dtic - y^ › dtic › tr › fulltext › u2 › 769495.pdfb wing jpan, ft c mean aerodynamic...
TRANSCRIPT
■ :'iWSl.ijrjlHU.--P.!! «'»*"'«! .1* ipii,-,-«!.■= »«UP«»«.«»»««--'^^!1'-11-1-IWP ■'"■ I «■J».!!.. il.lJ-i.t['.L.ll'■.!>■' Hi»i»ii.'.LI!^gw-<*'^'"»" ■_ ■■. pi, | B ■ ■ ILL« P a. m j i!. n ■ |. | ■ ii i. ii pj nt! i ■ m ■ ma
y^
AD-769 495
ANALYSIS OF CONTROL SURFACE AUG- MENTATION IN HIGH-PERFORMANCE AIRCRAFT BY THRUST VECTORING
Deas r . Warley, III
Air Fo^ce Institute of Technology Wright-Patterson Air Force Base, Ohio
March 1973
DISTRIBUTED BY:
KfiTl National Technical Information Service U. 3. DEPARTMENT OF COMMERCE 5285 Port Royal Road, Springfield Va. 22151
!■■■■■ "■- :—• - -"■■ "l**"T'' " ■—■***■■! I ■ * II ' '-
in i.»: i I i. in ."I ■ — =— ii-.—J,.,I i. ii —I,;J.I.. |i i ■ ., .Li ii immw ■-—p- .- m«- i IJ.JIIUU I I mppm l-UWW-W '-■ ,mmB^~. I I JIJIIJWLPII
•'
V
^
V
OS
Oi CO i>
ANALYSIS OF CONTROL SURFACE AUGMENTATION IN HIGH-PERFORMANCE AIRCRAFT BY THRUST VECTORING
THESIS
GAM/AE/73-14 Deas H. Warley III Second Lieutenant USAF
( Approved for public release; distribution unlimited.
■•produced by
f NATIONAL TECHNICAL INFORMATION SERVICE
U S Deportment of Commerce Springfield VA72131
III fc'iUh-^ffMMM'nri-i-1 ! --- - - -■-■^---■^■'»■*''i''^--^~i^ ' -■• * •■■ -- -- ■ ->■■ • ---^■■-=■->*—-—-"- -■ ■ -M«Mai-^aw.« rtH^r-infl-tmi-ii^-iiiii«*..-™ ■"-^3^-.üSS?üJLiijaii
?
WßBmaxmmtm&BPUl Mfffiüisi ."-.■"■■' ,'■■ ';">ji!iiiiw^,ipiJB!|ijp!iHM
UncJ a i.; ü i i I ed SlM llJltV I l.f.- ill, Itl.-Il
**a. ,t«Ä ■ ■».
DOCUMENT COHTKOL DATA • K & D iritv das vi/icfllit«n of r/f/i , ?■.■■/»' »>f ■ ./> T.n f ,i»i-* trnM *</!.*• ,imi.»MfiV>r rrtisi N irf<rr;' II7M*M thf ovt-rutt r* /">rf Js cttt^hHtoeti
T7«, M!."üi*i '.i'.c.'jiinv CLASSIMCAFKN t Ufll 3 IN A TINO AC T I VI T Y f {'orpot^fo author)
Air Force Institute of Technology (AFIT-F.N) Wright-Patterson AFß, Ohio 4 5433
ünclaacifled *b. G'-'OUf
REPOBI 1.ILI.
Analysis of Control Surface Augmentation In Iligh-Pcrforraaacc Aircrux'f. by Thruat Vectoring
* OE^tmi'iivi: NO'iiflVr \il ropuri .uij (nc/usiii
A FIT Thesis (:s) AuTHORiSi (Fitst nut w, nmlJIc initial, last ri«in>cj
Deas II. Wnrley III 2d/Lt U3AP
c REPOK r L»A TC
Harch 1973 f.«. CONTRACT Of< GKAN* NO
b. PROJGC T NO.
7(1. TOTAL NO. OK PAGES
£kM Ib. NO OK REt S
29 9«. O RIGIN A 1 QR*$ F\£PQR1 NUMDC^fS)
GAII/AE/73-14
'Jb. OT"-n>< RFPORT NO'S) (Any of/icf numbers f/ta( nmy />e assigned this f« port)
IS. OISTRI L 1JTION sr»TtM(.Sr
Approved for public releace; distribution unlimited
'AfjjarbVfiriüi'/Pöü'fie ralease; tAvV APR IPO'-il?* cr-iOP"N0 M,U'TAHV 4CT,v~,y
7-SMto '■ ■'. nIX, Cai/iai.i, USAF 'Oirei-. or of Information
Air Force Flight Dynamics Laboratory Wright-Patterson AFi>, Ohio
i? AfMi'. r<.-.c
The feasibility of engine thrust vectoring for lateral control of aircraft in the high angle-r^f-utfcack rogine uas investigated for an airplanes vlfch F-Ill churae'.criatice. Ine technique uaj ^oua.i to be effective in increasing tiu: unglu-of-nttaeü; at vhich departure occurs* The ,;'.::;hi3d used au effective cynawic directional ntabillty parameter to recount for ehe thrnoc ex fact alteration of the static lateral etability parameters C_„ ^ad C- ceuld not be uned to
"3 KP,dyn predict departure in Che model etudied, it was useful in evaluating the uffectiveneaa of the fchruot vectoring conccpta.
»./ fCU Unclassified
: -^^T-> ■ IHM *-—■
>wiwiMP«ii.inm'.wn. i. .«I.M.II ■MwpMlglllpgMiiMB^IiaBfWWWWWBglBgilgBjiBP1 PWgiPBBIiPPWPi '" """'Jl " IWPM»1-- II'1-IHU...II IIIPM I I ■! '""| ■'" | | M
tftnriww ti fcc '$r>77ü^-
KEY WORDS
Thruat vectoring
Control augmentation
Departure pruvoution
li Unclns.si.f i cd ■'■'"Ulllv C'l.l'.slll
. .,....,. rii^i'^ i • ' -.i~~. ...... v.
■--■»■—, .- .-,
i njn.iiii wniiiimii,.ijj,t.u.—. iil.I LimiJ. ill 1.1 11.1 li.Jii. I JiilU-Mi ,i«im
c ANALYSIS OF CONTROL SURFACE AUGMENTATION
IN HIGH-PERFORMANCE AIRCRAFT 3Y THRUST VECTORING
P
THESIS
Presented to the Faculty of the School of Engineering
of the Air Force Institute of Technology
Air University
in Partial Fulfillment of the
Requirements for the Degree of
Master of Science
by
Deas H. Warley III, B.S.E.
Second Lieutenant USAF
Graduc:e Aerospace-Mechanical Engineering
March 1973
Approved for public release; distribution unlimited.
«Is
— ■ - fif I,
J'W^^tM^.B.w.in.-Jjw?^U.->-, ■ mm*m WWW«. l J L^^llllllJ.'ISffWSIiWJPiB W.l.)JJIMH-W IPI#BW
8
o
(;
G
***::.. ■ ■■ —' -M
GAM/AE/73-14
Preface
Poor high angle-of-attack stability and control characteristics of
most high-performance aircraft costs the Air Force, millions of dollars
annually through loss of control accidents. Even the newest o£ the
operational fighter aircraft with their collection of strakes, slats,
fences, boundary limiters, sophisticated flight control systems end
enormous vertical tails, continue to experience loss of coatrol. The
report of the Stall/Post-Stall/Spin Symposium makes it apparent that
scientists, engineers, and officials of the Air Force and other related
agencies were aware of the need for an improved control technology on
which to base design, development, and testing of future aircraft and
to solve the problems of current operational aircraft. One possible
improvement is the use of thrust generated control moments and forces
to augment the aerodynamic forces in the high angle-of-atttvck regime.
It was my intention in this study to determine analytically the feasi-
bility of thrust control augmentation. If substantially Improved
handling and departure characteristics in the tiodel coul , be demon-
strated, they would serve as a basis or incentive1 for f cure studies
of actual hardware. I was also interested in improving the digital
computer program that solves the non-linecr equations of motion to
make it easier to understand and use, simpler to modify, and to have
better printed and plotted outputs.
I want to express my gratitude to my thesis advisor, Lt Col
Frederick F. Tolle, Associate Professor and Deputy Head of the Depart-
ment of Aero-Mechanical Engineering, for his interest, assistance, and
encouragement. I wish also to thank Capt Donald C. Eckholdt and the
ii
- • ■MifijMnriiBMi
uHPLsiuHHi 'i'1 ■ nmmmmi " " ■ ■■ ■ - "«' '■-•"•|"" ' .im..«. . .■ — . ......... :__.,_iu.,i...i» ' u
GAM/AE/73-U
personnel of the Aircraft Dynamics Group, Air Force Flight Dynamics
(" 'N. Laboratory. I am forever indebted to Capt Eckholdt for his willing
and enthusiastic guidance, counseling and ideas, and his enduring
patience. For my wife, «.here are no words to adequately express my
» appreciation for her patience, encouragement, understanding, and good
coffee during our past four years in AFiT programs.
Deas H. Warley III
I 1 c, I
iii
L. mil firriBM.. i in - , ■ *.rr.it i mii v ■■>*■ «i — ■'»■-—-. I --■-- --—-■- -^-■- <■..-.-i.--- m-■--.— ■■ — -.^.:^-.,^^.u^,-..— ._ ■ ■--j..--^ ,-■:, - gül
SJluUJiLPHMMWWPJiiLi,. I •■-"■- PWPP '■ ■UiaiPiftiiiiLpiLi.BiiMI'^.qwPB^BiiBiljiBiBlWpi
GAM/AE/73-1A
O
o
r
Contents
Page
Preface it
List of Figures , . vl
List of Symbols vii
Abstract xi
I. Introduction 1
Background 1 Approach and Scope 3
II. Development of the Model , 5
Aerodynamic Loss of Control 5 Model Equations of Motion 5
Engine Exhaust Deflection 7 Auxiliary Thrusters ..... 7 Programmed Equations of Motion 9
Control System ..... 11
III. Simulation Test Plan and Evaluation 13
Phase I -. 13 Phase J.I . . . . , 15
IV. Results 17
Phase I 17 Phase II 23 Overall Results 25
V. Conclusions 26
Conclusions , . 26 Recommendations 26
Bibliography 28
Appendix A: Aircraft Model Data 31
Appendix B: Equations of Motion 41
Appendix C: Simulation Results 45
u iv
-■ ■ ■■• - '■----'-■ ■ i ■■■■ ■-■■-■ ■ - .-.
:»mi,uii;i,i..»Hiin-ii!.i«n;pu 'mimiyu.-i.j-i.iipm ■ .i»mewwMmp»m»w>ni.wmmwini"-iiii njmw,f ijiimnim.'«.-' mfaammmnmmmH* WHWWMIP ""* I
GAM/AE/73-14
O
(..)
Page
Appendix D: Computer Program 70
Appendix E: Aircraft Modifications for Improved Directional Stability 92
Vita 96
r Liffwispw, mm-.-* ■ "■?-"■ M ■"■'■!»'■ '■ju.f--,...,w.-l..w,,.w,.w.y?iT?,M.^-,F^. ,»■-,—. .,«„,.. ..-™— ., i.-•.««.. I . i.qiW ■ i W>»«*-"...-...:!" i !. »>.!. i 1 ■ ."-~ *>--W-i.. Ml U.Jl..LMJ!,l|(S3^|
GAM/AE/73-14
O Figure
1
3
4
5
6
7
8
List of Figures
Page
Comparison of Stability and Lift Characteristics for Two Configurations 6
Definition of Thrust Augmentation Position and Angles x 8
Thrust Augmentation Authority Limits . . 12
Lateral Stability Characteristics 18
Lateral Stability Characteristics , . . . . 19
Lateral Stability Characteristics 20
Lateral Stability Characteristics , . 21
Lateral Stability Characteristics 22
U
0
vi
•-^--^■-^.-^■^^..; ,^..-,.u..^^--^,....*£....--■= ^-i^.-.^. ^^^^.^JU.,,^^^^ ,_^1_^.._^—^_...-_J, ... _. .. ._... -..
o
""" .1 ..■■^.■i.ijiij.i» - * ■-■T-M.I T-*-"T-' -•?■' - -Win ,!,■■■■■ I..I.IH.-I-... 1..L.. i.: m^^n.i '■"■■«■■ ■.^Mn.jWHiWffM^W^lWW»'^' *r»««!Rf"w™'WT*!TO!«^^ .>Wi.«-7^T«nTq..«i4.«i.j |ii .,!)'■■ .*'.'!I!!".B.>'-W?™»™w « ..HIN wi._. in IIIP-*.*--I.
GAM/AE/73-14
List of Symbols
A aspect ratio, non-dimensional
b wing jpan, ft
c mean aerodynamic chord, ft
(L lift coefficient
C.,C. non-dimensional rolling moment coefficient 0
C non-dire.isional pitching moment coefficient m
C ,C non-dimensional yawing moment coefficient n no
C non-dimensional longitudinal force coefficient
C non-dimensional lateral force coefficient y
C non-dimensional vertical force coefficient z
g acceleration due to gravity, ft/sec2
h altitude, ft
I engine rotor moment of inertia, slug-ft2
I moment of inertia about longitudinal body axis, slug-ft2
ü
C
I moment of inertia about lateral body axis, slug-ft 2
I moment of inertia about norroal body axis, slug-ft z
I product of inertia, slug-ft2 xz
K. control gains (i - 1,2,3,...)
L rolling moment, ft-lb
Lj—.L- rolling moment due to thrust, ft-lb
M pitching moment, ft-lb
vil
Itef! H ■■■■■ .i. n.lfc! .l..Mt*^. —•■■-•-• —■--■ -—- ■■.-■.-..^- -J- ^^—ää****—****-***^*.^-,,---,-!! r|---.-, ) , - ^ , J-.>.^„.,^. ^ ..... ■,-L~^.: ^l----.:. I»:-. .. , j , rüfM jMlmAJ^J^U
2
w"-^w mwii'.'-y pjM ifpBjyfiww gpgifj |W iwwmwp"" ■!■.' w ^ »«'■ ■, ■' I™ H »W jffBI ■ ^«B»*"■ r . .■i.ji.m .„ Hiii,jL.BL»ji!imj»iii P.inpwtwiui.^;,jw^.fj^*.ji.'im-mi"..i'!wf^wf ji.M.w..<a ^* "■""■■■ ■" . -P^IPgrgppiBiWl
GAM/AE/73-14
O M^.Hj
c
KWT,NT
P
q
r
s
Tl
T2
u,vvw
W~ »W_
X
h
*WT
Y
yT
z
ZT
a
pitching moment due to thrust, ft-lb
aircraft mass, slugs
yawing moment, ft-lb
yawing moment due to thrust, ft-lb
rolling rate, rad/sec
pitch rate, rad/sec
yawing rate, rad/sec
wing area, ft2
left engine thrust, lb
right engine thrust, lb
linear velocity components along the X, Y, and Z body axes, respectively, ft/sec
velocity, ft/sec
wingtip thrust forces, lb
body axis longitudinal force, lb
body axis longitudinal force due to thrust, lb
auxiliary thruster position length, ft
engine nozzle position lengths, ft
body axis lateral force, lb
body axis lateral force due to thrust, lb
body axis vertical force, lb
'jody axis vertical force due to thrust, lb
angle of attack, deg or rad
vertical thrust deflection angle, rad
viii
, i gEJMlf"MMi ... ~V,---^ ■>,-.:-—-i_ . I ~.JdM
"!■»* yw" ■**■!. "J"-J-PC-V*-^ -■»»»ii-wr*
GAM/AE/73-14
n 111. T.umiipw -i^t. iip J ..ii niw ■ ^i"i i am.» i bin wmi ■ i mm wmiiv*9?:MMm.v*>m ■ WMWIUIIMI ' p mgawpBHip'"""-' ■ WWBIPlfWPllW|^
1
o
(
0
e
6
angle of sideslip, deg or rad
lateral thrust deflection angle, rad
aileron deflection, positive when trailing edge of right aileron is down, deg
stabilatoz deflection, positive when trailing edge i;; down, deg
rudder deflection, positive when trailing edge is down, deg
6 angle of pitch, rad
p air density, slugs/ft3
$ angle of bank, rad
i> heading angle, rad
to engine rotor angular velocity, rad/sec
The aerodynamic coefficients and derivatives, and the moments of
and product of inertia, are with respect to a body-fixed system of axes.
A dot over a variable signifies the time derivative of that variable.
Aerodynamic Coefficients
C " n n6 90
*ß w
C o Q cos a 0,dyn l"ß
~ C sin a x 0
O
ix
w ,-.-.. --..- tan Ma —;■ -.^■■■- -■-
Ü
GAM/AE/73-14
PUppiMÜPlBpiUffPBimPli B Bjpps m immmmmm »II-. i' nAß.^n... m •tw*-^^.^.^^^^m^-^ntm'^mmmnAMiAj\ >xvum»\^
o 3cl 2 » —-
P 2V_
C_ -—r 3C n aEk
2V
3C c - —Jf> yp 32k
P 2V_
e 3ci
2V n
3C _ n aik
2V_
?c __y. 3ik
2V_
3C,
'1. 36 6a
3C
nx 36 6a a
3C
*« 96<
3C. 2 B =■
1* 36 6 r r
3C
"tu 36 6r
3Cy V 36
6r r
3C in
mq 3ä£ 2V
3C _2 36
3C z 36
«M
3C in
r "SB"" e
■■ - •■*"iitiri,«iii""'irfii ■i»Mt'ni,iriiiii-i"iii r i ^"-■—Mfc^—- --■--■- ^^^--^ -^ -- -^ .
.... HIIIH-.I |lll(«lll,l«™fm ..IJiJUIIiLJiLIH.
( J
GAM/AE/73-14
o Abstract
The feasibility of engine thrust vectoring for lateral control of
aircraft in the high anglc-of-attack regime was investigated for an
airplane with F-lll characteristics. The techniqi..■> was found to be
effective in increasing the angle-of-attack at which departure occurs.
The method used an effective dynamic directional stability parameter to
account for thrust effect alteration of the static lateral stability
parameters Cno and CfcQ. Although the effective Cno _, could not be p P PfCyn
used to predict departure in the model studied, it was useful in eval-
uating the effectiveness of the thrust vectoring concepts.
G
xi
MBMfc— mi iwir ■ ■■-- I -"-•■■■ -uarFmm«
mmmpHNHPfiBIP WP " PPIB1? * ""■■ ™wM-wiw^uiiraiMiiMWjijLp.. ■ " »"« w-'-., "■■" ■■»■■■■ 1HBHBW . .*» i pupprgp« w^™vr-*w^'»""«' in«-- «■■W.J» I'.-W -II 111 flip.« W.L.I ..,fc^l4.lMll«...4..Ll I »■■"! Ml 1.11,1^111]
GAM/AE/73-14
o ANALYSIS OF CONTROL SURFACE AUGMENTATION
IN HIGH PERFORMANCE AIRCPAFT BY THRUST VECTORING
I. Introduction
(
Most modern high-performance aircraft when flying at high angles-
of-attack exhibit poor lateral-directional stability and contvol r
characteristics which can lead to inadvertent departure or loss of
control. The problem is to maintain control of the aircraft after it
has lost aerodynamic lateral-directional stability until the classical
stall angle-of-attack has been exceeded.
Background
Loss of control (departure) normally occurs when a pilot uninten-
tionally exceed? the normal flight envelope boundaries while performing
a maneuver. The situation is particularly probable and critical in
maneuvers such as landing, air-to-air combat, and precision weapons
delivery because of extreme pilot workload and stress level. Severe
loss of control may lead to operational restrictions which reduce the
mission effectiveness of the weapons system.
Air Force safety records indicate tha,- accidents dua to loss of
control account for almost 25% of all aircraft losses and almost 60%
of all aircrew fatalities. The cost of these losses is estimated to be
more than 40 million dollars annually (Ref 23). As of September 1972,
at least 10 of the 22 F-lll accidents (aircraft destroyed) were
attributed to loss of control. At an estimated unit cost of 20 million
dollars, the price tag for the F-lll loss of control accidents is a
staggering 200 million dollars.
• - 1 i ,-iifrVil
GAM/AE/73-14
o
c
In. the late 1950's (Ref 29) the consensus among contractors and
the military was to trv to solve the problem by more fally exploring
the spin characteristics of each aircraft, and by teaching pilots
proper spin recovery techniques. Subsequently, it has been found that
most high-performance aircraft have a myriad of complex spin modes,
several of which are non-recoverable. The loss of control accident
trend of recent years and the complexity of the spin problem'led to
the expected shift apparent at the 1971 Stall/Post-Stall/Spin Symposium
(Ref 5). Emphasis is now placed on either preventing the spin by elim-
inating the possibility of departure or controlling the spin by develop-
ing and installing spin recovery devices.
Despite advances in analysi.s3 synthesis, development, and testing,
aircraft frequent .y reach the fully operational status before departure
problems are discovered. At that points the expense of a complete
research and development program or a large scale modification program
usually leads to a less than optimal solution. The corrective action
has been to train the pilot or limit him by regulation in order to
avoid the problem, or make minor configuration modifications in order
to mitigate the problem.
Several examples of modifications to the alrframe, control system,
or both are described in Appendix E. Few of the modifications imple-
mented to date have appreciably improved the directional stability
characteristics of the aircraft. Additionally, all of the devices
discussed have at least one of the following drawbacks:
1. The effectiveness cf the device is limited to a particular
flight regime.
2. Margin-of-safety zones created at the performance limits deny
^M. »■■^.J^l llllll fc" .!■!. II *—***■•*•■■ ■ -- — — I • --■ —
vnnnflnpiff •'■■.*
GAM/AE/73-1A
full use of the maneuver envelope.
( v' 3. Pilots object ctrongly to any devices which limit cr override v
their control of the aircraft.
Spin control by using spin recovery devices is an excellent con-
cept but is linuted by the fact that there is insufficient reliable
spin data to evaluate thoroughly such a system. Data acquisition is
costly in both time and money, is complicated by the existence of
several unique spin modes for each aircraft configuration, and the
extensive flight testing required could lead to further aircraft losses.
These facts lead to the conclusion that airciaft must be designed
to be directionally stable at angles-of-attack up to and just beyond
the classical stall. Directional stability and control can be achieved
by careful kfcrodynamic design of r.he external geometry of the airframe.
/- - end control surfaces, by the addition of nonconventional control sur-
faces or forces, or by using advanced active flight control systems.
Directional stability through aerodynamic design alone has beer, achieved
on only one modern high-performance aircraft, the Northrop F-5/T-38.
Since the majority of high-performance aircraft do not have aerodynamic
directional stability, the only alternative that will provide stability
without sacrificing maneuverability is to provide lateral-directional
control by non-aerodynamic devices.
Approach and Scope
The objective of this study was to investigate the feasibility of
using thrust generated yawing Troments and side forces to augment the
aerodynamic lateral control at high angles-of-attack. The study Was
limited to a single aircraft, the F-lll, which has directional stabil-
ity characteristics typical of many modern high-performance aircraft.
3
(
■ !-■- - ÜMB --• - ■ -- -<■ - w&äaämsm ■■■ ■n..-™-*»-^---■■-—~* „-„^v.^^..^«■a- ^an- .-.-ü»^.^.^.-^-»*..
GAM/AE/73-14
o
f
A computer program was developed (Appendix D) to model the air-
cr™'t using a six degree-of-freedom, non-linear formulation of the
equations of motion. It was based on a similar program developed at
the Air Force Flight Dynamics Laboratory (Ref 6). The non-linear
aerodynamic data obtained from NASA was based on wind tunnel and model
flight test data modified to match the performance characteristics of
the F-lll. While the computer program car. be used for spin analysis,
the data is valid only up to departure; therefore, this study is limited
to investigating the application of thrust vectoring to prevent depart-
ure.
The approach is to determine lateral stability criteria as a
function of angle-of-attack arid sideslip, and to evaluate the influence
of thrust cctrol augmentation on this criteria. This permits an
analytic demonstration of the feasibility of thrust control. A dis-
cussion of methods of implementing thrust control and a short synopsis
on the state-of-the-art is presented; however, actual hardware design
is not included.
C
i i il^—i ■ ■ r i^ i ■ .
W*IM«-'fM.«l JH.:l.iitJ.'.IW*?H
.0
(i
GAM/AE/73-14
II. Development of the Model
Aerodynamic Loss of Control
The boundary of the aircraft maneuver envelope can be defined by
the angle-of-attack that corresponds to either maximum lift or zero
dynamic directional stability. Configuration A shown in Figure 1
maintains positive dynamic directional stability at all angles-of-
attack. The aircraft will stall in the classical sense when the angle-
of-attack of maximum lift is exceeded, and will not experience uninten-
tional departure or loss of control. In contrast, configuration B will
depart from controlled flight when the dynamic directional stability
parameter (Cn„ , ) approaches zero prior to the conventional stall
point. Since this departure occurs at an angle-of-attack that is often
considerably less than that of maximum lift, the result is the loss of
a large portion of the high angle-of-attack maneuvering capability. It
is in this angle-of-attack range that the forces and moments generated
by thrust can be used to augment those of the control surfaces whose
effectiveness has been diminished due to adverse air flow character-
istics.
Model Equations of Motion
The system is modeled by the boJy axis, non-linear, six-degree-of-
freedom equations shown in Appendix B. The forces (X, Y, and Z) and
the moments (L, M, and N) are expanded as functions of the aerodynamic
and thrust effects. Two general categories of thrust control augmenta-
tion are considered. The first deals with cases where the augmenting
thrust system produces or exerts both control moments and control
forces on the aircraft such as that produced by deflection of the
ili|l..l»IMUail.iwm.r^..i»M^mn»-|..uWjiii.i.i]ui^n>J1. ._ , , , n |«I_. RH. p |. | i m|iMiL,i.. ■ »MUM. 11 lllll.l... j .,«, i.m im^nnj.juilig»
c:
GAM/AE/73-14
2.0-
1.5
CL i.o
/ / Configuration
0.5- / / A / / // // // /
O.OI c > 5 10 15 20 25 30 35 40
<2T (degrees)
.04-.
.03- /
.02- .____/
Cn oi- >*,dyn
o.o- ^^Zz -°
-.01-
0 5 IO 15 20 25 30 35 40
CC (degrees)
FIGURE 1. Comparison of Stability and Lift Characteristics for Two Configurations.
t.
-■■■,■■■«-„«■.■ *.,..-—-*.^..^—.^.■...^.-,.---..I„^^J^^i(ltrtirlr m.iV..-..,.,..^^=.-... ^
—. jppK ■ *1?WIIII*J.«IM " PÜ «i ■ IHBHWIMU»! I...I...I.! ,1.1— p p. i Ij-J
GAM/AE/73-14
O
r
engine thrust. The second category applies to cases where the augment-
ing thrust system produces only control moments.
Engine Exhaust Deflection. The model assumes that engine exhaust
can be deflected by scheduling the exhaust nozzles for asymmetric
closing or by flow separation induced by injection of bypass or bleed
air at the nozzles. Although the actual hardware is not discussed,
the technology exists and is currently being applied to VTOL aircraft
(Ref 3, 8, and 26). Engine thrust is assumed to be an external force
acting on the aircraft at the nozzle position. The lengths x„, yT, and
s_ define the location of each nozzle in the body axis reference frame.
T, and T„ are respectively the left and right engine thrust forces.
Defining cu to be the thrust vector sngle with respect to the x-z
plane and ß_ to be the thrust vector angle with respect to the x-y
plane, the thrust can be expressed at any general angular position.
Maximum thrust vector angles are restricted to within the thrust
deflection limits (15° maximum) achievable by ai- injection techniques.
Resolving the forces and -loments from Figure 2,
Xj - (I1 + T2) cos aT cos BT (1)
*T - (Tx + T2) sin ßj (2)
ZT " " (Ti + V sin °r (3)
LT " (T1 " V yT Sin °T " (T1 + V ZT Sin &T (A)
Mj - - (Tx + T2) xT sin aT + (^ + T£) z^ cos aT (5)
NT - - (Tx + T2) ^ sin ßT + (Tx - T2) yT cos 0T (6)
Ü Auxiliary Thrusters. Using a rpaction control system (RCS) util-
izing high pressure compressor bleed air or small rockets in coupled
,.■ ■■-■'■■'• ,,- —-i-- ■-■- - - 1-_t^aäiä. [»■Hl Ifc I ' I ii ■ - - ■ - - -■•
IUL»^._._LII,»,.,.,.,., ,,.,K, „Li« .,..,.;„.. . ^..mm-
O
GAM/AE/73-1A
WTI
WT./
^/VT
Engine Thrust
Auxiliary Thrusters
FICUBE 2. Definition of Thrust Augmentation Position and Angles.
( v
-.11^ I ■!■■! > I I II II- ■■ - II MhlMlilB» | | ||,r ■ -• • ■■■■ ----
. ..U. .. .11. Ulli" Ulli. J-WIIW ,WWii*^JiJ»imi^l^.*-WM.t^.'l«WW"»ia^W-«»''i!U..ii<iiii»g^jt^
o
GAM/AE/73-14
pairs (for example: four nozzles located in opposing pairs at each
wingtip and aligned parallel to the x body axis), control moments can
be generated without the presence of translation producing forces.
Assuming the auxiliary thrusters act only in the x-y body-axis plane,
the result from Figure 2 is the yawing moment equation,
Nwr " (wTl " V V (7)
Programmed Equations of Motion. Equations (1) through (7) are
combined with the non-linear equations developed in Appendix B. The
aerodynamic quantities are expressed as non-dimensional coefficients
and derivatives that fit the data package (Appendix A). The resulting
equations of motion to be programmed are as follows:
• ov2<? u « -g sin e + rv - qw + ^^-^ (C + C Se) ° ^ 2m x Xr oe
( ) + £ (Tx + T2) cos ccT cos ßT (8)
■ OV2<5 v - g c6s 9 sin <j> + pw - ru + -t—- (C + C 5a + C 6r)
2m y ^a ?&v
+ £S(CyP+Cy° + m(Tl + T2) sin3T (9) 7p Jr
• pV2S w ■ g cos 0 cos * + qu - pv + ■'- (C + C 6e)
Zm z Zf oe
(
" m (T1 + V sin aT (10)
*.*,-**.*, ,....,, r~~.——_^„ ., .—■-«*■■-■■»—jMWM—aii^toMtitiwaMni ... — .. .. ._ ....-,-.. ..- „.
tlvmm9mvwwtmmri tmrmmrm* B —| jppjBjipj ,n .I. i. .^.HP». i ..ifp... ngjpag. i-wjm ■!■ a — ■,»IIJI'-- ■'» ■«' "W^iqw
GAM/AE/73-14
o I I - I * x z xz
^z pV2Sb [C + C 6a
+ C. 6r +^r (C„ p + C. r)] hr 2V p v
+ Iz [(^ - T2) yT sin (Xj. - (^ + T2) Zj sin ßT
I *z ^,2 pV2Sb [C + C 5a + C 6r
l6a n 6r
O
(..
+ 2V(Cn" + Cnr" + I« K^ - I,) yT cos 6T P t
" <T1 + V *T Sin BT] + Xxz \ - V *WT
+ (I - I +1)1 pq + (I I - i - I z) qr x y z xz r^ y z z xz n
+ 1 I q W xz r * r
f PV2SC (Cn + C 6e + Iv C q) öe q
- (T1 + T2) x^ sin aT + (T^ + 1^ z^ cos cT
+ I (r2 - p2) + (I ■ - I ) rp - r Ir „r
r - v 4 pV2Sb [C + C 6a + C 6r n n 6a *6r +2V (CnP+Cnr)]+(Tl-T2) yTcosßT
P r
" <T1 + V Sln *T + \ - WT2> *WT + Xxz (P
(11)
(12)
qr)
+ dx - iy) pq + q ir wr)
The Eulcr relationships are developed in Appendix B.
(13)
10
-raw, ■■■in i -. -...■■ ■■-^_J.._... . ^_..■-.--- .- : ; .^-:^,._ .■■
PWBJBW^W—WWW ^BHiBnaLiwWPffWff1 WH
o
r. V /
L
GAM/AE/73-14
Control Svstem
A key objective of this study is the comparative evaluation of
the response of the aircraft model to control surface deflections with
varying degrees and types of chrust augmentation. For this reason,
the influences of the F-lll self-adaptive flight control system and
the dynamics of pilot response are purposely removed from the control
loop. A simple, closed-loop, feedback control law based on yaw (ß),
yaw rate (r), and roll rate (p) is used to command aileron and rudder
control surface deflections.
«a - \ P (14)
6r - K2 r - K3 (0 - 3cofflmand) (15)
The control gains are purposely kept at the minimum values necessary to
maintain wings-level at low angles-of-attack. The low gain levels will
not inhibit departure or stall in the high angle~of-attack re^me by
inadvertent over-control. Maximum control deflection angles are
specified in Appendix A.
Thrust augmentation authority limit3 (TVA'J) shown in Figure 3 are
used to schedule both the engine exhaust deflection system and the
a* »ciliary thruster system. Since control augmentation is necessary
only in the high angle-of-attack regime, the authority is scheduled as
a function of angle-of-attack, rudder deflection angle, and a maximum
specified thrust control moment. The engine exhaust nozzles are
assumed to lie in the x-y plane and the thrust deflection is restricted
to produce only yawing moments and longitudinal and lateral forces. To
facilitate comparison between the two systems, the maximum moment
Q produced by the auxiliary thrusters is identical to that produced by
engine exhaust deflection.
11
in. iiuir "-"
r
qigggMffirB-lW-if"" .'-' - papg ^J)"""1 in i ■ ip.iPWL I.H..MN mmmqmzm&mmm
GAM/AE/73-14
(
(
TVAU i.o-
o-
—c»* TVAU
'"X .__
* s. - -.0005
-.0010
-.0015
•*■— /
/ /
/ / /
/
-i 0 1 > 0 10 20
a 30 40 50
(degree« )
60 70
i.
FIGURE 3. Thrust Augmentation Authority Limits
(C_ of Model for Comparison) n6r
L 12
■a.--*.,-W. ;-M .-..-_ -^■,..^.--v^-ll|.-
GAM/AE/73-14
c III. Simulation Test Plan and Evaluation
The simulation and evaluation of results are divided into two
phases. The first phase is run solely to generate dynamic stability
parameters for co-.Farative evaluation of each configuration. The
second phase consists of several "flights" of each configuration at
high angles-of-attack using various flight control parameters to pro-
duce maneuver envelopes based on criteria to be defined.
Phase I_
One simulation is run for each of the following configurations:
a. Basic configuration with no thrust augmentation
b. Engine exhaust deflection augmentation
(1) 50% authority limit (6° maximum deflection).
f (2) 100% authority limit (12° maximum deflection)
c. Auxiliary thruster augmentation
(1) 50% authority limit
(2) 100% authority limit
To provid» a basis for comparison, the authority limits and algorithm
for the auxiliary thrusters are designed to produce moments equal to
those developed by the engine e ;haust deflectors without the force
effects.
Evaluation of each simulation in this phase will be based on the
static lateral stability parameters (Cng and Cj^g) and the dynamic
directional stability parameter (Cn„ , ). The derivation of Cn„ , J r S.dyn "ß.dyn
can be found in Reference 19. This report and others (Ref 5 and 28)
show good correlation between divergence characteristics prrdJcted by
Cn« . and actual aircraft divergence characteristics. The method
13
M ■■■--
TZZSXM* „,, ., .„....,-. ...n.,.:^L,,,.H1^jW, .... ,. >«.i>><m!.. M-P« ii-i -~..i.. i ji, m\ ifiiii mtmmt'-m»»r- ...nmiumw
GAH/AE/73-14
for determining these parameters is different than the normal method of
/' extracting CQQ and C^g from wind tunnel data and then calculating a
CJJO . . Since thrust effects do not appear in the characteristic
equation used for the derivacion of Cno . , terms are defined to com-
bine both the aerodynamic and thrust effects as one parameter. The
elevator control will produce a gradually increasing angle-of-attack up
to stall or departure. Aileron control will be used to minimize roll
and maintain wings level. The rudder and thrust augmentation devices
will be driven by a sinusoidal commanded sideslip angle. The resulting
motion is large sinusoidal oscillations in yaw and yaw rate with a mini-
mum of variation in the other states.
An effective C and Cp is calculated at each time interval (0.1
seconds) in the simulation with the thrust effects included.
O C, - Ct ♦ Ji Lthrust (16) eff o pV Sb
21 C - C + IT. . (17) n ., n „,,2C, thrust eff o pV Sb
CJJ, and Cn are interpolated values calculated in the computer simula-
tion based on the data (Appendix A) and exclude the effects on the
rolling and yawing moments produced by roll and yaw rates.
The change in sideslip (Aß) is calculated for the same time incre-
ment and the static lateral stability parameters are estimated by
h -IT11 (18) Ycff A0
i Ar ACneff (19)
o S.eff* Aß
14
- I JM —
r
- '----—■-•■ - ■"»■ MILI.IILJ, ■■■ .i ii i I ■ II -i -J imrn^i
GAM/AE/73-14
and the dynamic directional stability parameter Is estimated by
O i. C - C cos a - — C. sin a (20) ne,dyn n3,eff Xx %HLZ
The values of effective Cno, Cj,„, and Cno . are determined and P P p»cyn
plotted as a function of angle-of-attack. The results are an indica-
tion of the combined aerodynamic and thrust effects on the stability of
the system.
Phase II
For each simulation in this phase, the aircraft configuration is
flown to departure or stall. To provide variation in departure atti-
tudes, sideslip command (3C) in the rudder control (Equation 15) will
be set at a different value for each simulation. Several simulation
runs are made for each of the following configurations:
a. Basic configuration with no thrust augmentation
b. Engine exhaust deflection augmentation
(1) 50% authority limit
(2) 100% authority limit
c. Auxiliary thruster augmentation
(1) 50% authority limit
(2) 100% authority limit
d. Engine exhaust control with rudder fixed at neutral
.(1) 50% authority limit
(2) 100% authority limit
In the final sets of simulations (Part d), the rudder will be
fixed at ?-ero deflection and the deflected engine thrust will substi-
(' tute for the rudder as a lateral control device. The authority for
15
■-ji-ifii-.-««.,-. -■ -..*,,~.-, -...
——- ■ —-■*■■»■« — ■■- ■■_--^^.,.-. .._,_^ ,.„.r__
>-! i I PVP«MMIIIV|IMHni!mHHBIpnpM«pqC|
GAM/AE/73-14
(
each of tl _se configurations will use the limits indicated for all
angles-of-attack. The thrust control will be maintained at full
authority limits for all angles-of-attack. The purpose of the simula-
tions in Part d is to provide soino comparison of the control effective-
ness of rudder alone versus thrust alone.
To evaluate and compare the resulting time histories of each
simulation, divergence boundaries are established based on two
different criteria. The first compares the sign of the first and
second time derivatives of beta (8). If each is of the same sign (both
positive cr both negative), the time and aircraft attitude is recorded
and a departure condition is defined. The series of departure condi-
tions recorded for each configuration are plotted on a graph with
angle-of-sideslip (ß) as the ordinate, and angle-of-attack (a) as the
abscissa and labeled the "Beta Condition Departure Envelope". The
second criterion of departure is the completion of 20° of spin; when
this occurs, the aircraft attitude and time at the 20° point are re-
corded. The results are plotted in ct-ß coordinates and are labeled
"'Spin Condition Departure Envelope".
It is important to realize that these envelopes are not the
"maneuvering envelopes" defined in the flight manuals. Both are simply
diagnostic tools for comparing the effectiveness of each thrust aug-
mented configuration.
16
-•'-"—-• -•-"• *-" - - T -;- ..,-, ..i-g ■■_-iajä--:irfg_. -
,uLl, >i<i»|iip. i|. LI j.» ii^ .unu» 11. ..I« immmmmmmmmmmmmm mmmm wmytmimm wm*mm ■"■ ■"-«■-■»-'■'-Iü .«!»"*-■■ ■**!
o
GAM/AE/73-14
IV. Results
Phase I_
The first simulation of this phase shown in Figure 4 was run with-
out thrust ajgmentation. The resulting Cn , was compared with
previous results (Ref 19 and 22) and provided baseline data against
which to evaluate the effectiveness of the thrust augmented control.
Correlation was limited to angles-of-attack less than 35° which was
the maximum angle-of-attack in the previous calculations. The present
method gave surprisingly good agreement and established confidence in
the method used in the computer program for calculating an effective
Cjv, j directly from the simulation. The remainder of the Phase I
simulation results are shown in Figures 5 through 8. The apparent
flattening of the curves in Figure 5 is due to a scale change.
The most significant effect of thrust augmentation was the exten-
sion of the angle-of-attack boundaries of departure. The fact that
simulations did not depart when the calculated CnR , became negative
was probably due to the .simplified control system used. As shown in
Table 1, both the sign change CJ. CUR , and the maximum attained angle-
of-attack are improved with the thrust augmented configurations.
Since the authority limits; for thrust control were based on the
rudder effectiveness (Cn* ), it was noted that the lower limit selected
occurred right at the Cnfi crossover. At this point, the authority
limits were altered to allow the thrust augmentation to begin at an
angle-of-attact. of 20° and reach full authority at an angle-of-attack
of 40°. The simulations were run again and the results (Appendix C)
indicated decreases in the anglc-of-attack where the sign of the
17
kjuiif iud
GAM/AE/73-14
P.DP t.ao it.m u.m x.w *o.po 4».w M.OO M.DO TC.DO ALPHA - DEG
UJ / i
K luv «J-
/' ♦
/
•V
*'/
0.0P ».00 If.OO t4.00 lt.00 40.KJ 4».00 K.00 M.P0 «.00 fllTHfl - DEC-
m*
*s* Ref 19 data
.00 (.00 If.00 Ct.00 St.DO 49.00 41.00 K.O0 »4.00 7 .00 flLrnfl - DEC-
HUN NUrtBEK «147
FIGURE 4. Lateral Stability Characteristics
(No Augmentation)
18
■■■——■ : ■-■■— .„..._ ■-^—-^■■-.■:.■:■■* . -
ii.i .»"im mjM.i-11 .], um u.H- iiiji.LilJH.-li-ll.!i»tU, HHIL.IUI III" ■»■« i.lHWimWlJM^IJ . ■lW»"ll|4lll|»IIIIW»I..I.I.IIH.IIUIIIl.ll. HI —^1^^
GAM/AE/73-14
(' .
(,
I CD r 3« *1
'D.OD >.0D If.DO 14. PO St.PO 49.P0 4».DO K.DO M.D0 Tt.PO ALPHA - OEfr
i»
fa»* ■
u.» III" I a o1
it ^
/
/v * *
--/'
*+«♦
D.OD ».00 ic.oo M.w «.Po 40.OP «.DO w.ro H.PO Jt.ro
D.OD 1.00 IC.DO tl.W «.00 40.00 RLrnfi - OE&
ic.ro H.ro M.po rt.ro
nun Nimocn •431*6
FIGURE 5. Lateral Stability Characteristics
(Exhaust Deflection with 50% Authority Limit)
19
_ ..■■■....- ^ ^.-..^-l:. mM^tM,tl
, ■ Ü-. i i im-m
fmvmmrm ■'■'•*' i..p>.—ni:"'"l.'l. ...WII.W.1-U.IL-II ■'1^
GAM/AE/73-14
O
P
•
<■ s m
♦ ♦ B ♦
. D • -^« ♦ o» A ^ ♦r ♦
Ejo
♦ ♦
l Ny J B V ♦ u« x ♦♦ E«» V 5T"
\ k
******
B ^ f
'DIOD «loo ii.ro ti.ro Jt.DO 40.00 4J.P0 se.ro f4.ro 7t.ro RLPHfl • • DEC
^ ■> •H
V
-k
D /> ̂ a t> / \ b» / \ «•* / V ■
/ \ w» t >k
U-D- i f **♦♦ ♦. * kj' j * ♦♦ i / ♦ «
K k*
1 Uln
if V ♦ k. -. «* *
♦ ♦ ♦ ♦♦♦♦*
4.
V. E «»a
'P!OD »!OD ii.ro «.pa St.00 40.00 19.00 «.oo f4.ro 7t.ro ALPHA • ■ DEC
„ •« w •
* • ♦**♦. T ♦ *» at r
4 h. • *
?--. ■ 4 * X«» * * >- 0
• ^v**0*****^^
1 ^■■'- « 1 ^ I» o ». 1 ^
0* V A X f
1
s iV/ /
B 1 ^"^ 1
'oloo i'.OO if. 00 14.00 3t.ro 40.00 4f.oo ff.ro f4.ro 7t.oo ALPHA - DEC
RUN KUHtiCH -43145
c FIGURE 6. Lateral Stability Characteristics (Exhaust Deflection with 100/.;Authority Limit)
20
-«111«*!
i iiii«iiiii,nimii^wKipp-«wi.ji).iiii>iTjLi aWHyyj—W^B^BWWpiggpppi H"'-'v L«i!lilf.l,^,.ii.ipp.|(i»i,i!. ji,»jiiiii.W!>«
GAM/AE/73-14
o
o
1 m m »" V ♦ ♦♦♦♦
♦ \
Ml /♦ ft -♦-w /♦
Uje»
m$ in*" % ^% ♦ ♦
1 ct ^ ♦ ♦ •— v ♦* Us X, A ?• v 1 4* \ k /**
J B ^/
f
'oloo »'.00 ii.ro J4.ro St. 00 ALPHA -
40.00 DEC
41.00 K.OO «4.00 7t.ro
.* V v"
A o / i L . V / \ b» / \ 1 ** m z V J*; ^ j ^ ♦
tu 1 J / V* 1 / % * K t— Ult;
'.«»■ \ ♦** <%' X U
♦
6 ♦
***4» 'ploP »loO li.DO C4.P0 3«.W 4o.ro
DEC 4s.ro sc.ro C4.ro '(.00
» f w~ \
. • ♦ **n. 2*j
» 1 «V **
/ it. 4»
V?, < a:» *> >- o i 1 ♦/ «_ -~J/**^ S __ ♦
0v
•**w^^ ^ si S* -tr»/ x f 3
1
f
6 'pioo »lap ii.ro ci.ro Jf.PC
Pi.rHfi - 49. DO 0CG
4».00 ».00 H.ro »e.ro
• PUN NUnBCK -4JH5
Ü FIGURE 7. Lateral Stability Characteristics
(Auxiliary Thrusters with 50% Authority Limit)
21
—■'-—■ ■-■ ■---■- - - IIMfMhlll llll I MM
■-*. '—-..*4f ■!,.!- ■!»-i.. m i -nuitB nnww^ttgwBBip^iiw'^JwiFwwp^wii - ' .in-..i.. i 'Piwpi
GAM/AE/73-14
O
G
C7
♦ ♦ *
i.oo ii.ro ».00 Jt.w «oTöö 4>.oo «Too u.oo it.oo ALPHA - DEC
I et
a»« ■ t \
/
A ♦ ♦ ♦ 4
P.OP ».00 l«.P0 14.CO it.DO 40.00 4f.P0 K.00 (4.00 U.00 flurMO - DEO
m
"mo •
u.
*•» >- o
1
2E- 1
4«
* *
099 X f 5
e :\/ f
1, P.00 (.00 t*.00 C4.00 JC.00 «.COO 4*.00 5«.00 M.W »t.00
BLrMP - DEC
RUN NUtlBER ■43145
FIGURE 8. Lateral Stability Characteristics (Auxiliary Thrusters with 1007.Authority Limit)
22
—
TO.ii.wi.i.^.jmLiB
;,i iBjpiSgpi .LW.il UW.I! 'i'iwgi'nW
GAM/AE/73-14
o effective C„„ , became negative. This indicated that rather than an
"p, dyn
increase as expected, the lateral stability of the thrust augmented
configuration had decreased. For verification, the simulations were
again run with complete time histories and the departure angle-of-
attack for each thrust augmented configuration with the 20°-40°
authority limits was approximately 5° lower than that of the 30°-50°
authority limits. Since the original authority limits with initial
thrust deflection at 30° angle-of-attack and maximum thrust deflection
at 50° angle-of-attack had produced satisfactory rasults, it was
decided to proceed to Phase II with the authority limits unchanged.
c
TABLE 1
Summary of Phase I_ Simulations
Configuration
Maximum Deflection Angle(des)
0
Angle-of-Attach
of Si,dyn Sign Change(deg)
30.4
Anj at
»le-of-Attack Departure
(deg)
No Augmentation 50.0
Exhaust Deflection 0 31.7 55.6
Exhaust Deflection 12 30.7 61.5
Auxiliary Thrusters * 6 30.7 55.6
Auxiliary Thrusters *12 30.8 61.5
* Equivalent in moment to exhaust deflection of maximum angle indicated.
i (
Phase II
The intent of this phase was to provide an alternate method of
evaluating the effects of thrust augmentation, independent of the
23
\M\*mammam*i ■--■■■
F..-.! IF! I ■ ■«-«
i nimm.! '^HIJI MI.I.JWH..II.
GAM/AE/73-14
method used in Phase I. The rationale for this method arises from the
( \ apparent relationship which exists between angle-of-attack (a) and
sideslip (3) at the time of departure. The idea was to select 3 and
increase a until departure occurs over a wide range of sideslip in
order to form an envelope which would describe the non-linear nature of
their relationship at departure. Unfortunately, the procedure proved
to be time consuming and costly in relation to the value of the results
obtained.
The key to defining the envelope was the development of proper
criteria to accurately determine ehe departure condition. Using the
first criterion, the first and second time derivatives of sideslip, it
was found that departure occurred in the first seconds of simulation
while examples of the full time histories shown in Appendix C show the
s~- departure occurring at times of 20 to 30 seconds. Several variations
in the method of calculating the rates and applying the test were tried
in an effort to improve the criterion. For example, minimum magnitudes
of 3 and 3 or minimum elapsed times were imposed as conditions required
before the test could be applied. None were successful; the computer
program indicated false departure immediately after the imposed limits
were exceeded.
Similar difficulties were encountered using the developed spin
condition. Since the angles-of-attack and sideslip oscillate violently
and rates are unpredictable once the spin has developed, it was diffi-
cult to predict how far to backtrack from the test point to the actual
departure point.
Examination of the time histories did not indicate why these
methods failed. The correct criterion for defining departure will have
24
(
_;j,..^ ■ ■-■■■ -- — -- ----- ■■■- ■■-•■--■-.-- -..■+. -f ti.tmSitMiahlMäm*. Mttnaaiimm mi mir
.,"—.„■-.,- '-- -i-T—■"■ --I-— :-■■ ■■-, .-i- .... - - .,■,!!-.~I.-.I. ^- L.I...IH..III ...i ..I., i J i-.JniUM.IllHIIBIIIIH 1 II» ■ I I I , 11 l|N| I irj|TO1|TJTTOWpn|WH1—I
GAM/AE/73-1A
to be based on several of the simulated states due to the non-linear
( \ nature of the problem.
Overall Results
Sample time histories of simulation runs for some of the configur-
ations are shown in Appendix C. With the control law used, the model
in each case increases in angle-of-attack until departure occurs.
Examination of full time histories indicated that with thrust augmenta-
tion, the maximum angle-of-attack reached before departure is increased
by 5° to 10°. There is little apparfr ': increase in the g loadings; all
are well within pilot tolerances.
Surprisingly, the use of lateral thrust control with the rudder
held fixed provided controllability nearly equal to that of the rudder
alone. Obviously, the vertical tail and fixed rudder have a signifi-
v , cant stabilizing effect. This simulation does not infer the use of
thrust in place of the rudder, but suggests that thrust deflection
could provide emergency control device if the use of the rudder is lost.
a condition quite possible during or after combat engagement.
Time histories for some of the simulations used in Phase I aie
also shown in Appendix C. The magnitude of the sinusoidal sideslip
command ($ ) is unrealistic for a real aircraft, but provides a suitable
and simple method for extracting C , C« and C . nß B 3,dyn
25
--■ ----■• ._. - i ■ ■ i. jjMi»MimMii i r i ■! ii
.i, ^iJ.ji»iLyji.i«(Pi«™i!Ä!»piMLii!i«ii!w*ie^!Mi»«iiw« ii m<mmmm**w*i*e^*mrmmmm9*m^mmtm*m0nmBm]wmi!mMib.m
(
GAM/AE/73-14
V. Conclusions and Recommendations
Conclusions
The results of the Phase I simulation indicate that both the
engine exhaust deflection and the auxiliary thrusters are effective
lateral control augmentation devices. The maximum angles-of-attack
attained prior to departure using either of the augmented configura-
tions were up to 11.5° greater than those of the conventional model.
The calculation of an effective Cn , compared well w.-'th values
from a previous study (Ref 19) for the same aircraft configuration.
Although it could not be used to predict the exact departure point in
the model used, the effective C-. , was a useful tool for selecting
the thrust control law authority limits.
The presence of side forces and the slight reduction in longi-
tudinal thrust present with the use of exhaust deflection had little
effect on the response of the model. The predominc^ control factor
was the moment generated by either augmented configuration.
Thrust deflection alone was shown to be an effect device for main-
taining control in the event of rudder control loss.
Recommendations
The following recommendations are made regarding the use of thrust
control augmentation in high performance aircraft.
1. An appropriate follow-up to this study would be to investigate
the hardware aspect in detail to determine:
a. expense of implementation
b. time responses of various control hardware (considerable
work has been accomplished in the areas of thrust control on V/STOL,
26
Idhllll t liWiTllMllii»-"-''-"-'"-"-' ^—■■•— -^-~^i--~.^-.-^ -.,---:. |,|||-i,-.,rMMi^iilÜ|fci*aaMITi -Jfcijfl*-' .J-.-..^-:-^^T_1-^.^.,^J.^J-. ■ ^_;.:..^_,-^_ ^„.„^ , ...^ -:-_.,.,..,,...,.,..... ... ........
n.J. UI.L".."WWJJ.ii- pai ■ ) 'lM-^P-"Jlipj,U Uli.» Ll.^ l.L I) .III ,l|ll!) a".?'1 ■-:"W-Jtt''ja.-*^l'"l^'Wa»M'Wl'.>
t \
4
( •
GAM/AE/73-14
aircraft and RCS rockets on re-entry vehicles).
2. The use of augmented control by thrust vectoring should be
applied to other multiple and single engine aircraft with histories of
lateral-directional stability problems at high angles-of-attack.
3. A suitable criterion for determining the. departure point in
the six-degree-of-freedom, non-linear simulation needs to be established.
This would allow the calculation of an a-8 maneuver envelope from the
computer simulation.
27
., -.v,,^-.-.^.,-.,...,-.-.... . ■—-.^^.^.^^.t^i;.,^-. _„. ...... ^.-...i^^,, iwüüünufc'Mgw-TiiB 11 ■—i i to ■■--'— '- — älüMM■"•*-■
-i-i iFie*!,iiiiu.w."iftu ii.i...m Um HBÜWBDH
GAM/AE/73-14
(
Bibliography
1. A Proposal For A Stall Inhibitor And Automatic Departure Prevention Device. CAL Proposal #3362. Buffalo^ New York: Cornell Aero- nautical Laboratory, Inc., October 1971.
2. Adams, William M., Jr. Analytic Prediction of Airplane Equilibrium Spin Characteristics. NASA Technical Note D-6926. Washington: National Aeronautics and Space Administration, November 1972.
3. Advisory Group for Aerospace Research and Development. Fluid Dynamics of_ Aircraft Stalling. Conference Proceedings #102. North Atlantic Treaty Organization, France: AGARD, April 1972.
A. Aeronautical Systems Division. Ad Hoc Team Report on F-lll Stall/ Post Stall/Spin Prevention Program. Wright-Patterson Air Force Base, Ohio: ASD, August 1970.
5. Air Force Flight Dynamics Laboratory. Stall/Post-Stall/Spin Sym- posium. Wright-Patterson Air Force Base, Ohio: AFFDL, December 1971.
(
6. Bowser, D. K. and T. J. Cord. Post-Stall Transients Computer Program. Wright-Patterson Air Force Base, Ohio: Air Force Flight Dynamics Laboratory, September 1972.
7. Burk, S. M., Jr. Exploratory Wind-Tunnel Investigation of Deploy- able Flexible Ventral Fins For Use As An Emergency Spin Recovery Device. NASA Technical Note D-6509. Washington: National Aero- nautics and Space Administration, October 1971.
8. Carlson, N. G. Development of Flight-Weight Deflection Device Ana Actuation System For TF30-P-:-. Engine. i'WA-3266. Harcford, Connecticut: Pratt and Whitney Aircraft Division, United Aircraft Corporation, December i967.
9. Chambers, J. R. and E. L. Anglin. Analysis of Lateral-Directional Stability Characteristics of A Twin-Jet Fiahter Airnlane At Hii'h Angles 01" Attack. NASA Technical Note Ü-5361. Washington: al Aeronautics and Space Administration, August 1969.
Nation-
10. Chambers, J. R.; E. L. Anglin; and J. S. Bowman, Jr. Effects of A Pointed N£se On Spin Characteristics Of A Fi ghter Airplane Model Including Correlation With Theoretical Calculations. NASA Technical Note D-5921. Washington: National Aeronautics and Space Adminis- tration, September 1970.
11. Convair Aerospace Division. F-lll Loss of Control Characteristics. GD Report /'FZE-12-392. Fort Worth, Texas: General Dynamics, CAD, August 1972.
28
*MW^^^W»-. ■ in n
GAM/AE/73-14
O 12. Convair Aerospace Division. F-lll Stall/Post Stall/Spin Prevention
Program. GD Report #FZE-12-366. Fort Worth, Texas: General Dynamics, CAD, July 1971.
13. Convair Aerospace Division. Reduction in F-lll Stall Accidents Through Stall Inhibitor and Landing Configuration yarning. GD Report. Fort Worth, Texas: General Dynamics, CAD, July 1972.
14. Dynamics of the Airframe. Navy Department Report #AE-4 II. Washington: Bureau of Aeronautics, September 1952.
15. Eckholdt, D. C. and M. S. Dittrich. Performance, Stability and Control. United States Air Force Academy, Colorado: Department of Aeronautics, 1967.
16. Etkin, Bernard. Dynamics of Atmospheric Flight. John Wiley and Sons, Inc., 1972."*
17. Gilbert, W. P. and C. E. Libbey. Investigation Of An Automatic Spin-Prevention System For Fighter Airplanes. NASA Technical Note D-6670. Washington: National Aeronautics and Space Administrations, March 1972.
18. Grafton, Sue B. and Ernie L. Anglin. Dynamic Stability Derivatives at Angles or Attack From -5° to 90° For A Variable-Sweep Fighter Configuration With Twin Vertical Tails. NASA Technical Note D-6909. Washington: National Aeronautics and Space Administrations, October 1972.
19. Greer, Douglas 11. Summary of Directional Divergence Characteristics of Several High-Performance Aircraft Configurations. NASA Technical Note D-6993. Washington: trations, November 1972.
National Aeronautics and Space Adminis-
20. Hancock, G. J. Problems of Aircraft Behaviour At High Angles Of Attack. AGARD-OTAN DPP/16A/67. North Atlantic Treaty Organization, France: Advisory Group for Aerr-pace Research and Development, April 1969.
21. Klinar, W. J. A Study By Means of A Dynamic-Model Investigation of The Use of Canard Surfaces As An Aid In Nocovering From Spins As A Means For Prcv/ntin-": Directional Divergence Near The Stall. NACA Research Memorandum L56323. Washington: National Advisory Committee For Aeronautics, May 1956.
22. Libbey, C. E. and J. S. Bowman. Radio-Controlled Free-Flight Spin Tests Of A 1/9-Scale Model of The F-111A Airplane. NASA Technical Memorandum SX-2008. Washington: Administration, May 1970.
National Aeronautics and Space
29
" -"-trtt. |
r fflvppmi Li.«.." «.. ■ ■■■I . t.LmiMVM.UK ■*■.■■ Jll
GAM/AE/73-14
C
23. McElroy, C. E. and P. S. Sharp. An Approach To Stall/Spir. Devel- opment And i'er.t. American Institute of Aeronautics and Astro-
nautics Paper #.71-772, July 1971.
24. McKinzie, G. A.; J. H. Ludwig; E. N. Bradfield; and W. R. Casey. P-1127 (XV-6A) VSTOL Handling Qualities Evaluation. AFFTC Tech- nical Report No. 63-10. Edwards Air Force Base, California: Air
Force Flight Test Center, August 1968.
25. Moore, F. L.; E. L. Anglin; M. S. Adams; P. L. Deal; and L. H. Person, Jr. Utilization Of A Fixed-Base Simulator To Study The Stall And Spin Characteristics Of Fighter Airplanes. NASA Tech- nical Note D-6117. Washington: National Aeronautics and Space
Adminstration, March 1971.
26. Morello, S. A.; L- H. Person, Jr.; R. E, Shanks; and P.. G. Culpepper. A Flicht Evaluation Of A Vectored-Thrust-Jet V/STOL Airplane During Simulated Instrument Approaches Using The Kestral (XV-6A) Airplane. NASA Technical Note D-6791. Washington: National Aeronautics and Space Administration, May 1972.
27• Program Management Plan, Advanced Development Program, Stall/Spin. PMP RCS: DD-DR&E(AR)637. Wright-Patterson Air Force Base, Ohio:
Air Force Flight Dynamics Laboratory, March 1972.
28. Weissman, Robert. Criteria For Predicting Spin Susceptibility Of Fightcr-Tyne Aircraft. ASD-TR-72-48. Wright-Patterson Air Force
Base, Ohio: Aeronautical Systems Division, June 1972.
29. Wright Air Development Center. Airplane Spin Symposium. 57 WCLC- 1688. Wright-Patterson Air Force Base, Ohio: WADC, February 1957.
( .
30
.. ^■---■^-.._J_--„^^„. Jjma^,- if Uliil lillilir'ir " ' — -■'<•■-■ ■"■ J-^--*»tJM"'iit^.w-^.:„-^:1^^^ ■,.--■..-.>- .-.a..
>, , ..«.I—^.>l>—l W 1 ! ■ ■ ■'■ m '" - "I.- m ■- HUPBW
GAM/AE/73-14
Appendix A
Aircraft Model Data
(Ref 20 and 23)
A three-view of the F-111A modeled for this evaluation is shown
in Figure A-l. The non-linear aerodynamic coefficients and derivatives
are prssented in Table A-l. The following are the aircraft model
general parameters.
Overall:
Length 72.13 ft
Height 17.12 ft
Weight 50,000 lbs
Wings:
Span 63.0 ft
Area 525 ft2
Sweep 26c
Mear Aerodynamic Chord 9.04 ft
Aspect Ratio 6.97
Inertial Terms:
50,000 ft2 - slug
315,200 " "
xz
,351,500 "
. 0
. 0
u
31
"' -■ "'m mi 1 MMdMJMT , |^i,- >,„,----■
.■t-.j^K^fii .1.1}mmipp. . ■ -■■ .■■iiinuui.j-wiiii. 'iwii'Mi BW|WWgiHiPWIWWIgfllWWPBPIPtWWWPWBPi
"1 GAM/AE/73-14
Maximum Control Surl'ace Deflections:
C)
(
6e 10, - 25 deg
6 a ±15 deg
6r ±30 deg
32
..-^.^.^■-~^ ^-■^-^:,J-J^-E,^i^ -- - ■■ ■ >.—, ^^^^ü^^— >,
ij**Mj AJiIU-.-WVIT ».i■. '■■ njijtjgy»'■■nff.w.iPJffBm,JIMmh*"r- >i..w.H»*'BWW!I-""W.'. I.IIUMin P.wwi. ipi■ im,!, uwwii,w«....n,i,■■■! »u..Ljjipi-^m «Pvi.m ■■-■. i !»i^ i PII im nm läppWWIIH HUBS WWü.wuPW J | tmmmmm^^^m'^^'m^vimm^mmmiif!m^r^^mm^^^nr^
GAM/AE/73-U
C
FIGURE A-l. Three-View of the Aircraft Configuration.
33
'■--""- ■■-■'- ■■ -- —■i^--* ^-■■■■-^ -^- ■ -■■■■■ ■■ '-•"--■■^--—■-'•*--■ ■■■^■- f.-,,- ,-~-^ at —„„...-—
r
mmmmxmmm -" ii i in» i i W«™W"1I i .. .u.iJltH
GAM/AE/73-14
( ooooooooooooooooooooo OOOOOOCOOOOOOOOOOOCOO «l-J-JWONHCO-J^CMJMninMflOHNHrl OOOOrHCMcn-*r\OrHmc>encMrHOOOOOO
o
"8 u
ooooooooooooooooooooo ooooooooooooooooooooo t^r^t^t>-COeM\Dr»COCOCOCOvOa\lMOrHrHrHrHrH HHHHHNNNNNHOHOiBOHHHi-IH
I I I I I I I I I I I I O I I I I I
( >
*o « O o o o o o o o O O o o O O o o o o o o o
u I-l O o o o o o o c O c o | ^ o O o O o o o c o r*> CM en \D en r-\ o n m o ON Cl CO CC T—1 r-~ ON CO rH CN o vO
o i-l rH IH rH o o <r o CM r» CM rH r» ̂ O CM <r rH o o rH rH
o rH •H 1 CM CM 1 1 w
W *J C <U •H u «H «4-1
rH 0) O 01 < O o O o o o o o O O o o O o o o o o o O O o A rJ O o O o a o o o o o a c c o o o o o en O o
w o* <r C\ ON \D CO cc o 00 ^C CO m c I-- LO r^ m o o en <r m ►J u CJ h r-t I-l rH rH rH r—', iH rH CM en in O in -3- CM rH rH rH rH rH rH
§ 1 a , 1 1 1 1 1 1 1 1 I I 1 1 1 1 1 1 1 I , 1 H 8
& o u <
<fl O o o o o o o O o o o o O o O o o o o o o Pu U O o o o o o c o o o o o O o o o o o o >—s o
c I-l rH rH rH rH o rH 0> ^c CO o v£ o <r rH r-- m m ̂ ** <r m o rJ o o o o o o o rH rn m ̂ T r^ rH rH cn <r o rH o o o
I I I I I o I I I I I I
«0 P. U
5n u u V a
ooooooooooooooooooooo ooooooooccocoooocoooo envocMo>en-j-env.ocr>'^vO<no^3-<'Coo^3'CCr-Hen OOrHrHCMCMCMCMCMCMmCMr^inrHrHOOinvDr^
HHrl I I
I momomomomo'nomomomo
rHrHCMcMencn«3-vjmmvDvcr>r»oücX3o\
V,
J
"1 GAM/AE/73-14
id «o
o
60
n 0) p.
ooooooooo\oooooN<jNO>o>o>r^voir>in«3-mv£>mcM ooooooooooooooooooooo ooooooooooooooooococ. o oooocoooooooooooooooo I I I I I I I I I I I I I I I I I I
«a «o e
60 V TJ
u <u p.
OOOOOCOOOCOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOO
I I I I o
60
u
OOlHOOiH'HrHi-lr-'CNrHOOi-imfOCSfvJCMC^ ooooooooocoooocoooooo OOOOOOOOOOOOOOOOOOOOO
i * r r i r r r
n «j
• g 4J •H C U o •H o i»-l «*^ »»./ >U 60
0) (U fH o n 'O
1 u «o <! c* VJ
o o Q>
3 1 3 •a
o
60 <U
u •a o
c u u 0)
a.
OOOOOOOOOOOOO OOOOOOOOOOOOO OOOOOOOOOOOOO
MWHOOOHN OOOOCOCO O C O o c o o c oooooooo
o O O I I
T-lrHlHr-liH^r-liHO T^vOvOvCvO^CvOvDvDvp oooooooocc
OOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOO
I I I I I I I I I I I I I I I I
u 60
u 4)
lf|<JWHO\ONnN<MT|^OvrHOin-*lftOLlOO «nrof^roP'inrOr-irncNrgr-ii-i-.tr-ioCOOOC OOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOO
I O I
Jd 60 (X t)
33 o »n r-( I
I
Oi/"i©"">oiriOiAciriomomoinomo i-iH<NCMmfnv3-<j-inirivo^of^.r«.ccooc>
35
— -
*——"«'■'— ■ < ■-.—
GAM/AE/73-14
c O 0)
0*
ooooooooooooooooooooo OOOOOOOOOOOOOOOOOOOOO «tf«4<rcMaifir^O<NOcni-iOOCOOOOOO oo©«tff»cs\or^r^<rivoooooooooooo
N(NNNNCMNnn'*'Cf<'H I CO CM I I H N I I I I I I I I I I I I I I I I I
00 o>
U 0)
"tM<10flNO<OHiON>»<JN<*00000 voo\OOOrHrvi«crr-.vOTH<Tr^i-|cot-i>*'<f<-«a-«j-
©oooooooooooooooooooo I I I I I I I I I I I I I I I I I I I I
to 01
o» -a «o
N M U 01
Oi •w
ID 4J
/•""s c • o> *J •H fi O o •H o U-< /-N v-/ IK 00
01 0) H o 01 *o
1 u «o < X n
u O 01 M 1 p. ►4 V-*
§ a) I •a 0
01 <
Ninifi^-*incoo>jio(M»o>jNoo>ooootsN lHt-li-lr-li-li-li-tCNrMCNCMr-l.-^iHi-tCi-lf-HOOO OOOOOOOOOOOOOOOOOOOOO
I I I I I I I I I I I I I I I I I I
rHmOminvor^oococMr-tmrooomr-.cNOCM^Oi-i vciiri-jnMrioCnNn-jvt-j-ctiAioininvo OOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOO
I I I I I I I I I I I I I
ooooooooooo^ovrcMocNoovi-oo OOOOCooocor^-crimONCO<rc'ja>f*">cy>G'>
I IrHHrHtMCMrHrHiHrHrHr-lrHr-liHrHiH I I I I I I I I I I I I I I I I
o
OOOvooo.-it-it-iooomr-vJ-SNi-^vToou-ir^cvifM
OCNJMCMO^fi^CTvONr^-jOf^fOmcoromvj^-^- OOOOOOOOOOOOOOOOOOOOO r r r ,•••••■ ° •
,C 60 0. 0)
O u-i o I
m oinoinomo^noinomomomo Hr-tr>4cMnmsr«3'inm\c>\or^r>.(»ooo>
3G
■■-_■- -^ ... ■ n i it I nt ■ r
wnm '"" ■"" ,™,u,..j.i, . ■J.wiii«
GAM/AE/73-1A
ooooooooooooooooooooo
ooooooooooooooooooooo I I I I I I I I I I I I
OOOC OOOOQOOOOOOOOOOOO O soi^^vccNvoooooiricosrr^r^eocMOooocir»» ei nncinciNOHNNnciHOHM<nflNH ooooooooooooooooooooo
I I I I I I I I I I I I I
ooooooooooooooooooooo CM nnnrtnNOHNnnNONHONNHOO
ooooooooooooooooooooo I I I I I I I I I I
ooooooooooooooooooooo \Ov£>mmv£>CMLO>£)>-tr~i-(nrTl^a3CX3i-HvCt^<-00 HHHHHHOONMNHOrivfnMOOOO ooooooooooooooooooooo
I I I I I I I
c o u
4: M i
0>
o I co
■ •rl Ü
•H «n **-! cu o o CJ
1
o rH
I
o CM
I
ooooooooooooooooooooo ooooooooooooooooooooo oooocoocooococoocoooo ooooooooooooooooooooo ooooooooooooooooooooo
ooooooooooooooooooooo NNMNNHOOMNNHHPl-}>JNOHHrl ooooooooooooooooooooo
I I I I I I I I I I I I I I I I
ooooooooooooooooooooo N^NCn-j-jH^mTOCmoonnNir, <r iy\ ooooooooooooooooooooo I I I I I I I I I I I
o
< o CO
I
ooooooooooooooooooooo •j^stnnciONnNr, rirtOHsiionMHO ooooooooooooooooooooo
o oooooooooooooooooooco <-<j-nnro^joMfvJ'-ftnsTfOfn<rr->p^u-inmf-j ooooooooooooooooooooo r i* r r r r ,••■••••
It 60 U 0)
33
I lOOiOOiOOi/^. o
r-< i-( CM CM CO Cl vj omomomoino ioio>j3vor^r»-ooooa>
i
L 37
■MM
-i ..J.-II.. < iiii.iu. ■ II ill i II. II lll.JIUJI.ipi ■"» ■""" I. '■"■'■ I —^WWH^^<^li—«^P*^W^^»^"WW
GAM/AE/73-14
o
s u
OOOOOOOOOOOOOOOOOOOOO OOK10CC!J<HN«03hONfl»TvOOOOMiON(0
• fOONinMJvOWOsf-*>OMCOCCCOi3iW(MPOV O OOOOOOrHOOOOOOOOOOOOOO
* o {\ i* r r r r r r r r r r r r r r r r
ooooooooooooooooooooo • h'JvtUlNHOOlNCN^N'^ffiONCIrt-JUl
O t~<ocN<j'vot^.r^u"i«.l-roc>-s-iriOvOf-»r~.f-^r"-r>»r-- ci ooooooooooooooooooooo
f i* r r r i r r r r r r r r r r r r r r
OOOOOOOOOOOOOOOOOOOOO • '«fNNWiCMCOHinNM'IOiflHNnNOHM
O ooNn-j-a npiHHHNn-jiriinininunom es ooooooooooooooooooooo
f r r r r r r r r r r r r r r r r r r r
ooooooooooooooooooooo sriONHn^no\oc rooMONOoor-*voo^or-» OOHNNCMNHHOCOHHNNCJHOON ooooooooooooooooooooo
i r i r r r r r r © r r i i i i i o r r
ooooooooooooooooooooo o? ooooooooooooooooooooo w o ooooooooooooooooooooo
<*». ooooooooooooooooooooo ' I
*J ooooooooooooooooooooo G CO 0 4J o c
•H H o • ooooooooooooooooooooo
1 «rl O r-lrOOOf^OOCTsvOr^vCr^mfNCOCOOr^OI-^^CS < «M iH OOOHMNHHOCCCOrNMNMNNM
<H I OOOOOOOOOOOOOOOOOOOOO W <u : ►J O III
§ o
ooooooooooooooooooooo C O <J^NO<rOn^Nin(0<r!OCMNNN5iff\0 >> <N OON<t>j>JMHrtHOHnininnLiir, >i<Mfi
"O I OOOOOOOOOOOOOOOOOOOOO o U I
• OOOOOOOOOOOOOOOOOOOOO O r-frirrivo00omr~-o>nf**ir~tnoorvJ'>jrorvlc>j(vl «*> r-locN<-vov£>>ß«crcici:^r'->or-.r~-.i-»r-.r>»r^.r--.t^ I ooooooooooooooooooooo
II*'
• ooooooooooooooooooooo O o>H-<tt-ivov£)vou~iLnr~icoor-Ha>r^-r-(tNninmv£) •» i<iHNifliNai!rii^vOinnvD^cocoov5\Cimc\a>
I ooooooooooooooooooooo I I
momou">omoinou"iomou">oi/"io"">o I i-t<HCNf>4rorosr<i-u-iuivOvor^.r-.coeOai
(0 00 4J <u <u •a m ^
rt ^~\ X 60 tu <u H "O
38
r GAM/AE/73-14
O
«NOOOOOOOOOOOOOOOOOOOO • o\vDo<oeoMCi\OHirnotsn<fin^OMOOin-J
«* Ht^srsrvj-fOforosi-invrMoor-isTi^ooot-ftN ' l' l' i' I'HH'H
I I I
o CO
©oooooooooooooooooooo
HcNCMCMt-iooooooooot\isrr-»a>rHmsj-
I I I I I I HrlH I I O
OOOOOOOOOOOOOOOOOOOOO • COVßl^.vOOU~lrHrHr^f^Otnr-|CMC-|Ovr><^OOCN|CM
O «*coH«Nc*iHCMvo<rr-i<rvOCT\oocor»-oa>ocMrv fN CNHi-lOOfMrorofr)fOmcso>-<<yisJ-r~a\fOirivo
I I I I I I I I I I I I I I I I I
I u V
o
OOOOOOOOOOOOOOOOOOOOO H\omO{Ncoci,-ir~cMc7NOr^cc\ioorgoor-inro o^r-voinvocsiooorrirHr-)inO'HOO<rrHaiOCT\<r
I I I I I I I I I I I I I I
OOOOOOOOOOOOOOOOOOOOO a>ronr~-oooo<jr-it-ic\ror-vDr^romro>oi»c>-3' csr»»vr>c")«.-rrHocor")r-»Ot-ir--i<roOLrir-ic^i-ir>.
o
4J Ö m o *J O ti w <U
•H H o
1 ■H «5 <4J
«4-1 W OJ ■J o Sq u
I I I 1 I I I I I I I I I I I I I
• OOOOOOOOOOOOOOOOOOOOO O ^c^HiHcNc^r^c^ror^roin^rinoomooc^^-r-ir-i
i i r i i i i i r r r r r i' H pi H H I I I I
1 O
3
OOOOOOOOOOOOOOOOOOOOO cs oimf-'roe^f-ic^cMcNco^rr^r^^i-icMcMccr^voo I HrHiHOOtNfsirOrOc-4^JrHiHcM-*vDOOOf*"l'ni~~
I I I I I I I I I I I I I I I I
OOOOOOOOOOOOOOOOOOOOO tn*tfvocjor-rHrooocMcsjro<r.-Hc*inr~r^cQLnco HNNNHOOOOHHOOHNinNO>Hn>J
I I I I I I I I I
• OOOOOOOOOOOOOOOOOOOOO •» «-(cncN4iHt-<r~c^ioocrifrioo<rr>.c>jooa>rHvDoror^
I I I I I I I
(0 60 *J <U <D -o pa \~*
H) /-v x. 60 a <V
SI
U1 I
o m o i/ioiooiAo»/'tOirio«no rHCMCNmm«*<i-inirivtjvor»
•r. o "■> o r* oo co o\
39
r ■ ■»Uli
GAM/AE/73-14
ooooooooooooooooooooo • fMrHOOi^'-<OvjDr*!-ir--c^mcvj.-tm^c»3,ma\>»
O »3-vo**iH\ocNi^r->>3-T-i<r<rrjc»ioooo»3-cMiHOO
o I I I I I I I I I I I I I I I I I I I
8 ooooooooooooooooooooo i-)rHtnr^r-o>r>.<Mnr>.vocMOO-3"-*rr>Ot^OO
I I I I I I I I I I I I I I I I I I I
OOOOOOOOOOOOOOOOOOOOO
O pJ<Noco\x>mcNOO<ri-J-oooocovoomr~r^r^ui «v| ficorocMcMpsicsiHHeMCMmcncMCMnforOfOOfo
I I I I I I I I I I I I I I I I
OOOOOOOOOOOOOOOOOOOOO ifl<*NOOo\coifiH<rijv(NcN»io«jrso<*»oeo HiHrHiHrHOOOOOOr-lrHOOOOrHiHrHr-l
I I I I I I I I I I I I I I I I I I
o 4J c n o 4-1 O C \^ CO
•n ft t)
1 •H < <♦-(
«w w (U .J o pq u
o r-i
I
ooooooooooooooooooooo ooooooooooooooooooooo OOOOOOOCOCOOOOCCOOCOO OOOOOOOOOOOOOOOOOOOOO ooddoddoooodooooooodd
ooooooooooooooooooooo incoi^.p,iOvoc\!HcriCNiav<rc>oc">o*3-r--a\Or-» HrlHHHHHHHriNNNHHHHNNnn
•a o
I
o I
ooooooooooooooooooooo •?riH*N.nt>jiriioocN<nn(n^NNvori
• ooooooooooooooooooooo O vo^r^CTifiocMOO-crtHcNr-iorNvrocmi-ivoo
• OOOOOOOOOOOOOOOOOOOOO O MOMNniOH<J-ia!NNNfl0OIOri00CMflO «» <}'COoor«-<ror~»eo.v3-r-ir>in^(rtr^rHComr-i^HCN
o (0 M 4J 0) 41 "O
.c to
33
OvAOiOOmOUIOiAOiOOmOmOiriOiOO iH i r-trH<Ncsfntn<r>3-4nir»vo>or^.f^oococTi
I
40
™ ■* ^----v- ■--.-».j«Pi..ii-.«j-jlii ..■iw..i,i>jj.HVw«i>fi;iil j;j.iiij.ij.wii«iii.ii■»].,,iMi i|«BnMMM^IM!PPW^^P^^u!<*n9^WP«|mnpRnpW
GAM/AE/73-14
o Appendix b
Equations of Motion
(Ref 14, 15, 16, and 25)
Assuming
1) negligible earth rotation,
2) negligible changes in moments of inertia,
3) x-z is a plane of symmetry,
4) h is the only significant rotor term, and
5) negligible changes in the rotor term,
the force and moment equations in the body-fixed reference frame
(Euler's equations) are
X - mg sin 8 = m[u + qw - rv]
Y + mg cos 8 sin <t = m[v + ru - pw]
Z + mg cos 8 cos 4> ■ m[w + pv - qu]
L " V " Xxz (* + pq) " (Iy " V qr
M " V " X» (r2 - p2) - (I* - V *> + r W H - Itf - Ixz (p - qr) - (Ix - Iy) pq - q^u.
Rearranging the equations for use in the computer program,
u B g" sin 8 - qw + rv m
v ■ — ■*• g cos 8 sin $ - ru + pw
w ■ — + g cos 6 cos i> - pv + qu m
(B-l)
(B-2)
(B-3)
(B-4)
(B-5)
(B-6)
(B-la)
(B-2a)
(B-3a)
41
-■■"-■- ■- ■■•-■" Wj-.JJMBM^a^afa^M^^^il^Ui^B^i
GAM/AE/73-14
p • (I t + I N+I (I -I +I)pq v z xz xz v x y z' ^H
C (l,ly - I22 - Ix2
2) gr + lxzIrgg)r} (B-4.)
q - \ {M + I (r2 - p2) + (Iz - Ix) rp - rl ü>r) (B-5a) y
r - \ {N + Ixz (p - qr) + (Ix - I ) pq + q^W.} (B-6a) z
Using the proper transformation matrix to obtain the Euler angle
rates from the angular velocities,
<J) «• p + q sin <j> tan 8 + r cos <j) tan 9 (B-7)
8 - q cos $ - r sin <J> (B-9)
\Ji « (q sin <(> + r cos 40 sec 8 (B-9)
To record the changes of altitude, down-range distance, and cross-
range distance, the earth surface reference frame is used assuming a
V . - flat earth approximation and positioning the origin at the initial air-
craft position.
x ■ u cos 8 cos ty + v (sin <f> sin 8 cos ^ - cos (J> sin \JJ)
+ w (cos <J> sin 8 cos i> + sin <p sin ty) (B-10)
yo ■ u cos 8 sin + v (sin 4> + w (cos <{> sin 8 sin \\> - sin <J> cos 4>) + v (sin (J> sin 8 sin t + cos 4> cos i|>) (B-ll)
z ■ -u sin 8 + v sin 4 cos 8 + w cos A cos 8 (B-12) e
The preceding equations (B-la through B-6a and B-7 through B-12)
constitute the state equations used in the computer program.
The aerodynamic angles are described in the body axis reference
frame by the relations:
a - tan"1 - (B-13;
ß - sin"1 ^ (B-1A)
42
,-■■■■ - ,»„.iä. ■ , ■ ^-- .w- ■■_>—- -,-,■ „■ nYr „- ,,a ^^^Ij^-jj^
GAM/AE/73-14
Derivation of the equations for the rates of change in angle-of-
( attack and sideslip:
Differentiating equation (B-13),
• . H2 -w" (B-15) u2 + w2
Differentiating equation (B-1A),
& - V^l_ (B-16) VW -v2
where,
V-^ü + ^v+^w (B-17)
The forces (X, Y, and Z) and the moments (L, M, and N) are
separated into aerodynamic and thrust effects. The aerodynamic
effects are expanded to suit the data package as functions of angle-
( of-attack, angle of sideslip, angular velocities, and control surface
deflections. The aerodynamic force equations are:
1 „ „2 x6<
Xaero " 2 P V' S (Cx + C~- *e) <B"18>
Y - ~ P V S [C + C 5a + C <5r aero 2 y y6 yß b (B-19)
+ fv (Cy P + Cy r)l Jp JT
Zaero " 1 P V* S (Cz + Cz, *e) <B"2°) oe
Laero " 7 P V' Sb ^i + \ 5a + \ 6r + |v <C* * + H *» oa or p r
(B-21)
M .« " \ p V2 Sc [C + C 6e + §- C q] (B-22) aero 2 m m. 2v m nJ v ' oe q
N ^ ^ p V2 Sb [C + C 6a + C 6r aero 2 l n nx n. 5a 6r h (B-23)
p + C i n P r
+ 2v(Cn P + Cn r»
43
^.■j-^-i--^^... - ■-,.-,, ....-.-,-.■■ ttUfj^nmm ng
.M.. . — „I ...... —""-■"-' '' ^"-Ul.i.1 .1 . i..i.!ilnw^1^!PHJiaHlWM ^WPW™MU«».I.II.....IM. i..
o
c
GAM/AE/73-M
The thrust effect equations are developed in the main report.
C FIGURE B-l
Body Axis Systen and Related Angles
44
■ iiiiT —• ii . mat -- -,,-~-~-°-|Mi^—ii
■ >■ w mi i"T" Wft
1 GAM/AE/73-14
(
Appendix C
Simulation Results
o
c
45
---—^ — ■---"- - ii ^■■i|-
.7M>-«»!»p* , .m... ■—■ -■■■■ ! ■ -■«-■■■., '■■'■■■■
c.
GAM/AE/73-1A
o I
»♦♦♦ ^♦♦v~:
♦♦t ♦ ♦
0.00 f.00 16.DO 14.00 36. DO 40. DO ALPHA - DEC
«.DO 66. DO «4.00 7». 00
i /
Aw ♦ ♦
..♦♦*
O.OD i.aj If.DO (4.PO JC.C0 40.00 41.00 ».DO 64.DO Jt.DO ALPHA - DEC
UJ.
T^f^K a> .»*V<
~„ *-t
0.00 1.00 If.00 «4.DO Jf.00 ALPHA
40.00 OEC
4(.DO 66.00 (4.00 7C.D0
«<UN NUMBER •43146
FIGURE C-l. Lateral Stability Characteristics
(Exhaust Deflection/TVAU - 50%/Lower Authority Ranges)
46
_ — ■
GAM/AE/73-14
w*^^^mmw-»»"W"* «iJJULJi4A«M.ii
C 1
e
!- (CD
f w
I V e o
e _ o
■
U.D- 1
K 4~
CD»
if a
e *D
s
4*
hi 1
>-D
fe- hl
T* i°.
e
4
♦
♦ ♦ ♦ ♦ ♦ 4 ♦ *
•
♦
4
,00 10.00 tÖ.DO 3Ö.D0 40.00 (6.00 (Ö.DO TO.OO »6.00 ALPHA - DEO
1 /u; , 4 ♦ ♦ *
«0.00
.00 10.00 tO. 00 30.00 40.CO SO.DO (0.00 70.00 80.00 ALPHA - DEO
* 4
* 4 4**
4 ^ * t* 4»
<mm***i,t?+Lm. jm-*—?*** *♦ 4*»
30.00
- rV • - . 4 4
4
4
V .00 10.00 tO.TO 30.00 40.00 (0.00 (0.00 70.DO 80.00 ALPHA - DEC
RUM HUtlSER -4$lit?
S0.00
( - FIGURK C-2. Lateral Stability Characteristics
(Exhaust Deflection/TVAU ■ 100%/Lower Authority Ranges)
47
■:-—---—Ml -•*-■- --■-— tutttt ^1
^■H^FWPWW^IW .in uniiLj..i..Ultimi» Hi ii i —u I I.I..I.IIL. ■■'"-»Mlll»ll|l.¥ll .1,1.1 I. ..-,
GAM/AE/73-1A
( * M
♦ a
o u. b
CO
♦
♦ ♦ ♦
B ♦
VoB t'.OO It.00 «4.00 «.DO BLPHfl
40.DO 4f. DO «.DO 64.00 7t.0O - 0EO
Jk
o
bo ■ / V~ £"• i a >—
bin «ob
u
♦ ♦
♦ B ♦*».*-*
V öD i.ao ic.po 14.00 x.oo ALPHA
40.00 48.00 «.00 M.00 H.D0 - 0EG
-* •"
*
m
W X
i-"
CJ»-
1 ^ * ♦ •♦♦* . ***** ♦
1 *
S 1
V.OD «l00 1».DO (4.DO «.00 flLfrlfl
40.00 4».DO W.DO M.00 Tf.00 - OEG
RUM NUHBER -4314$
FIGURE C-3. Lateral Stability Characteristics
(Auxiliary Thrusters/TVAU - 50%/Lower Authority Ranges)
48
- — .
M.I M.l-J-M..!.LJ!!PP*PII. <^l..iipjHi.Mll.lll .LJI,lll7 LJLIf^WWWIIMiJP»l»»WPI ■ ■.I . ■ i ■iiuiiLnuB m ni,<Mi« 9VPPPQOT
GAM/AE/73-14
o
o
c
s 1 t»!
r MM ■ wtuwpfaimgii ——■»
♦ ♦ ** t
'DlOO *.00 16.DO M.BO Je.00 tO.00 41.00 SS.DO (4.00 7C.00 ALPHA - DEO
L*
fa? i
cc
J>? ^
/ ♦t
■*^
'ajio »loo l*.0O U.D0- «.CO 40.00 49.00 SS.DO «4.00 71.00 ALPHA - 0EC
ti.00 JC.00 «.w ALPHA - 0E&
If. 00 ft.00 #4.00 7C.00
RUN HUtlBEl» -43145
FIGURE C-4. Lateral Stability Characteristics
(Auxiliary Thrusters/TVAU »100%/Lower Authority Ranges)
49
- -•■— -■- ■ - - iTimrm ......— -"--,n
mi,if-.K.iji >■.!(..! nip I W.*< mti^iMiWUHJI ■ WÄPW ■ III IIIMIIHIMI ^^^^^mt ■ ■■ i IUI w^OTfM)
GAM/AE/73-14
o
/-
U
4a. w
is.ro to.oo tT.off TII1E - 5EC
3«. DO Jt.DO 4Ö.D0
B R ,', BETR COW BND
o ur °o I"..
n E
00 g
0 DEGREES
O.00 4.00 ».00 It. DO 16.00 10.VO ».00 TI(1E - 6EC
I».DO Jt.00 JC.OO 40.00
CJ©
u o
o o • 'S
a 'o,oo 4.00 1,00 11.00 Lf.PO CO.00 (4.00 tME - «EC
W.OO Jt.00 ».DO 40.00
e
o
o' t
0.00 4s.C0 •.00 lt,DO li.ro w.oo 14.00 npe -» SEC
ti.OO 3C.D0 je.oo —1 40. DO
PUN NUnBEK 101
FIGURE C-5. Simulation Time Histories
(Exhaust Deflection/TVAU =100%)
50
„f.y-..-.---.^. = -. ,—-:_, ■ ■ ._■--,-^„.^ ^ - — .^»^
TV ■ ■■..' iLL.i!"'rr.n."i ■■L««-'
GAM/AE/73-14
r
ü
wv o'
ojao
■*> o.oir
iTöö Too iiröö ij.oo to.oo ei.m wiöö jelöo J».DO «o.oo TIME; - 6EC
'olöo 4TÖÖ TOD ilTöö iOö JO, DO et. DO «üöö iOö wTöö W. DO TinE - 5E.C
4.00 1.00 lt.00 IS. DO tO.OO C4.D0 V.DO K.DO 3S.00 40.DO nne - 6EC
4.00 LOB ICOO tf.00 W,M (UDO M.OC 3C.P0 3fr. CW 40.PO nne - SEC
KUN NUMBER 101
FIGURE C-5 (Cont:.). Simulation Time Histories
(Exhaust Deflectlon/TVAU =1002)
51
, -^■■^^■^ i —■ -
r -■HI »p— 11 in i.i w, i ii I, mm 1^.,^, n, ,
GAM/AE/73-14
(' )
öS i oft
i
•-» or \ 5 *-B 5 • \ jj'OflO «'.00 1.00 11.00 16.00 M. 00 %i,00
Tint - sec ».00 tt.C» JC.DO 40.00
! öS A
i /\ l\ A A A Co COO LA •Al A at
S*5 v^ ^ \J \J \J \J 1
tt'o .OD i'.OD 1.00 IS. DO 16.00 tO.DO «4.00 TIHE - 5EC
tl.DO Jt.00 36.00 40.00
Of „ /\
A A A A f ^*S \ ^s 2 O V_/^ ^A AM 1
00 4.00- ».00 u.w 10.00 tP.OO t4.00 TINE - 6EC
».DO Jt.oo je.oo 40,00
^5.
• 1 v
E
OD 4.00 1.00 It.DO- tf.DO tO.PC t4.00 TipE - 6EC
tv.oo Jt.DO «.00 40.00
•r
,5- ~\
\
00 to. DO 40.00 10. DO •o.no loo.oo itq.oo DISTANCE - FT «10*
140.00 1*0.00 110.00 too.00
RUN NUnBER 101
FIGURE C-5 (Cont.). Simulation Time Histories
(Exhaust Deflection/TVAU ■ 100%)
52
»mm ■■"*■*—[ . imi JMMMI ■
i.jirv ■*■*■ !JI««™I p™ W,IP»yWI^WFJWi^ll.Wl.!l|..l||ll,l.„p»W,l WWPWffWW— B -mi "vmmmmt
GAM/AE/73-14
(
(
ct v UJ
1
0a
CCfc, Of' tu
SS 0.00
-'S'
e>%. »ft
•-
t»
«SO-
UTH-
ED' *Töö iTöö it.oo ip.oo tö. oo «.DO wTöö n.oo li.co w.uo TME -. 6EC
♦üö 1.00 lt.00 If.DO tO. 00 «.00 £0.00 »,00 ».00 40.00 TIHE - 6EC
«.DO I«.00 tO.ÜQ «.00 M.D0 «.DO If. PO 40.00 TIME - 6EC
=T"b.O0 4.00 8.00 lt.00 If.00 W.DO It.00 M.PO It.00 If.00 40.00 TinE - 6EC
£ 'o.oo to.oo W.PO fo.oo to.oo wa.oo ito.oo tto.oo ifo.oo IBO.OO toa.oo £. DISTANCE - rT »10
RUM NOnöEA 101
FIGURE C-5 (Cont.). Simulation Tine Histories
(Exhaust Dcfiectlon/TVAU «100%)
53
>-.^...-.l- --. w„... . -„„-„„nim i - | ■ - - - ■ iwii I
GAM/AE/73-14
* 11
e g|
•1 X
6
A ^^V— •
¥ .00 4.00 1.00 it.w i*.w to.ro (4.W tf.OO K.00 w.oo 40.00
Ö8.
Id e
•s e
!*• ?2.
A/ \/ -NM A/ \fl A/ \
v J'D.OO 4.00 (.00 it.ro if.ro u,oo ti.ro
nne - «EC tf.OO jt.ro H.00 40.00
„', Bern CÜMPNÖ
6 U
»I MB
0 DEGREES
-^
v^ A IV V 2. *0 .00 t.OO f.00 u.ro if.oo to.ro t4.ro
Tine - SEC tf.ro x.ro jf.w 40.00
«SI
Vi a
o
_ A ^ v\ fv W 1/ ^\y ^^
« 'oloo 400 t.OO It.00 if.ro to.ro t4.co TinC - «EC
w.ro x.w Jf.00 4f.W
. 2"
u «ii
o' -Ay> vA Ai ̂ A I ^ \> ' V u\ 1
s -JO i.oo »,otr ic.ro If.rO W.W «4.« line - «ec
tt.W x.w j*.ro 40.00
HUN NUtlBEK l(K
FIGURE C-6. Simulation Tine Histories
(Auxiliary Thrusters/TVAU »100%)
54
:' ■ .. ■ W't v— _^k--
GAM/AE/73-14
(
C
!
B **1
u w
*S8
u
•erf
IB.»
B
ö
»E *'
CJ
•B
Cl
«loir
0.00 4.00
/
"0.00 «Toö ÖTÖ5 lt.00 lf.00 tO.W (4.00 tf.00 JT~" ~I
nne - «EC oo s*,w «#.oo
—I ».00
0.00 4.0P (.00 IC.00 lf.00 «0. CO (4.00 tt.00 K.VO 99.V9 40.09 Tine - «c
n't.lC 4.00 1.00
ft»
nun Ntm&er lot
FIGURE C-6 (Cont.). Simulation Time Histories
(Auxiliary Thrusters/TVAU -100%)
55
-.. ^ -..--■. ...- ■
"■■"■ mmmmirn wwrBwwwii w '■ > "^ '- " ■"■"■■ ! IIIIIJHtMIWI... Ill.iWHW^—.p., "StWiPW^i BBEWW m
GAM/AE/73-1A
tf 0.00
fa f *1 (u(
JLt»
M
ti # 2T"I— te 0.09
X3'
I
2?
0.00
»9
I «*
S! *D,00
1—" I «.00 0.00 It. DO u.oo tO.PO ».DO ».DO H.W ji.OO 40.DO
Tine - 6EC
A 4.00 i.00 It .00 IS.00 tO.DO (4.00 ».DO
TME - 5EC "JTDÖ Jt.00 40.00
—I 1 4.00 ».00 tt.ro I*.09 f0.ro «4.00
Tine - sec ».oo Jt.ro jf.ro 40.ro
"\
h UK-* *-^.00 4.00 ».00
ff
1*
it.ro if.ro tv.ro (4.00 TinE - cec
n.M se.w je.» 4P.ro
to.ro 40.00 »3.00 10.ro u: in itq.ro t40.ro u:.oc 113.00 tea.03 0I6TAKCE - FT «10*
idJN HünBCP lot
FIGURE C-6 (Cont.). Simulation Time Histories
(Auxiliary Thrusters/TVAU =100%)
56
■ ■ - ■ 1 ■ II «IM—I uli,
V .'
GAM/AE/73-14
11
Ä —
8s *T>.00
if bJ
,- o.ca
SB
<'.ao
t.oo
«.to IC.W If.uO {0.00 «4.00 TIHE - 6EC
a.DO «.DO K.00 40.00
1.00 ic.oo I «.CO tO.DO €4.00 TIHE - 6EC
».00 «.DO ».DO 40.00
H 0.00 4.00 1.00 It.00
g
If. 00 to. 00 U.00 Tins - SEC
».00 «.00 IC.OO 40.00
lt.O> I*.DO to.« ».00 nnE - <cc
».00 K.VO ft.OO 40.00
nr+——i ——i 2 o.oo to.oo %o.m #0.00 M. 00 100.03 IfC.rO IM.OO '»O.OO liO.00 zto.oo
RUN NUMBER 10t
FIGURE C-6 (Cont,)- Simulation Tino. Histories
(Auxiliary Thrusters/TVAU «=100%)
57
'■■■" ■■■■ --- ■ -- ■- ii .ii ■ .. i ■■ ^tÜMUkii : __ ■ J_. :- .^ ..■■.,. ■ ■■ —■ ■- ■-■■■-
Ww^prewB ■ -i« »■ JJ. i inmiM.iiw.| »i im »Li.. ■1>I,III„.IMII..J B m . i IM
GAM/AE/73-M
AAAAT
o
< £
0*0.00 ♦»Off ».00 11.00 .«.00 tO. 03 «.00 t».O0 X.0O Jf.00 40.00 Tine - «EC
0.00 i.00 ».00
FUN KUnaCR l«
FIGURE C-7. Simulation Time Histories
(Rudder Fixed/Thrust Control/TVAU =100%)
58
i" ■■^iM'ru
».^ji^wj;wwuj.fi»iw,.iu.«i-grTwr,^|wwmt.«1.^ ■■ ■■.-' | " —^B^M
GAM/AE/73-14
D-.00
o
•) 9.00 at o: I
4.0D ».00 It.00 if.CO tO.DO (4.00 ti.DO 32.00 X.DO 40.Dv HUE - «EC
'o.oo «.00 f.OU it.ro i*. oo to.oo M.DO «.BO st.oo x.o» w.oo TIHE - «EC
« "9 ».00 »COO I«.I/O tO.W U.K TIME - 6EC
O.OO «„DO Jv-.OO «.00
RUN «unocn 103
FIGURE C-7 (Cont.). Simulation Time Histories
(Rudder Fixed/Thrust Control/TVAU =100 {';
59
- - - —- m
I III II 1.1 ^■■Jl.ll—Ijp.ljl, III,, . ,-. ■ ...v-.-r-r.
GAM/AE/73-U
C if«
\ O
\ d'° .CO 4.00 t.ao it. 00 it.oc to.00
Tin? - 5£C t*.W tf.DO Jt.OQ K.00 40.00
o
0.0 rat» — •■
de C 1 Sg
*-v 00 4.00 f.00 It.OJ I«. 00 tP. DJ Tine - SEC
«4.00 ».00 «.00 K.D0 40.00
og
1
k A A A A A ( v \ 2 e
a!.
w V —/^ ^A N\l\ 1 5
.00 4.00 1.00 It.00 I«.00 to.00 Tine - sec
tt.DO tl.00 X.P0 J«.P0 40.00
»-5
5' ZZ
.00 4.00 • .00 It. 03 I*.TO to.00 Tine - «ec
<4.00 ft. 00 Jt.00 J*.0O 40.00
i 5" ~^X ZDt» •— • \ 5T> .00 to. 00 W.03 in. 00 »0.C0 103.00 Itä.OO
OUTfWCC - FT »10 (40.00 IM.00 ItO.00 too.00
KUN NUneeit 103
( , FIGURE C-7.(Conr..). Siisulation Titr.a Histories
(Rudder Fixed/Thrust Control/TVAU «100%)
60
.-i.--^.. .i-^^-i^.,-.- ....=... ii^g, | | m f w.n-^jMlMMi^^ätiijj... .... ^.■^■■-.
■ !■■.....■'.- HI—|.IHU1iwyi»u.|.rW IJI ■>■■■■! H^ffBI
GAM/AE/73-14
fie
ui
«•!
I»
o
Sv ft:" tu
>- 'o.flo
■y-w
4.00 ».SO lt.00 [«.00 tO. 00 (4.90 TIME - 6EC
o.oo Jt.Otf UTBO W.OO
t.fio f.oo it.ca «.00 tO.00 «4.03 TME - «EC
CT.00 ».DO W.W *40.W
rsi PJJ0 4.C0 ».00 lt.00 if.M tO.00 t4.O0 Tine - sec
O.M Jt.PO W.W 40.00
It. 00 tf.OO to.DO (4.00 TlflC - «EC
tt.OO St. 30 S«.00 49.00
•»'fl.OO tO.OO 40.00 «0.00 »0.00 100.9" tto.oo 140.0* tw.oo KO.OO «pa.» £ DISTANCE - r\ «IO*
*UN nunoEK 103
FIGURE C-7 (Cont.). Simulation Time Histories
(Rudder Fixed/Thrust Control/TVAU =100%)
61
i itmnf-^-- -- ■ " --'~;—'--
GAM/AE/73-14
a! 'U.OD *!Öö ilüö ü.po ti.ro tö. po eToö w.W ü.oo »,w io.p TltlE - 6EC
BETP C0W1PND VPRIES
"0.00 4.00 f.00 IC.PO l*.PO tO.IV (4.PO CO.00 K.PO 3t. 03 4P.00
IP I
i'-K/v\A/W ±5. ö'ploP 4l0P .'.00 «■»> "-°°ln€™tC M-W *M ^ "•" "-W
HUN NUtlBCK -43147
FIGURE C-8. Simulation Tir.-.u Histories
(No Augmentation/Sinusoidal 3 ) c
62
GAM/AE/73-14
o
( •
B i
a in
5ß »-•
I
**. 'O.OD 4.09 (.00 U..P0 l*.0O td.TO C4.00 ti.BO Jt.00 K.00 40.00
une - 6EC
B
o >AA/\,
D.00
B
UJ
o
ccCJ O 0.PU 3t OS
4.00
».00
0.00 4.00 1.00
'0.00 4.00 (.00 It. 00 It.00 W. CO (4.00 tt.PO «.00 S*.00 40.00 une - «ec
(.00 It. 00 »».00 tO.W tl.00 t(.PO 3C.00 3*.00 10.00 Tine - tec
run Kinnen -«147
FIGURE C-8 (Cont.). Simulation Time Histories
CNo Augmentation/Sinusoidal 0 )
63
■ r ■ i in 111 »■■ ■!■■ || ,1 - 1,1 I ,
i. 1I.H1II..IUJ.,I.I,.I I I I -I- JHUJUWI« ■UMLUinjuiiilil, i II I ill ■>——WWg«^CT^HWBI^^»WWIIWPW^—^^W^
GAM/AE/73-14
c
c
2»
w 5*
fc.»
o*t>.oo
bi
5« 00
4.00 9.00 it.PC lt.00 10.00 M.W 11.00 it.00 5*.W W.00 Tine - «EC
ts.eo w.oo to.oo to.oo 103.00 uu.w 110.00 1*0.00 110.00 toa.co 0UTPNCC - fT «10'
KÜN NUneCR ■43147
FIGURE C-8 (Cont.). Simulation Time Histories
(No Augmentation/Sinusoidal 3 ) c
64
tiaMäiH-- ni 1*1.11 ■■-■■- a Hi —^^ -. 1 1 ^MürMf - i -~^--
GAM/AE/73-14 H ( ;
("'
fx'P.OP 4.00 l.oo it.oci
2*7 "^ 2 o.oo
"•POrt„"-l><> t«.£U> Cf.PP
Tint - 6£c K.ro x.n 40.00
£T).00 4.00 ».00 tt.ro i#.ro tp.oo M.po Tine -sec
".ro j«.oo x.po «O.PO
10.00 40.00 fo.oo fo.ro iM.oo ito.co no.oo iro.ro iio.ro eoo.ro 0I6TPNCE - FT .10
RUN NUMBEH ■43147
FIGURE C-8 (Cont.)- Simulation Time Histories
(No Augmentation/Sinusoidal 3 )
65
i ■!■ ■-iiithaiT"-''-•-*•" ■ I -•---• i i -■' -
- .MI ,r,mrmimw,«ViM— ■■* M^"' psüppn^mim
C
O
R
i
GAM/AE/73-14
tt.ro is. DO 2o.ro ei.oo tJ.ro Tine - SEC
J«.DO 40.00
o iS
o D
1 £
^5 a? 'o.oo *.OO «TOO iOö tc.ro tö.oo ei. DO zi.oo jt.oo äOö w.oo tt TIME - SEC
8
BETA COWlflND VARIES
'0.00 4.00 ».oo it.ro ts.ro to.oo u.oo ZS.DO jt.oo K.OO 40.ro HUE - SEC
UJ
' ß
O 'o.OD 4.00 f.00 tt.ro tf.ro lo.oo «4.00 tt.ro it.ro sc.ro 40.00 tine - SEC
RUH NUnBER •43146
FIGURE C-9 . Simulation Time Histories
(Engine Dcflection/TVAU »100%/Sinusoidal ß )
66
■ i 11
GAM/AE/73-14
-—m .... m pu i. HI . w» ■ «,-.. -»..... «-<-. i^——.. r"—••■"-*-—-»'*■ 1
n
( :
c
0.00 4.0D f.OP It.00 16,00 (0.00 ft.00 TME - 6EC
».00 «.DO 3«. 00 40.P0
40.00
HUN Nunaen -43146
FIGURE C-9 (ConL.). Simulation Time Histories
(Engine Deflection/TVAU =100%/Sinusoidal ß ) c
67
-J.^.-^Jfc>-^>.^Ji^1||-jI| -,-:--.■■....:.■■ ■ , ■■._.■
r GAM/AE/73-14
■ f« ^pppppfiwpi WLI'II HI JIIII i.Ji.jlMWWWWPWi^^^g^W^*^ ni.Jiiii.-t '■■
O
o
v.,
«8 a3l
ri'D^OO 4100 ».0D H.DO 16.00 10.00 t\.0O HU» «I» 39.00 W.DO TIME - 6EC
&vw\AA/vwvA
nne - 6EC «.TO 'e.oa it.oo w.ro
10.09 «.iw w,o»> »a.!» »cc.ro itq.ro orsTPNce - FT «icr
i4a.ro tfo.oo ifo.ro -iro.ro
«UK Nir.ftER -43MÖ
FIGURE C-9 (Com.). Simulation Ti:r.e His'orics
(Engine Deflection/TVAU =1 )0%/Slnuooidal 8J
Rv.
68
i.MTii-iTfi» -•- "-iiim J-' - - •• ' ^^mutjtamum Ttmnnl -■—- mtiiiMli"'-'■■■'■-
'" y..:, ,...„„w.T^?rw?.IWJ..f..^,yW,^„,.,., I,,,, ,!!■!.., , . L um?mm!mmm*fmmm.MHimmM*mwmmm!mmm* -~~.. _....,.,..„, „^
GAM/AE/73-14
(
ItJ» 16.00 to.DO ti.DO ti.DO jTÖÖ JTDO 40.00 TIHE - SEC
6n
o
& Ui _i u5 a, ■
VOO *rÖD iTÖÖ ttTÖo 16. DO to.DO «4. DO ti.DO 3C.D0 J6.D0 W. DO TIHE - 5EC
It.DO If.DO tO.DO C4.D0 «.DO Jt.DP ».DO W.DO Tine - SEC
»« o z
g 0.00 tO.W «0.00 §0.00 »3.00 103.00 ItS.OO tW5,0Cr 1*0,00 llff.00 100.00 DISTANCE - FT »ICT
tUti KUnBEK -A3146
FIGURE C-9 (Cont.). Simulation Tina Histories
(Engine Defleetion/TVAU =100%/Sinusoidal g ) c
69
IIIJ! |l WP^W»^«BIMH"J««JU I
I (
GAM/AE/73-14
Appendix D
Computer Program
70
-i urn liianrrm k.*te i ■-'-" tMej^^mm^mM—--■*»■-
c c
~~%
GAM/AE/73-1A
PROGRAM RESFCNS(INPUT,CUTPIT,T AFE5=I N*>UT , TAPE6 = CITFUT,PLOT,TAFE7)
C c C THIS PRCGF-Af IS Ä SIX DEGREE OF FREEDOM SOLUTION USING C THE GENERAL NON-LINEAP, 9O0Y-AXIS SYSTEM EQUATIONS CF C HOTION ANC EULEP ANGLES... C C OEAS K WJRLEY, 2LT, US AF AFIT/EN/GAM-73 C £ *«*«»* ««««««4*4««»»«*****»** **** «»»«««»*«.♦«««««.«.»««»*«***».»*****«.«
c c c C ••• OlhENSICN STATE VAF1AFLES c
CIMEN'SICN V (12), YP(12) C c C ••• COMMCN FIIES NAMED FCR SUBROUTINES ANC MAIN PROGRAM C c
( : C 1) MfIN PROGRAM ANC SUBROUTINE GENERAL PARAMETERS C
CCMHCN/C*AIN/EFCM0,AV,fiVC5,AV0T,JA,A0,PI,TCPI,TRIMCFT,NE6R, lTHRU$lfTH9L'S2,Al,A2, A 3, 01,62,3 3,T1,T 2, FEO, SIGH Cf THE C, ANGLE , 2GA»GP,GC,CE,rA,r)R»TRTl,TH'2,AL,eE,ALPHAT,STAt<T,CNEE,CLEE,VCPT, 6SFE,CFE,VR,CKCR,CNCR,CHCF,THRUS,T=»IM,BETAT,wTl,WT2,yWT,CONT,Zf'T, 7AL0T,?EDT,ALCFT,3ECPT,TCPT,XT,YT,ZT, IX, IY , IZ ,1X7; IR , W=> ,MAS S ,G ,S , eB,C*C»,C>GE, CZ,C70E,C NCKJEJCMQJRV R2,ROh,STHE,C THE, T VGAIN
c v C 2) AIRCRAFT AEFCCYNAHC COEFFICIENTS IN NCN-C1MENSIONAL FCRM
C CCMMCN/CCCEF/FCY (2 1, ° ) ,ECN (21, <9 ) ,ECL (21, <?) ,ECM ( 21, °) ,ECX (2 1) ,
lECXOF(21),Fr2CE(21),ECVCE(21),ECMQ(2 1) , ECYCP (2 1) ,EC NC? (21) ,ECLCR<2 21),ECYCA(21) ,ECNBA (21) , ECL CA (2 1 > ,ICY P ( 2 1) ,ECNP(21) ,ECLF(21) ,ECYF(2 31),ECNR(21),ECLR(21) ,ECZ(21)
C C 3) PAWMETE9S USEC BY ^LOTTING SUBROUTINE C
CCHMCN//ALFHM«<0 2),BETA<«.0 2),VEL('»02),P(««C2),LCCF,O(«40 2), IK » .0 2), ALT (fc(2),THETa (<-G2) ,PHI ( 102) , PSI (<<02) ,YC(7) , 1IME(U0 2) , 2OISTC«02) , TR AVC0 2) , AX(U02),Av f i*0?l , AZ( t»02) ,?£LE(!*02) , CELA (<<G2) , 2CELR(«*P2),TGVC.a2) »TH-ST («♦ C2), CNE (<«0 2) , CLE («<C2> »CNßEFF U02 > , «tLOP,CALF(i«C2),ALOOT(<«02),BFDOT (<402)
C c
( , EXTFRNAL GYKHES REAL 1X,IY,I2,IXZ,IR,*ASS
C C
71
~. , ^
"■^iii ■'■'...l.^lWMI|-gl".-l!W.il^M?,^^|_ijal. . TU. nil. !-^w*f ■- ^■■-.M!:' -II.P»IIJI .IIH.M.. u.i, wm-mi," inmiMPpiHi mmmm
GAM/AE/73-14
o c c c c c
c c c c c c
c c c c
c c c c c c c c c c
c c c c c
••• INPUT TJ-E TRIM CPTICN (TRIMOPT), CONTROL GAINS, AIRCRAFT GEOMETRIC ANO CONTROL PARAMETERS, AIRCRAFT AEROCYNAMIC COEFFICIENTS, AND INITIAL CCNDITIONS.
NAHELIST/CMAS/TRIKDFT,GE, CA,OR ,Y0»SIGHO ,THEC,FEO,LC0P NAHELIST/GECh/IX,IY,I7,IXZ ,IR,WR,MASS,S ,C,E ,TFFlSl,THRL3 2,XT,YT,ZT NA^ELIST/CCEF/E^Y,CCN,ECL,EOM, ECX, EC7,E CXCE , ECZCE .ECMOE, E'? HO , ECY03
i,ECNOF,ECLCF ,ECY0A,ECLCA,ECNOA,ECYP,ECNF ,ECLF,ECYR,ECNR,ECLR REA0(5,CATAS) REAO(R,CECH> REAC<5,CCEF)
••• OEFINE PARAMETERS USED AS CONSTANT COEFFICIENTS IN THE STATE ECLBTICNS ANO AS ANGLE/RADIAN RATIOS.
ALPHAT=PETAT=T=0. 3 G=32.171.0 J BWGT=.1*AV $ TCPI=2.*FI ! A2sS*R/2. S B1=IXZMIY«IY + I7) { T1=TFPUS1 S TRT1=T1/THFUS $
5 PI-3.1M5926535 t AV=1B0./PI t ANGLE-PI/2. S Ai = S/(2.**ASS)
A3-S*C/2. ? REAOER=TRIM = CHCP=STARI = C. E?=IZ+IY-I7.**2-IX7»*2 ? B3=IX*IZ-IX7*»2 T2=THRUS2 $ THRUS=T1*T2 TRT2=T2/THRUS t XKT = 5e.
NEAR=0 AO=i./(2*PI) AV05=2. *AVOT HT1=WT2 = XWT=ZMT=0.
♦«» DEFINE INITIAL CONCITIONS.
0060J=1,7 60 Y(J)=YC(J)
Y(8)sTHEOJY(c.)=SIGHO5Y(10) =FEO?Y(li) =Y(12) = 0.
»♦» SELECT CESIREO TRI* OFTIONS (TRIMOPT) USING THE FOLLOWING COCE»
0. "* NC TRIM 1. ■ STRAIGHT ANO LEVEL 1. = STEADY CLIfS (WITH opQpcp INITIAL CONCITIONS) i. - STEAOY CESCENT (WITH PROPER INITIAL CONDITIONS) *. - CCOROINATED TURN
IF(TRIHCFT.EC.C) GO TC 9 IFCTR1MCFT.EC.2.) GO TC 10
••• TPIH CCNCniON FOR STRAIGHT ANO LEVEL FLIGHT, STEADY CL IHE , CS STEACY CESCENT
CALL TRIH1(Y,YF) IF(CHCF.EC.i.) GO TO 6 GC TO 9
10 CONTINUE
/2
..■.. Wim«*-«--PM ! i k ,u I...WI i i ■I^HJMJPI« -..n^iiuwiwwmpBwp^n
GAM/AE/73-14
C C C ••• TRIh C0NC1TI0N FOR TURNING FLIGHT, C c
CALL TRIH2(Y,YF) IFICHCF.EC.DGO TO 6
9 CONTINUE C C •*» PRINT CLT FIXEO PARAMETERS AND INITIAL TRIMKEC CONDITIONS C
CALL FRINTlO) Y<2>=1.
C C *** THE SCLLTICN IS NCW WORKED USING THE RKGXY7 INTEGRATION C ROUTINE AND THE OESIREC AIRCRAFT CONTROL SUBROUTINE. C
0077J=1,LCCF CALL CCNTRL(Y,YP,T) IF<CCNT.EC.O.)C-0 TC 5 CALL VECTOR(Y,YP>
5 CCNTINLE 00 76 JFK=1,2G CALL FKGXYZ(f,Y, YP , 12,. 0 C5 ,.00 C 000 5, GYRATES) IF(NEAR.EQ.l) GO TC 87
76 CONTINUE C C •«• OESIREC PARAMETERS ARE STORED FOR THE PLOTTING SUBROUTINE C
GA=J CALL STORE (Y,YF)
C 77 TIME(J)=T
GO TO 88 87 LCOP=J-l 88 CONTINUE
C C ••• SUERCUT1NE CUTPLOT IS CALLEO ANO RESULTS ARE FRINTEC C AS A FUNCTION OF TIKE. C
CALL SPFVAL(Y,Y") CALL CtTFLCT
6 CONTINUE STOP END
o 73
mMmmmmtmmwm*tomja*m^*.'**im^m -^ --■-■-—■—- ■ ■-^—■■■■ - ■--■^--^..■- -^.-.-- - ■ ■--■-^j^
--*«-■———, ->-.i--%-^™—'>- —- .1 ii ii. »i n pg ■■. ■!■■■ ■■ ^MW.ii.ii|Tmiii|iljll.l#p^ wuia»-!-
GAM/AE/73-14
c c c c c c c c c c
c c c c c
c c c
SUBROUTINE GYRATES (T ,Y ,YP)
••• THIS SUGRCLTINE CONTAINS THE STATE EQUATIONS USEC 6CTH IN SETTI THE T»lt* hEC CONDITION AND IN THE PROGRAM SOLUTION. DATA IS LINEARIZEC WITH RESPECT TO THE PARTICULAR AIRCRAFT ATTITLCE EA TIM'. TUS SU39CUTINE IS CALLED. IT IS CALLEC SY THE MAIN PROGRAM lit AS AN EXTERNAL BY SUDROUTINE RKGXYZ.
DIMENSION Y(12),YP(12)
C0MMCN/CHAIN/eF.CMD,AV,AVC5,A\/0T,J4,A0,PI,TCPI,TRlH0FT,NEAR t
lTFRUSlfThRlSZ,*l,A2,A3,eilE2,'J3,Tl,T2,FEC,SIGHC,THEC,ANGLE , 2GA»GB,GC,CE»CA,0R,TRTi,TRT2,AL,PE,ALPHAT»START,CNEE»CLEE,VCPT , 6SFE|CFE»VR,CYCR»CNCR,CHCF, TH°'JS ,TRIM , HET AT ,WT1, WT2 , XWT ,CON T , Z H , 7ALDT,EECT,;LCFT,3ErPT,TCFT,XT,YT,ZT,IX,IY , IZ,1X2 ,IR ,WR,MASS,G ,S , 6B,C, CX, CXCE, C2,G Z D E, C *,CKDE »CM Q,RVR2, ROH, STHE,C THE, T VGAIN
COMHCN/CCOEF/ECY(2 1T9) ,ECN ,21,9),ECL (21, 9) ,ECM ( 21,9 ) ,ECX (2 1) , 1ECX0E(21) ,ECZCE(2i),EC^CE(21),ECMQ (21) , ECYCR (21) »ECNDR (21) ,ECLCF(2 21),ECYCA(21) ,ECNOA (21) , ECLCA(21),ECYP(21),ECNP(21),ECLF(21),ECYR(2 3l),ECNR(21) ,ECL;:(21) ,£C7(21)
REAL TX,IY,I2,IXZ,IR,KASS
*«* VARIABLE COEFFICIENTS ARE OEFINEO FOR USE IN THE STATE EQUATION
VRsSQRT(Yd) »*<fY(2)»'24Y(2)**2) RCH=.0 0 237 8* « 11.-. 00 0 0 0683»Y(7 ))•♦<»• 256) RVR2=FCH*( V<?«»e) VCVR = Y (2)AR CTHE = CCS(Y (3)) IF(APS(CTHE) .LT..0001) NEAP = 1 IF(NEAR.EC.l) RETURN IF(AQS(Y(1)) .L7.1.E-2C) GO TO 53 AL=ATAN2(Y(3),Y( 1) ) GC TO 5U
53 AL = SIGN(AN'CLE,Y(3) ) 5(» CCNTINLE
BE=ASIN(VCVF) SFE=SIN(YMC)) STHE = SIN(Y (fi)) CFE=CCS(Y(1C)) SPSI = SIN(Y (9)) CFSI = CCS(Y (<?)) SET=SIN(°FTA1) C8T=CCS(:?ETAT) SAT = SIN(ALFI-M) CAT = COSULFHM)
74
— - ' -
ii ■■■ii.Bja.i. ,■. . i ■ mmmmmsmom ■ ■ '■"1*i
GAM/AE/73-U
C C C c
C
c
••» AERCOYNAMC COEFFICIENTS ARE EXTRAPOLATED AS A FUNCTION OF THE AIRCRAFT ATTITUCF (ALPHA AND ?ETA>.
JAsAVC5*8L*3 je=AVCT*PE*5 IF((AL»AV),G IFUAV'AL).1 IF((AV*5£).L IFUAV'BE).G IALI=SMJA-2 ALI=I«LI 0L0S=(AV»Al_- ieEI=10*(JE- BEI^IPEI 0eL0T=(AV*eE CX-(ECX(JA*1 CZ=(ECZ(JA4i CXDE=(ECXCE( CZDE=(EC2CE( CKDE=(ECPDE( CfG =(ECHQ ( CYÜ<?=(ECYCR( CNOR=(ECNCR( CL0R=(ECL0P( CYDA=(ECYCM CNDA=(ECKCM CLOA=(ECLCM CYP = (ECYF ( CKP =(ECNF < CLP =(ECLP ( CYR = (ECYR ( CNR =(ECNR ( CLR =(ECLf? ( CYA=(ECY(J*+ CLA=(ECL(J/>4 CNA=(ECN(JA* CHA=(ECMJA4 CTAF=(ECY(jA CLAP=(ECL(J/> CNAP=(ECN(wA CHAP=(ECM,jß CY=(CYAP-CYA Cl=(CtAP-CU CK=(CNflF-CNfl CP=(CPAF-Cfö
E.<=D.) JA = 20 E.-10. )JA = 1 E.-^0.)J° = 1 J.;0.) J9=6 )
*LI>.'5. 5)
-?EI) )-ECX )-ECZ wA*l) JM1) wß+1) JA41) JUI
JA+I) ^m> ^A*l) JMD JA-H ) ..Ml) *A4l) JA+1) wA4l) J,J3) 1,J3) 1,J3) j,vl) 41,jq 41,JT ♦1,J<3 41,JT
)*C3L )*C3L )*C3L
/10. (JA))*CL0 (JA>)*CL0 -ECXCE(JA - EC Z C E {JA -ECHCE (JA -ECMC (JA - FC Y CM JA -ECNCR(j; -FCLCMJA -ECYCMJA -E0NCfl(JA -EfLTA(jA -ECYF (JA -EC NF (JA -ECLF -ECYR -ECN5 -ECL« -ECY(J£,J -ECL (J^ ,J -ECN(JA,J -FCK (J1 ,J + D-ECYU 4-D-ECHJ 4-D-ECMJ + 1)-ECMJ 0T4CYA OT4CL/J OT+CI^A 0T4Cf*A
(JÄ (JA (JA (JA
54-ECX Ü+-EC Z )) »0 L ))*0L ))*nL ))*0L ))*3L »>*0L ))*0L ))*0L ))»0L ))*0L ))*0L ) ) »0 L >)*TL ))*0L ))*DL ))*0L E))*0 E))»0 P))»0 S))*C A,J3 4- A,J3* A,J3 + A,J3 4-
(JA) (JA) C54-ECX0E C54ECZ0E C54-ECMDE CS4-ECMQ C5+ECYQR C54ECN0R C34ECLDR C54-ECYDA C5+ECN0A O^FCIDA C5+EC YP C54-ECNP C54ECLP C5+ECY«? C5 + ECNR 054-ECLR LC£54ECY( L05+ECL( L05+ECM( LC54£CM( 1))*0L05 1)) *OL05 1)) »OL05 1)>»0I05
(JA) (JA) (JA) (JA) (JA) (JA) (JA) (JA) (JA) (JA) (JA) (JA) (JA) (JA) (JA) (JA) JA,JP) ja,jp) JA,J") JA,wB) 4ECY (JA,J641) ♦ECL(JA,JR4l) +ECN(JA,J34l) ♦ ECMJA,JP4l)
C C
Q1=CX4CX9£«CE C2=CY4CYCA*CMCY0R*0P4.5»B»(CYP*YC4) 4CYfi»Y (6)) / \(R 03=CZ4C?nE»nE C<=CL4CLC.^C^4f:L0D»r:fi4.5»n* (CLF*Y(t») 4CLR*Y(6))/VR 0?=CK4CHCE"Cf 4,5»n*C^';r-Y (5 )/VD
Q6=CN4CNCA»CMC,J')R'DR4.S»PMCNP»Y(<») 4CNP* Y (6)) / VR
75
. .- -~ —■ ■-■ ■ ■■ --•■
™™r^™- """"•^PiPPW
GAM/AE/73-14
(
c
c c c c c c c
c
c
c
c
c
c
c
c c
c c c
*•• THE STATE ECUATIONS FCtLOW WITH THE STATE VARIABLES DEFINEC £St Y(1)=L Y(2)=V Y(3)=W eCCY AXIS SYSTEM Y(«»>=F Y(5)=C Y(6)=R BGCY AXIS SYSTEM Y<e> = THUA Y<9)=FSI Y(10)=PHI EULER ANGLES Y(11)-XE Y(i2) = YE Y(7)=ZE EARTH AXIS SYSTEM
YP(i)=-G*STHE»Y(6)*Y(2>-Y(5)*Y(3)+Ai»RVR2*Cl*(Ti*T2)*CAT*CeT/hASS 1»CWT1*WT2)/KASS
YF(2)=G»CTHE»SFE*Y (<») *Y (3) -YC6 ) *Y( i) * (T i*T2) »SET/MASS 1*FVR2»A1*G2
YF(3)=G'CTHE*CFE«-Y(5) *Y(1) -YC») *Y(2) -CT 1 + T2) »SAT/MASS 1*"RVR2*A1*C3
YP(<»> = <I7MFVF2»A2»Q<«4 <Tl-T2>» SAT*YT-(T14T2>*SET*ZTJ *IXZ*( FVR2**2* iC6-(Ti + T2)*yl*S3T+ 'T1-T2)*YT*CPT)fB1*Y(m*Y(5)+ I?2*Y(5)*Y(6)*Y (5)*I 2R*WR*IXZ)/E3 4(WTl-VJT2)*XKT*IXZ/e3
YP<5)=(RVR2*Ä3*15-(T1+T2)*XT*SAT+(Tl+T2)*ZT*CAT+IXZ»(Y(6)*»2-Y(«(>* l*2>*(IZ"IX)*Y<e>*Y <<0«Y(e>*IR*WF>/IY
YF(6) = (RVF2»/!2*a64-(Ti-T2)*YT'CPT-(Tl4T2)*XT*SQT + IXZ»(YP('») -Y<5> *Y< 16)) + (TX-IY)*Y {U) *Y (5>4Y(S> *IR*WF)/IZ 2MHT1-WT2)*XM/I?
YF(.,) = YU>»S7l-E-Y<?>«CTH£*$FE-Y<3>*CTHE*CFE
YF(8)=Y(5)«CFE-Y<6)*SFE
YP(9) = (Y(5)»SFEtY(6) *CFE>/CTHE
YF<10)=Y(«»)4 <YF(9)*ST»-E>
YP(ll)=Y(l>*CTVE*CPSl4Y<2) * <SFE*ST HE *CPSI-CFE*SFSI> *Y (3> * ( CFE«S1KE 1»CPSI+SFE*SFSI)
YF(l2)=Y(l)»CThE*SPSl4Y(2)*(S'rE*STH£*SPSH-CFE*CFSI)*Y(3)»(CFE*STHE i*SPSI-SFE*CFSI)
»*» CALCULATICN OF EFFECTIVE CN flNO CL GE = CL*((T1-T2)»YT*SAT-(T1+72)*ZT»SBT)/(RVR2»A2) GC=CN4((Tl-T2)*rT'CBT- (Tl*T2)*XT*SBT♦(WT1-WT2)*XHT)/(RVR2* A2)
»»• CALCULATICN OF FIRST DERIVATIVES CF ALPHA, BETA, ANO VR
VCTMY(1>*YF <1HY(2>*YF<2) 4Y(3) *YP(3)>/VP ALOT=(Y(l)*YF(3) -Y(3>*YP(1))/(Y(1)**2 + Y(3)**2) eCOTs(YP(2)»VF-Y <?>*VCT)/Ol«X DLMX = VR»SCFT (VF**2-Y ( 2 ) »*2 )
RETURN END
76
I !■ !-—I ■•••■■ ■■ ■ ■
GAM/AE/73-14
o c c c c c c c c c c c
SUBROUTINE ClTPLOT
THIS SUBROUTINE ^LCTS THE CESIREB OUTPUT AS A FUKCTICh CF TIME.
««««***«***««««***** »**♦»♦****** *******#**♦***************** *****
CCKMCN/CfAIN/EECMO,AV,S(6) ,TRIHCPT,SK(2 6) ,START , AA,Ee,VOPT COMMON//ALFH* (402) |BETA(fi0 2)fVEL(l»02>tP((i0 2) fLCCFiQdOZ) f
1R(«I0 2) |ALT(«fC2)»THETAH02) ,PHI («»02), FSI («»02) tYOC7) |TIME(«»0 2) f 20ISI (4C2)9TR^(H02),AX (i*C2> ,Af U02), AZ (<»Q2) tCELE <<»0 2),CELA <^C2) , 3DFLR(UC2<,K-W<<0?> »THRST (U 02), CHEt «»0 2) , CLE <U02> ,CNBEFF U02 ) f
<»LCF, CALF (<♦ C2 >, LOOK <«Q2) ,aEOOT U02) VV=VOFT*10C.MRIMOFT + 1CCOOCQ.»BECMD
CALL FLCT(C. ,-12.»-3) CALL FACTCR(.C) CALL SCALE (T m,10.,LCCF,l) CALL SCALE (ALF1-A,2.,LCCF,1) CALL SCALECBE'fl, 2. ,LCCF,1) CALL SCALE (VEL»2.,L0CF,1)
( \ 1 CALL SCALE(ALCCT,2.,LCCF,1)
CALL SCALE (EECCT,2.,LCCP,1) CALL SCALE IP,2.,LOOP,1) CALL SCALE(C,2.,LOCP,l) CALL SCALE (P. ,2.,LOOP,1) CALL SCALE(TKETA,2.,LCCF,1) CfcuL SCALE CPHi2tf LOCFtl) CALL SCALE (CELE,2. ,LCrF,l) CALL SCALE (CELR,2. ,LCCF,1> CALL SCALE (CELA,2. ,LCCF,1) CALL SCALE(A>,2.,LCOP,l) CALL SCALE (M,2..LCOP,l> CALL SCALE(A2,2. ,LCOP»l) CALL SCALE(C1ST,10.,LCCF,1) CALL SCALE(ALT,2.,LCCC,1) CALL SCALE(TRAV,2. ,LOCP,l) CALL SCALF(ThRST,2.,LCCF,i) L=LOCF+i H=LOCP*2 PHI(L)=TGV (L) = -130. PHtMJrTGV (H) = i30. CALL FLCT((. ,22.,?) CALL FLCT(17.,22,,2) CALL FLCT(17.,0. ,2) CALL FuCT(C. ,C.,2)
c CALL FLCT13. ,2.,-?) CALL FLCT(C.,17.,2) CALL ;LCT(12.,17,, ?) CALL FLCT(12.,C. ,2)
77
J
r w -'-^™—1--T—T WI.J.....lHg.w,».—,,K , mm ,.,,.. .U1, ^pp^ppp „lll,,,^^^^,,, - „
c
GAM/AE/73-14
CALL FLCKC. ,0.,2) CALL SYMSOL(7.,.25,.15,10HRUN NUMBER,0.,10) CALL NUM9ER(C.5».2 5i .l5fVV |0«;-i) CALL FLCK'. ,12.«5,-3) CALL AXIS'C. ,C.,10HTI"E - SEC,- 10,10.,0 . »TIME(L),TIHE(M)) CALL AXIS(C. ,C, 11HALFHA - DEG , 11, 2. ,90 . , ALFHA ( L) , flLPHA(M) ) CALL LINE HUE, ALP HA, LCCF, 1,0,7 5) CALL FLCKC. ,-2.,-3) CALL AXIS(C.,C.,10HTIPE - SFC, -10» 10 ., 0 . ,TIHE(L) ,TICE(M ) CALL AXIS(C. ,C.,19HALFHA-DCT - CEG/SEC, 19, 2. ,9 0., ALCOKL),
lALOOT(M)) CALL LUE (11 hE,ALOCT,LCCF, 1,0,7 5) CALL FLCT(Q. ,-3. ,-3) CALL AXIS (C. ,C.,10HTIPE - SEC, - 10, 10 ., 0 . ,T 1ME (L) ,TI PE (M) ) CALL AXIS;0. ,C.,10HBETA - CEG, 1 0,2 ., 90 . , GET A (L ) ,°ET MM) > IFCSTART.EC.l.) GO TO 1 CALL SYM3CKC.2,2. C, .15,12HPETA COMMANO , 0, 0,12) CALL NUMBER(C.2,1.7, . 15,PECMD, 0.,-l) CALL SYM9CL(C.6il.7,.l5,7HCEG^EES,0. 0,7) GO TO 3
1 CCNTINUE CALL SYHECL(.Z,1.7t.l5,l9HEETA COMMAND VARIES,C*,19)
3 CONTINUE CALL LINEtTIhE,SETA,LCCF,1,0,75) CALL FLCT(C. ,-3. ,-3) CALL AXIS(C. ,C.,10HTIvr - SEC,- 10,10.,0. ,TIM£<L),TIHE<H)) CALL AXISU. ,C.,19H 9ETA-DCT- CEG/SEC , 19 ,2. 0, 9 Q . ,B ECOT (L) ,
lBECOT(H)) CALL LUEUn^EnCT,LCCF,l,0,7 5) CALL FLCKC,-3.,-3) CALL AXIS(C.,C.,10HTI*»E - SFC, - 10, 10 ., 0 . ,TIME(L) ,TIHE (M) ) CALL AXIS( C. ,C, 11HP - CEG/SEC,11, 2. ,90. ,F(L),F ir)) CALL LINEUm,P,LC9P,l,0,75) CALL FLCT<15.,-«».5,-3) CALL FLCKC. ,22. ,2) CALL FLCK17.,22.,2) CALL FLCT(17.,C. ,2) CALL FLCKC. ,C.,2) CALL FLCK2. ,2.,-3) CALL FLCKC. ,17. ,2) CALL FLCK12.,17,, 2) CALL FLCK12 .,C. ,2) CALL FLCKC. ,C.,2) CALL SYHeCL(7.,.25,.lE,lCHFUN NUMBER , 0. , 10) CALL NUMBER <c.. 5, .2 5, .15, VV,0.,-1) COLL FLCK1. ,13.5,-3) CALL AXIS(C,,t.,10HTUE - SEC, - 10, 10 . ♦ 0 . »TIME (L ) ,TIKE CP) ) CALL AXISCC. ,C.,11H0 - OEG/SEC ♦ 11, 2. ,90 . »C (L), 0 (M) ) CALL LINE(TUE,Q,LCOF,1,0, 75) CALL FLCKC. ,-3. ,-3) CALL AXIStCClOHTI^E ■ SEC,- 10,10.,0. , TIME<L) ,TIHE(M)) CALL AXISCC. »C, 11 HP - CEG/SEC , 11, 2. ,90 t ,R <L), R <H)) CALL LINE (TIKE,'.,I COP,1,0, 75) CALL FLCKC. ,-2.,-3) CALL AXIS(C. ,C.,10HTIME - SEC, - 10,10 ., 0 . ,TIME (L ) ,TI HE (M) )
78
-■■■*- TU --.r-iM r l
irs .*IHP4P.J!.^!WJUW..lJ^iJ«>4u.!WiW
GAM/AE/73-14
CALL AXIS (C. ,C, 11HTHETA - OEG , 11, 2. ,90 • »TI-ETA (U, THETA(M) ) f" • CALL LINE(TIfE,THETA,LCCF,l,0,75) ^ CALL FLCTCO. ,-3.,-3)
CALL AXISCC. VG«»10HTIKE - SEC,-10, 10 ., 0 . ,TIM? CD ,TUE (P>) CALL AXISCC. ,0.,9HPHT - CEG,9, 2 .,9 0. »PHI CL) ,FHI CM)) CALL FLCTCC. , 1.0,-3) 0027J=1,L0CF NC=2 IFCJ.EC.DGO TO 26 IFCAPS(PHICJ-1)-PHICJ)).GT,50.) NÜ=3
26 XX=TIfECJ)/TirECM) YY=PHICJ)/FH1(V)
27 CALL FLCTOX ,YY, NO) CALL FLCTCC.,-1.0,-3) CALL FLCTCC. ,-2.,-3) CALL AXISCC, »CiOKTTME - SEC, - 10, 10 ., 0 . »TIME CD ,W ECM)) CALL AXISCO. ,0.,19PTU^KS APT GRAV VECT, 19 ,2 . ,90 . ,TGV (D , TG V (H )) CALL FLCTCO. ,1.0,-3) OC 13 J=1,LCCF N0=2 IF (J.ECU GC V) 12 IFCARSCTGVCJ-D-TGVC J)).GE.5C.) NO=3
12 XX^TI^ECJ) /T If-EC «) YY=TGV(J)/TG\ <H
13 CALL PLCTOX,YY,UO> CALL FLCTCC. ,-1.0,-3)
( j CALL FLCT(15.,-<».5,-3) CALL FLCTCO. ,22.,2) CALL FLCTC17,,2?.,2) CALL FLCTC17.,0.,2) CALL FLCTCC. ,C.,2) CALL FLCTC2. ,2.,-3) CALL FLCTCC. ,17.,2) CALL FLCTC12.,17.,2) CALL FLCTC12.,0. ,2) CALL FLCTCC. ,C.,2) CALL SYH9CL(7.,.25,.15,10HRUN NUMBER,0. , 10) CALL NUMPERCe.5, .2t,.15,VV ,0.,-l) CALL PLCTCl. .12.5,-3) CALL AXISCC. »ClOVTI^E - SFC, - 10,10 . ,0 . ,TIME CD ,TIMECM>) CALL AXISCC ,C, 19KELC\<AT0K 1ISF- D?G, i$ , 2. ,9 0 • ,OELE iL) ,D ELE if)) CALL LINE(TlME,f)ELf,LCCP,l,0,75) CALL FLOTCC. ,-2. ,-?) CAuL A>:T-f C. ,0.,10HTIME - SEC,-10,10.,0.,TIMECD,TIME(M))
| CALL AXIStC. ,i.,17r'! CCER TISP - OEG,17 , 2 . ,9C.,CcLRCL)»DELRCf )) I CALL LIS?cmE,3tLP,LCCF.l,0,75) , CALL FLCT( C. ,-2. ,-3) I CALL AXISCr. ,C, 10FTI"E - SEC, - 10, 10 . , 0 . »TIME (D »TIME (M) )
CALL AXISCC. ,C, HHAILESCN PISP - CE G , 1 6 ,2. sr:o . , CEL/ CL ), DE LÄ ( M !) CALL LINECTUE,')ELA, LCCF,1 ,0,75) CiV-L FLCT CO. ,-2. ,- ?)
( CALL AXISCC ,C lQtTIME - SEC,-10, 10 • ,0 • ,TIMECD ,TIr*E <»0 ) CALL AXISCC. ,C,,l7l-tfcLCriTY - FT/SEC , 17 , 2 . , 90. , VEL ( I) , VELC f») CALL LIKECTIvEt«/iL,LCCP,l, 0,75) CALL FLCTCC. ,-2. ,-?.)
79
(
('',
( J
GAM/AE/73-14
CALL AXISCO. CALL AXIS(C. CALL LINECCI CALL FLCK15 CALL FLCKG. CALL FLCK17 CALL FLCK17 CALL FLCT(0. CALL FLCT(3. CALL FLCT(C. CALL PLCK12 CALL FLCK12 CM.1 FLCT(0. CALL SVH8CK CALL NU*EER( CALL FLCKi« CALL AXIS(C. CALL AXTS(0. CALL LIKE CTI CALL FLCKC. CALL AXIS(C. CALL AXIS tC. CALL LUEC1I CALL FLCT(Q. CALL AXISCC, CALL AXIS« C. CALL LTNEUI CALL FLCKC. CALL AXIS(C. CALL AXISCC. CALL LINEJTI CALL FLCKC. CALL AXIS(C. CALL AXIS(C. CALL LINKOI IFCSTAR7.NE. :ALL SCALE<C
SCAL^(C SCALF (C SCALC(C FLCKlS
CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL L=LOP*l M=L*1
FLCK17 PLCTQ7 FLCKG. FLCK3. FLCKC. FLCK12 FLCT(12 FLCKC. SYt'GCL« NLMGER( FLCK2.
,C.,13H0ISTANCE - FT,-13,10. ,C.,13hALTITUDE - FT,13,2.,9 ST,ALT,LCCF,1, 0,75) .,-<♦,5,-3) ,22. ,2) .,22.,2) .,0.,2) tC.,2) ,3.,-3) ,17.,2) .,17., 2) ,,0. ,2) .C.,2) 7.,.25,.15,1CHRUN NUMBER,0., <=.5,.25,.15,VV,0.,-1) ,13.5,-3) iC.tlOHTIPE - SEC»-10,1Q.»0. ,C.,18HX 6CCFLEPATICN - G,18 ►E,*X,LOCP»l»Q »75) i-3.,-3) ,C.,1DHTIVE - SEC,-10,10.,0. ,C.,13HT ACCELERATICN - G,16 ► EfAYf LOCFilfO ,75) ,-3.,-3) , C, in J-TIw? - SEC»-10, 10.,0. »C.il'JHZ ACCELEP1TION - G,18 (■E,U,LOCF,1,0 ,75) ,-3.,-72) ,C.»10HTIME - SEC,-10,10.,0. ,C.,12HThfilST - L3S,12,2.,90 fE,TMRST,LCOP» 1,0,75) ,-3.»-3) ,C, <3F0ISTANCE - FT,-13,10. ,C.,16hCRCSS RANGE - FT, 16, S"J,TRAV,LCCP,1<C,75> 1.) GO TC 5 ALF,9. ,LOF,i) ^E ,<♦. ,LCF,1) LE ,<♦. ,LOP,l) rEE^F, *♦. ,LCF , 1) •, -<t .5 ,- 3 ) ,22. ,2) .,22.,2) .,0. ,2) ,C.,2) ,3.,-3) ,17.,2) .,17., 2) .,C ,2) » C ., c ) 7.,.?5,. 15,10HRUN NCMP ER , 0. , IC)
,C.,OISKL),OISKM)) 0.,ALT<L),ALKH))
10)
»TiPECDtTmrn) ,2.,C0.,AX(L),AX(M))
,TIME(L),TIKE(W)) ,2.,90.,AY(L),AY(M))
tTlPECL)vYIt'E<t'H ,2.,90. ,A2(L) »AZM))
,TIPE(L) ,TIKE<»0) .,THRST(L),THRST(M))
iC.tOISTCL) ,DIST(M)) 2. ,90. ,TRAV(L) ,TRAV(H>)
15,10HRUN NUMPtR,0., C..5, .25, .15,W,0.,-1) ,12.,-3)
80
-■-■ i -——; -a .,._ —,-.-..-
GAM/AE/73-1*
i rnmemamm
CALL AX1SCQ. ,C.,11HALFHA - DEG,-11,9.»0. CALL AXIS (0. ,0., 11HCN-OETA-EFF ill»'*. ,90. CALL LINr(CALF,^SE,LCP,l,-l,3) CALL PLCT(C.,-5.,-31 CALL AXISCO. ,C.,11HALFHA - DEG ,-11,9 ., 0 . CALL AXIStC. tC* 11HCL-BETA-EFF, ll,i». ,90. CALL LINE(CALF,CLE,LCF,1,-1,3) CALL FLCTCO. ,-5. ,-?) CALL AXISU. ,C.,11HALFHA - TEG ,-11,9 ., 0 . CALL AXIS(C. id 15>CN«RETA«PYN-EFF,i 5,<*. CALL LINE( C/LF ,CNBEFF,LOF ,1,-1,3) CONTINUE CALL FftCTnRC 1.) CALL FLCT(12.,-12.,-3) RETURN END
CALF (L), CALF (P>) CNE(L) ,CNE(M>)
CALF (L), CALF m> CLE(L),CLE<M>)
, CALF (L), CALF <m ,90.,CNEEFF<L) ,CN9EFF(H)>
C
81
'^r^M^-^-i'-'T^S-"-' "^"W! IUl^—> ^*»mm,,,.jmr*j.n ..,^i.Wii, j ,,M ^ ,^.w,.^ I..BJJHIIJIIP1 9H ..API ii nupwiimpjppjuji^u,
C
(
c c c c c c c c c c c
GAM/AE/73-14
SUBROUTINE SFEVAl(Y,YP)
»♦* THIS StanOL'TIN', PE~FCRHS THREE FUNCTIONS 1 1) CC^ARISCN CF THE SIGNS OF THE FIRST ANC SECONC
CER1VATIVES OF BETA FOR OETERHINAT ICh CF Tl-E CEPAUURE PCiNT
2) CHECK'S Ihb VALIE OF PSI AS A SECCNC CEPARTURE CRITERIA CALCULATION CF AN EFFECTIVE C-N-5ETA-DYKAMIC
OIMENS CCMHCN 1THPUS1 2GA,G3, 6SFE,CF 7Ai.0T,P 8B,C,CX
CCMHCN 1RU02) 20IST(i« 30ELRC« «TLCP,CA
RFAL I 110 FCRMAT
1<«X,*AL BECM=E
100 FCRMAT UX,*AL
101 FCRMAT 103 FORMAT
1»ALPHA 2* CE ?//,5X,
10«» FORMAT FCRHAT FCRMAT MAX-LC 1-0 00 2 J IF(TIV eFOOT= TEST=P IFCTES CCNTIN CCNTIN PRINT 1=1*1 Jrj4l BEOOT= TEST=G IF(I.E IF(J.L irncs
,7
105 106
1 2
20
3)
ION Y( /CPAIN ,Tl-siS GCDE, E,VS,C ECT,AL ,CXOE, //ÖLPH , ALT m 02),TS C2),TG LFUG2 X,IY,I (1H1.7 CHA»,5 ECMC (1H FHA» <<*X , I«* (in»/ - ♦
GREES* ♦ANC A (in»/ (////, (////, OF-l
si,MAX E(J) .L EECCK ECCT(J T.GT.C UE UE 1QU
l;r.OOT ( ECCT (J C.3) C O.MAX) T.GT.C
12),YO /FECMD <,A1,A CA^R, >CR,CN CFT.3E C7,CZO MV:2) C2*,TH a v'(t»0 2 V U32) ),ALOO 2,1X2, >,*J*, >,*TET
>,'J*, >,»3ET ,2«*X, ///,'tX »F10.5 ,//,9X T PETA ///, * * 9E * P
\\2) »AV, 2,A3 T°T1 C?,C CPT, E,CM
,BET EfA < ), AX ,THS TUO IR,V 12X, A*,/
12X, A*,/ E12 . ,*TH ,* ,*AT CCf
TA/" SI C
AVC5 ,AVOT,JA,AC,PI,TCPI,TRIKCr,,N'EAR, ,E1, 62,3 3, Tl,T 2, F EC, SIGH C, THE C, ANGLE , ,TRT2,AL , PE, ALPHA T, ST ART, CNEE,CLSE,V CPT, hCF, TH3US »TRIM, ?ETAT,WT1,»»T2» XWT,CON T»Z>-T, TCFT ,XT,YT,ZT, IX,IY,IZ,IXZ,IR,KR,MASS,G,S, , CHO E,CM Q,RV P2,ROH, ST HE, CT WE, T VGAIN A(«.02),VEL^02),P (UC2) «LCCF »C UO 2) , <«C2> ,°HI {«,02), PSI («4C2),YO(7) , TIMEtUO 2) , (*i02),AY («402), AZU02) ,CELE(<*0 2) ,CELA U0 2) , ST (J»C2>iCN.E(<,02)»CLE<it02> »CN3EFF (f+02 ) , 2) ,PEDOT(tt02) ASS *CEL9*,llX,*0ELCN*,llX,»CELCL*,3X,»CSeEFF*, /)
•CELE*,iiX,»OELCN*,llX,*DELCL,',3X,*CNBEFF«, /) 5),3 (UX, F5.2)> E POINT OF DEPARTURE CCCURS AT*,//,12X, DEGREES»,//,8X,*ANC BETA = ♦,F10. 5, TIME = ♦|3XtF10.5»* SECCNCS*,
^ANO = »»F10.5,* CEGREES*) NO DEPARTURE OEFINEC«) ETA-COT CONDITION') CNCITION*)
1.5.) GO TC 1 s.>-3E0CT (J-l) )*EEOOT .) GO TC 20
jmEnOT (J + 1) )*5EOOT C TO 3
GO TO 1 .) GO TC 2 0
82
■mill—■ ^ =*.-.-- --a- _,■■■.-....
r i-;««*«■ ""UJI mnp
GAM/AE/73-1A
(
10
1=0 GO TO 1 PPINT 10 3,ALFhA( J) ,RETA(J> »TIHE(J) »BECMC PPINT 105 00 5 J=2,LCCF TEST=ASS(FSI IJ>*?6G.) IFCTEST.GT.lE.) GO TC 6 CONTINUE PRINT 1C<» GC TO 9 PRINT lC3,AtFHA(J> ,BETMJ> ,TIME(J) ,BECMD PRINT 106 CONTINUE PPINT 100 MAX=J-5 0FLT = 7IfE(J)-TTME(l) 1-1 OO 6 J=1,MAX IF(eETA(J).G1,5.) GO TC 7 IFC?FTA(J) .ECO.) GO TC 7 CLB=CLE(.J»/5ETA( J) CNP=CNE(J)/FETA(J) AIF=ALFHA(J) /AV CNBEFF(J) = (CNc*CCS(ALF)-(I7/IX)*CLR,rSlN(ALF)) IF{Ae?(CN5EPf (J1). GT.0.10) GO TC 10 CKBEFF(I)=CNFEFF(J> CLE(I)-CL° CKE(I)=CN6 CALF(1)=ALF**V 1*1 + 1 CCtlTINUE CONTINUE ICP=T-1 RETUPN PPINT 101,J,EECOT(J) ,CNEU),CLE<J) ,CNnEFF(J) , ALPHA (J),RETA (J) GC TC 7 ENO
L 83
mmm* ■■■ I -Tir-nfT
-i-t^-v«?»^,. , .,„ ^u««,,^^ %.WfA «PJ*W.*!I!LlPiK.M|.u l^f:i. itMif. pw, jpauBpp
GAM/AE/73-14 1 C c
c c c c
c,
( •'
SUBROUTINE SKFE(Y,YP)
*»♦ DATA STCRAGE FOR PLOTTING SUBROUTINE
OIMENS COMMON iTHRUSl HGAfGB, 6SFE,CF 7ALDT,E 8e,c,cx
COMMON 1RIV02) 2DISTU 30FLRC4 M.CP,CA
REAL I J-GA AX(J)= AY(J) = A7(J)= CELECJ OELR(J OELA(J \HRST( IF(Y(c IF(Y<9 TGV(J) OIST(J TRAVCJ ALPHA( ALOOT( EFTACJ BFOOT( VEL(J) P(J»=Y 0(J)=Y R(J)=Y ALT(J) THETAt IF(Y(1 IF(Y(1 PH(J) PSI(J) CLE(J) CNE(J> RETURN END
ION Y( /CHAIN »THRLS GC,PE, E,VR,C ECT.9L ,CXCE, //ÖL^H ,ALT (4 02),TS P2),TG LF(4C2 X,IY,I
(<YF(1 ((YF(2 ((YP (3 ) = CE )sOR )=CA J)=T1* ).GT.F ).LT.- =Y(°)» )=Y(11 >=Y(12 J)=AL* J>=ALC )=°E»A J)-9EC
(C»>* AV (5)»AV (6)»AV
= Y(7) J)-Y(5 01.GT. 0).LT. =Y(1C) =Y(9)* = GB = GC
12),YP(12) /SECMD,AV,AVC5,AVOT,JA,AO,PI,TCPI,TRIMCFT,NEAP ,
2,Al,A2.A7,BlfE?,93,Tl,T2,PEO»SIGHC»THEC»ANGL?t CA,TR, TRT1,TRT2,AL ,E?, ALPHAT,STA5T,CNEE,CLEE,VCPTf
YC»,CNCR,ChCP, TH5?US,TRIH,nETAT,WTl,WT2,XWT,CCNT,ZfTf
CFT,3ECPTtTDFT,XT, YT,ZT, IX,IY,IZ,IXZ,I*,WR,MASS,G,S, CZfCZOEtCV.^OE, CM afRVR2,R0H,STHEfCThE,1 VGAIN M«.3 2»,QETA(<«0 2),VELU02>fP('«02>,LCCFtQ<«iQ2>, C2)«THFTA(iiC21 fPHI(ii02)f PSKUC2) tYC(7) tTIHE(<i02) (
fV C*0 2), AX (^C2),ftY (W02), AZ < <4 02 ) , CELE U0 2) , CELA (^02) , VC»0 2) »THRST(«»0 2»,CME(U0 2>,CLE('»0Z) |CNBEFF(U02 )f
),ALOOT(H02>,BEDOTU02>
2,IXZ, IR,f ASF
)-Y(2) »Y (6)*Y(3)*Y (5>)/G) i-STHE )-Y(3) »Y U)*Y< 1)*Y (6))/G)-CTHE»SFE >-Y(i) *Y(5HY(2)»Y <<♦)> /G)-CTHE»CFE
12 1) YC9) = Y(9)-TCPI FI)Y(9) = Y(c)+TCPI AV ) ) «V TAV \, T*AV
)"Al/ PI) Y( 10)=Y(10 )-TOPI -FI) Y( 1Q)=Y(10)+TQPI ?AV AV/360.
84
— -
"'*"■"'"* J:''^ ". ' '■" -' .1 !'-■ .'UJWH.U1UJ.I imi.1 . I ».!»» I II J..L«.-. Illlll,,. U,,LH,I. Uli "<m
GAM/AE/73-14
C C C C c c
SUBROUTINE TPINl(Y,YF)
♦ #* AIRCPAFT OR OESCE
(DIMENSION Y( CCMMCN/CfA IN
iTHRUSl,Tt-FlS 2GA,GP,GC,0E, 6SFE,CFE,V°,C 7AlOT,EECT,H 8B,C,CX,CXCE,
CCHMCN.'CCCEF 1ECXCF(21>f£C 21),ECYDA(2l) 31),ECNF(2l>,
REAL IX,IY TI 100 FCRMflT(lFl) 101 FCRMAK22H 1
1E12.5,6H CCC 102 FORMAT (* AIR
1IGHT*,/,» *, 103 FCRMAT (23M 1QU FCRMAT C6H C 105 FCRMAT ( 9> 106 FORMAT (°H T 108 FCRMAT (51- E 109 FCRMAT (9H V
PRINT 100 PRINT 102 T=0. AL=ATAN2(Y(3 CCUNTER=0, Y<*0=Y(5» = Y(
7 CONTINUE CCUNTER=CCLN Y(8)=AL CALL GYRATES 0E=-fCPMTl + HPITE (6,10«« CALL GYRATES DESC7=-((G*C WRITE (6,1C5
2 CONTINUE IMJA.LT.l.C IF<EC?(JA),E IF (ECZ(JA). JACC=C IF (FCZ(Jfl). IFCECZ(JA).t JA=JA*JACC WRITE (6,1C8 GC TO 2
IS TRIMMEO FCR STRAIGHT AND LEVEL, r.LIMEING, KING FLIGHT
12),YP(121 /PE:10,AV,AVC5,AV0T,JA,A0,PI,TCPI,TRIM0FT,NEAR, 2, «1, A 2, 0 2,81, E2,3 3,T1,T2,FEC,SIGHC,THEC,ANGLE i CA,T?,TRTl,TRT2,ftL , °E, ALPHA T, START, CNEE,GLEE, VCPT,
KK,CNC9,CKF,THSUS»T:»IH,qETAT,WTl,WT2,XWT,C0NTtZr'Tl
CFT,^ECPT,TOFT,XT,YT,ZT,IX,IY,IZ,IXZtIR,V.R,MASS,G»Si CZ,CZDE,CMtCMnE,GMQ,RVR2fROHfSTHE,CTHEfTVGAIN /ECY(21,5> ,ECN (21,9),ECL(?1,9) »ECM(21,9),ECX(2 1), 2CF(21),cCMCE(21), EC^n (2 i) , ECYCP (21) ,ECNDRf _'1> ,EClCP(2 ,ECNOA (21) ,FCLCA(21>,£CYP(21) ,£CNP(21) ,EC'.t-,(21 ),ECYR(2 ECtR(21) ,FC7(21> 7,IXZ,I9,MASS
5 ITERATIONS ON TRIM,/IX »7HUCCT = ,E12.5,8H WOCT = , T = ,E12,E) CFAFT IS TRIhMED FOR STRAIGHT ANC LEVEL CR CLIPRUG FL «3(1H* ),////) TRIM CZ NOT 03 TAIN ADLE,/1<*H DESIRED CZ = ,E12. 5) E = ,F5,1) CESCZ = ,F7.?> I-RIS = ,E12.5) CZ (, 12 ,*th) = , E12. 5) F(l> = ,E12.5,SH YP(3) = ,E12.E,9H YP(5) = ,E12.5)
>,Y(1>)
n-Y (9) = Y(10)=Y(2) =0.
TE5+1.
<T,Y,YF) 12)*ZT/(RVR2*A3»MASS))/CMOE ) CE (T,Y,YF) CS(!\L) /(^VR2*A1)) + CZDE»0E) ) c*:sc?
R.JA.GT.21) GO TO 5 C.CESC7) GC TO 3 CT.OESCZ.AND.ECZUAU) .LT.OESCZ) GC TO 1
CT,TESC7) JACOM 1.CESC7) JAOC=-l
) JA,EC7(JA)
85
II.JIBJ.H-I J » i III , L.I.I I. I.. _; ... .JIB.!,.! I I . I .1.1 IJUIIWIIW^JJIII
GAM/AE/73-1A
v. *
CONTINUE AL=(JA-3)/£VC5 GO 70 <♦ CONTINUE AL-(UA-3)-(tC2(JA)-CES07J / (EC Z (JAU ) -ECZ (J A) ) ) /*V05
60 TO «♦ CONTINUE WRITE (6,1C3) CESCZ CH0P=1. RETURN CONTINUE
Y(1)=S0PT(CVR/(1.*TAN (AL)»»2)> Ym = SCRT(CVF-Y(l) **2>
Y(8)«AL CALL GY9ATPS <T,Y,YP5 THRUS=(G*SH <R)-RYR2*A1*CX+CX0E»0E) »MASS
Tl=TRTl*TH*Ui T2=TRT2*THRIS WRITE (6,106) THRUS CALL GYRATES (T,Y,Y«=) IF (CCINTEF.CT.13.) GC TC WRITE (6,1C=> Y»tl)tYB(j' YPC?) SttSs«"«».«^..^ .«S<YPC3».GT.*..C.
,APS(YP(5J).GT ..01)
8
1 GO TC 7 RFTUSN CCNTIME WRITE (6,101) RETURN ENO
Y»(i)tYF(3)fYP(5)
86
H-ilrti'■■ -äüMIIW I ■---■■'-—- -■'- J
<wm-*mmmmm i.ii .ui Mi i... .**>? i*tww*m*m..*nm •. ■ .■iiHiUPMP
GAM/AE/73-14
SUPRCU OIMFNS CCKKCK
iTHRUSl 2GA,G£, 6SFE,CF ?ALOT,P ee,c,rx
CCHMCN 1ECX0F< 2l)tEC\ 31)tFCN
REAL I
TINE T ICN Y( /OAir» ,TF»US GCiDE, Et VR,C EDT,£L ,CX0E, /CCCEF 21) |EC OA (21) R(21) , X.IYiI
PIV2 (Y 1?>, Y°
,YP) (12) ,AV
c ♦♦♦#**ENTER TUFK 7RIH h£RE »*#*♦»« C
RETURN ENO
( ;
L 87
M ■Müäffiai' gBUi rffiMrfrrriiiriiritw ajjjü ^rtiiMiMil ■^..■J.8.^.-^- ---—-.»■■, , ,-^,^i-ra ... i - ^=:.1MMi^-. ^.-<-:—.—f- --^_. .^-- ^ j ,^ i,-.itrirMi,ti,lii'aii-.ri 1
---■ ILI"J "<*W.I"I-
GAM/AE/73-14
C C C c c
SUBROUTINE FRINTKY)
*»* AIRCRAFT FAR4METER* AND INITIAL, TRIHMEO CONCITTCNS ARE PRIMED
110
11
10
OIMENS CCFPO
1THRUS1 2GA,Ge, 6SFE,CF 7filOT,P 8B,c,rx
REAL I ALPE=A KRITE( TPIF=1 PRINT PRIM FORMAT
1*»,30X 2»»92X, 3*4.8,^X <»X,*MAS 5,Ell.5 EMS* 7»,92X, 86»<«X,* 9T=*,E1
1 rCRMAT
2N5 • 3*»,EU **92X, «*»- 5*,E1<*. 6*»,cl«< 7*»,92X 8/,lX,*< 9.6,«.X, 10EP ni 21X,100
7 FCRMAT RETURN END
ION Y( /CFAIK ,TFRIS GC.CE, E,V«?,C EOT,AL ,CXOE, X,IY,I L*öV 6,107) • 110,IX 111, (f (1H1 ,/ ,22H»* c, f-< * * ** •*IX2= S=*, El ,5X,««F
INERT £*H«***
RIGM 3.7,<<2 (
**,31X .8,'>>, »***,/ Ö.22X,
,<♦(-*«»
«A1LE» SFLACE (IF»), (5H U
12) /EECH3 ,AV,AVC5 S,A1,A2» A2,ei, [ö,DR, TRT1,TRT <rCS,CNn!',CHCF, CFT,^ECPT,TCPT CZ»CZQF»O,CF0 2,IXZ, IR,fßSS
,AVOT,JA,AO,PI,7CPI,TRIFOFT,NEAR E2,T3,Tl,T2,FF.C,SinHC,THEC,ANGLE 2,AL ,RE,ALPMAT,START,CNE5,CLEP,V TH'-?US,TRIM,3ETAT,WT1,M2,XWT,CCN ,XT, YT,ZT, IX, IY,I2|IX2,I«J|HRfMAS S,CMQ,RVR2,R0F.,STFE,CTFE,TVGAIN
» » CPT , T,ZM, S,G,S,
Y(l) ,Y(3) ,ALPc
,IY,IZ tJ),J= ///, M * AI ,/),ix ♦>E1<*. 1.5,t»X «*♦*,/ 1A = *,E ,',1X, EhGPIE >,<<H**
?2X,«*H
*V(3) = ,1*,<«H
«FFI(0 *,/,lX = 2X,UH CN ni«
/),1H1 = »El
»IX 1,6 IX, FCR ,<*F
e,6 »*w »IX 12.
Z,MAS ) ,TFE tUOd AFT »#* *t
X,<*h* ING A
e,^x,
S,S, C,FE H*) , FARA *X,* ?**.
REA= '»»9 »FP£
»E 12.6 ,3(/,lX,<»H
,15X
C,9,IR C,SIGH /) »Ml METERS IX=*,E /»IX,'» •tEll. 2X,<*H* OUENCY HGINE
»9 »
»MR, C,Y ( X,«+H
•
It». 8
5,*»x ***
= *,E THRU %/, 2X,t4
T1,T2, 7),CE, **** f9
*»,3CX ,<«X,*I *»9?X, ,*CHCR /,1X,<+ 12.6,2 STSt IX ,t*H»
THRUS CA,CR 2X,<«H , **H*» Y=*,E UH»**
C = ',E
M,<*H LEF
**»,2 »3(/,
*,E1 #* » #
»/»l )=*, ,UF* ** ** FLAC »E 1* ) 2.5/
3 (IX
,5X, X, M Em. ***» >/>l E*FN .3,5
IX, <♦
*P(0
8,W £X,* X,t,H T = *, 3X,t+
***,92 W(0)=» )=*,F1.
,*PSI< IMTIA
E m. s,
30X,31 X,*»H**
,Ei^,8 i».8 ,MX
Q) = *,E L ALT! X,*ELE
/,3(1X
I-»»*
*»,/) ,22X, ,»G(C /,1X, 1««.3, TLCE = VATOR
IN ,1X,
)--*,
mx, SEI
CIS /,1X «» g
»**♦,/) **»/»3( l<t.8,t»X *»/»ix, 11.5, t*X ,5X,*PO ••♦»»/» T EK:IN '.XJ'TCT IX,100(
ITIAL
•*,/»ix E1^.8,U **,5X,»
w.8,56X PLACEMZ
2X,^H»*
,lX,Uh** 1X , <■ F « * • ♦IZ=»,E1
t*c FAf = * TAFY IE« 1X,«»F*** E = * ,E 12. AL TFRLS 1H*)) )
ccKcnic 5X,»L(C)
x,*«; (C) = TFETA (0) ,1X ,t)K»» j k F « • • * , KT8*VE1(« ,5X;";L: *»,/) ,<♦(
,?H H = ,E12.5/,5H A = ,E12.5)
88
■■'.(!- .-" ■"' "—■"«-'—■ '«■"-T „_i,, iij gwp^ispHBWilwpwBiBü-JMMM.IJ^I.=UM^IHW.-UHWJPW- MJIJ^P».>-I...IIIJI.IU'"H msym^wmt * WWWW " ^1
GAM/AE/73-1A
1 30 2 3 I»
6 7 8
9 10
20
21
22
23
2*»
11
12
13
1W 15 17
18 19
•AESCHJ) 1,1,3
SUBROUTINE FkGXYZ( X,Y,F3,N »HX, EMAX,F) CIMENSICN ^ (15>fY0(i5> ,YT( 15), YPU5) ,P0 (15) ,P1 (15) , F2 (1<3>, F3(15)
X0=X X=X*0X H=Q.5* (X-XC) H = H*H IFCAES(X-XC) DC t* 1 = 1,N Y0(I)=Y(I) H7 = H XT=X0 00 5 1=1,N YT(I)=Y0(I> ASSIGN t 7C X GO TO 20 CO 7 1 = 1,N YF(I)=Y(I> HT=0.5*H ASSIGN 9 TC * GO TO 20 CC 10 1 = 1, N YT(I)-Yd) XT = X0*>-T ASSIGN 11 TC K CALL F(XT,YT ,F0) 00 21 1 = 1,N Y(I) = YT(I) +C ,5'HT*F0(I) CALL F(XT + C.5*H.T,Y ;Pi) CO 22 1=1.N Y(I)a\t(IHM'(i 2071 C 6761* F0(I) +.292893 21?«P1<I)) CALL F(XT*0.E*HT,Y,P2) 00 23 1=1,N Y(I)=YTII)4H«(.7 0710€7 81» (P2(I)-Plt I)) ♦P2(I1) CALL F(XT4t-T,Y,P3) OC 2«» 1 = 1,N t<I) = YT(I>*FlM°0CI»*.E857e6«»3 8*Pl(IM3.*iit21356'P2(I>*P3( I)) /6.0
GO TO X, (6,<=,11> RKAX=G 00 12 1=1,N R=AGS( (0.0 3* (Yttt-YPIT)) )/Y(I> ) IF(APS(Y(I)) .LT.1. 1AX)R = AGS (10. 0 3MY(I)-YP(I)))/EfAX)
RVAX=AHAX1 (F ,mx) Y(I)=Y(I)MY (I)-YP (I) )/l5. 0 IF(R^AX-Ef-AX)13, 13,17 XC=X0+h IF(XO-X)15,1^,13 RETURN IF(RHAX-0. C3'FfAX)30,3:,2 H=HT XT = X0 OC 19 1=1,N YF(I)=YT(I) YKI)=YC(I) GO TO 8 ENO
89 J
«*«-■■ • «■' 'I' i!'.«.t. «!>. ---m i |_| .. . uq|Ma9W
UP. ifc.i ■■—« UIMU.HIHIII
GAM/AE/73-14
('
C c c c c c c c c c c
SUBROUTINE CCN'TRl.(Y,YP,T> DIMENSION V( lc), YP(12> CCMMCN/rMAIN/FECHD,AV,AVC5»AV0T,JA,'»0,PI,TCPI,TRIM0FT,NEAR »
lTHPUSl,THRLS<,ßltA2iÄ3»Bl»E2,33,T1,T?,FEC,SIGHO,THEC,ANGLE» 2GA,6BfGC,D5,CAt"3:?»TPTl,TCT2,AL,PE|ALPMAT,STfl';TfChEEiCLEEiVCPT» 6SFE|CFE,VP-,CHCRf GNCRjCHCP, THRU S »TRIM , PE TAT , WT 1» W T 2 , XWT ,CCN T , 2 H » ?ALOTfPEOT,ALCrT,9ECPl,TCFT,XT,YT,?T,IX,IY,TZ,IXZ»IP,WR,MASS,G »Sf 8B,CfCX|CXCEiC2iCZOF,Ct'tCfOE,CMQf1VR2iROH,STHEfCTHE,TVGAIN
REAL 2XvZY|X2flXZfiR,fASS CCWT=0. IFCT.LT,3.»RETURN
*** SPECIFY CONTROL PCCEt
VOFT=C. CONTROL SURFACES ONLY VOFTrl, THRIST VECTORING VOFTS2. HOHENT THRUSTERS
ANO SFECIrY THRUST CONTROL GAIN. TVGAIN= */. CF RLOOER ANGLE
•• SPECIFY BETA CONMANC IN DEGREES. TVGAIN=0.2 VCFT=0. BECFO-C. CCNT=1. 0E=-2S. OPMX=30. 0AMX=15. 3EC=IECMC/AV G1=.C5 G2=.5 G3=.0«5 T1=T2=1CCCC. OE=DE-T+3. IF<OE.LT.-25.) 0E=-25. BEC=BEC^C/AV DR-(G1»Y(6)-G2*(TE-PEC )) »AV OA=(G2*YU)MAV IF(APS (0 A) ,G1.CAMX)OA=CA«OAMX/A*S(OA1 IF(ABS'.C°) .G1.CRMX)ORsCR*0RMX/ABS(CR) RETURN END
( '
90
HP—,!-»**——.-f.". HOT» i>ll|IH..i<« mw^.m« m ■ i« -■■ •»■■>««-p|..<:
GAM/AE/73-14 1
g?
SUBPO OIHEN CGMKC
1THRUS ?GA.GP 6SFE,C 7ALDT, 8B,C,C
REAL IFCVO AlOEG IF(AL IF(AL IF(AL IF(\C IF(VC BETAT IF(V0 OR=0. RETUR CCNTI ORMX= HT1 = H AKG-T HTMX = HT=TV IF(DR iFtcn RETUR END
ITXNE
ts/C^ß 1,THR »GC i C F£,VP FECT, X,CXC IX.IY FT.EQ = fll*A DEG.L CEG.G TEG.G FT.EC FT.EC = TVGA FT.EC
N NUE 30. T2 = 0. VGAIN CT1 + T Al»V«T .LT.Ö .GT.Q N
VECTOR« Y,YF) Y ( 12),TP(12) IWE>ECMQ,A\l,AVC5,AV0T,JA,A0,PI»TCPI,TRIM0FT,hEAR, LS2tAi|A2|A3teif e2,3 3,Tl,T?,FEC,SIGHC»THECfANGLE , EfCetTJ.TRTltTCTS^LjEEiALPHAT.STAKTjChEEfCLEEtVCFT, ,C^C3, CUR, CFCP, THRU S,TRIM,RET AT, WTl,KT2,XWT,CCNT,ZKTt ALCr-T,nECPT,KPT ,X'T, YT.ZT, IX,IY, IZ,IXZ,IR,WR,MASS,G,S, E,CZ,^üE,C*,CH)E,CMQ,RVR2,ROH,STHE,CTHE,7VGßIN ,I3,IXZ,IR,"ASS
) RETURN .0 V T. T. T.
20.)TVAU=C. JO TVAU = (£LCEG-30.)/20. !C.) TVAU=1.
.2.) GO TC eg
.3) TVAUal, IN«TVAU»rR/flV •It) RETURN
*CCMX/AV 2) «*T*SIN(ANG> /XWT ^X'AES(QF/CRfX) .) *Tl=WT .) VT2=WT
91
1 '■■ —
■ - !»-«■!**« ■ . ||IJ,1I|.W^1J11.,^ ■ 1 . -«™ I .1-1 I- ■ ■ ...."-!' -—-.—— -,. •■«■i.i.ii pmmmmfimmtn* W.» ''llim\iyi fI" ■-«■■-'■■-«?T-JJUMl_.IJ.lMWt
GAM/AE/7J-14
r
Appendix E
Aircraft hodificntions For Improved Directional Stability
The majority of the high-performance aircraft built to date has
experienced directional stability problems which failed to surface prior
to aircraft reaching fully operational status. As previously discussed,
the corrective action is normally to impose regulatory limitations on
the crew in order to avoid that portion of the flight envelope vulner-
able to departure unless the severity of the problem necessitates minor
and/or major configuration modifications. The following are examples
of modifications to the air frame, flight control system, or both.
Air frame. Configuration Changes
One of the first problems to surface stemmed from roll inertial
coupling. The corrective modification applied to the F-86 and F-100
was to extend the vertical tail by more than a foot in length. The
same technique was attempted when later aircraft developed directional
stability problems and in severaj. cases, the increased tail size was not
only ineffective, but proved to be destabilizing in the high angle-of-
attack regime (Ref 9 and 19).
There has been considerable research conducted to determine the
effects of various wing modifications on directional stability. Drooped
leading edges were found to increase both directional stability and lift
characteristics at high angle of attack f>r certain wing-body combina-
tions (Ref 9). Although drag consideration precluded their use on high
subsonic aircraft, the concept led to the retractable leading edge slat
such as that used in the F-4 Agile Eagle program. Conversely, there are
several examples in Reference 19 of configurations vising leading edge
L 92
, ^ :
U, ij.1^H'JW»W.'JlWW«JJIIIMm*J"W>"'|.,i4''W->W-.|U-.I.U..I.-il.lMI'|IW-M.'W.L]|ll Llll.il I ■-! j '•" ' » I "--■-» !".
GAM/AE/73-14
slats or flaps that showed little improvement in directional stability.
Fixed vertical chin canards similar to those used for Reynolds
number effect correction on drop models have been used on a few aircraft,
Their effectiveness was limited to enhancing spin recovery (Ref 3, 5, 9,
21) and did little to improve directional stability.
Nose strakes such as those to be used on the Northrop YF-17 light-
weight fighter have also been shown to improve spin recovery capability
on model tests conducted by NASA (Ref 10). This improvement was only
apparent in the oscillatory type spin and no effect was apparent in the
flat spin mode. Similarly, no evidence of improved directional stabil-
ity was apparent with the strakes added.
Control Systen Modifications
Another of the early stability problems encountered in high-
performance aircraft was the pitch-up departure of the F-101. The
pitch-up occurred prior to stall and was followed immediately by
departure from controlled flight. Obviously, the condition was a
totally unacceptable risk during the landing configuration. Ihe
problem was initially corrected by installing a stick-pusher and warn-
ing horn (Ref 5). The stick-pusher solved the problem; but, created
new problems in the form of limited maneuvering capability and pilot
dissatisfaction. The stick-pusher was later replaced by the Honeywell
boundary control system (Ref 5). The boundary is calculated continuous-
ly by the system as a function of Mach number and compared to pitch
rate, angle-of-attack, control surface position. A limit function
based on this comparison controls the engagement of the system which
flics the aircraft at the c-ilculated boundary unless the pilot over-
rides the system with excessive stick force or reduces the stick force
93
i-«»«ii_wwi,-i.^.riiB IffifitM
(
II»>»«j-_^r' """■-"^""■■'" ■ — ■ - —J- ■ ..■..■....,..r.-,., .„„^.^»^„.nn i.ii..i,it1iu„tmu_|J_..iuai.L.uuii...j|un ,L-.u.-.linil.-IJ,>.'IW«JWMH»HIUJiii|i«li JI«ll|IIIJilll»|ill,»JlUI.-IUl^URJJt>pi[lllu.lL).l|JIJU.UIr —
GAM/AE/73-14
sufficiently to fly off the boundary, unfortunately, the boundary used
is that defined by r.he pitch-up condition which was never corrected.
The result is an artificial maneuver envelope that lies well within the
lift limited envelope. The region between the two envelopes is a
safety zone that without the stability problem could be vitally needed
in an air superiority situation. This may seem an unnecessary require-
ment for a reconnaissance/air defense interceptor aircraft; but, one
must realize, the weapon system is worthless as an interceptor if it
cannot defeat the aircraft it has intercepted.
A current example of a control system fix is the alpha-limiter/
beta-reducer departure inhibitor system to be installed on the F-lll.
The alpha-limiter senses angle-of-attöck to calculate a pitch rate for
driving the pitch damper, to reduce command augmentation gain, and to
increase stick force. Tl e beta-reducer feeds differential tail as a
function of angle-of-attack into the rudder for increased roll coord-
ination and provides yaw rate data to rudder control for sideslip reduc-
tion. The name of the system is the best statement of its limitations.
Like all control system cures for stability problems that are in u/e to
date, the alpha-limiter/beta-reducr.r creates a buffer or margin of
safety zone at the performance limits. Obviously, since departures
occur in critical maneuvers such as air-to-air combat, a portion of the
air superiority flight regime lies in the buffer zone. The loss of
this portion of the flight envelope may seriously hinder mission accom-
plishment.
Airfrainc/Control System Modifications
As mentioned previously, the leading edge slat configuration
common on many transport aircraft as a high lift device has been
94
-si^^SSi^^^^m^^-^^^^^ ,-,.... ...... .-■ ^.^g—.T^,^. ,„.., ,...,.^. _^.f,^.„-, _., . ■fj...;:^^^.;.. .,. ,- ■ ...
GAM/AE/73-U
successfully used as a device to improve directional stability. The
Agile Eagle (F-4E) modification by McDonnell Aircraft Company resulted
in a major improvement in lateral-directional stability at high angles-
of-attack (Raf 5); but, is also mentioned, this modification has not
been as effective on other configurations (Ref 19).
The use of small retractable vertical or horizontal canard surfaces
had similar effects to those fixed canards mentioned earlier. While
somewhat effective in affecting spin recovery (Ref 5 and 21), they
showed little evidence of improving directional stability. Similar
results were apparent using retractable nose strakes (Ref 10).
In 1959, Cornell Aeronautical Laboratory, under contract to the
Havy Bureau of Aeronautics, successfully improved lateral-directional
stability of the F7U-3 by installing enormous vertical canard-mounted
yaw vanes (Ref 1 and 5).
The fact that strakes, fences, spoilers slats, canards, oversized
vertical tails, and grotesque, ungainly yaw vanes are required to provide
some semblance of directional stability in various modern high-performance
aircraft is sound testimony to the statement made by Harold Andrews at
the 1971 Stall/Post Stall/Spin Symposium (Ref 5), "We still do not hava
the tools to design the a.'rcraft right in the first place ....".
95
.j^^ajaafcja.y-,,,.. . .. .„ .-..,^wJJa^_^
rjwii- -HJiNP»*!»" ii.iwiiMiijBiiwii. .i. ii „I I.HIB.HPHI.W!M i ■mipni^pji i|, . J—.-.J fpappppj .■ ■■»■ IPP.P ■■■■-■■■ IM
GAM/AE/73-14
Vita
Deas H. Warley III was born
He joined the United States Air Force as an enlisted man in February,
1961, after graduating from After returning
from a Vietnam tour in 1967, he attended college as a part-time student
and completed requirements for the Airman Education and Commissioning
Program. He received a Bachelor of Science in Engineering degree
(magna cum laude) from Arizona State University in 1971. After com-
pleting Officers Training School, Lackland Air Force Base, Texas, as a
distinguished graduate, he entered the Air Force Institute of Technol-
ogy in January, 1971, as a graduate student in the Aerospace-Mechanical
Engineering program.
Permanent address:
This thesis was typed by
96
—i -rum irfmü"""-—* nil