The Shuttle Program development schedule and the management decision to perform an orbital, manned mission on the first launch resulted in a requirement to develop realistic aerodynamic uncertainties for the preflight aerodynamic predictions. This paper addresses the methodology in developing two types of aerodynamic uncertainties. One involves the ability to reproduce aerodynamic results between various wind tunnel tests. The second addresses the difference between preflight aerodynamic predictions and flight results derived from analysis of past aircraft programs. Both types of uncertainties for pitching moment, lateral-directional stability, rudder power, and aileron power are presented. In addition, the application of uncertainties to flight control design and fight test planning is briefly reviewed

Underwood, J. M.

Young, J. C.

English

NASA Technical Reports Server

10164
THE DEVELOPI_NT OF AEROD YE_ilC b_CERTAINTIES
FOR TIIE SPACE SHITI'_.E ORBITER
James C. fo,_g and J_7 M. Underwood
NASA Johnson Space Center
_ous ton, Tey._s
ABSTRACT
The Shuttle Program development schedule and t_e. manageme=t
lecision to perform an orbital, manned mission on the first launch
resulted in a requirement to develop realistic aerodynamic
,ncertainties for the preflight aerodyzamic predictions.
This paper addresses the methodology in developing two =ypes of
lerodynamic uncertainties. One involves the ability to re_rQduce
lerodynamic results between var ious wind tunnel tests. The Second
iddresses the differences between preflight aerodynamic predictions
_nd flight results derived from analysis of past aircraft pr0gr am_-
_oth types of uncertainties for pitching moment, _ateral-directioual
_tability, rudder power, and aileron power are presented.
In addition, the application of uncertainties to flight control
lesign and flight test planning is briefly reviewed.
NOMENCLATURE
)
3 a
3.
L3
3
r
U
n
a
1"
L3
Span, inch-s
Mean aerodynamic chord, inches
Ai!e=on roll derivative, per degree
Dihedral stability, per degree
Rudder roll derivative, per degree
Pitching moment coefficient
Aileron yaw derivative, per degree
Directional stability, per degree
Rudder yaw derivative, per degree
Body length, inches
1 _,._9
J
t
https://ntrs.nasa.gov/search.jsp?R=19840002097 2020-03-22T07:48:01+00:00Z
Mach
MRC
S
5
a
5
r
ORI_NAL P_G_ i_
Math number OF POOR QUALITY
Moment reference center, fuselage station X o
inches
Dynamic pressure, psf
Reference area, lq. ft.
Angle of attack, deg
Angle of sideslip, deg
Aileron deflection angle, deg
Rudder deflection angle, deg
Wind tunnel - ADDB difference
= 1077
ADDB
AEDC
AFFTC
ARC
Calspan
DFRF
FCS
HST
HSWT
JSC
LaRC
LT?
NASA
NSWC
RI
TWT
UPWT
16T
Aerodynamic Design Data Book
Arnold Engineering and Development Center
• 4 -
Air Force Flight Test Center
Ames ResEarch Center
Calspan Corporation
Dryden Flight Research Facility
Flight Control System
Hypersonic Shock Tunnel
Bigh Speed Wind Tunnel
Johnson Space Center
Langley Research Center
Ling-Temco-Vough=
National Aeronautics and Space Administration
Naval Surface Weapons Center
Rockwell International
Transonic Plan Wind Tunnel
Unitary Plan Wind Tunnel
16-Foot Transonic
INTRODUCTION
Two management policy decisions made during the initial
development planning for Shuttle had a significant impact on the
approach to aerodynamic design and verificaticn. In order to meet a
compressed development schedvle, a decision was made to concurrently
design the FCS and conduct aerodynamic verification wind tunnel
testing. Realizing the predicted aerodynamics were likely t_ change
during the aerodynamic verification process, the FCS was designed to
be insensitive to "reasonable" changes in she aerodynamic
characteristics• As a result of this approach, the aerodyna_icists
were required to provide uncertainties on the preflight aerodynamics.
The uncertainties used in the FCS design were defined as tolerances,
which are the minimum error that is expected in the preflight
aerodynamics.
Secondly, thc decision to perform an orbital, manned mission on
the first launch highlighted the aerodynamicists" problems. This
1170
i decisi3n raised the =eneral question of how to maximi_e :he mission
safety vi_houl the benefit of either a graduated flight test program
(as used by the aircraft industry) or an initial unmanned flight
v _, , •c-==__t (as used by the early space program) The consequence of this
decision on the develop=cut of an aerodynamic data base resulted in
the prob!em of how to provide an estimate of maximum pomJible errors
in the preflight predicted'aerodynamics, especially in previously
uncharted flight regimes. _ovever, the estimated e_rors must not be
so great as to completely invalidate the FCS design. Thus, a set _f
"worst case" aerodynamic uncertainties, defined s_ varia:ions, was
developed. As part of the first flight certification, variationg,
combined with other system uncertainties, were used to "s_ress" the
flight ccntrol system through a mu!titude of simulations. As a
consequence, the initial entry was flown at a center of _avity and
with FCS gains which m_ximized the aerodynami: margins t_ereby
maximizing mission safety for these systems. . _
This paper briefly addresmes the development of the =ominal
preflight aerodynamics and details the methodology for es:abiishing
tolerances and variations.
PREFLIGHT PREDICTIONS
One _f the largest wind tunnel programs in history has been
conducted 1 for the development of the Space Shuttle. The Orbiter
(fig. 1) alone has been tested over 27,000 occupancy hours to
determine the performance and stability and control characteristics.
This extensive wind _unnel program provided the foundation for the
form lation and development of the ADDB 2. The ADDB is the result of
the combined efforts of the prime contractor and several NASA centers
and consists of a digitized set of tables developed from :he
engineering analysis and fairing of all valid experimental data,
complemente_ by e_pirical and theoretical data, and extrapolated to
flight conditions where appropriate. Thus, the ADDB represents the
"best es:imate" of the preflight aerodynamics.
TOLERANCE DEVELOPMENT
Sl.ce the wind tunnel data base is the foundation for the
preflight predictions, it is reasonable to assule that the minimum
error that could be expected (i.e. tolex-nces) would be the ability to
reproduce experimental results between various tests. Therefore,
repeat tests were performed uain_ various facilities, different
,o_els, and on occasion, different test organizations. Although the
[ iividual causes for aLy differences were not specifically
i_ .ntified, it is. felt the total difference is represents:ire of what
may be expected for wind tunnel test repeatability.
11:1
As an illustration of the mechanics of this procedure, consider
pitching moment coefficient, where repeat tests were plotted along
with ADDB estimates, as typically shown in figures 2, 3, and 4. From
figure 2, it can be seen that a 0.05-scale model, model 39-0, was
tested in both ARC ii x ll-Foot Facility and in the LaRC !6-Foot
Transonic Facility. Similarly, a 0.OlS-scale model, model 44--0, was
tested in three facilities: i) the LTV 4 x 4; 2) the LaRC 8-Foot
Tunnel; and 3) the ARC II x ll-Foot Facility. In addition, the 0.02-
scale model, model 105-0, was tested in the LaRC 16T tunnel. With all
these potential sources of differences, a peak-to-peak repeatabili=y
in C of approximately 0.006 was reaiized. This repeatability
m
represents the combined error sources of the following: I) the same
model in several tunnels (tunnel-to-tunnel repeatability); 2)
differ(nt models in the same tunnel (model-to-model repeatability)_
and 3) different test organizations (testing technique differences).
This ,[so includes any Reynolds number and blockage effects.
From this type of basic plot, the difference between the wind
tunnel results and the ADDB at various angles of attack were plotted
verse, s Math number, as illustrated in figure 5. Tolerances (wind
tunn,_l uncertainties) were obtained by fairing a curve through these
data points using cngineering judgement. The nominal angle of attack
(fig 6) was given a high weighting in the fairing process.
Aerodynamic tolerances for lateral-directional stability (AC
n B '
AC£8) are presented in figures 7 and 8, while tolerances for rudder
power (AC , AC ) are shown in figures 9 and I0. Aileron power
r r
ACn_ , AC_ ) tolerances are presented in figures II and 12. Table i
a a
presents the facilities and models used in this evaluation.
VARIATIONS DEVELOPMENT
It was felt the most reasonable approach to the development of
variations would be to analyze the wind tunnel to flight test
differences of past aircraft programs. Unfortunately, the
ve_i£ication of preflight predicted aerodynamics was not a major
objective of mos _ of e_- earli_ - flight test programs. This severely
limited the amount of data available for conducting flight test to
wind tunnel comparisons. The flight data base was further limited by
restricting the comparison to those vehicles which were geometrically
similar to the Orbiter. TLose vehicles chosen as applicable to
Orbiter are presented in table 2. Also presented are geometric
factors and other considerations pertinent to the vehicle
configuration choices.
1172
1
x
.f
|
._r
Fariations were established by fairing the differences between the
_-ight and predicted aerodynamics as a function of Math number. The
_elections of =he configura=ions and the fairing process are very
subjective in aature. For _his reason, a team of aerodynamicists from
AFFTC, NASA-DFRF, NASA-JSC, and RI was formed to conduct the analysis
and reach a concensus on variations.
The team's flight-to-predicted correlation and their recommended
variation fairings are presented as a function of Math number for C m,
figure 13
; Cn , figure 14; C_8, figure 15; C n_r, figure 16; C_ r'
figure 18; and C_ , figure 19. These figures werefigure 17; Cn_ a
a
taken in part f_om reference 3.
As can be seen from the flight correlation figures, the flight
data is limited to the lower supersonic speeds. I= Math regimes where
flight data was unavailable, variations were obtained by multiplying
the tolerances by a safety factor, usually 1.5.
Comparison of tolerances and variations at the lower Math numbers
indicate, as one might e_pect, that tolerances are less than
variations.
A more detailed dp-elopment of variations is found in reference 3.
These recommended variations were modified primarily to facilitate
computerization &nd included in the aerodynamic design data base,
reference 2. •
CONCLUDING REMARKS
Requirements of the Shuttle Program resulted in the development of
the first comprehensive set of uncertainties in predicting preflight
aerodynamics. In the process of the uncertainties development, a
systematic wind tunnel study has been performed which demonstrates the
need for testing multiple models/facilities when precise prefligh=
aerodynamic predictions are needed.
The application of these uncertainties resulted in a
desensitization of the flight control system to aerodynamics, thus
providing increased confidence in the safety aspects of conducting a
manned orbital mission on the first launch of the Orbi=er.
ACKNOWLEDGEMENTS
The development of variations and wind tunnel uncertainties was a
team effort in every sense of the word. Space does not permit
recognizing everyone who participated in this effort but the authors,
1173
as representatives of the Shuttle program, would like to recognize key
government and c,_ntractor personnel.
Special thanks to James ?. Arrington, Bernard Spencer, Jr. and
George M. Ware of LaRC; Joseph Cleary and Lee Jorgensen of ARC; and
Paul O. Romere of JSC for their effort in the development of wind
tunnel uncertainties.
The difficult task of establishing variations was accomplished by
a team composed of Joe Wei! of DFRF; 2_ul W. Kirsten of AFFTC;and Dave
Tymms of JSC.
Don C. Schlosser ably represented Rockwell International in both
endeavors.
REFERENCES
I. Whitnah, A. M. and Hillje, E. R.: Space Shuttle Wind Tunnel
Program Summary, AIAA-82-0562, March 1982.
2. Aeroaynamic Design Data Book. Vol. I Ozbiter Vehicle. NASA
CR-160903, Nov. 1980. (Rockwell Rept. No. SD72-SH-0060-IM.)
3. Weil, Joseph; Powers, Bruce G.: Correlationof Predicted and
Flight Derived Stability Derivatives with Particular Application
to Tailless Delta Wing Configurations, NASA TM-81361.
1174
¢
I,
/
ORIGiI','AL PAGE I,_
OF POOR QUALITY
TABLE I.- WIND TI_NEL TESTS USED r0R UNCERTAINTY EVALUATION
TEST ID
Traueouic
I. OAI45A
2, OA270A
3. 0A270B
4. LA70
. LA76
6. LA77
_. LAIII
_. LAII5
Supersonic
9. 0A1453
I0. 0A145C
II. 0A209
12. LA63A
13. LA63B
14, LA75
(5.) LA76
15. LAI01
16. LALI0
17. LAZI4
18. LA125
FACILITY MODEL
NO. SCALE
P_ BLOCKAGE
C
(xlO 6) (z)
ARC llxll 7T 39-0 0.05 5.9, 9.9, 17.8
LaRC 16T 39-0 0.05 7.9
LaRC i6T 105-0 0.02 3.1
CALSPAR 8 FT 44-0 0.015 2.1, 2.7, 4.7
LTV _x4 RSWT 44-0 0.015 4.5, 5.3, 5.9
ARC l!xll FT 44-0 0.015 4.7
LaRC 8 FT TWT 44-0 0.015 4.1
LaRC 8 FT TWT 44-0 0.015 2.5
39-0 0.05 3.0, 6.9, 8.9 " *
39-0 0.05 2.0, 5.0, 6.4, 7.9
105-0 0.02 3.4, 7.7, 10.4
44-0 0.015 1.2
44-0 0.015 1.2
44-0 0.015 1.2
44-0 0.015 4.5
44-0 0.015 1.2
44-0 0.015 1.2
44-0 0.015 1.2
105-0 0.02 1.6
ARC 9x7 FT
ARC 8x7 FT
AEDC A
LaRC UPWT-1
LaRC UPWT-2
LagC UPVT-2
LTV 4x4 RSWT
LagC UPNT-1
!aRC UPWT-I
LaRC UPWT-2
LaRC UPWT-2
i I .09
.65
.I0
.18
.74
.10
.24
.24
. r
TABLE 2.- ORBITER CORRELATION APPLICABILITY (ref.3) ¢
AIRCRAFT
IB-70 /
YF-12 /
X-15
TACTA. 58L /
WING
GEOMETRIC FACTORS
_ING !WISG SINGLE 'LARGE
FLAP iELEVO_ VERTICAL FCS
FLANFORM LONG. LATERAL TAIL
CONTROL,C0qTEOL
/
/
/
/
/ /
,' /
HPII5 /
s-58 /
YF-16
F-SSCW
/ /
/ /
/
*SEE REFERENCE 3 FOR AIRCRAFT IDENTIFICATION
REMARKS
GOOD FRED. BASE. N RANGE
CANARD, LIMZTED _ RANGE
r
GOOD M RANGE,
LIMITED _ L4.NGE
WIDE _ N lANCE
ONLY LIMITED DATA
CURRENTLY AVAILJLBLE
LOW SPEED DATA O]ILY
GOOD PREDICTIVE 3ASE,
M i_NGE
SOURCE OF RUDDEI
CONTROL DATA
jP
1175
21
GEOMETRY
AREA
SPAN
ASPECT PATIO
TAPER RATIO
SWE_P(LE}
DIHEDRAL
INCIDENCE
MAC
COMPONENT
WING VERTICAL T_IL
2SSOFT2
(249.9092 m2)
936.68 (23.8-4 _.5,I
2.265
0.2
81/45 DEG
3.5
0.5 DEG
474.81 (12.0602)
413.25 FT2
(38._922 rn2)
315.T2 (8.0193)
1.675
0.404
,_5 DEG
_w
w_
199.$1 (5.0752)
NOTE: UNLE5S OTItERYrlSE NOTED, ALL DIMENSIONS
ARE IN INCHES (METERS)
Vo:O-e.._,_
1$.o4s41
(IML)
I MOMENT
REFERENCE
I CENTER '-'7 /._/44_.72
Z0=372|. __ --_'_----J
(9.44ea) "----
I-RE_ROO_'E_n_J
1290.3 {32.T73G)
Zo:372
(23.8425)
Figure I.- Space Shuttle Orblter geometry.
ORJG,Ji'VAL P,_,3t__"
OF POOR QV_L:T',_
.C6
.04
.1: ', .02
r..) uJ
z.--O
_-o
-I- 0
o -.02
:E
-.04
O OA, tSA ARCltx 11 _ 0050
LAT_ LTV 4 • 4 44-0 (1015
O OAZTOA L,z,qC 16T ]SO 0 050
A OA270B LaRC lb-I" 1050 0020
LAT? ARC 11A 11 44-0 0015
lit LA115 LaRC | 'rYv'r 440 o.015
AE_OOYNAMIC DATA BOOK
RI
La_C
RI
pl
L_C _- _ -
L_C
I I I I I I I I I
2 4 6 8 10 17. 14 16 18
ALPHA, ANGLE OF ATTACK (DEG)
Figure 2.- Pitching moment, Mach 0.6.
1176
I-Z
u
O
m
u..
LL
LU
O
I--
Z
UJ
o
Z
'1"
svv OATASOUnCE _ _ SCALE ORGANIZATI(_
[] OAI45B ARC 9 x 7 39 0050 RI
(') OA209 AEDC A 10=3 0020 RI
/..= LA 76 LTV 4 • 4 44 0015 L,iRC
LA110 LIRC UPWT-1 44 0015 LaRC
AERODYNAMIC DATA BOOK
-.02
-.04
-.06
.04 -
_% ORIGINAL PAGE |_
.02 OF POOR QUALITY
0
I I I I ! I I i
-5 0 5 10 15 20 25 30 35
ALPHA, ANGLE OF ATTACK (DEG)
Figure 3.- Pitching moment, Mach 2.0.
!
4O
$VM DATA SOURCE FACILITY MOGEL SCALE ORGANIZATION
1"3 OA 145B ARC 9x7 390 0.050 RI
OA 145C ARC Bx7 29-0 0.050 RIA 209 AEDC A 1050 0.020 RI
V OA 209 AEDC A 105.0 0,020 RI
•_ LA 125 LaRC UPWT-2 44.0 _.a20 t=RC
0 LA 110 LaRC UPWT-2 44 O 0020 LaRC
AERODYNAMIC DATA BOOK
zP" 0.02 _ •
0.00 o
-0.02I-
_ -0.04
-0.06 I
!_-o.o8[ , , , , , , , , J
V
-4 0 4 8 12 16 20 24 28 32
ALPHA, ANGLE OF ATTACK (DEG)
Figure 4.- Pitching moment, Mach 2.5.
1177 %-
E
O
,02 -
.01
0
-,01
-.02
WIND TUNNEL
UNCERTAINTIES-'( /
I--,
ORIGh"qAL PA_E ;i-;_
O OF POCR QUALITY
• 0 [3 O
[] 0
0 5
o Ilsl
oo I 2o I
_- 12s I
L 3° i
I I I I I , ,t I I I ]
0.2 0.4 0.60.81.0 2.0 4.0 6.08.010
MACH NUMBER ..........
Figure 5,- Orbiter pitching moment uncertainty.
 oo- ,oo- I ,or
z o- _ 2oo- _ 2ooi-< 2ol----.+-n.i _"-'-__...-"I if-.,, i -_!!-_-" ....
o ...... • ....,.,. Z •!: !/V" ,i---.<_
LU " / "'_,_ I j%_ | I '
i < " I "-_'_ "4. !
._.. -50- "= 100-- i=7 1001- _ 10- J _//_ _! --i'i
/I "_ !l'J_
- f 711- _:
I I_ " --...
-100 L. 0 0 - ?2 "--i"/I , i I i I I i_ I 7 I
.4 .6 .8 1 2 4 6 8 10 20 30 :
MACH NUMBER
Figure 6.- Typical Orbiter eutry trajectory.
1178
.0010
.0005 -
¢CL
(J 0 -
<!
-.0005 -
-.0010
FLAGGED SYM - FLIGHT RESULTS
- 0
CK;G,',!;_L ....,-'_j ;g
OF POOR QUALITY
/_ WiND TUNNEL
I _ _15
O' co • • • • Oc_l
_'0 O•o,, ,,9 '_ •• °oo • I "_ 12s2°
0
I
0.2
! I I I ! ! 1 l !
0.4 0.6 0.81.0 2 4 6 8 10 ....
MACH NUMBER
Figure 7.- Orbiter directional stability uncertainty.
.0010
.0005
o
-.0005
-.0010
0.1
m
A _, ._-WIND TUNNEL
UNCERTAINTIES
A^ _ - sv'a =
o o oo;
I I I I I I l t I I
0.2 0.4 0.6 0.81.0 2 4 6 8 10
MACH NUMBER
Figure 8.- Orbiter dihedral stability uncertalnty.
1179
&
F
!
!
%
(.)
ORIGINAL P/_E
CF POOR QUALFrY
•ooo i o/ oFL_,GGED SYM -• WIND TUNNEL_ _;_g- NCERTAINTIES
ooo__- _ o_
0 " o': c_' i_._ _= : _0_ I
-.0002 -
-.0004 -
I
, t I 1 1 [ I I f .v j
0.1 0.2 0.4 0.6 0.8 1.0 2 4 6 8 10
MACH NUMBER
Figure 9.- Orbiter rudder yaw _erlvatives LmcertainEy..
SYMI = _
• NOMi
[] 0 :
<> 5 i
i
10_
O- 213
_ 125,
_13ot
,<1
1180
.0004
.0002
0
-.0002 -
0.1
-FLAGGED SYM - ALT RESULTS
IX WIND TUNNEL
! I I _ 1 I I l • I
0.2 0.4 0.6 0.8 1.0 2 4 6 8 10
MACH NUMBER
Figure i0.- Orbiter rudder roll derivatives uncertain:"y.
T
-.0010 , I z = , , ' ' ' '
0.1 0.2 0.4 0.6 0.81.0 2 4 6 8 10
MACH NUMBER
Figure ii.- Orbiter aileron yaw derivatives umcertainty.
.0010 -
.O0O5
_,, 0
0
-.0005
I
.0010
0.1
WIND TUNNEL
UNCERTAINTIES SYM
(3
O
A
0
Oo
0
[]
1 I 0 1 I I _ i l l
0.2 0.4 0.81.0 2 4 6 8 10
MACH NUMBER
Figure 12.- Orbiter aileron roll derivatives uncertainty.
NOM
0
5
10
15
2O
25
30
1181 t
+
.04
.03
' .02
.0!
J.l. _
0
OF pOOR QU_L'., ,
i
0.2
0
0
0
O XB-70
v YF-12
o HL-10
h M2"F3
VARIATIONS
0 0
0 0 0
V 0 --
0 0 : : :
I I r vv_ r
0.6 1 2 3 4
MACH NUMBER
Figure 13.- Correlation of flight mnd predicted pitching moment.
y.,.
if
1182
.002
.001
0
uJ
I-<1
...I
b.
-.001 I
-.002
0.2
O XB-70
v YF-12 - 935
d YF-12 - 937
HP115
Q X-15
r_ TACT ........
o B-58
VARIATIONS: : : : : : :
O _ ........
°o o _ Q
o _ c_ o o_,_____--o
i l 1 ! 1 j
0.6 1 2 3 4 5
MACH NUMBER
Figure 14.- Correlation of flight and 7redZ_cted direcziona[ stabi!_ty.
i--
i
.002
.001
LU [_
_J
-.001 I
-.002
0.2
0
/
V
0
| \
0.6
ORIGI?IALPP,CE _
OF POOR QUALII'i_
ooo0
o/o0
,3 XB-70
v YF-12 - 935
,_ YF-12 - 937
r',,HPl15
(3 X-15
(3 TACT
o B-58
VARIATIONS
O
,<p-<b-- o-----,-q----O-
I I I I
1 2 3 5
MACH NUMBEN
Figure 15.- Correlation of flight and predicted dihedral stabiliEy.
.00050
0
,._ .00025 -
ILl
0
0
-.00025-
-.00050 I
0.2
13TACT
0 HPl15 o
o B-58
o YF-16
O F-8SCW
m VARIAT'ONS
Q C
O
o
o
o_
rl
I I I J
0.6 1 2 3
MACH NUMBER
Figure 16.- Correlation of flight and predicted rudder y_ derivatives.
1183
f
0.0008 -
0.0004 -
C_
LLI
I..-
-J',d
LI..
-0.0004
ORIGII'ALPAG_ "_-_
OF POOR QUAL_,'T';
A
o
Z_
:. B-58
"- YF-16
- F-SSCW
-- VARIATIONS
I I ' --J
0.2 0.6 1 2 3
MACH NUMBER
Figure 17.- Correlation of flight and predicted ridder roll derivatives.
.0008
.0004
rr
O..
o
P" .,c_
..J
u.
-.0004
-.0008 -
0.2
0 XB-70
v YF-12 - 935
HPN5
od R-58
-- VARIATIONS
'_a _aL -- '_aR o d
2
o od
0 vO ° dodO _ ''--
o
I I ] I
0.6 1 2 3
MACH NUMBER
Figure 18.- Correlation of flight and predicted aileron yaw derivatives.
1184
.0024 -
.0016 -
o L
.L:J .0008
"-- I
_"O
._.1 ',d
0-
3
-.0008 -
ORIGIPT,_ : -; .....
" " i..'. "J
OF pozjR C':_
....... 7/
0
0 XB-70
v YF-12 - 935
¢ YF-12 - 937
0 HP115
o B-58
-'---- VARIATIONS
o
o
¢
_v---_ .... o-_---
o o
¢
I I I
0.2 0.6 1 2
MACH NUMBER
Figure 19.- Correlation of flight and predicted aileron roll d_rlvative.
3
1185


The development of aerodynamic uncertainties for the space shuttle orbiter

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