Aircraft stability and control data

SECTION I INTRGDUC TION The purpose of this document is to provide handling qualities investi- gators with readily usable data on various cl_rrent aircraft. Included are those data required to obtain transfer functLons relating the aircraft's response to control inputs. An analytical description of the aircraft's stability au_nentor is also given.

_or those aircraft for which complete information was available, the folIowLng summarizes the contents and presentation: ]. A y_eneral description is gLven_ including: a. Three-view drawing and reference geometry.

b. Flight envelope.

c. Nominal configuration (weight, inertias, and c.g.

location).

d. References.

e. Basic data sources.

A block diagram of the augmentor showing feedbacks, gains, and scheduling.

Trim angle-of-attack and elevator versus Mach number and altitude.

4.

Longitudinal s_d lateral nondimensional stability derivatives* versus Mach number and altitude for the trimmed nominal configu- ration.

Geometrical parameters, longitudinal and lateral dimensional derivatives, and longitudin_ml and lateral transfer functions for the nominal configuration at various flight conditions.

These data are usually given for body-fixed centerline axes (body axe s ).

For the remaining aircraft, some portion of the above is presented as dictated by the limits of the available data.

*_ese are given for the axis system of the data source.

TR-176-I I

The intention has been to makethis report completely self-consistent

insofar as symbols, nomenclature, definitions, etc. The system used is

described in three appendices. Appendix A covers axis systems, symbols

and notation, and definitions of nondimensional and dimensional stability

derivatives. Appendix B gives the axis system transformations for the

derivatives. Appendix C includes the aircraft equations of motion and

transfer functions used herein.

While complete coverage of each aircraft including only the "latest"

s_d "best" data would be desirable, the major criterion used was that the

data be immediately accessible to the author. This is why only isolated

flight conditions are given for someaircraft, and also why, as those

people more intimately familiar with each particular aircraft will recog-

nize, the data presented may represent an early estimate in the design

process and perhaps the "nominal configuration" is one which never left

the drawing board. The data have been reviewed and, although not all

those presented indicate unquestionable trends, those data known to be

based on only early "guesstimates" or showing unreasonable trends have

been deleted. As to how well the data can be expected to match the flying

aircraft_ it is assumedthat those for whomthis document is intended

know well the difficulties of obtaining derivatives from flight test data.

Every attempt has been madeto insure reliable translation, interpretation, and transcription of the data from their source documents.

The manufacturers of the aircraft described herein can not be held

accou_itable for tile infomnation presented, nor would they be bolmd to

concur in any conclusions with respect to their aircraft which might be

derived from its use.

'lYe- 176-l 2

SECTION II A-TA I c_ NOMINAL CRUISE CONFIGURATION FLIGHT ENVELOPE i Cleon Airplane 60% Fuel 40,000 X X W = 21,8891bs h, (ft) CG at 30%MGC Ix =13,635 Slug ft 2 Body 20,000 [y = 58,966 Slug ft z Ref.

X X X X I z = 67,560 Slug ft 2 Axes Ixz =2,933 Slug ft z REFERENCE GEOMETRY O0 .4 . 1.2 S = 375 ft 2 X Tronsfer functions given c = 10.8 ft for these flight condlHons b = 38.7ft I) LTV Vought Aeronautics Div. Rept. No. 2-53310/5R-1981, '_,-TA Aerodynamics Data Report" 21 Moy 1965 (U) 2) LTV Vought Aeronoutics Div. Rept. No. 2-53310/5R-5121, Rev. I ,"A-7A Estimoted Flying Quollties" 20 August 1965 (C) 3) LTV Vought Aeronoutics Div. ,"Updoted A-TA Aircraft LateroI-Directionol Cruise Device Configurotion Doto, 25 Augur 1967 BASIC DATA SOURCES Wind Tunnel Test ond

est,motes u

Some LoteroI-Directionol Derivotives Adjusted After Flight Test PITCH AXIS GZ , X = • v (ft/sec z) A-7A ' i) }-_: 55s + (Ib) 57.3 Ib _ep _._ .5 rad _j I

1-

-.25 rad rad/sec 152.2 rad i_

5z3 ft/sec2 I-

ROLL AXIS

(Ib) = 5L_ __] -L!2_iic.,_+,l (rad/sec) =-

. rod p i

rad _ .10 rad/sec I_ YAW AXIS (rad/sec) rR6 _rp A-TB (red/sec) I,_ _-_,

r --_. Cos 2.50 b

P _-J Sin 2.5 ° (red/sec) t red I__ __+1 = -2 5 rad/se_ F _KARI

aa

T.E. up l°t/I

(rcJd) _e (deg) 1.5 Figtu.e 11-2. A-TA [_tabilit¥ Au{_rtentation System I , ,ooof, ...........

Sea Level GO I0 (deg) \ _ _N35,000ft ..............

_f ....

2- i L i I

°6 .2

.4 .6 M .8 1.0 1.2 -I0 ,15,00Oft I I Sea Level -6 " (deg) I m 4 ....

-2 0 .2 .4 .6 .8 1.0 1.2 M TR--] 76-I _ .8

I

15,000ft .6 eL .2 O0 .2 .4 .6 .8 1.0 1.2 M .14 15,000ft .12 I CD .08

.............. Sea Le!: ¸-

.04 \ .2 .4 .6 M .8 1.0 .2 TR-176-1 7 6~----~----~-- ----~----~--- --~ ----~

(r~d)

+-- ---~---~--- ----

.2 1.0 1.2

.4 .6 M .8

°

2 . 0,.- - ---r--- - , -- ' -----, I

~ 15,000ft

1.6

Sea Lev~l\

\

~ 35,000ft

\

.8 --

"-'-,,- i

\

"- I

\ '-

"-

\ i 1 I) I

~ =-= ~

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--0 .... >

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.12 i-.-------:----r----,.---

l /p 35,OOOft

. 08 --

/~

/ / .04 15, OO Oft .

/

/ / I

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o --

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/

./ I

-. 04 - /'

0' Sea Level

I - I

- . 08

.2 .6

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.12 [---

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Sea Leve' ::r

35,OOOft

,

15,000ft ~

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C

O fV'

. 04

\ /

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tf

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-.04 -

o .4 .6 8

I ~ r~ -: i -I 10 .O4 I I Sea Level ', Cm M -.04 \ "_' 15,000 f, -.08 - \ \

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-.12 - ..

\ © ss,ooo, i

i I

i -'160 .2 .6 1.2 4 M .8 1.0 TR-17,]-i I1 .8

_.&.35.oo'o.t

.6 CLB e "" _ ' \ _.151000ft .4 ........ T"""..

.2 ..............

!

[ l t 0 o .2 .2 .4 .6 M .8 1.0 .4 .6 M .8 1.0 0 1.2 J..

-.60

......... -I ......... .......... !...... i....... 7-

/ Sea Level -.80

__ !___....._? e_ ,//-_

CmB e ! , ,,_ 15,00Oft -1.00 ..........

_ 35,00Oft I t -1.20 0 .2 .4. .6 M .8 1.0 1.2

[ L

Cy.8 -.7 1.- --------E_,_ -- -- ------ ............. i ......... 1 .............. 7..................

_ -.8 ............

Sea Level/_ I --'- -i ....

-I.0 ] i l 0 .2 .4 .6 M .8 1.0 1.2 -.06 ...... _-C__35_,QQQf 1 .....

-.lot- ............:f--_- .............

I J

/Sea Level "(.D ....... [C-;_- _---

I

-.izl i

TR- 17c7-1 13 .6 M .8 .2 .4 1.0 .2 .12 Sea Level 35,000 ft 15,000 Cn/_ ,10 li7_ .O8 .06 mR-17<7-1 14 .6 M ,8 1.0 .4 1.2 .2 0 o -.I C_p i Sea Level _3 35,oo; _i__ 15,ooo.

-.4 .....

-,5 .O6

I

I I i .O4 Cnp .02 15,00Oft l

t-

Sea Level ii135,000, ft -.02 -.040

.2 T '

L 35,00Oft C._r Sea Level _'_',,,u _. ".-,. -- ,-- 4,,..

I 15,00Oft O0 -- . .4 .6 M .8 1.0 1.2 0 .2 .4 .6 M .8 1.0 .2 Cnr , _/"'_ _'_ ,. Sea Level

/'i "\

t : I _ | 55, O00f,\ "NI5'OOOft -.s6--- J---_....... _ ........... ]............. t-----:, -- \ <- --- ....

!

-.40 ................. [

M 1.2 0 0 .2 z .6 .8 1.0

! ,5,ooof, p

-.01 (_._.._ I See Leve_ / -.02 -.05 _QR- _OL (Includes Spoiler Effects) _Q - .O8 .O6 C_.8 o

(')

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0 o .2 .4 .6 1.2 M .8 1.0 TR- 1 yC-I i9 !

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!

b b b b 0 oo _b PO TABLE II-A GEOMETRICAL PARAMETERS FOR THE A-7A I Note: Data for body-fixed centerline axis, clean flexible airplane -q Oh I S = 375 ft 2, b = 38.7 ft, c = 10.8 ft W = 21,889 ib, m = 680 slugs, c.g. at 30 percent MGC Ixz = 2,933 slug-ft 2 Ix = 13,635 slug-ft 2, !y = 58,966 slug-ft 2, !z = 67,560 slug-ft 2, FLIGHT CONDITION I I 2 3 4 5 6 7 9 35,000 0 0 0

h (ft)

15,000 15,000 15,000 15,000 35,000 0.6 0.3 0.6 1.1 0.6

M (-) 0.S5 0.9 0.9

0.9 BO 973.3 973- 3 a (ft/sec) 1,117 1,117 1,117 I,058 I,058 I,058 I,058 O. 000736 0 (slugs/f@) 0.002378 O. OO2378 O. 002378 0.001496 O. 001496 O. O01496 O. O01496 o. 000736 279 670 317 635 952 584 876 VTo (ft/sec) 1,005 1,164 91.5 534 75.3 301 677

ov /2(lb/ft2) 1,200 1,OLO

4.0 2.1 13.3 3.8 11.2 2.9 2.5 2.9 7.Y s o (aeg) 274 669 633 874

Uo (ft/sec) 1,004 3O9 951 1,163 579

36.8 44.3 54.2 33.9 72.9 41.5 58.9 76.2 58. I

Wo (ft/seo)

-8.8 --a._ -7.4 -3.35 -3.8 -3.8 -3.85 -4.95 -5.4 6eo (deg) 0 0 0 0 0 0 o 0 0 7o (deg) _'?- 9" 9Y- 9"0{- _-_" C_- _" 0_- 6L'_- _'_-_- L'Lfr- 6"gL-- LOGO0" o CgLO0"O 9L LO0"O £C LO0"O C_9ooo" o _?_oo'o _6LOO'O-- _OLO0"O O9 LO0" 0-- T_I_ I L_" L-- LL'L- 6C_'0- oCC" O- L_'L- £0"L-- 969"O-- o_" o- 99?'o- _000"o+ OL_OOO'O-- 9£ L O00" 0-- oLCooo" o- 9oCooo" o- 99_ooo" o- C9 Looo" o- LLLOOO'O- o9_ooo'o- £££oo" o- _C_o'o- _96oo" o- 0C5L0"0- LL_O0"O-- _6_o'o- CRL0"0- _o_o" o-- 6_90"0- e9 Z 0"6_- O_- 6o_- 9"66- 9"C_- 9L_- _9 L- "_'66- _'C_- nZ _6C0"0-- C_Co'o 6£_oo'o £ _9o" o.- ULgO" o- __0" O-- ?_0"0-- _gLO'O ??_oo" o- _Z 6LL" o- _6" L- LO'L-- _L'_- _Y" o- O?'C- _'o-- _C "_- 9L'L-- Od O4 ,f _9 X oi'_ _'LL CL'6 96"9 C9_ 9"LL +_C" T L9"9 LOGO0" o ).CCoo" o _£Lo'o.-- _LO'O- s9 LO'O C6LO'O- LC_O'O-- 0_0" 0-- o_9oo" o- 99 go" o--- _LO'O-- 6CCo'o LC_o" o 797oo" o 79_0"_ 9LCO'O 9t[LO'O 9%_o'o _'0 z 6"0 C'O 6"0 6"0 L'L 9"0 9"0 9"0 000"_ L O00(_L 000 ( _ L 000 _CL 0 0 000 c_C 000 c_ 6 9 L 9 ff _ C _ L _KIO I,I, ! CLI_O 0 J_ff-IDl'l, q <o b- Gu_Td_T _ elqTx_lj Um_TO (sTx_ GuTiz_%u_o p_xT.j-Xpoq zoj _ m%_C :_%oz VZ-V ZHZ EO_ _ZAIZVAI_{Z(I_IVII0!TK!Zk_C gV__IIC/IZID_I0q E-If :EIEVg TABLE I!-C LATERAL DIMENSIONAL DERIVATIVES FOR _ A-7A flexible airplane Note: Data are for body-fixed centerline axes, clean I -q O_ I FL!_T CONDITION 2 3 4 5 6 8 9 7 '_ 15,000 35,000 0 0 I5,000 I5,000 35,000 h 0 15,000 i 0.6 0.6 1.1 0.9 0.6 0.3 0.9 0.9 M 0.25 -0.310 -o.435 -0. 0847 -o. 145 -0.722 -o.187 -0.162 -0.314 -0.574 -0. 0021 6 -0.00427 -0. 00267 -O.OO15O -o.oo655 -0. OO691 -0.oi 05 -0. 0085 7 -O. 00274 Y6 a I O. 0347 0.0267 o.o626 o. 0537 o.o55o O. 0792 o.o43o 0.0307 0.0769 Y6r I h) L_ -3o. 6 -66.0 -14.9 -71 .2 -44.8 -8.79 -98.o

-11.9 i -29.2

!

-i .4o -3. oo -6.79 -7.31

-2. O0 -4.46 ! -1.38 -2.73

-9.75 !

! 0.843 o .563 o .868 o. 859 o.599 I .18 i.38 0.857 i .15 L r I i !

14.2 24.1 12.5 7.96 28.4 17.6 25.2 ! 3.75 5.34 L5 a !

6.55 11.2 i 7.27 3.09 11.4 I .82 2.22 13.2 7.27 L6 r I E ! i I ! 21 9 I. 38 I 3.12 10,2 4.72 i

1.28 5.74 1 0.948

17.2 -0.112 -o.116 -0.169 -o.o799 -0. 168 -0.0310 -0.207 -o. 087o -0.379 T -o.455 -1.33 -o .247 -0.541 -0.975 -0.369 -0.905 -i .54 -0.271 N r i i I I .01 1.64

o. 28o i 1.o4 0.652

o.4o2 2.08 i 7.37 N' I .56 6a I I !

-8.8O t -4.83 --2.54 -5.17 I -5.54 I8.61 --11 .I -1.56 -1.93 N$ r

t l

TABLE II-D ELEVATOR LONGI_TDINAL _ANSF_ FUNCTION FACTORS FOR _IE A-7A Note: Data for body-fixed centerllne axes, clean flexible airplane FLIGHT CONDITION I I 2 3 4 5 6 7 8 9 _L !

h 0 0 0 15,000 15,OOO 15,OO0 15,000 35,000 35,000 L_ M 0.29 0.6 0.9 0.3 "0.6 0. 9 I .I 0.6 0.9 t 0.230 0.367 0.383 o.39_ 0.277 0.316 0.316 o.185 0.229 sp 4.21 I .63 8.81 2.08 3.68 1.76 6.76 3.15 5.48 6DSp o.1oo 0.118 0.0620 o.589 o.ok49 (0.0616) o.o99_ o.79o (o o_4_) _p ; 1/Tm ) o.14o O. 071 0 (-0.o513) 0.0372 o.o75: (-0.o9oi) o.156 0.o698 o .0472 (1/Tp2) --18.8 -41.6 -8.18 -20.2 -30.6 -45. I -4L.3 -5.43 _8.4 I As -0.0214 0.0122 -0.00823 o.oo716 o.o_43 o. 0422 -0. oo316 O. 0202 O. 0728 N5 e !/T81 2.02 0.506 I .97 o.516 0.933 0-731 1.79 3.19 1.o9 i _/Te2 6.61 8,3_ 11.6 5.63 6.96 11 .2 5.70 A_ 5-75 9.13 12O 129 186 8.5 2_ 109 1'7'7 5! .i 190 !,'Tu I h) (0.14-11) o .665 (I .22) (0.369) o. 627 0.854 (0.899) 0.929 o.753 i _U (!/Tu2) 1.24 0.466 ( i. o3) 1.30 (2.28) (0.587) 0.89o (i .23) o.719 i _-_ (1/%3) i -318 -23.8 -22O i Aw -29. o -i® -99.6 -209 -43.2 -99._ 51.7 126 187 58.9 121 2_ 110 191 178 1/Twl w NB e .-o.11o -0.o_44 o.239 (-o.oo6o3) o. o5 67 (-0.0o939) (--0.0! 31 ) -o .o553 o.419 I (w (1/T_2) o.1o9 0.0210 (0.0773) 0.0386 0.0990 (o.o918) (0.o53o) o.o_9_ 0.0219 0.%: (I/Tw 3) 29.6 165 318 24.5 221 99.8 209 43.6 99.7 -o. 0624 O.Oh12 /'l'nl 0.00956 o.o719 -o. O949 o. oo225 0 .o_31 -0.o154 £ 0.0173 N6 e 6.21 15.6 29.3 5.41 11 .8 20.0 22.2 7.64 13.2 I/'i_2 -5 -57 -14.3 -23.3 -_.92 -I I.o -18.7 --21 . 2 -7.22 -12.5 1 I%,3 -165 -318 -23.8 -99.6 --220 -29.0 -209 -43.2 -99.4 Aa z -0.oo998 -0.oo2_ -O.00117 -0.00417 --O.OO4O5 -0.00147 -o.OO139 -o.OO17o -0. OO25O I/Tazl -o. 0506 o. Ol 20 0.0729 -o. Oh 97 O. OO627 O.'O445 o.o_25 ---0.0136 I/Taz 2 o.0197 6.33 15.6 11.8 20.0 22.2 CG 25.3 5.55 7.69 13.2 I/Taz3 -5.73 -14.3 -23.3 -5.o8 -I 1 .o --18.7 -21.3 -7.28 -12. 5 /Taz_ I

TABLE II-E

AILERON LATERAL TRANSFER FUNCTION FACTORS FOR THE A-TA

Note:Data for body-fixed centerline axes, clean flexibleairplane

I

FLIGHT CC_DITION

I 2 3 4 5 6 7 8 9 C_

I

h 0 0 0 15,000 15,000 15,0OO 15,0OO 35,000 _O00

M O.25 O.6 0.9 0.3 0.6 O.9 I.I O.6 O.9

0.0462 o.o411 0.018o O.O_L9 0.C_35 0.0214 0.0102 I/T s 0.0319 0.0191 I .62 4.46 9.79 0.968 2.71 6.17 1.28 I/T R 7.15 2.92 A 0.202 0.218 O. 237 o.231 o.156 0.179 o.189 o.114 0.128 _a I.81 4.68 2.91 1.65 2.29 3.66 I .81 5.o3 2,58 _d 28.4 5._ 2_.2 17.6 . 2_.I 14.2 3.79 12.5 7.96 Ap -o. o219 -0.0o23_ -o.oo113 -o. 0232 -0.00144 -0.oo_7 -o.oo137 -o.0o718 -43.00241 I/Tpl _a 0.217 0.217 O. 222 0.191 o.173 o.176 0.122 0.124 _p 0.173 I.49 3.05 4.91 I .27 2.34 3.87 I .62 2.64 5.33 % hD 5.42 28.5 3.81 25.2 17.7 24.1 12.6 8.0* 14.3 O.210 0.217 0.222 0.183 O. 173 0.124 o.177 o.175 0.119 N5 a I .51 3.05 4.91 2.34 I .62 1.29 3.87 5.32 2.6_ % 0.402 2.08 0.280 A r I.56 :' 1.37 1.6_ I.O_ 0.652 1.01 0.596 I .12 1.13 0.420 O.445 0.777 o.9_4 0.581 0.593 I/Tr I N r 5 a 0.0852 0.287 o.i&6 o._6 0.597 0.151 0.638 o.o198 _r 0.193 2.18 2.35 2.29 3.26 2.13 2.78 3.98 2.03 2.45 _r -0.0O274 -0.00216 -0.o_05 -0.O0857 -0.00150 -0.0O655 -0.0o691 -0.00267 --0.OO427 % 3.26 (o.885) 7.76 (0.726) 2.21 5.77 IO.7 0.793 (o.872) 11% I (_IB) _a (0.667) -O. 627 -0._4 (o._71) -1.63 -o.245 --0.113 0.422 (io.6) 11%2 (_) -233 63.1 86.8 188 78.2 -391 23.2 -147 -0.545 I/T_3 -0.766 -7.06 -8.61 -4.16 --0.477 -6.58 -2.51 -I .56 -0.o37_ (o.9_3) -i .16 -0.146 2.29 (0.798) 1.32 -0.596 o.29o (0.801) I/Tay I (_ay 2) (o.@8) -i .84 3.12 -2.66 5.92 (o._61) -7.93 o.961 (2.Zm) i/T_Z2 (_y2) -0.810 0.0896 (3.65) o. 0673 --o.29_ (3.79) 0.897 O.O_99 -0.113 _&y (1/Tay 3) CG 1.76 6.37 (1o.7) 7.10 .99 (-6.63) 9.31 3.92 1.3o ( 1/T_y 4) TABLE II-F RUDDER ]ATERAL TRANSFER FUNCI'ION FACTORS FOR THE A-7A Note: Data for body-fixed eenterline axes, clean flexible airplane FLIGHT CONDITION .

0 0 0 15,000 15,ooo 15,000 35,000 35,000 0.6 0.3 1.1 0.6 0.25 0.9 0.9 0.9 o.o462 0.0411 0.0i80 0.0214 0.0102 0.04:9 o.0435 o.o319 /T s 0.0191 i.62 _ .46 1.28 9.75 0.968 2.71 6.17 7.15 2.92 I/T R A O. 202 o .218 O. 231 0.114 o. 237 o.156 o.175 o. 189 0.128 _d .81 4.6,% 3.66 I .81 2°9i I .65 2.29 5.o3 2.58 2.22 11.4. 18.2 11.2 13.2 7.27 7.27 3.09 6.55 Ap ---0. 0224 -0,00242 -o.oo141 -0.00117 -0.0237 ©.00352 -0.00147 -0.00243 I/_1 -0.00723 2.68 8.31 4.31 6.63 5.35 2.33 5.56 3.16 4.39 1/Tp2 -3,38 -5.31 -7.88 -4.45 -6.33 -3.44 -4.38 -2.79 -4.55 1/Tp3 1.84 12.8 I .45 I0.8 6.21 10.9 6.89 7.03 2.75 Aq) 2.!!_ 2.78 5.37 8.29 4.3.5 6.64 5.53 3.27 4.4.3 NS_ r /%1 -_.11 -8.18 -5.53 -3. _8 -4.68 -4.61 -6.57 -4.76 -3.79 1/%2 -8.61 -11 .I Ar -I .93 -I .56 -5.54 --8.80 -4.83 -2.54 -5.11 I .13 4.33 6.12 9°87 0.553 2.35 2.64 I/Trl 7.31 0.578 r N5 r 0o41_ o.538 0.475 O. 674 o.473 0.440 _r o.535 o.79o 0.526 I .02 o.6_z 0.502 1.17 0.735 0.514-I o.381 % I .12 o,585 O. O430 0.0626 0.0769 0.03c7 0.0937 0.0550 0.0192 0.0267 % o.o347 -<).0624 -0.oo199 0.00_266 -0.O603 -©.00616 0.000578 O. 00271 -0.0021 6 i/% -0.0178 4.45 1.14 I .73 9.76 I/T_2 2.70 6.17 7.11 I .32 2.94 12o 186 54.7 63.6 113 '110 170 272 160 I/%3 12.0 62.9 314.1 22.4 51.5 9._ 52.3 15.6 30.4.

-0.0165 -O.123 -0.00502 -0.10_ O. 000648 O. 0227 -o. 00654 -0.0436 -0.0107 4-.43 6.16 i.87 9.57 I .27 2.69 7.06 I.36 2.97 -2. O0 _. 97 -7.84 --I .96 -3.69 -5.78 -8.91 --2.28 -3.81 2.60 5 °92 2.45 4.3o 6.80 9.77 1o.5 2._1 4.3o L TR-i (i-1 26

SECTION Ill A-4D Figo_re !Ii- ] !

A-4D

I FLIGHT ENVELOPE NOMINAL CRUISE CONFIGURATION Cleon Airplane 60,000 W = 17,578 Ibs CG at25%MGC Ix = 8090 slug- ft z Body 40,OOO I y = 25,900 slu9- ft z Ref.

Iz = 29,200 sluo-ft z Axes h(ft) Ixz = 1:500 stug-ft 2

/

20,000 REFERENCE GEOMETRY S = 260 ft 2 SL 1.0 0.2 c = 10.8 ft b = ?_7.5 ft Envelope for model A-4D-I X Transfer functions given for these flight condition REFERENCES I) Abzug, M.J. and R.L. Faith, Aerodynamic Data for Model A4D-I _OperotiormlFliqht Trainer, Douglas Aircraft Co.

Report ES-26104, November I, 1955 2) _Johnston,D.E. and D.H.Weir, Study of Pilot-Vehicle'Controller Integrotion for A Minimum Complexity AFCS, Systems Technology, Inc. Technical Report No. 127-1, July 1964 BASIC DATA SOURCES Wind Tunnel Test ROLL PITCH !

I

,_x= ?)

az .-.j P I _ep ..__+t< A-4D A-4D _ap + Kp" Gain in deg/deg/sec,scheduied for indicated air speed Filter _" t Low Pass ['0 I • Scheduled for indicated airspeed

K_ , Koz

YAW r (_rp A-4D r_ Note: n

L

System used on the A4D-2N model only.

Control stick steering mode shown Kr : Gain in deg/deg/sec, scheduled for indicated air speed Figure iii-2. A-4D _ Stability Augmentation System ao I0 (deg) \\35,000 ft

\\

\ .2 .4 .6 .8 1.0 M T_-I 7!]- 1 _.50 .8 CL .6 \ 55,000 ft .4

"

Sea Le ......

.2 0 .2 .4 .6 .8 1.0 M i 35,000 ft .06

/

\

\

.04 O0 ft .02 •2 .4 .6 .8 1.0 M TR-17g-I 31 CLcl _ All Altitudes .4 .6 .8 1.0 0 .2 M 1.4 1.2 1.0

/

All Altitudes

/

0.8 ] 0 .2 .4 .6 .8 1.0 M Tl_-176-1 32 o. q f

\

c0 co

/

O O O

i/

to j I ,4--.

m O O , r_h i 4 I !

i i !

l (D oo O (D O t_l Q 00 @ ,_- ea oa _. _0 m !

I I I i I E ¢.2 E_ -1.0 All Altitudes -I.2 -I.4 -I.6 -1.8 - 2.0

V

-2.2 .8 I.O Z .6 0 .2 M Cmq All Altitudes

!

_- 17_- I 34 It-- Q o LO o.

0 o.

_i ._.u_

C

cO

o---_

C_ ----- co ----C_ 0 --

0 \

\\

ro

\

ro

L

r_

;0,1 0_1 0 o _ _. _.

,_, 0,1 0 '_ I I I E i rj _L I E_ O O o.

o. o.

/

O O cO I OO ¢.D o__

i

L _,,.0 O,I O,1

--_ o

O O O "_- _" ¢.D OO O I I ! I O _7 _0 D-- _7 --.9 Sea Level

c_

-I.0 .......

(r+,)

15,0( ft -I.I ..............

-12 0 .2 .4 .6 .8 1.0 M

I

Sea Level 15,000 ft

r_ j

.m._.

_ " fl.mil.l_.

35,000 - -.2 -.3 0 .2 .4 .6 .8 1.0 M .4 5,000 ft .3 _/5,000 ft .2 Sea Level ---- .I 0 0 .6 .8 1.0 .2 .4 M TR- ; 7__-L Y( -.2 All Altitudes -.3 -.4 .2 .3 .4 .5 .6 M .06 Cnp .0, / Seo Level/ !

/ / t .02 / / 15,000 / / _J / 55,000 ft f .2 .4 .6 .8 1.0 M _-17_-i 38 .2 15,000 ft _._ C_. r Sea Level _- - _

5,ooo

(-)., 0 o .2 z .6 .8 1.0 M 0 .2 .4 M .6 ,8 1.0 Cn r %3 Sea Level 15,000 ft ¢ -._ 35,000 ft -.5 TR-176-I 39 o. o q

r_ I

\

L

co m \ o i i i - I .J _D o _I _ 0 I I 0 I' if) J 0 i i I1) _0 ._I 0 i ! 0

oo

i i i , o O_ Od 0J

J I- co

I I

J

I i i

i I

0 0 B o _ aJ o q q q o. q q I" q I !

I O 0 D 0 v D- I CY8 r All Altitudes

.2 L

.I 1.0 0 .2 .4 M .6 .8 0 .2 .4 M .6 .8 1.0 Cn8 r i -.06 ........ ' ...............................................

-.12 I .06

I

.04

seoLeve, y_

,5,ooo,,_+" _,++-35,ooo,, .02

l I

1.0 •2 .4 M .6 .8 TR-176-] 4] 0 0 (_ap) oz 0 0 £'£{ 9 "9{ (oas/as) °M ?"g9 9"9 {'@ ?'A 9"LL {'6?

og6 (oas/_s) °n sg6 9q?

£Ad 9L?

9_o t (_ap) % 0£'0 6"9 6"0 6"_ 9"9 07"0 £{s Lo{ @6 _7{t 9{9 ££9 9_L og6 (oas/%j) °SA s{6 9_o L 9£9 t_9d 9£{soo'o 9£{soo'o 967t00"o 96qtoo'o 967L00"0 967L00"0 9{£ooo'o 9{£ooo'o oJ ILLL LLLL {'{L6 95o L 95o L 9_o L {'{L6 9_o L (-) 6"0 9"0 o't 6"0 9"0 _'o gg"o _'o ooo'_{ ooo'd{ ooo'gL ooo'dt O00'gL O00'dL 0 0 (a_) 9 k 9 d _ { _ L _OI$1CAIOO $H0!_£ 8%fl_UT_ 0£0_ --: zx! _8%j-_nTs 00_98 = zI _8%J-gnIS 006_8 = X I _8%j-gnTS O_L_9 = xI %J 9"Or = o _%g _'£8 = q _8%J 098 = S <o b- :a%o£ C¢[-V _{Z HOg T_Z,I,ZKrV_IVcl _IVOI_Z2MOZO V-Ill Z_[V_ TABT__ IiI-B LONGiTUDiI_AL DiY_SIONAL DERIVATIVES FOR THE A-4D Note: Data are for body-fixed centerline axes, clean flexible air!o lane.

!

FLIGHT C OE_DIT!OI[ !

i 2 3 4 5 6 7 8 h c o 15, ooo _F_ ooo 15_ ooo 15, ooo 35, ooo 35, ooo x 0.2 0.85 0.4 0.6 0.9 1.o 0.6 0.9 X w 0.0687 -O.0215 0.052 0.0422 -0.0303 --0.0251 0.0227 --0.O212 X u -0.00934 -0.0298 0.000877 -0.00938 -0.0615 -0. 1343 0.000806 -0.02_2 XSe 7.6i2 --33.942 6.068 7.396 --19.723 --15.289 6.288 --3.8_:3 Zw -0.899 -2.23 -0.535 -0. 922 -I ._78 _ -i .892 -0.3874 -0. 677

I

Z u --0. 0765 -0.0982 -O. 0704 -0. 0533 --0.1174 -0. 0487 --O. 05 25 -0. 0869 Z_ e --42.08 --188.28 I --22.273 --56.68 --103.23 -94.606 --23.037 -_'3. 149 M w --0.0228 -0.0502 I -0.0131 -0.0204 -0.0379 -0.1072 --0.00908 --0.01739 M@ -0. 000763 --0. 00131 -0. 000476 --O. 000555 --0. 000902 -0. 000683 -0. 000270 -0. 000423 Xq --I. 151 --2.936 --0.670 --I .071 --i .93 k --2.455 --0. LS4 -0.876 M u 0.00232 0.00340 0.00253 0.00162 -0.00906 0.00263 0.001824 -0.00412 M_e -13.728 --63.987 -7.400 -19.256 --33.809 -7! .773 -$.096 I --14.084 I TABLE IIi-C LATERAL DIHZFSiONAL DERIVATIVES FOR THE A-4D Note: Data are for body-fixed centerline axes_ clean flexible airplane.

I O_ I FLIGHT CONDITION 6 7 8 I 2 3 4 5 h 0 0 15,000 15,000 15,000 15,000 35,000 35,000 1.o o.6 0.4 0.4 0.6 M o.85 o.9 o.9 --O.2484 --0.5755 -0. 1476 -0. 228 -0.3628 -0.358 --0.1 034 --0. 1596 Yv -0. 00582 -0. 00807 --0.00188 --0.0038 -0. 0055 6 O. 00207 -0. 000819 -0. 002763 Ysa O. 044 O. 0898 O. 02561 O. 03958 O. 0549 O. 049 O. 01791 O. 02487 %r !

-82.02 --17.557 -£0.7 --29.71 --I18. I --17.52 --35.95 -82.086 L5 --2.708 --0.761 --1.167 --I.813 --3.844 --I.111 --I.566 --2.503 1.113 0.475 0.6227 0.8731 I .776 0.613 0.812 I .208 T 44.89 8.1704 16.85 17.2 6£.359 8.99 21.203 39.282 L8 a !

22.943 4.1675 8.717 8.217 37.214 k.309 10.398 22.103 LS r 17.31 39.85 6.352 13. 203 67. 279 6.706 16. 629 £2.527 -0.029 0.02953 -O.0348 -0.02173 0.01647 -0.0260 -0.02513 i --0.00539 I -O.5761 -1.4 -0.3432 -0.5144 -0.899 -0.88 -0.2468 -0.3893

Hr

T 1.4875 5.484 0.538 1.769 17.43 3.212 0.5703 1.399 N8 a N' -6.1953 -26.642 -3.280 -7.78 -16.36 -16.562 -3.16 -6.744 8m

TABLE III-D

ELEVATOR LONGITUDINAL TRANSFER FUNCTION FACTORS FOR THE A-4D

Note: Data are for body-fixed centerline axes, clean flexible airplane.

FLIGHT CONDITION I 4 6 8 2 5 7

h

35,000 15,000 15,000 15,000 15,000 35,000

M o.4 o.4 o.6 o.6

1.0 o.9 0.85 o.9 0.214 0.435 O. 2838 0.3435 O. 233 0.2478 0.301 _sp 0.352 7.348 2.445 6.232 IO. 857 2.358 3.718 3.951 _sp 3.39 A 0.682 o.086 o.195 (-0.o6835) (0.02574) o.0859 (-0.oso) _p( I/Tpl ) O. 0735 O. 0822 0.08615 o.11o5 0.0747 (0,1019) (0.0563) (0t1101) a_o(I/Tp2) O. 1035 -I 4.083 -63.98 -7.4 -19.456 -33.805 -33.771 -8.096 A e --13.726 0.0112 O. 1284 0.02184 0.0319 0.00353 0.0926 -0.o0o615 N_) e I/Tel 0.0141 2.079 0.489 0.76 1.362 1.572 0.3591 o. 6259 1/Te2 0.8234 Au 7.628 -34.074 6.076 7.4o8 -19.776 -15.32 6.293 -3.878 I/Tu I 66.931 --12.608 80.193 99.8 --2O.49 --13.172 115.28 -160.9 N_e {u(I/Tu2) 0.584 (2.615)i 0.725 0.638 (G.98) 0.49 0.8554 (0.3383) _u(I/Tu3) 0.8481 (3.813) 0.4926 0.8042 (3.733) 2.824 0.3595 (1.337) Aw --42.08 --188.28 -22.274 --56.68 --103.23 -94.606 --23.034 -43.149 203.34 286.42 139.54 313.69 325.77 357.77 218.67 I/Tw I 149.77 5e O. 2653 -0.0238 0.249 0.4915 -0.0172 (0,01471) 0.0835 _w(I/Tw2) 0.0614 O. 0602 0.0546 0.0771 (0.1'127) 0.0965 0.o538 o.o516 _4_(I/Tw 3) O.O761 162.98 188.o4 Ah 42.565 22.946 94.496 23.728 57.02 42.898 --0.02081 -0.01842 o .o5o 0.1270 0.0299 o.oo436 0.01593 1/Thl 0.00122 _e 21 .62 8.454 24.916 27.426 8.58o6 13.376 13.782 1/Th2 11.623 -8.048 -I 2.282 -19.671 --7.71 2 -22.453 -24..502 -12.892 I/_ 3 -IO.415 -188.28 --22.274 --94.606 -56.68 -23.037 -43.149 --I03.23 Aaz -4 2.08 -0.00025 -...0.0181 -.0.00227 --0.0085 --0.0228 -0.00404 -0.000431 -0.000214 I/Taz I I/Taz2 0.00962 0.0301 0.00187 0.00835 0.05043 o.127 -0.0oo296 0.01805 I/Taz3 11.668 27.412 8.56 13.405 21.597 24.903 8.7174 13.762 --10.471 -24.484 --7.84 --12.321 --19.645 -22.437 -8.203 --12.868 I/Taz 4 TR-176-I 45 TABLE III-E AILERON lATERAL _ANSFER FUNCTION FACTORS FOR _KE A-_D Note: Data for bod_-fixed centerline axes, clean flexible airplane.

FLIGHT CONDITION 6 7 8 1 2 3 4 5 15,000 35,000 35,000 h 0 0 15,0OO 15,000 15,000 I.0 0.6 0.6 0.9 o.9 M 0.4 0.85 0.4 0.00508 0.00726 o.oo599 o.oo698 0.00_32 o. 0067 I/T s 0.00914 0.00568 2.772 o.7o13 1.137 I.O152 I.5346 2.48 I/T R 1.744 3.81 O. 0676 0.065 o. 0949 O.0885 o. 0966 0.09125 _d 0.112 O. 1207 4.4o3 3.999 _. 293 3.058 4.342 6.618 6.392 2.996 _o d 44.89 8.17 16.89 8.988 21.2<)3 39.282 Ap 17.199 64.36 -0.01182 -0.000211 -0.00185 "-0.00572 -O. 0OO233 -0.0085 -0.003 -0.00041 I/Tpl NIDsa 0.0923 O. 1015 0.0968 0.O717 0.0669 O. 0977 i_ p 0.1149 0.121 4.442 8.914 6.787 2.742 4.553 3.986 8.845 2.779 % 21.308 39.495 Acp 17.321 64.398 9.073 44.91 8.299 16.921 O. 0924 O. 1021 _(p O. 1149 O. 121 0.0991 0.0968 0.O70 0.067 4.439 8.891 3.985 8.843 2.798 6.789 2.76 4.55 % i.769 17.4_ 1.4875 5.484 0.5376 3.212 0.5703 I .39 0.873 2.601 0.9029 4.364 0.4868 3.054 0.3965 0.739 I/T r N_Sa o. 0847 o. 0946 O. 1024 0.0571 0.0185 -O. 0646 0.O17 0.0695 3.694 I .521 3.767 2.655 4.475 2.523 4.073 3.519 _r -0.0o38 -0.0o556 --6.OO582-0.00807 -0.001883 0.oo207 -0.o00819 -O.OO276

%

-0.1615 (o.9834) -0.723 -0.0447 -0.2036 (0.974) -0.369 185 a I/TGI(_) -2.178 4. 156 (0.5504) 1.704 2.537 2.2264 (0.4294) 1.368 1/T#2(a_) 3.287 f 629.29 -456 134.99 3048.0 -1396.8 -838.16 197.67 I/T#3 19.189 --7.665 -0.7967 --2.413 --5.294 2.193 -O.4781 --2.42 Aay --2.66 -0.1975 o.3891 (-0.8875) -0.0468 -o.1843 0.3626 -o.9o3 I/Tay1(_e_r2) (0.7012) 4.248 0.6872 (2.2183) 2.54 2.266 0.4622 1.651

i/%2(4,y2) (1.923)

(-16.43) 0.0215 (1.869) (-32.14) 0.0324 0.00935 (-2.903) CG -0"0505 (17.62_) 8.743 (4.149) 23.294 9.772 (3.712) (33.046) _y4(I/Tay4) 3.049 TR-176-1 _6 TABLE III-F RUDDER IATERAL TRANSFER FUNCTION FACTORS FOR THE A-4D Note: Data for body-flxed centerline axes, clean flexible airplane.

FLIGHT CONDITION I 2 3 4 5 6 7 8 h 0 0 15,000 15,000 15,00([) 35,000 35,000 15,0(90 o.6 1.0 o.6 M 0.4 0.4 o.9 o.9 0.85 O. 00726 0.00432 O. 0067 o.o0968 o.oo5o8 0.00595 o.oo658 I/T s 0.00914 2._,8 3.81 I .5346 2.772 0.7013 1.137 I .0152 I/TR I .744 A 0.0885 O. o966 0.09123 O. 0676 0.065 O. 1207 0.o949 _d o.112 6.618 6.392 2.996 4.403 8.293 3.058 4.342 3.955 4.167 8.717 37.21t_ _.309 10.398 22. 103 22.944 Ap 8.217 -0.OOO412 -0.00186 -0.000212 [-0.00851 -0 .ooo236 -O.0119 --O.003

1/ p1 -O.00576

3.743 4.375 2.552 3.208 4.359 4.534 2.587 1/_ 2 3.o_ i -3.997 --2.6 -3.207 --4.196 --4.2rF9 -2.664 --3.79 I/TP3 --3.O29 37.028 3.795 9.936 21-9 22.83 3.678 8.379

7.7o8

4.376 2.642 3._ 4.378 4.539 2.729 3.797

3o86

-3.98 -2.902 -3.33 -4.227 -4.293 -2.936 -3.90

1/T 2 -3.211

-_744 --I 6.362 -26.642 --I 6.562 -7.78 -3.159 --3 • 28 A r -6.199 2.786 0.393 0.930 2.t_95 3.815 1.348 0.615 I/_r 1.54s_ _r o. 1828 0.20 o.1783 0.363 0.272 o.2o7 0.308 _r 0.3075 I .128 0.850 0.578 0._63 0.718

o.7 38 1.032

0.049 0oQ179 0.0249 o.o9_9 0.0396 o.09 0.Iz_96

% o. 4

-0.0OO321_ 0.000941 -0.0175 -0.00939 0.00133 -0.o067 -0.0209 N_Sr I/% I --0.00945 2.485 2.76 0.711 1.145 3.812 1.537 1.0312 i/% 2 1.7532 303.67 342.14 210.29 289.01 212.32 153.O 300.91 I/T133 156.02 10.499 21.78_ 52.296 51.83 _.134 A_y 20.1 89.33 10.835

-o 86

I/_ayI -0.o219 -0.00154 -0.o39 -0.o147 -0.00224 -0.0326 -0.0141 1.760 1.54 2.489 2.752 0.717 1.150 1/Ta,y. 2 8.618 5.14 5.73 9,46_ 3.733 10.957

llTar

CG

--8.63 --3.411 -4.9

--3._19 -7.7 -4.49 -9.526

llTa

TR-176-1

SECTION IV

F- Io6B

Preceding page blank

i Figure iV- I i

F -106B

FLIGHT ENVELOPE 60,000 h(ft) /_ NOMINAL CRUISE CONFIGURATION Cleon Airplane W = 29,776

4o,0oo //.. j ×

CG at 50.5% MGC

// ; /

Ix = 18,634 slug-ft 2 "_ [y 177,858slug'ft2( Body Ref.

2%0oo _q v., X/ Zz 191,236 slug-ft t ( Axes Ixz 5,539slug "ftz ) _j'7 REFERENCE GEOMETRY o S = 695 ft 2 M c = 23.755 f -- Maximum A/B thrust __.m Military Thrust b = 58.15 ft X Transfer functionsgiven for these conditions REFERENCES : Weyel, A.E., A.H.Terp, C.A.Lunder, Description of F-106B Aircraft to Be Used as a Variable Stability Trainer, Service Engineering Div., Kc_:llYel_:_Ji:_ilbiL::NE:y_;m_cs,DeC'convl_o_, A Compilation of F-106 I Data From Various Convair Reports Contained in Letter, 14 May 1963_

F-106

I

YAW

PITCH

O_ !

F-106

F-_36

$ s+l

T_s.I

SCHEDULED GAINS

SCHEDULED GAIN and TIME CONSTANTS

.2O

.6 .16 -.5 .5

\

Ke

(J (I) ".4 /Kp

.08

\

.12 !

:_ -.3

"0

\

.04 v

_-.2

"0 0 .2 .4 .6 .8 1.0 0 .2 .4 .6 .8 1.0 PreSsure Rotio,ow/Po Pressure Ratio,/_H/Po

0 200 400 600 800

Dynamic Pressure, qc, Ibs/ft2 Figure IV-2. _-_06 -- Stability Augmentatiom System I V-A G_OME'IRICAL PARAMETERS _ _ F-IO6B I r-J --j I Note: Data are for bo_-f_l e_terlLt_ axe,, F-J s=695, b=38.1_, e=2_._, eoc_itlocatio=: _= 17._ , _=-3._ FLIG_ CORDITION I , 2* 10 11 12 S.L. 8,5. S,L.

_0,000 20,000 40,000 I_0,000 20,000 20,000 20,000 20,000 20,000 1.4 2.0 0.2 0.4 0.4 1.4 0.759 0.799 0.9 O.9 0.9 (--) 0.755 1,116 1,116 1,037 1,116 1,057 1,037 (rtl,,_) 1,037 1,037 1 ,o}7 0.00126? o.001267 0.ooo987 o. 001 267 0.000987 o.00o587 p (slug,/rO) o.00126? 0.OO1267 o.001267 o.00e_77 0.002577 0.002377 414 100_._ 7_ _3.2 933 871 1,4DO I,_9 1,9}6 108.6 39e 99.3 257.2 591 z_3 1,3_'a 949 1,100 39_ 1,199 29,776 29,776 29,776 w (_) 28,000 29,500 29,776 29,776 29,776 29,776 29,776 _3,000 _0,0(0) 964.7 964.7 964.7 964.7 _4.7 l_ss (s1,_s) 991 870 791.9 9e4.7 92_,.7 964.7 !,090 18, 6_ 18,6_ 18, 6_ 18,634 1 8, 6_A 18,634 18,6_ 18,6_ Ix (s1_ -ft2) _3,49o 18,74 _, 19,8o9 19,800 177,6_9 177,898 1'r/,858 177, 8'38 177,858 177,858 177,898 177,858 177,898 Iy (a1_-rt2) 195,196 1_,..._00 191,2_6 191,2_6 Iz (slug "I_2) 187,119 191,2)6 1 91,2_6 1 91,2_6 191,2_6 1 91,2_6 191,2_6 219,262 198,707 1_,_1 Ixz (slug-ft 2) 4947.1 331o.9 6o19.4 9,939 9,9_ 9,939 5,5)9 9,9_9 9,9_9 9,9_9 9,"r"_' 9,9_ 0.26 0._05 O._X_5 0.29 O.305 o._o9 0._ 0._ 0._ O._05 O._O5 0._05 xCU/C 4.42 _.O_ 18.0 11 .O 2.0 1.2 2.70 I .2 % (aeg) 3.88 4.9 2.7 9.4 0 0 0 0 0 0 0 0 0 0 0 0 • o (eel) 4._ 4.O_ 18.0 11.0 2.0 1.2 3.88 4.9 2.7 9.4 • 2.7 1.2 eo (eel) 212 4O6 868 78_ 78_ 1,0(0, 933 1,490 Uo (_l,ec) 60.6 _o 80 _6 82 99.4 93.1 73 wo (_l,,c) *Opt:_ del_ condition I 60"_- L_'_'- _L'L- LO'L- "_'_L- _0"9- _9"_" 6_'_- _'L- _<L"6- _L'O- _0_'0- _l'_- _._- 06"_- 8¢'_- _9" _" 89"E" [6" t- _" L- 9L'9- 66L'O- tG'O- _l_'o-

L_9"o- l_- I- gL_'O- _.I_'o- _6_'o-

9L_ "0- _'0- _'O- _9_'o- _L'O- L_O'O- ls_o" O- lo_o'o- _tt'O- _o_o'o- 8_0"o- L9_O" o- _'O- L81O'O- _%9o'o- g L_O'O- LO'_ OG'L IL'E _L'O- t" L_ 81"1 6"gL 6L'_ 0"9L 90_'o _9"_ O'_L- I._- _OL- _'6L- L'6_- _°_L- L" L9- _" LL-

_-%- Z._-

L_'6 L'LL 9o"I LO'_ L'LL _'6L /_5"_ L_'L 1_'9 _'E _'_ 8 L'_ L6 ° L 8_'L L_;'_ _Tg"L 6_'E 9_'_ _L'_ 9%'_

_9"_ _'L _9"_ 09"L

_" L- _._- b_'L- O_'_- 69't- 69"_" _,O'_- _'_- 6_'L- _L'_- %0"L- _I._- _'_L_- _'6L- _'_- 0"03- L'OL- oL'%- _9"9" 6"8L- 9"L_- G'og- L'_G- 9LL-

_6_0"0 _0"0 _0"0 1_o'o

o_6oo'o e69oo'o ._ tO'_O 6990" o 8010"0 08_0"0 66Lo'o _/t.O OOL'O (_'o _'_'_rO" 0 _980"0 _6_o.o 9_o'o 8ato'o 18_o'o oleo"o 80 _'o

Lo_ •o- _x

118'o- 60 t'O-" l_'_'O- 6g,_'O- 6_'0- lt_'o- b_L'O- ELL'O- tgg'o-- 9_t'O- _'o- ,< _l'o 6"0 6"0 E'o G_'O _I'o 6"0 _'0 _'0 o'_ "_'L _'i O00'Og "I'S 000'0_ .,I.Cj -'I'S 000'0_ O00rOg ooo ¢o_ ooo_o_ O00'Ot r 000'0_ 000'0_ _L LL OL EOI.T.I(IEO0 _OYI_ p_puTou T a,z_ SUOTO,.oa,zuoo oT%'s'8"[@o.,_,'_ oTo,.'sq-8 : _o_ &-AI _IEW I I E-_ 60 L'O OLL'O 6LE'O t_'o _Ot'O _tL'O ¢6o-o 9_'o _,LO" 0 _ L L'O oc_o'o iLgo'o _'_ i. 9 • Lt'_ 69"_ _.'_ g_- t 09"_ 99"9 _.'_ :.._/.. _ _-_ t_'O t_-_-o _'0 t_" t 6_g'o _/._'0 _¢-o L9_'o %_" t LLg'o 6_'o _]'o "_'o- L_'o- 9_'o- L6 t-o- 6tL-o- 6_Y" O- 8L'L- :--d.g'O- tlo'o- t6_'o- _f,O'o- ¢_o-o- c_L L- l_- g.g_- _- tO_- 9'_- t'9L- 9_t- _L- 9_t- 6_t- (le_'o-) (e_-o-) _o._ (o_6-0) (_-o_o-o) (6:=6"0) (trY'o-) _'_ 6_'L (z_9"o) _;"9 t._'_ (gg6"o) (_6.o) (°_):=_/t (oo) itg_'o) (og6"o) L_'_- (o_m'o) (_" t) _9" L- _6"_- LO'_- _9"_- i(LL9"O) (6 re'o) (_6;..o) CLo'o) (t_-o) (_-o) ( _). I %iz_ _C]" t Zo'9 (L_l_o'o) Lt'_ 6t'_ • _ (,_ t'O) (6L" t) _(_) _ff_ (o_-a) (6 t'g) (6_- t) (_9"_) 6aL'o- _._'o- (L6"a) 6:.0"0- (_9" t) tgo'O- _Lt'O- °_v 6"gL 6"g9 9"tt 6"%L LO L 9Lt L'gt _'_ _._ _-_ 9"_ 0"6_ _'0_ O'%t 9"0_ (oe_'o) (_6_.o) 6"L9 (6eL'o) _L g'Ot _ig Lt L _._ (_.o) 9_'_ O/'t _L'_ (_-o) Ct6"_) _'g _0"_ _'_ 9_'g _'0- Lg- t- LL_" O- tgS" O" L" t9- t_g'O- 9tt'o- _'_- _o'o- _'o- _-o- 900"o- 6610"0 OOL'0 9_6o'o 6_)'o (--_.t'O T_O'0 tO'O 6_0"0 L_'o _o-o gOt'O OLL'O L_'O •_g_ • o OOl'o 60 t'o 0_'0 _'0 9o_'o L_t'o _h'_" 0 Ot_'O _'0 66- t L6"t _$'t _'8 L_" t t_-t g6"t L_"L 9_'t _o-_ L6_'O 9 LL'o gL9" o 6_16"0 C_'O L_g'o _'_ 9o_'o _" _ t L'_'O 9_" t 69_'o °'zv "%/.z 60"_- to'L- _0"9- t_'_- _L'L" _'6- _'_t- 69" t- _'L- _e'_- _9"_- 6_"_" _L t'o ALS"O _L'O _L'O t6 t'O _9_'o _t'o _3' t'O _t'O ELt'O _OL'O LCS _'_ ¢_-g l_" L t9"_ L_'_ _6"_ 6_" t _'_'_ %t'_ %c_. 9 _'_ _b v "%/kb t-g'_- _'_L- _" t9- _-_- 9"_t- L" tL- 90L- _"6 t- 9"9_- o'_- _'9_- _'9_" t/t'o $6_'0 9g L'O tOt'O t6 t'o ose'o _t'O c_+_a • o ELL'O LOL'O Z_t'o _t'o _T_ _._ _0"_ _" t t9"_ LG'¢ 96-_ _-t 6c3"9 _E'g _c_/t Ot_OO'O- oLgoo'o- _,_goo • O- L'_IO" O- f, O00"O- _00"0- b_DO'O- tOO'O- "_ LO'O- 900"0- _ooo'o- LOO'O- _dv _/d o'_l- L'_'_- got- _'6t- 1"6_- _'_L- L" t9- _'LL- ,'9_- L'_- t'9_- _'9_- GL t'o iOt*O _'0 _gt'O 8L t-o 6Gt'O _'o 8_ L'O 9 t L'O 6g L°O _Lo'o c_6o-o l_'g tO'i_ _'_ L_'_ tO'_ b_'_ L_'_ _'_ _._ oo'a _L"_ _t'g 6t'_ _/t 60"g g6_'o 09"t b_9"_ _o'<:] %/.9"o 6_._ _.t '_'L 9L'_ L6-t o/to'o- e,'r,/L _o'o 69 t'o to-o- 99 to'o- _oo-o- OLO'O OLO'O LO0"O 900*0* _oo'o- o_o*o _0"_ 6"_ O'_'t 0"_ O'tt _'t L'_ _'t _'_ 000'0_ 0oo'_ OOC_c_a O00rg8 9ALr6_ 9LL_6_ 9LL_6_ 9LL"6_ 9AA_6_ 9AL_6_ 9LL'6_ 9LL*6_ OD _'0_ 6_ _'0_ c_.O_ 9_ _'C_ _'0_ _'0_ G'O_ _'_ _'0_ _'0_ q Capu%_%IV O00cOE O00rOi ooo_o_ "q'S .q-!

•q.S 000_0_ 000_'0_ O00rOtT 0_0_0_ 000_0_ _A'O _L'o _'0 6"0 6"0 _-o _'o _'L 6'0 o'_ _'t Ot 6 L 9 EL tL uoTsT_oo _q_i_ _0 L-_ DISY_ _0_ g_D_T_DY,_" _OI_D_ _._Sk_f_ q_%'I _O_'IIV D-AI _I_D_ TABLE IV-D RUDDER IATERAL TRANSFER FUNCTION FACTORS FOR BASIC F-I 06B FS I£bt C _n_ _tion 11 12 I0 5 6 I 7 i I..4 1 .4 2.0 0.4 0.4 0.9 0.9 o.9 0.2 I o. 755 0.795 0._5 MBch No., M _o,ooo 14o,ooo 20,000 20,000 20,000 S.L. S .L. 20,000 S.L.

20,000 20,000 20,000 Altitude, h 3o.9 3o.9 30-5 30.9 --4 30.5 26 30.9 30.0 30.9 _.5 30.5 CG 29 Oh 29,776 29,776 29,776 29,776 29,776 29,776 29,776 29,776 20,000 25,500 _,000 Weight _ 35,0oo I _9 I,ioo 223 I _952 297 109 1,199 951 3_ q, ib/ft _ o.oiol -o.oo9 -o.0o6 0.001 0.01 0 o.o_ 0.080 -o.o00 -0.01 66 -0.0164 0.1 69 I/Ts -O.017O 1.97 2.76 1.84 4.59 1.0_ 2.o9 o. 678 5.05 2.62 0.59e 1.60 2.19 I/T R 9.22 9.97 2.12 4.79 9.oi 2_iat 2.42 2.01 2.00 .4._ 2.54 2.37 2.&7 _b o.116 0.099 o.o7_ o.159 0.129 0.162 0.255 O. 162 0.224 0.178 0.16_ 0.175 So .4.18 5.29 7.91 11 .I 5.07 2.08 6.17 2.97 19.5 11 .I 9.51 7.06 A_r -0.0OI -O.O(X)9 -0.0009 -0.782 -o.oo9 -0.006 -0.015 -0._I -0.00286 -0.002T5 -0.049 -o.oo914 P/Sr i/_m 9._5 9.1o °0.002 I._4- 5.19 1.88 I .85 1.97 -0.001

(I .79)

(i ._) (i.72)

I/Tpr2(_Pr) -9.40 -9.98 -I .69 -9.29 o.8e9 -2.64 -2.09 -2.54 0.569

(0.0736)

(o.o7oi) (0.0693) I/Tprs(_Pr ) _.I_ 9.19 7.29

11 .0 .4.9_

6.09 2.81 1 9.9 1.9_ 6.86 9.32 10.9 A_r -9.45 -3.61 -0.808 -i .7.4 -9.9+ $/5r -2.12 -2.4.9 -0.406 -2.98

(i 44) (I .81 )

(I .67) I/T_r I (a_pr) 3.37 9.10 9.I_ 0.Sa3 i.99 1 .85 2.02 0.5.59 (0.0582) 1.99

(o._9)

(o._)

I/_m(;_) -I .44 -I .49 -I .91 -2.90 -3.28 -I. 63 -0.792 -6.1 6 -2.68 -2.75 -0.909 -2.55 Ar r 4.28 I .43 2.71 2.00 o.739 0.4_-2 2.18 o.43o 9.97 -o.427 -o._36 -o.431 r/Sr I/Trrl k_q .7_6 o.43o 0.674 o.99_ 0.680 I -74 (0. _89) 0.19 ° 2.4-8

kJq (0.975)

(0.349) (o.365)

_r(1 I_) •610 0.38_ 0.902 0..4_ o.2_ (o._62) o.58e 0.21.4 o.419 (9.28

(2._) (2.71)

rr (I/Trr ) 0.0_.4 o.o09 o.0o9 0.059 o.o_ 9 0.028 0.0438 0.02.5 0.067 0.0402 0.0039 o.o_7 A_r -0.004 _ -0.010 -0.021 -o.oo5 -0.053 -0.086 -o.oo4 -0.0O9 -0.259 -0.00111 -0.000727 -o.ooo53o _/Sr I/TGr I 1.98 2.7.4 4._6 I .89 I .07 2.07 0.780 9.08 2.11 0.690 2.95 1.96 I/T_r 2 18,4 219 13o 97.8 105 90..4 6o.o 100 81 .I 41.9 89.9 89.8 I/TOr 9 12.2 18.2 16.2 34.1 36.6 6.57 19.6 9.92 67 .2 31.6 [9+.2 27.9 Aa r -0.012 -O.Oli -o.o12

-0.01 0 -o.o_

-0.067 -0. 999 -0.004 (I .02) o.o061 _ 0.00696 0.00679 I/Tar I ((Oar)I I .99 2.74 1.08 4.29 1.89 2.05 0.90_ 6.89

ay/Sr 2.00 2.44 (o._)

1.59 1/Tar2(_a r) I -.4-99 -5.69 -2.4-4 -9.97 -2.4.2 -1.1 6 -5.65 -9.92 (CG)

-5..49 (1.21)

-9._I -9-3O I/Targ(ea r) 2 6.16 9.0_ 9.99 2.88 .4.99 9.25 1.88 5.1 7 4.16 4.29 -(o.2.49) 9.9e I/Tar_(_ar) 2 o.78_ 2.52

8.03 7.89

16.9 11.8 5.60 2.4.9 16.6 .4.71 6.40 29.9 A_ r -0.010 -0.012 -0.012 -0.01 0 -0.091 -o.o61 -o.i 95 -o.oo_ 0.00699 -0.300 o.o646 o.00670 I/T_'rl 0.844 1.99 2.90 ay/Sr 2.69 0.402 -6.36 0._28 -16.1 -5.96 -8.81 -6.09 I/T_r 2 (cockpit) -21 .5 -91.o -_.4 -9 •89 -8.19 (2.17) -5..47 (9.81) (3.08) -5.38

(9._) (2.99)

(a_r I )I/T_r5 10.9 8.94 8.69 3.39 5.99 9.26 (o.9_9) 9.99 (0.709) (0.66_) (0.890) (o.73o)

£_rl)I/T_r4

BECTION V

_-38

Preceding pageblank

_7

_-3 I c_ !

FLIGHT ENVELOPE NOMINAL CRUISE CONFIGURATION Clean Airplane 60,000 W = 90001bs CG at 23%MGC Ix = 1438 slug-ft 2 40,000 Ref.

Iz = 26,779slug "ft2 Axes T.y = 25,874 slug-ft2 I Body h(ft) [xz = 0 (assumed) /

/

20,000 REFERENCE GEOMETRY

/

I co S = 170 ft 2 i I c = 7.73 ft I SL 0.2 b = 25.25 ft Augmented Power ---- Military Power (J85-GE-5) REFERENCES X Lateral transfer functions given for these flight candltlon= I) T-38 Dynamic Stability, Norair Report NAI 58-704,April 1959 BASIC DATA SOURCES Wind Tunnel Tests

PITCH

__ _e T-38 8"

Io.__ _

IO.Ss+, ! I -° I

YAW

8rp 8r

SCHEDULED GAINS

1.8

1,4

1.6

o Kr {D

1.2

1.0

.8

\

Y

.6

C (.D

KSo

.2

18 20xlO0

0 2_ 4 6 8 I0 12 14 16

Impact Pressure qc ,I bs/ft2

T-38 -- Stability Augmentation System Figure V-2.

Tk- _76-i 59

OL_L 9LOL

t_LL

<0

0 = zxI _g%J-_nI_ 000_9[ = Zl # %J-BriTs 000_0{ = £I # %@-_nIs 009#9 = xI

OVA _{_ %_ "_'o #s_nI_ O'LL{ - m ¢_ql O00_OL =

<o b-

:_%o_

uolg_u_ljuoo _sTu_o Cs_x_ OUTl_Ogu_o p_xT_-£poq _o$ _%_6

$_-,T, ,_HZ _0£ T_,V,T, ZNV_V£ qVOIH,T, ZNO,_O

V-A [_I_VZ

TABLE V-B LATERAL NONDT}_SIONAL STABILITY DERIVATIVES FOR THE T-38 Note: Data are for body fixed centerline axes, cruise configuration I FLIGHT CONDITION -4 Gh I

2 4

h (ft) 25,000 50,000 50,000 40,000

25,000

o.6 o.8 1.0 O.L 1.0 o.8 1.0

M (--) i .25

4O6 1210

67o 893 1117 1017 774 968

( f$/sec ) VT o

-i .26 -I .26 -1.41 --1.20

-o.715 --I.27 -i .35 -i .35

cy 6

o 0 0 0 0 CY$ a

o.16o o.126

o.172 0.132 o. 183 0.097

o.155 O. 103

CY$ r Oh

-o.o86 -o.o86 -o. o8o

-o. 052

-o. o57 -O. 063 -0. o85 -0. 097

C_6

-0. 270 -0.365 -0.335 -0.390 -0.295

-0.320 -0.330 --O.275 C_p

o. 080 0.140

0.110 o.115 o.135 o.13o

o. 095 o.155

C_ r

O. 040 0.026

o.o53 0.032 o.o19

O. 037 o. o3o o. o069

C_6 a

o.o16 o.o_8 O. 021 o.o16

0.012 o.o15 0.oio3

0.017 C_6 r

o. 262 o. 24o O. 286

o.332 0.335 o.340 o.31o

o.315

Cn_

0.084 O. 076

o. o76 o.o78 o. 085 0.078 o. o52 O. 070

-0.470 -0.435 -0.490 --0.340 -o.49O -o.38o -o.5oo -o.53

Cnr, 0.0126 0.0126

0.0149 0.0137 0.0149

o.o13 o.o143 O. 0069

Cnsa

-o. 060

-0.o86 -o. io6 -0. o86

-o. o63

-0. 092 -0.092 -0. Io3

Cn5 r

TABLE V-C

LATERAL DIMenSIONAL DERIVATIVES FOR THE T-38

_9 I

Note: Data are

for body-fixed centerline axes, cruise configuration

-4 O_ I

FLIGHT CONDITION

1 2 3 4 5 6 7 8

h (ft) 0 0 0 25,000 25,000 50,000 50,000 40,000

M (-) o.6 o.8 1.o o.4 _.o o.8 1.o 1.25

Yv -O.311 -0.737 --0.98 -O.151 -0.4 --0.0982 -O.137 -0.232

0 0 0 O 0 0 0 O

Y8 a

0.0122 o.o188

o.o143

0.1 0.0391

o.o75 o.191

0.0675

Ysr

o_

-13.46 -21 •73

--46.24 -9.293

rO -123.03 -8.491

-29.69 -58.29

-].286

--0.8544

L ! -2.435 -0.588

-3.14 -4.3]6 -4.5 -0.727

P

0.246 0.296 0.567

1.242 1.8 0.4]7 0.767

L !

0.785

r !

7.941

5.727 5. 383

3.5o3 13.98

19.27 27.75 9.987

%a

4.305

8.065 2.269 2.691

L ! 8. 334 16.65 17.37 1.489

6r

4.0

7.402 16.77

62.18 23.31

2.72

17.65 37.71

o.0118 0.0429

0.0673 o.o198

0.132 O. 178 0.296

o. o965

I

-0.142 -0.30

-0.423 -0.O86

-0.1185

-0.736 -1.037

-0.597

Nr

!

0.806

0.2084

2.36 o.877 o. 298

0.0782

o.876 1.712

N$ a

--1.482 -3.245

-11.8 -5.984 -1.872

-6.2 -11.01 -1. ] 67

TABLE V-D AILERON IATERAL TRANSFER FUNCTION FACTORS FOR THE T-38 Note: Data for body-fixed centerline axes, cruise configuration FLIGHT CONDITION

2 4 8

h 0 0 0 50,000 50,000 40,000 25,000 25,000

M o.6 0.8 1.0 0.4 1.0 0.8 1.0 I •25

-o.oo14 0.oo141 o.ooo16 -o.oo31 -0.0043

-o.o13 -o. 00594

I/T s o.oo25

o.548 o.8o3 1 • 236

4.145 4.185 o. 6o5 2.275

i/T R 3.Ol 97

A

0.133 o.146 0.102 0.t 0.0585 0.0705

0.0527 (d 0.121

6.2 2.847 4.151

I.98 4.94 2.187

7-97

_d 4.251

10.0 5.727 5.383 7.941

27.75 3.50 13.98

Ap 19" 273 -o.o018

-o.ooo3 -0.012 i-0.00082 -0.00362 -o.ooo554

-0.0005

N_ I/Tpl -0.00091

0.108 0.12 0.127 0.0852 0.085 0.0473 0.052 0.0675 _p 4.382 6.473 9.628 1.703 5.137 2.081 2.856 4.365

%

!27.78 I0.01 3.515 14.0 5-745 5.4 7.96

A m 19.29

) (0.0829) (0.127) (o.o853) (0.047) (o.12) (0.0522) (0.068)

N_a I/T% (_) (o. Io8

(5.135) (2.086) (2.856) (1.719) (4.361)

(9-617) (6.471 )

1/%p2 (_cp) (4.381)

0.2084 o.8o6

0.877 2.36 O. 298 1.712 0.782 A r 0.876 1 •401

4.80 0.484 o. 638

I .52 5.4o5 o.535

I/Tr 4. 439

r N5 a 0.143

0.405 0.0827 0.423

0.47 0.129 0.192 _r 0.267 1.884 2.95 1.523 3.19 2.113 2. 765 4.345 ca r 2. 127

0.446 -0.64

-O.511 O. 289 -1 •323 -0.0074

-2.255

A_ --0.511

-0.o66

--0.0843 -0.21

-o. o353 (o.58) -0.0832 (0.706)

I/TPl (_#) -0. 167 N5 a t8.624

4.90 5. 334 (0.283) 7.439 (0.287) I .795

1/Tl_2(_ p) 6.926 1/T_ 3

TR-176-I 63

TABLE V-E RUDDER LATERAL TRANSFER FUNCTION FACTORS FOR _HE T-38 Note Data &re for body-fixed centerline axes, cruise configuration.

FLI_IT CONDITION I 2 3 4 5 6 7 8 h 0 50,000 50,000 40,000 0 25,000 29,000

0.8

0.8 I .O 0.4 I .0 O.6 1.0

M 1.29

0.00141 -O.013 O.0OO16 0.0025 -0.OO14 -0.OO594 -o.oo31 -0.0043

I/Ts

0.9/48 0.803 1.236

4.185 0.605 2.275 3.O197 I_. 145

I/TR

O.146 0.102 0.1

O.121 0.133 0.527 0.585 o.o7o5

7.97 I .98 4.94 4.251 6.2 2.187 2.847 4.151

8.33 16.65 8.065 2.27 2.691 4.305 17.37 1.49

Ap

-0.0003 -0.O119 -o.0oo92 -o.ooo5 -0.00082 -0.00361 --O.OO18 -0.000583 N_Sr I/Tpl

-4.522 -2.o6

-2.07 -o. 797 --3.311 --I.454 --I.395 (O.O081) I/Tp2 (_p) 2.1.94 1 .I0 4.79 I .905 3.341 I .423 I .408 (0.605) I/Tp3 ((Op)

17.245 i.31 8.215 16.5 7.91 2.14 2.59 4.237

AS -3.372 -1.526 -1.443 !(-O.O103) -4.557 -2.293 --2.11 --0.827 N_r I/T$I (_)

4.79 I .994 2.15 i.09 3.390 1.451 1.42 (0.608)

I

-6.2 -I 1.01 --II .8 --I.167 -9.984 -1.482 -1.872 -3.245 A r

3.o 4.114

4.196 O.561 2.252 0.519 0.78 -0.0_71 r I ITrl N5 r 0.674 O.14 0.206 (0.0302) 0.373 O.11 O.196 (O.193) r ( I/Tr2) 0.465 0.833 0.309 (0.367) 0.456 0.502 0.346 (1.23) a_ (I/Tr3)

0.o748 o.o191 0.067 0.0998 0.0391 0.0143 0.0122 0.188

%

-o.ooo63 --o. ooi 6 -0.00212 -0.0372 -0.0034 -O.OLO7 --0.0052 -0.oo41 N_Sr 1/TI31

2.994 4.075 4.2o5 0.65.5 2.302 0.558 0.810 1.23

I/%2

94.93 113.63 161.56 72.21 159.0 117.48 64.64 178.02

I I/T03

45.24 89.16 83.53 7.852 39.77 11.08 11.88 22.72

Aay

-0.0057 -0.0018 -0.00447 -0.0496 -o.oo561 -0.o14 -0.0063 -o.00398 I/Tay I 4.223 o. 683 3.89 3.799 2.322 0.565 0.813 1.226 NS_ r I/Tay 2 -3.027 -6.248 -9.098 -2.525 -5-987 -2.536 -3.709 -4.732 CG I/Tay 3 2.882 7.327 10.416 2.736 6.529 2.66 3.90 5.096

I/Ta_%

TR-176-1 64

SECTION VI

F-SA

6_

I Figure Vl-] I

F-5A

(_ONFIGURATIONS GAR-8- GAR-8 on wing tips I - Centerline Tank 40,000 150gal.tanks at W.S.85 h(ft) X 7501b. stores at W.S. 114.5 50gaL tip tanks X w 20,000 T-A - as I with 50% fuel 11" - 20001b centerllne store I000 Ib stores at W.S. 85 0 w_ ° • w w 7501b stores at W.S.I14.5 0 .5 M IJO 1.5 50 gal. tip tanks REFERENCE GEOMETRY X Longitudinal data given at these flight conditions,see Table E .5a S = 170 ft = for conflguratlon,_ ,and 7'e b • 25.25ft c • 7.75 ft REFERENCE I) Jex,H.R. and J.Nakagawa,Typical F-SA J=_oon_tudinol Aergdynomk_ Data and Transfer Functions for 14 Conditions, Systems Technology, Inc., Technical Memorandum No. 239-4, March 1964 BASIC DATA SOURCES Wind tunnel tests with corrections made per flight test.

I ._=

F -5A

I YAW PITCH F-5A

o5---2%

°'5s*' I L__

SCHEDULED GAIN SCHEDULED GAINS K8 = 0.2 deg/deg/sec 1.8 K_ = 1.35 deg/deg/sec

I00

1.4 Q_ 1.6 o.

1.2 .c_ u ._o 1.0

,o \ \

.c_ n_ \

O.8 .o

\ K I

0.6

2O

p- 0.4 e-

£

I- 0.2

I

-_ 2O

80 IO0

40 60

2 4 6 8 I0 12 14 16 18 20 x I00

Impoct Pressure, q'c, Ibs/ft2 Impact Pressure, qc, Ibs/fte

Figure Vi-2. F-SA -- Stabilit_ Au_memtation System

!

I _%BLE _q-A _ICAL PAn ZrOR _BE F-_A Rote : S - 170 tt 2, b - 25.2_ _, c - 7.73 t%, _o " 0.5 Data are for body-fixed stability axes.

FLI_IE CCRDITI_ 1 2 5 2 5 1o 11 12 13 12 I I-A II II gAa-8 GAR-8 gAa-8 ConfiKurat1_ns 0Aa-8 G_-8 I-A TT E_pty + DL_ Bz_Xe F_ps + Slate + Flaps _'Dl_ Bz_ke I-A 50_ Fuel 50_ Fuel 0 )0,000 20,000 0 0 0 k0,000 _O,0_0 0 20,000 0 0 0 h (_t) 0.286 0.8 0.875 0.875 0.87_ 1.25 0.875 1 ._ o.2o_ 0.875 0.70 0.70 0.50 0.50 M o -6o o 0 0 -60 70 (_eg) 0 0 0 0 0 0 0 0 1.0 1.0 0.5 1.0 4.0 1.0 2.0 1.0 1.0 1.0 0.5 1.0 _.0 1.0 a,- :./w _o, 70 2.8 2.8 7.0 2.2 8.0 1.0 0.8 0 12 2.8 1.2 3.2 12 9.0 1210 98o 1_-5o 228 910 980 85O _28 122 282 521 1,130 720 725 570 570 (Ibl_ 2) 210 1150 15_I0 61.9 1,1_0 I_,000 19,000 17,000 14,000 I_,000 I_,000 17,000 17,000

w (zbs) 1o, o00 10,000 10,0GO 10,000 10,000 12,000

0.22 O. _c' O. _'_ 0.2 O. _'_ 0.1k 0.12 0.1._ .05 0.17 0.15 0.15 0.15 0.I_" x@.g./8 _55 _55 590 57_ _ 526 528 511 21 --2.62 -_.62 --2.86 -5.77 --0._-5 1.0 --4.28 --6.26 --2.5'7 0.52 -I .55 --I.13 -I. 15 -1.80

6eo(_g)

_,600 P,,6oo 57,900 _, 700 57,900 _4,400 _,_00

5O,0CO 30,000 _0,000 30,000 51,000 57,100 57,900 11.6 11._ 11. b, 11.5 11._ 12.0 12.0 12.0 11._ 11.2 11.2 1o.5

ix (_zot) 12.o 12.0

"R.,TST.Is "_'o ,zo,; pe%oea.zoo,,, "o_'0 _:_ _I)om o]:_,s'_le _R_. %u'nooo_ o%= T aA.llg, SaAI:%'_AT,IOG.

oC_- O00_-- OgCe" O_LL-- OG6- ooo_ =. _ o oo_t oAt(t- o_ t OOOc_- oo_

0_" L-- O_'t-- O_'t- GG',- " I .(v,=ll) _)'_b

_" L- _-_-- "_g"t- %g" t- +_)_" _- 6_" L-- 9_'L-- _O'L-- 6_'L-- 9_'_-- 0 0 0 0 9t "0 00_'0- oLa'O- 0_0"0 O 0 0t0"0- o o_o'o- _o OOL "0--

g'9-- 8"9-- 8"L- L'6- _ L'6- g" _L- g'6- L'6- _'o_- .(_'=/0_o

8"9- 8"9-- 6 "9- 6-

Ot "O- Ot "0- OL "0- Ot "O- L'o- L'o- o" _- og'o- GOO'O- Coo"o- o_'_ _._- (_.q_)._b

L'O- C 6_g"0-

oL9"o- 989 "o- o_9"o- gkg"O-- gO" L-- t8%'C,- L69 O- R_'O- g'_'L • O- L_ ° [-

Lg_'o- 9tl" _.- _.9_'o- ..(_,=/_)

_o'o _00" 0 068OO "0 _6_oo'o 9gtLooo'o g_too'o LQgO0"O G69LO0"O _t_O'O _8_oo'o g+_LtOO'O G L Gooo" o _o6ooo'o o_ 9_tO0"O

0 o o 0 0 0 0 0 _LL "0 _LL "o o o (_,=I_) _

o 0 o_o'o o o 0 Q_O'O 0_0"0 0_0"0 OOt "0 0 o o OCO'O 0 og_o "o wco

o o o 0 0 0 0 0 0 o o o 0 o (w,_/_) _o

96_ "o _o'o _9_o'o _g_'o O_'L L_", _6LO'O-

_£_'o _9_ "o 9o_'o 0_90"0 _9_o'o _6"L 6_'o (we=It) _o

L_Zg'O _8"o L_8"O 9L6"0 9'6"0 8Sg'O _'0 _05"0 g_L'O _09 "0 gt_L"0

_'o _o'_ .(_,_/:) _o

o 0 o 0 og'o- o o_'o ga "o- 0 oL'o-- on'o w_o 0 9"O- o_'o Oh _'CS C-g _-g g'g _'g g'g C'g C'g

_'g g-_ g-g _'z t (_,_I_) _o

gL'_ gL'_ _'C _'C g_'_ 8_-g 8_'g LL'9- C_'L- _9°8 _" gg° L-- _g'O Lg "8'-- _'i- (_) %q 98"_- _9"_- 98 "9- "_- _o" _ g_'o- 0_" !.- o'L 8"_ 8"L g'_ 0"6 _t 0"_ o'8 _'_ 8"8 _t o 8"0 8"C (_,_) %0 _o'o ggr.o'o L_(O "0 LL_O'O _o'o L6LO'O 8iZO'O _0"0 O_L "0 0St "0 0_O'0 gLLO'O L_O "o 6Lso'o (Io _g'O . /Z'O _g_'o _L'O 8_'o _Lo'o 6Lo'o gg_'O 86"o _6"o _o'o _Go'o _t "o 0(_ "0 "IO 0 0 0 0 o

o o o9- o o o9- o o o (_) oz

og'o o_'o oL'o oL'o CL8"O gL_ "o gL8"o 8"o 9_'o _o_'o o+_-t GLS"O _-_. _/8"o w o o 0 o 0 0 000 '0_ 000'0_ o 0 000 tog 0 ooo'o_ ooo'o_ (_) q _d_Ix + V-I 8-1_vo X%c_ /,Z _@I v-I Ii ii Y-I I g-h'VO 8-h'vO 8-h'VO _L eL _t OL 6 8 t 9 NOLLI G_OD _OIq_ I \D [.._ _H I V_-_I _}_ _ 8SAI&VAI_G XV_OIB/_HI(INO_ T_II(II%_O._Oq E-IA _-3 I TABLE VI-C Oh I LONGITUDINAL DI)_SIGNAL D_IVATIVES FOR THE F-gA Note : Data are for body-fi_ed stability axes, quasi-steady aeroelastic corrections included.

FLIGW_ COIDITION ? 8 9 I0 II 2 3 9 6 El II GAR-8 I I-A GAR-8 @_ % _ Empty I-A I Configurations GAR-8 CAR-8 C_R-8 + Dive Brake + Dive Brake I-A 90% Fuel _1_ Fuel +TT _t_ +Slats + Flaps O 0 0 0 0 0 o 0 0 30,000 _,000 40,000 40,000 20,000 h (ft) 0.70 0.90 0.90 O.20_ O.286 1.40 0.8 0.873 O.87D 0.875 o.7o 1.25 .879 M O . 875 o.o167 0.00128 o.o14-4 0.0e22 0.0e76 0.0178 -O • 01 R6 0.(_o09 -o.o6o9 -o.o3oi 0.ooo_8 0.oi17 -0.00805 0.0101 X w (I/eee) -o.o_o9 -o.oi 82 -o.o919 o.c964 -o.o_oI -0.0198 -0.0362 -o.o_Yo -o.o9o9 -O.Olge -0.045Z -0.0909 -0.01 O9 -o.oo589 X_ (11sec) -I .61 -1.0_ -0.828 .2.22 -o.9o8 -o._,91 -0.521 -1.10 -I .86 -2.2_ -I .74 -0.754 -I .05 zw (llsec) -0. _7 -0.119 -O._'P9 o.4oI -o.0975 -o.71_ -0.0696 -0.0910 -0.0822 -0.124 o.118 -0.276 -o.197 -0.289 (11se_) O -24.1 -26.9 -78.6 -I 81 -_e9 -_79 -2_6 _3 -99.1 -97.7 -439 -I19 -IT_ -599 %e (ftlsee21r_a) -o._ooa -o.m 7_ -o.oi 69 -O.00892 -0.00061 -0.0408 -0.C_93 -0.0174 -o.o993 -o.oo838 -o.o138 -0.00399 -o.c_2? -o.oi 87 (11sec-ft) -0.0000199 -0.000o176 -0.000o176 0 0 -O.O000_a7 -0.00(X)891 -0.000109: -0.000114 -0.0OO019 0.000149 -O.0001_I o.oo_47 -0.0000599 _& (11ft) -o.969 -o.667 -o.66e -0._88 -0.888 -i ._8 -_ .99 -o.979 -1.08 -o.296 -o._72 -0.429 -o.9_o -I .9_ (I18eo) o.oooe66 o.ooo_7 o.ooo_77 o.o001 _9 O.O(X)626 o.ooo_ -o.eo_99 -O.0109 0.00589 0.000166 -O.O00_6e -0.00099 -0.001 93 O.OOOO757 M_ (llsec-ft) -_I .O -17.0 -16.7 -3.16 -9.91 -14. 9 -26.1 -99.8 -62.1 -91.9 -e4.e -63.2 -14.3 -73. i _e (11sec2/r,_) Note: The transfer functions given in Table E.gc) are based on the above derlvatives and the equations of Appendix C with additional corrections msde for Inertial Bending as follows: : -- 0.000162 red/ft/sec 2 (®_)z_ (_)_ + Uo_(z_-z@%) Ka z (First coefficient)13 =_I • (first coefficient) R - KazZ_ where subscript IBm corrected value (_S_)R R _ rigld-body + quasi-steady

(PC _n)z_ : (_--_)Z__ (DC _aln)_

aeroelastic corrections

TABLE VI-D

LONGiTUDL-_AL TRANSFER FUNCTIONS FOR THE F-SA

Data are for 0ody-fixed stability a_es; corrections have been made

Note :

for Inertial Bending

FLIGHT CONDITION I

I0 11 12 !3 14

I 2 5 4 5 6 7 8 9

Oh I 0 0 0 0 0 0 20,000 0 O 30,000 20,000 0 h (ft) 40,000 40,000 o.819 0.70 0.70 0.50 0.5o 0.875 I •40 0 •204 0.286 0.8 0.875 0 • 875 M o.875 1.25 I .O/0 2.0/0 _.olo 1.0/0 4..olo 1.0/0 0.5/-60 1.0/0 1.0/0 1.0/0 0.5/-60 1.0/O

_z/7o (de_) 1.olo 1.olo

12,000 14,0OO 14,000 17,000 17,000 I 0,000 I 0,000 10,OOO 1 9,000 1 7,000 1 4,000 1 4,000 Wt. I 0,0OO I 0,000 o.17 o.15 0.15 0._5 O._5 0.22 0.22 0.22 0.1 4 0.12 0.15 0.05 CG 0.22 0.22 4.81 4.95 5.5O 5. _6 5.65 11.4 1.43 2.1 4 2.82 3.78 8.05 7._9 %p 2.29 5.84 0.26_ 0.285 0.262 0.243 0.223 O. 325 0.128 0.286 0.I 88 0.I 82 0.270 0.215 _sp 0.266 0.121

A

0.126 o.o6o_ o.115 0.0852 o.118 O.0856 (-0.05465 0.197 0.147 O.O555 (-0.053O) (-0.0964) a_p (I/Tpl ) 0.0_7 (-0.O721) o.197 o.157 o.129 0.1o6 0._32 0.257 (o.io_) 0.1o8 0.142 o.155 (0.1165 (o.1285 _p (I/Tp2) 0.0761 (0.0750) -17.3 -17.o -67.0 -_.6 -_2.2 -80.4 -68.3 -5.16 -5.31 -14.6 -26.9 -64.0 ACe -14.6 -2_.0 0.01 6_ 0.0;_ "_!

0.O516 o. 0202 o.o_8 O.0461 0.0457 0.0170 0.0225 0.0159 0.O571 O.0534 _T e I/_ee I 0.0995 o.oo778 2.04 1.6o 1.46 O. 991 O. 724 3 • 3O I. 81 0.484 O. 379 O. 474 I. 03 I. 58 I/T%2 0.703 0.885 -4.06 -0.1 _ ! -_ .4_ -14.1 -_._8 -6.15 -9.91 1-47 O.810 -0.O269 _ -2.19 -9.74 NI _ Aue 0.970 2.26 2.42 9.55 2.79 o.9_2 0.969 4.72 -I .95 0.512 0.280 0.478 2.91 4.68

5e I/Tuel 0.580 0.602

-4.210 -288 -52.6 -I 57 -i 54 -294 100 98.6 273 -17,450 -68.6 -71.4 I/Tue2 586 525 -246 -244 -I 01 -99.7 -18o -610 -474 -24.1 -26.9 -79.5 -186 -438 -515 Awe -I 21 lO_ 96.5 95.6 168 129 lO5 I _I 210 29. 5 62. I 146 1 51 145 1/Tw e I _ 03 O.O82O o.116 0.116 o._-_ 0.0585

N_e aWe (I/T_e2) 0.0673 (-o.o563) 0.0969 (-0.03585 0.199 0.145 0.04_2 0.0501 (-O.00410)

o.1_ 0.111 o.I 57 o.5o9 o.165 0.233 (0.105) 0.159 0.139 O.161 0.666 (0.0576)

(o.o622)

_w e (I/Tve3) 0.0809 24.6 101 99.7 610 238 24.1 26.9 79.5 93.4 438 51 3 121 180 Abe 0.0110 c.o_ 8o O.01_D 0.025_ O.O5O5 o.o117 0.0432 0.0680 -0.0718 -0. 357 0.0108 O.O661 0.0355 O.0O309 J_e I/_'_I -12._ -11.9 -9.05 -7.98 -8.25 -15.5 -12.o -19.6 -18.8 -5.59 -4.50 -8.04 -11.0 -14.3 I/The2 13._ 12.8 9.75 8.67 12.4 17.o 8.72 21.7 1 9.6 3.81 4.95 8.56 1 2.0 1 5.9

I/_3

124.

26_ 9_.6 95.2 I _5 54.0 120 355 346 1 3.8 55.6 84.8 11 9 255

a' o 0 0 O

0 o o.oI_ o o o (o.o538) o NsZ I/T_' el (°_el o.o18o 0.01 80 0.02_4. 0.O110 0.o432 0.0499 -o.o714 -o.o536 0.01o8 (0.984) 0.0555 O.O5O5 o.oo3o9 0.0117

I/T_'_2 (;'zel

8.6o 18.1 17.2 9-7o 27.1 22.7 4.76 4.25 8.05 1_.5 20.6 22.5 12.8 15.0

Cpi ot o

o.o_68 0.0618 0.0781 0.0699 0.0613 0.101 0.0720 0.0871 0.O509 0.0276 0.0381 0.0379 0.o476 0.0559

SECTION VII F-I04

Preceding page blank

i Figure Vii- ] ch I

F-104

FLIGHT CONDITIONS I 2 3 4 5 Start End VMAX Takeoff Cruise Cruise VMAx Sea Level h(ft) Sea Level 30,000 30,000 30,000 Sea Level M .273 .84 1.0 1.9 1.36 W(Ib) 24,000 23,510 14,960 15,000 15,000 .046 .040 .18 .18 .18 xcslc On On Clean Cleon Clean Tlp External Tanks On On Clean Clean Cleon Pylon -3o -3o .3 ° -15 ° .3 ° Leading E_e Flaps 15 ° IS ° 0 ° 0 ° 0 ° Trailing Edge Note: Loterol dofo not ovoiloble REFERENCE GEOMETRY l s : 1 9 6 ft = b = 21.9ft C = 9.53ft REFERENCES Unpubllsh_Dota PITCH " r _ep F-104 ROLL" F-104

L _s __. -- _'s+l

YAW" r F-104

I

TS+I Figure VIi-2. F- i<)l_ -- Stability Augmentation System T_:- 176-1 7> TABLE VII-A GEOMETRICALAND INERTIAL PARAMETERS FOR THE F-I04 Note: Data are for body-fixed stability axes S = 196.1 ft 2 , c = 9.53 ft , b = 21.9 ft FLIGHT CONDITION ] 2 4 3 5 START END Vmax TAKEOFF

Vmax

CRUISE CRUISE SEA LEVEL Sea Level Sea Level

h (St)

30,000 30, O00 30,000 o.84 1.0 I .36

M (-) 0.273 1.9

a (ft/seo) 1117 995 995 995 1117

0.00238 0.00238

(slugs/ft 3) o.0oo889 O. 000889 O .000889

3o5 995 1892 1519

VT° (ft/sec)

44O

_= _v2/2(ib/ft 2) ]]0.5 31o 159o 2740

w (ib) 24,000 14,960 15,ooo

23, 31o 15,ooo

746 465 466

m (slugs) 724.5 65,000 64,500 56, 65O 56, 65o

ly (slug-ft 2) 56,650

O .O46 O.040 0.18 o.18 0.18

Xo.g./_

4.0 1.4 19.6 2.0 1.1 s o (deg) IO 0 O o 0

7o (_eg)

4.0 1.4 2.0 1.1 29.6 e o (deg) TR-176-1 76 TABLE VII-B LONGITUDINAL NONDIMLmNSIONAL DERIVATIVES FOR THE F-104 Note: Data are for body-fixed stability axes.

FLIGHT CONDITION I 2 3 4 5 h (ft) 0 30,000 30,000 30,000 0.84 I.0 I .36 1.9 M (-) o.237 o.o383 O. 0278 o.342 O.1375 C L 1. 125 O. 04 0.041 0.045 o.o365 C D O. 185 4.18 4.44 2.92 4-.97 5.10 CL(_ 0 0 eL& C_ o.8035 0.762 I. 071 O. 6925 1 .O15 CL6e 0 O CD_ I 0 0.1094 0.0255 0 o.040 O. 042 o.o38 0.045 CD M 0 0 0 0 0 CD6e -I .8o --I.496 -I. 564 -i.255 -I .319 Cm_ --3•44 -4.99 -3 •04 -2.oo5 -3.90 Cmc_ 0 0 0 0 0 Cm M Cmc t -5.615 --8.O3 --8.6O --4.59 -6.825 TR-176-I 77

TABLEVII-C

LONGITUDINAL DIMENSIONAL DERIVATIVES FORTHEF-IO4

Note: Data are for body-fixed stability axes.

FLIGHT CONDITION I 3 5 END START Vmax

TAKEOFF Vmax

CRUISE SEA LEVEL CRUISE Sea Level Sea Level 30,000 30,000 30,000

(ft)

1.0 I.36 0.84 1.9 o. 273

M(-)

-0.O106 -0.0224 -0. 0573 -0.115 -0.0352 X u (I/sec) O. 0211 O. 0209 0.0136 o. IO7 O. 0234

xw (I/see)

0 0 o 0 XB e [(ft/sec2)/rad] --0. 0422 -o. 0688 -o.214 -o.o513 -O. 0271 Zu (I/see) 0 o 0 o z_ (-) -1.05 --3.21 -0.440 -0.504 -0.959 Z w (I/see) -464 -927 --22. I -85.3 -199 ZBe [(ft/sec2)/rad] 0 o 0 0 O M u (I/see-ft) -0.000212 -0. 000375 -0.000239 -o. o00349 --0.0005 6 M_ (11ft) -o. 0228 -0.0142 -0.0348 -O. 107 -0.o156 M w (11sec-ft) -O.412 -0. 607 -I. 94 -o.598 -0. 279 Mq (11sec) --140 -30.8 -17.8 -57.2 --4.67 MBe (I/sec2) _-176-1 78 TABLE VII-D E_ATOR LONGITUDINAL TRANSFER FUNCTION FACTORS FOR THE F-I04 Note: Data are for hod ,-fixed stability axes FLIGHT CONDITION 2 4 I 3 END START Vm_ TAKEOFF Vmax CRUISE SEA LEVEL CRUISE O.84 1.0 1.36 1.9 Mach No., M (--) O.273 Sea Level 30,000 30,000 Sea Level 30,000 Altitude, h (ft) 18 18 18 4.6 4.0 CG (_ o) Weight, W (ib) 24,000 23,310 14,960 15,0(0) I0,000 o.2o6 O.161 0. 126 0.220 O. 197 _sp 2.21 13.0 3.48 4.83 8.16 _sp Along 0. 102 o.o932 0.277 (0.0o959) (o.008o8) _p (I/Tpl) O.O4O2 O. 140 o.o01 (o.o4w) (o.1o7) -_.66 -17.8 -14o -30.7 A e -57. I 0.01_ o.133 0. 0237 o .o_78 o.115 I/Te I N_e o.812 o.269 0.432 O. 767 2.51 I/Te 2 -2.00 -2.37 -4.19 -6.29 -19.6 I .11 2.26 24.8 -0.0391 3.61 I/Tu I 6.17 -113 -85.7 --62.2 -_3.2 I/Tu2 -22. I -85.3 -_6_ -199 -927 Aw _.7 175 23_ 231 1.55 I/Tw I o.o966 O. 102 0.275 (0.00967) (0.00833) _w (1/Tw2) o.147 0.O914 0.0_07 (0.0476) (O.107) a_ ( 1/T1_3 ) 46_ 21.8 199 927 89.3 0.00816 o.o971 0.115 0.0185 o. o217 IITI_ i 13.9 29.2 11.7 5.21 9.03 II_2 -8.41 -1o.7 -12.9 --22.7 -_.76 TR-176-1 79

SECTION VIII F-IOSB

Preceding pageblank

05o(3 poqsllqndun $:10N3_13-13_i IJ.g'll = 0 #_ 6"_£ = q zl_, gg£ - S AUI3N039 30N3_333_ suo//lPUOO $$$qi lo o/qDIIDAD lou olop IOJ_qo7 • 0 o9_ 0 0 o9t_ eSp3 ENJH!oJJ.

sdOl.l o oOZ o o oOZ ,6p3 _Jp¢_l UOOlO UOOlO UOelO "lcNSOg,l_-_ "lO60gt,-Z UOl.(d 5UlM squo£ oJ cO UOOlO UOelO UOOlO "1o60g9-1 "lD6099-1 eUllJO;UOO IOUJO;X':l 80£" 80£" eO£" g6;_" g6Z" o/so x OL£'g£ 000'0£ 0L£';£ 0£_'1t_ O£Z'lt_ (ql)M" I';_ ItP;_" 6" 6" 19_" IN O00'Ote leael oos O00'G£ O00'g£ IO^Ol ooS ($_) q qoooJddv xVHA j;oeNo.L JeMOd g t, £ ,Z ,I SNOIklQNO0 CHglld r_ I _0 p--

8goI--I

I E-_ L-IlIA _Y_ PITCH • -_(_ _- F- 05

_ep Se i I

K_} = Scheduled function of impact pressure qc

T

ROLL' F-105 Kp = Scheduled function of impact pressure qc YAW' P / ay _rp 8r F-105 ....

4, Ks 1.15s+l K_,, Kpr = Fixed gains Ka = Scheduled function of impact pressure qc Pigmre VIII-2. F-I05- gtabilit:F Aug_nent_tion System T_- 17(;- 1 83 TABLE VIII-A GEOMETRICAL AND INERTIAL PARAMETERS FOR THE F-105B Inertia data are for principal axes.

Note: S = 385 ft 2, b = 34.9 ft, C = 11.D ft FLIGHT CONDITION 3 5 I END POWER

Vmax

START CRUISE APPROACH TAKEOFF CLEAN CRUISE C LEAN CLEAN Sea Level Sea Level 35,0OO 40,000

h (ft) 35, O00

O.241 2.1 o.261 0.9

M (-) 0.9

968.5 973.3 1117 1117 973.3 a (ft/sec) o. ooo587 O. 00o738 o .000738 0.00237

o (slugs/ft3) O. 00237

269 2030 875 875 VTo (ft/sec) 86 1210 IO0 283

0v2/2(lb/ft 2)

30,000 35,37O 41 _23o 35,37o

w (ib) 41,230

128o 128o 1098 932 1098 m (slugs) Io, 300 1 2_ 600 I0_ 300 8 _700 8 _700 Ix (slug-ft 2) 140 _000 140,000 140,000 14o, 00o 140,000 ly (slug-ft 2) 181 ,ooo 177,000 181 _000 185,000 185,000 I z (slug-ft 2) o 0 0 0 0 Ixz (slug-ft 2) o. 3o8 o, 308 o. 3o8 O. 295 O. 295 Xc.g./_ 5.2 3.5 7.4 7.2 7.0 0 0 10.0 0 -5.0 7o (deg) 0.2 7.0 3.5 17.4 7.2 eo (deg) TR-176-I 84

TABLE VIII-B

j _- ,- LONGITUDINAl, DI_[F_ _, LJlJAL DERIVATIVES FOR ThE F-IOSB Note: Data are for body-fixed stability axes.

FLIGHT CONDITION 1 3 5 END POWER START CRUISE APPROACH TAKEOFF CRUISE CLEAN CLEAN Sea Level 40,000 h (ft) Se& Level 35,000 35,000 o.241 2.1 M (-) 0.261 0.9 0.9

-o.0263 -0.00751

-0. oo582 -0.00565 X u (I/sec) -0.029 o.o264 o.o86 0.0132 O. 00693 X w (1/sec) 0.0793 0 o 0 XSe [ (ft/sec2)/rad]! 0 Zu (]/see) -0.1585! -0.01386 -0.05 27 -0.1719 -0.0265 0 o 0 o

(-) o

-O .466 -0.406 -0.4 -0.59o Zw (I/sec) --0.311 -I 9.88 L] 35.9 -65 •19 -75.97 Z8 e [ (ft/sec2)/rad] --17.3 0 O -0. 0000101 -0. oooo 198 M u (I/sec-ft) -0. 0000119 -0. 00011 7 -O. 000259 -0.0oooo5 35 -0.000117 Mg- (I/ft) -_0.000259 -O. OO4 68 -0. 003£4 -0. O1 25 2 --o.oo819 M w ( 1/sec-ft) -0.00575 -0.303 -o .485 -o .485 -0.319 Mq (1/see) -0. 345 -21.0 -12.o3 --12.03 -2.7o3 M6e (I/sec 2) --2.60 TR-176-I 85

TABLE VIII-C

LATERAL DIMENSIONAL DERIVATIVES FORTHEF-IO5B

Note:

Data are for body-fixed stability axes, lateral data not

avaiJ able for flight conditions I and 2.

FLIGHT CONDITION POWER END APPROACH CRUISE CLEAN CLEAN Sea Level 40,000 35,000 o.241 2.1 0.9 -0. 1497 -0.1878 -0.213

Yv( I/sec)

-0.0021 -0. 00221 -0.00173

[(_/seo)/r_d]

0.0234 O. 0241 [(I/sec)/r&d] O. 0837

Y_r

--_1.1 I/sec 2 ) -21 .5 -I 39.8 -2.8 -3.14 -i. 185 I/see) i .251 i .966

L_ ( I/see) I .709

26.5

(I/see 2) IO.71 3.72

L_

2.86 14.37 (I/sec 2) 12.97 L_ 18.81 4.38 I/see 2 ) 12.39 O. 1341 0.324 O. 0729

I/see)

--0.242 --0.386 -0.382

I/see)

_ (

N ' -i. 08 6

(I/see 2) -I. 339

-0.277 6a

(I/seo 2) -4.71 -0.975 -I .989

_r TR-176-I 86

TABLE VIII-D

ELEVATOR LONGITUDINAL TRANSFER FUNCTION FACTORS FORTHEF-IOSB

Note: Data are for body-fixed stability axes.

FLIGHT CONDITION I 2 4 END POWER

Vmax

START TAKEOFF CRUISE APPROACH CRUISE CLEAN CLEAN CLEAN 0.261 0.241

Mach No., M (--) 2.1

o.9 o.9 Sea Level Sea Level

Altitude h (ft 40,000

35,000 35,000 CG (¢ _) 29.5 3o.8 30.2 3o.8 29.5 Weight, W (ib) 41,230 41,230 35,37o 30,000 35,370 o.281 o.1819 0.398 0.0893 0.253 _sp 2.o8 1.338 0.998 5.o6 2.71 _sp Along O.1016 0.0297 0.1295 o.o631 o.1869

{p

0.0201 0.1247 0.0223 0.0429 O. 1342 --2.60 --I2.02 --21.0 -I 2.03 -2.70 A 9 0.1026 O.OO6] 0.00891 0.0742 0.00827 1/Te 1 0,200 O.355 o.433 0.335 0.508 1/Te 2 -1.367 -o.452 --2.002 --1.708 --1.792 1 .o18 1.266 0.438 1.511 2.94 N_e

1/Tu1

-17.0 -696 -55.8 --15.02 -65.2

1/T, 2

-17.27 -65.2 -76.0 -19.88 -135.9 44.2 162 -139 36.9 1/Tw 1 0.0642 o. 0372 o.1258 0. 129 o.1838 O. 1287 0.044 o.1435 0.0204 0.0225 17.28 65.2 76.0 19.88 135.9 O. 004 66 O. 01292 O. 00439 0.01094 0.00737 I/Th I _e -3.37 -7.29 -7.48 --3.49 -12.49 I/Th 2 12.8 3.80 7.88 8.07 3.89 I/Th 3 TR-176-I 87

TABLE VIII-F

AILERON LATERAL TRANSFER FUNCTION FACTORS FORTHEF-IOSB

Note: Data are for body-fixed stability axes; lateral

data not available for flight conditions I and 2.

FLIGHT C OND ITION 3 5 END POWER Vmax CRUISE APPROACH CLEAN CLEAN CLEAN 0.241 2.1

MachNo., M (--)

o.9 Sea Level

Altitude, h (ft) 35,000 40,000

ca (_ _) 30.8 3o.2 3o.8

Weight, W (ib) 35,370 30,000 35,370 7.0 5.2 3.5 _o (deg) -0.00870 o.ooo676 0.00631 l/ms 2.13 1.382 2.95 I/T R Alat 0.184 O. 0545 o. 1531

_a

4.16 2.13 3.29 _d 10.71 3.72 26.5

Ap

0 0 O.OLO3 l/Tpl N_a 0.101 o. 0635 0.0744

_p

2.87 1. 674 3.44 -i.o86 Ar -0. 277 --1.339 --I.524 -1.503 -I .3 1/Trl r N5 a 0.564 o.6o0

(r o.465

1.686 1.718 I .398 _r --0. 00210 -0.00174 -0.00221 --622 O. 1427 0.1379 1/T#1 _a i.655 (-o.0573) 0.658

1/T#2 ([_)

6oi -133.7 (0.276)

I/T_ 3 (_)

TR-176-I 88 TABLE VIII-F RUDDER lATERAL TRANSFER FUNCTION FACTORS FOR THE F-IOSB Note: Data are for body-fixed stability axes; lateral data not available for flight conditions 1 and 2.

FLIGHT CONDITION POWER END

Vmax

APPROACH CRUISE CLEAN CLEAN CLEAN 0.241 2.1 Mach No., M (--) o.9 Sea Level Altitude_ h (ft) 40,000 35,000 30.8 30.2 30.8 Weight, W (lb) 35,370 30,000 35,370 7.0 5.2 3.5 _o (deg) --O.OO87O 0.000676 o.oo631

I/Ts

1.382 2.45 I/T R 2.13 Alat 0.184 0.0545 o.1531

_d

4.16 2.13 3.29 _d 2.86 14.37 12.97

%

0 0 O.01 O3

1/%1

P Nf_) r -I. 82 -I .499 -I. 109

1/%2

I .014 I. 63 I.738

1/%3

--4.71 -0.975 -1.989 A r 1.848 I.4 63 2.31 1/Trl _r 0.1028 -0.246 0.1601 _r 0.342 0.259 O. 838 0.0241 0.00538 0.0233 -0.0103 -0.0395 0.00369 1/T_1

4r

1.927 1.371 2.36

1/% 2

140.6 203 37O

1/% 3

TR-176-1 89

""4 NQI" _L_AED ?RECED_F_G PAG!

SECTION IX B-58

Preceding pageblank

Figure IX- ] I

B-58

I FLIGHT CONDITIONS NOMINAL CRUISE CONFIGURATION See Table 1T-A 50,000 X 40,000 h(ft) X 30,000 20,000 I0,000 0 _" REFERENCE GEOMETRY 2.0 <D 0 ,4 .8 M 1.2 1.6 S = 1542 ft = b • 56.8 ft c • 36.2 ft REFERENCES I) Bright, B.E., EIIIngton,J.D.,"Applicotlon of the Limit-Cycle Selfodoptlve Concept to the B-58 Lateral Directional Stobillty Augmentation System'.'

Thesis, Air Force Institute of Technology, GGC/E E/64-5, May 1964 2) Anon. ,NB-58 Flight Control System", Gen. Dyn. Fort Worth, FZE- 4-049, Nov. 1962 3) Jones, L.S. ,"U.S. Bombers BI-B70" Aero Publishing Inc., 1962 SOURCE Unknown ROLL PITCH I I B-58 ) YAW L_ / ay NOTE : K s , K4, K5, KT, Ke...Gains Scheduled r for Moch- Number K 2 , K 3 , K 6 , K 9 , Kjo...Goins Scheduled ___L for Altitude (Air doto computer not shown) The Augmentotion System for this oirplone is known to hove undergone severol modificotions. The system shown is of 1962 vintoge os documented in GD. Convair Report FZE 4-052, Dec. 196=?, being the Iotest ovoiloble doto Figure IX-2. B-58 -- Stability Augmentation System o/'© Ox {{'0 0{'0 {{'0 9_ "0 _ "0 9S'O

0 o (s_p) °z

0 0 s_L CO L 969' 6L_- zxI LLg'6_- ( S %$-gnIS ) 0{0_07 _ L 090 'o66 067_90_L OL_'LO_'L OLL'90_'L 0L9'90_' L o{s'697' L (_%j-_uIS) Zl 000 _ 4?0 _ t e69'619 000_690_L O00_6_OCL O00_690_L O00_?O_L ( g %J-gnIS ) £I ?_{'6{{ 6L_' L9{ {9{'{9{ 099'99{ oko'o{? ( _q.a-_=-Es ) xz 99L¢ 669*1 _9_ _97 gg9_ 699_ O00_06L O00_OgL 000 _06 O00_06L 000 c06 L O00_OgL O00'OgL (SqT) L_L Lg_L S_L 0o6 96{ oh 6L6 9LOL 9{6L L99 9LOL g9LL gggO00 "0 699000"0 9L?ooo'o 494000"0 kk{¢oo'o LL{eoo'o LL{¢oo'o

(_/S_T_) o

996 466 996 996 LLLL LLLL LLLL (o_s/%#) ¢'t 96'0 0"¢ t6"O t6"O t6"O ¢{'0 (-) 000'0_ 000'0{ 00_'_ 000'0_ o o o (_) q L 9 6 _ { _ L MOI$1QZO0 SHO!ff£ <o b- %J LL'9{ = o :%j sg"9g = ct :e%j S?g'L = S : o%oz 96-_ Z}KZ HO£ _ZmZIgV_V£ _IVOIKZZNOZ© V-XI Z_I_V_ TABLE IX-B LATERAL NONDIMENSIONAL STABILITY DERIVATIVES FOR THE B-58 Not e : Data are for body-fixed stability axes_ cruise configuration.

I .-a FLIGHT CONDITION o_ I I 2 3 4 5 6 7 0 0 40_ 000 44,200 30,000 40,000 h (ft) 0 0.91 2.o 0.98 i.2

M (-) o.32 o.91 o.91

VTo (ft/sec) 357.3 1016 1016 880.9 1936.2 975 1161.7 Cy_ -0. 6395 -0. 6375 -0. 674 -0.7665 -0. 6275 -0.732 -0.801 CYSa O. 1511 0.08655 0.0890 O. 1790 0.0187 O. 1862 O. 1791 Cyst O. 0929 O. 0527 O. 05725 0. 0954 O. 0232 O. 68075 0. 0545 kO k_ C_ -0. 1584 -O.0551 -0.0851 -0. 1345 -0.03942 -0. 1096 -0.1158 C_p -0. 1936 -0. 1585 -0. 1576 -0.2173 -0.2317 -0.2107 -0.2238 C_r 0.04479 0.08568 0.08553 O. 1102 0.07207 0.09543 O. 1071 C_$ a -0.1112 -0.04043 -0.03892 -0. 1041 -0.01782 -0.0729 -0.0010 C_6 r 0.001927 0.00729 0.007395 0.01227 0.003115 0.01328 0.0078 CuB O. 1014 O. 1242 0.0624 O. 1029 0.03207 0.0788 O. 1117 Cnp -0. 1143 -0.01082 -0.02935 -0.06118 0.01241 -0.03713 -0.04215 Cnr -0.2494 -0.2449 -0.2312 -0.2868 -0.2132 -0.2611 -0.2823 Cn6 a -0. 0405 -0. 03318 -0. 03317 -0. 0664 -0. 02038 -0. 0725 -0. 09275 Cn6 r -0. 06415 -0. 03561 -0. O35 63 --0. O633 -0.01382 -0. 053O -0. 03255 TABLE IX-C LATERAL DIMENSIONAL DERIVATIVES FOR THE B-58 Note: Data for body-fixed stability axes, cruise configuration.

I -4 O_ I FLIGHT CONDITION 5 6 7 0 0 44,200 3O,OOO 40,000 _ 40,000

(ft)

2.o o.98 1.2 0.91 o.91 0.32 0.91

H (-)

-0.105 -0.09 -0.426 -o.o654 -o.o962 --0.27 --0.09 _e 0.0201 O. 0267 o.oo287 0.0212 o. 0578 o. o356 o.o153 YSa o.o116 0.00814 0.00613 o.oo356 0.0382 o.o229 Y * 0.0131 _r LO O_ -11.08 -i i. 163 -8.394 -23.14 --7.575 -16.875 L_ -5.828 -0.63 -0.524 -I. 424 -0.381 -0.736 -i. 238 -0.469 !

o.214 o. 278 O. 251 0.212 0.221 0.724 o. 6o3 Lr !

-0.953 -3.965 -7.538 -11.194 --5.597 --3.516 -13.19 L5 a !

0.748 0.789 LSr 0.395 2.108 1.71 0.608 1.313 1.946 I_ I 1 8 5 8 13.71 3.818 1.895 2.317 3.202 -0.02 N_ --0.0141 -0.0631 --0.I05 -O.OO473 -O.0388 --O.0293 -o.159 N_ -0.222 -0.76 -0.459 -0.198 --0.231 -0.198 -0.909 N{a 0.157 -4.021 -2.865 -1.413 --2.29 -2.654 f -1.o69 NSr -0.669 --3.986 -2.589 -0.884 -1.614 -0.932 TABLE IX-D AILERON IATERAL TRANSFER FUNCTION FACTORS FOR THE B-58 Note: Data are for body-fixed stability axes, cruise configuration FLI(_IT CONDITION i 2 3 4 9 6 7 h (ft) 0 o 0 40,00O 44,200 30,000 40,000 M (-) 0.32 0.91 O.91 0.91 2.0 0.98 1.2 0.00426 0.0334 0.026 0.0134 0.029 0.017 I/Ts 0.o58 0.802 0.889 0.687 0.698 1.927 1.75 0.556 I/TR o.144 0.044 0.0O86 o.oi 65 0.0772 0.0296 0.009 _a 2.126 I .42 I.40 I.81 i.403 I-98 3.796 _d -3.516 -13.19 --11.194 -9.597 -3.965 -7.938 -o.953 Ap 0 0 0 0

I/Tp 1

Np 5a 0. I04 0.132 O.0784 0.085 0.096 0.192 _p 2.398 5.89 1.274 3.151 I •786 2.217 -I.413 -2. 654 Ar 0.197 -4.021 -2.865 --0.909 -2.29 r 1/T R -1.148 1.881 1.498 1.002 0.983 1.082 0.934 N5 a (r 0.678 --0.213 --0.249 -0.420 --0.174 -O.331 -0.295 1.677 1.o21 0.897 0.845 o.481 0.797 0.602 0.0212 0.00287 0.0267 O. 0202 0.0978 0.0356 o.o193 I/T81 (_8) 0.1624 -0.0838 -O.0941 -O.191 -O.018_ -0.073 --O.0171 _a I/T#2 (_B) 2.1616 1.198 0.798 0.226 0.695 0.467 0.920 I/T#3 -9.008 70.64 81.472 60.03 493.37 86.19 131.87

7.994 98.73 36.17 13.46 9.99 26.063 23.42

0.12 -0.210 -0.183 0.15 -0.02 -O.161 -0.036 1/Tay 1 (_ay2) I.OO9 0.69 I .839 O.35 o.948 0.993 0.458 i/T_2 (_2) CG (-2.255) (-2.8) (-6.618) -o.892 (-3._) (-3.3) --0.127 _ay3 ( I/TaY3) (3.097) (6.883) 1.733 0.89 (2.927) (4.896) (4.7_) a_y 3 ( I/Tay 4 ) TR-176-1 97 TABLE IX-E RUDDER lATERAL TRANSFER FUNCTION FACTORS FOR _{E B-58 Note: Data for body-fixed stability axes, cruise configuration FLIGHT CONDITION I 2 3 4 5 6 7 0 0 40,000 44,200 30,000 40,000 h (ft) 0 1.2 _.o o.98 0.32 M (-) O.91 O.91 O.91 0.058 0.00426 0.0334 0.026 o.o134 0.09 o.o17 I/Ts 0.556 0.8O2 0.885 0.687 0.698 1.527 1.79 A I/TR 0.044 0.0086 o.144 o.o_96 0.009 O.0772 O.0165 _d 2.126 I .42 1.81 I.hO3 3.796 1.40 1.58 2.108 O. 789 0.608 I.313 o.748 0.399 I .711 O 0 0 I/TPl 0 0 0 0 -3.247 -3.433 -3.319 I/Tp2 --2.969 --4.554 -5.859 --2.959 3.181 3.329 3.204 I/Tp3 2.713 4.065 9.365 2.818 -0.884 -1.614 -0.932 A r -O. 669 -3.986 -2.589 -I • 069 0.88 o.9oi I.o r I/Tr 0.964 I.607 I .615 0.786 N5 r -0.1o -0.2_26 -o.255 _r -0.326 0.167 -0.O561 -0.317 0.362 0.553 o.518 _r 0.665 0.436 0.636 0.534 0.00355 0.O116 0.00613 % O.0131 O.0382 0.0229 O.00814 -0 .o0171 -0.0043 -0 .O0445 I/T01 -0.0149 -0.00689 -0.00709 -0.008 N_ r 0.793 0.693 o.574 I/T_2 0.946 I.482 I .337 0.431 152.06 I/T_3 ' 51.355 150.05 113.43 131.44 248.84 139-37 11.303 7.126 Aay 4.669 38.813 23.266 7.173 6.886 -0.0135 -0.0131 I/Ts.j1 (_aY2) -0.0966 -0.O122 -O.O167 -0.0229 -0.0032 ........................

0.649 0.537 I/Troy 2 (a_y2) 0.446 1.46 1.243 0.394 0.748 (--3.394) (--3.14) _ay3 (I/TaY3) (--1.486) (-9.179) (-4.926) (--2.492) (-4.597) CG (3.62) (3.338) (I.828) (5-915) (5-398) (2.662) (4.788) °_y 3 (1/T&y 4) TR-176-1 98 flFDTION X NAVION Figure X-I

NAVION

I NOMINAL FLIGHT CONDITION oh I h(ft) = 0 ; M = .158 ; VTo = 176 ft/sec W = 2750 Ibs CG at 29.5 % MAC T x = 1048 slug ft 2 Ty = 3000 slug ft 2 T z = 3530 slug ft z Ixz = 0 REFERENCE GEOMETRY S = 184 ft z c = 5.7 ft b = 33.4 ft TABLE X-A TABLE X-B TABLE X-C GEOMETRICAL PARAMETERS LQN,GIT_INAL NONDIMEN_IONAL lATERAL NONDIMENSIONAL STABILITY DERIVATIVES FOR THE NAVION DERIVATIVES FOR THE NAVION FOR THE NAVION Note: Data for body-fixed stability axes, level flight Note: Data are for stability Data are for axes stability axes S (ft 2) _8o FLIGHT FLIGHT 33.4

b (ft)

CONDITION CONDITION

c (ft) 5.7

1 I

w (ib)

2,750 0 h (ft) h (ft) 0 m (slugs) 85.4 M (--) 0.198 M (-) o. 158

e.g. (_ MAC)

29.5 C L 0.41 VTo (ft/sec) 176

( sl_-_ 2)

I ,o48 C D O. 05 c_ o (deg) 3,000

(-_lug-_ 2)

CL= 4.44 Cy6 -0.564

Tz (sl_-_ 2) 3,930

CL& 0 CYSa 0

_z

CLM 0 CYSr O. 197 h (ft) CLSe 0._5 C_ -o .o74 M O. 158 CDc_ 0.330 C_p -0.410 a (ft/see) 1117 CDM O C_r O. 1o7 P (slugs/ft 3) 0.002378 CDSe O C$5 a O. 1342

VTo (ft/see)

C_5 r O. 0118 ib/ft 2) 36.8

-4=VTo2/2 (

- .36

Cn_ o.o7oI 0.6 cL o (deg)

M o

Cr_ -o.o575 7o (deg) -9.96 Cnr -0.125 Cmq Cn5 a -0.00346 Cn5 r -0.0717 TR-176-1 i01 TABLE X-E TABLE X-D LATERAL DIMENSIONAL DERIVATIVES LONGITUDINAL DIMENSIONAL FOR THE NAVION DERIVATIVES FOR TI-IEN&VION FLT. COND.

FLT. COND.

Xw O.03607 -0. 2543 Yv Xu -0.O45] YSa y* XSe 0 5r Zw --2.0244 r,f;.

--8.402 Zu -0.3 697 2.193 Zse -28.17 M w --<). 04997 28.984 Lsi 2.548 M_ --O.005 ]65 L_ r 4. 495 Mq --2.0767 M_ 0 -O. 3498 -0.7605

MSe --II. 1892 g

-O.2218 N ' 5a -4.597 TR-176-1 102 T I ' AB _E X-[ _' TAB[,E X-G TAB],E X-H E ] _VA TO I_ 1,0 t'q t_I TUD IN A ]iJ RUDDER libTEI{AI, T]{ANS],']:]I { AILERON LAI _'h",[lA.l_,'_{ANSFER j [ r TRANSI,'I,:]_ ]_ NC2ION FUNCTION FACTORS FUNCTION FACTORS U1ACTORS ]!'OR ']'H_J NAVION L;'OR THE NAVION FOB TLI]!] NAVION FLT. (]ON]). FLT. COND. VLT. COND.

o. 008'( 6

1/% o.oo87(; 1/T S

< sp o. dgP'{ 8.435

"'sp 3. (;083 I/TR 8. h3b 1/T R

A A A 0.204 <p O. 0801 _d o. 204 2.385 ._ 2.385 ._ O.2137 m d 2.548 A o --II .0114

%

Ap 28.984 N 0 I/THI O.0'.)231 11Tpl N_.P,r N_a 1/Tpl 0 -6.991 1/T_b 1.9164 1/Tp2 _p o. P33 6 3. 6064 A u --1.0161 IITp 3 c%o 2.136 u -4. 997 A r Nb e I/Tul 2.401 A r _. 2218 8. 639 I/T r I/Tu2 -280.39 F r ]/Tr 1 --1. 253 N_', r 0.1335 Aw --;'8. 171

<r

N_) a I/Tr2 1.543

1/% (1.98h O. 5345

N w _e I/mr 3 54.071 rw O. 086u 0.0707 Af{ A_ 0.2218 -0.0366 _% o. 25 63 1/Tpl N_B a 1/T_ 1 0.2285 8.795 Ah 28. 171

I/%_

I/T_2 77.78 65.352 1/Thl --I0. I08

fl

1/T[_ 3 N_ e 12.489 1/Th2 O. 01 65

A_

-o.o591 I/Th3 13. 122 1/Tay 1 8.335 Aaz --28.171 1/Tay 2 a Z --3.0074 CG NB e I/Tazl 0

1/% 3

3.894 I/Taz2 --10.108 I/Tay 4 #x:0 I/Taz3 0.0165 CG i/Taz4 13.122 TR-176-1 103 p_EcED_NGPAGE BLANK NOT FILMED, 8F_TION XI DC-8

Preceding page blank

_o5 P-3 I Figure XI-] I

DC-8

FLIGRT CONDITIONS Cruise Approach Holdh_g VNE Flight Condition :55,000 3:5,000 h(ft) 15,000 0.88 0.219 0.443 0.84 W(Ibs) 190,000 190,000 250,000 250,000 3.09 x I0 s 3.11xlO e 3.77x IO s 3.77x 10 6 [x (slug-ft 2) 3.56x106 3.56x10 s 2.94x10 s 2.94x106 Iy (slug-ft z) Axes t Stability Iz (slug "ftz) 5.58 x I0 s 5.88x106 7.13 x IO s 7.13 x 106 Ixz (slug-ft = ) 28x10 z -64.5x10 s 45x105 53.7 x I03 Xce IE 0.15 0.15 0.15 0.15 REFERENCE GEOMETRY S = 2600 ft 2 b = 142.3 ft c = 23 ft REFERENCES : Unpublished Dota

/9

TABLE XI-A GEOMETRICAL AND INERTIAL PARAMETERS FOR THE DC-8 Note : Data are for body-fixed stability axes S = 2600 ft 2 , b = 142.3 ft , c = 23 ft , Yo = 0 deg FLIGHT CONDITION ] • ,j 3 CRUISE APPROACH HOLD ING VNE

h (ft)

15,000 33,000 33,000 0.84 0.88 0.218 0.443

M (-)

1o58 982 982 a (ft/sec) 1117

o (s1_gs/ft 3) o. 002378 0.001496 0.000795 o. 000795

824.2 468.2 243.5 863.46

VTo (ft/seo)

71.02 163.97 270.0 296.36 = oV2/2 (ib/ft 2)

w (Zb) 230,000 230,000

190,000 190,000 7t43 7143 m (slugs) 59oo 5900 Ix (slug-ft 2) 3,090,000 3,110,000 3,770,000 3,770,000 3,560,000 3,560,000 2,940,000 2,91,0,000 ly (slug-ft 2) I z (slug-ft 2) 5,580,000 5,880,000 7,130,000 %,130,000 Ixz (slug-ft 2) 28,000 -64,5 O0 45,000 53,700 XCG/C o.15 o.15 0.15 o.15 (deg) o o o 0 @O 243.5 468.2 824.2 (ft/sec) 863.46 U o 0 0 0 0 (ft/sec) Wo 0 0 0 (deg) 35 _F TR-176-I 107

TABLE XI-B

LONGITUDINAL NONDIMENSIONAL DERIVATIVES FORTHEDC-8

Note: Data are for body-fixed stability axes.

FLIGHT CONDITION

h

0 33_ 000 33,000

15,000

M 0.21$ 0.443 0.840 0.S8

0.42 0.308 0.279 CL 0.98 0.0224 0.0188 0.0276 CD O. 1095 6.7442 6.8989 4.8762 c:4 _ 4.81 0 0 CLg 0 0.048 0 -1.2 0.02

CL M

o. 352 o. 358 O. 328 0.328 CL_ e 0.4862 0.212 0.487 0.2719 CD_ 0.00208 O. 0202 o. lOO5 o. 3(;'.) 3 CD M -0.97] 2 CD6e -2.413 -2 .ol 7 --1.478 -1.5013 Cm_ --6.62 --4.10 -6.83 -3.84 Cm_ -o. 006 -0.17 -0.02 -0.50 Cm m -14.6 -_5.2 -o.ool 17 --o .97t 2 Cmq TABLE XI-C LATERAL NONDIMENSIONAL STABILITY DERIVATIVES FOR THE DC-8 Note: Data are for body-fixed stability axes FLIGHT CONDITION 33,000 33,000

h (ft) 1D,O00

o.218 0.84 0.88 0.443

M (-)

468.2 824.2 863.46 243.5 VTo (ft/sec) -0.7449 -0.87268 -O. 6532 -O.7277 0 O CY_ a o.18651 O. 18651 o.18651 CY_r 0.18651 -0.16732 -0.17362 -0.137D2 C_p -O.15815 -o.4]6 -O.516 -o .538 C_p --O.385 0.146 0.132 0.147 C_r 0.248 -0.o83o8 -0.07965 -0 .o79o7 C_6 a -0.08595 0.021086 0.02166 o.o]9195 C_$ r 0.02189 O. 1 6044 O. 15471 0.12319 cR_ o. 1633 -0.0307 -0.0107 -0.00587 Cnp -0.0873 -0.161 -0.190 -0.199 Cnr -O.196 -0.00354 -0.003701 -0.003999 Cn6 a -O.O106 -0.08337 -0.O8337 -O.O8337 Cn_ r -0.08337 TR-176-1 109 TABLE XI-D LONGITUDINAL DIMENSIONAL DERIVATIVES FOR THE DC-$ Note: Data are for body-fixed stability axes FLIGHT CONDITION

h (ft)

19,000 33,000 33,000 0.218 o.84

M (-) o.443 o .88

-o. 000084(5

% (i/seo) -0. 000595 O. 000D99 o. 000733

-0.o2891 -o.o145 -o. oo7o7 -0.0471 -o. Ol Ii -o. oo714 -0.04 63 -o.o291 o.o629 0.0321 0.0043

xw (I/sec) -o. oP59

0 0 o 0

x6 e [(ft/sec2)/rad]

0 0622 -o. 25 o6 -0.1 329 -0.0735 ZU .... (]/sec) -0. ,_)06 0 0622 Zu (I/sec) -o.1329 -0.073[3 0 0 0 0

(-)

-o .806 Zw ( I/sec) -0.6277 -0.75g -o .845 [(ft/sec2)/rad] -34.6 -38.6 -lO.19 -23.'7 Z6 e -o. 000063 -0. 000786 -o. 0000077 -o. oo254

Iv]u .... (I/sec-ft)

-0. o00003 -o. ooo 78 6

% (i/_oo-ft) -0.0000077 -0. 00254

-0. O01 u(_ -o .o0o51

M@ (I/ft) -o. 00072 -0. 00052

-0.0111 -o. 0o8 7 -o. o107

£w (I/sec-ft) ---0.01 39

-0.7924 -0.924 -I. 008 -o. 991

14q(I/see)

-3.24 -4.59

M8e (I/see 2)

TT- 1 {'1 7.'-1 1 10 TABLE XI-E IATEI_&L DIMK_SIONAL DERIVATIVES FOR THE DC-8 Note: Data are for body-fixed stability axes FLIGHT CONDITION 2 3 1 • 33,000 33,000

h (ft) 15,000

0.84 0.88 0.218 0.443

M (-)

-0.0868 -0.1113 -0.1008 -0. o931

Yv (I/see)

o 0 0 0 YS_ [(11sec)Irad] o. 0288 0.0222 0.0233 o. 0238 YS_ [(11sec)Irad] -4.41 -i. 328 -5.02 -2.71 L_ (1/see 2) -i. 181 -I. 232 -I. 29 -o. 951

½ (l/sec)

0.346 O. 334 O. 397 O. 609 L_ (I/see) -1.62 -2.11 -2.3 -0. 726 L5 A (I/sec 2) o.612 0.1813 0.549 o. 392 L6# (I/sec 2) 2.14 2.43 I .301 0.757 N# (1/see 2) -0.0204 -0. 124 -0. o346 -0.01715

N5 (l/_eo)

-0.228 --o. 25 -0.257

-o. 26>

N_ (I/sec) O -0.065 2 -0.0788 -0.01875 -o. 0532

N_ (i/_ee _)

-0.o1164 -o.864 -1. 277 -0. 389

N_ (1/_ec2)

TR-176-I 111 TABLE XI-F ELEVATOR LONGITUDINAL TRANSFER FUNCTION FACTORS FOR _}IE DC-8 Note : Data are for body-fixed stability axes FLIGHT CONDITION 2 4 0.8h 0.218 0.443 0.88 Mach No., M (-) Altitude, h (ft) 15,O00 33,000 33,000 15 15 15 15 Weight W (ib) 190, OO0 230,000 190,000 2.50,000 O .434 o. 342 0.325 0.522 _sp 3.59 2.40 1.619 msp ZSlong 0.O606 o. 241 o.o31o (--0.0708) (I/Tpl) O. 0243 O.1635 O. 0877 (o.zo8)

% (I/Tp2)

--l. 358 -3.22 A0 -4 .>7 -5. I o. o6o5 0.01 354 O. 01436 I/TOl O. 0493 N 8 _e o.535 O. 075 O. 7,9',; o. 76 l/T82 --0.641 --O. 1489 I . O0 A m u I .08 o.816 I.279 o .449 l/Tu l N8 e -35.3 -72.7 -#{79 1/Tu2 279 -,'3.7 -34. G -38.6 A W -/o.19 33.0 110.2 -o. o361, G5. o I/Tw 1 w < ,% (I/%2) o.o781 o .o37 O. 13{3, (O.U3_7) N5 e o.1798 o. 0947 O.ODl l

ov (I/%3)

(1 15.5 ) 34. d 38.6 10.19 25.7 A_ -8.24 -8.63 -3.75 -5.95 1/T]4_ 1 -0. O0002G --0. 00182 0.O107 o.o_31

1/m 2

_ .83 7.29 9.P9 i oo .9 1/__ 3 -3_4.4 Aaz -I0.19 -23.7 O o 1/Taz I O 0 -8.24 I/maz2 -3.75 -5.95 0.010'7' o.o531 1/Taz 3 -O. O0182 --0. 000026 CG 9.59 1oo.9 1/maz4 4.83 7.29 TR-176-1 112 TABLE XI-G AILERON LATERAL TR_,iSFER FUNCTION FACTORS FOR 'I_{EDC-8 Note : Data are for body-fixed stability axes FLIGHT CONDITION o.84 0.88 0.218 0.443 Mach No., (-) 33,000 Altitude, h (ft) I5,000 33,000 CG (_ _) 15 15 15 15 190,000 230,000 230,000 Weight, W (ib) 190,000 O. 00404 -0.013 O. 00649 O. 00447 1/T s 1.121 I .329 1 .254 I .356 1/T R Alat O. 1061 o. Io96 O. 0793 O. O855

{a

o .996 1.197 1.495 I.589 _d -1 .62 --2.11 -2.3o -0.725

Ap

0 0 0 1/Tpl N p 0.223 o. 1554 O. 1094 O. 1072

(p

$a 1.620 I .166 0.943 1.515 -1.52 --2.11 -2.3o -0.726 A_ O. 223 o. 1o94 o. 1554 o. 1072 1.620 t .166 0.943 i .515 -0.0532 -o.o1875 -o. 065 2 -o. 0788 A r I.644 O. 998 1.589 I. 757 1/Trl r -0.392 -O. 345

(r -O. 656 -o. 727

N5 a I .242 2.23 I.323 I .259 _r O. 01875 o. 0652 O. 0532 -0. 0788 -1.036 -2.75 -0. 704

1/T 1

0.404 0.203 0.291

1/T72

1/TB3

TR-175-I 113 TABLE XI-H RUDDER LATERAL TRANSFER FUNCTION FACTORS FOR THE DC-8 Note : Data are for body-fixed stability axes.

FLIGHT CONDITION 0.84 0.88 0.218 0.443 Mach No., M (-) 0 33,000 33,000 15,000 Altitude, h (ft) 15 15

(¢ 15

230,000 190,000 230,000 190,000 Weight, W (lb) o. 00404 O. 00447 -o.o13 0.00649 I/ms i.254 1 .356 I .121 1.329 I/T R Alat 0.1061 O. 0855 o. 0793 o.Io96 [d I .495 1 .D89 o.996 1.197 COd 0.612 0.545 0.1813 0.392 Ap o 0 I/Tpl 2.43 1. 028 i.85 2.57 NP r I/Tp2 -3.oi -5.15 -2.13 -2.56

I/T> 3

0,612 o.545 o.1813 0.392 A_ 2.43 2.57 1.o28 I.85 q) I I/Tqpl N_r -3.oi -3.15 -2.13 -2.56 I/Tep2 I --0.864 --1 . 1 65 -1.277 -o. 389 A r I.276 1.377 I .124 1.335 I/Tr I r --0.0619 -0.0475 -o. 0743 -O.O451 _r N5 r o. 323 0.323 0.330 o. 339 _r o. 0288 0.0222 0.0233 0.0238 -0.00637 -o, o14 7) --0.00726 -O.O559 1/mpl P 1.323 1,141 1.217 1.297

1/T 2

N6 r f r 3o .2 52.6 pp. 0 16.47 1/Tp3 20. I 13.hS 18.33 5.79 Aay -0 .ot883 -o .Ol 7146 -O. 0347 -O.819 1/may 1 1 .122 I .231 i .535 -4).I 077 I/may 2 --1 .418 -1.494 --1.157 ( O. 994 ) 1/may 3 ( _ay) 1 ,723 I .819 i.147 (1.078)

l/may

Cd TR-176-1 114

APPENDIX A AXIS SYSTEm, SYMBOLS, AND DERIVATIVE DEFINITIONS I. .a_:T.8 IB_r_TEI_B _XB,U,P f v, --_/_ ............ "_, _--Inerticll Ref.

YB,Ys,v,q

ZB,W,r g XB, YB, ZB - The Body-Axis System consists of right-handed, orthogonal axes whose origin is fixed at the nominal aircraft center of gravity. It's orientation remains fixed with respect to the aircraft, the XB and ZB axes being in the plane of symmetry. The exact alignment of XB axis is arbitrary, herein it is taken along the body centerline reference.

XS, YS, ZS - The Stability-Axis System is that particular body-axis system for which the Xs_axis is coincident with the projection of the total steady-state velocity vector (VTo) on the aircraft's plane of symmetry. It's orientation remains fixed with respect to the aircraft.

A-I 2. SYMBOLS ft/sec a Speed of sound in air ft/sec 2 Lateral acceleration along the Y-Body Axis at the center of gravity (positive out right wing) !

ft/sec 2 Lateral acceleration parallel to the ay Y-Body Axis at a distance i x and i z from the

c.g., _ = _ + ix_-iz_

ft/sec 2 Normal acceleration along the Z-Body Axis az at the c.g. (positive down) I ft/sec 2 Normal acceleration parallel to the Z-Body a z Axis at a distance i x from the , = a z - lx_ c.g._ a z ft b Reference wing span ft C Reference chord CG Center of gravity lbs D Aerodynamic force (drag) along the total velocity vector (positive aft) ft/sec 2 Acceleration due to gravity g ft Altitude h slug-ft 2 Moments of inertia referred to body axis

Ix, ly, Iz

slug-ft 2 Product of inertia referred to body axis Ixz rad/sec The imaginary portion of the complex jcD variable s = _±j_ ft Distance along the X-Body Axis from the ix c.g. (positive forward) ft Distance along the Z-BodyAxis from the Iz c.g. (positive down) ft-lb L Rolling moment about the X-axis due to aerodynamic torques (positive right wing _own) A-2

L ibs

Aerodynamic force (lift) perpendicular to the total velocity vector in the aircraft's plane of symmetry (positive up) m Mass slugs M Mach number M ft- ib Pitching moment about the Y-axis due to aerodynamic torques (positive nose up) MAC ft Mean aerodynamic chord MGC ft Mean geometric chord N ibs Aerodynamic normal force along the Z-Body Axis bu___t positive up N ft-lbs Yawing moment about Z-axis due to aerodynamic torques (positive nose right) rad/sec P Roll rate, angular velocity about X-axis (positive right wing down) rad/sec q Pitch rate_ angular velocity about Y-axis (positive nose up) ibs/ft 2 Dynamic pressure, ]/2 p VTo r Yaw rate_ angular velocity about Z-axis rad/sec (positive nose right) Yaw rate gyro signal rad/sec rRG s Laplace operator, _+ jw rad/sec S ft 2 Reference wing area T.E.

Trailing edge u Linear perturbed velocity along the ft/sec X-axis (positive forward) U o Linear steady-state velocity along the ft/sec X-axis (positive forward) v ft/sec Linear perturbed velocity along the Y-axis (positive out right wing) ft/sec Total linear steady-state velocity VT o (positive forward) A-3 w ft/sec Linear perturbed velocity along the Z_-axis (positive do_m) W lbs Weight ;l't/sec Wo Linear steady-st_/Le velocity alonf{ the Z-axis (positive dovm) X ibs AeroCy_;lamic force along t!_c X-axis (positive forward) Y _]0s Aerody_lamic force along Y-axis (positive out right wing) ft Perpendicular distance from c.g. to thrust zj line (positive for nose up pitching moment due to thrust) ibs Z Aerodynamic force along Z-axis (positive down) rad Pert_irbed angle of attack (leg Steady-state (trim) angle of attack _o rad Sideslip angle deg Steady-state flight path angle 7o tad Aileron control surface deflection, 8a (includes spoiler effects, etc.), (positive for positive rolling moment) rad Elevator surface deflection from trim_ _e (positive for nose down pitching moment for aft surface) Trim elevator deflection deg F rad Rudder deflection Ipositive for nose left yawing moment (negative N)] A Denominator of airframe transfer function Damping ratio of linear second order mode particularized by the subscript e Pitch angle, fq dt for straight and rad level flight, positive nose up A-4 IncJ.ination of thrust line with X-axis deg _o [positive gives negative (--) Z force]

slugs/ft 3

Mass density of air rad/sec The real portion of the complex variable s = _± j_ rad Roll angle, (cos @o _P dt -sin e o _r dt) in straight and level flight, (positive right wing down) rad/sec Undamped natural frequency of a second order mode, particularized by subscript Special Subscript Aileron a d Dutch roll Elevator e Phugoid P r Rudder Roll subsidence R s Spiral Short period sp A-5 3, NONDIMENSIONAL DERIVATIVE DEFINITIONS a) Longitudinal Body Axis N C N = _-_ , positive up X CX = _ S ' positive aft IV[ CM -

c_ : _CN/_

Sc 2VT o

CN_ - c bc_/_

c

CNs : _c_/_s

2VT o

cxa : 8Cx/_ - _cM/_q

CMq c

CxM : _Cx/_M

cxs = 8cx/_s

b) Longitudinal Stability Axis L C L - _ positive up qS' D CD - _ positive aft qS' Ci_ = _CL/_ 2VT o Pitching moment CI_ - C _Cn/_ derivatives are

CLM = _CL/_M

identical to

Cr_ : _C_/_

CDc : _CD/a_ those for body axis

CI_ : _CD/_M

CD 5 = _CD/_5

A-6

c) Lateral Body and Stability Axis

Thoughphysically and numerically different_* see Appendix B, the

samesymbols are used for body axis and stability axis lateral rolling

and yawing momentderivatives. The sideforce derivatives (Cy, etc.) are

physically and numerically the same in both axis systems. Whenthe

rolling or yawing momentderivatives are given in this report the axis

system is specified. Whenusing the following all quantities should be

for the sameaxis system.

Y L N

Cy -

Cl - _Sb Cn - {Sb _s Cy_ = _Cy/_ CI_ = _CI/_ Cn_ = _Cn/_ _

2v ° _ 2v °

Cy_ = _Cy/_ CIp - b Cnp b 2VTo _Cl/_r 2VTo _c_/_r Clr - b Cnr - b Cl8 = _Cx/_ cn_ = 8Cn/8_ *The exception is the zero trim angle of attack condition.

A-7 4. DIMENSIONAL STABILITY DERIVATIVE DEFINITIONS The same symbols are used for body- and stability-axis dimensional derivatives. Care should be exercised so that a consistent set of quantities are used.

a) Longitudinal Body Axis X{_ = Xu + mu cos_o I/sec X u - - _ CXM - CX + _ CX_ I/sec pSUo ( M Wo ) m 2U o ' ]/sec I Wo M Xw _ 0SU2mO - CX_ - 2 U_o (Cx _ -2 CXM) oSVT2o ft o X_e = _ CX_ e sec'-rad I/sec Z_ - Su - Tu s:i.n[ o ] / S (-:_ C OSUo M _ CN + CN _ Zu - m - _ CNM ]/sec

p uo[ wo I M )]

Zw - 2m -CNc_ - _ _oo C N 4. _ CNM p2_ U o Z_ : - 4m VTo CN& 0SV_ o ft rb CN6 e ZSe = - _n see' r:Ad Zjm sec-ft k-8 Nil - OScU° I_ sec-ft + Cm - 2U----o 21y Cram sec-ft

I 1

- 2Iy Cmo_ + _ (Cm + _ CraM) pSc2 Uo = C_ sec-ft

_ _zy V_o

]/sec 2 I_ : UoM w ]/sec = UoM_ pS C2VTo ]/sec Mq - 41y Cmq oS CV2o I/sec 2 M6e - 21y Cm_e ]/sec b) Lateral Body Axis ]/sec Yv : (oSVTo/2m)Cy _ ft/sec 2 Y_ = VToY v ft/sec 2

Y_ : (pSV_omm)%5

ft/sec 2

Ys_ : (0SV_o/2m)% %

I/sec Y6_ : (pSVTo/2m)dy6r ]/sec 2

_B : (_SV_ob/2_x)C_ _

]/sec

= (pSVTob2/4Z_)Clp

]/sec Lr = (oSVTob2/41x)Clr A-9 I/sec 2

_5_ = (oSV_ob/21_)Clb

I/sec 2

_r = (oSV$ob/21xlCl_r

l/sec

Y_a = (oSV_o/2m)CYS_

I/sec 2

_ = (oSV$ob/2I_IC_ _

I/sec

Np = (oSV_ob2/_I z)c_.P

I/sec N r = (oSVTob2/41z)Cn r l/sec 2

N_ -- (pSV$ob/2Zz)C_ _

F] I/sec 2

N_ = (_SV_ob/21_)c_ _

I/sec 2 I/sec ]/see /sec 2 Lt_ r = (L_ r + IxzNSr/Ix)G ]/sec 2 ],t_ : (L_ a + lxzNSa/Ix)@ ]/sec 2 N' : (N@ + IxzL_/Iz)G I/see N_ : (N r + IxzLr/Iz)G ]/sec ]/sec 2 _!_' ( _ IxzLSr/Iz) G " r : N_r ]/sec 2

_q : (_ + I_z_/z_)_

G - I Ixlz A-tO I --4 ©_ I ./_ Xe, Uo CN U o = VToCOS a o Wo = VToSln _o

J

Cx _a_o_ Ys--- Ye Zs,Wo Zs I ON = C L cos ao+ C D sin _o (C_)B : C16 cos _o" C_ sin a b C X = C D cos _o- CL sin Go CIp cos£ao - (Clr+ Cnp)Sln ae c_ _o+ Cnr sin2ao (c_;) B = CN_ = CL_c°s _o-CLsln ao + CD_Sln ao+ CD cos ao (Clr) B = C1 r ces!_e - (C_ r -Clp)sin _e cos &o" Cn F sin2_o CN& = CL_ cos _o (c_)_ = C16 cos a o- Cn_ sin a e CNM = CLM cos Go + CDM sin _o (end) B = Cn_ cos ao+ CI_ sin a e CN8 = Ci6 cos Go+ CD5 sin _o Cnp cos2_o - (Cn r-clp)sin _e cos &o'CI r sinlAe (c_)B = CX_ = CD_ cos _o'CD sin o_-CL_ sin _o-CL cos _o (Cnr) B = Cnr coS2ao + (Clr+ C_p)sin o_ cos _o + Cip sin_%e CXM = CDM cos _o- CL M sin <_o (c_)_ = Cn6 cos ao+ CI_ sin a e CX 8 = CD5 cos _o- C_ sin _o Cm, Cm_ , Cm_ , Cmq , Cram , Cm_ -t_NCHANGED Cy_, CYSr , CYsa - t_CHANDEP

] .L y APPENDIX C EQUATIONS OF MOTION, TRANSFER FUNCTIONS, AND COUPLING NUmeRATORS I • Longitudinal a. E quat i on s -X w Wos+g cos ej s-X_ u XSe

-4

(1-Z_)s-Z w -Uos+g sin 8 0 w = Z6e @ M6 e --(M_s * Mw) s2- MqS - q. = -se }_ = --w cos @o + u sin e o + (U o cos e o + w o sin eo)e a z = sw- Uoq + (g sin eo)e ' ixS2@ a z -- a z b. Transfer Functions @ N_e 5 e A I) Denominator, A = As 4 + Bs 3 + Cs 2 + Ds + E

A --

B = --(Mq + Xu)(I -- Z_) - Z w - Mc_ c = MqZ w- Mc_ + Xu[(Mq)(1 -- Z_) + Z w + M_] -- XW_ + WO[M_Z u + _(I -- Z_)] + g_ sin @ O C-I t

D -- -x_(Mz_ -_.h) -M_y= +MqK_z_ +g[%z_+M_(I -z,_oos 0 o+Wo(ti>_ -t_Iz_)

+ g(%-%x_)_inOo

E -- g(MwZ _ - M_Z_)oos eo+ g(M_IXw - %X_)_i_ Oo

5 _umerator s

2)

N_ = Aes 2 + Bes + C e

A o -- z_ + M_(1 - z_)

B 8 = XS[M_Z_+ Mu(1 - Z_.)]+ Zs(Mw-I%X _) -MS[Zw+ XI_(I - ZQ)]

% -"x8(_vz_i-M_z w) + z_, (M_x_-_)+ _,%( zj,_- x_, u)

N_ = Aus 3 + Bu s2 + CuS + Du A u = X5(I - Z.)

w B u = -XS[Mq(I - ZQ) + Zw + M_] + ZsX w - Wo[ZsM _ + _o(I - ZQ)]

Cu--x_(M_z.-vh)- z_(g% oos 0o+ Mqx_) + _%[_- (_ oo_eo)(1-z,)]

+ Wo(ZwM_-_) + _x_% _i._o

Du : g(ZwM5 - MwZs)c°s 00 + g(XsMw - Ms_psin _o N_ = Aw s3 + Bw s2 + CwS + D w Aw= Z 6

Bw = -%(Mq+ x_)+ Uo_ + x_z_

Cw = X_(ZsM q - UoMs) + Wo(ZsM u - MsZ _) - gM 5 sin 00 + Xg(M_Uo - Z_Mq) D w " g(ZJ_ - %Z_)cos 0 o + gMsX* sin 0 o- XsMug sin 0 o C-2 N_ = A_s 3 + B6s 2 + C_s + D_ A_ = - cos eoA w + sin 0oAu = - COS @OBW + sin @OBU + (U O cos e O + W O sin 0o)A @ O_ = - cos @OOw + sin eoC u + (U O cos @o + No sin 0o)B @ D_ = - cos @oDw + sin eoD u + (U O cos e O + W O sin eo)C @ .t

_f'= _a[? +B_'zS3 +c4_ _+_ab+E '

&z Ba_ = B w - ixB e - UoA 0 Ca_ = Cw - ixC e - UoB 0 + g sin @oAe Da_ = D w - UoC e + g sin 0oB e Ea_ : + g sin 0oC 8 To obtain az, let ix = O.

2. Lateral a. Equations Wos + g cos 0 o Uos-g sin 8o] E- s- Yv - Y5 a Y5 r

- _o _

VT o

IF

!

! !

--L r = --I_ S(S--%) L5 a L5 r !

-._ -._ iNsa , N5 r

s-N r _ v : VTo _ sv + Uor --WoP- g(cos 8o)C_ !

: _p_ + _r tan DO ay + iXlat sr -- izS p S S ] r COS 8 0 S c-3 b. Transfer Functions ___= N_a r N_r etc.

_a Alat ; _r - Alat 4 2 I) Denominator, Ala t = as + bs 3 + cs + ds + e a = I !

b = -(y_ + L_+ Nr)

U o WoL _

o ---- N_ + L_(Y_ + _) - N_L_+ Y_

VT o VT o U o

d _ --(_- _) + Yv(_9_r- _) _ (_ cos 0 ° + N_ sin O o)

VT o VT o Wo VT o e = -_g [(I%N_- N_I$) cos e o- (N_- L_) sin 0o] VT o 2) 8 (5 a or 5r) Numerators = _s 3 + _s 2 + c_s + D_

A_ : Y_

---Y_[_" + N_]- N___Uo +__w° L_'

B_

VT o VT o , U o

Y_ (_'_- _r) + L_--g co_ _o+ (%_ - %_)

c_ -- VT o VT o Wo , , , , , g + -- (NgL r -- LgNr) + N_ V_ T sin 0 o VTo o D6 = -_g (N_L r -- L_Nr) cos 0 o + -_g (N_I,_ -- N_I_) sin 0o VT o VT o c-4 [__ • • N_5 = Ap s3 + Bp s2 + Cps + Dp !

Ap = L 5 = LS(Nr + Yv) + NSLr - , , , , . , , , , UO Cp = Y_(LrN _ -- L_N'r) + L_YvN' r -- NsYvLr + (L_N_ -- N_L_) VT ° Dp - VT o N_ = Ar s3 + Br s2 + Crs + D r A r = N_ * T ! ! T Wo , , C r Y_(I,_N_- N_%)- L_YvN _ + N_YvL _ +- (LsN_ -- N_L_) = VTo Dr VTo N_ = Acs 2 + Bcs + C A¢ : Ap + A r tan 6) o Be : Bp + B r tan 8 o C¢ : Cp + C r tan 8 o c-5

N_ A' s4 C_ys 2 = ay + B_ s3 + + D_s + E'ay

ay VToA_ + iXlatAr izAp B'ay = VToB_ + UoAr -WoAp + iXlatBr - IzBp C_ = VToC _ + UoB r -- WoB p - g cos QoA¢ + iXlatC r - izCp D !

V T D_ + UoC r - WoC p - g cos 0oB ¢ + iXlatD r - izD p o UoD r- WoD p- g cos eoC ¢ To obtain ay, let Ixlat = i z = O.

c-6