Estimation of Handling Qualities Parameters of the Tu-144 Supersonic Transport Aircraft from Flight Test Data

APPENDIX A - MANEUVER DESCRIPTION

The pilots and test engineers were briefed before the flight test program and the experiment objectives and test procedures were explained. Descriptions of the individual test procedures for each of the maneuvers used in the handling qualities prediction are taken from reference 10 and given below: Pitch Frequency Sweep Conditions: Minimal Turbulence, Autopilot Off, Autothrottle Off, No Throttle Position Changes 1. A test engineer in the back of the airplane should carefully monitor the control column position, load factor, and pitch attitude time history responses plotted on a computer screen in real time during this maneuver. The time scale should be expanded so that a frequency limit of TBD cycles per second for the input can be easily judged. Once this frequency limit is reached, the engineer should tell the pilot to stop making inputs to prevent excitation of the 2.5 cycle per second first bending mode of the airplane.

2. Trim airplane for hands off level flight. Do not retrim during the remainder of this maneuver.

.

Begin data recording and record 5 seconds of hands off level flight data.

4.

Slowly cycle the control column back and forth with an amplitude large enough to obtain +/- 0.2g load factor and/or +/- 5 to 15 degree pitch attitude excursions.

Make two complete 20 second cycles of the control for a total of 40 seconds of input. The cycling of the control should be centered around a position that produces airplane oscillations that center around the trim pitch attitude. Control wheel and rudder pedals should be used to minimize roll and yaw response.

5. Slowly increase thefrequency of theinput. Adjustinputamplitudesothatthe

amplitudeof airplane motionremainsaboutthesameasin step4. It is importantto

increase frequencyslowly,sothatthereis enough middlefrequency contentin the

data. Whenthe amplitudeof airplanemotiondropsoff sharplyor the input

frequency reaches TBD cyclespersecond,stoptheinput. Shoulda structuralmode

become excited,terminate inputimmediately.Thecombinedinputsfor steps 4. and

5. shouldlast about80 - 100seconds.

Record 5 seconds of hands off data at the end of the maneuver.

.

- 2- Roll Frequency Sweep Conditions: Minimal Turbulence, Autopil0t Off, Autothrottle Off, No Throttle Position Changes 1. A test engineer in the back of the airplane should carefully monitor the control wheel position, roll rate, and roll angle time history responses of the airplane plotted on a . - .- =q • ..... computer screen in real time during this test. The time scale should be expanded so that a frequency limit of TBD cycles per second for the input can be easily judged.

Once this frequency limit is reached, the engineer should tell the pilot to stop m',ddng inputs to prevent excitation of the 2.5 cycle per second first bending mode of the airplane.

.

Trim airplane for hands off level flight. Do not retrim during the remainder of this maneuver.

.

Begin data recording and record 5 seconds of hands off level flight data.

.

Slowly cycle the control wheel back and forth with amplitude large enough to obtain +/- 5 to 15 degree roll angle excursions. Make two complete 20 second cycles of the control for a total of 40 seconds of input. The cycling of thecontrol should be centered around a position that produces airplane oscillations that center around a ,i wings level roll angle. Rudder pedals should only be used if the airplane oscillations do not remain centered about the initial heading angle. Control column should be used to minimize pitch response.

. Slowly increase the frequency of the input. Adjust input amplitude so that the amplitude of airplane motion remains about the same as in step 4. It is important to increase frequency slowly, so that there is enough middle frequency content in the data. When the amplitude of airplane motion drops off sharply or the input frequency reaches TBD cycles per second, stop the input. Should a structural mode become excited, terminate input immediately. The combined inputs for steps 4. and 5. should last about 80 - 100 seconds.

Record 5 seconds of hands off data at the end of the maneuver.

.

Yaw Frequency SweeJ_ Conditions: Minimal Turbulence, Autopilot Off, Autothrottle Off, No Throttle Position Changes 1. A test engineer in the back of the airplane should carefully monitor the rudder pedal position, yaw rate, and heading angle time history responses of the airplane plotted on a computer screen in real time during this test. The time scale should be expanded so that a frequency limit of TBD cycles per second for the input can be easily judged. Once this frequency limit is reached, the engineer should tell the pilot to stop making inputs to prevent excitation the 2.5 cycle per second first bending mode of the airplane.

2. Trim airplane for hands off level flight. Do not retrim during the remainder of this maneuver.

3. Begin data recording and record 5 seconds of hands off level flight data.

4. Slowly cycle the rudder pedals back and forth with an amplitude large enough to obtain +/- 5 to 15 degree heading angle excursions. Make two complete 20 second cycles of the control for a total of 40 seconds of input. The cycling of the control should be centered around a position that produces airplane oscillations that center around the initial heading angle. Control wheel should only be used if the airplane oscillations do not remain centered about a wings level roll angle. Control column should be used to minimize pitch response.

, Slowly increase the frequency of the input. Adjust input amplitude so that the amplitude of airplane motion remains about the same as in step 4. It is important to increase frequency slowly, so that there is enough middle frequency content in the data. When the amplitude of airplane motion drops off sharply or the input frequency reaches TBD cycles per second, stop the input. Should a structural mode become excited, terminate input immediately. The combined inputs for steps 4. and 5. should last about 80 - 100 seconds.

. Record 5 seconds of hands off data at the end of the maneuver.

Pitch Doublet Conditions: Minimal Turbulence, Autopilot Off, Autothrottle Off, No Throttle Position Changes 1. Trim airplane for hands off level flight. Do not retrim during the remainder of this maneuver.

2. Begin data recording and record 5 seconds of hands Off level flight data.

3. Pull back on control column sharply and hold input for 5 seconds, push forward on control column sharply and hold input for 5 seconds, and then release the control column to neutral position. Inputs should be large enough to produce +/- 0.2g load factor and/or +/- 5 to 15 degree pitch attitude excursions. Control wheel and rudder pedals Should be used to minimize roll and yaw response.

Record 60 seconds of hands off data at the end of the maneuver.

.

%.: ._:--_ 7. '_ :=_ ---- _-

i 44

Roll Doublet Conditions: Minimal Turbulence, Autopilot Off, Autothrottle Off, No Throttle Position Changes .

Trim airplane for hands off level flight. Do not retrim during the remainder of this maneuver.

, Begin data recording and record 5 seconds of hands off level flight data.

3.

Rotate control wheel sharply one direction and hold input for 5 seconds, rotate control wheel sharply the other direction and hold input for 5 seconds, and then release the control wheel to neutral position. Inputs should be large enough to produce +/- 5 to 15 degree roll angle excursions. Control column should be used to minimize pitch response.

. Record 60 seconds of hands off data at the end of the maneuver.

Yaw Doublet Conditions: Minimal Turbulence, Autopilot Off, Autothrottle Off, No Throttle Position Changes ° Trim airplane for hands off level flight. Do not retrim during the remainder of this maneuver.

, Begin data recording and record 5 seconds of hands off level flight data.

3.

Push one rudder pedal sharply and hold input for 5 seconds, push the other rudder pedal sharply and hold input for 5 seconds, and then release the rudder pedals to neutral position. Inputs should be large enough to produce +/- 5 to 15 degree heading angle excursions. Control column should be used to minimize pitch response.

. Record 60 seconds of hands off data at the end of the maneuver.

APPENDIX B - ERROR PROPAGATION

The standard errors of the generic parameters introduced in (3) and (4) are not equivalent to those of the transfer function coefficients of the models from the military standard; however, the estimated standard errors can be used to estimate the errors of the desired coefficients through a linearized error propagation formula. Reference 20 explains uncertainty analysis in detail, but a short development of the theory and application to an example on the longitudinal mode is presen!ed below.

Consider a general case in which an experimental result, x, is a function of N variables, y_: ? _ - . ° , , : - x = x(y I, Y2, "'", YN)- (33) Equation (33) defines how to determine x from the known value of the variables y,. The uncertainty in the result is given as L t,°y, , LoyzO× +'"+L0y N XN , (34) where the Ux.i represent the uncertainties in the dependent variables y_.

The uncertainties of the estimated parameters and their functional dependence on the military standard coefficients are known; thus, equation (34) can be used to determine the desired standard errors. For example, the short period damping ratio is given in terms of 7 - : : the estimated generic parameters as (35) Applying (34) to (35) yields

%. = It, akj t, ako _ko

(36) = +CYk, + . kl 4k3/2 Ok0 Similarly, for the remaining coefficients, _t0sp = 2k_------i(Yk0, (37) and (38)

=( B '/=

(YI/T02 = (IB) +[.--'_-(YA) J " The errors of the final two parameters, K e and "c, are estimated directly.

These error propagation formulae were used for all of the estimated parameters; however, they are only linear approximations of the errors. The first-order analytical functions were validated using a Monte Carlo simulation which multiplied a random variable with a mean of zero and variance of one by the standard error of each estimated parameter.

The product was then scaled by adding the estimated parameter value. For example, for the parameter k0, a new parameter, k0', was created as !

(39) k 0 = k 0 +G(ko)*r, '=:[ : 7:7_:=:=: 5 2 := =: = ?

where r represents a Gaussian distributed random variable. The Monte Carlo estimate of the short period natural frequency is then 7 : (4O) A random number generator was used to crea{e=iO00 values for-r and thus 1000 Gaussian distributed values for tO_p. The mean and standard deviation of the Monte Carlo simulation should be very close to that estimated by the analytical functions. ;The other variables were checked in the same fashion. Figure 22 illustrates the distribution of each of the checked variables for the parameters estimated from test point number 2.4-16.1A. A small table on each plot indicates the mean value and standard deviation for both the analytic function and the Monte Carlo simulation. These values indicate that the simulation validated the analytical functions.

TABLE 1: Summary of geometric, mass, andinertiacharacteristics of the Tu-144.

196 ft l0 in (60.0 m) Length 88 ft 7 in (27.0 m) Span 98 ft 8 in (30.1 m) Nose Tip to Leading Edge of MAC 76 ft 5 in (23.3 m) Length of MAC 4716 ft-' (438 m _) Wing Area 1.66 Wing Aspect Ratio 76 deg Wing Sweep, Inboard Portions 57 deg Wing Sweep, Main Panels 303,000 lb (138,000 kg) Weight* 38,805,000 lbf-ft-' (1,635,000 kg-m 2) Roll Axis Moment of Inertia, Ixx* 417,797,000 lbf-ft-' ( 17,606,000 kg-m _) Pitch Axis Moment of Inertia, Iyy* 450,222,000 lbf-f( (18,973,000 kg-m z) Yaw Axis Moment of Inertia, Iz_* -6,486,000 lbf-f( (-273,000 kg-m _) Roll-Yaw Product of Inertia, I_z* * Average values over all yaw frequency sweeps.

+1 +t +J +1 +! +1 +1 +1 +1 +1 +1 +1 +1 +1! +1 +1 +1 +li +1

2_

_,IJ,-- _o m ¸[..3 -u -u -u _ i_._ = I,,_ u-1 _ ." + + +++!

_ _ _._ _i_._ ID.., + Z <Z Z< <,< _<<<_ =_ E = • -= ":d @ "_ "_, "= -, _q U.1 ,_,t < F-, •- = _': _ _ _ _ ._ ,.,'_ '_ _. _ :-_-:-2_- '= '_ = ._ _ = g _= IE i E Zi

_-,,. ._ _ =_<<<_ .-

_"2_

i

o., _-- _ -__ __ >

L < i['- _r.j _Z Z_ __=

!

5O z TABLE 3: Coordinate location of instrumentation.

Parameters X (it) Y (it) z (it)

-4.4 -2.7 Airspeeds & Pressures Angle of Attack + 15.7 - 1.4 [ -2.4 Sideslip + 15.7 + 1.0 [ 0 Rate Gyros & Accelerometers + 106.6 - 1.3 +2.46 Notes: • The origin of the coordinate system is at the base of the nose boom/tip of nose cone.

• Axis System: +X is measured longitudinally from nose to tail +Y is measured vertically up +Z is measured laterally out the right wingtip Note that this is a left-handed coordinate system.

o o o o o olo olo _ o o E °_ I-- o rn o oo o oloo o o_ oo E 0 __000_ O_ "C" I-- _D I:: V) _D ._m II o Z ¢0 C') CO OD CO OD CO 09 CO CO 09 09i > .,.,t

• oooOoOo i

-a c_ ooooloooooooo Z Z • ± _ • : =_

&

O_ r..)o n_ 0 i © ,_._ _, cD (=) ,",,'-04C',1C'4¢%1_--,-'',--'_--':'-i':-- > •_ _ © 00_00 ,...., O00iO00 u.

4) !=" 7 _ _ ._ 0 _.-' _ _ _ '_-_ = A_"_ t_ _n • i_ ----N_i _ < 4) I--

=_gZoo oo

g_m_oo oo

._._O0_i_ 0 II II II II II II II II <m<m<m<!m<m<m IIIIl!ll!lliltl 0000000000_ 00_0_00_ _00 000000,_ 0 _,_ _ _ 00 _ _,0 _ 0 _ _ _ _ _i O_ _ _ 00000 __ _ _ _ _ ............ i ...... i .............. _ .......... | • • 0 _ _ _ _ _ _ 0 _ _ _ _ _ 0 0 0 010 0 0 0 0 0 0 0

® o!ooooooooo_!_oo,o_o_oo!_oo

_ _0_ _0 _ _0_ _ _ _ _i_ _ 00_ _ _0000 ____ _ .......... i,,i ...... i .............. i .................

_ _ _ _ _!_ 00 _ _ _ _ 000000000000

Z-

u.

• oO oOoOoOoOoOOoOoOoOoOO oOoOoOOoOOoOoOOoOoOoO

oo oooooooooooooo oooooo

• _ _ _ __ o o

._ ._ ._ ._ ._ ._ ._ ._ _ _ ,_ m ._im ,<m Z I1.

I"-

oi o o o ojo o o o o o ol

E oo°oioo°°°°_ °- i .......... : .... ............

"" G'_ LO cO _ LO CO _ C_I ¢0 1,0 _0 CO 0_0_ i __ I_ _ ....................... i .... .............

.... ............. o _ _ c;i_ _1_ _ _ a;

o _ oo_, gi-_g_'_.'_2°°°°i°°'°°°°°'°

_L _i_ .... 1 .... I " " "1 ........ l "1 * ..... _ " _ = oooooooooooolooo oooooooooooo

. ggggo oooooggogooggogggggg_o_o_ggg gg

hZ._- o o o o o g o o g g o g o,_ ,- ,_., g ,_o _,_ _ o _io i _

:

ooo

QQ ....... _ ____ -_-_._-_-_-_-__-_.-_-_-_-_wwwwwwwwwwww,,..,.

._._._._.._._._._.._._._.._._._:._wwwwwwww _ <mo<mo<mo<m<m<m<m<m<m<m<m<m ..i ..... i..,i ........ i,i.

_NNN'NNNN'NNN'NNNN N NNNNNNNNN'N E 00_0000000_00000

o _oooogooo_

..__ .._ ..

.- ___v._v_ _ _ _ _ _ _0_ 0_ _ 0 ____'___ •. _,_,_,_ _ o 000000_i0 O0 .................... | ..............

iO 0 _ _ 000000 _ _ 0000 _ i_ i i ' _ioooo!oooiooo'ooiooiooo io oo 'oo'oo'ooo

_o o

ooo§ioOOoOOO o oOOoOoOoOoOOioOoOo °

E Z I-- 0'00000000000 00000000000!0 o o o o o ooooo olo o o o o!ooio o o oo o .... '.l..!.i.

_ ._ 000000iO00000 O000000000 _= _ ooo!ooooooooo oooooOOOlOOOO 00000000;o00oo00oo0000000 X X X X X X X X X X! X X X X X X X X X X X X X Xl _ _ W W W W W W _ W W WIW W W W W W W W W W W _iW Wl .g <m<_m<m<m<m<i_<m<m<_<m<m<m Z iiiit11111 III IIIIIII NNNiNNNINN_N NiNNN_NNNNN_N TABLE 5: Recommended Short Period Requlrements for Class III, (a) Category B and (b) Category C (a) Cate_ . B 17, see Max _sp Min rosoT02 Level Min _sp , ,,,,,,,,,, 1.00 1 0.30 2.00 0.10 0.60 2 0.20 2.00 0.20 0.25 (b) Cate_ . C Level Min _s,:, Max _ 1:, sec Min ro_pTo_, 1 .... 0.35 1.30 0_10 1.40 2.00 0.20 0.70 2 0.25 0.25 TABLE 6: Recommended Roll-Mode Time Constant for Class HI, Cate[_¢)ry B and C Level Max T R, sec .............

1 1.4 2 3.0 3 10.0 TABLE 7: Recommended Dutch Roll Frequency and Damping for Class III, (a) Category B and (b) Category C (a) Category B Level Min _d Min _jroj Min roa 1 0.08 0.15 0.4 2 0.02 0.05 0.4 0 -- 0.4 (b) Catego_ C Level Min _d Min _arod Min rod 1 0.08 0.10 0.4 2 0.02 0.05 0.4 3 0 0.4 TABLE 8: Normalized pairwise parameter correlation matrices from simulated data for (a) EEM for one measurement, (b) EEM for two measurements, (c) OEM for one measurement, and (d) OEM for two measurements. Shaded values indicate those defined as having a high correlation.

k I k o B 1.000

i

0.027 0.673 0.030 0.768 (a) kl .

1.000 0.735 0.790 0.807 0.875 (b) kl 1.000 -0.085 1.O00 0.956 -0.292 -0.136 0.896 0.888 (c) k o 0.990 0.890 (d) OCt. 00') OJ'r- 090,,I O,ICO .r-O_l ,T-CO I_.CO _'0'5 OOJ 0 _-" "_- 0 ",-" 0 O0 0 O0 0 O_ 0 O0 0 tO O T- 0 T- 0 0 0 0 0 I_ OJ 0 0_. 0 T- 0 T- 0 T- 0 "r- 0 OJ 0 00. 0 OJ 0 0,1 0 O,.l 0 66 66 66 66 66 66 66 oo 66 66 66 L.

W .r- I_- 0000 O'f- _.- 0,1 .v-- O_ ,_- LO k"_l 0') _-- OJ T- '_- O_ t.O t_ O,I 0,.I (_0 0,.I O) OT- ,,_. T- 00_- I_ ",-- 0_1 CO r,,o "_" I_ r..D 0_ LO I_ I._

_s O O 00 O tO O t,Q O tO O LO O O_ O O,I O O O I"- 0 L'_I O

6 6 .....

T- O O O T- O '1"- 0 _- _'- O 0,10 0,1 0,10 T- O T- O ¢= 0 _" I_ CO "_'1"_. 0000 i'_. OJ 0)(3") (.O '_J" I'_1_. OO tO (.O I_. "_t" (_ CO 00 03*- tO O "_" 0 O0 _-" (,O 0 O0 _,'- 0 _'- I_ C_I 0") _" I_ _0 O0 0 O0 .r- CO 0 CO 0 0") 0 03 0 tO O (.O 0 r,.O 0 I_. 0 I_ 0 66 66 66 60 66 o6 06 66 66 66 6o ._ _ 6 o .... 6 6 6 o o 6_ L_ n_ ¢.3 O O O O O t- t- ('- < t- t- c- t- C C 0 O O ._O O [..

O" O" O" O" O- O- _ "_ O O _ ¢) (_ _) (I) • o _ o o '-'u u _,, _ _ I-- I-- r_ r7 n r'n O rO _0 _0 O0 O0 O0 O0 _0 _0 _0 _0 _0 _0 _0 _0 _0 _0 _0 _0 _0 _0

oo 6o oo oo o6 oo 6o 6o 6o 6o

o

W _ _ _0 _0 _0 _0 _0 _0 _0 _0 _ O0 . .

v v v v v v v v v v m O_ _ _ _ _ _ O_ _ _ _ _0 _0 _0 _0 _0 _0 _0 _0 _ _0 oo oo 60 60 oo 60 60 6o 06 oo W _ _ O_ _ 0 _ O_ O_ _ _0 _ > _ oo 66 o6 60 6 6 06 06 06 o6 _ _ O_ O_ _ _0 _0 _ O_ _ _0 _0 _0 _0 O0 _0 _0 O0 _0 _0

_o _o _o _o _o _o oo _o _o _o

v v _ v v v v v v v O4 09 CO 09 ,,'- 04 r,,.. _ 0 0 (1) UO [,..) .,r, "0 N " _ 0 .a 0 ,.¢, < e-- or) (19 09 0 CO ",-- 0,1 _,-- 0.1 09 CO O9 09 09 O9 09 09 O9 i 0 0 0 0 0 0 0 0 0 .-- _ o ut.

¢,) 6O _.1 0 0 0 0 0 0 o 0 0 0 0 Z d d d d d d o d o o d A A A A A A A A A A A ,,e- to n- © C_ o t.- t- "0 0 0 OJ OD OJ ',-- _'- I_- _t 0 0 CO (_0 O) CO (0 0 0 0_1 (_ _ _-- '_-- ',-- _ 0_1 0_1 OJ o o o o o o o o o o o © I-- k- 0 0 0 0 0 0 -_ LL _ LL -Q LL _ LL _ tl.

c_ I-- I-- Z a_ o > _.1 0 0 0 0 0,--_ 0 0'-" 0 0 0 0_1 ",'- 0,1 0,1 Oq v 0,1 ",-" V "- ,v- T- Z O d o o o ,-, o d _, d d d A A A A A _-_ A A _'--_ A A A t- O rr o ._1 O m m m rn 0 0 0 0 0 0 o o O 0 _ '_- _ 0,.I _ _ _ (D 0'_ O_ 0 0 0 0 (Dr) 0"_ O_ I_ m 0 0 0 0 0 0 0 0 0 0 .< [..

iz o I'- Z n t--

TABLE 11" Average parameter estimates for differentflight conditions.Pitchrateto

longitudinalsticktransfer functioncoefficients.

Flight Condition

K0

_sp _sp

0.3 < M < 0.4

8.2<t_ < 11.0 1.2 0.76 1.15 0.74

0.8 < M < 0.9

6.0 < tx < 6.2 1.9 1.2 0.64 2.2 0.22

1.2<M< 1.6 0.19 0.75 0.36 4.8 < o_< 6.4 1.55 0.39 0 0"_ LO (.0 LO "c:_" ,-- _" CO 0") 0") LO 00 03 0 04 ,_" CO 0 _:t w.. _" ('Y 0 wJ" 0 ",-- 0 ",- 0 LO 0 O0 0 LO 0 0') 0 OJ. 0 I_... 0 CO O I._ ",- 0 ,-- 0 "_"- 0 ",-- 0 ",- 0 ",-- 0 ",- 0 ",-" 0 ",-- 0 ",,-- 0 ",-- 0 6666 6666 60 66 6o 66 66 66 66 v v _ v v _ v v v &.

ILl •_ OCt) 0 "_" LO "T-- 0)','- LO _'-- ",--04 "r-O,I 0)'," LO','- OIL") OO LO "0 _ O) 0 O0 0 _:t 0 CO 0 ":t O LO 0 04 0 O) 0 0 0 O0 0 1"-. 0 lb.

,. 06 06 .-6 .-o .'-o _-o .-o oo .-6 06 60 C CO 00 CO O0 _ CY O_ 0 (.O 00. O_ LO LO _" O_ _" L.O I_ LZ'_ 0_t LO O_ O0 CO O0 _ O_ _ _ _ O0 r (0 _ 04 0,1 CO T- rO T- 0 I._ 0 LO • _-" 0 04 0 T-- 0 T-- 0 0_1 0 04 0 I_ 0 '_" 0 LO 0 LO 0 U'_ 0 6o o6 66 6o o6 66 66 o6 66 6o 66 v v v v v v v v v v v •_ _ O_ _ _ _ 0 _ 0 _ 0 _ 0 _ 0 _ 0 _0 _ 0 _ 0 _ _ - _6 66 o6 o6 6o o6 o6 66 06 06 66 OO O 0,,11",.. O OO 01".. CO OO O') "r" OD CO O0 0O CO"-- I'..I".. 0)(.0 & 03",-" O_ 0 _0 0 ",-- 0 0 0 r..O "_- LO ," "_'- 0 T-- T- (.O 0 CO 0 ,.; o_o oJo ,_o _o coo ,-oo ,-oo oo _o _o _'o o 66 06 6o 66"66 oo ",-o ",-o "--6 o6 6o v _ v v v v v v v _ v o 0 (1) I'- • o o 04 _- 04 O_ 0 0.1 CO CO _ 03 CO (.0 T- _ 0"} O0 OD 03 03 a _ 6 o .... 6 6 6 6 6 e_ [.- o e-- or >- , _ 0 (I) • (I) • _ _ _ (1} 0 C.) r_ 0 rj 0 0 C: LL. C LL _- o o o o o o o o o (/3 Or) or) ._ O3 0 o3 co e., O3 O3 °3 _ °3 O') uo uo "7 "T "7 ' ' "7, "7 5 "T o4 cg ai & o,i _ o4 o4 _ ,",J O4U') "_I" I.O '_I" C") r..O _I" 0DI.O O'_" oO_ I'_ '_I" (JD C:_ I.O O "_I" O CO 0 '_I- O LO O 04 0 04 0 _,-" O T- O ",- O T- O ',-- E) T- O T- O ",-- O 66 66 66 66 6o 6o 60 6o im O In (_ 0 "f- "_I" _ _-- 0 I_. I'_ I_ (.O F",. I_ _ L_ _" I.i.I •-_ I_ _" C_I O_ _" CO _ O_ 03 03 C") O_ 0,1 CO L_ _" S _o _o _o _o _o _o _o _o oo o6 o6 66 66 60 66 66 c O'_r.,D 0_0") C_IO 0_I" COO 041",. _f,.D COI_ 04 0 03 0 C_. 0 C_I 0 03 0 CO O _-- 0 04 0 oo o6 oo 06 o6 o6 6o o6 m _- .,- o'_ _ _- _ _1. _- ,_. L_. Lo I_ 00 04 _1- _ _, co o 04 o 04 o _ o c,_ o _"_ o o_ _- 03 o - oo 6o 6o 06 66 66'66 o6 E m ft.

CO (:_ I.O (30 C_I CD O r,.D _ 1 _- 04 I.O 04 0 i'_. _ CO O CO O O_ O _ O O O I_00 (:0 1- _O O _'o _o ._o _o _o 0_o o_o _o oo 6o o6 06 06 oo oo o6 o O O O O O O O _ O O O O e-" _- e- c- im O o

O o e e

< m < m < nn < CO CO 03 CO CO 0O n _- T T T T T , !

_I" "_" _1" _I" _1" '_" O4 * : L TABLE 13: Average parameter estimatesfor different flight conditions. Yaw rate to rudder pedal input transfer function coefficients.

Flight Condition 1/T r 03d _r K r _d 0.3 <M<0.4 0.15 0.31 0.83 8.2 < a< 11.0 0.36 0.47 0.8 < M < 0.9 0.13 0.23 0.50 1.0 6.0< c_< 6.2 1.1 1.2<M< 1.6 1.5 0.15 0.56 0.35 0.23 4.8 <_<6.4 m IJ.

0 _" 0 o _1" _ _ ',- ",-- _ 0 ",-- 0 0 6 0 0 0 0 0 z-- TABLE 15: Average parameter estimates for different flight conditions. Roll rate to lateral stick input transfer function coefficients. First-order model.

Flight Condition 1/TR

Kp 'rp i 0.3 <M < 0.4 8.4 2.4 0.10 8.2 <_< 11.0 0.8<M<0.9 6.0 < c_ < 6.2 16.6 3.2 0.09 1.2<M< 1.6 2.0 6.7- 0.14 4.8 <o_< 6.4 _.. C7) _-- 0_ 0 I"_. 0 I'_ 0 r..D O 1.00 _.. 0 CO0 I_.. "T- _f" O r.,.D O 0 0 "_'" 0 T- 0 "_'- 0 ".'- 0 T- 0 T- 0 ",," 0 0 0 "_" 0 T-" 0 66 66 66 6o 66 6o 66 66 66 66 66 @ C v v v v v _ v v _ _ _0 _0 _0 _0 _0 _0 _0 _0 60 6o 6o 6o 60 6o 6o 6o _ _0 _0 _0 O0 _0 _0 O0 _0 - ® 60 6o 6o oo oo o6 oo 6o

# g g o

Im c_ Q. cl 0,1 0_1 O_ Cq Cq Cq 0,1 e- Z I'-.. I'_ CO (30 0') (1) .i,- '1", T "i" _T T T * o_ TABLE 17: Average parameter estimates for different flight conditions. Roll rate tO lateral stick input transfer function coefficients. Third-order hybrid model.

Flight Condition l/mR

'[p 4, 0.3 <M<0.4 0.12 8.2 < c_< 11.0 0.18 2.5 0.8 < M < 0.9 0.13 6.0 < ot < 6.2 23.8 0.30 0.83 2.8 1.2<M< 1.6 0.16- 1.5 2.6 0.17 8.7 4.8 <o_< 6.4 : :---_ _t j 7 : --5 -' _--_ o Z (I) _J rr .J c_ o t3_

"8

d

_e

-_ - t_.

.E " -_

-_._ 3

x:E o

- __

Z 13- Z

z z z _, _ z z

rl- o o rn m L) (D 0 0 0 0 (_ t_- _ cO I_ Q0 _" _D LID 0 (.D 0 '_" _ ",- CO 6 o 6 6 o 6 o o If) I_- O4 I_ I_- O_ I_- o (.D t.o to CO (g) 0 I_ _o _ _ CY 04 ",-- ",-- "-5 _o o4 co fad tO t.O O (g) (.0 CO _-- 04 _ _ o,.I 0 0 0 0 O O O O O_ ",- CO 0 I_, 0_1 _t" CO e, O0 _0 130 CO 6 6 6 6 6 o o 6

g

B | co o,4 _D o3 o_ o_ o4 o .o 04 03 04 03 CO _-- 0_I = o 6 6 o o o o o !

0 0 ('- C O" O- 0" q) .(,..,

=_ _ _o_ o_ -_ - m_

I-- >- >- >-_

_ _ _ <_. "_._ >-_

e-- _-- (-- I-- o o o

_g _g -.P:"_-_o

£ £ £

0 • • O. _2

o o c_ (,.9 < 03 CO _'_ CO 0'3 03 03 CO N m Z O_

|

T T T T T T c_, c_, g * Z L_ v o_ .l== !

>, LT_ r.

;> t-_ _ _ t--- II il

'E !7- ..,or_ li {

7 -- :.....................+..................... :......-............. 4 ....................

6.5 : f :r i _ * 5.5 _, ; ,' i , ; ........................

4.5 ' ' 0 20 40 60 80 100 120 Time. sec (a)

il .easureO

• : I - - - Estimated .......... ") ........................ i. q I , i !

i : i

ii/ ii

_3 - • i _ ..... _'/"i;_-;_,/'_--/'_ .......

, ! l_,l_ ', _' % • 0 ........ _ .... _L ................1..................... i .....

0 20 4(3 60 80 100 120 Time, sec FIGURE 2: Data Compatibility results comparing measured and calculated (a) angle of attack, and (b) sideslip angle.

Z 1 I I Pitch Rate, deg/seg "/ ............. !.................... _...................

!

............................................................ ............................................................

...................................................... ............................................... i_.___....._ -1 • : _ / J .......... }i ...... L._J....._,__..J______.,___ _-,_J_ ....... _._ ...__. _._._ _ J_._ J..__L . __ -2 3.2 3.4 3.6 3.8 4 4.2 4.4 Time, sec FIGURE 3: Time skew in response of aircraft to control surface deflection. Longitudinal doublet, test point number 2.4-15.4A.

1.5 _ --t--- i t b _ _ ' P I _ ' _ l

I ..... .o_e, I i ::A

"' s muUate_ I i ! 1 0.5

!°

-0.5 -1 -1.5 20 40 60 80 100 120 Time, sec

(a)

0.3 _ • r-, , r :' =' ' _-' !

t

-0.1 -0.2 .................... z !

: !

i..................... i..................

-0.3 ___,__,_ L ...... J_ .... i , • , 0 20 40 60 80 100 120 Time, sec

(b)

FIGURE 4: (a) Simulated and model time histories for pitch rate for EEM, and (b) residuals from output fit.

= = 2.5 1.5 0.5 _ t?. -o_.oo... ......

1.6 ' ] ' I ' I ' I ' I ' 1 ' t ' I ' I ' I ' I ' I ' I _ w"]-_-'-]---r" [ _ | • ] _ ] r-V_ ....................................... t .................................................................................

1.2 0.8

iiii!iii iiiiiiiii iii iiiiiiiiii!!ii!ii! i!i!i !ii iii i!i! ii iii

0.4 _-l..._L..x-Lx-.l.. -.l _ 1 _- I a. L [ F1CURE 5: Summary of parameter estimates with 2_ error bars for pitch rate to longitudinal stick transfer function.

1.2

i 1

0.8

ilt iiiiiiiiiiii i !t! ilt

0.6 0.4

................ i ii i iiiiiii iiiiiiiiii i1

0.2 3.5 i'l'l'l'l']T_7_[r_lt''i 'i'_"'l'l'l'l'l'l'l' q 2.5 8 1.5 0.5 _, 9 ........

_4 _4 d _ _ _4 _ _ d _4 c4 _ e4 c4 _ _ _4 _4 c4 _4 FIGURE 5: Continued.

z 8O m 0.22 0.2

iiiiiii!il iiiiiiill iiiiiill ii ii'ii! ii ii ii iiiiiiiiiiiiiill

0.18 0.16 _ l , 1 __ I ___u_j.._4..j , L i J L I _ [ _ .i _ .I._L__J_u I LJ J [ _....L__._I._. [..L J.., - 4 4 4 4 4 4 4 4. 4 4 4. 4 4 4 _. 4. 4. 4. 4 4.

c4 c4 cj ¢4 _i ¢_ c4 ¢4 ¢m ¢,i ¢4 ¢m cJ _ ¢4 ¢m e4 N _ _ ¢u FIGURE 5: Concluded.

1.5 0.5

!o

-0.5 ............ ....................

-1 a = 9.5 deg.

h = 7200 ft. i _, , _ i , , , ] , _.t__J.__, I. , , , I _ _ -1.5 0 20 40 60 80 100 120 Time, sec (a) 1.5 -''' '] _'-_-_-*'' i '-'T7 _'i''Me'as'ured'ii _-. ':/_ ................. i .................. - .... Predicted t 0.5 o "0

I iiiii iiiiiiiiii

-0.5 -1 _±.__.t_ i i ] I i I i I E I I ___. t i : i R J [ i ] i L -1.5 0 5 10 15 20 25 30 Time, sec (b) Parameter Values, Standard Errors (in _arentheses), and Flyi _ualities Prediction K0 1/To2 Csp tOsp 1:0 O)spTO, Category Level Reason for Not Level 1 0.633 0.796 I. i39 0.200 1.799 B 3 "co> 0.20 0.995 (0.07 ! ) (0.047) (0.056) (0.002) (0.009) Z2 FIGURE 6: Comparison of measured, estimated, and predicted time histories of pitch rate.

Test point number (a) 2.4-16.1A for estimation, and (b) 2.4-16.4A for prediction.

Measure I i

1.5

..... Est'mate ! ....................... i............. ......... i................... ......................

o 0.5

¢ : _ i = L _ E_ "_ 0 ¢ ..................... _ .... ...,_ .......... . . _.._ -0.5 i :: i ' i M = 0.89 ! i _ -1 | h=33000ft. ] :: i i ]t:Jll_ .... L_ _ .J _._/..._..L..__,t.._J._.J_...._.... L t [ .J-. J L L • _ • !1 ] _ _ - -1.5 0 20 40 60 80 100 20 Time, sec (a) 1.5 - ' ..... -' ! .... ! ' ' L '. L '. " L L - - f\ i ! i---Measuredf 0.5 (o • ! ! _ i i "0.5 " i i / ! i -1 _ .................. _........................... _ ........... _......... _ ............................ ? ..........................

-1.5 - _ .L_ ...... _.__...... i.................... !i .................. _........ _ L._.I_.__L_J.. ................

-2 0 5 10 5 20 25 Time, sec (b) Parameter Values_ Standard Errors (in _arenthes.es)r and Flyi 1_;Qualities Prediction Ko 1/To2 _sp ¢°sp ZO ¢.0spTO2 Category Level Reason for Not Level I 1.972 1.137 0.607 2.261 0.217 1.989 B 3 1:0>'"0.'20 (0.031 ) (0.057) (0.0] 7) (0.042) (0.003) FIGURE 7: Comparison of measured, estimated, and predicted time histories of pitch rate.

Test point number (a) 2.4-15. l B for estimation, and (b) 2.4-15.4B for prediction.

1.5 I Measured li i! !

_ _ ! .

0.5 .... ;................._ ....................... .; .......................i......................._- ......... ;.....................

o g o d- -0.5 'i .....................

-1 .............. i....................... ....................... ! .......... _.L._i .....................

cc=4.8 deg. I h =49000 ft. J -1.5 0 20 40 60 80 100 120 Time, sec (a) _--T"T1 i .... ] .... I ' ' ' ' q .... I .... i ....

i i i i I Measured I j 0.5 ......... __" ..............[! .......'_---i ..... 1_ .... Predicted l _-0.5 ° -1 -1.5 0 5 10 5 20 25 30 35 Time, sec _) Parameter Values, Standard Errors (in--_areniheses), and Flyi _°Quaiities-Predlcilon K0 I/T02 _sp (°sp 1:0 (OspT0_ Category] Level Reason for Not Level I 0.362 0.348 1.541 0.183 4.257 B 2 % > 0.10 0.649 (0.015) (0.008) (0.012) (0.002) (0.005) FIGURE 8: Comparison of measured, estimated, and predicted time histOries of pitch rate.

Test point number (a) 2.4-12.1B for estimation, and (b) 2.4-12.4B for prediction.

1.5 , ,= _ ! !, ! , -- Measured I :: i ::_ !

..... Predicted II ! i , lit i !

m i i " r' i i 0.5 , i , , if _ 0 ......... !..,.......... ; .... /. .... ; ...... ; ......

r : p " t " _ ..... P .............. I_ ................

-0.5 .... i ....................

-1 -1.5 0 20 40 60 80 100 120 Time, sec Figure 9: Comparison of measured and predicted time histories of pitch rate. Test point number 2.4-16. I B predicted with 2.4-16.1A parameter estimates.

1.6 1.4 1.2 0.8 0.6 0.4 ..... : ..........................................................................................................................

0.2 .._._.._1 , t i | , _ _ I , I i I _z_Lj.|. , I , I , I , I I ] , I , I , L-_..: :::: : :: ,-6 _ _ _i ,,6 ,,,'J _ _4 _5 "_ _ _ _ _ e6 _ _ :,-_ ,-; 1.4 _' i]r_ ! _:1 'i _l ___ I ' I _ I _ J ' T-_ I ' t ' I I _ I

/

1.2 .... 4............................................................................................................................

0.8 0.6 ....................................................... ...................................... ..........

0.4 0.2

tii!i!!i iti ,! I!IIIIII ii! l

4 _ 4 _ 4 4 _ 4 _ _ 4 4 4 4 4 _ 4 4 4 N N N N N N N N N N N N _ N N N N N N FIGURE 10: Summary of parameter estimates with 2cy error bars for yaw rate to rudder pedal transfer function.

Z 0.8 0.7 0.6 0.5 .... iiiiii iii iiiii iiiiiiiii iiiiiii iiii iiiii iiiiiiiii! iIi Iiiiiiii iiii iiiiiiiiiii iii iiiiiiii iii iiiiiii iiiiiii 0.4 0.3 0.2

iii i iiiii iii! iiiiiiiii iiiiiiiiiiiiiiiiiiii i! i iii iiii!ii !iii

0.1 1.6 ' I ' I ' I ' I ' I ' l ' I _ I ' ] ' I t I ' I ' i _ I _ II *T i I " I _ F''r- 1.4 1.2 s _ 0.8 0.6 FIGURE lO: Continued.

0.2 _T, , , , , , , r ,-r-__ ]-_r-,-, , , , , , , , , , , , , 0.18 0.16 I-,

iiii!iii!iiiiiiiiiii ii!iiiii!iiiiiiii iiiiii

0.14 0.12 0.1 2=l..2c2J_J....l L _ I:...L L..a__.L L-L--I_LJ--J I..J._.L_L..L.J-_e.J_J_E___J__._I e_l o,!

m m c,i c,i e,i _ ..,.i e,i ,'..i ,",,i e,i _ ,',.i e,i _i e,i o.i e,i e.i FIGURE I0: Concluded.

J

m 1.5 !: ' ' ' Me'asurerd Ii ........

il ..... Es,imated li

s" : _ i , i _ i 0.5 ................ i ........... J i ............ _ ...... _. ................................ ,.....................

g ¢9 - _ i / " / i i t : , t : t "O -0.5 : , ! a=9.1 deg.

i _ ','i h =7ooo..

_..L...J.._ ...... J.._...L_.L__L--.L-_______]. ___....._.............i ........ "..... A ........

-1 0 20 40 60 80 100 120 Time, sec (a) 0.8 ..... Predicted ....................... !................... " ............... i .................................

t OeasureOI

0.6 t - ! _ _ i " E i _ !

i ! , !

! _ .

0.4 i i, ! ................ .:.f.................................

0.2 ! i, i i "-" 0 ............... _ ................................... i ......................

' f' " k " -0.2 .................................. i ............................... i.................................... i................................ , ..s i /i i -0.4 -0.6 0 5 10 15 20 Time, sec (b) Parameter Values Standard Errors (in ,arentheses ), and F!yi a_:Qualities Prediction K, lfF, f.l) d "l_ r _do3_ Category Level Reason for Not Level I 0.467 0.486 0.505 0.804 O. 170 0.406 B None (0.007) (0.088) (0.052) (0.051 ) (0.004) FIGURE 11 : Comparison of measured, estimated, and predicted time histories of yaw rate.

Test point number (a) 2.4-16.3A for estimation, and (b) 2.4-16.6A for prediction.

1.5 -- Measured l! IE i, j i ..... Estimated [: i , i_ _ i , .i....................... 7................ ;'i ............... i.....................

0.5 ,,' i : i k ............

h.Z -0.5 -1 -1.5 0 20 40 60 80 100 120 Time, sec (a) 7 _T-_ , t ' ' ' "-T-T7 ' _ ' ! .... "' ' 1..' ' '

:1 -- Measured I i i !it M=0.87

-[ ..... Pred cted II i i a = 6.1 deg.

1.5 :1 I i "-_ ............. i................. ::I "=3t°°o".

; : : i ! i !

! ! i , i i i ................ ? .................?.................!........_ ..........!.................!.................... ..............

! ! i j ! i i : ! ! _ ! ! !

0.5 ................ i................. i................. i...... _--i................. i................. i................

"0 .... i ............. " ................. i- -- ri ................. i ....... : - i ! !/ i i i : ,, / ! i -0.5 ................i ............_ i............," ',-_.. .'--.-- i.............. i..............

-1 0 2 4 6 8 10 12 14 Time,, sec (b) Parameter Values Standard Errors (in 9arentheses), and Flyin£ Qualities Prediction 1/Tr _ t% "r r _jt% Category Level Reason for Not Level I K r 0.238 0.725 1.216 0.158 0.882 B 1 None 1.558 (0.027) (0.024) (0.029) (0.003) (0.016) FIGURE 12: Comparison of measured, estimated, and predicted time histories of yaw rate.

Test point number (a) 2.4-15.3A for estimation, and (b) 2.4-15.6B for prediction.

9O 1,5 . _ • _ _.2" ...... _. ..........................

i • ! i i -1 -0.5 !

-1.5 0 20 40 60 80 100 20 Time, sec (a) 1.5 ........._ .................;!_'_....._ ............................_..........................

J - i i t i i - i i r i i - i i r i !

0.5 t_ - i ! _ i i - :: :: r i :: - ! ,, ! _ i Z - } "_ / _ // i t -0.5 - / i _ i i _/ -1 0 5 10 15 20 25 Time, sec (b) Parameter Values, Standard Errors (in _arentheses), and Flyirlg Qualities Prediction K r I/T, _ COd t_ _d_0d Category Level Reason for Not Level 1 0.550 0.275 0.191 1.453 O. I 15 0.278 B 1 None (0.oo8) (0.024) (0.012) (0.017) (0.004) FIGURE 13: Comparison of measured, estimated, and predicted time histories of yaw rate.

Test point number (a) 2.4-12.3A for estimation, and (b) 2.4-12.6A for prediction.

=- 3.5 2.5 ii! iiii! !!i!!!!i!iii iiiill iiii!-iii!!!!! !i ii iii! tii ii!i!iiiiiiiI!! !!t!!!!I!!! !!!!!!!!!! !!!

1.5 0.5 4- 4- 4, 4. 4,. 4- 4. 4, 4 4,. 4- 4,. 4, 4,- 4 4- $ 4..4.

FIGURE 14: Summary of parameter estimates with 2_ error bars for roll rate to lateral stick transfer function• First-order model.

_-s± z_ = 0.2 0.16

iiIZZIiIiiiiTiiiiiiiilZiiill ZIIIIIZZIIIIII tliiiii ZIIZ_

0.12 0.08

iiI ii Iiiiiili ii i!iiiiiiiiiiiliiiii!iii iiiii iiii!iiii!iii ti i i ii iiiii iiiii

0.04 __,.._L____t_ L._ J...j..J._. L _A _ ..L_J_...l. _L._L_L.._...L.L..L._...L_L.L..,_J._±.._.._l .,_.1___ -0.04 _ N N N N N ,"J N N cJ ,"J ,'q _ _ N N _ N FIGURE 14: Concluded.

i ' _ _ '_ ' _ ' i ('" ' ' ' t , _ r-[- , .....

;I -- Measured I i i -I ..... Estimated I i i i -_ m-_ ..................... _ ...... ] .......... --:+......... i ............. _ .....................

- i i ' , ! i ................. _.L! .............. " ........ ;............. ::- _ ..................

" ' ...i ...... i I ..........

........ , I i i "_ 0 ¢) (:3.

-2 -4 -6 0 20 40 60 80 100 Time, ,3Pc (a)

i I ..... Measured I ' " : '

, ............ __ ............ :- ................._ ...............

4 _i ..... Predicted I _ : ................._...... '; . { ............ i...............

"¢3 -2 -4

...................... ' ..................... ': o 1

i i i_. 4 ...... i,,,i ...... i,,,i .....

-6 0 2 4 6 8 10 12 14 6 Time, see (ID _= i Parameter Values, Standard Errors (in parentheses)i and F1)' 1_ qualities Prediction Kv i fr R _o Tk Category Level Reason for Not Level 1 10.077 2.801 0. i 01 0.357 B 1 , None (0.636) (0.211) (0.015) FIGURE 15: Comparison of measured, estimated, and predicted time histories of roll rate.

First-order model. Test point number (a) 2.4-17.2A for estimation, and (b) 2.4-17.5A for prediction.

= i | F.

10 i ¢.)

&

O "O -5 -10 20 40 60 80 100 120 Time, sec (a) ....... -I -_ T • • _ _ i _ r _ r I T , , '7 ,i ...... q' I ---- - Measured I]11 4 .......................................... " ...................... iJ. ....................

I

t ! i, Predicted iJ ............. i....................... T .....................

& ,,-i .... -"..

{3 -2 El.

-4 • . .t .......... 4.............................................

i I -6 =6.2 d_g. I............ i........................ i....................... _ ....................... T .....................

h = 31000 ft. I i i i i -8 0 5 10 15 20 25 30 Time, sec Parameter Values_ Standard Errors (in 9arentheses)r and Flyi 34 Qualities Prediction Kp If[' R To T_ Category Level Reason for Not Level I 17.598 3.392 0.132 0.295 B 1 None (0.982) (0.259) (0.012) FIGURE 16: Comparison of measured, estimated, and predicted time histories of roll rate.

First-order model. Test point number (a) 2.4-15.2A for estimation, and (b) 2.4-15.5B for prediction.

"; -2 -4 -6 __L I ! ] | l I -8 0 20 40 60 80 00 Time, sec (a) [I -- Measured I i i ._ ! ) ..... Predicted I " .]................. :'............S -_:_t ..........._................_...............

_ 2

g

_ 0 _4 -2 _ \, -4 '. . _ _ i !) _=4.6deg.

i i "- - _ " i i i I . = 4aooo ft.

-6 0 2 4 6 8 10 12 14 16 Time, sec (b) Parameter Values, Standard Errors fin _arentheses), and Flyi n,gQualities Prediction Kp I/'T R "C o T R Category Level Reason for Not Level I 7.546 2.392 0.137 0.418 B I None (0.337) (0.127) (0.01 I) FIGURE 17: Comparison of measured, estimated, and predictedtime histories of roll rate.

First-order model. Test point number (a) 2.4-12.2B for estimation, and (b) 2.4-12.5B for prediction, ,I,[,l_l'l_l_l,l'{'l'i'i'l't_++l'l'l'l ' ........... _++! .................................................... !]+ ++ +!++ +!..................

w 1 , I , I , ] , I , I , I , I , I t t L [ t.-L..._+=...L_.L-.J-..I.-J.___ 0.5 ' I ' i ' I ' I + I ' I ' I _ I ' i , I ' I ' I ' I + I + I ' I ' I ' I ' I ' 0.4 0.3 0.2 0.1 O e_ e_ N N e_ N N N N ed N ed N N e_ e_ e_ N N FIGURE 18: Summary of parameter estimates with 2cy error bars for roll rate to lateral stick transfer function. Third-order hybrid model.

1.8 I _ t _ f • I r'FT'V_r_ -_ I ' t ' I _ I ' I ' t ' I ' I ' I ' I ' I ' t ' 1.6 1.4 S _ 1.2 0.8 0.6 i....i....!..

0.4 < e < m" < m o < m < m < "" < m < m 4.5 3.5 _= 2.5 1.5 0.5 < _ < m < m 0 < _ < m < m < _ < [] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 c FIGURE 18: Continued.

| 0.2 0.18 0.16 0.14 _ 0.12 0.1 0.08

i!! !!i !!!i!i!!i!!!!!!!!!!!! !!!il !iiiiiiii! ilii!! i!ii! !iii

0.06 _-J....J....J_.J t_LI..J...J....LJ.__J. , _ , , , I , L__.L.L_.._...J.._L._L_. I__L] • 0.04 ,_ m ,,_ ,"n .<t[ t'n O < _1 ._ _3 ,_ ,"n ._ ,"n _ rn _ N e,i N N N cJ e,i N ¢,i r,i N c,i ¢J ¢J e,i N N FIGURE 18: Concluded.

-- Measured , ;, ..... Estimated _._ ............... _...................... , ......... _ .bid .L_.t_ ....................

; LI [ :' ", , . : i . i ?v _t_ .................. "r : ' 1 •. i " k: ............. i .. I' ...................

_o

" i , [ :_

_-2

....... ':............. i.................i_: " i i ..................

{5.

-4 ................... :- ....................... _....................... _................... ;--+t t_a_q i_ 'J ............................

_--o._ I .............. i.............................. L;............ 2i:..................

-6 c( = 8.2 deg. '1 i == i i h = 6200 ft. J i { :: i -8 0 20 40 60 80 1 O0 120 Time, sec

(a)

'1 -- Measured I i ,'_ ..... Predicted I i............ J---?-i- ..................................................... : ................

! :, i ' ':k'.f-_i _ ,, _ i :_ _) ! i i _ _ i _ I Ji" 'k',,,_ ! ,, _ ._ ..... ................. i .......... ., .._:'. ................. :: .......................

"_ 0 P, = I , i ............... _ ............ i ................ _ ......... :....... .: ................. _ ................

-2 { ' : - - i i i M=035 -4 ................ i ...... ,.... i ............. ? X i t o_=8.3deg.

! " i i i ii h=6ooo..

-6 0 2 4 6 8 0 12 14 16 Time, sec (N Parameter Values, Standard Errors (in parentheses), and Ryi ]_, Qualities Prediction co, 1FF R "co T_ Category Level Reason for Not Level l _= 0.163 0.782 2.791 O.I 15 01358 B 1 None 13.456 (0.627) (0.019) (0.047) (0.203) (0.010) FIGURE 19: Comparison of measured, estimated, and predicted time histories of roll rate.

Third-order hybrid model. Test point number (a) 2.4-17.2A for estimation, and (b) 2.4- 17.5A for prediction.

2O :i -- Measured I !t ..... Estimated l! ................................................................ it, _..............

10 ..................... -, ....................... !....................... _" ...................... -:' .......... '-I-. -i_N-# _ ...............

- i ' , , i I i ] Illil ij rj,T I ° 5 ..................... !....................... !....................... ? .......................... 1----_ - _ i ...........

" i '_ -: t I ..................... ._ ....................... ._ ....................... ._ ................

-5 -10 M=o._ I............. _ ....................... "...................... :....... '!_':;i ', ..............

ec =6.1 deg. i i j_t_! _, h=32000ft. I ' !::'hi(!

-15 0 20 40 60 80 100 120 Time, sec (a) i .... Measur ,, : ; ..... Preaicte_ il , i i i I _ _l]ed 14 ! , i_ r_ : i ; ' II ,, !, ................... • ........................ i J

go

_i ! it' 5.

............... i........................ i....................

-5 ..................... i_ ....................................... i M=0.88 _ cc =6.2deg.

: d h = 31000 ft.

[ I __J I l I I -10 ..... T, , , 0 5 0 15 20 25 30 Time, sec (_) Parameter Values, Standard Errors (in parentheses), and Flyi ag Qualities Prediction (% I/T. _:p T_ Category Level Reason for Not Level 1 23.999 0.355 0.898 2.662 0.170 0.376 B 1 None (0.693) (0.039) (0.054) (0.186) (0.006) FIGURE 20: Comparison of measured, estimated, and predicted time histories of roll rate.

Third-order hybrid model. Test point number (a) 2.4-15.2A for estimation, and (b) 2.4- 15.5B for prediction.

:1rMeasured I i _ i;

-I..... Es"ma'°_ I ] t

5 .......................... _ ................... i............................ !....... _................... _ .... _ _ .........

] : f ,_"','9: , 0 ......

-5 ...................................... i ............................ : .......................... , " r fr .........

' i i :; _tq t' LI rl M=1.59 , i :, , l-I : ! it , bl oc = 4.4 deg. i i _-! h = 48000 ft. i i i -10 L_, , , I , , , i .... --1 ....... i , , , 0 20 40 60 80 1O0 Time, sec (a) mr

-- Measured I i ,._

..... Predicted I] ......... _ ....... _.......... :_",1 .......... T................ T ...............

a _'C',i / i i/ i 4 .............. _ ................. -_ ................ i....... r............. _ ................. r ...............

i i i _ i i 2 .............{ ................. i................. +---'r ........ { ................. ".: ................

i i ] _ - ' i g, .... 4 ................. 4..---_..... : ..... ..m__

_o

i ; :: ' i i i d. -2 i ; i }, _ i i i ............... ;. ........... _-...: .............. i................. -_................. _ .................. :...............

-4 i _ ' ! i ............. 4-................ _.- : -6 ,,, ..... .......

-8 0 2 4 6 8 10 12 14 16 Time, sec (h) Parameter Values, Standard Errors (in _arentheses), and Flyi ag Qualities Prediction .................

K# _¢ 03_ ]/W R l_p TR Category Level Reason for Not Level 1 i, I 1.886 0.054 1.201 2.874 0.179 0.348 B I None (0.252) (0.006) (0.049) (0.087) (0.004) = FIGURE 2 l" Comparison of measured, estimated, and predicted time histories of roll rate.

Third-order hybrid model. Test point number (a) 2.4-12.2B for estimation, and (b) 2.4- 12.5B for prediction.

N | !

c- ._o ==4 LL £3 ,=2 O_ 0.3 0.4 0.5 0.6 0.7 0.8 0.9 I/T0 2 i I _imolation I_nalytical h_ i ................ I .... I .... I .... / "5 IJ.

/

O t,-, O 13_ 0.65 .... i .... i j w_,: 'i_ ........ --

r_ I', I I_''°'"''''"1.... _' .... k!

.......... i............... _ ...................... :, ...... _ 4 _r'_ol ,,- i,,", t- O == LL JO I , i rl ................................ .........

0.9 1 1.1 .2 1.3 1.4 (Osp FIGURE 22: Results of Monte Carlo simulation for longitudinal parameter estimates.

REPORT DOCUMENTATION PAGE For_ Approved OMB No 0704-0188 I Pul_ic repod ng burden for th s co ect on of information is estimated to average I hour per response, including the time for re, hewing instructions, searching existing data sources gather ng and maintaining the data needed and romp et ng and reviewing the collection of information Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington He_lquaders Services, Directorate for Inforr_..ation Operations and Reports, t 215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reducbon Project (0704-0188), I Washin_lton.DC 20503.

1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED August 2000 Contractor Report 4. TITLE AND SUBTITLE 5. FUNDING NUMBERS Estimation of Handling Qualities Parameters of the Tu-144 Supersonic Transport Aircraft From Flight Test Data NCCI-29 6.AUTHOR(S) 537-08-23-21 Timothy J. Curry 8. PERFORMR,_G ORGANIZATION 7. PERFORMING ORGANIZATION NAME(S) ANDADDRESS(ES) REPORT NUMBER George Washington University Joint Institute for the Advancement of Flight Sciences Langley Research Center Hampton, VA 23681-2199 10. SPONSORINGJMONITORING 0. SPONSORING/MONITORING AGENCY NAME(S) ANDADDRESS(ES) AGENCY REPORT NUMBER National Aeronautics and Space Administration NASA/CR-2000-210290 Langley Research Center Hampton, VA 23681-2199 11. SUPPLEMENTARY NOTES Langley Technical Monitor: James G. Batterson 12b. DISTRIBUTION CODE 12a. DISTRIBUTION/AVAILABILITY STATEMENT Unclassified-Unlimited Subject Category 08 Distribution: Nonstandard Availability: NASA CASI (301) 621-0390 13. ABSTRACT (Maximum 200 words) Ix_w order equivalent system (LOES) models for the Tu-144 supersonic transport aircraft were identified from flight test data. The mathematical models were given in terms of transfer functions with a time dela_ by the military standard MIL-STD-1797A, "Flying Qualities of Piloted Aircraft," and the handling qualities were predicted from the estimated transfer function coefficients. The coefficients and the time delay in the transfer functions were estimated using a nonlinear equation error formulation in the frequency domain. Flight test data from pitch, roll, and yaw frequency sweeps at various flight conditions were used for parameter estimation.

Flight test results are presented in terms of the estimated parameter values, their standard errors, and output fits in the time domain. Data from doublet maneuvers at the same flight conditions were used to assess the predictive capabilities of the identified models. The identified transfer function models fit the measured data well and demonstrated good prediction capabilities. The Tu-144 was predicted to be between level 2 and 3 for z all longitudinal maneuvers and level I for all lateral maneuvers. High estimates of the equivalent lime delay in the transfer function model caused the poor longitudinal rating.

= 15. NUMBER OF PAGES 14. SUBJECT TERMS _2 System Identification; Flight Test Data Analysis; Closed Loop Modeling; 16. PRICE CODE Handling Qualities; TU-144 Supersonic Transport A06 20. LIMITATION 17. 'SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION OF ABSTRACT OF REPORT OF THIS PAGE OF ABSTRACT UL Unclassified Unclassified Unclassified 5tanOara I-orm L_.JU(HEY. _'-,U_) NSN 7540-01-200-5_:_Jg Prescribed by ANSI Std. Z-39-18 298-102