lateral aerodynamic parameters

8/2/2019 Lateral Aerodynamic Parameters

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o

5)

T E CHN I C A L N O T E

OR THE F-SC AIRPLANEM A N E U V E R I N G F L I G H T

William T. SaitLangley Resedrcb CenterHumpton, Vu. 23665

N A T I O N A L A E R O NA U T IC S A N D S P AC E A D M I N I S T R A T I O N W A S H I N G T O N , 0. C. M A R C H 1977


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TECH LIBRARY KAFB, NM

2. Govemment Accession No.I. Report No.4. Title and SubtitleNASA TN D-8276LATERAL AERODYNAMIC PARAMETERS EXTRACTEDI11111111111l11I1lllllI11lllllI1Ill

~3. Recipient's Catalog No.5. Report DateMarch 1977

0334002

IN MANEWERING FLIGHT7. Author(s)

William T. Suit~9. Perform ing Organ ization Name and Address

NASA Langley Research CenterHampton, VA 23665

2. Sponsoring Agency Name and AddressNational Aeronautics and Space AdministrationWashington, DC 20546

8. Performing Organization Repo rt No.L-10742

10. Work Unit No.505-06-93-01

11. Contract or Grant No.

13. Type of Repor t and Period CoveredTechnical Note

14. Sponsoring Agency Code

FROM FLIGHT DATA FOR THE F-8C AIRPLANE 6. Performing Organization Code

Unclassified Unclassified 44 $3.75

5. Supplementary Notes

- .6. Abstract Flight-test data have been used to extract the lateral aerodynamic parameters of the

F-8C airplane at moderate to high angles of attack.tions of the airplane from steady tur ns with tri m normal a cce ler ati ons fro m 1.5g to 3.0g.angle-of -attack variation fro m tr im was negligible.

The data we re obtained during perturba-The

Although wind-tunnel data indicate that the rolling and yawing moments are somewhatnonlinear with angle of attack, the angle-of-attack variations are small; therefore, the linearaerodynamic coefficients extracted from the flight te st s perm it computation of motion timehistories which a re in close agreement with the measured tim e his tor ies . The aerodynamiccoefficients extracted fro m flight data were compared with sev er al other s et s of coefficients,and the extracted coefficients resulted in characteristics for the Dutch roll mode (at the high-est angles of a ttack) si mi la r to those of a set of coefficients that has been the basi s of s ev eralsimulations of the F-8C.


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LATERAL AERODYNAMIC PARAMETERS EXTRACTEDFROM FLIGHT DATA FOR THE F-8C AIRPLANE

ITS4 MANEWERING FLIGHTWilliam T. Suit

Langley Res earch CenterSUMMARY

Flight-test data have been used to extract the l ate ral aerodynamic par ame ter s of theF-8C air plan e at modera te to high angles of attack. The data were obtained durin g pe rt ur -bations of the airc raf t fro m steady turns with tri m no rmal accelerations from 1.5g to 3.0g.The angle-of-attack variation fro m tr i m was negligible.

Although wind-tunnel d ata indicate that th e rol ling and yawing moments are somewhatnonlinear with angle of attack, the angle-of-attack variations are small; therefore, thelinea r aerod ynamic coefficients extr acted fro m the flight te st s perm it computation of motiontime histo ries which are in close agreement with the measured time histories.dynamic coefficients extracted f rom flight data were compared with sever al other s e t s ofcoefficients, and the extracted coefficients resul ted in c harac teris tics for th e Dutch ro llmode (at the highest angles of atta ck) sim il ar to tho se of a s e t of coefficients that has beenthe basis of several simulations of the F-8C.

The aero-

INTRODUCTION

The National Aeronauti cs and Space Administration (NASA) is curr ently involved inres ear ch on fly-by-wire control syste ms for aircraft. A discussion of t he NASA fly-by-wire program is given in reference 1. The air cr af t c urren tly used by NASA as a tes t bedto study digital fly-by-wire sy st em s is an F-8C airplane with a standard airframe. Pre-viously determined aero dynamics of the subject airplan e came prim ari ly fr om wind-tunnelte st s and analytical calculations, and the mathematical aerody namic model of the airp lanewas considered to be reasonable, especially for trimmed level flight. To substantiate theexisting linear aerodyna mic model for the F-8C at mod erate to high angles of attack, so meflight te st s were made with the angle of att ack as high as 16'.

A maximum-likelihood extraction pro cedu re was used to analyze the flight data.this procedure, a se t of equations of motion is used to calculate aircr aft response to speci-fied co ntrol inputs. Initial estim ates of aerodynamic par ame ter s (either fro m theory o r

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fr om wind-tunnel tests) are used for the initial motion computations. An iterative digitalcomputer program then sel ect s a se t of aerodynamic p ar am et er s that minimizes the diffe r-ence between the computed profiles and the flight profiles. This pro gra m has been used todetermine the aerodynamic param ete rs for sev era l aircra ft in the l g trimmed-flight condi-tion. (See refs. 2 to 4.) The details of the program are contained in refere nce 5 and in theappendix of this report. The pro gra m has not been used previously for la te ra l flight datataken at moderate to high angles of attack with a trimme d norm al acceleration greater thanlg. The progr am can be used as long as angle-of-attack variations from tr im are small,so that the assumption of li near ae rodynamics will not be violated. Analytical and wind-tunnel studies have shown that most of the lat era l aerodynamic p ar am et er s can have non-linea r variations with angle of atta ck over the range used in thi s investigation and that someof the se variations can be significant (ref. 6). Fo r each of the individual flights used in thi sinvestigation, th e variati ons in angle of atta ck from the t r im angle of attack were le ss than1 during 90 perc ent of the ti me history and always less than 2 Therefore, a linearmodel for the aerodynamics was considered adequate to describe the motion of the airplane.The linearity assumptions were successfully used in extraction of the longitudinal aerody-namic parameters for the F-8C at moderate to high angles of attack, and the resul ts a r egiven in reference 7.

The purpose of this paper is to present the lateral aerodynamic par am et er s of theF-8C airplane as calculated f rom flight data obtained ne ar t ri m a t Mach numbers of 0.7 and0.8, with no rm al accelera tions of 1.5g to 3.0g. Also pre sen ted are the equations used andadditional information on the flight data.extraction procedure and a discussio n of the resu lt s of the study.

These are followed by so me comments on the

SYMBOLS

Values ar e given in both SI and U.S. Customary Units. The measu rement s and cal -culations were made in U.S. Customary Units.

acceleration measured along Y body axis, g unitsaYb wing span, m (ft)-C wing mean geom etric chord, m (ft)g accel erati on due to gravity, 9.81 m/sec2 (32.2 ft/ sec 2)

h altitude, m (ft)

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IM

P

U

vV

W

CY

P

'a'e'r

moment of iner tia, kg-ma (slug-ft2)Mach number

period of oscillatory motion, secra te of roll, rad/s ec o r deg/secrate of pitch, rad/sec or deg/secrate of yaw, rad/sec or deg/secwing area, m2 (f t2)t ime, se c

component of velocity along X body axis , m/se c (ft/sec)air cra ft total velocity, m/s ec (ft/sec)

component of velocity along Y body axis, m/sec (ft/sec)air cra ft weight, N (lb)

component of velocity along Z body axis, m/sec (ft/sec)body coordinate axes through airplane center of gravity

angle of attack, r ad or d eg

angle of sid esli p, ra d or deg

aileron deflection (positive for left ro ll), r ad o r degtail-plane deflection (positive for tr ailin g edge down), ra d o r deg

rudder deflection (positive for trail ing edge left), r ad o r degdamping ratio

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e pitch angle, ra d o r deg

P air density, kg/m3 (slugs/ft3)@ bank angle, ra d o r degCoefficients and derivatives:

rolling-moment coefficientc2yawing-moment coefficientCn

CY side-force coefficient

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cnP

C"6 r

cyPacv

Subscripts :

C computed

f measured in flightt tr im conditionsx,y,z body coordinate axes through aircraft center of gravity

A dot over a symbol signifies a derivative with res pec t to time.

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EQUATIONS O F MOTIONThe equa tions of motion used in this study are re fe rr ed to the body-axis s ystem

shown in figu re 1 and are as follows:Y -direction:

1 2 g Pbv = pw - ru + g cos 0 sin @ + - p V S -2L

Rolling:

1

Yawing:

1

Auxiliary equations:

ay = A ( + + ur - wp - g cos e sin @)g6


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4 = p + (q sin cp + r cos G) an eThe three-degre e-of-freedom equations (eqs. (1)to (3)) were solved for the lateral

motions. The longitudinal var iab les u, w, q , and 8 used in these equations we re theflight-measure d values, and hence the nonlinear contributions of these t er ms were used inthe equations.

FLIGHT DATA

Desc ription of AirplaneThe airplane used, a modified prototype F-8C, has been a flight-test vehicle since it s

manufacture in 1958.jet engine embedded in the fuselage.The cen ter of gravity was at 29.0 pe rcen t of the mean ge ometr ic chord.was pa ral lel to and 10.16 cm (4 in.) above wat er line 100.char acter istics of the airplane are given in table I.

The F-8C is a single-seat, high-performa nce airplane with a singlePitch control is achieved with a' unit horizontal tail.

The X body axis(See fig. 1.) The geometric

Flight TestsThe data used in this rep ort wer e obtained from flights made at the Hugh L. Dryden

Flight Resea rch Center, and are shown in figure s 2 to 6. The pilot was instructed t o fly acoordinated turn at nominal Mach numbers of 0.7 and 0.8 with nominal t r im angles of at tac kof 9 and 13'. The worst case of ang le-of-attack variat ion is shown in figure 3 , where, ascan be seen, the angle of attack varied fro m the tr im angle of attac k by less than 2 A 1variation in (Y represents a 0.2g variation in nor mal acceleration. The airpl ane stabilityaugmentation sys tem s were off during the tes ts. The actua l te st conditions for each indi-vidual run are given in table 11.were calculated as a function of the percent of fuel in the air plan e and were obtained fromtables supplied by the Dryden Flight Res ear ch Center. The m a s s and moments of ine rti aused are average values f or the test duration. Since the ma ss varied less than 3 percentand the moments of in er ti a by less than 1 percent, the se variations were not accounted forin the paramete r estimation.

The airplan e mas s and moments of in ert ia listed in table 11

Pertinent data record ed during the flight test s included lateral acceleration ay;the difference between total pre ssu re and static p res sur e measured on a nose boom extend-ing 1.83 m (6 ft) in front of the air plane ; pitch attitudeyaw rat e r; roll rate p; indicated angle of at tack a and indicated angle of sid esl ip pmeasu red by vanes on the nose boom; pr es su re altitude; control surfa ce positions ailer on6, and rudder 6 ; and time t. The full-scale rang e of the instruments is given intable m. All the data wer e recorded on magnetic tape by an onboard recor der using a

8; bank angle @; pitch rate q;

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pulse-code-modulation (PCM) recording system . Additional information on the data acqui-sition sy ste m can b e found in reference 6.

Data PreparationThe data wer e initially recorded, digitized, and calibrated at Dryden Flight Research

Center. A digital tape with the data in engineering units was s ent to Langley Re se ar chCenter. The accel erati on data were corre cted for instrume nt location. The difference intotal pres sure and static pr es su re measurements was assumed to be the dynamic pressure.Density was determined fr om the standard atmosphere tables for the measured pr es su realtitude and the air spe ed was calculated from dynamic pre ssu re. The indicated angles ofattac k and sides lip wer e correct ed for the effects of air cr af t angular rates. The linearveloc ities along the vehicle body axe s were ca lculated fr om the airspeed, angle of att ack,and angle of sideslip. All data were recorded on tape at the ra te of 20 points per second.The tapes were then ready fo r use in the extraction program.

RESULTS AND DISCUSSION

Data for the flight conditions listed in table 11were used with the mathematical modelgiven in order to determine iteratively a se t of aerodynamic derivat ives for each of theflight conditions.shown in figures 2 to 6, with the measured data represented by dotted lines.time histories shown a r e those attained after the differences between the measured and cal-culated time histories became small.

The measured and computed time histories for each flight condition areThe computed

The difference was considered sma ll wheneverl R - I R ' i + l < 0.1, where R is the estimate of the e r r o r covariance matrix, as definedI R I iin the appendix, and i re fe rs to the ith iteration. This inequality will be ref er red to as

the cost function c riter ion.were in close agreement with the flight-record time hist ories .the pa ra me te r values determined were consistent fr om run to run. Table IV gives the stan -dar d deviations of the computed states from the measur ed states at convergence. Theinver se squ are of each quantity in table IV was used as a diagonal term in the weightingma tr ix to obtain the fit of computed data to flight da ta shown in figures 2 to 6. The stan-dard deviation of each f i t can be see n to be l ess than 3 percent of the full-scale instrumentrange, which was assum ed to be the uncertainty in the meas ured data (see table III). ForSome quantities, the stand ard deviation was les s than 1 percent of the full-scale measuredquantity.

The figures show that in all tests, the computed time historiesIt should al so be noted that

The derivatives extracted for each flight condition (the derivatives which resulted ,inthe computed time histories of figs. 2 to 6) a re listed in table V along with their estimatedsta nda rd deviations (Cram&- Rao lower bound). It should be noted that for M = 0.818


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and a t = 8.2', a single set of numbers is given which fits the data for both aileron inputand rud der input. The sing le set was determine d by using th e values fr om the two runsthat were least affected by correlation and that had the smallest standard deviations.As can be seen, this single set gave a good f i t to all the data taken at M = 0.81 witha t = 8.2'. If the estimated standard deviations of the par am et er s were less than 10 per-cent of the values extracted, confidence in the values obtained was indicated.eters which we re not considered well determined wer e C yThe deriva tives which we re not considered well determined do not usually have a strongeffect on the motion of the air fra me. Ther efore , it is difficult to excite the air fra me sothat the re w i l l be sufficient information in the data for a confident extraction of thesederivatives.

The param -Cy,, Cy6,, and Cn6 .P' a

When analyzing the extrac tion re su lt s, the effects of corre latio n must a ls o be con-sidered. If correlations between para met ers a r e high, erroneous param eter values can

res ult , and the inversion of the mat rix M ( t i j T R - l M ( t ii (defined in the appendix)i=1c J

can be affected. The most obvious effects of corr elatio n a r e two pa ra me te rs ass umi ngerroneous values but the fit to the data remaining good, or the cost function oscillating or

diverging because the matrix [ M(ti)T R - l M ( t i j is nearly singular (refs. 2 and 8).The correlation matr ice s for the aerodynamic pa ram ete rs extracted a r e shown intables VI(a) to VI(e).t e r values seemed unreasonable, and convergence problems we re encountered in only onerun.

i=1Although s ome co rre lat ion s we re high, none of the e xtracted p ara me-

For the run in which convergence problems o ccur red, a procedure discussed in ref-erence 2 was initially,used to determine par ame ter values. This procedure first examinedthe covariance matri x to determine which pa ra me te rs we re potentially correlated. Thecovariance matrix f or the ru n with a t = 1 3 O and M = 0.66 indicated tha t C wa sz6acorrel ated with Cz and Cz and that Cn was correlat ed with Cn and Cn Forthis particular run, the correlation affected the convergence of the algorithm.the convergence, eithernately held fixed. Initial ly Cz and C

P P 6a P P'To improveand C o r CzP , Clp, CnP , and Cn were alter-'26, "6 r P

were held fixed, and CzP, Clp, CnP, and6a "6 rwere allowed to change for se ve ra l iterations. Then CzP , Clp, Cn 3 and CncnP P P

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Y -direction:

Rolling:I Z - IY

IXfi = -rqt

Yawing:

4 p + r tan e t cos G~

The damping rat ios and the periods of the Dutch ro ll fo r various mathematical models aregiven in table VIII. Also given in table VIII a r e the per iods and damping rat ios of the Dutchrol l mode calculated f rom the actual flight data (where th er e was sufficient fr ee oscillationto make the calculations). As expected, when the period and damping ra ti os we re calcu-lated using a mathematical model based on par ame ter values fro m refere nce 6, the dampingratios were less than when the extrac ted model was used. Thi s conclusion is illustrated byfigures 7 o 9. The analy sis of the Dutch ro ll has demonstrated that se ve ra l sets of param-eter values will give a fair'fit to a se t of flight data and similar stability characteristics;

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however, for a given set of data, the extracted mathematical model gives the best f i t tothe data.

CONCLUDING REMARKS

Tes t data obtained during flights of the F-8C airpla ne at moderate to high angles ofattack have been used to determine the lat era l aerodynamic pa ra me ter s of the airplane atfour flight conditions. The te st s were conducted with the airpla ne trimme d in a steadyturn, with angles of attack approximately 9' and 13O, and with Mach numbers of 0.7 and 0.8.

The extracted par ame ter s wer e consistent f ro m run to run and resulted in a fit to theflight data that varied by less than 3 percent of the full instrument range. The param etervalues obtained we re in fair agreement with values obtained from wind-tunnel and analyticalmethods. The adequacy of the extracted se t of pa ra me te r values was further substantiatedby showing that ot her s e t s of p ar am et er values did not f i t the flight data as well as theextracted set. However, period and damping ratios of the Dutch roll modes that were gen-erated by the par ame ter se ts used for comparison were close to those generated by theextracted parame ter set.

Analytical and wind-tunnel studi es have shown that s ev er al of the la te ra l aerodynamicpa ra me te rs can vary with angle of attack over the angle-of-attack range tested. However,fo r each individual flight, the angle-of-attack variation fr om tr i m was so sma ll that thelin ear aerodynamic model used was adequate to des cri be the motion of the airplane.fore, the existing para met er extraction program could be successfully used.

There-

Langley R ese arc h CenterNational Aeronautics and Space AdministrationHampton, VA 2 3 6 6 5December 1, 1976

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APPENDIX

PARAMETER ESTIMATION PROCEDURE

The parame ter estimation procedure used in this study is an iterative procedure,5.L (aerodynamic pa ra me te rs , weights, and initial conditions) :

The procedu re maxi mizes t he conditional likeli-

- 1(zi,f 4i , c ) R-l(zi,f - xi,c)i=11(27r)lI21R1 ' I2L =is the estimate of the er r o r covariance matrix, 2 is the vector describing the

of the airplane, T denotes the transp ose, and -1 denotes the inverse. The statesin the likelihood function we re v, p, r , $ and ay. The calculated states Z-1,cre determined by using the equations of motion prev iously introduced. In these equa-the longitudinal quantities u, w, q, and 8 we re input directly into the equations

om the flight data tape. The weighting ma tri x is R-l , wheref- 1N

R = Diagonal 1 1 - Zi,c) (Zi,f - x i,cIJ= 1 Jesul t of maximizing the likelihood function is a para met er -updated equation which is

r 1 -1 1N NA E =11.(ti p - l .(ti)) 12 M(tiy R- l (Zi , f - zi ,cj

i=1 i= 1- is the vector of aerodynamic coefficients to be determined, M is the matrixof the calculated states with res pec t to the unknown par ame ters . (See

5.) The estimated parameter covariance matrix isua re root of each diagonal element of the covarianc e mat rix (estimated stand ard devia-

is directly related to the uncertainty in the extra cted par am et ers , and the off-diagonal13


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APPENDIXt e r m s are used to indicate correlations between par am et er s. The pro gra m, whose devel-opment is discussed in reference 5, calculates the m atr ice s and vectors required to gener-ate Ac'. The program then use s A c' to change the aerod ynamic coefficients iterative lyuntil a f i t to a set of flight data is obtained. The st ep s in the pro gram operation are:

(1)Choose values fo r the p ar am et er s to be identified.(2) Integrate the equations of motion usin g the cur ren t values of the aerodynamic

(3 ) Compute the state covariance matrix R and the weighting matrix R - l .(4 ) Calculate the cost function, which is the determinant of R.(5) ntegrate the set of differential equations for the sensitivities and then form the

pa ra me te rs chosen, and get time histories of the states.

matrix M .(6) Fo rm the maximum likelihood estimation equations fo r the pa ra me te r update(7)Determine the new para met ers using C = Ccurrent + AE.(8) Use the new

AE.+ +

as the current value for the next iteration, and continue the pro-cess at step (2 ) until the cost function cr iteri on is satisfied.

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REFERENCES

1. Deets , Dwain A.: Design and Development Experi enc e With a Digital Fly-by-Wire Con-tro l System in an F-8C Airplane.F-8 Digital Fly-by-Wire Con trol Syst em, NASA TN D-7843, 1975, pp. 13-40.

Descripti on and Flight Tes t Resu lts of th e NASA

2. Suit, William T. : Aerodynamic Pa ra me te rs of the Navion Airplane Extracted F ro mFlight Data. NASA TN D-6643, 1972.

3. Williams, Ja me s L.; and Suit, William T.: Extr actio n Fr om Flight Data of LateralAerodynamic C oefficients fo r F-8 Air cra ft With Su pe rcr iti cal Wing. NASATN D-7749, 1974.

4. Suit, William T.; and Williams, Ja me s L.: La te ra l Static and Dynamic AerodynamicNASAara met ers of the Kestrel Aircraft (XV-6A) Extracted From Flight Data.

TN D-7455, 1974.5. Grove, Randall D.; Bowles, Roland L.; and Mayhew, Stanley C.: A Pr oc ed ur e fo r Es ti -mating Stability and Control Parameters From Flight Test Data by Using Maximum

Likelihood Methods Employing a Real-Time Digital System. NASA TN D-6735, 1972.6. Sal ter , T. R.: XF8U-1 and F8U-1 Aerodynamic Data.

No. NOa(s)-53-1075, 54-605, 55-170, 57-187), Chance Vought Airc ra ft , Nov. 4,1954.

Rep. No. 8906 (Contract

7. Suit, William T.: Extraction Fr om Flight Data of L ongitudinal Aerodynamic Coeffi-cients in Maneuvering Fligh t fo r F-8C Ai rc ra ft . NASA TN D-8019, 1975.

8. Stepner, David E.; and Mehra, Raman K. : Maximum Likelihood Identifica tion and Opti-ma l Input Design fo r Identifying Aircra ft Stability and Contro l Derivatives. NASACR-2200, 1973.

9. USAF Stability and Control Datcom. Contr act s A F 33(616)-6460 and F33615-74-C-3021,McDonnell Douglas Corp., Oct. 1960. (Revised Jan. 1975.)

10. Thelander, J. A.: Ai rc ra ft Motion Analysis . FDL-TDR-64-70, U.S. Ai r Fo rc e, Mar.1965. (Available f ro m DDC as AD 617 354.)

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TABLE 1.- GEOMETRIC CHARACTERISTICS O F THE F-8C AIRPLANEFuselage length, m (ft)Wing:

. . . . . . . . . . . . . . . . . . . . . . . . . . 16.52 (54.17)Area, m2 (375)Aspect ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4Span, m (ft) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.88 (35.67)Mean geome tric chord, m (ft) . . . . . . . . . . . . . . . . . . . . . 3.59 (11.78)

Vertical tail:Area, m2 (ft2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.14 (109)Aspect ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5Span, m (ft) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.89 (12.75)

1.17 (12.56)

(ft2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34.88

Rudder area, m2 (ft2)Horizontal tail:

. . . . . . . . . . . . . . . . . . . . . . . . . . .Area, m2 (ft2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (93.4)Span, m (ft) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.52 (18.1)Length (center of gravity to one-fourth of tail mean geometric

chord), m (ft) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.06 (16.6)

8.68Aspect ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5

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TABLE II.- FLIGHT CONDITIONS

Mass"kg slugs

9574.41 656.06

INominal altitude , Nominal Nominal Tr imeflection,levator Tri m bankangle,6e,t +t,ft deg deg

7Run number II 1

Moments of inertiaaIX IY IZ IXZ

kg-mz slug-ft2 kg-mz . slug-ft2 kg-m2 slug-ft2 kg-m2 slug-ft21 2 500 9 200 118 00 0 86 800 124 000 91 600 4030 2970

-7.4512.0 -10.3

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TABLE m.- INSTRUMENT RANGES"

aYV0

Rangert0.5g30.91 to 515.15 m/sec (101.34 to 1689.0 ft /sec)*30*gook20 deg/seckl0 deg/seck40 deg/sec-5' to +30k20

0 to 21 000 m (0 to 63 000 f t )-15Oto +45O*2 lo

~

'v was calculated fr om v = V sin P . Individual se nso rs a re bas-ically more a ccu rat e than 3 percent of full scale ; however, becau se ofunknown e r ro r s, the effects of incompatibilities between measu red sta te sand processing e rr or s, the system accuracy was assumed to be 3 percentof the full-scale range of the instrument fo r the data used during theextraction procedure.

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.. ..

9,deg

9.213.08.2b8.2I-12.0

TABLE N .- STANDARD DEVIATIONS O F COMPUTED STATESFROM MEASURED STATES AT CONVERGENCE -

M

0.71.66.81.81.78

Standard deviation of -m/sec0.3048

.4023

.2804

.3200

.4755

1 P,ft/sec1.01.32.92

1.051.56

rad/sec0.013

.018

.O16

.028

.030

r,rad/ sec0.0041

.0031

.0026

.0022

.0040

@ >rad

0.068.031.019.036.048

a Y ,g units0.008

.013

.010

.019

.011aAileron input.bRudder input.

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TABLE V.- EXTRACTED VALUES O F PARAMETERS ANDESTIMATED STANDARD DEVIATIONS

-I I Extracted values (and standard deviations) for -

0.103(0.0018)-0.036

(0.0045)-0.62

(0.027) 1-0.13

(0.00 13)-0.01

at = 9.2'M = 0.71

Paramete rs

-0.80(0.03)0.18

(0.09)

cyP'YP

1 '16,

0.45(0.45)

-0.051(0.0012)

-0.121 '" 1 (0.003)-0.31

(0.009)0 .511 (0.027)1 Clr0.0321 '16 1 (0.0024)0.102I I (0.00 3)

-0.045

-0.40(0.0 26)-0.12

(0.0027)-0.012

(0.00 13)I I ~

at = 13'M = 0.66

~

-0.80(0.04)0.17

(0.11)0.45(0.7)0.06

(0.03)-0.112

(0.0013)-0.28

(0.0034)0.33

(0.027)0.028

~ -~

(0.0009)-0.046

(0.000 7)

a t = 8.2'M = 0.81

(a)-0.80(0.06)0.37

(0.12)0.45(0.5)0.06

(0.026)-0.14

(0.0015)-0.36

(0.004)0.37

(0.03)0.037~- -

(0.00067)-0.055

(0.00052)0 . 1 1

(0.00 2)-0.06(0.003)-0.33(0.02)

-0.115(0.0007)-0.0084(0.0007 9)

-

a t = 120M = 0.78

(b)-0.74(0.035)0.13

(-0.15)0.45

(-0.6)0.06

(Fixed)-0.11(0.002)-0.22(0.008)0.24.~ .

(0.02)0.03

(Fixed)-0.044

(0.0008)0.095(0.003)-0.04(0.01)

(0.02)-0.33

-0.115(Fixed)-0.0004(0.001)

aThe values given we re d etermined by taking a weighted averag e of the resultsbThe vehicle wa s excited by using a n ailero n input only.

from ru ns using ailer on inputs only or rudd er inputs only.

20


23/47

TABLE VI.- CORRELATION MATRICES FOR EXTRACTED AERODYNAMIC PARAMETERS

CYp. 0.002 -0.093 -0.2 0.088 -0.035 0.072 0.0950.002 1 -0.58 -0.13 -0.034 -0.0 1 0.015 -0.024cyP

cy6rCy, -0.093 -0.58 1 0.3 0.06 0.03 0.18 0.003

-0.2 -0.13 0.3 1 0.016 0.006 0.014 0.021I Clp 0.088 -0.034 0.06 0.016 1 0.63 -0.37 -0.46

-0.035 -0.01 0.03 0.006 0.63 1 -0.54 -0.350.50

4 - iI clp

-0*541c1, 0.072 0.015 0.18 0.014 -0.37

(a) a t = 9.2' and M = 0.71, with both aileron and rudder inputs

0.064 0.13 0.15 -0.19 -0.19 0.19

-0.064 -0.060 -0.066 -0.045 0.063 -0.0210.046 -0.032 -0.044 -0.16 -0.04 -0.060.025 -0.038 0.009 -0.011 -0.002 -0.02

___-+0.70 0.73 0.51 -0.61 -0.59 0.59 10.89 0.40 0.45 -0.36 -0.13

-0.45 -0.43 -0.35 -0.19

~~ ~

-0.066 -0.044-0.0450.063 -0.04

-0.021 -0.06

0.15 0.009 0.51 0.45 -0.35 0.018 0.48 0.76 1 -0.68 -0.53 0.93-0.011 -0.61 -0.36 -0.19 0.025 -0.44 -0.63 -0.68 1 0.68 -0.64-0.002 -0.59 -0.13 0.13 0.16 -0.22 -0.76 -0.53 0.68 1 -0.61-0.02 0.59 0.44 -0.41 -0.10 0.40 0.86 0.93 -0.64 -0.61 1

-0.19p+


24/47

-0.13 0.11 -0.02 0.19 0.13 -0.095 -0.02 0.10

TABLE VI . - Continued(b) a t = 13' and M = 0.66, with both aileron and rudder inputs --t0.19 -0.10 0.15230.050-0.066 1I 0.5 I 0.46cyP I II I -0.33 1 0.14 I 0.07 1 0.16 1 0.051 1 -0.065 1 -0.12 1-0.02 -0.16 1 -0.006yp 0.5 I 1 1-0.19Cyr I 0.46 1-0.19 I 1 0.56 I 0.07 I 0.04 I 0.12 I 0.08 I 0.122 1 -0.03 I 0.009 -0.11 1 -0.06

1 -0.13 1 -0.33 1 0.56%, 1 I 0.004 1 0.014 1 -0.024 1 0.024 1 0.057 1 -0.027 1-0.006 0.04 1 0.02 -0.018 10.11 I 0.14 I 0.07% 0.004 ~ 1 ~ 0.6 ~ 0.5 1-0.09 1 0.804 ~ 0.21 1 0.18 -0.58 I -0.47 0.365 I

-0.02 1 0.07 1 0.04clP 0.014 1 0.6 1 1 0.062 -0.26 1 0.756 1 0.10 1 Oy7 -0.33 1 -0.045--0.63 -0.09 0.085-0.3500.19 1 0.16 1 0.12' 1 , 1 -0.61 1 -0.176 ' -0.41 1-0.140.024 1 0.5 1 0.062 10.024 -0.09 -0.26 0.6 1 '710.378 '-0.351 0.10 -0.31 0.06--7.13 1 0.051 1 0.08%, 0.049 ~0.057 0.804 1 0.756 -0.176 -0.378 I 1 0.267 I 0.150 -0.360 -0.17 1 -0.045 ~-0.027 0.21 0.10 -0.41 -1:): ~ (I:%:.62 ~ y 6 2 0.11 ' -0.61

-0.006 0.18 0.17 -0.14 -0.31 -0.440.8970.86 1

0.04 -0.58 -0.33 -0.63 -0.31.06 1 -0.360 0.11 ~ -0.31 1 0.50.02 -0.47 -0.045 -0.09 -0.171 -0.61 ' -0.44 0.5 1

-0.018 0.365 I 0.085 -0.350 0.049 -0.045 0.897 0.86 1 -0.587 -0.636L -0.587 ~-0.10 -0.006 1 - 0 . 06~ -%, -0.636 ~0.152 -0.050 1 -0.066 1


25/47

TABLE VI.- Continued( c ) cut = 8.2 and M = 0.81, with ailero n input

I CL -0.07 0.03 0.03 0.59 0.86 -0.42 1 0.43 0.32 -0.3910.68 0.46 -0.33 0.43 1 0.74 -0.74e+! .08 c--- -0.830.22 -0.09 -0.09 0.49 0.36 -0.53 0.32 0.74 1___i - ,cnPc% -0.28 0.095 -0.013 -0.44 -0.45 0.24 -0.39 -0.74 -0.83 1

6 r0.21 -0.11 -0.036 0.65 0.40 -0.41 0.33 0.94 0.89 -0.79

1

0.330.940.89

-0.791

1

(4 ~ (a) (a)-0.43 -0.003 1 0.07 -0.09 0.07 -0.07 0.18 0.22 -0.28 0.21-0.61 0.09 0.05 -0.08 0.03 -0.15 -0.09 0.095 -0.11--0.1 -0.004 0.19 0.03 0.08 -0.09 -0.013 -0.036

acy6,, c26r, nd Cn6 could not be identified since the control disturbance wa s from an aileron input.r


26/47

TABLE VI.- Continued(d) a t = 8.2O and M = 0.81, with rudder i npu t

I cyp I I I I I~~,-~

0.80 0.87 0.53 , -0.10 -0.24 -0.22--0.09 0.07 ~ -0.09 ~ -0.14F+-. i

1 -0.19 -0.10 !-0 .08 0.11 11

1 - 7 -

I--C 0.60 0.05 I-0.150.13 -0.15 0.75--

I

a and Cn6 could not be identified since the control disturb ance was a rudder input.a


27/47

TABLE VI.- Concluded

-0.120.74___( 0.1 -0.74 1 0.03

-0.47.Iyr II(e) Q t = 12O and M = 0.78, with aileron input

, 10.04.25 -0.04 -0.03 ' -0.05 I -0.06 0.06 i

0.07 0.16 0.11 0.07 1 -0.05 I -0.15 -0.03I--

Ncn

%,cn6,

11.15 -0.04 -0.03 0.38 0.07 -0.2 0.05 0.88 0.80 0.64


28/47

TABLE VII. - PARAMETER VALUES FROM OTHER SOURCES

-0 .0351

- 0 . 0 3 2 1-0 .30 1 - 0 . 3 3

Values obtainedusing ref. 9

- 1 . 0 0 -1.00

Values fro m ref. 6

Parameterscy = 8' I at = 12't a t = 8.2'M = 0.8 1 M = 0 .8 M = 0 . 8 1

cyP - 0 . 8 20 .175 I 0 .180.45 I 0 .450.39 I 0 .195

-0 .126 1 - 0 . 0 9 2 - 0 . 1 1 5- 0 . 2 4 0 1 -0 .085 - 0 . 3 3 60.057 1 0.0700 .014 1 0.007

- 0 . 0 6 0 1 - 0 . 0 6 0cnB 0 . 1 4 3 I 0 . 0 9 2 0 . 1 7

Pn~.

- 0 . 1 7- 0 . 1 0 4 I -0 .052II -0 .004 -0 .0005

2 6


29/47

TABLE VII1.- PERIODS AND DAMPING RATIOS FOR THE DUTCH ROLL MODE-Case

A

B

C

D

E

F

M

0.71

.66

.81

.78

a. 8

. 8

O tdeg

9.2

13

8.2

1 2

8

12

pf ;ec2.2

2.2

2.2

2.2

-pC,sec2.6

2.5

2.3

2.2

2.0

2.2

{f~

0.2

.2

.2

.2

-{C

1.23

. 2 3

.20

.19

.17

.12

Conditions

Parame ters extracted fro m flight dataas given in table V.

Par ame ters extracted from flight dataas given in table V.

Par ame ters extracted fro m flight dataas given in table V.

Par amet ers extracted from flight dataas given in table V.

Paramet ers fro m reference 6 as givenin table VII.

Paramet ers from reference 6 as givenin table VII.-~

aFrom reference 6 model.

27


30/47

6 positive: t rai lin g edge left' t r

6, positive: left a ile ron trailin g edge up

=I6.52 m (54.17 ft)

,

Iwater line 100 2Figure 1.- Sketch of airplane.28


31/47

9.144 .57

00)

2 0

> -4.57-9.14

301 5

Vu)0 2i- 1 5

-3 0

t, sec 3 0Figure 2.- Comparison of meas ured data with tim e histo ries computed byusing para met ers given in table V for flight data taken at M = 0.71and a t = 9.2O, with both rudder and aileron inputs.29


32/47

7

1 1 1 1 I 1 1 1+.10.05

CIcdk- 0Ll

lo

-.05- . lo

t, secFigure 2. - Concluded.

30


33/47

.10

.05ac? ? Oa" -.05

-.lo

4020

-2 0-40

t, se cFigure 3.- Comparison of measu red d ata with time h is to ri es computed by

using par am ete rs given in table V for flight dat a taken at M = 0.66and a t = 13', with both aileron and rudder inputs.

31


34/47

2010

z o-10-20

Md7

III I-T4 1 1 11 1 1 1 1 1 1

t, se c

Figure 3. - Concluded.

32


35/47

I I I I I I I I I I I I

la0F'"T-.5 ~~

-1.0 E

I l l 1

LLU

0 2 4 6t, sec

4 020

i-20- 4 0

8 10

Figure 4.- Comparison of meas ured data with t i me histo ries computed byusing par ame ter s given in table V for flight data taken at M = 0.81and a t = 8.2O, with ail ero n inputs.

33


36/47

~I,....-...~ I -.......I1 1 1 . 1- I 1 1 1 1

Figure 4. Concluded.

34


37/47

t, se c

Figure 5.- Comparison of measured data with time hi sto rie s computed byusing par am ete rs given in table V for flight data taken at M = 0.81and a t = 8.2', with rudder inputs.

35


38/47

.150

.075acdk 0

-.075..cd0

-.150

ComputedMeasured...........

-.05

acdkk0

Ti1 1 J 1 1 1 1 1 1 1 1t, sec

Figure 5.- Concluded.

36


39/47


.2

.1aJ

2 0i -.l

- 212.196.10

VaJ' 0Ei-6.10-12.19

3 .01.5

-e2 0s"

-1.5

-3.00 4 8 12 16 20t, sec

Figure 6 . - Comparison of mea sur ed data with tim e his to ri es computed byusing pa ram et ers given in table V for flight dat a taken at M = 0.78and at = 12O, with ai lero n inputs.

37


40/47

..... . . , .. .. . . -

ComputedMeasured....e......

5EnkLo

.10-05

0

- 05- . l o

Figure 6 .- Concluded.

38


41/47


-1 I=-

12.196.10

E Oal\>

-6.10-12.19

-L, --

E l I I

~ l l , l l l l l , l l ! , l l l l l l l

- I . ! !

I I I I I I I I I I I I I I I I I I I I

2kaP O L tciI I I I I

t , sec

Figure 7.- Comparison of measured data of figure 4 with the time hi stori es computedby using the pa rame te rs of reference 6 as given in table VII for C ase E.

39


42/47


~.

aE..k10

.05..........................H

- . l o*05L-L-L*.........................Zkk.50

.250

-.25

0 2 4 6.50 t , sec

TrnTrTrl l I 1111 I l l 18 10Figure 7. - Concluded.

40


43/47

Computed............Measured.6

0 -3aa"

[D

2 O- .3-. 6

.2

0[D\- 02i -.l

-.2

4020

>-2 0-40

- 5 10 15 20 25t, s e c

Figure 8.- Comparison of measured data of figure 5 with the time his tor ies computed byusing the pa ra me te rs of refe rence 6 as given in table VII for Case E.

4 1


44/47


acdk..cdW

aCdk.kW

.10.05

0

-.05

- . l o

.10

.050

-.05- . l o

.50II) .255c1M 0&cd -.25

7n 0 5 10 15 20 25.3v t , sec

Figure 8. - Concluded.

4 2


45/47


5025

U

0 2i.2 5

50

t, sec

Figure 9.- Comparison of measured data of figure 6 with the time histories computed byusing the para mete rs of reference 6 as given in table VII for Case F.

43


46/47


.50v) .25Yrld1M oF

cd -.25

0 4 8 12 16 20- 3 0 t, secFigure 9. - Concluded.

44 NASA-Langley, 1977 L-10742


47/47

A E R O N A U TI C S A N D S P A C E A D M I N IS T R A T I O NWA SH I N G TO N , D . C . 2 0 5 4 6

NASA

P O S T A G E A N D F E ES P A I DN A T I O N A L A E R O N A U T I C S A N D

S P A C E A D M I N I S T R A T I ON45 1

POEITMASTER : If Undeliverable (Section 158Postal Maniial) Do No t Return

T he aerolzautical and space activities of the United States shall beconducted so as to contribute . . . o the expansion of human knowl-edge of phenomena in the atmo sphere and space. Th e Administrat ionshall provide for the widest practicable and appropriate disseminutionof inf orm atio n concern ing its activities and the results thereof.-NATIONAL AERONAUTICSN D SPACE ACT OF 1958

SCIENTIFIC AND TECHNICAL PUBLICATIONSTECHNICAL REPORTS: Scientific andtechnical information considered important,complete, and a lasting contribu tion 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. Also inciudes conferenceproceedings with either limited or unlimiteddistribution.CONTRACTOR REPORTS: Scientific andtechnical informa tion generated under a NAS Acontract or grant and considered an importantcontribution to existing knowledge.

-

TECHNICAL TRANSLATIONS: Informat ionpublished in a foreign language consideredto merit N ASA distribution in English.SPECIAL PUBLICATIONS: Informationderived from or of value to NASA activities.Publications include final reports of majorprojects, monographs, data compilations,handbooks, sourcebooks, and specialbibliographies.TECHNOLOGY UTILIZATIONPUBLICATION S: Inform ation on technologyused by NASA that may be of particularinterest in commercial and other-non-aerospaceapplications. Publications include Tech Briefs,Technology Utilization Reports andTechnology Surveys.

lateral aerodynamic parameters

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