APPENDIX A
APPENDIX A STRUCTURAL AND AERODYNAMIC REPRESENTATION OF THE SCAR ARROW-WING CONFIGURATION This appendix contains graphical representation of 18 symmetric vibration modes and the aerodynamic panel representation of the SCAR arrow-wing configuration.
The structural vibration modes used in the generalized equations - of motion are shown in Figures A-l through A-18. Each of the elastic modes is shown in front, side and top views of the right side of the airplane. The modes are symmetric with respect to the airplane center- line. Each line plotted represents the motion of a streamwise set of points on a surface (wing or wing fin). The single point that appears to the right in each view represents the horizontal stabilizer which was assumed to be rigid for these analyses. For ease of determining structural motion the point representing the horizontal stabilizer has been plotted as i f ' i t were at the same waterline as the wing. The displacements shown in the model plots represent only those perpendicular to the surface. Therefore, the wing fin (three horizontal lines) does not show any vertical displacement in the front and side views.
The aerodynamic panels used to represent the primary surfaces and the control surfaces in the three-dimensional plate doublet finite element solution for aerodynamic forces are shown in Figure A-19. The control surfaces defined for possible use in the FSS are shown by the four shaded areas on the right wing. Generalized motion of the panels shown were used to generate unsteady aerodynamic force coefficients for the ai rplane.
A-l E 4227 Freq. = 0.98 Hz
FRONT
I l l l i
SIDE
r
TQP
st Figure A-1: 1 ELASTIC MODE SHAPE A-2 Fl "eq. = 1.19 Hz
FRONT
I . ,
SIDE
TDP
nd Figure A-2: 2 ELASTIC MODE SHAPE A-3 Freq. = 2.16 Hz
FRONT
SIDE
C
TOP
rd Figure A-3: 3 ELASTIC MODE SHAPE "A-IT Freq. = 2.40 Hz
FRONT
SIDE
r
TDP
th Figure A-4: 4 ELASTIC MODE SHAPE.
A-5 Freq. = 2.77 Hz FRDNT t » » « — » i t • SIDE
TDP
-th UI Figure A-5: 5 ELASTIC MODE SHAPE A-6 Freq. = 3.12 Hz
r
FRONT
BIDE
C
TOP
th Figure A-6: 6 ELASTIC MODE SHAPE "A-7 Freq. = 3.39 Hz
FRONT
' '
'I till
5IDE
TDP
th Figure A-7: 7 ELASTIC MODE SHAPE A-8 Freq. = 3.80 Hz FRONT SIDE
c
TOP
;th
UI Figure A-8: 8 ELASTIC MODE SHAPE A-9 Freq. = 4.11 Hz
FRONT
SIDE
r
TDP
Figure A-9: 9 ELASTIC MODE SHAPE A-10 Freq. = 4.85 Hz
FRONT
' '
SIDE
c
TOP
;th m
Figure A-10: 10 ELASTIC MODE SHAPE A-11 Freq. = 4.94 Hz FRDNT I r f • < • ' SIDE:
c
TDP
;th u
Figure A-ll: ll ELASTIC MODE SHAPE A-12 Freq. = 5.77 Hz
r
FRONT
* I i * » ,
SIDE
c
TDP
,th U1 Figure A-12: 12 ELASTIC MODE SHAPE A-13 Freq. = 6.23. Hz_
FRONT
ifn II I
SIDE
TOP
,th UI Figure A-13: 13 ELASTIC MODE SHAPE A- \k Freq. = 6.62 Hz FRONT • • 51DE
TDP
th Figure A-14: 14 ELASTIC MODE SHAPE A-15 Freq. = 6.87 Hz
C
FRONT 51DE
r
TDP
-Th L Figure A-15: 15 " ELASTIC MODE SHAPE A-16 Freq. = 7.64 Hz
FRONT
BIDE
c
TDP
t!l Figure A-16: 16 ELASTIC MODE SHAPE A-17 Freq. = 7.84 Hz FRONT
1 i
BIDE:
c
TOP
th Figure A-17: 17 ELASTIC MODE SHAPE A-18 Freq. = 8.39 Hz
FRONT
BIDE:
TDP
ftfi"
UI Figure A-18: 18 ELASTIC MODE SHAPE A-19 BL~ METERS WL~ METERS 5 10 15 20 0 5 .1 i WL~ INCHES 8L -INCHES 0 200 400 0 200 i i WING FIN BL~ METERS 0 5 I f BL~ INCHES </, 2000 0 200 Ul
r i i
5 2100 C 55 ° 2200 £ 2300 CO o a 2400 QQ HORIZONTAL STABILIZER RIGHT WING Figure A-19: AERODYNAMIC PANEL IDEALIZATION A-20
APPENDIX "B"
APPENDIX "B" FSS SYNTHESIS ROOT LOCI AND AIRPLANE CHARACTERISTIC FREQUENCIES AND DAMPING RATIOS Root loci are shown for V , V_ and 1.2 V.. at Mach numbers of 0.9, 1.2 and 2.7 in Figures B-I through B-IX. Gain root loci for the nominal system only are shown for the 1.2 V.. analytical flutter clearance conditions. Gain loci for the nominal system and for + .785 rad (45 deg) of phase added in the feedback are shown for V and V...
Damping and frequency of the airplane rigid body and structural modes with the FSS and HSAS are compared to damping and frequency of the airplane with HSAS only for V V and 1.2 V at Mach numbers of 0.9, 1.2 and 2.7 in c> D D Tables B-I through B-IX. Damping and frequency of the airplane characteristic modes with the HSAS included in the mathematical model were generated subsequent to the FSS synthesis to verify FSS performance and compatibility with the airplane basic flight control system.
c
B-l o o GAIN NO.
11.8(.3) 15.8(.4)
(Flutter
23.6(.6)
mode)
o o - • C M Selected operating[gain:
—^
13.8 rad/m/sec
(.35 rad/in/sec )
O O - - 0 o o CO o a » -• to o a o o CJ o o -x- o o o CM •4- -2.00
2.ob -10,00 -8.00 -6.00 -4.00 0.00
Figure B-l: GAIN ROOT LOCI FOR MACH 0.9, 1.2 V D B-2 DO 6000 2 1 4 5 O R I G . 4 / 7 1 o o CO O O OJ § CO OJ o o OJ OJ o OJ e o o - -O3 o o . -CO o o •3* 0.00 -10.00 -6.00 -4.00 -2.00 2.0~0 -8.00 Figure B-l: "CONTINUED' B-3 DO 6000 2145 O R I G . 4 / 7 1 o o • ID o o • rr o o
\
o o - -o o o •CO en o o en o o o o • e\) en o o -10.00 -8.00 -6.00 -4.00 -2.00 0.00 Figure B~-ir~"cONflNUEb" B-'t DO 6000 2145 O R I G . 4 / 7 1 o o • cu (O o o • o <£> •00 in o o • to in • a* in o o • ru in o o
• o
in
o o 4-oo
\
o o .<£> —I -H -H -H -4.00 -2.00 2.06 0.00 -8.00 -6.00 -10.00 Figure B-l: CONCLUDED B-5 DO 6000 2 1 4 S O R C G . 4 / 7 1 o o
GAIN
NO.
1 7.9(.2)
Selected operating gain: o
. . g o :
4.6 rad/m/sec
- -OJ
(.117 rad/in/sec )
o o • - -o Q
r
O O CO o : r o a CM o o -e e-- .
o o •OJ
—I 4-
-8.00 2.ob -10.00 -6.00 -4.00 -2.00 0.00
Figure B-2: GAIN ROOT LOCUS FOR MACH 1.2, 1.2V r B-6 D O 6000 2 1 4 5 OR1G. 4 / 7 1 o o • • o tn o o • •CD C\J O O •(O CO O O • :r r\j o o •CM CM O O • • O <M O O . .GO O O O o 4- 2.0"3 -10.00 -8.00 -6.00 -2.00 0.00 Figure B-2: CONTINUED B-7 o o .CO o o o o * - -e\j o o - -o o o •00 en o o -co en o o • :r en o o -ru en o o -H —I -10.00 -8.00 -2.00 0.00 -6.00 -4.00
Figure B-2: CONTINUED
B-8 o o •CM CO O O CO O O •00 in o o • co in o o in o o •C\J in o o • o in o o
\
..en co
-f-
—H -10.00 -8.00 -6.00 -U.OO -2.00 2.C& 0.00 Figure B-2: CONCLUDED
B-9
o o
—I——
NO. GAIN
7.9(.2)
o Selected operating gain: o - -OJ
4.6 rad/m/sec
(.117 rad/in/sec )
o o o Q o (O CJ o o •4- •4- •4- -4-
-10.00 -8.00 -6.00 -4.00 -2.00 0.00 s.ob
Figure B-3: GAIN ROOT LOCUS FOR MACH 2.7, T.2V D B-10 D O 6000 2 1 4 5 O R I G . 4 / 7 1 O o .o en o o •CD CM • to CM O o CM •CM CM CM O O . .QO o o . .(O I I /**' o o Q , -t- •+- -4- -I- -10.00 -8.00 -6.00 -14.00 -2.00 0.00 2.00 Figure B-3: CONTINUED B-ll O O 6000 2 1 4 5 O R I G . 4 / 7 1 o o • .(O
-i—a-
O • CM O o CD CO ID CO CO + CM CO O o •4- •4- -I- -10.00 -8.00 -6.00 -4.00 -2.00 0.00 Z.ffi Figure B-3: CONTINUED
B-12
D O 6COO 2 1 4 5 O R I G . 4 / 7 1 o o ro to o o o to o o OD in o o to in o o in o • CM in o o in o o
+5
o o •4-
-2.00 0.00 2.dB
-10.00 -8.00 -6.00 -4.00 Figure B-3: CONCLUDED 8-13 D O 6000 2 1 4 3 O R I G . 4 / 7 1 o o NO.
!
2 •15.8(. 4) (Flutter 23.6(.6) mode) .o o Seleete_d_operating gain: -•C\J
11.8 rad/m/sec
(.3 rad/in/sec )
o o - - O O 'CD
+.785 rad
o
(+45 deg) o
i -.785 rad i_M5 deg)
' ph'ase
j ( t y p )
o o o o C\J o o o o •CM •4-
2.ob -10.00 -8.00 -6.00 -U.OO -2.00 0.00
Figure B-4: PHASE-GAIN ROOT LOCUS FOR MACH 0.9, V Q D O 60OO 2 1 4 5 O R I G . 4 / 7 1 o o -2.00 -10.00 -8.00 -6.00 -4.00 0.00 Figure 8-4:7 CONTINUED" B-15 DO 6000 2145 O R I G . 4 / 7 1 o o • CO a a o •3" O O o o -o 3* o o -CD cn o o . -co o o
s
en o o 4- -M -H -H -6.00 -4.00 -10.00 -2.00 0.00 2 ( -8.00 "Figure B-4: CONTINUED 8-16 OO 6000 2145 O R I G . 4 / 7 1 o o •CM (O O O • - -o O O • . .00 in o o -4-to in o o in o o CM LO o o d to o o -l-oo o o • to
H- 4- —I
-4.00 2.CJ6 -10.00 -8.00 -6.00 -2.00 0.00 Figure B-4: CONCLUDED B-17 DO 6000 2143 O R I G . 4 / 7 1 o o GAIN NO.
6.7(.17)
• 1
:-.785 rad (-45_deg).
O o Se 1 ected operating gain'.
- -CM (Flutter 3.9 rad/m/sec p mode) (.1 rad/in/sec }
i +.785 rad
o i (+45 deg) o [phase i(typ) o : r o o K * CM o o -4- . - C M •4- -f-
2.ob -10.00 -8.00 -6.00 -4.00 -2.00 0.00
Figure B-5: PHASE-GAIN ROOT LOCUS FOR MACH 1.2, V Q B-18 DO 6000 2 1 4 5 ORIG. 4 / 7 1 o Q
' f ''
o o •OD CM O O . -to o o -.3.
o o •CM CM O O CM O O . .00 o o -4- -10.00 -8.00 -6.00 -4.00 -2.00 0.00 2.00 Figure B-5: CONTINUED B - I 9 DO 6000 2 1 4 5 ORIG. 4 / 7 1 o o .CO rr a a - -3T O a • o :T o o o o - to cr> o a --a- o o o o •4- •4- 0.00 -10.00 -8.00 -6.00 -1.00 -2.00 Figure B-5: CONTINUED B-20 OO 6000 2 1 4 9 O R I G . 4 / 7 1 o 'to o Q •O to O a • 09 in o a • to LT> o o a o - -CM o o - -o cs o o o -+- I I
-10.00 -8.00 -6.00 -4.00 -2.00 0.00 2.dB
"Figure B-5~f~ CONCLUDED B-21 DO 6000 2145 OBUG. 4 / 7 1 o o NO. GAIN ^^ 1 7.9(.2) _2 ISJtLiL I Selected operating gain: o
s-,785 rad
o
(-45 deg)
"3.9 rad/m/sec v
• -CM I
(.1 rad/in/sec )
,:(Flutter
mode)
O o
I+.785 rad
,(+45 deg)
phase i(typ) o o • • o o o o k * OJ o o •OJ -4- •4- 4-
-10.00 -8.00 -6.00 -4.00 -a. oo 0.00 a. ob
Figure B-6: PHASE-GAIN ROOT LOCUS FOR MACH 2.7, V D B-22 OO 6000 214S ORIG. 4 / 7 1 o o • GO CM •<£> CM O O o Q •CM CM O O CM O O O O . .to o o -•4.00 -2.00 0.00 -10.00 -8.00 -6.00 2.00 Figure B-6: CONTINUED B-23 DO 6000 2 1 4 9 O F t l G . 4 / 7 1 o o -to o o o o • • .(V o o CD <*> o o . . to <*»< O o o o -10.00 -8.00 -6.00 -4.00 -2.00 0.00 a.
Figure B-6: CONTINUED D O 6000 2 1 4 5 O R l G . 4 / 7 1 o o .CM to • o to o o o o + to o o in o o in o o O o I
i
-10.00 -8.QO -6.00 -2.00 -4.00 O.QQ 2.
PI Guwf¥-~6r~ CONCLUDED"
B-25 DO 6000 2 1 4 5 O R I G . 4 / 7 1 NO. GAIN 13.8(.35) 2 27.6(_ 7J j-.785 rad o K-45 deg) p phase - -CM Selected operating gain: . , £ (typ) 5.9 rad/m/sec ;(.15 rad/in/sec ) O O « +.785"rad - -o (+45 deg) o O o oo o o o C\J o o •C\J
2.ob -in.oo -6.00 -4.00 -2.00 0.00
-8.00 Figure B-7: PHASE-GAIN ROOT LOCUS FOR MACH 0.9 B-26 O O 6000 2 1 4 3 O R I G . 4 / 7 !
o o • o en o o • •00 C\J o o • •CO cu o a ru o o * • cu ru o o • o ru o o + 03 o o o o • a* -H -2.00 0.00
-10.00 -8.00 -6.00 -U.OO 2.00
Figure B-7: CONTINUED B-27 DO 6000 2 1 4 5 ORIG. 4 / 7 1 o o o o 8.
+ c\j o a
*
o o o -I-CD O O + <P O O to O O •C\j <n o o —I «-
-6.00 -10.00 -8.00 -4.00 -2.00 0.00
Figure B-7: CONTINUED B-28 OO 6000 2 1 4 5 O R I G . 4/ 7 t o o .C\J CO o o CD o o oo LO o o • co in o o o o • t\i in o o • • o in
I
o o o o -4- -co -10.00 -8.00 -6.00 -4.00 -2.00 0.00 2^00 Figure B-7: CONCLUDED
B-29
D O 6000 2 1 4 5 O R I G . 4 / 7 1 o o
-*—h
W. GAIN '
1 6.7(.17)
_2 13.8(.35)
Selected operating gain: -.785 rad o , ___ _, o ; 1^45 deg)
2.0 rad/m/sec - -CM
phase (typ) O O - -O
+.785 rad
(+45 deg) O O o o CO o a o o OJ o o o o CM
-10.00 -8.00 -6.00 -n.oo -2.00 0.00
Figure B-8: PHASE-GAIN ROOT LOCUS FOR MACH 1.2, B-30 DO 6000 2 MS O R I G . 4 / 7 1 .o CO o o • 00 C\J o o • .to CM o o •CT CM O O •CM ro o o • -o CM o o - -CD o o . .CO • =r -4- •4- 2^00 -10.00 -8.00 -6.00 -14.00 -2.00 0.00 Figure B-8:""CONTINUED B-31 D O 6000 2145 O R I G . 4 / 7 1 o o * .CO 3* o o o o •C\J a* o o + 0 o o • CD CO o o •CO en o o i • •IT <n o o o o -10.00 -8.00 -6.00 -4.00 -2.00 0.00 "Figure B-8: CONTINUED B-32 D O 6000 2 1 4 5 OR1G. 4 / 7 1 o o 1 1 i • i "• CO I o -o CO o i o .03 in i I I o o O , -co in i o o -a* in I * \ o hOJ in i o -o in
8 i
i
i o
-CD -r
ii
i
i
i 0
i o
i i 1
10.00 -8.00 -6.00 -4.00 -2.00 o'.oo sldfi
Figure B-8: CONCLUDED B-33 DO 6000 3 1 4 9 O R I G . 4 / 7 1 o o J H —h
r "NO: G t T N ~
.__2 ZJjliL
Selected operating gain: o o
2.0 rad/m/sec
- -c\j 785 rad
(.05 rad/in/sec )
45 deg)_ phase o o • - -o rad (+45 deg) o O o CD • • o a o o • CVJ o o CM -f- -10.00 -8.00 -6.00 -4.00 -2.00 0.00
2'.ob
Figure B-9: PHASE-GAIN ROOT LOCUS FOR MACH 2.7, DO 6000 2 1 4 5 O R l G . 4 / 7 1 o o • • o on o o . CD C\J o o •(O OJ o o ru o o CM o
*
o.
- -CD, o o . .00 Ot; O •,^ . .to o o —I -H -H -10.00 -8.00 -6.00 -4.00 -2.00 0.00 2.00 Figure B-9: CONTINUED B-35 D O 6000 2 1 4 5 O R I G . 4 / 7 1 o o •CO o o =r
* I
o o o o + 0 o o •CD m o o.
o o
+J
o o 4-<\J o o * I -H -H -4.00 -2.00 0.00
-10.QO -8.00 -6.00 z'M
Figure B-9: CONTINUED B-36 O O 6000 2 1 4 5 O R l G . 4 / 7 1 o o CO o o * • O CO o o • CD 1 0 O O • CO in o o + =r o o • rvj in o o - o in o o --co o o -CO —I -2.00
-10.00 .-8.00 -6.00 -u.oo 0.00 2.0D
Figure B-9: CONCLUDED
B-37
O O 5000 2 1 4 5 O R I G . 4 / 7 1 TABLE B-I AIRPLANE DAMPING AND FREQUENCY COMPARISON AT 1.2 V - MACH 0.9 Q
Airplane with Airplane with
HSAS HSAS & FSS
Damping Frequency Damping
Frequency
ratio, £ rad/sec ratio, £ rad/sec
.587 1.15
Short period .551 1.15
Structural modes
.057 6.30 .080 5.58
'
-.075 13.45
.009 13.46
.189 14.66 .104
17.53
.011 17.16 .005 17.08
.010 19.15
.017 19.05
.072 19.74 .097
21.61
.376 20.75 .482 23.60
24.71
.008 .003 24.63
.021 29.83 .085
29.57
.062 30.47 .009 29.73
.001 33.68 .011 33.60
.209 33.70 .174 34.44
.016 38.54 .016
38.15
.004 39.67 .006 39.66
.020 42.75 .016 42.44
\
47.78 .015
.014 48.11
B-38
TABLE B-II AIRPLANE DAMPING AND FREQUENCY COMPARISON AT 1.2 V - MACH 1.2 Q
Airplane with Airplane with
HSAS & FSS
HSAS
Damping Frequency Damping Frequency
ratio, £ rad/sec ratio, £ rad/sec
.449 1.46 .447 1.42
Short period
Structural modes
6.72 .066 6.70
.066
.066 13.57 .048 13.16
14.30 .063 14.68
.029
.010 17.24 .008 17.24
19.40 19.32
.077 .050
.024 29.44 .043 21.89
.102 23.85 .127 22.96
25.46
.039 25.37 .033
.018 30.17 .018 30.18
.098 32.02 .101 31.87
•
35.57 .058 35.68
.059
.019 38.66 .019 38.56
.200 38.91 .200 38.90
40.04 .041 40.04
.040
.022 43.14 .022 43.04
i
.015 48.04 .015 48.21
B-39
TABLE B-III AIRPLANE DAMPING AND FREQUENCY COMPARISON AT 1.2 V - MACH 2.7 Q
Airplane with
Airplane with
HSAS HSAS & FSS
Damping Frequency Damping
Frequency
rad/sec ratio, £
ratio, £ rad/sec
Short period .245 1.62 .244 1.62
Structu ral modes
.023 7.04 .027 6.70
.048 12.08 .070 12.06
.014 14.93 .020 14.94
.009 17.25 .009 17.25
.030 18.98 .030 18.99
21.22 .024 21.38
.016
.036 23.78 .035 23.71
26.16 .013
.014 26.16
.011 30.37 .011 30.38
.044 34.56 .046 34.55
37.41 .012
.013 37.40
.010 38.83 .009 38.80
.071 41.95 .073 41.91
43.47 .010 43.38
.010
.053 46.94 .051 46.94
'
\
.015 48.48
.015 48.31
B-kO TABLE B-IV AIRPLANE DAMPING AND FREQUENCY COMPARISON AT V - MACH 0.9 Q
Airplane with Airplane with
HSAS HSAS & FSS
Damping Frequency Damping Frequency
ratio, £ rad/sec ratio, £ rad/sec
Short period
.480 1.06 .426 1.13
Structi jral modes
.044 6.37 .069 5.94
.001 12.83 13.47
.023
.123 13.25 .463 18.57
.019 12.17 .019 17.02
.231 18.25 .135 17.11
.018 19.19 .011 19.30
.032 20.12 .049 20.53
.014 .015
24.88 24.80
.085 30.04 .095 29.38
.017 30.08 .011 30.00
.145 32.02 .130 32.45
008 34.43 .012 34.51
.011
.010 38.71 38.56
.011 39.99 .012 40.00
.016 42.87 .015 42.68
t
.011 .012 48.04
47.83
B-41
o
TABLE B-V V - - MACH 1.2 AIRPLANE DAMPING AND FREQUENCY COMPARISON AT Q
Airplane with Airplane with
HSAS HSAS & FSS
Damping Frequency Damping Frequency
ratio, £ rad/sec Ratio, £ rad/sec
.367 1.33 .369 1.33
Short period
Structur
al modes
.049 6.69 .052 6.65
.059 11.78 .082 11.74
.031 14.50 .042 14.60
.019 17.16 .018 17.14
.061 18.20 .060 18.23
.023 20.79 .080 21.14
.071 21.69
.019 21.30
c
.029 25.58 .029 25.62
.014 30.28 .014 30.29
.089 30.51 .089 30.40
.037 35.78 .037 35.83
.128 36.30 .128 36.27
.016 .016 38.81
38.87
.047 40.53 .048 40.56
.017
.017 43.14 43.08
\
.012 48.03 .012 48.13
TABLE B-VI
AIRPLANE DAMPING AND FREQUENCY COMPARISON AT V - MACH 2.7
Q Airplane with Airplane with HSAS HSAS & FSS Damping Frequency Damping Frequency ratio, £ rad/sec ratio, £ rad/sec .213 1.40 .210 1.40 Short period Struc :ural modes .022 .019 6.90 6.86 .040 11.10 .055 11.05 .013 14.80 .016 14.80 .011 17.09 .011 17.09 .025 18.31 .024 18.31 .016 21.14 .021 21.23
c
.026 22.65 .024 22.'59 .010 25.99 .010 25.99 .010 30.41 .010 30.41 .047 .047 32.81 32.78 .008 37.21 .008 37.21 .047 38.72 .011 38.69 38.73 .050 38.71 .013 .008 43.37 .008 43.32 45.22 .036 .037 45.24 48.31 .011 48.41 .011
v
TABLE B-VII AIRPLANE DAMPING AND FREQUENCY COMPARISON AT V - MACH 0.9 G
Airplane with Airplane with
HSAS HSAS & FSS
Damping Frequency Damping Frequency
ratio, £ rad/sec ratio, £ rad/sec
Short period .407 .96 .386 .99
Strudtural modes
.034 6.41 .046
6.26
.083 10.71 .166 10.30
.038 13.90 .040 13.85
.103 16.57 .086 16.35
.028 17.47 .030 17.49
.053 19.46 .051 19.57
.011 20.27 .015 20.28
.015 25.12 .016 25.10
.099 28.44 .097 28.33
.013 30.24 .012 30.21.
.080 31.93 .080 31.96
.012 34.92 .013 34.96
.008 38.78 .008 38.75
.014 40.38
.014 40.37
.013 42.95 .013 42.89
.010 47.88 .010 47.95
•—
B-M*
TABLE B-VIII AIRPLANE DAMPING AND FREQUENCY COMPARISON AT V - MACH 1.2 G Airplane with Airplane with HSAS HSAS & FSS Damping Frequency Damping Frequency ratio, £ rad/sec ratio, f rad/sec .299 1.21 .296 1.21 Short period •Structui -al modes .035 6.66 .037 6.63 .056 10.56 .070 10.53 14.50 .025 14.48 .028 .047 16.62 .046 16.57 .021 17.62 .021 17.62 .021 20.69 20.81 .023 .044 21.19 .042 21.05 .023 25.63 .022 25.64
c
.081 29.08 .081 29.05 .011 30.36 .011 30.36 .076 34.36 .076 34.34 .030 35.86 .030 35.87 .012 38.97 .012 38.95 .040 41.16 .040 41.18 .014 43.15 .014 43.13 .010 48.02 .010 48.06 i TABLE B-IX AIRPLANE DAMPING AND FREQUENCY COMPARISON AT V - MACH 2.7 G Airplane with Airplane with HSAS HSAS & FSS Damping Frequency Damping Frequench rad/sec ratio, £ rad/sec ratio,£ 1.20 .173 1.20 .176 Short period Structural modes 6.76 .015 6.77 .016 10.18 .038 10.15 .033 14.65 .012 14.65 .013 16.70 .017 16.70 .017 17.81 .014 17.81 .014 f .015 20.84 .016 20.86 21.97 .016 21.96 .016 .008 25.87 .009 25.88 .009 30.44 .009 30.45 .043 30.81 .043 30.80 .026 36.03 .026 36.02 «• .010 36.74 .010 36.74 39.06 .011 39.04 .011 43.26 .007 43.25 .008 .024 43.97 .025 43.98 \ .008 48.26 .008 48.23