APPENDIX A
APPENDIX A AIRPLANE EQUATIONS O F MOTION USED I N THIS STUDY The l i n e a r a c c e l e r a t i o n s of an a i r p l a n e i n a moving a x i s system are given by t h e v e c t o r ‘equation are and t h e corresponding f o r c e e q u a t i o n s Equation (Al) is g e n e r a l and may be resolved i n t o any d e s i r e d c o o r d i n a t e Because t h e use of p r i n c i p a l body axes s i m p l i f i e s t h e r e s u l t i n g equa system.
t i o n , . t h e s e axes were used f o r t h e six-degree-of-freedom equations. The wind v e c t o r gW is d e f i n e d i n Earth-fixed a x e s , X I , X2, and X 3 , head winds are n e g a t i v e , and $A is d e f i n e d i n p r i n c i p a l body a x e s , x i , x2, and x3. The X 1 and x1 axes are p o s i t i v e i n t h e d i r e c t i o n o f f l i g h t and t h e X 3 and x3 axes a r e p o s i t i v e downward. (See f i g . 12.)
I n o r d e r t o o b t a i n t h e f o r c e equations i n t h e p r i n c i p a l body a x e s , it is necessary t o transform t h e wind from the fixed-axis system t o t h e body-axis system. This is done by using t h e n i n e d i r e c t i o n c o s i n e s o b t a i n e d . f r o m t h e standard $, 8, and CP Euler transformation. The d i r e c k i o n c o s i n e s R i j are obtained from rt R i j , t h e d i r e c t i o n c o s i n e rates, are given by where
Li1 = r ~ i 2 - q ~ i 3
i i 2 = p ~ i 3 - r R i 1
( A 3 1 t
i i 3 qRi1 - PRi2
1 .
By using e q u a t i o n s (A2) and ( A 3 ) , equation (Al) may be w r i t t e n i n component form as
F1 irl + tW,1R11 + +w,2R21 + iw,1R31 + qv3 - rv2 = R31g + - ( A 4 1
m
APPENDIX A
APPENDIX A The v a r i a b l e s p , . q, and r are the angular v e l o c i t i e s of the a i r p l a n e i n prin ' c i p a l body axes and are obtained from the equations of a n g u l a r lpotion which, i n component form, are ( A 8 1 The aerodynamic f o r c e s and moments are f u n c t i o n s of t h e r e s u l t a n t v e l o c i t y
VA given by
3 , = $A - ?W
as are t h e parameters a, a , 8 , and b . Because of the wind shear s t a b i l i t y
d e r i v a t i v e s normally neglected (such as
CD,, Cmu, Gnu, C z q , and C should
"cp -+ be included i n t h e formulation of t h e f o r c e s and moments. The wind v e c t o r Vw i n c l u d e s steady winds, turbulence, and wind shear. Head winds are negative.
A n examination of equations (A41 t o (A6) i n d i c a t e d t h a t i n a d d i t i o n t o t h e u s u a l terms, t h e terms Gw 1 , t w , 2 , and Cw,3 are r e q u i r e d . These terms are wind a c c e l e r a t i o n terms and may arise from turbulence or wind shear. I n models f o r turbulence, it is f a i r l y easy t o write the model s o t h a t t h e a c c e l e r a t i o n s are a v a i l a b l e for equations (A4) t o (A6). I n t h e case of wind shears, p a r t i c u l a r l y where recordings of a c t u a l wind shears are used, o b t a i n i n g t h e r.equired a c c e l e r a t i o n s is not q u i t e so s t r a i g h t f o r w a r d . I n o r d e r t o have a c o n s i s t e n t method of s p e c i f y i n g wind shears, t h e following method is suggested. A n acceler a t i o n may be w r i t t e n as a product of a v e l o c i t y g r a d i e n t taken over some charac t e r i s t i c length and t h e rate of change of t h i s l e n g t h . Thus, The length 11 over which t h e g r a d i e n t is determined should be 30.48 m , a l e n g t h t h a t is c o n s i s t e n t w i t h t h e r e p o r t i n g of v e r t i c a l wind shears. Thus, winds sepa which h a s rated by 30.48 are s u b t r a c t e d &d divided by 30.48 t o o b t a i n dv/d!2 t h e dimensions of sec-l. Thus, wind a c c e l e r a t i o n s f o r equations ( A h ) , (A5), and (A61 are given by
APPENDIX A
APPENDIX A (A121 (A131 where dv,,l/dR, dvw,2/dR, and dvw,3/dR are the velocity gradients and usu ally written as v;,~, vi,2, and v&,3.
Equations (ALII, (A61, and (A81 are the longitudinal equations of motion and were used to calculate the airplane motions presented in this report.
, ' For the stability calculations presented in this paper, the longitudinal equations of motion were transformed to stability axes. (See fig. 12.) After making this transformation and substituting the trigonometric equivalents for
the direction cosines and using the definition of l', I' = 6 - a , the longitudi
nal equations of motion in stability axes are (A141
7j - v ; , 1 sin r COS r - v ; , 3 cos r + g sin r = Fy,l
m
-~ - vr;,lv sin2 r + v ; , 3 v cos2 r - g cos r = Fy,3 (A151
m (A161 In these equations $A is now a single component vector in the yl-direction in stability axes, and called V. Equations (A141 to (A161 were linearized by making the usual assumptions that v = u o + u a = a0 + Aa
I r = r o + y
where the zero subscripted terms are the steady state and u, Act, and y are I the perturbations from the steady state. For the linearized equations, it is convenient to use uu and uW which are constants in place of Vi,1 and These parameters are defined as v&,3.
APPENDIX A
APPENDIX A The linearized equations of motion are
esrU sin2 ro + 5 cos2
(- uo UO
The forces and moments were expanded and in matrix form these equations, writing CL for Act and for (su + Ow, become For ow = 0, these equations reduce to the equations given in reference 8 and for OT = ow = 0, they become the usual longitudinal equations of motion.
APPENDIX B
APPENDIX B AIRPLANE CHARACTERISTICS AND FLIGHT CONDITION The airplane used in this study is considered a typical narrow body modern jet transport airplane powered by four engines, each having approximately 67 233 N of thrust.
The dimensional and mass characteristics are - c = 7.01 m S = 267.9 m2 m , ~ 90 909.1 kg I2 = 9 933 300 kg-m2 p = 1.2929 kg-m-3 The aerodynamic data for the stability axes, center of gravity at 0.25F5, are 0.43633 rad flap 0.87266 rad flap
zcr -55.055 m-rad-l-sec-2 -52.68 m-radm1 -secm2
ZU -0.29024 sec-l -0.29024 sec-l
-3.2708 m-rad-l -set".' -3.2708 m-radm1 -sec-2
-1 .0075 m - r a d ' l -sec-l -1 .0075 m-radm1 -sec-l -2.63428 m - r a d ' l -secm2 -2.63428 m - r a d ' l -sec-2 -5.9803 m-rad-l-sec-2 -6.48907 m-rad-l-sec2 -0.02385 sec-l -0.04568 sec-l XU -0.1568 m - r a d ' l -sec-2 -0.1568 m-rad-l-seC2 ' 6 e -0.809 r a d ' l - s e c ' 2 -0.8468 rad-l-sec-2 M, -0.5 13 r a d ' l - s e c ' l -0.5481 r a d ' l -sec-l -0.175 rad-l-sec-l -0.18778 rad-l-see-' Md, -0.00095 m-l- s e c ' l -0.00095 m-l-sec-' MU -0.73733 radm1 -sec-2 -0.75038 rad-' -seC2 Mg e 2 1
APPENDIX B L
APPENDIX B L The basic f l i g h t c o n d i t i o n used w a s a l a n d i n g approach along a 3O g l i d e
set a t 0.43633 r a d . The approach speed w a s 77.12 m-sec'l , t h e
s l o p e with f l a p s by t h e manufacturer.
speed recommended
APPENDIX C
APPENDIX C PHUGOID STABILITY I N W I N D SHEAR The phugoid mode may be approximated by assuming t h a t c o n t r i b u t i o n s of the i n e r t i a l terms and aerodynamic damping terms t o t h e t o t a l a p p l i e d moment are much smaller than t h o s e due t o changes i n u and a. Under t h e s e assumptions and f o r uw = 0 , the s t a b i l i t y determinant obtained from equation (A18) reduces t o
-z, - @;a, s i n 2 ro -Z, -UO s + g ( s i n - uu s i n 2 r o )
= o ( C 1 ) UO -MU -% 0 T h i s determinant expands t o an equation of t h e form s 2 + 2 c p p s + wp2 = 0 and A s Mu f o r most aircraft is extremely small OP z e r o , t h e e x p r e s s i o n s f o r 2cpup and up2 may be f u r t h e r s i m p l i f i e d by n e g l e c t i n g t h e terms t h a t c o n t a i n 4 Mu. When t h e Mu terms are omitted, t h e e x p r e s s i o n s f o r 2cpup and up2 become +
2 c p p = -xu - L s i n ro(1 - ou COS T o ) (C5)
UO
APPENDIX C
APPENDIX C Since t h e c h a r a c t e r i s t i c equation (C2) is a q u a d r a t i c , both 2cpwp and must be p o s i t i v e t o guarantee t h e asymptotic s t a b i l i t y o f t h e phugoid; %:erwise, a t least one r o o t o f t h e equation w i l l have a nonnegative real p a r t so t h a t t h e phugoid w i l l be u n s t a b l e . The curves f o r 2cPw = 0 and up2 = 0 and ou are shown i n f i g u r e s 13 and I ! . These curves as f u n c t i o n s o f were c a l c u l a t e d by using e q u a t i o n s ( C 5 ) and (C6) w i t h a p p r o p r i a t e data from appendix B. This information is combined t o determine t h e r e g i o n s where equa t i o n (C2) would be s t a b l e or u n s t a b l e . The r e g i o n s o f s t a b i l i t y and i n s t a b i l i t y are shown i n f i g u r e 15 as f u n c t i o n s ro and ou. Most f l i g h t - p a t h a n g l e s l i e i n t h e i n t e r v a l - ( ~ / 1 8 ) 5 To 5 ~ / 1 8 , which is t h e r e g i o n between t h e v e r t i c a l l i n e s i n f i g u r e 15. This f i g u r e c l e a r l y shows t h e effect o f wind s h e a r (Ju on t h e phugoid s t a b i l i t y i n landing (ro < 0 ) and l e v e l f l i g h t s (ro = 0 ) . I n t h i s case, t h e a i r p l a n e is stable f o r a l l wind s h e a r s t h a t have ou < 1.0. However, f o r c l i m b i n g f l i g h t s ( T o > O ) , t h e region of s t a b i l i t y is much more restricted f o r negative wind s h e a r s .
That t h e u n s t a b l e c o n d i t i o n f o r (su > 0 i n f i g u r e 15 is s o l e l y a f u n c t i o n of ou and n o t a f u n c t i o n o f t h e a i r p l a n e parameters can be seen by r e w r i t i n g equation (C6) as Since is t h e lift-drag r a t i o o f t h e a i r p l a n e and is p o s i t i v e with normal Zu/Xu values between 5 and 16, it can be shown t h a t t h e s i g n o f depends on t h e up2
s i g n o f cos ro - (5, cos2 ro. To a good degree o f accuracy, t h i s means f o r
normal f l i g h t - p a t h a n g l e s t h a t a value o f '5, > 1.0 w i l l cause t h e a i r p l a n e t o have an u n s t a b l e phugoid mode. This r e s u l t is immediate f o r a small a n g l e approximation on T o . Thus, it is only necessary t o determine t h o s e combina t i o n s of v;,~ and Uo t h a t give ou = 1.0 t o determine whether t h e a i r p l a n e is s t a b l e or u n s t a b l e f o r p o s i t i v e s h e a r . A curve f o r estimating t h i s s t a b i l i t y is shown i n f i g u r e 4 ( a ) . This is a s e r i o u s type of i n s t a b i l i t y as it arises from an i n t e r a c t i o n of t h e a i r p l a n e and its environment and no aerodynamic changes t o t h e a i r p l a n e w i l l c o r r e c t it.
The i n s t a b i l i t y f o r negative s h e a r (au < 0 ) (see f i g . 15) is n o t a simple function of ou as i n t h e case of p o s i t i v e s h e a r . The effect o f n e g a t i v e s h e a r on s t a b i l i t y can be computed by u s i n g equation ( C 5 ) ; however, it is a f u n c t i o n of t h e a i r p l a n e parameters as Xu appears i n equation ('25). Generally speak i n g , t h e i n s t a b i l i t y f o r uu < 0 is a d i v e r g e n t o s c i l l a t i o n i n s t e a d o f a p e r i o d i c type motion encountered f o r p o s i t i v e shear (au > 0 ) .
REFERENCES 1. Brown, David A.: Wind Shear Threat Spurs Drive To Find Remedies. Aviation Week & Space Technol., vol. 104, no. 14, Apr. 5, 1976, p. 32.
2. Aircraft Accident Report: Iberia Lineas Aereas De Espana (Iberian Airlines) McDonnell Douglas DC-10-30, EC CBN Logan International Airport, Boston, Massachusetts, December 17, 1973. NTSB-AAR-74-14, National Transportation Safety Board, Nov. 8, 1974.
3 . Aircraft Accident Report - Eastern Air Lines, Inc., Boeing 727-225 John F.
Kennedy International Airport, Jamaica, New York, June 24, 1975.
NTSB-AAR-76-8, National Transportation Safety Board, Mar. 12, 1976.
Effect of Shear on Aircraft Landing.
4. Luers, James K.; and Reeves, Jerry B.: NASA CR-2287, 1973.
5. Hamel, P.; and Bucholz, F. G.: Gust Effects on the Dynamics of Aircraft During Landing Approach. NASA TT F-12,751, 1970.
6. Working Group of Flight Mechanics Panel: Approach and Landing Simulation.
AGARD-R-632, OCt. 1975.
7. Gera, Joseph: The Influence of Vertical Wind Gradients on the Longitudinal Motion of Airplanes. NASA TN D-6430, 1971.
8. Fujita, T. Theodore: Spearhead Echo and Downburst Near the Approach End of a John F. Kennedy Airport Runway, New York City. PB 254009, Nat. Environ.
Satellite Service, U.S. Dep. Comm., Mar. 1976.
9. Sherman, Windsor L.; and Winfrey, Sylvia W.: Preliminary Study of a Possi ble Automatic Landing System. NASA TN D-7611, 1974.
10. Pinsker, W. J. G.: Theoretical Assessment of the General Stability and Gust Response Characteristics of STOL Aircraft. R. & M. No. 3686, Brit. A.R.C., Feb. 1971.
1 1 . Neumark, S.: Problems of Longitudinal Stqbility Below Minimum Drag Speed and Theory of Stability Under Constraint. R. & M. No. 2983, Brit. A.R.C., 1957.
12. Etkin, Bernard: Dynamics of Atmospheric Flight. John Wiley & Sons, Inc., c. 1972.
t 13. Nicks, Oran W.: A Simple Total Energy Sensor. NASA TM X-73928, 1976.
14. Joppa, Robert G.: Wind Shear Detection Using Measurement of Aircraft Total Energy Change. NASA CR-137839, 1976.
15. Crane, Harold L.; Sommer, Robert W.; and Healy, Frederick M.: Effects of Reduced Airspeed for Landing Approach on Flying Qualities of a Large Jet Transport Equipped With Powered Lift. NASA TN D-4804, 1968.
Tail wind Head wind r I I I I
0' i . I o I I I I 1
-8 -6 -4 -2 2 4 . 6 8 ,10 Wind speed, m-sec'l Figure 1.- Variation of wind speed w i t h a l t i t u d e for a s t r o n g wind shear.
Head winds are negative.
-4 ir A
I Vertical 0,
wind
velocity, 4
m / sec
I I I I I 1
I I I
2800 3200 3600
1600 2000 2400
0 400 800 1200
D, distance along approach path,m
Figure 2.- Updrafts and downdrafts t h a t co-existed w i t h t h e v e r t i c a l shear shown i n f i g u r e 1 .
N I maginary or= -3.5 oT = 0.99725
rT = l- O
-
-
I
o = o \
\
I I I .002 .OM ,606 Figure 3 . - Root-locus p l o t f o r t h e phugoid mode ro = -0.05236 r a d i a n ; (Jw = 0; (JT = (JU * 1 . 0
. a
- Approach speed range for general aviation aircraft .6 Unstable -1
v ' sec . 4
et transport w , 1' Approach speed range for . 2 Stable 90 130 170 210 250 290 330 370 -1 Uo, m-sec ( a > Boundary f o r a l l aircraft.
Figure 4.- Phugoid s t a b i l i t y boundary f o r p o s i t i v e v e r t i c a l wind shear.
Ow 0.
OT = 0 , ;
Ub = 67 u , = 77 U, = 87
3.2, .4c 3.4 3.7- 4. 2- 3.6.
3 . 8
. 3!
4 . 1.
.3c 4.8- 4.3
5 m 9- 4 . 8
: 1 .25 5 . 1- V' sec w, 1' .20 6.1.'
a 4- 5 m 80
8.9 .15 17.4 140.20- 130. 1
-
10 138.9 146.80- 130.8
I 1
- L _I _I
.05 50 -60 70 90 100
u , , m-sec-1
( b ) Effect of changing approach speed on t h e phugoid s t a b i l i t y .
The numbers below curve are times t o damp t o h a l f amplitude, and those above are time t o double amplitude.
F i g u r e 4. - Concluded.
I n t e g r a t o r and g a i n
- + I
i Servo Airplane f Gain Differentiation and g a i n
r
Figure 5.- Block diagram of automatic p i l o t used i n s t a b i l i t y s t u d i e s .
W Iu C u r v e Wi A 0 0 B -6.10 0
140 r
C 6.10 0 D -6 10 2.0
120 n
E -6 10 0.5 E S ' a ?
U +
.-
t : a 60- Shear ends, h = 50 m 40 r
20 -
I I I I I J O O 400 800 1200 1600 2000 2400 2800 D, distance along approach path, m ( a > A l t i t u d e .
Figure 6.- Control-fixed motion of an a i r p l a n e i n wind s h e a r .
Uw = 0.
UT = 0,; Curve W.
I A 0 B -6 10 C 6 10 D -6.10 0.5 E -6 10 -0.5 F 6 10 G 6 10 -2 0 . I - A B
-
-. 1
-
-. 2
I I I I I I 1
-. 3-
Figure 6.- Continued.
W W
*08 t
-. 08
Curve wi U
T
-. 16
A 0 0 B - 6 1 0 0 C 4 10 0 -. 24.
D -410 20 E -410 0. 5 F 4 10 -0.5
-. 32 8
G 6.10 -20 1 I I I I 1
-. 40 I
0 400 800 1200 1600 2000 2400 D, distance along approach path, m ( c > Flight-path angle.
Figure 6.- Concluded.
120 T
C u rve 'i Shear starts, B -6.10 0 h = 106 m
- - - - - -
D -6.10 20 H -6.10
20 3 , terms neglected
E 2- 80 a- U =I e a Shear ends, h = 50 m 0 400 800 1200 1600 2000 2400 2800 D, distance along approach paah, m ( a ) Altitude.
Figure 7.- The effect of deleting wind acceleration terms i n t h e kinematics of the a i r p l a n e equations when t h e wind shear is p o s i t i v e .
UT = 0,; w VI Motions are c o n t r o l f i x e d .
uw = 0 .
W m
C u rve W. I (JT
B - 6 0 10 0
D - 6 0 10 2 m 0
H
-6.10 2 . 0 3 terms neglected
W
B
I I . I I I I 1
400 800 1200 1600 2000 2400 2800
D, distance along approach path, m
(b) Pitch angle.
Figure 7.- Continued.
.08 Curve T *i
B -6.10
D -6.10 2. 0
H -6.10 2.0 vw terms neglected
-. 08
a
-
m c m %
S L
-. 16 b
.v J= m
.-
I LL
-. 24
-. 32
1 I 1 I I I 1
-. 4 0
0 400 800 1200 1600 2000 2400 2800 D, distance along approach path, m ( c ) Flight-path angle.
Figure 7.- Concluded.
W W
\\
Shear starts, h = 106m E r U S 2= 2 z a" Shear ends, h = 50m Shear ends, h = 50m
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
C u rve (5 'i T C 6 . 10 0 C 6 . 10 0 G 6.10 -2 0 G 6.10 -2 0 2c
I 6 . 10 -2.0 ? t e r m s neglected I 6 . 10 -2.0 ? t e r m s neglected
W W I 400 800 1200 1600 2000 2400 .2800
D, distance along approach path, m
( a > A l t i t u d e .
Figure 8.- The effect of deleting wind a c c e l e r a t i o n terms i n t h e kinematics o f the a i r p l a n e equations of motion when the wind shear is negative.
OT = a , ; ow = 0. Motions are c o n t r o l fixed.
C u rve W.
I
C 6 10
G 6 . 10
-2 0
.
I 6.10
-2.0 3 terms neglected
W
- 3 I I I I 1 I I
400 800 1200 1600 2000 2400 2800
D, distance along approach path, m
(b) Pitch angle.
Figure 8.- Continued.
& .08 C
-. 08
a-
C u r v e
W. 0 I C 6 10 0
G 6 . 10 -20 vw t e r m s neglected
I 6 . 10 -2. 0
-. 24
-. 32
I I I I I I I
-. 4c
1 400 800 1200 1600 2000 2400 2800 ; D, distance along approach path, m ( c > Flight-path angle.
Figure 8.- Concluded.
v R
V = Desired airspeed
C Figure 9.- Block diagram of speed c o n t r o l system.
f W i t h flight-path and airspeed controls
\\
I I 0 400 800 1200 1600 2000 2400 2800 D, distance'along approach path, m (a) Altitude.
Figure 10.- Comparison of airplane motions in positive wind shear.
UT = Uu = 2;0, with and without automatic flight-path and speed controls.
. I m Q) U a- a 5 ' 0 c m l z V e n
-. 1
LWith flight-path and airspeed controls
\
V C o n t r o l fixed 0 = 2 . 0 U
-. 2
\
-. 3
0 400 800 1200 I600 2000 2400 2800 D, distance along approach path, m ( b ) P i t c h angle.
Figure 10 .- Continued.
& W & & L W i t h f l i g h t - p a t h a n d a i r s p e e d control
\
\
\\t.Control f i x e d I I I I I
I I
400 800 I200 I600 2000 2400 2800
( c > Flight-path angle.
Figure 10. - Concluded.
140 -
Shear starts, h = 106m E a ; P =I
.- - +
W W - p a t h and airspeed controls
2 6 0 -
Shear ends, h = 50m
- - - - - - - - - - -
-
D, distance along approach path m ( a ) A l t i t u d e .
Figure 11.- Comparison of a i r p l a n e motions i n negative wind shear.
UT = uu -2.0, with and without automatic flight-path and speed controls. uw = 0.
2.5
Flight-path and airspeed control r C o n t r o l fixed
I
0.1 1 kE= and 2.5
Flight-path and airspeed control c
.- UJ I
L
-. 32
- 401 I I I I I I I
* o 400 800 1200 1600 2000 2400 2800
D, distance along approach path, m ( c > Flight-path angle.
Figure 1 1 . - Concluded.
x1 I x2 x3 y3 Stability a x e s , yl,y2'y3 a n d p r i n c i p a l body axes, x l ' x r s M o v i n g axes, XI1, X2', X3I a n d p r i n c i p a l body axes , xl, x2' x3 Earth-fixed axes, X 1 ' Xp X3 I n t e r mediate axes a r e not labeled a n d a r e shown as dashed l i n e s Figure 12.- Coordinate systems and Euler angles. The order of r o t a t i o n f o r t h e Euler angles is 9 , 8 , and c p . The moving axes t r a n s l a t e with air plane and remain parallel t o the earth-fixed axes. P o s i t i v e d i r e c t i o n s are shown.
25 w > o
25 0 < o
P P P P -10
25 w < o
25 w > o
P P P P -20 -30
Figure 13.- Combinations of ro and ou t h a t make t h e 2cPwp term
of equation (C5) zero.
Ln
u2 > o
P 1 1 I I I I I I I I . I
-nI 2 - 4 ~ 1 9 d 3 -27rl9 -19
0 xl9 2x1 9 TI3 4x19 7d2
rO Figure 14.- Combinations of T o and oU t h a t make t h e term up2 of equation (C6) zero.
c (0 U U U - 10 -20 -30 I I I I 1
d 9 27d 9
d 3 4 d 9 7d2
Figure 15.- Regions of s t a b i l i t y f o r equation ( C 2 ) obtained by combining f i g u r e s 13 and 1 4 .
NATIONAL AERONAUTICS A N D SPACE ADMINISTRATION WASHINGTON. D.C. 20546 P O S T A G E A N D F E E S P A I D N A T I O N A L A E R O N A U T I C S A N D OFFlC I AL BUS I NESS S P A C E A D M I N I S T R A T I O N PENALTY FOR PRIVATE USE 5300 SPECIAL FOURTH-CLASS RATE
U S M A I L (E]
BOOK A 770610 SOO903DS 431 001 C 1 U DEPT O P TBE A I R FORCE AP WEAPONS LABOBATOBY ATTN: TECHNICAL LIBBARY (SULI KIBTLAND A P B N H 87117 : If Undeliverable (Section 158 Postal Mnnunl) Do N o t Return “The aeronautical and space activities of the United States shall be
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