Results From F-18B Stability and Control Parameter Estimation Flight Tests at High Dynamic Pressures

APPENDIX A

LONGITUDINAL MANEUVER TIME HISTORIES

Figures A-l-A-20 show time histories of longitudinal doublet sequences. A typical time history is shown for each of the 20 flight test conditions. This appendix shows actual aircraft responses to the four longitudinal single-surface inputs (SSIs) and qualitatively shows how well the parameter estimation program, pEst (ref. 1), was able to match the actual response time histories. Aircraft response parameters include angle of attack, pitch rate, pitch attitude, and normal acceleration. The solid line is the response parameter measured from flight data. The dashed line is the pEst program-estimated response at convergence obtained by integrating the equations of motion using the pEst program estimates of the stability and control derivatives.

Only selected windows of data were used in the pEst program analysis. Some of the data between subsequent SSI inputs were removed from the pEst program analysis to minimize integration drift. The data removed were from times when the aircraft was no longer responding to the previous SSI input. The time history points not used in the integration are indicated by the step discontinuities in the dashed line.

The control-surface positions measured by the control-surface position transducers are also plotted.

For the longitudinal sequences, the SSIs were done in the following order: symmetric leading-edge flap, symmetric trailing-edge flap, symmetric aileron, and elevator (stabilator). A 5-sec delay was built in between each SSI.

u u u u u deg I I I I I -2 I I I I I qp deg/sec I I I I I -10 ! ! ! ! !

p deg I I I I I -2 I I I I I a n , g -2 i i i u u F 5sa I f 1

-,_-,' # ,,, ,-, - - - -L _,"/. ""

deg -- --m'_ ...._ _ ,.,., . . ...

• . .. .., ..... .....=.. ....

i- _ .- ._ !

I I I I. ,,,, I I -5 0 5 10 15 20 25 30 Time, see 000398 Figure A-1. Large doublet sequence (Mach 0.85 at 15,000 ft).

u u u u u P (_, deg I I I I I -1 I I I I I q, deg/sec _r..: .. .'--_. .._. _._--_-.:._- :._:__ -5 I I I I I -10 I I I I I , deg I I I I I -2 I a n , g -1 n n n n n I I./_STE F j I .- /_Se

.... _., ___-"--/,_.. = "_-"

I (_, .......... _ ---__-__-__-__-----_----_'.--_- _--__-- - -.----" I/"__--._-. _-c# • "-'"- -" -_-_" _,/ .'_'_ deg o -_..._; ....................... _.,..,..,,...... ......... _....... _.

-'_--Ss a --5 I I I I I 0 5 10 15 20 25 30 Time, sec 000399 Figure A-2. Small doublet sequence (Mach 0.85 at 10,000 ft).

u u u u u (_' 1 deg -- -__.._-_-'= _ __ _.._--_----__ _. -- I I I I I -1 I I I I I q, deg/sec 5 -5 u u u u u e, deg rm"N,s_m..,a_---- -- -- -- I I I I I -2 I I I I I an, g I I I I I -2 I _ I I I I n n 5 i --._Ssa 5 | i _ TEF _ _- e (_,

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

deg .... •.. . ............ • !: ........ y. .. ..

I .i I I I I I -5 0 5 10 15 20 25 3O Time, sec 000400 Figure A-3. Small doublet sequence (Mach 0.85 at 5,000 ft).

I I I I I (_, deg I I I I I -1 q, deg/sec -5 I I I I I -10 3 m m m m m , 1 --_l . m- % _ _ _ deg I --1 a n , g I I I I I --1 m m m m m ; "t_ _I'EF /--Ssa [. -/ /--5 e (_, deg • "-- " _ t' _ _ :_, _ _ .... I,-_ I .,.., I I I I I -5 0 5 10 15 20 25 30 Time, sec 000401 Figure A-4. Medium doublet sequence (Mach 0.9 at 15,000 ft).

I I I I I deg I I I I I -1 qp deg/sec -5 I I I I I -10 n n n n a_L n p deg

_ ;___ LY -

I I I I I -2 I I I I I an, g I I I I I -2 I I I I I ._-. 5LEF / " F 5TEF |"-FSsa 5

, I .i /--e

deg -'_ . -- _ .... L "-I ""- ..... /" " " " " - -

_" ._ ._"=':.'.- ---?':"- :2 -." ,_'.T -.----'.-:.--- -T_ ;_

I,.."

I I I I I -5 0 5 10 15 20 25 30 Time, sec 000402 Figure A-5. Medium doublet sequence (Mach 0.9 at 10,000 ft).

i i i i i "t (_, deg I I I I I -1 I I I I I q, deg/sec -5 I I I I ,_ I , deg _r I"_-" J _ 1 _" _ _ I I I I I -2 I I I I i_ I an, g I I I I I -2

../-5 , ' ', sa

I TEF - I (_,

._----- ..- J I _ __

deg I I I I I -5 0 5 10 15 20 25 30 Time, sec 000403 Figure A-6. Small doublet sequence (Mach 0.9 at 5,000 ft).

i i i i i (_, deg I I I I I -1 I I I I I q, deg/sec I I I I I -5 u u u u u , deg -1 an, g 1 :- .... --,."---_';_-_ r --- 0 n I I I I I • FSLEF I "IF 5TEF " -FSsa' (_, deg

• I L _ _ .-" .". _..__

_. - . .-. " "-.-------'3 -- . -:_ -'--.-- -'--." _ .....

_.. ---

I I 5e_ I I I '- I I -5 0 5 10 15 20 25 30 Time, sec 000404 Figure A-7. Large doublet sequence (Mach 0.95 at 15,000 ft).

I I I I I (_, deg I I I I I -1 q, deg/sec -5 I I I I I (_, j deg 1 I I I I I -1 I I I I _ I an, g I I I I I -1 I I I I I .F 5LEF 7 'FSTEF '-"# 5sa (_, I

_. r ij. _ _

deg

_:.-...:....- ...... =.-.-.:-.._ _: :_-_

I I I _" J I I -5 0 5 10 15 20 25 30 Time, sec 000405 Figure A-8. Large doublet sequence (Mach 0.95 at 10,000 ft).

I I I I I deg I I I I I -1 q, deg/sec I I I I I -5 I I I I I , deg -2 I I I I I I I I I I a n , g I I I I I -2 -F 5TEF ..,F 5sa F (_LEF f J 6, • J I I deg

0 _--..-:-_..----.-._--=:_., __. _...__---=..--.__

"2

I I I I I -5 0 30 5 10 15 20 25 Time, see 000406 Figure A-9. Medium doublet sequence (Mach 0.95 at 5,000 ft).

2.5 l l l l l l 1 tL 2.0 deg 1.5 1.0 I I I I I I .5 I I I I I I q, deg/sec I I I I I I -5 m m m m m m , deg I I I I I I

2° i

1.5 an, g 1.0 .5 I I I I I I / FSTEF F 5sa 5LEF / I I I I (_, "_ J t i_ L,.. ...--..

deg

-_ %_

I I I I t..J I I -5 0 5 10 15 20 25 30 35 Time, sec 000407 Figure A-10. Large doublet sequence (Mach l.l at 25,000 ft).

2.0 I I I I I 1.5 deg 1.0 .5 I I I I I I I I I I q, deg/sec I I I I I -5 I I I I I 0, deg -1 I I I I I 2.0 I I I I I 1.5 a n , g 1.0 .5 I I I I I /_aTEF F(_sa • .F (_LEF (_, I I t deg "J" .I I - : ..... ".. "-'"'.-'-i. ".?-:-.

I I I I I I" I -5 0 5 10 15 20 25 30 Time, SEC 000408 Figure A-11. Large doublet sequence (Mach 1.1 at 20,000 ft).

21 m m m m m

i

(_, deg -1 I I I I I -2 I I I I I q, deg/sec I I I I I -5 1.0, , , , ' t' , _s deg --,5 I I -1.0 I I I

3 I

an, g m m m m m /_ _sa • -- /-- (_I'EF "/1 /_ 5LEF I _/ (_, ./ _ i l deg _._---'..._: . . ___._--=___ ...... _ _._ ,_J- -- _ .. -12-_-. ............ - • ..1...i.

! .i 5e-/

I I I I I -5 0 5 10 15 20 25 30 Time, sec 000409 Figure A-12. Medium doublet sequence (Mach 1.1 at 15,000 ft).

1.5 I I I I I f 1.0 deg .5 I I I I I -.5 I I I I q, deg/sec I I I I I -5 O, deg I I I I I I I I I I an, g I I I I I I I I I I 5TEF i w-N,,w"_._ _ ..... _t-.' " _ --.-- - - .

(_, deg __// ............................. ! ./. ............ ...

I I I I I -5 5 10 15 20 25 30 Time, SEC 000410 Figure A-13. Small doublet sequence (Mach 1.1 at 10,000 ft).

i._ ' ' ' ' '_ I

1.0 P_ deg .5 _ _ ,' .....

--.5 I I I I I q, deg/sec I I I I I -5

2.5 ' ' ' ' ' I

2.0 deg 1.5 - I 1.0 .5 2.0 i i i i i 1.5 an, g 1.0 I I I I I .5 I I I I I f 5TEF C 5sa (_, • / I, i Ii p5 e deg

___ _ __ __ :?L T.--.--:_ _ _ -.-_._-_. --_-.-._

;,i;J ,, I I I _,1 I I -5 5 10 15 20 25 30 Time, SEC 000411 Figure A-14. Large doublet sequence (Mach 1.2 at 25,000 ft).

1.0 i i i i i .5 ^ o/., deg 0 --,5 I I I I I -1.0 I I I I I q, deg/sec I I I I I -5 2.5 2.0 , m m deg 1.5 1.0 I I I I I .5 2.0 I I I I I 1.5 an, 1.0 g .5 I I I I I I r I_ I I I 5LEF II ,F_TEFI__ " IFSsa'-- FSe (_,

_'-._.'- ;--..T.:._ "_---.-= ........ i_

deg 0 • o., .o "., • ,.m, ,o • • ................ •1 "•1 • " .... '•° '• •" • '• •• I I I, .,,., I I I I I -5 0 5 10 20 25 15 30 Time, sec 000412 Figure A-15. Medium doublet sequence (Mach 1.2 at 20,000 ft).

1.0 I I I I I .5 [ deg 0 --.5 -1.0 I I I I I q, deg/sec I I I I I -5 1.5 1.0 (_, .5 deg -.5 2.0 1.5 a n , 1.0 g .5 I I I I I I I I I I /- _/_5-rE F .-'1 /--Ssa /_5 e

_ ..: ........................ ........... :-_ -W'Zvz-z

(_, I deg "Z'_ L EF ..................... _L. _"1 ........

I I I I I -5 5 10 15 20 25 30 Time, sec 000413 Figure A-16. Small doublet sequence (Mach 1.2 at 15,000 ft).

I I I I I t deg -.5 -1.0 f I I I I I -1.5 I I I I I

A

q, deg/sec I I I I I -5 -3.0 u u u u u -3.5 deg _.0 _.5 -5.0 I I I I I an, g I I I I I I 1_ _I'EF I/-- 5sa "- .- 1----', - -.... i- n .........

........ •%._- =_.-'.. -';_ __;_" _r _-.-_.?..:. ........

(_ I I deg ...,.

I I -2 • "LLEF =. J I I I I -4 0 10 15 20 25 3O Time, sec 000414 Figure A-17. Small doublet sequence (Mach 1.2 at 10,000 ft).

1.0 I I I I I .5 deg 0 --.5 I I I I I -1.0 I I I I I q, deg/sec ,,.=.,_....:,___.,,,,.-_-.%_.:___-=..,,.____. _,_ _ _.- - _.- ,.-.-_ • Ir i i i i i -5 1.5 1.0 e, .5 deg -.5 2.0 I I I I I 1.5 a n , 1.0 g .5 I I I I I I IF (_sa 8e ' " '1 5TEF ' I[ -!/_ ' _'- ' / I • I-- I_\ (_, _ .

deg • . ...................... i. 1 "_' " " "'" *" "'%°" "" "''

" I I

I I I I I -5 0 5 10 15 20 25 30 Time, see 000415 Figure A-18. Medium doublet sequence (Mach 1.3 at 25,000 ft).

.5 I I I I I ¢ _' -.5 deg -1.0 I I I I I -1.5 I I I I I q, deg/sec I I I I I -5 1.5 i i i i i 1.0 O, .5 deg I I I I I -.5 2.0 I I I I I 1.5 an, g 1.0 I I I I I .5 ' 7 -I f--ST_ I" '/--Ssa ' _-5 e ' i I / -_" I ' \,i_,_ __------_--- , _ - ........ _ ;_-._.:._-., ....................... _"..... I I deg -2 ..................... !_.i"' .................

I I I I I -4 5 10 15 20 25 30 Time, sec 000416 Figure A-19. Small doublet sequence (Mach 1.3 at 20,000 ft).

I I I I _ I -.5 o_, deg -1.0 -1.5 -2.0 I I I I I q, deg/sec I I I I I -5 -3 I I I I I -4 (_, deg -5 I I I I I -6 I I I I I a n , g I I I I I I I I r--i _ _I'EF I - if ksa ' _.F Be' f I I I

--

1" I............. .. "'"

- ........................ L, J

I I I I I -5 0 30 5 10 15 20 25 Time, sec 000417 Figure A-20. Small doublet sequence (Mach 1.3 at 15,000 ft).

APPENDIX B

LATERAL-DIRECTIONAL MANEUVER TIME HISTORIES

Figures B-l-B-20 show time histories of lateral-directional doublet sequences. A typical time history is shown for each of the 20 flight test conditions. This appendix shows actual aircraft responses to the five lateral-directional single-surface inputs (SSIs) and qualitatively shows how well the parameter estimation program, pEst (ref. 1), was able to match the actual response time histories. Aircraft response parameters include angle of sideslip, roll rate, yaw rate, bank angle, and lateral acceleration. The solid line is the response parameter measured from flight data. The dashed line is the pEst program-estimated response at convergence obtained by integrating the equations of motion using the pEst program estimates of the stability and control derivatives. Note that in figure B-5, no measured angle of sideslip exists. In this case, the flush airdata sensing angle-of-sideslip measurement was not available; therefore, the angle-of-sideslip response parameter was weighted low in the pEst program.

Only selected windows of data were used in the pEst program analysis. Some of the data between subsequent SSI inputs were removed from the pEst program analysis to minimize integration drift. The data removed were from times when the aircraft was no longer responding to the previous SSI input. The time history points not used in the integration are indicated by the step discontinuities in the dashed line.

The control-surface positions measured by the control-surface position transducers are also plotted.

For the lateral-directional sequences, the SSIs were done in the following order: rudder, differential leading-edge flap, differential trailing-edge flap, aileron, and differential stabilator. A 5-sec delay was built in between each SSI.

0 • i -- II A .-..._ _[_, @r - w deg -2 I I I I I I -4 P, deg/sec -50 -1 O0 I I I r, deg/sec I I I I I I -10 I I i _ I deg I I I I I L_--_ I -20

.5 , , ' I

ay, g --.5

I _ ;' i _1. ""

5, 0 deg -10 Z5 r --_--5dLE F | i_--SdTE F Ii_J_--5 a _dh_ I I I I I I -20 0 5 10 15 20 25 30 35 TimE, SEC 000418 Figure B-1. Large doublet sequence (Mach 0.85 at 15,000 ft).

T ! T deg -5 5O P, deg/sec -50 -100 r, deg/sec -10 I I I I (_), deg I I I I I I I -20 .5 I I I ay, g -.5 ' 'i _ I_ ' _ ' deg -10 /Sr Z_dLEF "" 5a 5dh _ I I I I I I I -20 5 10 15 20 25 30 35 40 Time, sec 000419 Figure B-2. Large doublet sequence (Mach 0.85 at 10,000 ft).

-5 5O I I I I I I I P, deg/sec 0 -50 r, 0 deg/sec I I I I I I I -10 40 I I I I I I I 2O deg -20 ,5 ay, 0 g --15 ' ' rt ' r_ I ' p./] ' ' (_, deg -10 r _-- 5dTE F I I I I I I I -20 0 5 10 15 20 25 30 35 40 Time, sec 000420 Figure B-3. Large doublet sequence (Mach 0.85 at 5,000 ft).

J_p deg -5 -10 I I I I Pp deg/sec I I I I I I -50 rp deg/sec -10 deg -20 .5 ay, g -.5 10 I r _ ' _ "1 ' ' ' / l deg m R O -20 0 5 10 15 20 25 30 35 Time, sec 000421 Figure B-4. Large doublet sequence (Mach 0.9 at 15,000 ft).

deg -5 5O P, deg/sec I I I I I I -50 10 I I I I r, deg/sec

o t

-10 deg I I I I I I -20 .5 my, g -.5 f-'l' ' I'_ ' P/'I '

j I I I.r I I I ''_

(_, deg -10 Z_ r _'_ LI_LEF _ ;_.i__ 5dT: _)__5 a _J _" I_h _ I I I I I I -20 0 5 10 15 20 25 30 35 Time, sec 000422 Figure B-5. Large doublet sequence (Mach 0.9 at 10,000 ft).

4 I I I I I I deg I I I I I I -2 P, deg/sec I I I I I I -50 r, deg/sec I I I I I I -10 .__ .____.__A ,-, deg I I I I I I -20 ay, g -.5 i 10 " - "1 - " " " (_, deg -10 _-- (_dTEF (_a (_d LEF I I I I I I -20 0 5 10 15 20 25 30 35 Time, SEC 000423 Figure B-6. Large doublet sequence (Mach 0.9 at 5,000 ft).

2 I I I I I deg -2 I I I I I P, deg/sec I I I I I I -50 r, deg/sec I I I I I I -10 40 I ' ' ' '

I

(_), deg -20 my, g --.5 I I I I I ___.,._ I-,_ .,. _ .

(_, deg -10 5dh r OdLEF a I I I I I I -20 0 5 10 15 20 25 30 35 Time, sec 000424 Figure B-7. Large doublet sequence (Mach 0.95 at 15,000 ft).

2 !

deg -2

--" t

-4 I I I I Pp deg/sec I I I I I I -50 rp deg/sec -10 deg -20 .5 ay, g -.5 deg -20 0 5 10 15 20 25 30 35 Time, sec 000425 Figure B-8. Large doublet sequence (Mach 0.95 at 10,000 ft).

j I r r_ '= J " L.J I ,i"=-- _ " "-4' 1.

I deg I J 1,./ It I I I I I I I -2 P, deg/sec I I I I I I I -50 r, deg/sec -5 deg I I I I I I I -20 .5 ay, g -.5 [ _ ,e- l t i I PI (_, deg _5 a t j_'- 5dh -10 0 5 10 15 20 25 30 35 40 Time, SEC 000426 Figure B-9. Medium doublet sequence (Mach 0.95 at 5,000 ft).

I I

deg HTF-

-5 I I I I I I -10 P, deg/sec I I I I I I -50 5 i i i r, deg/sec -5

o t

-10 (_, 20 deg I I I I I I my, g --.5 ' I- L I'_ (7 "1"1' (_, m m deg -10 Z_ r L_'S/dLEF %SdTE F _t'_--5 a t(_h _ I I I I I I -20 0 5 10 15 20 25 30 Time, sec 000427 Figure B-10. Large doublet sequence (Mach 1.1 at 25,000 ft).

deg I I -2 5O P, deg/sec -50 I I I r, deg/sec I I I I I I I 40 I I I 2O O, deg -20

° i

.5 ay, 0 g --.5 v_, 0-- ...... ! _ .... _ - deg Z5 Z_l .. h_ -10 r 5dLEF v_--SdTE F 5a 5 d I I I I I I I -20 0 5 10 15 20 25 30 35 40 Time, sec oo_28 Figure B-11. Large doublet sequence (Mach 1.1 at 20,000 ft).

deg I I I I I I -2 P_ deg/sec I I I I I I -50 r_ deg/sec _--,,t,_ - _-z'--,AL,,--_'-"_.-'._l -_-r_ I I I I I I -10 deg I I I I I I I I I ay, g --.5 deg

o .... _- _ l - - --"; '.-'. -_-"_--'_ _ _" = °_ _--_J_,_._

I I I I 1

-'°I - ""_--_ _--5 5dh

_'Sr I ZS: LEF I _-- 5dTEIF I a I -20 0 5 10 15 20 25 30 35 Time, sec 000429 Figure B-12. Medium doublet sequence (Mach 1.1 at 15,000 ft).

deg I I I I I I -2 P, deg/sec I I I I I I -50 r, deg/sec _,;='.'.- ,= .-=- -;. -,._-:._.=- .=__;- _-..-:_._'_t_i_ I I I I I I -10 (_, deg -20 .5 ay, g -.5 r-- t _ I_ I (_, deg __J-_" -----Sal I I I I I I__, -_/._dh _'-= -10 5 10 15 20 25 30 35 Time, sec 000430 Figure B-13. Small doublet sequence (Mach l.l at 10,000 ft).

_, 0 deg -10 I I I I I I -20 5O P, deg/sec -50 5 I I I I r, deg/sec -5

o t

-10 I I I I 2O (_), deg I I I I I I -2O .5 I I I I my, g I I I I I I -.5 I I _i.| I I (_, deg -10 - _J_ 5a 5dh _ /Sr ZSdLEF % 5dTEF I I I I I I -20 5 10 15 20 25 30 35 Time, sec 000431 Figure B-14. Large doublet sequence (Mach 1.2 at 25,000 ft).

deg -5 I I I I I I -10 P_ deg/sec -50 10 , , , , , r, j/_ 0 deg/sec -10 4O 2O deg -20 .5 ay, g --,5 deg -10 -20 5 10 15 20 25 30 35 Time, sec 000432 Figure B-15. Medium doublet sequence (Mach 1.2 at 20,000 ft).

13, deg -2 I/,' deg/sec P' 0 -50 I I I I I I I r, deg/sec -5 -10 deg , m m r - I I I I I I -20 .5 i i i i my, g

o t

-.5 5dLEF--__ ' |1"_1 , _ ' w= I l-t I " I (_, deg -5 " _//_r'" , , , "1'_--(_dTi EF L_l (_a _(_:_ -10 0 5 10 15 20 25 30 35 Time, sec 000433 Figure B-16. Small doublet sequence (Mach 1.2 at 15,000 ft).

deg -2 50 I I I I I P, deg/sec

o t

-50 I I I I I r, deg/sec I I I I I I -10 deg -20 .5 I I I I I ay, g -.5 5dLEF •"t ............... _-_....... ____; __. rl _ ;, deg -10 5 10 15 20 25 30 Time, sec 000434 Figure B-17. Small doublet sequence (Mach 1.2 at 10,000 ft).

deg -5 -10 P, deg/sec I I I I I I -50 r, deg/sec -5 I I I I I I -10 (_), deg -20 .5 I I I I ay, g I I I I I I -.5 I I I I 5, 0 deg -10 5 r ZSdLEF 5 d I I I I I I -20 0 5 10 15 20 25 30 35 Time, sec 000435 Figure B-18. Medium doublet sequence (Mach 1.3 at 25,000 ft).

deg I I I I I I -2 50 I I I P, deg/sec .0 -50 r, deg/sec -5 -10 (_), deg -20 .5 my, g I I I I I I -.5 i i i -_ 5dLEF _ F 5dTEF _ 5dh

, ! _ '-/

(_,

deg .... : ,_ =_'= _ ='= ,_ ___= I .,'_,'-=-

I I I I I I I -10 5 10 15 20 25 30 35 Time, sec 000436 Figure B-19. Small doublet sequence (Mach 1.3 at 20,000 ft).

I r I I #,h deg I I I I I I -2 P, deg/sec .0 -50 r, deg/sec -5 -10 (_), deg -20 .5 my, g I I I I I I -.5 I I I 5dLEF | "IF 5dTEF RF 5a X. _/'-Sdh (_, _ L I--. ;_'__ _1 I .............. !__;_ ......

deg

-

v__5. "_ U , -

rl I I I I I -10 5 10 15 20 25 30 35 Time, sec 000437 Figure B-20. Small doublet sequence (Mach 1.3 at 15,000 ft).

APPENDIX C

STABILITY AND CONTROL DERIVATIVE INCREMENTS

OBTAINED FROM PARAMETER IDENTIFICATION ANALYSIS USING

CONTROL-SURFACE POSITION TRANSDUCER MEASUREMENTS

Tables C-1-C-5 show tabulated stability and control derivative increments as defined in

equations (26)-(30). These increments were obtained from the parameter estimation program, pEst (ref. 1), analysis that used the control-surface position transducer (CPT) measurements. Increments are defined by subtracting the simulation-predicted derivative from the flight-determined derivative and averaging the results from multiple maneuvers at each flight condition. The increments are separated into Mach number and altitude breakpoints. In some cases at Mach 1.05 and Mach 1.15, fight data were nonexistent, and interpolation or "hold last value" were used to complete the tables.

Table C- 1. Normal-force coefficient derivative increments as a function of Mach number and altitude (pEst program analysis with CPT surface positions).

Derivative Altitude, Mach nmnber increment kfl 0.85 0.90 0.95 1.05 1.10 1.15 1.20 1.30 5 0.06979 0.10511 0.11234 ACN b 10 0.05551 0.10475 0.11663 0.04612 0.05003 0.08459 0.11127 15 0.06213 0.09266 0.09976 0.03911 0.04582 0.07782 0.10983 0.12842 20 0.04476 0.05243 0.14339 0.09625 0.12896 25 0.04476 0.04255 0.10496 0.08776 0.09853 5 4).02561 4).00946 4).01352 ACN a 10 4).01667 4).01694 4).01819 4).01027 4).01382 4).01688 4).02451 15 4).01614 4).02590 4).02641 4).00823 4).01305 4).01867 4).02429 4).01023 20 4).01622 4).01915 4).02130 4).01651 4).01248 25 4).01622 4).01640 4).02592 4).02085 4).00373 5 1.44609 4).88377 4.66942 AC N q 10 0.56552 9.97219 15.63990 6.73941 _.85784 1.82020 3.82213 15 17.78343 4).63701 3.46427 3.36077 0.15169 2.53439 4.91708 10.73700 20 _.89814 3.46065 M.72085 9.26574 M.92922 25 _.89814 4).87555 1.10987 4.99502 5.22792 5 4).01505 0.00100 4).00655 ACN_LE F 10 4).00764 0.00122 4).00390 4).00662 4).00519 4).00148 4).00526 15 4).00536 4).00376 4).00285 4).00242 4).00365 4).00266 4).00167 4).00321 20 4).00178 4).00259 4).00091 0.00127 4).00149 25 4).00178 4).00099 0.00048 0.00055 0.00232 5 4).01020 4).01002 4).01697 ACN_TE F 10 4).00604 4).00962 4).01594 4).01186 4).01156 4).00980 4).01177 15 4).01090 4).00866 4).01222 4).01038 4).00789 4).00902 4).01015 4).01156 20 4).00953 4).00833 4).00942 4).00839 4).00965 25 4).00953 4).00756 4).00974 4).00845 4).00916 5 0.00221 4).00118 0.00045 10 0.00243 4).00128 0.00016 4).00028 0.00000 0.00016 0.00143 15 4).00094 4).00237 0.00084 4).00061 0.00028 0.00049 0.00070 0.00169 20 4).00111 4).00104 4).00009 0.00078 0.00047 25 4).00111 4).00115 0.00060 4).00029 0.00023 5 4).00091 0.00391 0.00297 ACN_ 10 4).00239 0.00767 4).00033 4).00213 0.00221 0.00146 0.00128 15 0.00248 0.00840 0.00181 4).00200 0.00102 0.00143 0.00185 4).00173 20 4).00063 4).00100 4).00451 0.00460 0.00154 25 4).00063 4).00032 4).00161 0.00101 0.00263

Table C-2. Pitching-moment coefficient derivative increments as a function of Mach number

and altitude (pEst program analysis with CPT surface positions).

Derivative Altitude, Mach number increment kfl 0.85 0.90 0.95 1.05 1.10 1.15 1.20 1.30 5 4).02569 4).02804 4).02636 ACre b 10 4).02702 4).03087 4).03054 4).03110 4).03501 4).04122 4).04251 15 4).02291 4).03043 4).02895 4).03334 4).03816 4).04185 4).04554 4).05075 20 4).02895 4).03558 4).03928 4).03554 4).04253 4).04872 25 4).02895 4).03558 4).03941 4).03684 4).04000 4).04767 5 0.01002 0.00897 0.00736 10 0.01013 0.01078 0.01016 0.01054 0.00571 0.00577 0.00559 15 0.01062 0.01112 0.01163 0.00921 0.00696 0.00577 0.00458 0.00389 20 0.00902 0.00830 0.00397 0.00424 0.00449 25 0.00902 0.00977 0.00595 0.00401 0.00383 5 _.54772 M.26513 6.46124 10 _.63694 0.83941 _.90439 4.12364 4.40901 3.45007 2.74548 15 3.69810 0.29697 6.54682 4.01878 3.67101 2.64762 1.62424 1.65979 20 4.42074 2.91068 6.14382 0.42716 4).48362 25 4.42074 2.36339 _.78240 0.10917 4).09082 5 0.00053 0.00005 4).00006 ACtaBLE F 10 0.00020 0.00043 4).00046 0.00250 0.00292 0.00517 0.00587 15 0.00024 0.00085 4).00030 0.00172 0.00407 0.00454 0.00500 0.00634 20 0.00172 0.00267 0.00484 0.00432 0.00523 25 0.00172 0.00195 0.00317 0.00431 0.00483 5 4).00019 4).00016 0.00094 A C mSTE F 10 4).00023 4).00021 0.00091 0.00119 0.00155 0.00119 0.00112 15 4).00049 4).00061 0.00016 0.00102 0.00075 0.00082 0.00088 0.00104 20 0.00073 0.00053 0.00043 0.00021 0.00031 25 0.00073 0.00051 4).00006 4).00014 4).00020 5 4).00260 4).00271 4).00267

ACre 8

10 4).00244 4).00212 4).00242 4).00135 4).00133 4).00130 4).00179 SOl 15 4).00229 4).00176 4).00212 4).00110 4).00109 4).00117 4).00125 4).00227 20 4).00080 4).00054 4).00072 4).00087 4).00137 25 4).00080 4).00060 4).00082 4).00030 4).00062 5 0.00144 0.00083 4).00083

AC

m, 8 10 0.00148 0.00236 4).00054 0.00262 0.00120 0.00091 0.00139 e 15 0.00073 0.00267 0.00170 0.00231 0.00224 0.00169 0.00114 0.00082 20 0.00276 0.00298 0.00244 0.00122 0.00093 25 0.00276 0.00296 0.00180 0.00083 0.00078

TableC-3.Side-force coefficient derivative asa function of Machnumber

andaltitude (pEstprogram analysis with CPTsurface positions).

Derivative Altitude, Mach number increment kfl 0.85 0.90 0.95 1.05 1.10 1.15 1.20 1.30 5 0.00173 0.00062 0.00293

ACy b

10 0.00103 0.00143 0.00141 0.00058 0.00175 0.00301 0.00427 15 0.00158 0.00096 0.00178 0.00074 0.00022 0.00084 0.00146 0.00126 20 0.00074 0.00058 0.00049 0.00104 0.00228 25 0.00074 0.00017 0.00140 0.00113 4).00096 5 0.00335 0.00242 0.00156

ACy_

10 0.00310 0.00196 0.00201 0.00245 0.00480 0.00410 0.00340 15 0.00288 0.00241 0.00215 0.00295 0.00402 0.00357 0.00312 0.00293 20 0.00295 0.00501 0.00362 0.00274 0.00318 25 0.00295 0.00471 0.00373 0.00285 0.00339 5 0.06451 0.27906 0.00729 ACyp 10 0.10673 0.07833 0.15440 0.06123 4).01400 4).00799 4).00197 15 0.11420 0.19665 0.05983 0.12477 0.14625 0.08136 0.01648 4).21429 20 0.12477 0.21426 0.14234 4).06754 4).16882 25 0.12477 0.14287 4).01868 0.06878 4).08240 5 1.59471 1.89223 1.47315 ACy r 10 1.08063 1.53549 1.44936 1.98186 1.47642 2.07620 2.67598 15 1.05871 1.62551 1.08966 1.16967 1.52738 1.24590 0.96441 2.17252 20 1.16967 1.20035 1.63484 1.17422 1.75038 25 1.16967 1.69706 1.13978 1.24084 1.56621 5 0.00054 0.00028 4).00046

AC

Y_ 10 0.00032 0.00046 4).00023 4).00125 4).00108 4).00110 4).00112 F 15 0.00032 0.00062 0.00003 4).00122 4).00131 4).00122 4).00112 4).00102 20 4).00122 4).00103 4).00135 4).00123 4).00089 25 4).00122 4).00088 4).00109 4).00123 4).00091 5 4).00018 4).00019 4).00020 ACY_dLEF 10 4).00009 4).00011 4).00034 4).00030 4).00030 4).00031 4).00032 15 4).00003 4).00024 4).00023 4).00029 4).00052 4).00038 4).00024 0.00016 20 4).00029 4).00052 4).00032 4).00023 0.00021 25 4).00029 4).00038 4).00024 4).00031 4).00014 5 4).00068 4).00041 4).00037 ACY_dTEF 10 4).00043 4).00037 4).00021 4).00086 4).00105 4).00143 4).00181 15 4).00039 4).00052 4).00008 4).00063 4).00071 4).00088 4).00105 4).00136 20 4).00063 4).00059 4).00090 4).00093 4).00103 25 4).00063 4).00058 4).00066 4).00073 4).00079 5 0.00000 0.00014 0.00021 10 4).00002 0.00002 0.00021 0.00006 0.00008 0.00024 0.00040 15 0.00008 4).00011 0.00033 0.00011 0.00009 0.00013 0.00017 0.00030 20 0.00011 0.00011 0.00024 0.00024 0.00026 25 0.00011 0.00026 0.00026 0.00032 0.00030 5 0.00062 0.00013 0.00057 10 0.00051 0.00038 0.00049 0.00073 0.00080 0.00092 0.00103 15 0.00067 0.00020 0.00056 0.00053 0.00039 0.00056 0.00073 0.00124 20 0.00053 0.00035 0.00061 0.00082 0.00115 25 0.00053 0.00040 0.00071 0.00078 0.00090 Table C-4. Rolling-moment coefficient derivative increments as a function of Mach number and altitude (pEst program analysis with CPT surface positions).

Derivative Altitude, Mach number increment kft 0.85 0.90 0.95 1.05 1.10 1.15 1.20 1.30 5 0.00255 0.00284 0.00240 AC1 b 10 0.00227 0.00289 0.00264 0.00181 0.00168 0.00166 0.00165 15 0.00204 0.00254 0.00244 0.00175 0.00143 0.00142 0.00141 0.00138 20 0.00175 0.00153 0.00123 0.00143 0.00138 25 0.00175 0.00142 0.00150 0.00129 0.00104 5 4).00071 4).00083 4).00017 ACI_ 10 4).00051 4).00091 0.00001 4).00054 4).00073 4).00071 4).00068 15 4).00048 4).00072 0.00003 4).00037 4).00033 4).00039 4).00046 4).00037 20 4).00037 4).00026 4).00037 4).00032 4).00026 25 4).00037 4).00022 4).00018 4).00006 4).00009 5 0.06601 4).02057 0.00743 AClp 10 0.10004 4).05228 0.03795 0.11243 0.10277 0.08755 0.07232 15 0.08280 0.00995 0.03442 0.07916 0.13382 0.10325 0.07268 0.03075 20 0.07916 0.09547 0.09121 0.04021 0.02686 25 0.07916 0.04632 0.05471 0.06143 0.02816 5 0.12767 0.11411 0.14699 AC1 r 10 4).00724 0.02933 0.03625 0.15072 0.08140 0.17372 0.26603 15 4).16914 4).06754 0.13239 0.10671 0.13990 0.08385 0.02779 0.10871 20 0.10671 0.11046 0.07153 0.01493 0.06237 25 0.10671 0.24774 0.02164 0.02590 0.14876 5 0.00001 4).00012 4).00014 AC18 10 4).00003 0.00000 4).00017 4).00027 4).00019 4).00019 4).00019 r 15 4).00004 4).00006 4).00011 4).00026 4).00030 4).00024 4).00017 4).00013 20 4).00026 4).00024 4).00024 4).00018 4).00014 25 4).00026 4).00017 4).00021 4).00018 4).00016 5 0.00022 4).00080 4).00149 AC18dLEF 10 0.00016 4).00044 4).00088 4).00141 4).00144 4).00150 4).00156 15 0.00019 4).00007 4).00031 4).00079 4).00084 4).00096 4).00108 4).00109 20 4).00079 4).00021 4).00042 4).00044 4).00058 25 4).00079 0.00031 0.00013 4).00001 4).00016 5 0.00012 0.00007 0.00000 AC18dTEF 10 0.00008 0.00017 0.00004 4).00010 4).00014 4).00014 4).00014 15 0.00003 0.00003 0.00003 4).00012 4).00010 4).00009 4).00007 4).00003 20 4).00012 4).00010 4).00009 4).00007 4).00003 25 4).00012 4).00010 4).00004 0.00000 4).00001 5 0.00029 0.00019 0.00013 10 0.00027 0.00015 0.00013 0.00011 0.00010 0.00018 0.00025 15 0.00018 0.00016 0.00015 0.00002 0.00001 0.00008 0.00016 0.00021 20 0.00002 4).00007 0.00004 0.00008 0.00011 25 0.00002 4).00009 4).00002 0.00002 0.00002 5 0.00011 0.00013 0.00012 10 0.00004 0.00018 0.00004 0.00002 0.00002 0.00007 0.00013 15 0.00006 0.00001 0.00003 0.00002 4).00007 4).00002 0.00002 0.00005 20 0.00002 4).00002 4).00007 4).00001 4).00001 25 0.00002 0.00000 4).00004 4).00009 4).00007

Table C-5. Yawing-moment coefficient derivative increments as a function of Mach number

and altitude (pEst program analysis with CPT surface positions).

Derivative Altitude, Mach nmnber increment kfl 0.85 0.90 0.95 1.05 1.10 1.15 1.20 1.30 5 4).00093 4).00092 4).00092

AC%

10 4).00072 4).00081 4).00079 4).00063 4).00103 4).00113 4).00124 15 4).00072 4).00077 4).00090 4).00061 4).00074 4).00089 4).00104 4).00096 20 4).00061 4).00078 4).00098 4).00095 4).00092 25 4).00061 4).00073 4).00104 4).00096 4).00065 5 4).00055 4).00052 4).00022

AC

n_

10 4).00058 4).00061 4).00029 4).00009 4).00080 4).00078 4).00076 15 4).00061 4).00063 4).00036 4).00019 4).00053 4).00060 4).00067 4).00045 20 4).00019 4).00071 4).00088 4).00069 4).00048 25 4).00019 4).00076 4).00086 4).00073 4).00053 5 0.03857 0.02943 0.02655 ACnp 10 0.02005 0.00187 0.03523 0.02757 0.04900 0.04749 0.04598 15 0.01695 4).00060 0.03056 0.01556 0.02198 0.03568 0.04938 0.02957 20 0.01556 0.03388 0.04157 0.04543 0.03165 25 0.01556 0.03649 0.05389 0.05040 0.01259 5 4).11558 4).15808 4).09831 ACn r 10 4).10645 4).16395 4).18070 4).13104 4).12559 4).15489 4).18419 15 4).17609 4).26857 4).11925 4).07472 4).06409 4).08337 4).10265 4).19113 20 4).07472 4).09351 4).11078 4).11250 4).18217 25 4).07472 4).17234 4).15027 4).14854 4).11559 5 4).00001 0.00000 0.00025

ACna

10 4).00001 4).00001 0.00015 0.00058 0.00048 0.00036 0.00024 r 15 0.00003 4).00008 0.00003 0.00058 0.00055 0.00039 0.00023 0.00017 20 0.00058 0.00049 0.00037 0.00023 0.00020 25 0.00058 0.00041 0.00030 0.00026 0.00020 5 0.00005 0.00006 0.00011

AC

nSdLEF 10 0.00005 0.00005 0.00012 0.00011 0.00013 0.00013 0.00014 15 0.00003 0.00007 0.00011 0.00011 0.00013 0.00013 0.00012 0.00008 20 0.00011 0.00012 0.00013 0.00012 0.00008 25 0.00011 0.00010 0.00010 0.00010 0.00012 5 0.00011 0.00008 0.00005

AC

nSdTEF 10 0.00012 0.00011 0.00006 0.00023 0.00026 0.00033 0.00040 15 0.00010 0.00011 0.00004 0.00019 0.00018 0.00026 0.00034 0.00036 20 0.00019 0.00018 0.00024 0.00029 0.00030 25 0.00019 0.00017 0.00022 0.00025 0.00025 5 4).00002 4).00004 4).00005

AC

n_ 10 0.00003 0.00000 4).00004 0.00001 4).00001 4).00003 4).00005 a 15 0.00002 0.00001 4).00005 0.00000 4).00001 4).00003 4).00005 4).00007 20 0.00000 4).00002 4).00002 4).00004 4).00007 25 0.00000 4).00002 4).00001 0.00000 4).00005 5 4).00002 0.00001 0.00001

AC

n_dh 10 0.00004 0.00006 0.00001 4).00011 4).00019 4).00021 4).00023 15 0.00005 0.00005 0.00001 4).00009 4).00011 4).00017 4).00022 4).00026 20 4).00009 4).00015 4).00020 4).00019 4).00023 25 4).00009 4).00013 4).00018 4).00019 4).00018

APPENDIX D

STABILITY AND CONTROL DERIVATIVE INCREMENTS OBTAINED

FROM PARAMETER IDENTIFICATION ANALYSIS USING ROTARY

VARIABLE DIFFERENTIAL TRANSFORMER MEASUREMENTS

Tables D-l-D-5 show tabulated stability and control derivative increments as defined in

equations (26)-(30). These increments were obtained from the parameter estimation program, pEst (ref. 1), analysis that used the rotary variable differential transducer (RVDT) measurements. Increments are defined by subtracting the simulation-predicted derivative from the flight-determined derivative and averaging the results from multiple maneuvers at each flight condition. The increments are separated into Mach number and altitude breakpoints. In some cases at Mach 1.05 and Mach 1.15, fight data were nonexistent, and interpolation or "hold last value" were used to complete the tables.

Table D- 1. Normal-force coefficient derivative increments as a function of Mach number and altitude (pEst program analysis with RVDT surface positions).

Derivative Altitude, Mach nmnber increment kfl 0.85 0.90 0.95 1.05 1.10 1.15 1.20 1.30 5 0.07809 0.10914 0.10919 ACN b 10 0.06830 0.10718 0.11536 0.04568 0.04449 0.08381 0.11574 15 0.07070 0.09748 0.10378 0.03827 0.04401 0.07744 0.11088 0.13640 20 0.04756 0.05518 0.15042 0.09891 0.13077 25 0.04756 0.04487 0.10897 0.09163 0.10244 5 4).00728 4).01387 4).00236 ACN a 10 4).00858 4).02191 4).00885 4).00414 4).01226 4).01370 4).02097 15 4).01349 4).02377 4).01936 4).00506 4).00991 4).01608 4).02225 4).00856 20 4).01476 4).01698 4).02070 4).01672 4).00916 25 4).01476 4).01338 4).02561 4).02017 4).00391 5 4.51911 34.07513 0.07418 AC N q 10 0.73089 52.93171 14.75774 1.11457 3.47850 8.48389 8.33281 15 23.01455 5.46610 0.68781 2.58764 21.08836 13.95645 6.82453 12.85931 20 5.99556 8.52812 M.66909 9.22458 7.61891 25 5.99556 8.24887 4).61660 15.81876 9.91289 5 0.00166 0.02428 4).00847 ACN_LE F 10 4).00325 0.00913 4).00210 4).01255 4).01261 4).00059 4).01224 15 4).01199 4).00318 4).00352 4).00507 4).00418 4).00416 4).00414 4).00888 20 4).00678 4).00632 4).00294 4).00116 4).00510 25 4).00678 4).00392 4).00101 4).00096 0.00309 5 4).00881 4).00463 4).01523 ACN_TE F 10 4).00416 4).00487 4).01598 4).01207 4).01233 4).00973 4).01191 15 4).01124 4).00568 4).01246 4).01010 4).00631 4).00829 4).01026 4).01193 20 4).00913 4).00821 4).00936 4).00834 4).00958 25 4).00913 4).00740 4).00948 4).00807 4).00863 5 0.00350 0.00034 0.00064 ACN_ 10 0.00311 0.00112 0.00075 4).00073 4).00031 0.00035 0.00104 SOl 15 4).00117 4).00233 0.00124 4).00122 0.00007 0.00018 0.00029 0.00150 20 4).00155 4).00162 4).00070 0.00032 0.00030 25 4).00155 4).00159 4).00011 4).00058 0.00004 5 4).00452 0.00992 0.00335 ACN_ 10 4).00331 0.01215 4).00041 4).00333 0.00364 0.00153 0.00146 15 0.00371 0.00981 4).00399 4).00125 0.00354 0.00242 0.00131 4).00235 20 4).00226 4).00162 4).00548 0.00251 0.00197 25 0.00226 0.00229 0.00242 0.00099 0.00050

Table D-2. Pitching-moment coefficient derivative increments as a function of Mach number

and altitude (pEst program analysis with RVDT surface positions).

Derivative Altitude, Mach number increment kfl 0.85 0.90 0.95 1.05 1.10 1.15 1.20 1.30 5 4).02366 4).02982 4).02506 ACre b 10 4).02554 4).03175 4).02787 4).02852 4).03026 4).03489 4).03600 15 4).02204 4).03159 4).02693 4).02836 4).03375 4).03526 4).03677 4).04625 20 4).03303 4).03591 4).03018 4).03663 4).04162 25 4).03303 4).03633 4).03219 4).03426 4).04425 5 0.01243 0.01251 0.01023 10 0.01263 0.01280 0.01386 0.01222 0.00748 0.00530 0.00501 15 0.01232 0.01310 0.01366 0.00989 0.00711 0.00590 0.00470 0.00595 20 0.01140 0.01030 0.00448 0.00592 0.00354 25 0.01140 0.01122 0.00749 0.00495 0.00575 5 0.06823 0.98749 3.29898 10 _.54572 4).51536 O.14333 5.20828 3.41662 1.45447 3.02996 15 3.21019 1.10825 O.48105 3.29556 0.08441 1.51519 2.94598 2.45931 20 0.41598 1.01649 6.46238 4).69409 0.53175 25 0.41598 0.06170 0.94509 0.06909 1.67706 5 4).00061 0.00099 4).00343 ACtabLE F 10 4).00012 4).00020 4).00228 0.00204 0.00224 0.00529 0.00655 15 4).00078 0.00043 4).00223 0.00039 0.00401 0.00442 0.00483 0.00640 20 0.00043 0.00188 0.00487 0.00432 0.00548 25 0.00043 0.00067 0.00283 0.00428 0.00434 5 4).00101 4).00061 0.00036 ACtuaTE F 10 4).00081 4).00078 0.00035 0.00066 0.00084 0.00082 0.00079 15 4).00119 4).00094 4).00024 0.00031 4).00022 0.00018 0.00057 0.00080 20 4).00015 4).00017 4).00005 4).00011 4).00007 25 4).00015 4).00032 4).00077 4).00069 4).00059 5 4).00212 4).00160 4).00209

AC

m,_ 10 4).00163 4).00125 4).00179 4).00087 4).00090 4).00103 4).00153 sa 15 4).00145 4).00070 4).00181 4).00067 4).00063 4).00079 4).00095 4).00202 20 4).00032 4).00009 4).00029 4).00051 4).00120 25 4).00032 4).00011 4).00031 0.00002 4).00033 5 0.00448 0.00690 0.00349

AC

m, 10 0.00550 0.00821 0.00353 0.00592 0.00456 0.00333 0.00346 e 15 0.00563 0.00801 0.00371 0.00432 0.00503 0.00410 0.00318 0.00373 20 0.00600 0.00588 0.00438 0.00399 0.00218 25 0.00600 0.00584 0.00439 0.00366 0.00364

TableD-3.Side-force coefficient derivative increments asa function of Machnumber

andaltitude (pEstprogram analysis withRVDTsurface positions).

Derivative Altitude, Mach number increment kfl 0.85 0.90 0.95 1.05 1.10 1.15 1.20 1.30 5 0.00265 4).00005 0.00447

ACy b

10 0.00138 0.00132 0.00177 0.00050 0.00183 4).00153 4).00489 15 0.00196 0.00069 0.00283 0.00105 0.00078 0.00123 0.00168 0.00180 20 0.00105 0.00078 0.00071 0.00201 0.00247 25 0.00105 0.00025 0.00205 0.00127 4).00089 5 0.00357 0.00307 0.00161

ACy_

10 0.00369 0.00277 0.00228 0.00306 0.00503 0.00416 0.00330 15 0.00300 0.00336 0.00229 0.00343 0.00487 0.00397 0.00307 0.00289 20 0.00343 0.00578 0.00409 0.00296 0.00315 25 0.00343 0.00521 0.00433 0.00317 0.00375 5 4).01047 0.54748 4).10553 ACyp 10 0.15762 0.25652 0.25682 0.12048 0.01360 4).01863 4).05085 15 0.14575 0.36796 0.03738 0.19439 0.26463 0.12335 4).01793 4).24676 20 0.19439 0.30710 0.16524 4).11841 4).19469 25 0.19439 0.16126 0.05737 0.15680 4).04527 5 2.03979 2.29597 1.90942 ACy r 10 1.64535 2.16166 1.92500 2.06169 1.54622 2.20620 2.86617 15 0.60019 2.07808 1.45936 1.60374 1.73333 1.46482 1.19632 2.47005 20 1.60374 1.07318 1.41458 1.14416 1.70608 25 1.60374 1.39307 0.46331 0.74092 1.67241 5 4).00006 4).00047 4).00082

AC

Y_ 10 4).00026 4).00011 4).00093 4).00166 4).00146 4).00144 4).00142 r 15 4).00026 4).00005 4).00051 4).00146 4).00143 4).00143 4).00142 4).00117 20 4).00146 4).00130 4).00144 4).00134 4).00119 25 4).00146 4).00130 4).00122 4).00147 4).00112 5 4).00015 4).00063 4).00025 ACY_dLEF 10 4).00023 4).00031 4).00075 4).00079 4).00076 4).00064 4).00052 15 4).00003 4).00051 4).00030 4).00073 4).00119 4).00073 4).00027 0.00007 20 4).00073 4).00096 4).00083 4).00029 0.00043 25 4).00073 4).00050 4).00049 4).00070 4).00034 5 4).00057 4).00044 4).00033 ACY_dTEF 10 4).00048 4).00044 4).00019 4).00063 4).00092 4).00134 4).00177 15 4).00021 4).00047 0.00000 4).00048 4).00051 4).00078 4).00104 4).00122 20 4).00048 4).00036 4).00088 4).00082 4).00089 25 4).00048 4).00034 4).00040 4).00052 4).00069 5 4).00002 0.00003 0.00020 10 4).00014 4).00011 0.00018 0.00004 0.00000 0.00015 0.00030 15 4).00001 4).00029 0.00032 0.00008 0.00004 0.00008 0.00012 0.00020 20 0.00008 0.00004 0.00021 0.00017 0.00019 25 0.00008 0.00027 0.00018 0.00026 0.00020 5 0.00076 4).00003 0.00085 10 0.00070 0.00026 0.00053 0.00070 0.00081 0.00094 0.00108 15 0.00102 0.00040 0.00070 0.00052 0.00036 0.00056 0.00077 0.00112 20 0.00052 0.00043 0.00067 0.00091 0.00108 25 0.00052 0.00053 0.00070 0.00085 0.00081 Table D-4. Rolling-moment coefficient derivative increments as a function of Mach number and altitude (pEst program analysis with RVDT surface positions).

Derivative Altitude, Mach number increment kft 0.85 0.90 0.95 1.05 1.10 1.15 1.20 1.30 5 0.00281 0.00325 0.00333 AC1 b 10 0.00242 0.00310 0.00311 0.00237 0.00203 0.00150 0.00096 15 0.00194 0.00250 0.00265 0.00206 0.00175 0.00158 0.00141 0.00152 20 0.00206 0.00194 0.00136 0.00164 0.00155 25 0.00206 0.00225 0.00175 0.00144 0.00109 5 4).00079 4).00096 4).00052 ACI_ 10 4).00068 4).00100 4).00013 4).00093 4).00119 4).00117 4).00114 15 4).00060 4).00084 4).00002 4).00057 4).00058 4).00060 4).00062 4).00052 20 4).00057 4).00054 4).00056 4).00059 4).00049 25 4).00057 4).00066 4).00042 4).00024 4).00023 5 0.04713 4).07282 4).14428 AClp 10 0.07963 4).06273 4).04300 0.00651 0.01161 4).01882 4).04925 15 0.09243 0.02729 4).00118 0.04349 0.09590 0.06625 0.03661 4).04897 20 0.04349 0.02379 0.03129 4).01717 4).02633 25 0.04349 4).07799 4).00805 0.03298 0.00016 5 0.29574 0.14842 0.13387 AC1 r 10 0.05536 0.11723 0.09417 0.22771 0.00858 0.15274 0.29691 15 4).13846 0.10623 0.21498 0.08709 0.13068 0.10934 0.08799 0.15764 20 0.08709 0.13782 0.02241 4).00901 0.11797 25 0.08709 0.00515 4).07076 4).00445 0.18159 5 0.00002 4).00016 4).00010 ACI_ 10 4).00004 4).00009 4).00016 4).00026 4).00021 4).00020 4).00018 r 15 4).00011 4).00011 4).00016 4).00026 4).00027 4).00021 4).00016 4).00010 20 4).00026 4).00024 4).00017 4).00017 4).00013 25 4).00026 4).00008 4).00019 4).00017 4).00014 5 0.00032 4).00051 4).00082 ACISdLEF 10 0.00029 4).00029 4).00047 4).00060 4).00054 4).00069 4).00083 15 0.00027 0.00000 4).00010 4).00034 4).00044 4).00062 4).00080 4).00038 20 4).00034 0.00018 0.00000 4).00002 4).00021 25 4).00034 0.00071 0.00043 0.00021 0.00010 5 0.00004 0.00004 4).00003 ACI_dTEF 10 0.00005 0.00013 0.00003 4).00012 4).00013 4).00016 4).00018 15 4).00003 4).00007 0.00002 4).00010 4).00009 4).00008 4).00007 4).00007 20 4).00010 4).00007 4).00009 4).00006 4).00003 25 4).00010 4).00004 4).00001 0.00002 0.00000 5 0.00018 0.00010 0.00012 10 0.00018 0.00007 0.00010 0.00008 0.00006 0.00014 0.00023 15 0.00007 0.00004 0.00010 4).00003 4).00003 0.00005 0.00013 0.00011 20 4).00003 4).00011 0.00000 0.00005 0.00008 25 4).00003 4).00009 4).00006 4).00002 4).00002 5 4).00001 0.00005 0.00015 10 4).00004 0.00008 0.00002 4).00005 4).00008 0.00001 0.00009 15 4).00004 4).00011 4).00005 4).00013 4).00018 4).00015 4).00013 4).00008 20 4).00013 4).00010 4).00017 4).00010 4).00009 25 4).00013 0.00009 4).00011 4).00019 4).00018

Table D-5. Yawing-moment coefficient derivative increments as a function of Mach number

and altitude (pEst program analysis with RVDT surface positions).

Derivative Altitude, Mach number increment kfl 0.85 0.90 0.95 1.05 1.10 1.15 1.20 1.30 5 4).00107 4).00112 4).00106

AC%

10 4).00079 4).00094 4).00085 4).00058 4).00109 4).00090 4).00071 15 4).00082 4).00081 4).00104 4).00067 4).00079 4).00096 4).00113 4).00109 20 4).00067 4).00074 4).00099 4).00109 4).00099 25 4).00067 4).00055 4).00103 4).00089 4).00066 5 4).00057 4).00054 4).00026

AC

n_

10 4).00065 4).00064 4).00032 4).00024 4).00087 4).00081 4).00076 15 4).00064 4).00079 4).00037 4).00026 4).00065 4).00066 4).00068 4).00048 20 4).00026 4).00083 4).00093 4).00073 4).00048 25 4).00026 4).00097 4).00097 4).00079 4).00056 5 0.03266 0.02126 0.00569 ACnp 10 0.00872 4).00292 0.01324 0.00747 0.04265 0.04765 0.05264 15 0.01713 4).01846 0.01258 0.00839 0.00685 0.02623 0.04561 0.03788 20 0.00839 0.01497 0.03027 0.04652 0.03668 25 0.00839 0.00346 0.03422 0.03814 0.00903 5 4).14721 4).20850 4).17061 ACn r 10 4).16353 4).21550 4).22506 4).14360 4).16997 4).19693 4).22389 15 4).19311 4).40989 4).20990 4).11683 4).11609 4).14923 4).18237 4).25447 20 4).11683 4).12992 4).21220 4).19752 4).24631 25 4).11683 4).22664 4).22742 4).22180 4).20911 5 0.00025 0.00022 0.00043 10 0.00024 0.00020 0.00042 0.00072 0.00060 0.00046 0.00032 15 0.00026 0.00018 0.00027 0.00070 0.00067 0.00050 0.00033 0.00027 20 0.00070 0.00065 0.00050 0.00032 0.00029 25 0.00070 0.00059 0.00044 0.00039 0.00031 5 0.00007 0.00009 0.00024

AC

nSdLEF 10 0.00008 0.00007 0.00021 0.00025 0.00022 0.00020 0.00017 15 0.00004 0.00010 0.00018 0.00020 0.00024 0.00020 0.00017 0.00008 20 0.00020 0.00020 0.00021 0.00017 0.00007 25 0.00020 0.00017 0.00016 0.00015 0.00015 5 0.00009 0.00006 0.00003

AC

nSdTEF 10 0.00010 0.00010 0.00005 0.00017 0.00022 0.00029 0.00037 15 0.00007 0.00008 0.00004 0.00015 0.00014 0.00023 0.00031 0.00029 20 0.00015 0.00013 0.00020 0.00025 0.00026 25 0.00015 0.00012 0.00017 0.00019 0.00021 5 4).00002 4).00004 4).00005

AC

n_ 10 0.00003 4).00001 4).00003 0.00000 4).00001 4).00002 4).00004 a 15 0.00000 0.00001 4).00005 4).00001 0.00000 4).00002 4).00004 4).00006 20 4).00001 4).00001 4).00002 4).00003 4).00006 25 4).00001 4).00001 0.00000 0.00001 4).00004 5 4).00004 4).00001 0.00000

AC

nSdh 10 0.00001 0.00003 0.00000 4).00009 4).00018 4).00020 4).00022 15 4).00001 0.00002 0.00000 4).00010 4).00011 4).00015 4).00019 4).00024 20 4).00010 4).00014 4).00019 4).00018 4).00022 25 4).00010 4).00008 4).00015 4).00017 4).00017

REFERENCES

1. Murray, James E. and Richard E. Maine, pEst Version 2.1 User's Manual, NASA TM-88280, 1987.

2. Maine, Richard E. and Kenneth W. Iliff, Application of Parameter Estimation to Aircraft Stability and Control: the Output-Error Approach, NASA RP-1168, 1986.

3. United States Naval Air Systems Command, Preliminary NATOPS Flight Manual: Navy Model

F/TF-18A, A1-F18AA-NFM-000, Feb. 1980.

4. Carter, John F., Production Support Flight Control Computers: Research Capability for F/A-18 Aircraft at Dryden Flight Research Center, NASA TM-97-206233, 1997.

5. Whitmore, Stephen A., Roy J. Davis, and John Michael Fife, In-Flight Demonstration of a

Real-Time Flush Airdata Sensing (RT-FADS) System, NASA TM-104314, 1995.

6. Maine, R. E. and K. W. Iliff, Identification of Dynamic Systems, AGARD-AG-300, vol. 2, Jan. 1985.

(Also available as NASA RP-1138, 1985).

7. Gainer, Thomas G. and Sherwood Hoffman, Summary of Transformation Equations and Equations of Motion Used in Free-Flight and Wind-Tunnel Data Reduction and Analysis, NASA SP-3070, 1972.

8. Iliff, Kenneth W. and Richard E. Maine, Practical Aspects of Using a Maximum Likelihood

Estimation Method to Extract Stability and Control Derivatives From Flight Data, NASA

TN-D-8209, 1976.

REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188 Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing 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 Headquarters Services, Directorate for Information Operations and Re )orts, 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503.

1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORTTYPE AND DATES COVERED

November 2000 Technical Publication

4.TITLE AND SUBTITLE 5. FUNDING NUMBERS

Results From F-18B Stability and Control Parameter Estimation Flight

Tests at High Dynamic Pressures

WU 529-61-14-E8-14-00-SRA

6. AUTHOR(S)

Timothy R. Moes, Gregory K. Noffz, and Kenneth W. Iliff

8. PERFORMING ORGANIZATION 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) REPORT NUMBER

NASA Dryden Flight Research Center

RO. Box 273

H-2424

Edwards, California 93523-0273

10. SPONSORING/MONITORING 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) AGENCY REPORT NUMBER

National Aeronautics and Space Administration

NASA/TP-2000-209033

Washington, DC 20546-0001

11. SUPPLEMENTARY NOTES 12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE

Unclassified--Unlimited

Subject Category 08

This report is available at http://www.dfrc.nasa.gov/DTRS/

13. ABSTRACT (Maximum 200 words) A maximum-likelihood output-error parameter estimation technique has been used to obtain stability and control derivatives for the NASA F-18B Systems Research Aircraft. This work has been performed to support flight testing of the active aeroelastic wing (AAW) F-18A project. The goal of this research is to obtain baseline F-18 stability and control derivatives that will form the foundation of the aerodynamic model for the AAW aircraft configuration. Flight data have been obtained at Mach numbers between 0.85 and 1.30 and at dynamic pressures ranging between 600 and 1500 lbf/ft 2. At each test condition, longitudinal and lateral-directional doublets have been performed using an automated onboard excitation system. The doublet maneuver consists of a series of single-surface inputs so that individual control-surface motions cannot be correlated with other control-surface motions. Flight test results have shown that several stability and control derivatives are significantly different than prescribed by the F-18B aerodynamic model. This report defines the parameter estimation technique used, presents stability and control derivative results, compares the results with predictions based on the current F-18B aerodynamic model, and shows improvements to the nonlinear simulation using updated derivatives from this research.

14. SUBJECTTERMS 15. NUMBER OF PAGES Active aeroelastic wing, Control derivatives, Maximum likelihood estimates, 16. PRICE CODE

Parameter identification, Stability derivatives

A07

17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATION OF ABSTRACT OF REPORT OFTHIS PAGE OF ABSTRACT

Unclassified Unclassified Unclassified Unlimited

NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89) Prescribed by ANSI Std. Z39-18 298-102