lateral stability and control … stability and control derivatives of a jet fighter airplane...

NASA TECHNICAL NOTE

<:[ IO

i NASA TN D-6905

LATERAL STABILITY AND CONTROL

DERIVATIVES OF A JET FIGHTERAIRPLANE EXTRACTED FROM FLIGHT

TEST DATA BY UTILIZING

MAXIMUM LIKELIHOOD ESTIMATION

by Russell V. Parrish and George G. Steinmetz

Langley Research Center

Hampton, Va. 23365

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION • WASHINGTON, D. C. • SEPTEMBER 1972

https://ntrs.nasa.gov/search.jsp?R=19720023363 2018-06-26T21:06:21+00:00Z

1. Report No.

NASA TN D-69052. Government Accession No.

4. Title and SubtitleLATERAL STABILITY AND CONTROL DERIVATIVES OF AJET FIGHTER AIRPLANE EXTRACTED FROM FLIGHT TESTDATA BY UTILIZING MAXIMUM LIKELIHOOD ESTIMATION

7. Author(s)

Russell V. Parrish and George G. Steinmetz

9. Performing Organization Name and Address

NASA Langley Research CenterHampton, Va. 23365

12. Sponsoring Agency Name and Address

National Aeronautics and Space AdministrationWashington, D.C. 20546

3.

5.

6.

8.

10.

11.

13.

14.

Recipient's Catalog No.

Report Date

September 1972Performing Organization Code

Performing Organization Report No.

L-8378Work Unit No.

501-39-00-02Contract or Grant No.

Type of Report and Period Covered

Technical NoteSponsoring Agency Code

15. Supplementary Notes

16. Abstract

A method of parameter extraction for stability and control derivatives of aircraftfrom flight test data, implementing maximum likelihood estimation, has been developedand successfully applied to actual lateral flight test data from a modern sophisticated jetfighter. This application demonstrates the important role played by the analyst in com-bining engineering judgment and estimator statistics to yield meaningful results. Duringthe analysis, the problems of uniqueness of the extracted set of parameters and of longi-tudinal coupling effects were encountered and resolved. The results for all flight runsare presented in tabular form and as time history comparisons between the estimatedstates and the actual flight test data.

17. Key Words (Suggested by Author(s))

Lateral stability and control derivativesMaximum likelihood estimationsParameter estimation

19. Security Classif . (of this report)

Unclassified

18. Distribution Statement

Unclassified - Unlimited

20. Security Classif. (of this page) 21 . No. of Pages 22. Price*Unclassified 51 $3.00

For sale by the National Technical Information Service, Springfield, Virginia 22151

LATERAL STABILITY AND CONTROL DERIVATIVES OF A

JET FIGHTER AIRPLANE EXTRACTED FROM FLIGHT. TEST DATA

BY UTILIZING MAXIMUM LIKELIHOOD ESTIMATION

By Russell V. Parrish and George G. SteinmetzLangley Research Center

SUMMARY

A method of parameter extraction for stability and control derivatives of aircraftfrom flight test data, implementing maximum likelihood estimation, has been developed,and successfully applied to actual lateral flight test data from a modern sophisticated jetfighter. This application demonstrates the important role played by the analyst in com-bining engineering judgment and estimator statistics to yield meaningful results. Duringthe analysis, the problems of uniqueness of the extracted set of parameters and of longi-tudinal coupling effects were encountered and resolved. The results for all flight runsare presented in tabular form and as time history comparisons between the estimatedstates and the actual flight test data.

INTRODUCTION

A method of parameter extraction for stability and control derivatives of aircraftfrom flight test data has been developed at the Langley Research Center (ref. 1). Thismethod, utilizing maximum likelihood estimation, has been applied to actual longitudinalflight test data from a modern sophisticated jet fighter airplane (ref. 2) to establish themerits of the estimation technique and its computer implementation.

In the present study, the application of the method to actual lateral flight test datafrom the same airplane has also been used to establish the merits of the estimation tech-nique and its computer implementation by extracting, from the flight data, a set of stabil-ity and control derivatives that are well defined in terms of their standard deviations.During the analysis, the problems of uniqueness of the extracted set of parameters and oflongitudinal coupling effects were encountered and resolved. The results presenteddemonstrate that the technique provides sufficient information to identify the uniquenessproblem, if one exists, in terms of parameter correlations. The results also demon-strate that sufficient excitation of the aircraft will yield a unique set of derivatives andthat incomplete modeling will be indicated by a poor fit of the data.

The flight test runs utilized in this study are lateral responses generated by rud-der and/or aileron deflections in the neighborhood of ±10° and ±20°, respectively. Thechanges in angle of sideslip, roll angle, rolling velocity, yawing velocity, and lateralacceleration are typically ±10°, ±30°, and ±40° per second, ±15° per second, and ±0.2g,respectively. The parameters extracted were the standard linear body -axis lateralstability and control derivatives, with additional nonlinear derivatives dependent uponangle of attack. These nonlinear derivatives were found to be necessary due to stronglongitudinal motion present in some of the flight test runs.

SYMBOLS

Measurements and calculations were made in the U.S. Customary Units. They arepresented herein in the International System of Units (SI) with the equivalent values inthe U.S. Customary Units given parenthetically.

lateral acceleration at center of gravity, g units

a.y T lateral acceleration at accelerometer location, g units

b wing span, meters (ft)

c mean aerodynamic chord, meters (ft)

'1

damping-in-roll derivative, ——-, per radian

2W

rolling -moment coefficient

ac,effective-dihedral derivative, —-, per radian

ac,C; = —- per radianZ H

ac,—=:• per radian

rolling-moment coefficient at |3 = /S™, 6r = 5r, T> 6a = 5o3 6 ,6 x '*T' r,T' a,T

(Cj ^ C; at a = a» per radianV tr/« Lr T

clK\ C7 at a = «_, per radian4 r

Cn yawing -moment coefficient

3Cn per radian

8Cni- per radian)\

,2Wacn

static directional-stability derivative, , per radian

9Cn5 = -ST" per radiana 9oa

acn per radian

nV yawing-moment coefficient at 0 = 0T, 6r = 6r T, 6a

PT' r,T' a,T '

(cnp) cnp

at a = «Ti Per radiana

Cn at a = a- per radianQ!T a

side-force coefficient

, , .• per radianfl^Pb^9l2v7

per radian

9Cy— - Per radian

8/3

3C-yCv,- = — - per radianY

acv

(CY)« « K side -force coefficient at /3 = /3T, 6r = 6r _,, 6a = 6a -

HT r,T' a,T

T °YP at * = *T

g acceleration due to gravity, meters/second (ft/sec^)

Ix aircraft moment of inertia about the body X-axis, kilogram -meters2

(slug -ft2)

product of inertia of aircraft referred to body X- and Z-axis,kilogram -meters2 (slug -ft2)

IY aircraft moment of inertia about the body Y-axis, kilogram -meters2

(slug -ft2)

r\!•£ aircraft moment of inertia about the body Z-axis, kilogram -meters^

(slug -ft2)

2slope of linear variation of Cj with a, per radian

r

oslope of linear variation of C^ with a, per radian

Kc slope of linear variation of Cn with a, per radian2

Kc slope of linear variation of Cn- with a, per radian2

6a a

Kg slope of linear variation of Cy with a , per radian2

m mass of fueled airplane, kilograms (slugs)

p rolling angular velocity, radians/second

q pitching angular velocity, radians/second

r yawing angular velocity, radians/second

S wing area, meters^ (ft2)

u velocity along longitudinal body axis, meters/second (ft/sec)

V true airspeed, meters/second (ft/sec)

v velocity along lateral body axis, meters/second (ft/sec)

w velocity along vertical body axis, meters/second (ft/sec)

Xy accelerometer offset coordinate from center of gravity along longitudinalbody axis, meters (ft)

Yy . accelerometer offset coordinate from center of gravity along lateralbody axis, meters (ft)

Zy accelerometer offset coordinate from center of gravity alongvertical body axis, meters (ft)

a angle of attack, radians

oirp trim angle of attack, radians

/3 sideslip angle, radians

/3T trim sideslip angle, radians

6a aileron deflection angle (positive when right aileron is deflected down),radians

5a T 'aileron deflection angle at trim, radians

6r rudder deflection angle (positive when trailing edge is deflectedto the right), radians

6r -T, rudder deflection angle at trim, radians1 >•"•

r fit error

y,A arbitrary parameters

6 pitch angle, radians

0 roll angle, radians

p mass density of air, kilograms/meter3 (slugs/ft3)

A dot over a variable indicates the time derivative of that variable.

FLIGHT TESTS

The flight test data were provided by the U.S. Naval Air Test Center at PatuxentRiver, Maryland. The flight tests were conducted by Navy test pilots as part of an inves-tigation with a McDonnell Douglas F-4 airplane. Five different lateral response runswere made: three during one flight test of the airplane and two during a second flighttest. The first three runs were made at an altitude of approximately 6096 m (20 000 ft)at Mach numbers of about 0.6, 0.7, and 0.8, respectively. Control inputs for these runswere rudder only, rudder and aileron, and rudder only, respectively. The other two runswere made at an altitude of approximately 11 277.6 m (37 000 ft) at Mach numbers ofabout 0.9 and 0.8, respectively. Control inputs for these runs were rudder only and rud-der and aileron, respectively. The stability augmentation system (SAS) was deactivatedin order to provide full response for all the test runs.

For each of the test runs, the airplane was trimmed by the pilot at the desired alti-tude and Mach number and held for a short period. Then the control input or inputs wereapplied. No attempt was made to null any longitudinal motions. Roll and pitch angles aswell as Mach number, pressure altitude, rudder deflection, aileron deflections, and cali-brated airspeed were recorded every tenth of a second. True airspeed was determinedfrom figure 1 of reference 3 using Mach number, pressure altitude, and temperaturefrom flight tests and resolved through angle-of-sideslip measurements to yield lateralvelocity.

Lateral displacement of the control stick in the F-4 airplane produces a combinationof aileron and spoiler deflections. The aileron deflection is limited from 0° to 30° down-ward and from 0° to 1° upward. The spoiler being located on the upper surface of thewing has no downward deflection and is limited to upward deflections between 0° and 43°.In the flight records only the aileron deflections were recorded. Aileron-deflection datawere used in the following manner to yield a single control input, which reflects a spoiler

effect. The assumption was made that a negative reading for either the right or leftaileron was the indication of an aileron input. It was further assumed that the spoilereffect on the opposite side of the negative aileron deflection was equivalent to a positiveaileron deflection of the same magnitude. Hence, by doubling the magnitude of the nega-tive aileron deflection and applying the sign convention of a right aileron to the magnitude,a single right aileron input, which is effectively the total aileron input, could be used inthe equations. It should be noted that the aileron coefficients (Cyfi , Cj_ , and Cn5 \

extracted by this program reflect the effect of both aileron and spoiler. Since these con-trol surfaces are physically linked, it is impossible to uniquely determine the coefficient •of each aileron and spoiler without additional information.

Instrumentation consisted of rate gyros located slightly forward and at foot level ofthe pilot for measuring pitching, rolling, and yawing velocities; accelerometers locatedin the left wheel well for measuring lateral and normal accelerations; and vanes on a noseboom for measuring angle of attack and angle of sideslip. (See fig. 1.) No documentationwas available from the Navy as to the accuracy of the instrumentation, although the methodof parameter extraction (ref. 1) typically yielded the following signal-to-noise amplituderatios (the noise amplitude was the 2-sigma level):

Lateral velocity 18 decibelsRolling velocity 24 decibelsYawing velocity 20 decibelsRoll angle 22 decibelsLateral acceleration 8 decibels

AIRCRAFT MATHEMATICAL MODEL

The equations of motion used by the computer program (ref. 1) were modified con-tinually during the analysis. However, three basic models evolved. The first modelconsisted of mainly lateral motion, the second model contained longitudinal coupling, andthe third model contained longitudinal coupling and nonlinear lateral derivatives. Thenonlinear derivatives KQ , KQ, , KQ , KC , and KQ permit variations withYp t/3 ir np n§a

angle of attack in those particular derivatives that exhibit such dependence in wind-tunnelresults (ref. 4). The three models can be obtained from the following equations:

V . g COS

p -

K

Iz

12V

K^ (a-«T)\(5a"6a,T)+KCn6a( T

i r b

s p tanta»COS

cos 6 sin

The first model, mainly lateral motion, can be obtained from the basic equationsby requiring all longitudinal variables (u, w, 9, a, and q) to be constants and the non-linear derivatives KCV , KQ , KQ , KQ , and K^ to be zero. The second

P £/3 ^r nP §amodel, containing longitudinal coupling, can be obtained by using the longitudinal flightdata as inputs to the equations in the same manner as rudder and aileron deflections areused. The third model, containing both coupling and nonlinear derivatives, is obtainedfrom the second model by not restricting the nonlinear derivatives to zero.

The nonlinear derivatives K^ , K(-. , KQ , KQ , and KQ , as well as

the longitudinal coupling terms, were discovered to be necessary in order to fit the flighttest data, as is demonstrated in the next section. Also demonstrated in the next sectionis the problem of uniqueness mentioned in references 1 and 2.

RESULTS

The conditions for the five flight test runs are listed in table I. The analysis ofthese runs involved two major problems: uniqueness and longitudinal effects. Theresults are presented in a manner to illustrate how each problem was encountered andthen resolved.

Uniqueness Problem

Before presenting the uniqueness problem as encountered in this study, it would bewell to describe the problem and the means of detecting its presence. The problemitself can be best described as follows: Given a set of parameters that minimize the fiterror between measured and computed variables, does another set of parameters existthat will yield the same fit error? If the answer is yes, a uniqueness problem exists.Detection of the problem is facilitated by the use of the covariance matrix provided bythe maximum likelihood estimation technique. Minor manipulation of this matrix, asdescribed in reference 1, yields pairwise parameter correlation coefficients which esti-mate the degree of linear dependence between two parameters. Figure 2 illustrates theexistence of a uniqueness problem due to linear correlation between arbitrary parametersX and y. Values of X and y that lie on the line of dependence yield the same fiterror. However, it should be emphasized that two parameters may exhibit high correla-tion without indicating a uniqueness problem. Thus, it is necessary for the analyst totest any parameters with significant correlation coefficients to determine whether auniqueness problem is present. The test is simply to determine whether the fit errorchanges as the parameters vary along the line of dependence. The procedure for carry-ing out the test is to assign to one of the correlated parameters several values in therange of interest and then extract the other parameter's values; this determines the line

of dependence. In figure 2, the fit error r does not change as A. and y vary alongthe line of dependence. Thus, a uniqueness problem is present. If the fit error didchange, both parameters would be identified by the estimation technique at the point ofminimum fit error and no uniqueness problem would exist, although the parameterswould still be correlated. In this hypothetical illustration, the correlation between Xand y is perfectly linear and will cause divergence of the estimation technique when anattempt is made to extract both parameters. However, in the use of real data, the pres-ence of noise usually prevents perfect linear correlation, and thus divergence.

Figure 3 presents the model responses generated by the estimates of the stabilityderivatives of test run 1 and the respective flight test data, using the first model with alllongitudinal variables fixed as constants (average values obtained from the flight data foreach variable). (Note that symbols in figure 3 and subsequent machine plots presentingmodel responses and respective flight test data are not the standard symbols defined inthe Symbols section.) Table II presents the estimates of the derivatives obtained, andtable in presents a form of the covariance matrix for these estimates. Diagonal ele-ments of this matrix are the standard deviations of the estimates, and the off-diagonalterms are correlation coefficients. As denoted by the asterisks of table in, Cyo, ^Yn'and CYr; C^, CZp, and C^; Cn/3, Cnp, and Cnr; and C^ and Cn/3 all have sig-

nificant correlation. Investigation of these parameters revealed the existence of a unique-ness problem.

A major cause of uniqueness problems is generally admitted to be insufficientexcitation of the aircraft (for example, ref. 5). Test run 1 had rudder deflections only.Test run 2 contained both rudder and aileron deflections, and the model responses gener-ated by the derivative estimates for this test run and the respective flight test data areshown in figure 4. Again the longitudinal variables were fixed as constants during theextraction process. Table IV presents the estimates of the derivatives obtained, andtable V presents the modified covariance matrix. As pointed out in section 7.8.3 of ref-erence 5, the likelihood of obtaining a unique set of derivatives is increased when both arudder input and an aileron input are used to excite the airframe, as is evidenced by thelack of correlation exhibited in table V.

Longitudinal Coupling Effects

Examination of figure 4 (test run 2 responses) reveals poor fits for all the lateralvariables; these poor fits indicate a possibly incomplete model. The longitudinal datafor test run 2 are presented in figure 5 and indicate a substantial amount of longitudinalmotion. Use of the longitudinal data as input, together with the modeling of angle ofattack dependence of some of the derivatives, resulted in the extraction of a new set ofderivatives for test run 2. Figure 6 presents the model responses generated by this set

10

of derivatives and table VI contains the derivatives and their standard deviations. Nosignificant correlation was present and, thus, a unique set of derivatives has beenextracted. It should be noted that a lack of confidence exists for all the Cy deriva-tives with the exception of Cyo, due to the large standard deviations of the estimates,as is the case with some of the nonlinear derivatives.

Solution of the Uniqueness Problem

The uniqueness problem of test run 1 was resolved by fixing the values of the non-linear derivatives and (Cy A > C^ , and Cnr at the values obtained in test run 2

\ / Cc rri "

(the wind-tunnel results presented in ref. 4 show these derivatives to be fairly insensi-tive to Mach number variations in this flight regime) and extracting the remaining deriv-atives. This same procedure was used to solve the uniqueness problem of test run 3,which also had a rudder-only input. The model responses generated by the final esti-mates of the derivatives for test run 1 and test run 3 are shown with the respective flightdata in figures 7 and 8, respectively. The values of the derivatives and their standarddeviations are presented in table VII for test run 1 and table VIII for test run 3.

Test run 4 had essentially a rudder-only input, whereas test run 5 had both rudderand aileron inputs. Again, the results of test run 5 were used to solve the uniquenessproblem of test run 4. The model responses generated by the final derivative estimatesof test run 4 and the respective flight data are shown in figure 9, and the estimates withthe standard-deviations are presented in table IX. The results of test run 5 are presentedin figure 10 and table X.

The total results of the analysis are summarized in figures 11 to 13, which illus-trate the variation of the extracted derivatives with Mach number, altitude, and angle ofattack. The results shown in figure 13 are presented with the intercept values locatedat the trim angle of attack (symbol location) and the slope of the lines determined by thenonlinear derivatives.

CONCLUDING REMARKS

It is believed that the importance of the analyst, exercising engineering judgmenttempered with estimator statistics, has been aptly demonstrated by the results of thisstudy in recognizing and resolving the problems of uniqueness and longitudinal couplingeffects. Thus, the extraction technique and its computer implementation have been shown

11

to provide the means for identifying both modeling and uniqueness problems and to yielda unique set of derivatives from actual lateral flight test data, provided the flight datacontain sufficient information.

Langley Research Center,National Aeronautics and Space Administration,

Hampton, Va., August 4, 1972.

REFERENCES

1. Grove, Randall D.; Bowles, Roland L.; and Mayhew, Stanley C.: A Procedure forEstimating Stability and Control Parameters From Flight Test Data by UsingMaximum Likelihood Methods Employing a Real-Time Digital System. NASATN D-6735, 1972.

2. Steinmetz, George G.; Parrish, Russell V.; and Bowles, Roland L.: Longitudinal Sta-bility and Control Derivatives of a Jet Fighter Airplane Extracted From FlightTest Data by Utilizing Maximum Likelihood Estimation. NASA TN D-6532, 1972.

3. Aiken, William S., Jr.: Standard Nomenclature for Airspeeds With Tables and Chartsfor Use in Calculation of Airspeed. NACA Rep. 837, 1946. (Supersedes NACATN 1120.)

4. Bonine, W. J.; Niemann, C. R.; Sonntag, A. H.; and Weber, W. B.: Model F/RF-4B-CAerodynamic Derivatives. Rep. 9842, McDonnell Aircraft Corp., Feb. 10, 1964.(Rev. Aug. 1, 1968.)

5. Wolowicz, Chester H.: Considerations in the Determination of Stability and ControlDerivatives and Dynamic Characteristics From Flight Data. AGARD Rep. 549-Pt. I,1966.

12

TABLE I.- FLIGHT TEST CONDITIONS

Testrun

12345

Altitude

m

6 0966 0966 096

11 277.611 277.6

ft

20 00020 00020 00037 00037 000

Machnumber

0.6.7.8.9.8

Center ofgravity,

% c

32.1931.8531.4929.1829.11

Input

RudderRudder and aileronRudderRudderRudder and aileron

TABLE II.- DERIVATIVE ESTIMATES OF TEST RUN 1 OBTAINED WITH MODEL 1

CYfl -0.392

-npCr

Cr

1.97

3.75

-0.0487

-0.0938

-0.355

-0.230

0.00221

0.120

0.162

-0.0664

0.0462

13

.

<o£

u

*H

~1— t V.J

jj

HpSj C«5 coEHj>r

p CQ.

g cf

^EHmO rH

<OTH r-O

(j i

PS"

EHCO *-

W (EH

rH

co aH 1*°H

§H „^^ f*-i"W owu2 ^ri o3 r**^ cOU

1

• "rH (>H

hH O

w,JPQ2 r*^M O

CQ_t^

CJ

CMCO

o

mooi

CDO

0

COooi

i— iTH

o1

c-oo

iH0o

CD0O

OJinoi

*TH

OSO

.£.

inOJo"

CDTHOJoo

CI

o

CM*1O

COTH

oi

COoo

inTH

o

mTH

oi

rH1— 1

o

COOo

THTH

o

CDmo

.£.

inOJ0

OJCDCD

O

*ineno

1 £

U

c-coo

c-oo

1

CMOo00

oo

1

inTH

o*1

COoo

mo0

CDoo

COCD

01

OJCOCO

TH

inOJ

o

.iHOJ

O

i- r

0

COOo1

oCO

o1

inCO

oi

CDCM*

O

inoo

CMi-H

O

in

o

COoo*

COCOoo

COCD

O1

CDinoi

OJinoi

H K

0

*ino

in°°.Oi

CMcoo

#THOJ

o1

o

01

*oOS

o

*

OJ

o

CM

COoo•o

cooo

CDoo"

THTH

o

CDoo

rH5 c

r-Ju

CMin0

^I>o

1

m£—0

1

CDl>0

1

CDinoi

*OJCO

o

S0

•*CMOJ

o

inrH

O

inoo

cooo

iHOC)

a sr>*

1in0

inCO

0i

coino

COinoi

OJinoi

COi— iCDOO

• *OJcoo

*ooso

CMrH

0

COoo

THTH

o"

t-oo

i r) ***$

U

co

oi

THrH

O

CMi— 1

O

CO1— 1

0

coCO1— 1oo0

OJmo

CDinoi

o

o1

ino0

inrH

O

inl-H

O1

rHrH

O1

4 <•

cT

CMCDO

1

•*

OS

o

•it-CDOJ*

O

OJir-rH0o0

COrH

O

coin0i

CDD-

OI

rH03

O

'

COCM

O1

^0o

1

mrH

oi

COoo

1

° cU

OJinoi

*CDOT

O

OSCMrHOo

•)(•CDO3>O

CMrH

O

COin0i

mc-o

1

CMCO

o1

mCO

o

CMOooo

cooo

1

COoo

u

OJCDo

CMCDCOoo

*CDOS

o

•it-

OS

0

rHrH

O

inCD

OI

t-

o

inCO

o'

oCO

0|

i>o1

COrH

O'

ino0i

O

CMCOCO0ooo

OSCDO

1

OJinoi

CMCD>

O

co• fo

1

.[

in*

o

CMin0

H4

ino

COoo

t-coo

CM

•O

CMCO

o

^ <CCO

.

c0• rH

rtr— 10)rHrHOO

"Srto*rH• rH

g)• rH

CO*

M)

14

TABLE IV.- DERIVATIVE ESTIMATES OF TEST RUN 2 OBTAINED WITH MODEL 1

CY ................................... ...... -0.303p

Cy ......................................... 0.858

CYr ........................................ . 2.18

Cy6 ........................................ -0.00341

CVR ........ .............. .................. 0.0252Yfiaq ......................................... -0.0452

C7 ......................................... -0.126h

Clr ................................. ........ 0.277

C;. ......................................... -0.0121t6r

C; ......................................... -0.118

^aCn/3 .......................................... 0.105

Cn ......................................... 0.0670n"P-0.266

0.0519

Cng 0.00710

15

cct<oco

Oc

Go

fi*

)

t?"rj

•O

,"*iu

IH

O.

cT

c?

a

Q

"O

O

O

J*o

CO.

O

OiO

COo0

CO00

1-H1-1o

enoo

§o1

fo0

o0

CMCM

0I

in1-H

01

CO

0

CD1-H

O1

COo

COt-o

0COo

0>•

CV11-H

o1

inoo

c-o0

cnoo

t-0o

CM0o0

tno0

1— 11-H

0

oCM

01

ino0

COCO

o

c-iH

o1

CDt-o

c-iHCO

o

COt-o

a

O

i-H

01

COO

o

oo

o0

_,1-H

o

1-Hoo

1—)o0

CD1-1

01

CO1-1

o1

CO

01

1-HCO

o

COCOQ

1

COCOCOo

COt-o

•*!*CDo

?• >0

§o

0o

0o1

COo0

1

COo01

0o1

cn0o'

CM

0

c-oo

00

COo0

1

o

1o

COCO

<?r-1-H

o1

CO1-1

o1

H «>o

0o

0o1

COCMo

CMCM0

1-HCM0

1-H

01

4oo

cn0o1

0CMo'

090o1

c-oo

COo0

1-Heoo

CDCO

0

eo

0

3 «

Ho

1-1

01

in0o

COeoo

1

COCM0

1

1-HCM

o'

in•"J"0

0COo

c-00

go

in1-Ho0o

COoo1

1-Ho0

COr-l

0

in0o

in1-H

o

* -2o

COCM01

iniH

o1

COCDo1

enCD0

c-coo1

in

o

COoo

1

1-1

o

CMCOo0o

go

oCM

o1

t-o0

CO1-1

0

0CM

o1

CMCMo1

3. ^U

CMCM0

CM0o

c-coQ

1

CM

o

t-eoo1

in1-H

o1

1_leoo

1

T-l

0o

5o

-0o

o001

CMiH

0

CD1-H

o1

TH

o1

1-10o1

2. I

o

COo01

COCMo1

CO1-H

01

1-1o1

eooo1

CM§o1

1-HCMCOoo0o

1-HCO

o1

§o1

0COo

so

0>0o1

1-1o01

inoo

0o1

4 C

o

50

COo01

in1-H

0

cn0o

t-iH

o1

CDCO

oo0o

CMooQ

'

in1-H

o

in

o

in••*o

in

o1

0o1

iHo0

CM0.oo1

cn0o1

kl0 «

o1

CO

o

CM1-H

0

1-Hc-0

c-o

COCM

o0o

t-iHQ

'

eoo0

c-co0

c-coo1

1-HCM

0

1-HCM

o

COoo1

1-H1-H

o

c-o0

cn0o

« so

0

o

CO1-H

0

inc-o

t-in1-Hoo

pc-0

enoo'

*vH

0

CM

°

cnCO0

00CMQ

'

CMCMo

CO0o1

o1-H

0

§o

1-H

o

x ae

COeoo

inoo

CMcnCM0o

inc-0

Jc-o

tn1-HQ

'

CO1-10

-co0

COCD

0

COeoo

1

COCM

o

§o

1

cn00

t-o0

CDo0

I-u

§o

CDt-o.§o

in0o

CO

o

CM1-H

o

eoo01

COCM0

CMoo

in

0

ino0

1

oo1

1-H0

o

CO00

inoo

CO0o

I"Oco

COc-moooo

COoo

COCO0

orr

0

00

o

5o1

COoo1

CMCM

o

COCM

o1

1-1

o1

c-00

COo0

1-H1-H

o1

CM1-1o

I

cnoo1

i Aco

16

TABLE VI.- FINAL DERIVATIVE ESTIMATES OF TEST RUN 2

OBTAINED WITH MODEL 3 FOR ot^ = 0°

Estimate

-0.341

0.086

KcYp 2-3

1.27

-0.035

Cy6 0.0363,

-0.0382

-0.73

Cj -0.363

-0.085

0.60

C/.. -0.0163*6r

C7. -0.0350*5a

Cn. 0.101

0.0990

Kr -0.90Cnp

Cnr -0.229

Cnc 0.0527

-0.00074

KCn6a °-04

Standard deviation

0.0142

0.271

5.60

0.301

0.0163

0.0180

0.000996

0.0524

0.00574

0.0175

0.681

0.000632

0.000429

0.000791

0.00801

0.152

0.0164

0.000617

0.000614

0.0139

17

TABLE VII.- FINAL DERIVATIVE ESTIMATES OF TEST RUN 1

OBTAINED WITH MODEL 3 FOR « = 0°

Estimate

-0.295

0.086

Kc 2.3YP

Cyr • •• .' 1.6

Cv . . -0.0240*6r

-0.0388T

'. -0.73

-0.363

-0.132T

. 0.60

q6 . . -0.0160Cn . . . . • 0.0870

fC n \ 0.0823

Kr -0.90CnP

Cnr -0.228

Cng 0.0510

Fixed from test run 2.

Standard deviation

0.0238

*

0.513

0.0232

0.000879

*

*

0.0206

*

0.00132

0.000393

0.00291

*

*

0.000521

18

TABLE VIE.- FINAL DERIVATIVE ESTIMATES OF TEST RUN 3

OBTAINED WITH MODEL 3 FOR = 0

EstimateCY -0.293

P0.086

T2.3

1.20

CY, -0.05135r

(ClQ\ -0.0486V P/tfT

Kr, -0.73%

C7 -0.363Lp(Cj \ -0.0318V 'iVaT

Kr 0.60ClrCV -0.0164L8r

% . • 0-0987

0.0974r

Kr -0.90Cnp

Cnr • • • -0-228

Cng 0.0483

Fixed from test run 2.

Standard deviation0.0138

1.09

0.0164

0.000643

*

*

0.0143

0.000648

0.000491

0.00423

0.000618

19

TABLE IX.- FINAL DERIVATIVE ESTIMATES OF TEST RUN 4

OBTAINED WITH MODEL 3 FOR a = 0°

Estimate-0.269

0.090

KCyp 2-3

CYr 1-03

-0.0767

0.0602

-0.0549

-0.367

-0.282

0.170

0.80

Cj -0.00363

C,K -0.0244*5a

Cno 0.107

0.125

Kcnp -°-90

Cnjr -0.158

Cng 0.0542

16 \ -0.00529

0.04n5a

* Fixed from test run 5.


0.578

0.0155

*

0.000979

0.0244

*

0.000978

*

0.000533

0.00369

0.000506

20

TABLE X.- FINAL DERIVATIVE ESTIMATES OF TEST RUN 5

OBTAINED WITH MODEL 3 FOR «„ = 0°

Estimate-0.383

0.090

KCv 2.3*P

cYr 1.01CY* -0.0473

°rCY- 0.06026a

-0.0577

Kc, -0.367%

C, -0.282*P

0.0362

Kc 0.80lr

Cj -0.00360*6r

C, -0.0244*6a

Cno 0.0965

0.0987

Kr -0.90Cnp

Cnr -0.158

CnR 0.05256r-0.00529

0.04

* Fixed from test run 2.


0.181

1.21

0.0342

0.00931

0.00752

0.0875

0.00531

0.0410

0.824

0.00145

0.000682

0.00107

0.00526

0.493

0.0351

0.000907

0.000342

21

03CO

•T-(

tsoO

C!<D

03

g

.1

22

21.6

O r = 7.832 x 10

F = 1.362 x 10-10

21.4

21.2

F = 1.362 x 10-10

F = 1.362 x 10-10

-10

F = 1.362 x 10-10

F = 1.362 x 10-10

-2 -1

Figure 2.- Hypothetical illustration of correlation of two parameters.

23

- flight data

.2

to •!zCE

X n|_J *UCEa;Qi -.10

-.2

-

ivv%,».

f i l l

Jr^rv1

1 1 1 1

/I

/Jy

1 1 1

V

1 1 1 1 1 1 1 1 1

*-v> - v'

1 I I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 110 15

TIME(SEC)20 25

Dfl(

RflD

IRN

S)

i i

• •

• •

•09

>C

O

»C

00

-

-

E

mil MM MM MM MM MM MM MMI

MM MM10 15TIME(SEC)

20 25

Figure 3.- Model responses generated by derivative estimates of test run 1with longitudinal variables constant.

24

_UJtoX.toDcr

1.6

.8

o

-.8

1.R

=

- t i l l 1 1 1 1

t\,V1 1 1 1

*\\.

JJ 1 1

A/ •

1 1 1 1

H#

V

MM 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

+ flight data

- computed response

160

~ 80

UJ

\ 0I—

> -80

-160

-

till MM

•&

* \

MM

f-IMM

V /V

MM

w

MM MM MM MM

-

-

-

i i ir

48.76

24.38

0

-24 .38

-48.76

(-)

X

1.0

^ .5D<XQL^-* ft1—4

Q_ -.5

-1.0(

—

"

Sfe%

ii-U

?m&

M i l

(

Jill

^M i l

./

MM

\ f

MM

"X,,.

MM MM MM MM) 5 10 15 20 2

TIME(SEC)

Figure 3.- Continued.

25

+ flight data

- computed response

•so pr

.25

CD

-.25

-.50 1 1 1

_±£

1 II 1 1 1 II 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 110 15TIME(SEC)

Figure 3.- Concluded.

20 25

26

- flight data

•sir

to -iZcrt—io -0cr

ce-.lQ

-.2 _LL10 20 30

TIME(SEC)40 50

.4

co -2zcr»— iD -0cra:

s-s

-.4

—

—

-

1 1 1 1

-s^s

1 1 1 1

2k.

(\\

I/

1 1 1 1

kh1 LJ\

t i l l 1 1 1 1 t i l l 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 110 20 30

TIME(SEC)40 50

Figure 4.- Model responses generated by derivative estimates of test run 2with longitudinal variables constant.

27

1.0 t i l l I I I I I I I I I I I I I I I I I I I I I I I I I I I I 1 I I I I I I I

+ flight data

- computed response

20 30

TIME(SEC)


28

+ flight data

- computed response

10 20 30

TIME(SEC)


40 50

29

- flight data

767

~ 7420LU

^717

3632

667

E

\_S-

= |M

^

II 1 1

^Se-

ll 1 1

-v-\_/^.

1 1 1 1 II 1 1

\

1 II 1

^ \

1 II 1

\\

1 1 1 1 1 1 1 1

-

—

—

Ji ir

233.78

226.16

218.54

210.32

203-30

CJLU

W( F

T/S

EC

)•—

i

i—S

en

en

oo o

o

o

-

^vA

-

tin

A/ I A

AV

1 1 1 1

\l

1 1 1 1

/-•"V

1 1 1 1

^AA/

II II

b/v

INI

fl^r-w

1 1 II

V*™

1 1 1 1 1 1 1 1

-

-

• -

1 1 ir

30.48

15.24

0

-15.24

-30-48

_LUCO

u -LUtnto -0a<x

a

-.2 1 1 1LI.L

A fcA i tfU^j

I 11 I II I I I I I I u_

.30

1 C

THE

TR(R

RD

)i

i•

• •

o

en o

c

-

§wA*

-

till

^V

1 1 1 1

A*\J

1 1 1 1

fff^i

mi

JUA \

I I I I

vxX^

1 1 1 1

^

1 1 1 1

^^

1 1 1 1 1 1 1 1 II 1 110 20 30

TlhE(SEC)40 50

Figure 5.- Longitudinal data of test run 2.

30

- flight data

10

CD 5LUaac 0a_a: -5

-10

-

=^A

—

-T IM

i4/V1 1 1 1

V

i 1 1 1

/+***

1 1 1 1

^A/V

I 1 1 1

l

1 1 1 1

/yv*r""w

1 1 1 I

•\ffff~jt

I 1 1 1 i I 1 1 I 1 1 110 20 30

TIME(SEC)


40 50

31

2CT

+ flight data- computed response

Q_ -

-1.010 20 30 40

TIME(SEC)50

Figure 6.- Model responses generated by final derivative estimates of test run 2with longitudinal data as input.

32


20 30

TIME(SEC)


40 50

33

- f l i gh t data

U( F

T/S

EC

)S

OI

CO

O

i ~J

U

O1

00

C

-J

ro

-j

TO

< -

-

—

till Il l l

^r— v

I l l l I l l l

^~-

I l l l

x— '"

I l l l

r'

1 1 1 1

^—•^

M 1 1 1 1 1 1

-

-

=nit

215.43

207.87

200.25

132.63

185.01

OUJ

W( F

T/S

EC

)i §

8 o

g

8

-

L--^W"

-

till

^

I l l l

"

I l l l

A^/

UN MM MM MM MM Illl

-

—

—

1 1 ir

30.48

15.24 _0UJ

0 J£

-15.24 3

-30.48

.2

0 -1UJOD^5 -oCDcr

-.2.2

— .1CDcr25 .0crUJ

»—

-.2C

-

-

—

tl 1 1

3

—

—

"Tl 1 1

I l l l

I l l l

I l l l

1 1 1 1

*/M M

Vnvy/ — i

I l l l

eT*~

I l l l

v^

1 1 I I

I l l l

\nrf\J\r

I l l l

I l l l

nntMr

I l l l

M M

wrM^

I l l l

1 1 I I

I l l l

1 I I 1

I l l l) 5 10 15 20 25

TIME(SEC)Figure 7.- Model responses generated by final derivative estimates of test run 1

with longitudinal data as input.

34

- flight data

RLP

HfU

DE

G)

en tv

> rva

en

• •

• •

o

en

o tn

o

t^yf

-

-

- f i l l

wW

| 1 1 1

nv/y

1 1 1 1

*J

1 1 II

JVUl/Vfcnr1 »V

1 1 1 1

*-WV>/

1 1 1 1

rvy''

1 1 1 1

<\yvW

1 1 1 1 Mi l 1 1 1 110 15TIME(SEC)

20 25

.30

.15

.00C.D

-.30 in 1 1 1 1

4tj9'

I I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

10 15 20

TIME(SEC)


1 1 1 1


25

35

.8 till I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I

nnht 1 1 1 I f M 1 1 I I M n 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I I 1 1 1 1 1 1 1 1 1 I I 1 1 1 1 rl-pu . 3 8

+ flight data

- computed response

50CLLLL I I I 11 I 111 11 I I M 11 I I 11 11 11 11 I 11 I I 111 Mi l10 15TIME(SEC)


36

- flight data

- . p h i 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 n 1 1 1 n i8 12

TIME(SEC)16 20

Dfl

(Rfl

DIR

NS)

i Jc

b u=

co

-.8

-

**- «j-

—t i l l

m

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 18 12

TIME(SEC)16 20


37

- flight data

OUJto

u_

B63

813

788

7B3

-

-

-

• t i l l

•v^~«

INI

-w^*—

INI

"^

INI

>^— t^— w

INI

rv-Nx1 •••%

INI

" — "•

INI

x^^

INI INI

' -

E

E

nit

263.04

255.42 _CJUJ

247.805^21

240.18^

232 .56

100

— 50OUJ

-50

-100

.2 IT

o -1UJtn

aa:

.0

-.2 I I I I

1 1 II 1 1 1 1 1 1 1 ii

30.48

15.24

0

-15.24

-30-48

OUJ

1 1 1 1 III 1 1 1 1 1 1 1 1 1 1 1 1 I ILL I I I I

THET

FUR

RD

)i

i•

•

0

«

•

ro *

- o

•—

ro

=-

-

1 1 IIINI

V

1 1 1 1

U-~v>

1 II 1

vMr

1 1 1 1 II 1 1

yJuuJ*

1 1 1 1

vA-v\

1 1 I 1 1 1 1 1 1 1 1 18 12 16 20T I M E ( S E C )

Figure 8.-Continued.

38

- flight data

5.0

CD 2.5

aac 0in.a.ac-2.5

-5.0 1 MM MM MM MM M 1 1 MM MM MM 1 M 18 12TIME(SEC)

16 20

.4

to .2i—i3 -0(J3

cr*=-.e

-.4. -Ml 1

>M 1 M MM MM M i l 1 1 1 1 MM MM 1 1 1 1

+ flight data

- computed response

8 12

TIME(SEC)


16 20

39

-.urn 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

-160 till MM INI Mil INI INI Mil MM MM I I I f-MR


Q- -.25

.Kni-f I I I I I I I I 11 I I I I I I I I I I I I I I I I I I I I I I I 11 I I I 11 | | i I i i i i0 4 8 12 16 20

TIME(SEC)


40

- flight data

tozcr•—iocrcc

.2

.0

-.?

-

-

-

till

-rf-^Vor'

II 1 1

AJ\\\

1 1 II

rL•'"•'"\rvNl

1 1 1 1 1 1 1 1

k- ^ -W^

1 1 1 1 MM MM 1 1 1 18 12

TIME(SEC)16 20

1.0

co -5cr5 ocr

cr -.5o

-1.0

-

i >^

• f i l l

^

MM

—

MM MM MM MM MM MM MM

-

MM4 8 12

TIME(SEC)16 20


41

- f l i g h t data

308

oo-aIK

FT

/SE

C)

SCO

CO

C

co

en

cCO

C

O

CO

I E

-

-

tl 1 1

^^^w^

1 1 1 1

'V. /VA

1 1 1 1 JJ 1 1 1 1 1 1 Ml 1 1 1 1 1 1 1 1 1 1 1 1 1

-

-

-

u ir

276-75

269.13

261.51

253-89

246.27

oUJ

100

~ 50OUJto•s. 01—u_5 -50

-100

=wv/>

-

-

t i l l

^\/"V\*i^"

1 1 I I

^AA^A^^

1 1 1 1

n. /\v \

I I 1 1

*/Y

/ "

1 1 1 1

-wy »- --

1 I I 1

V' . 'V . *

1 1 1 1

A n *vy\ 1 L^V¥Vr

I I 1 1 1 1 1 1

-

-

-

1 1 ir

30-48

15.24

0

-15.24

-30.48

_UJ

.2

cj •!UJ

to .0aCEC£

5-1

-.2

.2

aCE

^ .0CE1—UJX -.1

-.2

-

-

-

till 1 1 LL

—

—

- t i l l

SryvvV

1 1 1 1

1 1 1 1

^\J1 1 1 1

e\

1

1 1 1 1 1 1 1 1 1 1 1 1 M i l 1 II 1 1 1 1 1

•wvM

1 1 1 1

/ V

1 1 1 1

fjwrvl

1 1 1 1

-wv— w

1 1 1 1

^N

1 1 1 1

Vv^

1 1 II 1 1 1 1 MM0 4 8 12 16 20

T I M E ( S E C )


42

- flight data

RLP

HR

(DE

G)

en r

o ro

en

• •

• •

o

en

o

en

a

^vvy\

-

-

till

Vvw1

1 1 1 1

^vwW-

1 1 1 1

^A i

ill!

/v/

1 1 1 1

rVA/W

1 II 1

VnTS

1 1 1 1

A/yYW

1 1 1 1 1 1 1 1 1 1 1 1

8 12

TIME(SEC)16 20

.4

to .2

=> .0

CE ~<2

-.4(

E

E£.*I+^V

-T IM

J-Jy^t

+

JJJJ_

jAjT

1 1 1 1

\ /

1 1 1 1

*Nn.

II 1 1^

1 1 1 1

isiJ

1 1 1 1

**s*

1 1 1 1 1 1 1 1 1 1 1 1

+ flight data

- computed

response

) 4 8 12 16 20

TIME(SEC)


43

i .n 111 I I I I I 11 11 I 111 11 I I i 11 i 11 i i 111 I 111 i i i II


8 12TIME(SEC)


44

- f l ight data

.2

CO •!ZccD .0CCce

£-'-.2

-

^~ \

till

fJ1 1 1 1 1 1 1 1 1 1 1 1

^JL*

1 1 1 1

v>*

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 18 12

TIME(SEC)16 20

Dfl(

RR

DIfl

NS

)i

»-en

o

en

b

-1.0

-

-

-

—

till J i l l

\1 1 1

1

/—(J^

1 1 1 1 1 1 1 1 mi 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 18 12

TIME(SEC)16 20


45

- flight data

801

•7*76OLU

^751Y—Lu

0726

701

-

- /

-

tl 1 1II II

r**1

\ M 1 M II

/•/"V

1 1 1 1

^_

II 1 1 II II III 1 1 1 1 1

-

—

-

1 1 if"

244.14

236.52

228.90

221 .28

213.66

OLU

120

en

W( F

T/S

EC

)

§ 8

o

g

-

-

-

tl 1 1

w—*^

1 1 1 1

V/

MM

A

1 1 1 1

\yv~v

MM

L

1 II 1 MM 1 1 1 1 II 1 1

-

—

-

Mir

36.57

18.28 _0LU

0 WDr:

-18.28 2

-36.57

•2fr

o •*LU(O

£ .0ocr

s--.2 l 1 1 1 1 1 1 i M i

\/

MM 1 1 II

.2

— .1cr8: .0cri—LU tn: -.1

,AW

=-

tl 1 1

tvMTW

1 1 1 1

^-^^\TV

1 1 II

y-vA

1 1 1 1

kv^Arv\

1 1 1 I

\v

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 16 12T I M E ( S E C )


16 20

46

- flight data

COUJa

a: -l

10

5

0

-5

10(

—

-u ,

^"

11 1 1 1 III

v/

MIL

/^

II 1 1

Y j-J • -

MM

"x.

MM Mi l MM Mi l MM3 4 8 12 IB 2

TIME(SEC)

.4

IO .P1—

- .0CD

>- g

-.4C

=

^

K

^ 1 1 1)MM

H

A

*Jr_

MMi

*^~

MMe

?K^B

MM\

-M->-*

1 1 1 11

1 1 1 12

1 1 1 11

1 1 1 16

1 1 1 12

+ flight data

- computed

response

0

TIME(SEC)


47

+ flight data(_) .0UJtorr\ ITCO UQCC

<H

-1.2

.2

~-x, . 1O -1LU

" nto .It-CDCE01

S"1

80

un•"k *iU0LL)

h-

*—

-80

r y

ti l l

-

*A! }

^111—

f+W-

E\

till

.\

-M

MM

JVMM

AlniMM

/

1 1 1 1

\X1 1 1 1

v/M M

^w- ^

MM

Af •

MM

\

MM

,-i

W

MM

*$

^

MM

f*

1 1 1 1

fe.

\

1 II 1

>M4-

1 1 1 1

1 1 1 1

1 II 1

1 1 1

II 1 1

1 II 1

MM

1 1 1 1

1 1 II

1 1 1 1

MM

II 1 1

—

—

=i \r

- compute

24.38

1O 1 QIc .13 __^

LJUJ

O co<!n

1O 1Q ^*-Id- 13

-24 .38

1.0

-. .5QCCK at— i

S -.5

-1.0I

-

- '^

t i l l

rf\

\

UN

/VINI

. -rfW*H^

MM

titijsc&

MM

4^

1 1 1 1 III 1 MM 1 1 1 1 1 1 1 1J 4 8 12 16 2

TIME(SEC)


48

A Altitude 6096 m (20000 ft)

Altitude 11277.6 m (37000 ft).15

.1

.05

-.4 r-

0

.

-

1

A

1 1

-.3

-.1

0

.6

I

.7 .8

Mach number

Figure 11.- Variation of stability derivatives with Mach number.

.9

49

Altitude 6096 m(20000 ft)

Altitude 11277.6 m(37000 ft)

-.02

.1

.05

.1

V .05a

-.05

0

.6

I

.7

I

.9

Mach number

Figure 12.- Variation of control derivatives with Mach number.

50

Altitude 6096 m(20000 ft) r

Mach 0.6

Mach 0.7

Mach 0.8

Altitude 11277.6 m(37000 ft)

» Mach 0.8

O Mach 0.9

.4

.3

.2

.1

-.05

\ 0

-.3

.01

-.01

Figure 13.- Variation of parameters .with angle of attack.(Symbol at trim angle .of attack.)

NASA-Langley, 1973 2 L-8378 51

Le* Bla

NATIONAL AERONAUTICS AND SPACE ADMISTRATION

WASHINGTON. D.C'. '20546 .,',

OFFICIAL BUSINESS

PENALTY FOR PRIVATE USE $300FIRST CLASS MAIL

POSTAGE AND FEES PAID

NATIONAL AERONAUTICS AND

SPACE ADMINISTRATION

NASA 451

nncTM A CTCD . If Undeliverable (Section 1'.PUS I MASTER. posM| Manual) Do Not Re,

"The aeronautical and space activities of the United States shall beconducted so as to contribute . . . to the expansion of human knowl-edge of phenomena in the atmosphere and space. The Administrationshall provide for the widest practicable and appropriate disseminationof information concerning its activities and the results thereof."

— NATIONAL AERONAUTICS AND SPACE ACT OF 1958

NASA SCIENTIFIC AND TECHNICAL PUBLICATIONS

TECHNICAL REPORTS: Scientific andtechnical information considered important,complete, and a lasting contribution to existingknowledge.

TECHNICAL NOTES: Information less broadin scope but nevertheless of importance as acontribution to existing knowledge.

TECHNICAL MEMORANDUMS:Information receiving limited distributionbecause of preliminary data, security classifica-tion, or other reasons.

CONTRACTOR REPORTS: Scientific andtechnical information generated under a NASAcontract or grant and considered an importantcontribution to existing knowledge.

TECHNICAL TRANSLATIONS: Informationpublished in a foreign language consideredto merit NASA distribution in English.

SPECIAL PUBLICATIONS: Informationderived from or of value to NASA activities.Publications include conference proceedings,monographs, data compilations, handbooks,sourcebooks, and special bibliographies.

TECHNOLOGY UTILIZATIONPUBLICATIONS: Information on technologyused by NASA that may be of particukrinterest in commercial and other non-aerospaceapplications. Publications include Tech Briefs.,Technology Utilization Reports andTechnology Surveys.

Details on the availability of these publications may be obtained from:

SCIENTIFIC AND TECHNICAL INFORMATION OFFICE

NATIONAL AERONAUTICS AND SPACE ADMINISTRATIONWashington, D.C. 20546

lateral stability and control … stability and control derivatives of a jet fighter airplane...

Documents