfor thesamefive selectedflightswhichhavebeencoveredin Figure 1.For four ofthe flights the graphshavesimilarfeatures.For all the five flights, the largestmagnitudeof thenegativecorrelationoccursat thetimegapvaluesbetween450msand725ms.This timegaprangeiscomparablewith 350to 650ms,whichis thefirst timegaprangefor 8-hcorrelationsin Figure1. Forzerotimegap,anappreciablenegativecorrelationexistsin all thefiveflights.Forbothpilots,thermsvaluesof ailerondeflectionsfor flightswithdelay areappreciablylargercomparedwith thoseforflightswithoutdelay.Thermsvaluesof airplaneheadingdo nothavethe samecharacterasthatofthermsvaluesof ailerondeflections.

Figure5 providesthecoefficientof crosscorrelationbetweenrudderdeflectionandairplaneheadingversustimegap.In thebestandaverageflightswithdelayfor pilot P3 appreciablechangesappearinthecorrelationwith timegap.In therestof thethreeflights thecorrelationisratherinsensitiveto thetimegap.Therawdatain AppendixA helpsto tracethis insensitivityto an inactivityon thepilot'spart in usingtherudder for headingcontrol.Thepilot P3hasusedruddermovementmuchmorethanpilot P4.For theaverageflight of pilot P3withdelay,therudder-headingcorrelationin Figure5hassimilarfeaturesastheaileron-headingcorrelationin Figure4. Thissimilaritymaybean indicatorof coordinateduseof rudderandailerons.

Figure6 hasthecoefficientof crosscorrelationbetweenelevatordeflectionand aileron deflectionversustime gap.Thecorrelationfor the five flightsdoesnot seemto haveany commonfeaturesexceptthatthecorrelationis rapidlychangingbetweenpositiveandnegativevalues.

Figure7 hascoefficientof crosscorrelationbetweenelevatordeflectionandrudderdeflectionversustimegap.Fourof thefive flightsshowappreciablenegativecorrelationsfor zerotimegap,although

sucha featurebetweenthemovementsof elevator and aileron may not be worth emphasizing. In

general, the correlation graphs for the five flights do not have any common features.

Figure 8 presents the coefficient of cross correlation between rudder deflection and aileron deflection

versus time gap. For different flights, at zero time gap, the different values of correlation coefficient

appear to represent the pilot's coordinated use of rudder and aileron. No common features are

discernable between different flights, perhaps, because of the lack of use of the rudder by the pilots.

The hardware facility in the present simulation system, perhaps, demotivated pilots from using the

rudder. The system hardware does not have rudder pedals, instead, the rudder pedal movement is

simulated by the rotation of the joystick as described in the section on "The Simulation System."

An overall consideration of all the correlation graphs suggests that for reasonably well defined flights,

the cross correlations between pilot input and airplane response versus time gap reveal interesting

features of the pilot dynamics. When the aileron-heading and the rudder-heading correlations for a

flight are considered together, they reveal the presence or absence of coordinated use of ailerons and

rudder by the pilot. Consideration of correlations amongst the parameters that represent longitudinal

motion of the airplane and correlations amongst the parameters that represent lateral motion of the

airplane support the generally used approach of separate studies of longitudinal and lateral dynamics

of an airplane in flight.

Additional research work may be recommended to find certain characteristic features of cross

correlations between pilot input and airplane response. Such characteristic features would then help in

determining different progressive stages of pilot training on simulators.

Pilot II h.' I II h:P1 73.8

P2

P3

P4

51.2

7.5

9.4

0.60

0.51

0.23

0.25

77.1

66.4

18.2

18.7

1.02

0.20

0.45

0.72

Table I: Comparison of the Pilot's Performance in Their Best Flights With and Without Transport

Delay, h' and _i' are the rms values of altitude changes and elevator deflection changes, respectively,

subscript n is used for flights with no delay and d is used for flights with 500 ms delay.

9

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-0.6

_2oTAU

0.6

0.4

0.2

colt, 0

-0.2

-0.4

P3_AD.bdop

'P3ADohdop'

Oglmax m0.325452 0 tau m19.975

=Ollm£n m00.464615 • tau 00.425

tvoB m 10005.5 evoDKP - -1.55348

rmmi m 21.7423 rmmDKP - 0.462317

-0.6 .

i I I ,

0 2 4 6 8

i * * i i

10 12 14 16 18

TAU

20

Figure I: Cross Correlation Coefficient Between 5 and h

vs. x for the Five Selected Fiights of Pibts P3 and I)4. B

is the pilot's best flight without additional transport

delay. BD and AD are the pilot's best and average

flights with additional transport delay of 500 ms. (5 =

elevator deflection, h = airplane altitude, x = time gap).

10

0.4

0.2

*"ORB 0

-0.2

-0.4

J i

0 2 4

P4_Bb.cLhe

'Pl,Bb.aiho' •

CORRmlx mO.36BgB5 0 rio m3.575

n I i , i i J

6 $ 10 12 14 $6 18 20

TAU

i

0.61

0.4

0.2

301i 0

-0.2

-0.4

-0.6

0

II IIP3_BDb.c lho

'PqBOb.cihl' •

;Oltimax m0.398765 O tiu m3.45

i n i n n J I i i

2 4 6 8 10 12 14 16 18 20

T&U

P4BDb.clht

L 'P4_BDb.aihe' '0.8 OERmsx -0.660987 • teu -1.525

_OIL_ltin m-0.296106 0 tau mO

0.4 _v_a_ - 0.115164 IvoOKP - -1.7435

_o_" 8. 032S6 *..D,, - 0.724540.4i( t

0.2 II/l\_

_Oil 0

-0.2

-0.4

-0.6

-0.8

i i J i a | | I o n

0 2 4 6 8 10 12 14 16 18 20

TAU

__.____lL I I I II II I "_i

0.4

0,3

0.2

0.1

-0.2

-0.3

-0.4

n

i

_3_AOb.c lha

" P3_ADb. c .I.lle " ,

:Olllmax m0.3'1986_. M tau m4,'lS

i I , n I I i I I

2 4 6 S 10 12 14 16 18 20

TAU

Figure 2: Cross Correlation Coefficient Between 8 and

dh/dt vs. • for the Same Selected Flights Which Arc

Covered in Figure I. (8 = elevator deflection, h =

airplane altitude).

II

P3Bc.hdep

'P3_Bc.hdep' -

0.4 :ORRmax mO.245911 0 tsu m92.575

CORRm_n --0.356171 e tau mO.4

avefl m 10004.4 aveDEP - -2.59663

-0.4

i J i

20 40 60 60 1OC

TAU

P4 Bc. hdep

"P4 Bo.hdep' •0.8

_ORRmax n0.625233 0 cau o94.975

0.6 :ORRmXn m-0.34346 I) tau o85.75 d_kLveH m 10006 aveDJEP - -1.98802 /0.4_..msH u 9.38642 rnsO£P - 0.245737

0.21"

_OBR 0 [/-0.2

-0.4['

-0.61'

-O.8 I'

0

i

20 4O 60 8O 10(

TAU J

P3_BDe.bdep

t 'P3_BDc.hdop' •0.6 _OBBmax m0.6429_Z _ tau m16.4

DEP - -1.55635

m 0.45004

0.4_

COBB 0

-0.2

-0.4

-0.6

-0.8

0 20 40 60 80 101

TAU

P4_BDo .hdep

0.6 'P4_BDo.hdep' 4

:OBBaax m0.207152 i) t_u o45.775

.'OBBm£n m-0.479025 Q t:su mO.35

0.4 sveB m 10000.9 avoDEP m ol.7435

rmstf o 18.6935 :maDEt_ . 0.72454

0.2

:OBID. 0

-0.2

-0.4

-0.6

0 20 40 60 80 100TAU

.--,--,--.L _

0.5

P3_ADc.hdep

'P3_ADc.hdep' •

_ORBma: m0.349134 e tau m24.575

COBBmXn --0.78089 0 tau n43.575

svoB m 10005.5 eveOEP • -[.55348

ruaB m 21.7423 rmaDEP - 0.462317

60 80 10(

TAU

-L

i

0 20 4O

Figure 3: Cross Con'clarion Coefficient Between 8 and h

vs. x for z up to 100 Seconds. For the same flights,

goes up to 20 seconds in Figure 1. (5 = elevatordeflection, h = airplane _lrimde).

12

P3Do.pdmp

'P3_Bo.pdap' •

0.3 _ORRmex .-0.0594986 • tau -19.975

CORRILn 100.25259S 0 taU .0.725

0.2 pveeSZ - -0.340902 *veOAe - -0.00677262_aBESZ m 0.544824 FIsDAP - 0.046264

..iF

con o F................

-o.:, F

* * i r r i r * *

0 2 4 6 8 10 12 14 16 18 20

TAU

II

P4_Be.pdap

0.2 'p4_Be.pdap _ "

:Ollmlx --0.0995051 0 tau mlE.10.15 :ORRnAn --0.151271 0 _eu mO.7

lvOPSI " -0.S10125 aveDAP - -0.000792701

0.05

:Oil 0 .........

-0.05

-0.2

-0.15

-0.2

* i t i t * J i i

0 2 4 6 8 10 12 14 16 18 20

TAU

.- ms mn::lP

P3_BDI.pdtp

0.4_ ' P3_BDo. pdap* •

m-0.279572 0 t*u -0.

F:::::" 0.206,39.+.oA,. -oo..160.2 0.482938 =nsDAP 0.101864

::3/-o.4F • i i i i i i , t

0 2 4 6 8 10 12 14 16 18

TAP

0.4

0.2

00.4

20

P4.BDe. pdsp

'P4 BDe.pdap* "

:O|Rnex ,0.236366 e tau -10.375

:,BRian --0.372959 • ¢au .0.65

lvePSZ m 0.135562 aveDAP - -0.0352947

_usPSI - 0.881634 rnsD&P - 0.0135028

* i , i i * i i ,

2 4 6 8 10 12 14 16 18 20

TAU

P3_kDe.pdsp

0.4 'P3_ADe.pdap' •

:Ollmax -0.164808 9 _au -6.3250.3 _Ollm£= m00.290042 0 tsu m0.45

IVIRIZ e 0.260222 nveDA_ - -0.0412342

0.2 rIIPIZ m 0.50166 rlsDAP m 0.209219

-0.2

-0.3

-0.4 J , , i i i i i

0 2 4 6 8 10 12 14 26 18 20

TAU

, I

Figure 4: Cross Correlation Cocfficicm Between 8, and

¥ vs. % for the Same Selected Rights Which Are

Covered in Figure 1. (8, : aileron deflection, xp =

airplane h_ding).

13

o.41

0._11

0.2

0.1

¢011 0

-0.1

-0.2

-0.3

°0.4

P3_Bd.pd=p

"PS_Bd.pdwp" *

:OIRmox m-0.212113 0 tau m4.775

:OBRm,n m-0.320394 0 tau m18.22S

svePSZ " -0.340S02 *voOIP = 0.00345877

rmmeSZ - 0.544824 :moDRP m 0.00462673

0 2 4 6 8 10 12 14 16 18 20TkU

m_

P4_Bd.pdrp

'P4_Bd.pdwp' •0.4

:ORIImax m-0.264649 0 tau 012.15

0.3 :ORnmln m-0.329402 @ tsu 14.7Shve_OSZ i -O.510125 aveDIIP -- 0.003)709

0.2 :nsPSZ = 0.276421 rnsDlIP • 0.00264825

0.1

:011 0 ................

-0.1

-0.2

°0.3

-0.4

0 2 4 6 8' 10 12 141 16 18 20

TAU

mm_KJ

0.6

0.4

0.2

COB& 0

-0.2

-0.4

-0.6

0

P3_BDd.pdrp

'P3_BDd.pd_p' •

:OIImaz m0.420246 0 tsu m11.575

=ORlmlnJl_3582 0 ts_lmO_

tveP$_lJZ . _UJle_6eJmSsJmqJ_eDKPDRp 01_.00285273

* , , * * , | * ,

2 4 6 8 10 12 14 16 18 20

YAU

0.2

0.11

_ORIE 0 I

-0.1

-0.2

p4_DDd.pdrp

'P4BDd.pdrp" '

:ORBmax m-0.0441563 0 tau m4.325

:ORRa_n m00.187214 • tau mOtvoPSZ 8 0.135562 *veDSP = 0.000455656

_mIPSZ m 0.881634 rnsDEP = 0.00253255

, , , * | ,

2 4 6 8 10 12 14 16 18 20

TAU

b_qa_s-- l_

0.2

0.1

r'OIIt0

*0.1i

°0.2'

P$_ADd.pdrp

'P3_ADd.pdrp' ,

=ORBmsz m0.0621841 • tau m6.4S

:O1imLn =-0.155183 O tau =0.575

avePJZ m 0.260222 avuDRff m *0.00741358

=mSPJX m 0.50106 rmJORP m 0.0104627

* * , , , , * , ,

2 4 6 8 10 12 14 16 18

TAU

2O

!I

Figure 5: Cross Correlation Coefficient Between _, and

¥ vs. x for the Same Selected Flights Which Are

Covered in Figure I. (8, = rudder deflect/on, _ = airplane

heading).

]4

P3Bg.sdep

0.3 _OmRmaz -0.181784 0 taU --5.525

_ORKmla m--O.257131 0 taU m17.575

_voDAP " -0.0067?262 *veD£P " -2.59663

0"2_,DA, - 0.0R264 rnsD_P - 0.2320_

o-,k ^j\ / X /

i J i i i i _ i i i

0 2 4 6 8 10 12 14 t6 18 20

TAU

P4_Bg. adep

_0111max m0.0850131 g tau m10.425_OIIIlmlll m-0.117406 8 tau m16.725

0. I _veDAIP m -0. 000792701 IIveDEP - -1. 98802

p:m,DAP - O. O_.87 r_lq_45737

o.os f. _ / _ •

:0../ A.,/ i __!°P/-- I/ ....

'' V ',-o. os V , ._

"0"1 r

-0. 15

0 2 4 6 6 10 12 14 16 18 20

?AUI

1F3_BDq.adep

"@$_BDq.adep' ,o

FOilmax m0.108808 0 tsu -12.35

FORImLn m-O.Z2456§ 0 tmu m7.925

0.1 _voDAP i -0.0246216 avoD£Jl_ -1.55635

:.,t v V-_ .15F

* J i , + i r J J

0 2 4 6 8 10 12 14 16 18 20

T&U

cOl1 0

-0.11.

-0.2

P4 BDq adep

Lo,.2...o 17,31 . t.u .12 8 '.4-.h,-.d-.' .

0"2_OIImLII m--0.167236 81 tau mZ0+qrl_§

laveDA P . -0.0352547 aveDEP -i-_.743S

0.1 'mmD_lt_ m 0.0835021 rnsDf[P - fb.7_454

, , i i i i i * i

2 4 6 8 1.0 12 14 16 1,8TAU

2O

i

m

P3_ADqsdep

.15' "P3_ADq. Idop" ,

=Ollmlx m0.103305 0 tSU mO

1 _O|ls£n moO.IllS32 I tau m7.6]_lfoDAP - -00412342 avoDEP - -2S5348

sDA_ m 01052SS rnaDE_ m 0.46231?

CC • 0 ..................................

- .05

0.1F

- .25i l l i l i i _ l

0 2 4 6 8 10 12 14 16 18 20

_XU

Figure 6: Cross Correlation Coeffi¢icnt Between _ and

8, vs. z for the Same Selected Flights Which Are

Covered in Figure 1. (_5 = elevator deflection, _, =

aileron deflection).

lS

II_I_L i ----

P3Bf. rdep

0.2 :Omimsz m0.18150$ 0 tJu -3.6

;OJIJIJl+i,I+_I¢O. '1299+'J 6 I_ t, mu 1.1) l,,veDRIp"'b 0"%.00345577 .veDIIP - -2_663 I

_'IIll - O. 46]:673 =.sOEP . 0 ,_0.I

:011 0 ]

/"0"11-0.2

* I n i i i i i n

2 4 6 8 10 12 !4 16 18 20

?AU

P4_B_.rdop

0.4 _u mS,47..'Pq..Bf.rdop'_" ' ,,

0,3k_O,q/Im.tn m-0_302588 I tau ..0.2

__035709 _v.DSrp . -I..98502

-...ooo![,...,............:.-,.-+-.-.----0

-0

0 2 4 6 IS 1O 12 14 16 . 18 20

?AU

__...... -_--_+_

P3_ID f. rdep

0.4 _

-_OIIIID ---0.351578 B tdIU mO.§5

.v.DIP - 0.00285273 .v.DEp . -1.55635

-0.4

0 2 4 6 $ 10 22 14 16 18 20

TAU

O.

0.1

O.

0.0:

'11 ,

0.0t

-0, :

-0.;

P4_BDt.:dep

, 'P4_BDf.rdep' ,

Oltmax -0.0307454 e cau m3.05

20111£a a00.160276 0 _au m[0.TSIveDBP -- 0.000459656 sveDgP e "1.7435

PmoDIP " 0.002932S9 rnnDgP i 0.72454

TAU

P3_ADt.rdep

'P3oAD£.rdep' .0.4 _OIRmaa ---0.136746 @ ta_ -0.025

:OIInLa --0.345831 I tsu m8.425IVIDIP m "0.00741358 aveOEP i -1.55341

0.2 _IIDIP i 0,0104627 :IIDIP m 0.462317

11 0_ ...................................................................

0 2 4 6 8 10 12 14 16 18 20?&U

Figure ?: Cross Correlation Coefficient Between 8 and

8, vs. _ for the Same Selcct_.d Flights Wh/ch Arc

Covered in Figure I, (8 = elevator deflection, +, = mdclcr

deflection).

16

_ll BE]B

P3 _8h. adrp

0.:3 Oilimax _0.253288 • tau -0.25

0.2

0.1

COJt| 0

-0.1

-0.2

-0.3

'P3 Bh.adrp' ,

mmJLn m--0.0162541 10 tau u19.97 c;

AP w -0.00677262 svJl_nP - 0.00345877

AP m 0.046 0.00462673

• 2 4 6 8 10 12 14 16 18 20

TAD

®U [ I

P4Bb.md_p

:O||m*x -0.0763326 0 tsu -18.075 |;OiRmln m-0.0205183 @ tmu m2.175 _ |

,veDA, - -0.0007,2701 ,veDB_ w O_i_03_ ;

0.05 _-.o^P - 0.02,5287 ..,o. - 0.0¢z._._. .;,. f

-0.05

-0.1

i , i i

0 2 4 6 8

I i i | i

10 12 14 16 18 20

TAt/

j inl i

P, BDh.adrp

0.3'P, BDb.ad=p' ,

:OBRma_ -0.208236 • tau _0

0.2_ORRmln m-O.137686 @ tau m3.425

_veDAP o -0.0246115 sveDRP m 0.00285273

_pDAP m O.101864_T_msDRP m 0.00460978

-0.2_

-0.3F

0 2 4 6 8 10 12 14 16 28T&U

P4_BDh. adwp

0.,F' P4_BDh. 8drp '

C01tlmax m0.215876 0 tau ,,0

0.2FOItEmLm m-0.0583524 • t:atu m16.175laveDAP w -0.0352,47 aveDRP - 0.000455686

_msDAP o 0.083,028 rmsOmP m 0.00293255

)aa o [ 3t_%awrqm_d_4_ _ _: _q

-0.11.

-0.2 F

-0.3

0 2 4 6 8 10 12 14 16 18 20

TAU

mm

P,_ADh.adrp

0.4F

'P$_ADb.sd=p ° ,

0 3_Ol_max m0.277801 ff tau mO

" _ORRm£a m-0.167684 • ttu m17.,5Ldrm,oDAP m "0.0412342 avoDRP m -0.00741358

O-2_sDAP m 0.109285 ::8DRP m 0.0104627i !

_Oll 0 ..........................

-0.1

-0.2F

-0.31.

-0.4k , m i i i J i i

0 2 4 6 8 10 12 14 16 18 20

TAU

Figure 8: Cross Correlation Coefficient Between _, and

5, vs. _ for the Same Selected Flights Which Are

Covered in Figure 1. (8, = rudder deflection, 8, : aileron

deflection).

17

CONCLUSION

In the study of straight level flights on a simulator with pilot in the loop, the root mean square values

of altitude variations for flights with a 500 ms additional delay are twice or larger compared with their

respective values for flights with no delay. This is in agreement with the other recent studies which

indicate deterioration in flight with 300 ms transport delay. The graphs of cross correlations between

pilot input and airplane response versus time gap reveal interesting features of the pilot dynamics. A

time gap of 350 to 600 ms appears to include three steps of altitude control, these are pilot's reaction

time, time gap between stick movement and resulting elevator deflection, and the time gap between

elevator deflection and affected altitude change. This observation, however, requires further

exploration because introducing a 500 ms additional transport delay does not make any visible

impact on the correlation graphs of a flight.

The correlation between elevator deflection and time derivative of altitude becomes zero at the same

time gap when the correlation between elevator deflection and altitude has a local maximum or

minimum value. An examination of the aileron-heading and the rudder-heading correlations suggest

that similarities or lack of similarities between the two kinds of correlations correspond to the

presence or absence of coordinated use of aileron and rudder by the pilot. Additional work is

recommended to investigate cross correlations between pilot input and airplane response to search for

their characteristic features which would determine different progressive stages of pilot training on

simulators. The UNIX based simulation system that has been installed and used for the present work

is suitable for a future study of the Pilot Induced Oscillations. The installation of rudder pedals

suitable for the UNIX based simulator system is strongly recommended as an improvement in the

system.

18

NOMENCLATURE

Symbol

ms

rms

t

"u

"um

H (t)

avg H

h (t)

h'

hi+j

V (t)

A

avg A

5 (t)

_ (t)

5r (t)

CORR (x)

DEP

DAP

DRP

HDOT

PSI

SEL

MEL

INST

AIAA

NASA

PIO

CPU

SGI

Description Units

Milliseconds.

Root mean square.

Time. instant

Time gap. seconds

Time gap for the maximum absolute value of negative correlation, seconds

Instantaneous value of airplane altitude, feet

Time average value of altitude for a 3 minute flight, feet

H (t) - avg H, fluctuating part of altitude, feet

rms value of h.

h at the (i + j) time interval of a flight, each interval is 0.025 ms. feet

Heading, zero indicates Northward direction.

(t) - avg _, fluctuating part of heading.

Elevator deflection, positive for upward deflection.

Time average A for a 3 minute flight.

5 at the i'h time interval of a flight, each interval = 0.025 ms.

rms value of 5.

A (t) - avg A, fluctuating part of elevator deflection.

Fluctuating part of aileron deflection.

Fluctuating part of rudder deflection.

Coefficient of cross correlation between two signals with time gap x.

Stick deflection for elevator or deflection of elevator, according to context.

Stick deflection for aileron or deflection of aileron, according to context.

Pedal movement for rudder or deflection of rudder, according to context.

Time derivative of H. ft. / sec.

Heading, zero indicates Northward direction, degree

Single-Engine Land (aircraft type).

Multi-Engine Land (aircraft type).

Instrument Rating (FAA-certification).

American Institute of Aeronautics and Astronautics.

National Aeronautics and Space Administration.

Pilot Induced Oscillation.

Central Processing Unit.

Silicon Graphics, Inc.

milliseconds

19

REFERENCES

. McRuer, D. T. and Graham, D. (1981), "Eighty Years of Flight Control: Triumphs and Pitfalls of

the Systems Approach," Journal of Guidance, Control, and Dynamics, Vol. 4, No.: 4, pages 353 -

362.

, Ashkenaz, I. L. (1984), "Twenty Years of Handling Qualities Research," Journal of Aircraft, Vol.

21, No.: 5, pages 289 - 301.

3. Washizu, K., and Miyajima, K., (1963), "Controllability Limit of Human Pilot," AIAA Journal,

Vol. 3, No.: 5, Pages 941 - 947.

4. Smith, R. H., (1963), "Comment on Controllability Limit of Human Pilot," AIAA Journal, Vol. 3,

No.: 10, Pages 1980 - 1981.

5. Smith, R. H., (1977), "Theory for Longitudinal Short Period Pilot Induced Oscillations," Air

Force Flight Dynamics Lab, Wright Patterson AFB, OH, AFFDL-TR-77-57.

,

.

Bjorkman, E. A.,1986, "Flight Test Evaluation

Induced Oscillations," Air Force Institute of

AFIT/GAE/AA/86J-1, December 1986.

of Techniques to Predict Longitudinal Pilot

Technology, Wright Patterson AFB, OH,

Hess, R. A., and Kalteis, R. M., 1991, "Techniques for Predicting Longitudinal Pilot Induced

Oscillations," Journal of Guidance, Control, and Dynamics, Vol. 14, pages 198 to 204.

, Cardullo, F. M., and George, G., 1993, "Transport Delay Compensations: An Inexpensive

Alternative to Increasing Image Generator Update Rate," AIAA Paper No. 93-3563-CP.

, Middendorf, M.S., and McMillan, G. R., 1991, "The Effect of Simulator Transport Delay on

Performance, Workload, and Transport Activity During Low Level Flight," AIAA Paper No. 91-

2965-CP.

10. Williams, J. P., and Johnson, Y. A., 1997, "Pilot Input and Airplane Response Cross Correlations

on a Flight Simulator With and Without Transport Delay." Presented at the AIAA Southeastern

Regional Student Conference, Atlanta, GA. (A copy of the paper is included in Appendix B).

20

11.Norlin, KenA., 1995, "Flight Simulation Software at NASA Dryden Flight Research Center,"

AIAA Paper No. 95-3419.

12. Roskam, J., 1995, "Airplane Flight Dynamics and Automatic Flight Controls," Parts I&II, DAR

Corporation, Lawrence, KS.

13. Goto, N., and Matsuo, T., 1988, "Identification of Pilot Dynamics in a System with a Choice of

Feedback Structures," Journal of Guidance, Control, and Dynamics, Vol. 11, No. 2, pages 159-

166.

14. Etkin, B. and Reid, L. D., 1996, "Dynamics of Flight Stability and Control," Wiley, New York.

21

APPENDIX A

The graphs of the raw data for the five selected flights of pilots P3 and P4. These

flights are discussed in the main text.

B represents the pilot's best flight without additional transport delay.

BD represents the pilot's best flight with additional transport delay.

AD represents the pilot's average flight with additional delay.

The x-axis in all the graphs shows time from 0 to 180 seconds. The control input

signals and the airplane response signals are plotted on the y-axis.

H = airplane altitude (ft.).

HDOT = dh/dt (ft./sec.).

PSI = airplane heading (radians in this appendix, degrees in the main text).

DEP represents joystick movement (in.) to deflect the elevator.

DAP represents joystick movement (in.) to deflect the ailerons.

DRP represents rudder pedal movement (in.) to deflect the rudder.

On a proportional scale, DEP, DAP, and DRP may also be interpreted as the

deflections of elevator, ailerons, and rudder, respectively.

A1

l__B_Izt P4_Bxlat

"4O 3

5_1. A

._!t_V' w'_ u"!l vW "it _ v u _ - v

0 ,;n ]00 1_0

• sO 3

'[/I - A.-,^]-"-." L

=" r,A^fl. ^ ^ A$,

-$.

0 ,_n IGI 1 sn

dO 3

i .... i .... , , * ,

]__BDAat

.... i .... i .... ! • , ,Inn 150

oJ _

O 50 100 150

dO 3

P4 BDAat

lo-[_VI/'VVIIV "V'vv_,IvV U"' "11_ '_ I'ib' II v_l-2o'.y, _ - v! v U i"

O _ 100 I_0

002- ; i /;_

O 50 I00 1_

dO 3

I__ADAat

"-,, ........ i ........O 50 100 1_0

"=: A fh,ooi - _ _j'_,

Figure AI: Airplane altitude, time derivative of altitude,

and airplane heading vs. time for the five selected flights.

For nomenclature, please see the first page of Appendix

A.

A2

P_J_B_lat P4_Bxlat

-2o+"54"_°+f| ' --"_. :" L A .| ., 1_ • _ IL . . t _, J_ • .

3a 'I1/'P' Iv l'J'_ i'_v- V'vl/"_/_'v _V "v-v-- "v 1'-" Y ''-'_ _I

o35-! ............. ]

0 50 100 150

03-02 -;

Ot-

O0 2

-01 £

-02 -

JO )ltO ]1_1

-I0 ,,

-2_

0 r.n 1nn 1._

D3_

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Figure A2: Pilot inputs to move the elevator, aileron,

and rudder, respectively vs. time for the five selected

flights. For nomenclature, please see the first page of

Appendix A.

A3

APPENDIX B

Copy of the paper "Pilot Input and Airplane Response Cross Correlations on a Flight Simulator With

and Without Transport Delay. " The paper was presented by Jason Paul Williams and Yusef Ali Johnson at

the AIAA Southeastern Regional Student Conference, held on April 10 and 11, 1997 in Atlanta, GA. The

work reported here was performed as part of the present project under the NASA Dryden grant number

NAG 2 - 4006.

B1

PILOT INPUT AND AIRPLANE RESPONSE

CROSS CORRELATIONS ON A FLIGHT SIMULATOR

WITH AND WITHOUT TRANSPORT DELAY

Jason Paul Williams

Under_aduate Senior

Yusef Ali Johnson

Undergraduate Senior

Aerospace Science Engineering Department

Tuskegee University

Tuskegee, AL 36088

Presented to:

The AIAA Southeastern Regional Student Conference

April 10, 11 1997

Atlanta, GA

•____....aper has bee'? re_'iewed and appr°ved f°r presentati°n by: ___

Dr. Vascar Godfrey Harris, Professor Dr. Syed Firasat Ali, Associate Professor

This paper has been reviewed and approved for presentation by: (')

Dr. S yed F. Ali

AIAA Faculty Advisor

B2

Abstract

Four volunteer pilots were required to maintain given altitude and heading on a computer based stationary flight

simulator of the F-15E fighter airplane. One set of flights was obtained without any additional delay between the

stick input and the appearance of airplane response. In another set of flights, a 500 ms additional delay was used.

The deviations in altitude and heading and the fluctuations in the altitude indicated that the flights with 500 ms delay

were appreciably deteriorated. This is in agreement with the other recent investigations. The cross-correlations

between elevator deflection and altitude reveal interesting aspects of pilot's performance. In particular, these

correlations reveal that different pilots exercised a variety of techniques for maintaining straight level flights. The

C++ source code, which is used for the computation of the desired correlations, is also included.

B3

Introduction

For human operators in a feedback control system, their ability to adapt to variations in control tasks is generally

acknowledged as a significant advantage. Baron _ says, "With training and proper feedback, pilots are capable of

adapting their control strategies to a wide range of task variables." Baron, however, reminds us that this adaptive

capacity is not unlimited. The transport delay or a delay between input signals and their response is one of the most

important factors that needs studies for different flight situations to understand whether they fall within the pilot's

adaptive capacity. The papers published by Cardullo et al 2, Lusk et al 3, and Middendorf et al 4 are some of the recent

studies on the effect of simulator transport delay on pilot's performance and on the ways of compensating delays.

The present paper offers a study of the airplane responses to stick inputs with and without an additional transport

delay. Four volunteer pilots conducted straight level flights on an F-15E flight simulator. The pilots used the joy

stick to maintain a given altitude and a given heading. Two sets of flights were conducted. In one set the standard

simulator was used and in the other a 500 ms additional delay was programmed between the stick input and the

appearance of airplane response on the monitor. The deflections of elevator and ailerons were treated as pilot's

inputs, and the altitude and heading of the airplane were treated as the responses. In the present study the average and

rms values of the elevator deflection and altitude signals as well as the cross correlations between these two signals

are presented as the statistical tools to compare pilot's performances. A C++ code to compute the desired cross-

correlations from the flight data is provided in the appendix. The present paper is included in the final report on a

flight simulation research project at Tuskegee University sponsored by NASA Dryden Flight Simulation Research

Center under the Grant NAG2-4006, June 1994 to January 1997.

Back_mound

The simulation software, which represents the dynamics of flight of an F-15E fighter, has been installed by NASA

Dryden Flight Research Center on an SGI 4D/420 IRIS workstation. On the IRIS alone, the simulator could be

operated by a mouse. To operate the simulator by a joystick, its graphic software has been moved to an SGI

INDIGO 2 workstation. The two workstations are connected through ethernet. Thus the F-15E simulation software

used in the present study operates on three central processing units, two on an SGI IRIS workstation and one on an

SGI INDIGO 2 workstation. The pilot in the loop operation is comprised of the simulation software, the pilot, and

B4

a BG System joystick called a FlyBox. Norlin 5 has provided a description of the software design, model

development, and simulation capabilities of the system together with a description of other NASA Dryden Systems.

The F-15E simulation is coded with a FORTRAN shell and C support routines and operates on a UNIX - based

platform. The integration scheme in the simulation has been optimized for real time operation. The code has the

flexibility to program a desired transport delay between the stick input and the airplane response on the monitor. In

a simulated flight, the digital data on forty-two different flight parameters can be recorded at every 25 ms time

interval. The flight parameters include the altitude, heading, and velocity, as well as the deflections of elevator,

rudder, and ailerons. Provisions for turbulence and gust, although available, were not used for this study.

Experimental Protocol

Four volunteer pilots conducted the required flights for the experimental study on the F-15E airplane real time

simulation. Three of the them were experienced licensed pilots and one of them had no prior experience of flying.

In this paper, the volunteer pilots are named as P1, P2, P3, and P4. The ages, flying hours, and license status of the

pilots are PI: 69 yrs, 3200 hrs, SEL, MEL, INST; P2:48 yrs, 100 hrs, SEL, MEL, INST; P3:23 yrs, 830 hrs,

SEL, MEL, INST; and P4:26 yrs, no flying experience.

In every test flight a pilot was required to maintain straight level flight for three minutes duration heading toward

North, with pre-adjusted throttle for flying at 450 knots indicated at 10,000 ft. altitude with autotrim off. During the

flight, the pilot inputs to the joystick were limited to elevator and aileron deflections only. A measure of

performance, named rsws score, was calculated for a flight from its altitude and heading data. An rsws score is the

square root of the sum of the weighted squares of maximum deviations in heading and altitude. Let A h in ft. be the

maximum absolute deviation from the required 10,000 ft. altitude. Let AW in degrees be the maximum absolute

deviation from the required Northward heading. Then

rsws = sqrt [(AW) _ + (A h/10) 2] (1)

It is obvious that a smaller value of the rsws score represents superior pilot performance. Two kinds of test flights

were conducted. One kind of flight simulated a normal flight without inserting additional delay between stick inputs

and the appearance of airplane response on the computer monitor. The second kind of flight had a 500 ms transport

delay programmed between the stick inputs and airplane response. For each of the two kinds of flights, a pilot was

B5

trained and evaluated by conducting several three minute flights and by calculating the respective rsws scores. An

asymptote in performance consisted of six consecutive flights of the same kind in which the pilot did not break his

own rsws score record. The flights of each kind that represented the asymptote in performance for every pilot formed

the data base for further analysis. In addition to the rsws scores, other criteria were also considered to compare

different flights. For the present paper, attention is focused on the elevator deflection, A as input signal and altitude

of airplane, H as the response or output signal. The time average values of A and H are avg A and avg H. The

fluctuating parts of the two signals are 8 (t) = A (t) - avg ,5 and h (t) = H (t) - avg H, where t represents time. The

rms value of 8 and h are denoted by 5'and h'. The cross-correlation between _5and h for arbitrary time gap x is

denoted as CORR (x) and defined as:

t=T

1 jCORR(_) = T 5' h' _i(t) h(t + "_) dt

t=0 (2)

The simulator provides data at every 25 ms interval, thus a 3 minute flight has 7201 data points for each signal.

The cross-correlation is therefore calculated as follows:

( -3

CORR(j) h(7200 --j) 5' h' i÷j

i= 1 (3)

To cover a time gap, ":, of 20 seconds for correlation, CORR (j) is calculated forj = l, 2 ..... 7201. For each kind of

flight for every pilot, the correlation graphs, CORR (_) vs x are obtained for only three flights amongst the six

flights that determine the asymptote in performance; these three flights are the best, the worst, and the average based

on the rsws scores. An initial estimate of 20 second maximum time gap, x, was considered sufficient for

correlation. Upon considerable computations we learned that longer time gaps would have been desirable.

Flight Data Analysis

In Table I, P1, P2, P3, and P4 are the four volunteer pilots who conducted two kinds of straight level flights of three

minutes duration. The column 1 for each flight has rsws scores. A lower value of rsws indicates better pilot's

performance The columns 2 and 3 have rms values of elevator deflection in degrees and altitude fluctuations in ft.,

B6

respectively; their lower values also indicate better pilot's performance. From Table I it is apparent that 500 ms

transport delay has caused deteriorated pilot's performance. Middendorf et al 4has noted that 300 ms delay resulted in

significant deterioration of pilot's performance. Lusk et al 3 have conducted an elaborate study on the delay

compensation. With 300 ms delay they observed more significant deterioration in heading performance than in the

altitude performance. Consideration of pilot P2 in Table I brings up an interesting aspect of pilot's strategy. Unlike

other pilot's, the pilot P2 has smaller rms value of elevator deflection for the flight with transport delay than the

flight with no transport delay. To obtain improved understanding of pilot's performance, cross-correlations are

obtained between the elevator deflection and altitude. From amongst the flights that represented asymptotic

performance of a pilot, only the best, the worst, and the average, are processed to report the cross-correlations. Thus

for the two kinds of flights by every pilot, a total of twenty-four cross-correlation curves are reported. Figures 1, 2,

3, and 4 show the cross-correlations between the fluctuating parts of elevator deflection, _5(t) and the altitude h(t + _)

for the time gap, x ranging between 0 and 20 seconds. The positive value of _ represents upward deflection of the

elevator that gives decrease in lift on the tail and which should result in nose up tendency of the airplane. Thus the

positive 5 is expected to result in positive h. Twenty-three out of twenty-four correlation graphs show negative

correlations for the time gap values near zero. While conducting their test flights, the pilots had observed that in the

event of leaving the stick free, the airplane had a tendency to climb up. To arrest the climb up tendency, the pilot

moves the elevator down that gives rise to negative correlation. Thus the negative values in the first part of the

correlation curves reveal lack of trim. Let "E_ be the time gap at which the negative correlation has the maximum

absolute value. The xmis ranging between zero and 600 ms and it does not seem affected by the transport delay. We

would expect xm to provide a measure of the pilot' s reaction time delay but its apparently unpredictable variations do

not meet the expectations. It may be noted here that Roskam 6 assumes 100 ms reaction time for test pilots and 120

to 200 ms for other pilots. For larger time gaps, most correlation curves show appreciable positive values. It is

suspected that they are caused by the Phugoid oscillation of the airplane, reinforcing the desire to extend time gap

delays to larger values.

B7

.

References

Baron, Sheldon, "Pilot Control." Human Factors in Aviation, Academic Press Inc., 1988, pages 347-385.

2. Cardullo, Frank M., and G. George, "Transport Delay Compensations: An Inexpensive Alternative to Increasing

Image Generator Update Rate," AIAA Paper No. 93-3563-CP, 1993.

3. Lusk, Steven L., C. D. Martin, and J.D. Whiteley, "Time Delay Compensation Using Peripheral Visual Cues

in An Aircraft Simulator," AIAA Paper No. 90-3129-CP, 1990.

4. Middendorf, Mathew S., and G. R. McMillan, "The Effect of Simulator Transport Delay on Performance,

Workload, and Control Activity During Low Level Flight," AIAA Paper No. 91-2965-CP, 1991.

. Norlin, Ken A., "Flight Simulation Software at NASA Dryden Flight Research Center," AIAA Paper No. 95-

3419, 1995.

. Roskam, Jan, Airplane Flight Dynamics and Automatic Flight Controls, DAR Corporation, Lawrenece,

Kansas, 1995, page 765.

B9

Conclusion

For all pilots observed in the study during straight level flight on a simulator, the additional transport delay of 500

ms, between the stick input and appearance of airplane response on the monitor, results in appreciable deterioration

of the flight. This is in agreement with the other recent studies which indicate deterioration in flight with 300 ms

transport delay. The cross-correlations between elevator deflection and altitude signals support a belief that in a non-

perturbed flight, different pilots exercise a variety of techniques for maintaining straight level flight. It is proposed

that cross-correlations between the elevator deflections and aileron deflections shall provide an improved

understanding of pilot's technique on a flight.

Acknowledgments

This work is part of a research project on "A Low Cost Simulation System to Demonstrate Pilot Induced

Oscillations," sponsored by NASA Dryden Flight Research Center under grant number NAG2-4006. We wish to

thank Dr. Syed Firasat Ali, PI on the project, for providing us with the opportunity to participate in flight

simulation research and for his guidance and encouragement. From NASA Dryden, Larry Schilling's support and

encouragement, and Ken Norlin's expert help on the simulation software remained vital for maintaining the progress.

Thanks are due to Dennis Ezell, whose contributions to the project have been significant in initiating flight

simulation research at Tuskegee University and in motivating fellow aerospace engineering students to engage in this

research. We are thankful to Dr. Amnon Katz from the University of Alabama and Dr. Vascar G. Harris from

Tuskegee University, who are both pilots and aerospace engineering professors, and who remained available for

valuable guidance and contributions. The advisement on software issues received from Dr. C.L. Chen, Abraham

George and Ernest Kashiri is sincerely appreciated.

B8

S.vmbol

t

"t

'Cm

A

avg A

8

8'

5 (t)

h i÷j

h'

h (t)

H

avg H

hu

A_g

rsws

CORR(x)

SEL

MEL

INST

Nomenclature

Description

Time

Time gap

Time gap for the maximum absolute value of negative correlation

Elevator deflection, positive for upward deflection.

Time average of heading for a 3 minute flight.

8 at the time interval of a flight, each interval is 0.025 ms.

rms value of 8.

A (t) - avg A, fluctuating part of heading.

at (i + j) the time interval of a flight, each interval is 0.025 ms.

rms value of h.

H (t) - avg H, fluctuating part of altitude.

Flight altitude.

Maximum absolute deviation in altitude, from 10,000 ft.

Time average value of altitude for a 3 minute flight, ft.

Heading, zero for Northward heading.

Maximum absolute deviation in heading, from zero deg.

Square root of the sum of the weighted squares of maximum

deviations in heading and altitude.

Coefficient of cross-correlation _5(t) and h (t + "_).

Single-engine Land (aircraft type)

Multi-engine land (aircraft type)

Instrument Rating (FAA certification)

Units

instant

seconds

seconds

degree

degree

milliseconds

degree

milliseconds

feet

feet

feet

feet

degree

degree

B 10

Pilot Flight Without Transport Delay Flight With Transport Delay of 500 msi 2 3 1 2 3

P1 73.8 77.1

P2 51.2

26.4 0.60

29.3 0.51

3.2 0.23

3.7 0.25

66.4

52.2 1.02

33.5 0.20

5.8 0.45

6.3 0.72

P3 7.5 18.2

P4 9.4 18.7

Table I: Comparison of Pilot's Performance in Flights With and Without Transport Delay.

1 - Average rsws for the best 5 flights, 2 - 5' deg in the best flight, 3 - h' ft in the best flight.

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B 15

Appendix

The complete program written in C++ is enclosed. The program reads the F-15E simulation data after the data file

has been converted from binary to ASCII. The program was compiled on IRIX 5.3 C/C++ compiler 4.0.2 on the

SGI Indigo2 workstation. Pages 15 to 17 contain the Correlation Source Code. Pages 18 and 19 have the

Correlation Header. Page 20 has the Script Source Code. The program prints out the calculated correlation values

and the jargon for plotting the graphs on a GNU Plot Program. The Script file separates the jargon from the data,

and it creates a script file for the GNU Plot Program.

B 16

#include <fsUrea:. h>

#include <s:riz_._#include <mar_h. h>

|include "corrJ..._.;_"_define i 7200

void main( )

(

c.hax fileName(80} ;

char FileName(BO] ;

char bu£fe:(8O] ;

char :exu(255] ;

char CAll0] ;c_a: CB[IO] ;

char FileDaca(80! ;

char FileLoad(80] ;

in¢ chart;

inc i. ii = O, j = O.k = O;

in: n(10! ;inn w:

in= of:

in,- po+,",r-:double [Y;

double d;double e;

double Numb:

double y_;double y1:

double xmin:

double y_J_:double max:

double ymax:

/* co¢-_elanion header "/

/* maxL:u, number or points "/

I* inpun film "I

/* oun_u= film "/

I" buffer "/

I* noces character vari_ule "/

I" name of A(n + cau) °I

/" _ of S(_) "1

/* number of c_els "/

/*¢_Ca poin¢er */

/e ¢oz_elanion Cy_e "//* maxiumcoz_ela=ion factor

/* enrer maxiumnumber of poin= */

/" _au value acmaxiumcozTela=ion °/

/" _au value ac miniumcoE_elanion */

/* dana buffer */

/. maxium ¢orEela_ion "/

/" m_J.um correla=ion "/

/" miniumx value of _raph "/

/* _iumy value of grap_ "/

/- maxiumx value of _:aph */

/_ maxium y,_lue of _aph "/

*/

CORR DA_oSCO:'r. coEr;

reRame:

¢OUC << " Film: ";

tin >> fileName, /* film of the ,¢ii */

¢ou_ << " EnCIE _.he maxi,,,- ¢ozTmla_ion factor ";

c_ >> cf; /* encer ma._.um coz':elacion facno: "/

cou_ << " EJ_er number of points *;

tin >> poin¢; /, enrer maxi,mntmber of point */

cou_ << " Please choose and co:Tale=ion (H_D_=I, PSX_D_F=2. PSI..=P,F=3}: ";cLn >> w; /" coE_ela_ion salec:ion */

/t opens _he dana file. if non file exisu _hen _he file name is asked

for a_ain -/

ifsuream fin(fileName, ioe::norreaue);

if (_fin)

(cou_ << * Unable _o open :: " << fileName << ° "** file no= found *** in\n';

noun << " Please re-enrer _he filename, in%n';

gOCO rename;}¢ou= << " in Filename • << fileS, me << • was found, is" :

/t reads -,meede¢l _a_;en Tel= by :he qe¢_ara proq_.'a., "Ifor ( i = O; i < 5: i++ )

(f_J_ >> bu£fe=:

}

fin >> chart: /* ¢e_da _ nmobe= of chanele */

couc << "in This file has • << ¢ban << " channels, in';

I" reads and soc'_s _J_e number of channels "I

B 17

re: ( i- 0: i < (chart+2): i++ )(

fAa >> buffer:if (![sc_c:_tbuffer.'T')_| ( _[0l = j;}if (!(su:c=pCbuffe=.'H'))) ( all] = j;}if (!(sc:c=p(buffe:.'?SZ')))( n[2] = _;}if (!(eC:==p(bu_fec,'OAP'))) ( a[3] = j:}if (!(eC=c=p(bu£fec,'OEP*))) ( n[4l : j;}if (i(eC_-=mp(buffer.'DRl_')}) ( n[51 = _;}

}

/" reads and sorus uhe claca co _ieE co=Tecc arTays "/while ({fin>> Numb) && (k < (point)) ]

£f ( ii == -(01if ( ii == nil]if ( ii == -[21if [ ii := n(3|if ( ii == n(4|if ( ii .m n[S]li++_if (ii=m (than+l)}

( DATA.T[k| = Numb; }( DATA.K[kl = Numb;}( DATA.PSZ[k| • Numb; }( DATA.DAP[k| = Rumb: }{ DATA.DEP[k] = Numb; }{DATA.DP-P[k] = Num_; }

(ii = 0; k++1}

I" closes C.he i_c file "lfin.close( ) ;

/* sees valuel i_ic&lize CO the coEEolaCion heedere/DATA. of•of ;DATA.www_DATA. k•k;DATA. COEE () ;

/e finctS _he maxium u;_er and loweE points of _hm ¢oEralacion "/¥I '• DATA.COR_A[O] ;5=0;yu • DATA.C0KPA(0] ;em0;for ( i • Os i < Of; i++ )(

if(yl • (DATA.COR_A[i|) |(yl • (DATA.C0_UPA[A| };dsi" (.025) ;})foc ( i • I; i < of; i++ )(

if(yu < (DATA.COR3A[i]) ) (yu ,, (DATA.COKPA[i] ] ;eeL" (.025) ; }}if(fahs(yu) < fa_s(y_] ) (U=y_;} cou, c <<U;if(fahs(yu) • fabe(yl))(U=_u-} couc <<U:

= ((DATA.TAU[cf-1]) ".2+DATA.TAU[cf-I] );

y,d.u - -(fabe(U+U'.SO) | ;ymax -(labs( U+U'.50)];

Rename:cou,_ <,c • Film: ";cin •> rileName: /- name of _he oucpuc file "/C0u_ << " EuneE one llne of co.enos for da_a file :\n';cin.i_nowe(1,'\n*); /" enter notes on r.ha _aph "/c4 n .geCline ( r.oxl:. 255 ) ;

/" sects the ohm file name "/• scz_rl (Fl_eDa_a,Flleb_me) ;

8tLT=I;_ (F_.leLoad, Fllel_hune) ;eclat (F1].el..oed,. • .gl_'} ;if (w==l.|(

s_'cac (Y_leDa_a, ".haaS" ) ;s£Ecac _CA, "/_'l ;sr.Ecac (C_,*DEI"} ;

B 18

)

(

}if(

)if(

)ifC

(w=m2 }

e_:a_ (FileDa_a, " ._dap" ) ;s_rcat (CA. "PSZ') ;s_cau (C3, "D_') ;

(w==])

s_Ecat (FileDa_a, " ._dzlP" );at,Teen (CA, •PSI" );s_E=at (C_,'_RP'} ;

(w==4)

s_ca_ (FilaOaca, " .ed=_') ;s_zrcat (CA, "D_') ;strca= (_. "DP_'} ;

(w==5)

eC_:at (FileDa_a, • .eden') ;strcat (CA, "U£P') :m_cat (C:m. "_') ;

/- opens output file °/ofs_=eam fout(FileData, ioe::noreplacs);if {!four)(

ccna_ <¢ " Unable to create and _rci_m _ocouL <c • Please re-enteE _he fil_. \n\n';

goLo R@n,ame:)

/" wE£uem scripn _az_en "/foul << "% mec title \''<cFileDa_a<<'\'\n';fourfour:foulfOuLfoulfourfou,.foulfou=fou_

• fou_fouc

• << FileJ_sme << " "'* file aLread_

<c "| met xla.]oel \'TA_\''<<'\n°:<c -% met ylabel \'COU.\' O,-10"<c'_n';<< "0 met la_m_ 1 \'CORRmax ='<<yu<¢" _ _au =.<<e<c'\' at "<< _:Lin'.9 <<',"<< "t met label 2 \'COl_min ='<<yl<<" _ _au ='<cd_<'\" at "<< x=_'.9 <<.,"<¢ "# see label 3 \'a_'<<CA<<" = .<¢DATA.aveA_<" ave'<<CB_<" = "<<_kT_.a_<< "# ee_ label 4 \'_'_S'<ccA<<" = "_<DATA.x_uA<<" r_s'_<C_¢<" = "<<CIkTA._'J<< "O p_o¢ (x='<< _An <<':'<¢ _wx:<<'| ['<< ymA_ <<-:'<_'ymax<<'| \0-<<FileData<<'\'\n';<<'l cauti] corrCi] • << "\n';<<-1 • << fileN_me << "\n';<<'| * << _e.xt << "\_';<<'# =au(i] cor_(i] • << "\n';

I- writes remulLs, to ou=;n;t file "Ifor [ t = 0; i < cf; i++ )(

fou_ << DATA.TAU(i] <<'\_" << DATA.C0RPA(i] << "\n';

)

fou_.cloee(}; /- closes ouLpuc file "couc << "\r_ilename "<< FileDa_a << " was c=eated. \n';c_ut << "\nNc,_ run ec_ip_ and use .<cFileDa_a<<" scEip_ film.\n';

B 19

-- # include <=ar._. ]_# 4,,elude < fscream. _>

edefi=e i 7200

class CORR(public :

Ant w:inc cf;Ant z:dmzble T[I|. HILl. PSZ[I|. DAP[I]. DEP[I]. DRP{I|. TAU[I]. CORPA(I|;

double C, h. psA, clap, dep. ct_p;

dingle areA. ave6;

double sqdA. s_ :

dingle coz'p, coL'n:double m. sadS;double mqA. s--,qS:double smOOCh, smooch;double A[I|;double S[1] ;double difB[l| ;double difA[l] ;_2e corpA;double co='AA tdingle cauz

COZy() ( )-COP._( ) { }void Scot= ( )(

T(z]-c, H(z]-h, PSZ(z]-ps£, DUCzl,xbm, D_(zl-de_, _(=]'_'_:)vold coc_ ( )(

/" sees all sum variables Co ze_places chert co_'=ecc signals Co be corela_ea Co A and Band sums A and B "1

• smA = O, s,,,m= O, smsqA • O, smsq6 • O, smcorn . O, sm=o:_ i O;

££ (w--_)(

£or ( i - O; £ < k; i++ )

(A(i] ,, H(i|;B(£] = DEP[i|;smA = smA + A[i| ;sin6 • s.US + B[/]:

)}£_ (w-=2)(

£oc ( £ - 0; i < M: i+_ )(

A(A] = eSZ(il;B(/] = DB4P(:LI;i = saA + &(/l ;sa8 - laa + 8[£1 ;

)}

{

B 20

};

for ( i : 0; i < k: i+÷ )(

A(£| ,, PSZ(i];B(i| : DA_Ci|;smA = areA _ A(i] ;stub = s ''a ÷ BCi];

)}£_ (w=-4 !{

for ( i = 0; i < k; i_ ){

A(tl ffi oe.,eCil;_(i] ffi v_[£1;smA = smA + a[£] ;rids = sma + 8(£];

))i£ (w==5)(

for ( £ = 0; i < k; i*-- ){

A(£] = nkPCil;sCil = DEZ'(£I;smA = m ÷ A[i] ;am8 = sin8 ÷ B[£];

))

avaA = smA/(k) ;avsB = smBl (k);for (i = 0; i < k;i*-)(

dlfB[l] =(B[i] -araB};d/fA[i| = (A[i] - areA) ;scab = powidifB(i]. 2.0);scala = pow(difA[£l. 2.0) ;samoa. = =naqA - sc_A:_S = smsqS .,. sqclB-

.}_msc_ • mqA/(k} ;ImsO • smsqSl (k) ;mS = (sqrc(mnsqS) } ;rmJA = (s_-_:(:m.sqA) } ;for (j = O; _ < cf ; _,'....){

f0= (£ = O; £ < (k-j÷L);£_-+)(

¢orp = difB[£l * cttfA(i._l;811C0_ ,= 8me'O_lP 4- ¢OZ'p;

}cau = j * 0.025:

I* average of A */I" average Of B "I

/* difference between B(:L] and aveB "//* difference bem,'ean S[£] and. ayes "I

/* Ems value of A "//* Z'ms value of B "/

¢o_A = smco_-_/(Ck - j) " rms8 " _A}; /* ¢orralacion cooficionc *Ism"Oz_ : 0;TAU[_] = cau:C0RPA(_] : co_A; /" correlation coe£icien: a_ay "/

B21

OtacJ.uda <fa_._eaa.h>ll-clude <s_zi_g. b._void mean( )(

char file_ame (80 ],into i.-:

II enter filenamo

cia >_. file_ame:COU_ << " \n Filen_une " << file_ame << " _ found. \n" ;ifsr.:eam f_[fila_amo, io8: :not=ear'.e) ;

s_rl[l| = "\0":n,, O;wb_le (file_a,-e(n] != '.'}(s_rl[O] = file_an,e{n] :smrca_ ( fileLoad, scrA} ; n++:}

smrcam (££1eLoad. ".;If" ];couc << " \n Filename ' << fileLoad << • was creamed. \n\n" ;

ceu_ << • Now run gnuplo_ and load \' "<< fileLoad<<'\" \n';ofs _ream fou= ( fileLaad. £=s: :no=e_Lace ) ;

fOE (i=0 pi<8 ;i_-}{fln.ge_(buf£er.2] ; fin.ge_llne(WRITE,2SS] ;fou_ << WRITE<<'\n';

}

huffer[255], WRITZ_255]=' ",_ileLoad[80|,sCrl[80|;

B 22