Stability and control derivative estimates obtained from flight data for the Beech 99 aircraft

(NISl_-T_-72863) STABILITY A_D CO_ITttOL g79-2013_ DEI_IVATIVE ESTIMATES OBTAINED FRO"I FLIGBT DATA FOR TEE BEECH 99 _IRCRAFT (N_SA) 38 p HC AO3/MF A01 CSCL 01C Unclas 172_ I c, 3/0 8 NASA T_.ehnical Memorandum 72863 STABILITY AND CONTROL DERIVATIVE ESTIMATES OBTAINED _j FROM FLIGHT DATA FOR THE BEECH 99 AIRCRAFT Russel R. Tanner and Terry D. Montgomery April 1979 ,•.,i •:•I i:!

j_ NASA Technical Memorandum 72863 ?

STABILITY AND CONTROL DERIVATIVE ESTIMATES OBTAINED FROM FLIGHT DATA FOR THE BEECH 99 AIRCRAFT Russel R. Tanner and Terry D. Montgomery Dryden Flight Research Center Edwards, Califorr, i_ Nat,onal Aeronaut,cs and Space Adm,n,strat,on STABILITY AND CONTROL DERIVATIVE ESTIMATES OBTAINED FROM FLIGHT DATA FOR THE BEECH 99 AIRCRAFT RUSSEL R. TANNER AND TERRY D. MONTGOMERY DRYDEN FLIGHT RESEARCH CENTER INTRODUCTION Reliable estimates of stability and control derivatives are essential for flight simulations and handling quality evaluations of aircraft. In response to the growing need for reliable derivative estimates, the NASA Dryden Flight Research Center developed a technique for obtaining the sta- bility and control derivatives of aircraft from flight data (r_f. l) and developed a set of FORTRAN computer programs to implement the technique (ref. 2). This method of derivative extraction is based on a modified maximum likelihood estimator that uses the Newton-Balakrishna_ algorithm to perform the required minimization.

These computer programs were used to determine the stability and control derivatives of a modified Beech 99 alrplane. The aircraft, flown as a co- operative effort by NASA, Beech Aircraft Corporation, and the University of Kansas Flight Research Laboratory, was utilized to study the effects of separate surface stability augmentation (ref. 3). Data were obtained with the aircraft in a clean configuration and with one-third flap deflec- tion. This report presents the Beech 99 derivative estimates obtained with the modified maximum likelihood technique and compares these esti- mates with predicted values.

SYMBOLS A, B, C, D, R System matrices normal, longitudinal, and lateral an, ax, ay accelerations, g b reference span, m coefficients of lift and drag C L , CD coefficients of roll, pitch, and C_, Cm, C n yaw moment coefficients of normal and lateral CN, Cy force CG center of gravity C mean aerodynamic chord, m G measurement noise spectral density matrix acceleration due to gravity, m/sec z g moments of inertia, kg - m 2 IX , IXZ, Iy, IZ J cost functional m mass, kg roll rate, deg/sec P q pitch rate, deg/sec dynamic pressure, fi/m z q r yaw rate, deg/sec S wing area, m 2 t time, sec T thrust coefficient C T total time, sec U control vector V velocity, m/sec weight, kN longitudinal, lateral, and normal axes

XAN, XAY distances of an and ay accelerometers

forward of center of gravity, m X state vector computed observation vector ZAY distance of ay accelerometer below center of gravity, m Z measured observation vector angle of attack, deg angle of sideslip, deg aileron, elevator_ and rudder 8 a, 6 e, 6r deflections, deg measurement noise vector q pitch attitude, deg vector of unknowns roll attitude, deg Subscripts: derivative with respect to indicated p, q, r, _, 8, 6a, 6e, 6r quantity 0 bias Superscripts: matrix transpose

DESCRIPTION OF THEAIRPLANE ANDINSTRUMENTATION

The modified Beech 99 airplane used in this analysis is a 14-_eat, twin

turboprop commercial airliner with low wings and retractable landing gear (figs. l and 2). Tables l and 2 list important geometric and mass charac- teristics of the Beech 99 airplane. The test airplane was modified so that there were two independently operable control surfaces where there is normal- ly only one; however, only one set of rudder, aileron and elevator surfaces was used during the test flight. The extra surfaces are shaded in figure I.

These extra surfaces remained in fixed positions during the flight.

The instrumentation of the airplane consisted of a standard package used for the measurement of stability and control parameters, including three-axis angular rate gyros, attitude gyros, and linear accelerometers, along with boom-mounted angle of attack and angle of sideslip es. The data were filtered with 40-hertz passive analog filters, then sompled with a 9-bit pulse code modulation (PCM) system and telemetered to a ground station for real-time monitoring.

The analysis used in the derivative extraction accounts for the effect of instrument location on the measurement of linear accelerations and flow angles. The instrument locations used in the analysis of the flight data are presented in table 3. Table 4 lists the resolutions of the instrumen- tation system used in the analysis.

TEST PROCEDURES AND FLIGHT CONDITIONS The Beech 99 airplane was flown in the cruise configuration for half of the maneuvers analyzed and at one-third flap setting for the remainder. All maneuvers were flown with the center of gravity at approximately 26 percent of the mean aerodynamic chord. Most of the maneuvers performed were simple aileron, rudder, or elevator pulses.

All data were obtained during a 2-hour flight in smooth air. F_fty-six maneuvers were performed for derivative estimation over an angle of attack r_ _e from 1.5 to 4.5 degrees, a velocity range from 65 to lO0 meters Qer second and an altitude range from 1800 to 3200 meters. Table 5 lists the flight condition corresponding to each maneuver.

METHOD &F ANALYSIS A maximum likelihood method of analysis was used to determine a complete set of linear body axis stability and control derivatives from the 56 maneu - vers performed in flight. The digital computer program used is called the modified maximum likelihood estimator, version three (MMLE-3) which is an out- growth of the program described in detail and listed in reference 2. The program is discussed briefly in appendix A_ Further information is available upon request from the Dryden Flight Research Center. The analysis technique is an iterative technique that minimizes the difference between the measured

aircraft response and the computed aircraft response by adjusting th -,_ stabil-

ity and control derivative values used in calculating the computed r(,_nse.

This method can be modified to include _ priori information from pre_,_s calculations, flight tests, or wind tunnel tests; however', no _ priori infor- mation was used in this Beech 99 analysis. The maximum likelihood techni- que is described fully in reference I.

In addition to giving derivative estimates, this method provides uncer- tainty levels for each derivative. The uncertainty levels are proportional to the approximation of the Cramer-Rao bounds described in reference l, and are analogous to the standard deviations of the estimated derivatives. The larger the uncertainty level, the more uncertain the validity of the estimated value. The uncertainty levels obtained for derivatives from different maneu- vers at the same flight conditions can be compared to determine the most valid estimate. The uncertainty levels provide additional information about the validity of the derivative estimation. Further information on the interpre- tation of uncertainty levels is included in reference 4.

The digital computer program used in the data analysis is capable of pro- ducing one set of derivative estimates based on multiple sets of data. The lateral-directional derivative estimates in this report result from the simul- taneous analysis of both rudder and aileron maneuvers. Analysis of rudder and aileron maneuvers simultaneously usually results in improved derivative estimates, as shown in reference 4.

The cost functional minimized by theprogram is given in appendix A.

The matrix G in this cost functional acts as a signal weighting matrix. For this analysis, G was chosen to be diagonal with values given in table 6.

RESULTS AND DISCUSSION For all _6 maneuvers flown with the Beech 99 airplane, the measured air- craft response compared satisfactorily with the computed response based on the maximum likelihood estimation. A typical longitudinal maneuver is shown in figure 3, and a typical lateral-directional double maneuver is shown in figure 4. The measured (solid-line) and computed (dashed line) response of the aircraft are in excellent agreement in these figures. Some maneuvers pro- duced better agreement than others; however, on the average, the agreement was quite good.

An atypical maneuver combining aileron and rudder inputs is shown in figure 5. This maneuver was performed to determine any nonlinearities in aileron effectiveness. The excellent fit in figure 5 based on a linear model indicates that there was no significant nonlinearity in aileron effectiveness.

The MMLE stability and control derivative estimates based on the analysis of this maneuver were in excellent agreement with estimates from more conven- tional maneuvers. The analysis of this maneuver required that the small angle approximation (in bank angle) be removed from the mathematical model (see appendix B}. All other maneuvers were analyzed using small angle approxima- tions.

The estimates for 56 maneuvers (19 primarily with elevator inputs, 21 primarily with rudder inputs, 15 primarily with aileron inputs, and one with simultaneous aileron and rudder inputs) are presented in figures 6 and 7.

The longitudinal stability and control derivative estimates are pres- ented in figure 6, while the lateral-directional estimates are displayed in figure 7. Each symbol indicates the derivative estimate for one maneuver, and the vertical bar associated with the symbol represents the uncertainty level for that derivative estimate. The square symbols are used to indicate one-third flap down maneuvers. Manufacturer predicted derivatives based on a combination of analytical predictions, wind tunnel tests, and flight test results are shown along with the MMLE-3 derivative estimates for comparison.

The manufacturer's predictions of derivatives that are functions of thrust coefficient (CN , CN , Cm , and Cn ) are indicated by dashed lines a 6 e 6e for thrust coefficients of 0 and 0.1. This range of thrust coefficients in- cludes the values observed in flight (see table 3). The manufacturer's pred- ictions for the derivatives that are not functions of thrust coefficient are indicated by a single dashed line. These predictions are valid for both cruise and one-third flap down configurations. Details of the mathematics involved in the presentation of the manufacturer's derivatives are given in appendix B.

LONGITUDINAL DERIVATIVES Figure 6 shows the MMLE-3 longitudinal derivative estimates for the Beech 99 aircraft along with the corresponding predictions of the manufacturer.

Comparison between the flight estimates and the manufacturers predictions shows close agreement except for the derivative Cm For some unexplained reason, the flight data did not produce consistent estimates of this deriva- tive. Other flight estimated derivatives are consistent, with the exception of the estimates of Cm and Cm resulting from one maneuver at an angle of q 6e attack of 4.25 degrees. The plots of CN_' Cmq' CN_e' and Cm6e are nearly constant with angle of attack, showing no observable effect of flap deflection.

All these parameters show good agreement with the manufacturer's estimates.

LATERAL-DIRECTIONAL DERIVATIVES As with the longitudinal derivatives, the lateral-directional deriva- tives are plotted with the manufacturer's estimates (fig. 7). The deriva- tives , C n , Cy , Cy , , and C are quite con- C_B C_p, P C_r' Cnr' _a 6r C£_r n6r sistent with the derivative estimates of the manufacturer.

C_ i s for '6 a

the most part smaller than the manufacturer's estimates, while CnBand CyB

are consistently larger in magnitude than the manufacturer's estimates for

both cruise and one-third flap configurations. On the whole, the lateral-

directional derivative estimates are repeatable and show consistent trends

with angle of attack.

CONCLUDING REMARKS

A complete set of linear stability and control derivatives for a Beech

99 airliner was determined using a modified maximum likelihood estimator.

The derivatives were extracted for both the longitudinal and lateral-direc- tional modes. The maneuvers were flown in smooth air at angles of attack ranging from 1.5 to 4.5 degrees. The first Z9 maneuvers were flown in the cruise configuration and the last 27 were flown in a one-third flap down configuration. The one-third flap down configuration had little effect on most of the stability and control derivative estimates. All 56 maneuvers produced satisfactory results. In general, derivative estimates from flight data for the Beech 99 airplane were quite consistent with the manufacturer's predictions, which are based on a combination of wind tunnel data, analytical estimates, and flight test data.

Dryden Flight Research Center kational Aeronautics and Space Administration Edwards, CA, November 27, 1978 -,B t_ J APPENDIX A MAXIMUM LIKELIHOOD ESTIMATION PROGRAM AND EQUATIONS OF MOTION The analysis for this report was done with the MMLE-3 computer program, an outgrowth of the MMLE program (ref. 2). MMLE-3 is a general maximum like- lihood estimation program used at the Dryden Flight Research Center. This section briefly describes the features of MMLE-3.

The maximum likelihood estimates are determined by minimizing the dif- ference between the aircraft measured response and the calculated response determined by integrating the aircraft equations of motion. This response difference is formulated as a cost functional (discussed below). The min- imization of this functional is performed by varying the aerodynamic ;'oef- ficients in the aircraft equctions of motion.

In genera] form, the equations uf motion are: R(t) _(t) = A(t) x(t} + B(t) u(t) y(t) = C(t) x(t) + D(t) u(t) +Gq(t) The system matrices (R,A,B,C,D) can be time functions because of the varia- tions of q, V, B, and _ during the maneuvers. Time varyin§ matrices were not used in the analysis of the Beech 99 data, except for the maneuver shown in figure 5.

The maximum likelihood estimates are obtained by minimizing the cost functional dt where _ is the vector of unknowns, z is the measured response, and y_ is the computed response based on _. MMLE-3 uses a Newton-Balakrishnan iterative algorithm (ref. 2) to perform the minimization.

The equations of motion used in this report are given below. In many cases, average values of parameters are used to obtain time invariant system matrices. These equations of motion use small angle approximations for 6, but not for _, B, or _. Symmetry about the XZ plane is assumed. All engles in these equations are in radians. The longitudinal state equations are: (_ = - m_V S CL + q + V _ (cos O) (cos _) (cos e) + (sin B) (sin a)

[ ]

_Iy = qSc C m

O = q(cos ¢)

The longitudinal observation vector consists of the state vector concatenated with an observation of normal acceleration. The equation used for computing normal acceleration is: _]S CN + XAN an = mg _ _ In e)'panded form, the longitudinal aerodynamic coefficients are: C N CNaU 6e + = + CNG CN 0 e Cm = Cm_ + 2_V + Cm 6 e + Cmq Ge Cmo and C L = C N (for low o) The lateral-directional state equations are: = m_V S Cy + p(sin _) - r(sin a) + _v(COS O) (sin (_) (hi x - hIxz = qsb C_ #I X - lblxz = qsb Cn @ = p + r(cos _) (tan O) The lateral-directional observation vector consists of the state vector con- catenated with lateral acceleration given by: _ ZAY XAY ay = m_g S Cy g _+ _ g

-'I

In expanded form, the lateral-directional aerodynamic coefficients are:

Cy = Cy _ + Cy 6 + _r +

5a a CY6r CYo

+ 6 +

+ C_p_+ C_rrbC_6 6a C£6 r

a r C_O Cn = Cn_ + C n _ + Cnrr _ + Cn6 6 p a + Cn6 8 r + Cno a r APPEND,X i,

"MANUFACTURER'S DERIVATIVE ESTIMATES"

Reference 5 contains the manufacturer's estimates of the total force and

moment coefficients of the Beech 99 aircraft. These estlmates are in an ana- lytical form which permits generation of stability and control derivatives by partial differentiation. These derivative estimates are valid for both the cruise and one-third flap configurations with the exception of the two esti- mates of CL . The resulting derivative estimates are functionally dependent on the thrust coefficient. The derivative estimates and methods of the manufacturer are presented here to allow direct comparison of these estimates with flight results.

The longitudinal derivative estimates are as follows: C L 0.096 + 0.151T c p_r deg (Cruise) C L 0.101 + 0.151T c per deg (I/3 flap) Cm = O.OlO + O.OlO Tc per deg _c/4 Cm5 = -0.034 - 0.032 T c per deg e Cm_ = -43.1 per tad Cm = -3.40 per rad q The lateral-directional derivative estimates are as follows- C = 0.014 - 0.0015 T per deg nB c -0.0023 per deg c_ Cy@ = -0,010 per deg C -0.0014 per deg n6 y- 0.00017 - 0.000022 _ per deg

Cy6 = 0.0025 per rad

r C -0.20 - 0.197e per rad n r +0.05 + 0.623_ per rad C£ r CYr = 0.394 per tad 0.0079 - 0.762e per rad Cnp C£p = -0.515 per rad -0.199 - 0.38_t per rad Cyp C£6 = 0.0027 per deg a -0.0015 per deg TOTAL THRUST where T C qS At the steady state, low angle of attack conditions at which derivative extraction maneuvers were performed, the following approximations are valid: W C L - i Tc = CO From reference 5" CD = 0.0275 + 0.0625 CL2 Thus, Tc = 0.0275 + 0.0625 { W y

\qS !

.... CC_ This equation shows that the cruise thrust coefficient is a function of dynamic pressure, q, alone, because W and S are known constants.

W = 39.59 kN S = 26 m 2 _Jb_tituting these known values into the thrust coefficient equation, 0.145 T = 0.0275 +_ c During the Beech 99 flight, dynamic pressure varied between 2 and 5 kN/m 2.

Tc ranged from approximately 0 to 0.1. With this in mind, the Beech derivative estimates for the airplane were computed at the Tc extrema, and these estimates were plotted with the flight-determined derivatives.

ThL derivatives Cm and Cn_ must be resolved to a flight center of acl4 gravity position of 26 percent of the mean aerodynamic chord. This is ac- complished in the following equations: Cm = Cm - CL (CGflight - CGc/4 )1 ac/4 e Crib Cn_Beech Cy_ (CGflight CGc/4)(c/b ) For T = O, C C = -0.0289 per deg m C = 0.0014 per deg nB and for T = 0.1, C C = -0.0313 per deg m CnB= 0.00125 per deg mean percent aerodynamic 1Reference center of gravity (CGflight) is 26 chord.

li REFERENCES I ° I1iff, Kenneth W.; and Taylor, Lawrence W., Jr.: Determination of Stability Derivatives From Flight Data Using a Newton-Raphson Minimization Technique. NASA TN D-6579, 1972.

.

Maine, Richard E.; and Iliff, Kenneth W.: A FORTRAN Program for Determining Aircraft Stability and Control Derivatives From Flight Data. NASA TN D-7831, 1975.

.

Jenks, Gerald E.; Henry, Howard F.; and Roskam, Jan: Flight Test Results for a Separate Surface Stability Augmented Beech Model 99. NASA CR-143839, 1977.

.

Iliff, Kenneth W.; and Maine, Richard E.: Practical Aspects of Using a Maximum Likelihood Estimation Method to Extract Sta- bility and Control Derivatives From Flight Data. NASA TN D- 8209, 1976.

.

Agnihotri, A.K.: Engineering Aerodynamics Report (BAR I050) - Aerodynamic Data for KU/Beech AACS Test Bed (PD 280). Beech Aircraft Corp., Report No. E 22213 ASC, Sept. 12, 1972 TABLE I. GEOMETRIC CHARACTERISTICS OF BEECH 99 AIRPLANE Wi ,Ig: Reference area, m2 ....................................... 26.01 Reference chord (mean aerodynamic chord), m .............. 1.98 Reference span, m ........................................ 13.98 Aspect ratio ............................................. 7.54 Ailerons: Area, (total)m 2 .......................................... 1.29 Chord, m ................................................. 0.28 Span, (each) m ........................................... 0.24 Flaps: Area, (total) m2 ......................................... 3.51 Span, (each) m ........................................... 3.78 Chord, m ................................................. 0.08 Horizontal tail- Area, m2 ................................................. 9.29 Span, m .................................................. 6.82 Mean aer-lynamic chord, m ................................ 1.41 Aspect ratio ............................................. 5.0 Angle of sweep, deg ...................................... 17.0 Elevator: Area, m 2 ................................................. 2.45 Mean aerodynamic chord, m ................................ 0.39 Vertical tail: Area, m 2 ................................................. 4.17 Span, m .................................................. 2.32 Mean aerodynamic chord, m ................................ 1.92 Aspect ratio ............................................. 1.29 Angle of sweep, deg ...................................... 19.5 Rudder: Area, m2 ................................................. 1.12 Mean aerodynamic chord, m ................................ 0.55 Reference center of gravity, percent of reference chord ..26.

t TABLE 2. MASS DATA FOR BEECH 99 AIRPLANE Full Fuel Condition Mass, kg ................................. 4036.15 CG, percent of reference chord ........... 26% IX , kg - m 2 ............................... 16,900 Iy, kg - m2 .............................. 23,900 IZ_ kg - m2 .............................. 38,900 Ixz, kg - m 2 ............................. 3,520

TABLE3. INSTRUMENT LOCATIONS RELATIVE TO REFERENCE

CENTER OF GRAVITY Distance Forward of Distance below

Instrument

Reference CG, m reference CG, m B 7 0 a n 0.381 ax - - - 0.102 ay -1.5 0. I02 TABLE 4. INSTRUMENT RESOLUTIONS FOR BEECH 99 DATA Signal Resolution 0.07 deg 0.08 deg p 0.25 deg/sec q 0.08 deg/sec r 0.08 deg/sec e 0.18 deg 0.35 deg a O.Olg n ax O.O02g a O.OOlg Y 6 a 0.08 deg 6 e 0.06 deg 6 r 0.10 deg V 0.07 m/sec _p TABLE 5. MANEUVERS AND FLIGHT CONDITIONS Case Flap Dynamic Thrust Angle of Velocity, mlsec Number Setting Pressure, Coefficient Attack, kN/m 2 deg. deg.

1.7 99 0 l 4.73 0.034 1.7 98 0 2 4.62 0.034 1.7 97 0 3 4.56 0.034 1.6 99 0 4/8 4.77 O. 034 1.6 98 0 5/7 4.68 O. 034 O. 034 1.6 101 0 6/9 4.67 lO 4.95 O. 034 1.9 100 0 II 4.56 O. 034 1.8 100 100 0 12 4.61 0.034 1.8 lO0 0 13 4.63 O. 034 1.8 1.8 98 0 14/17 4.50 0.035 1.8 99 0 15118 4.69 0.034 0.035 18 97 16/19 4.53 99 0 4.83 0.034 15 21 4.75 0.034 1 6 98 97 0 22 4.67 0.034 I 5 97 0 23 4.65 0.034 I 5 99 0 24/26/27 4.80 0.034 I 5 I 5 lO0 0 25/28/29 4.80 0.034 0.057 32 67 15 30 2.23 0.057 34 67 15 31 2.20 32 2.20 O. 058 33 67 15 33 2,]7 O. 060 3.5 65 66 15 34/37 2.10 O. 058 3.3 68 15 35/38 2.25 O. 056 3.1 67 15 36/39 2.22 O. 057 3.2 4.2 65 15 40 2.04 0.062 0.060 4.4 66 15 41 2.07 0.061 4.4 65 42 2.09 0.061 4.3 65 IS 43/46 2.08 0.063 4.4 64 44/47 2.03 0.062 4.3 63 45148 2.04 2.24 0.056 3.0 66 66 15 2.20 0.057 3.1 65 15 5l 2.15 0.059 3.1 65 15 52/55 2.14 0.059 3.2 0.059 3.2 66 53/54/56 2.16

.j

P TABLE 6. WEIGHTING VALUES USED IN ANALYSIS OF BEECH 99 DATA Signal Diagonal element of G INVERSE a 35 per deg q 45 sec/deg e 55 per deg 3nn per g 8n _- 42 per deg p 8.5 sec/deg r 40 sec/deg ¢ 15 deg a 500 per g Y A c) Figure 1. Beech 99 airplane. Dark areas denote extra control surfaces which remained in fixed positions during the test flight.

2O i U h

in

_ll &.

Figure 2. Three views of the Beech 99 airplane.

F

J Measured i - - calculated deg

k

_ r a n , _F

I

I

,i

de9

oL

1o qr deq/sec L +IO F J

i /\

deg ! V +" L o I _ 3 4 Time, SeC Figure 3. Typical longitudinal maneuver, calculated ckeg

°'_ _ _

ay, q -O,L _e_ 40 r -4o _- -Z u Time, see (al A_ler_h _ublot Figure 4, lypica I %aterol.directiOnal d(lut_le i,_neuwer'.

o ,t, p o ,-...... \_ deg ,,./ -I0 _- ay, q lot • : C _ -_,.-,,_..._-_'_::=':'" i \ r-, ?'_ ,.

o_'_c, _ _ _._ _,_." -

2,t de_ 1 _e_ t L 0,2 r ay, 0.0 .__J- \ -:CO '- ..

Flap deflection, deg

4-

O o [] 15 Manufacturer's estiinates C_ Uncertainty level ?- C N T per deg I i i -4 Tc= 3.i Tc = 0 Q(} .-4 t _'__o 4'.00 5_.00 61.00 ! .DO 2.00 L.O0 c_, deg C_ Flap deflection, deg O o []15 .... Manufacturer's estimates --T-- L Uncertainty level T Q 7 " ..-e C ze in l_ c3 per deg #.

(: All T c f9 00 {.oo {.oo --_'.oo 4'.oo e'.oo s_.oo _,deq (a) CN, Cm_ Figure 6. Summary of longitudinal derivatives.

Flap deflection, deg O 0 Manufacturer's estimates Uncertainty level &D CD O T i 4 _D T c = 0.i .-4 c N _'.

_e T c = 0 per deg ,3.

_D 2-r. O0 r" r 'r 1 3.00 4.00 5.00 6.00 '_o.oo _.oo _, deg Flap deflection, deg [] 15 .... Manufacturer's estimates (D -r- Uncertainty level O (%1 ";' o.

.-w 31I ,o ¢,,,) o.

C,mSe T = 0 !

c F per deg O T c = 0.I =o I r- ¥ 6.00 3'.00 4.00 5.00 ]_,00 2T.OO '_, deg (b) CNh o, Cmh e Figure 6. Continued.

C_ Flap deflection, deq O 0 [] 15 Manufacturer's estimates C_ -[ Unc_ctainty level CI i C m q All T per rad c Q C3 1' "I Aoo 2_,o_ ' 4".oo _ .oo JO.O0 3 .On S .00 :_, deq (c) c mq Figure 6. Concluded.

Flau deflection, deq _]15 -- __ Manufacturer's estimates _ Uncertainty level ¢9o M Cn8 T c = 0.i per deg TC = 0 C3 O '::b.00 1.00 2'.00 3'.00 4'.00 5'.00 _.00 _,deg ° Flap deflection, deg O 0 _15 - Manufacturer's estimates C_ o.

___ Uncertainty level o o?- ¢4 C p All T per deg c ?.

O _o.oo ,loo _oo 3'.oo ,'.oo 5',_ Aoo r_,deg (a) Cnp C_# Figure 7. Summary of lateral-directional derivatives.

' i Flap deflection, deg _315 Manufacturer's estimates Uncertainty level

±

-" "--"_ All T c % b

?0%0 £oo 2'.oo _'.oo ,'.oo

5.00 6.00 _,deg ¢'4 =;- Flap deflection, deg [] 15 Manufacturer's estimates (D Uncertainty level Q ,_L--- o" (D ¢W (D C :,- P.

p I] All T per rad o _r ,m c %

l

t

F I

_'o.%o

2.00 3.00 4"r. O0 b. OFl F ._qU _, deg

(b) C_

Cnp ' p Figure 7. Continued• s Flap deflection, deg O 0 _15 Manufactu[er's estimates Uncertainty level

i

] C_ r per rad -- A11 TC O 5'. O0 6.00 ,00 l'.O0 2.00 3.0D 4'.00 e,deg o Flap deflection, deg & O 0 _15 Manufacturer's estimates Uncertainty level g _J_ O _4 _t &- r per rad All T c O r ¢3 #4 I '1 !'oo Loo 4.00 5'.00 6.0_

%

,00 I .00 _,deg (c) Cnr, C_r Continued.

Figure 7.

m Flap deflection, deg []15 ...... Manufacturer's estimates T_ Uncertainty level o m C _a A11 Tc per deg ?- O

_.oo 1',0o

2'. O0 3'. O0 4'. O0 B'. O0 6'. O0 a, deg LO Flap deflection, deg O 0 []15 Manufacturer's estimates _t Uncertainty level -l _1_ qc_ All T c a per deg 6- 1" .oo t'.oo 2'.oo 3_.oo 4.00 _.oo s_.oo ,deq

(d) C , c_

n6a 6a Figure 7. Continued.

L O O- Flap deflection, deg O 0 _315 Manufacturer's estimates O Uncertainty level o AlI Tc m C n6 r per deg o ¢N o o !

%%°

I'.00 2'.00 3'.OD 4.00 _'.oo 6'.00 cx,deg O Flap deflection, deg 03 0 _15 Manufacturer's estimates (D Uncertainty level CD CD ! • C3 -_ c per deg AlI Tc T ,0O I .O0 _.o0 D0o 5'.o0 e.oo ,de_ (e) , C_ Cn8 6 r r Figure 7. Continued.

b _4 Flap deflection, deg o 0 [] 15 _ Uncertainty level ¢m J Cy. :_.

0 a per deg I'.00 5 .CI8 6.013 2.00 3.00 4.00 x t d e q Flap deflection, deg O 0 [] 15 Manufacturer's estimates Z Uncertainty level

T

Q.-, ]I Cv 6 r per deg All T C i i' I'.00 2.00 3_00 4'.00 5'.00 6.00 r .00 _,deg A (f) Cy , _,, 6a '_" Figure 7. Continued.

T e4 Flap deflection, deg _315 -- -- Manufacturer's estimates O Uncertainty level O .-4 O

ITT

C y i_ D All T c t per deg (D N o (D I e9 T ] ! •O0 2'. 00 3 •00 4'. 00 5 _. O0 6'. O0 '0.00 ,d erl (g) Cy_ Figure 7. Concluded.