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NASA TN D-64

TECHNICAL NOTE

CALCULATION O F WIND COMPENSATION FOR LAUNCHING
OF UNGUIDED ROCKETS By Robert L. James, Jr., a.nd Itonald J. Harris
Langley Research Center Langley Field, Va.

APR 17 1961

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

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WASHINGTON--

April 1961

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
TECHNICAL NOTE D-645
CALCULATION OF W I N D COMPENSATION FOR LAUNCHING
OF UNGUIDED ROCKETS
By Robert L. James, Jr., and Ronald J. Harris
SUMMARY
A method f o r c a l c u l a t i n g wind compensation f o r unguided m i s s i l e s
i s derived which has a g r e a t e r degree of f l e x i b i l i t y t h a n t h e previously
proposed methods. Most of t h e e a r l i e r t h e o r i e s were based on a common set of assumptions which are (1)v e h i c l e motions i n p i t c h and yaw are independent, (2) l i n e a r aerodynamic coefficients with respect t o flow
incidence angle a r e used, (3) launch angles f o r wind compensation a r e t h e d i s p e r s i o n angles computed by using t h e weighted wind, and ( 4 ) f a c -
. t o r s used t o determine azimuth correction are computed f o r t h e standard
launch-e l e v a tion angle
Elimination of t h e f i r s t two l i m i t a t i o n s i s t h e r e s u l t of using a three-dimensional t r a j e c t o r y simulation w i t h arbitrary wind and nonlinear aerodynamic c o e f f i c i e n t s with r e s p e c t t o flow incidence angle. The l a s t two l i m i t a t i o n s were removed by t h e unique a n a l y t i c a l methods used i n the present paper.
U t i l i z a t i o n of t h e wind-compensation technique i s demonstrated by using t h e Shotput vehicle as a model. P o s t f l i g h t simulations of f o u r of t h e s e m i s s i l e s w i t h t h e use of measured winds show t h a t i f t h e winds are known, very good accuracy can be obtained by using t h e proposed method.
A wind-compensation system f o r t h e unguided Scout-SX-1 i s presented i n t h e appendix. This system w a s developed by using t h e assumptions and methods presented i n t h i s paper. The e r r o r s obtained a r e of about t h e sane magnitude as those found f o r t h e Shotput system; y e t t h e missile configurations and performance h i s t o r i e s are very d i f f e r e n t .

2
INTRODUCTION
The advent of high-altitude-performance missiles has made the consideration of factors causing trajectory deviations o r dispersion a necessity. One of the main contributors to the dispersion of an unguided vehicle is wind, and the purpose of this paper is to present a method for minimizing this effect on the trajectory.
During the past decade several theories have been proposed for calculating wind compensation, and results of flights made with the use of these methods have been good in some cases and very poor in others. Most of the previous work was done by using a similar set of assumptions which can cause large errors. These assumptions are:
1. Vehicle motions in pitch and yaw are independent.
2. Linear aerodynamic coefficients with respect to f l o w incidence angle and small angular perturbations are used.
3 . Launch angles for wind compensation are the dispersion angles
computed with the use of the weighted wind.
4. Factors used to determine azimuth correction are computed for
the standard launch-elevation angle.
The first assumption is poor because the azimuth change is greatly dependent on the elevation angle. The trajectory should be computed in three dimensions so that proper coupling effects between pitch and yaw can be simulated.
Assumption 2 can cause large errors since most vehicles are more sensitive to the wind early in flight when the flow incidence angle can be well into the nonlinear range.
Assumption 3 is a direct misconception of the wind problem and can
cause very large errors. The angular dispersion is computed by using the weighted wind, and the compensation angles required are assumed to be equal and opposite to these deviations. It is necessary to perform an iteration to determine the proper launcher angles. This assumption also causes additional errors in pitch since the effect of gravity varies with the launch elevation angle.
The errors introduced by assumption 4 are related to assumption 1.
If the wind-compensation procedure calls for a change in the launch elevation, then the yaw-compensation factors should also be changed. This is due to the change in yaw sensitivity associated with the elevation angle.

3
Probably t h e most well-known wind-compensation procedure i s t h a t described i n reference 1. I n t h i s paper the rocket i s assumed t o t u r n instantaneously i n t o t h e wind so t h a t t h e vehicle a x i s i s always tangent t o t h e t r a j e c t o r y . I n addition, the wind-weighting f a c t o r s are assumed t o be i d e n t i c a l i n p i t c h and yaw.
I n reference 2 t h e theory of reference 1 i s improved, as f a r as t h e v e h i c l e response i s concerned, w i t h t h e use of more complete m i s s i l e equations. These equations, however, a r e s t i l l l i m i t e d t o one plane, and a l s o t h e same weighting f a c t o r s i n p i t c h and yaw are assumed.
Applications of t h e s e t h e o r i e s t o d i f f e r e n t missiles w i t h some
s l i g h t adjustment are described i n references 3 t o 6. I n some of these
a p p l i c a t i o n s , d i f f e r e n t weighting f a c t o r s i n p i t c h and yaw have been assumed, b u t t h e assumptions l i s t e d previously are again made.
A mu.ch Fmproved wind-compensation scheme w a s developed f o r the
L i t t l e Joe booster and i s presented i n reference 7. This a n a l y s i s w a s
based on a six-degree-of-freedom t r a j e c t o r y simulation which i s described
i n reference 8. The vehicle motion is, therefore, very accurate but t h i s
wind-compensation method has l i m i t a t i o n s and disadvantages which are n o t necessary if the proper procedure i s followed. For instance, the analysis i s l i m i t e d t o very low a l t i t u d e s ; and although it i s t r u e t h a t a l a r g e percent of t h e wind e f f e c t occurs a t t h e lower a l t i t u d e , t h i s i s a n unnecessary l i m i t a t i o n which can be removed without making t h e procedure more d i f f i c u l t . The system f o r t h e Little Joe involves a l a r g e number of c a r p e t p l o t s . The method e n t a i l s a n i t e r a t i o n i n obtaining t h e launcher c o r r e c t i o n s which must be done a f t e r t h e wind i s measured. This r e s u l t s i n a l a r g e amount of computation and graph reading during t h e l a s t few minutes of t h e count down.
The wind-compensation procedure which i s included i n t h i s paper w a s not developed as an improvement of t h e t e c h n i q u e . f o r t h e L i t t l e Joe. I n f a c t , t h e two methods are q u i t e d i f f e r e n t although both were based on the same t r a j e c t o r y simulation.
I n t h e wind-compensation procedure of the present paper, the a l t i tude limitation i s not made and the i t e r a t i o n i s involved i n the development and not during t h e count down. Also, t h e scheme only c o n s i s t s of conventional two-dimensional p l o t s which are simple and easy t o use. The amount of t r a j e c t o r y simulations and labor necessary t o develop the correction graphs is considerably less.
None of t h e l i m i t a t i o n s f o r references 1 and 2 are assumed i n t h i s a n a l y s i s . There are a f e w simplifying assumptions, causing n e g l i g i b l e e r r o r i n t h e solution, which are described as they a r e applied.

4

SYMBOLS

In the present paper, distances are measured in U.S. feet
(1 U.S. foot = 0.3048006 meter).

cA,0

axial-force coefficient at zero flow incidence angle, dimensionless

Cm

pitching-moment coefficient, dimensionless

c%

rate of change of pitching-moment coefficient with pitching

velocity, &m

1

= cnr’ radian

C 9

rate of change of pitching-moment coefficient with rate of

change of flow incidence angle, Z m

1

normal-force coefficient, dimensionless
yawing-moment coefficient, dimensionless
rate of change of yawing-moment coefficient with yawing
(3)’ velocity, - ZIl 1 radian

D IX IY
=2 MY
Mys

reference length, ft rolling moment of inertia, slug-ft2
pitching moment of inertia (Iy = Iz), slug-ft2

yawing moment of inertia, slug-ft2

pitching moment, ft-lb

rate of change of pitching moment with pitching velocity,

Y aM
as

=Mzr’

ft-lb-sec
radian

5

yawing moment, f t - l b

rate of change of yawing moment with yawing v e l o c i t y ,
f t-lb- sec radian

- % ar ’

pitching velocity, radianslsec

yawing velocity, raiiians/sec time a t which missile i s considered i n s e n s i t i v e t o wind

missile linear velocity relative to earth, ft/sec t o t a l m i s s i l e l i n e a r v e l o c i t y r e l a t i v e t o wind, f t / s e c h o r i z o n t a l wind v e l o c i t y r e l a t i v e t o e a r t h , f t / s e c

h o r i z o n t a l wind v e l o c i t y component from t h e e a s t , f t / s e c h o r i z o n t a l wind v e l o c i t y component from t h e north, f t / s e c

earth-fixed axes, dimensionless

components of m i s s i l e v e l o c i t y along XE-, YE-, and %-axis, r e spec ti v ely, f t /see
center-of-gravity d i s t a n c e from nose, f t

center-of-pressure d i s t a n c e from nose, f t

flight-path angle i n pitch, deg

launch elevation angle, deg

f l i g h t - p a t h angle i n yaw, deg
f l i g h t - p a t h angle i n yaw i n plane normal t o plane of t r a j e c t o r y and tangent t o t h e instantaneous f l i g h t path, deg
launch azimuth compensation f o r Wind, deg

6

'I

flow incidence angle, radians

4

rate of change of flow incidence angle with time, radians/sec

OW

wind d i r e c t i o n r e l a t i v e t o true north, deg

h

no-wind f i r i n g azimuth, deg

JlW

angle between Vw,h and p r o j e c t i o n of m i s s i l e c e n t e r l i n e

i n XEYE-plane, deg

SHOTPUT CONFIGURATION CHARACTERISTICS

The method f o r wind compensation presented i n t h e present paper i s not l i m i t e d t o any s p e c i f i c missile. However, due t o t h e complex nature of t h e problem, t h e procedure as o u t l i n e d i s applied t o a p a r t i c u l a r m i s s i l e ; namely, t h e Shotput vehicle. The Shotput i s a two-stage s o l i d propellant rocket vehicle used t o test the inflation techniques f o r the 100-foot-diameter balloon s a t e l l i t e . These m i s s i l e s a r e f i r e d from NASA Wallops Station.

The Shotput e x t e r n a l c h a r a c t e r i s t i c s are presented i n f i g u r e 1. The configuration shown i s t h e one which e x i s t s a t launch and during
first-stage burning ( i n t h i s section, only data pertaining t o the vehicle
during f i r s t - s t a g e burning a r e presented). The f i r s t - s t a g e propulsion
system c o n s i s t s of a Pollux rocket motor and two Recruit r o c k e t s which
are used t o increase t h e acceleration at launch and burnout a t about
2 seconds. Aerodynamic s t a b i l i t y i s obtained by using f o u r 8' wedge f i n s having an area of 15 square f e e t per panel. The m i s s i l e i s 384.6 inches long and has a maximum diameter of 33 inches.

The aerodynamic parameters f o r t h i s missile are presented i n f i g -
ure 2. Figure 2 ( a ) shows t h e aerodynamic c o e f f i c i e n t s as a f u n c t i o n of Mach number f o r various values of 7. Included are Cmq, Cmi, C A , ~ ,

CN, and x

It w a s assumed that t h e vehicle has r o l l symmetry although

CP'

the Recruit rocket motors produce an unsymmetric e f f e c t . The aerodynamic

c o e f f i c i e n t s a r e based on a reference area S of 1 sq f t and a r e f e r e n c e

length D of 1 f t .

P l o t s of t h e time varying parameters are presented i n f i g u r e 2(b) f o r time from launch t o f i r s t - s t a g e burnout a t 32.5 seconds. Included i n t h i s f i g u r e are weight, xcg; t h r u s t , IY, Ix, and My Again t h e
9'
assumption w a s made t h a t t h e v e h i c l e has r o l l symmetry.

7
The nominal performance of t h e Shotput v e h i c l e i s shown i n f i g u r e 3
as p l o t s of a l t i t u d e and v e l o c i t y v a r i a t i o n s with range. These data were computed i n the IBM 704 e l e c t r o n i c data processing machine using t h e aerodynamic parameters presented above and the t r a j e c t o r y program dis-
cussed i n reference 8. An ICAO standard atmosphere ( r e f . 9 ) and a launch
angle of 7 8 O were used i n t h e s e computations.
ANALYSIS
The wind-compensation procedure derived h e r e i n involves f o u r a s p e c t s . They a r e an adequate t r a j e c t o r y simulation, s e l e c t i o n of wind p r o f i l e s , development of wind-compensation graphs, and a wind-weighting procedure.
Trajectory Simulation
The requirements f o r a t r a j e c t o r y program needed f o r a windcompensation procedure are (1)that t h e t r a j e c t o r y be t h r e e dimensional, ( 2 ) t h a t provision be made f o r a r b i t r a r y wind v e l o c i t y and azimuth and
(3) t h a t nonlinear aerodynamics w i t h respect t o flow incidence angle be
included. The f i r s t two requirements are obvious since, i n t h e conside r a t i o n of s i d e winds, t h e t r a j e c t o r y i s three dimensional and t h e wind v e l o c i t y and azimuth a r e a r b i t r a r y . The t h i r d requirement i s imposed because t h e i n t r o d u c t i o n of surface winds during launch can c r e a t e angles of a t t a c k l a r g e r than 90°, which g r e a t l y exceed t h e l i n e a r range of t h e aerodynamic c o e f f i c i e n t s .
A t r a j e c t o r y simulation incorporating the above requirements i s
presented i n reference 8. I n a d d i t i o n t o the above requirements, t h i s
simulation assumes a vehicle w i t h s i x degrees of freedom and aerodynamic symmetry i n r o l l and t h e m i s s i l e p o s i t i o n i n space i s computed r e l a t i v e t o a f l a t nonrotating e a r t h . This t r a j e c t o r y simulation w a s programmed
on t h e IEN 704 e l e c t r o n i c d a t a processing machine and i s t h e b a s i s f o r
a l l t r a j e c t o r y computations made i n t h i s paper.
S e l e c t i o n of Wind P r o f i l e s
The winds a t some geographical locations have been measured and recorded over periods of t h e longer than a year. These measurements i n d i c a t e t h a t t h e wind v e l o c i t y g e n e r a l l y increases with a l t i t u d e u n t i l a peak i s reached a t t h e j e t stream and then decreases r a t h e r a b r u p t l y .
Recordings made a t P a t r i c k A i r Force Base, Cocoa, F l o r i d a a r e presented
i n reference 10. These annual recordings were used as a b a s i s f o r
s e l e c t i n g p r o f i l e s t o be used i n t h e wind a n a l y s i s .

8
The annual p r o f i l e i s shown i n f i g u r e 4. This curve r e p r e s e n t s
the wind v e l o c i t i e s which were measured over a y e a r l y period. The s c a l a r
winds i n d i c a t e d on t h e curve were not exceeded about 96 percent of t h e
t i m e . Also shown i n f i g u r e 4 a r e t h e l i n e a r wind p r o f i l e s which were
used i n the a n a l y s i s . The maximum wind p r o f i l e assumed t o be 40 f t / s e c
i s shown as a l i n e a r approximation t o t h e annual curve. The o t h e r prof i l e s shown i n t h i s f i g u r e are f r a c t i o n a l m u l t i p l e s of t h e b a s i c curve. It should be noted t h a t a p r o f i l e i s referred t o i n terms of t h e surface wind v e l o c i t y of t h a t p r o f i l e . There were a t o t a l of f o u r wind p r o f i l e s
considered which represented surface winds of 10, 20, 30, and 40 f t / s e c .
A m i s s i l e i s i n s e n s i t i v e t o wind above a c e r t a i n a l t i t u d e . For the Shotput vehicle t h i s a l t i t u d e w a s determined t o be 42,000 f e e t as i s shown i n a subsequent s e c t i o n of t h i s paper. Thus, t h e l i n e a r pro-
files of figure 4 are stopped at t h i s altitude. I f the s e n s i t i v i t y
range had extended above 42,000 f e e t , t h e assumed p r o f i l e s would be extended also; and t h e i r slopes would be changed so t h a t t h e curve f o r 40 f t / s e c would c l o s e l y approximate t h e annual p r o f i l e .
The assumption t h a t t h e wind w i l l vary with a l t i t u d e on t h e day of f i r i n g as one of t h e s e p r o f i l e s i s not made i n t h e a n a l y s i s . The devia t i o n from t h e p r o f i l e s of t h e measured wind i s taken i n t o account by weighting t h e wind which i s discussed i n a subsequent s e c t i o n .
Derivation of Wind-Compensation Graphs
I n t h i s section t h e development of a set of wind-compensation graphs i s presented. The r e s u l t i s a graph of launch-elevation and launchazimuth angles as a f u n c t i o n of wind azimuth and v e l o c i t y . Throughout the following a n a l y s i s , assumptions a r e made which a r e d i f f i c u l t t o prove d i r e c t l y although t h e y seem c o r r e c t i n t u i t i v e l y . These assumptions are only pointed out as they are passed and are subsequently checked as a group by making sample computer runs with varying wind conditions.
It i s convenient t o d e f i n e here some of t h e terminology used i n t h e analysis. Consider t h e following diagram:

9
- 2,

J

ZE

Earth fixed axes '

XE

The f l i g h t - p a t h angle i n p i t c h i s given by

yP

=

sin'

1&
V

where V i s t h e m i s s i l e v e l o c i t y r e l a t i v e t o t h e ground and can be expressed as

The f l i g h t - p a t h angle i n yaw can be expressed a s

10
Note that t h i s angle i s i n t h e plane of t h e missile v e l o c i t y v e c t o r and i s not an e a r t h p r o j e c t i o n . The p r o j e c t i o n of t h e yaw f l i g h t - p a t h angle i n t h e plane of t h e e a r t h i s given by

These yaw angles are r e l a t e d t o each o t h e r through t h e following equation:

s i n y ' = sin y cos y

Y

Y

P

(5)

The time at which t h e wind i s no longer e f f e c t i v e i s c a l l e d t e , and f o r Shotput t h i s value i s 25 seconds. This corresponds t o an a l t i t u d e of 42,000 f e e t which'was pointed out above.
The nominal, no-wind launch elevation f o r Shotput i s 78O, and t h e
nominal values of t h e preceding f l i g h t - p a t h angles a t t e = 25 seconds are

yy' = oo
yp = 67.3O
Wind conditions cause changes i n some o r a l l of t h e s e angles depending on t h e wind d i r e c t i o n .
Head and t a i l w i n d s . - Consider f i r s t t h e e f f e c t s of head and t a i l winds. Since t h e missile i s s t a b l e and t h r u s t i n g during t h e p o r t i o n of the t r a j e c t o r y being analyzed, it weathercocks. A head wind p i t c h e s t h e missile down and a t a i l wind p i t c h e s it up. T r a j e c t o r i e s were computed with various head- and tail-wind p r o f i l e s and t h e r e s u l t s of t h e s e com-
putations are shown i n f i g u r e 5 as a p l o t of t h e f l i g h t - p a t h angle i n
pitch, YP, a t t e ( 2 5 s e c ) a g a i n s t wind v e l o c i t y a t t h e surface. The conditions of t h e s e t r a j e c t o r y simulations a r e shown i n t a b l e I as runs 1
t o 9. The launch elevation w a s held constant a t 78' f o r a l l of these
trajectories.
T r a j e c t o r i e s were a l s o computed with no wind f o r various launch elevation angles, and t h e change i n f l i g h t - p a t h angle w a s computed by using the equation

r

t

11

a7P = 7P,0 - (Tp)te

where

i s the flight-path angle a t launch. In figure 6,

is

7P, 0

A7P

p l o t t e d a g a i n s t launch e l e v a t i o n f o r t h e no-wind cases, and a l s o curves

are shown f o r head winds and t a i l winds. The no-wind t r a j e c t o r y s i m u -

l a t i o n s are shown i n t a b l e I as run 1 and runs 10 t o 12. Data f o r t h s

head winds and t a i l winds were available f o r a launch elevation of 78

as presented i n f i g u r e 5 (runs 2 t o 9 ) and f o r a wind of 40 f t / s e c with

varying launch elevation i n runs 13 t o 18. The family of curves shown

i n t h i s f i g u r e w a s obtained by i n t e r p o l a t i o n between t h e s e data p o i n t s .

It was stated previously t h a t t h e desired value of

was 67.3O.

Therefore, f o r the i d e a l case, equation ( 6 ) can be written,

7P, 0 - AyP = 67.3'

(7)

This expression can be solved g r a p h i c a l l y with the use of a 45' l i n e

) p l o t t e d against 7 which i s also p l o t t e d i n f i g u r e 6. A p a i r

(yP, 0

P,O

of d i v i d e r s set a t 67.3' can be moved u n t i l t h e value set i s t h e d i f f e r -

. ence between t h e 45' l i n e and one of t h e curves. The l e n g t h corresponding

t o 67.3' i s i l l u s t r a t e d i n f i g u r e 6 i n t h e p o s i t i o n f o r determining 7P,O

f o r a head wind of 20 ft/sec. It can be seen that the value of 7P, 0 i s 82.8' f o r t h i s wind condition. The r e s u l t of t h i s g r a p h i c a l s o l u t i o n

i s t h e c w e shown i n f i g u r e 7. This figure gives t h e launch elevation

needed f o r wind compensation i f t h e e x i s t i n g wind i s a head o r t a i l wind.

Hence, i f compensation f o r head and t a i l w i n d s were t h e only considera-

t i o n , f i g u r e 7 would s u f f i c e .

By making a comparison of f i g u r e s 5 and 7 it i s readily seen that

the t r i a l and e r r o r process described above i s very necessary. A head-

( 7 d t , wind p r o f i l e of 40 f t / s e c gives a value of

of >lo ( f i g . 5) which

i s 16.3' lower than the desired value o f 67.3'. Now, if t h i s charge i s added t o t h e launch-elevation angle of 7 8 O it gives 94.3' f o r t h e corr e c t e d launch angle as compared t o 87.8O which i s shown i n f i g u r e 7. T h i s i s an e r r o r of 6.50 i n t h e launch-elevation angle which, of course,
could not be t o l e r a t e d . Carrying out a similar comparison f o r a t a i l
wind of 40 f t / s e c i n d i c a t e s t h a t an e r r o r of 8.5' would be m a d e .

Side winds.- The next s t e p i n t h e a n a l y s i s i s t h e consideration of
side-wind components o r winds from any direction. The angle qW i s

t

?

defined as t h e angle between t h e launch azimuth and t h e h o r i z o n t a l component of wind ( t h e h o r i z o n t a l wind component i s assumed t o be t h e t o t a l wind v e c t o r ) as shown i n t h e following diagram:
/Wind vector
1 Launch azimuth

The v e c t o r s i l l u s t r a t e d i n t h e diagram are a l l i n t h e h o r i z o n t a l plane.
Trajectory simulations were made f o r various values of $w and wind p r o f i l e s assuming a launch-elevation angle of 78'. The conditions
of these computations a r e shown i n t a b l e I as runs 1t o 9 and runs 19 t o 30. Also shown i n t h e t a b l e a r e values f o r y and yyl which a r e
P
l i s t e d a t t,. These values were computed by using equations (1)and ( 3 ) and were p l o t t e d against JIw f o r t h e d i f f e r e n t wind v e l o c i t i e s as i n figure 8. The curves were p l o t t e d f o r p o s i t i v e values of qw; however, the d a t a can be used f o r e i t h e r p o s i t i v e o r negative values of qW with
the signs of ( Y ~ ' ) ~ , being opposite from those of qw.

The next f i g u r e constructed w a s made up of d a t a presented i n f i g -

ures 5 and 7. Figure 5 gives

f o r various head- and tail-wind

(Tp )te

v e l o c i t i e s , and f i g u r e 7 gives t h e launch e l e v a t i o n needed t o compensate
f o r t h e s e winds as a f u n c t i o n of wind v e l o c i t y . By making a c r o s s p l o t of t h e d a t a i n t h e s e f i g u r e s , it i s p o s s i b l e t o c o n s t r u c t a curve of
p l o t t e d a g a i n s t t h e c o r r e c t launch e l e v a t i o n . This r e s u l t i s (7p )te

shown i n f i g u r e 9. Thus, f o r any value of

obtained from a

1

4

t r a j e c t o r y i n which t h e launch elevation was 7 8 O , it i s possible t o
o b t a i n from t h i s f i g u r e t h e launch elevation which i s required t o make
('PIte equal t o 67.3O o r t h e nominal, no-wind value. For example, sup-

pose a t r a j e c t o r y were computed by using a launch-elevation angle of 7 8 O

and some head- o r tail-wind p r o f i l e . If the

under these condi-

t i o n s came out t o be &lo,then the launch elevation needed t o f l y t h e
no-wind t r a j e c t o r y can be read from figure 9 as 71.3'.

It isaassumed t h a t t h e curve of figure 9 i s v a l i d f o r wind condi-
t i o n s o t h e r than head and t a i l winds. I n other words, i f a value of
Mte i s obtained with a launch angle of 78' f o r any wind v e l o c i t y o r

d i r e c t i o n , t h e launch elevation necessary t o compensate f o r t h e e r r o r

i n p i t c h can be read from t h e f i g u r e . By making t h i s assumption, it i s

p o s s i b l e t o determine t h e c o r r e c t launch elevation f o r each value of

( ( i n f i g u r e 8. Values of

are read i n f i g u r e 8 and then

yp) te

7p>te

t h e c o r r e c t launch angle i s determined from f i g u r e 9.. The r e s u l t s are
shown i n f i g u r e 10. I n t h i s f i g u r e i s p l o t t e d t h e c o r r e c t launch e l e v a t i o n as a function of \c;r f o r various velocity p r o f i l e s . This curve

gives t h e wind compensation i n t h e launch e l e v a t i o n f o r any wind azimuth and various v e l o c i t y p r o f i l e s . Note t h a t t h i s f i g u r e a p p l i e s f o r posi-
t i v e o r negative values of qW.

The problem remaining i s t h e determination of the azimuth compensa-
t i o n graph. By rearranging equation ( 5 ) t h e following expression i s
obtained f o r t h e yaw angle i n t h e plane of the e a r t h :

It can r e a d i l y be seen t h a t as

increases, t h e value of

becomes

l a r g e r than t h e value of

7 '.

7P The reason f o r t h i s i s t h a t

yY 7

is the

Y

Y

yaw angle i n t h e plane of t h e missile and yY i s t h e p r o j e c t i o n of t h i s

angle i n t h e e a r t h plane. Hence, as t h e p i t c h angle increases, t h e pro-

j e c t i o n becomes l a r g e r f o r a given value of

I . For t h i s reason, the

yY

d i s p e r s i o n problem becomes very c r i t i c a l when unguided r o c k e t s a r e

launched a t steep launch angles.

14

It i s assumed t h a t t h e d a t a f o r

i n figure 8 can be used

f o r any launch elevation i n the neighborhood of 78' ( t h i s assumption
along with o t h e r s w i l l be proven v a l i d i n a subsequent s e c t i o n ) .

After wind compensation, t h e p i t c h angle

w i l l be 67.3' a t

7P

'> 25 seconds. By using t h e values of (7Y te from f i g u r e 8 and 7P = 67.3O

i n equation (8), it i s possible t o determine values of

f o r each wind
yY

d i r e c t i o n and v e l o c i t y p r o f i l e . These values were computed and a r e shown

i n f i g u r e 11.

Consider t h e following diagram showing t h e geometry of t h e wind problem i n t h e h o r i z o n t a l plane:

t True north

/

It can be seen i n the diagram t h a t
where 8, i s t h e wind d i r e c t i o n r e l a t i v e t o t r u e north, 7y,0 i s t h e azimuth compensation f o r wind, and A i s t h e desired azimuth a t t e .

By transposing and s u b s t i t u t i n g 90' f o r A ( s i n c e east w a s t h e desired
d i r e c t i o n of f i r e f o r Shotput), t h e following equation i s obtained:

- qw yy,o = goo - e,

T h i s equation i s solved by using a graphical solution similar t o t h a t

( used previously i n solving equation ( 7 ) . The values of

in fig-

yy) te

ure 11 are-measured r e l a t i v e t o the launch azimuth of t h e missile; t h e r e fore, (yY)te must be equal i n magnitude and opposite i n sign t o 7Y,O

i f t h e v e h i c l e i s on course a t t,. (See the preceding diagram..) A

( 4 5 O l i n e i s a l s o shown i n f i g u r e 11 p l o t of qw against qW) so t h e

- - values of qW yy,o Or *w (-YJte

can be obtained f o r various

- values of goo 8, which are assumed. The following table includes
some sample c a l c u l a t i o n s using t h i s procedure. The arrow shown i n f i g ure 11 corresponds t o t h e f i r s t calculation i n t h i s table.

After t h e value of Jrw i s determined, it i s possible t o determine

I

t h e launch-elevation angle from f i g u r e 10. Values of launch e l e v a t i o n

are a l s o given i n the above t a b l e .

If t h i s procedure i s carried out f o r each velocity p r o f i l e and

wind-direction angle 8, from'0 t o 360°, it i s possible t o construct

t h e f i n a l wind-compensation graph as shown i n figure 12. This graph

I

gives t h e launch azimuth and elevation angles needed t o compensate f o r

any wind d i r e c t i o n and f o r t h e various v e l o c i t y p r o f i l e s . It should

be noted t h a t t h e desired azimuth i s 90' and that t h e curves would be

s h i f t e d right o r l e f t f o r other values.

These curves only apply t o wind-velocitx p r o f i l e s l i k e those assumed previously and wind d i r e c t i o n s which are i n v a r i a n t with a l t i t u d e . Theref o r e , t h e curves are not very u s e f u l alone s i n c e wind d a t a a t f i r i n g time

16
w i l l generally show d i r e c t i o n changes with a l t i t u d e and t h e v e l o c i t y w i l l probably not d u p l i c a t e t h e assumed g r a d i e n t .
In order t o a l l e v i a t e t h i s limitation, a wind-weighting procedure i s used which e f f e c t i v e l y determines t h e v e l o c i t y p r o f i l e and wind d i r e c t i o n which most nearly agree with t h e a c t u a l wind conditions. This procedure i s discussed i n the next section.
Wind-Weighting Procedure
Previously i n t h i s paper it w a s pointed out t h a t assumed wind prof i l e s were used i n t h e a n a l y s i s . Before wind-compensation angles can be obtained by using f i g u r e 12, it i s necessary t o determine t h e l i n e a r p r o f i l e t h a t most nearly approximates t h e a c t u a l wind conditions a t launch time. I n o t h e r words, some weighting procedure must be used which relates a c t u a l wind d a t a t o one of t h e assumed p r o f i l e s .
The a b i l i t y t o compensate f o r winds depends g r e a t l y on t h e accuracy of t h e wind d a t a which a r e used. A discussion of t h e various wind measuring techniques and t h e i r inherent e r r o r s i s beyond t h e scope of t h i s report, but it should be emphasized t h a t accurate wind d a t a are necessary before good r e s u l t s can be obtained with a wind-compensation procedure.
A s t a b l e m i s s i l e i s most s e n s i t i v e t o winds e a r l y i n f l i g h t when i t s v e l o c i t y i s low and t h e a l t i t u d e i s low. The s e n s i t i v i t y decreases rapidly with increasing a l t i t u d e ; hence, it follows t h a t more weight must be given t o t h e low-altitude wind d a t a . A l a r g e percentage of t h e s e n s i t i v i t y occurs i n t h e f i r s t 1,000 feet of a l t i t u d e i n most cases.
Obviously, t h e r e i s some p o i n t along t h e t r a j e c t o r y of a v e h i c l e a f t e r which t h e wind no longer has any noticeable e f f e c t on t h e f l i g h t path. The f l i g h t time te when t h e missile reaches t h i s p o i n t i s taken as t h e end p o i n t f o r t h e consideration of wind e f f e c t s ; a corresponding a l t i t u d e determines t h e cutoff a l t i t u d e f o r t h e wind p r o f i l e s .
A s t a b l e m i s s i l e tends t o yaw, o r weathercock, i n t o t h e wind. The vehicle does not t u r n completely i n t o t h e wind but t r i m s a t some angle of yaw determined by t h e r e s p e c t i v e v e l o c i t i e s of t h e missile and wind. I f t h e missile i s t h r u s t i n g , t h e t h r u s t v e c t o r i s a l s o yawed through t h e same angle and f l i g h t - p a t h d e v i a t i o n s become evident. I f t h e weathercocked m i s s i l e i s not t h r u s t i n g , however, t h e only e f f e c t of wind on the f l i g h t path i s d r i f t and, i n most cases, t h e m i s s i l e v e l o c i t y i s high and d r i f t can be neglected.
Burnout time, thus, appears t o be a s u i t a b l e endpoint f o r t h e wind consideration. It should be noted that t h e vehicle may become v i r t u a l l y

i n s e n s i t i v e t o wind a t some t i m e before burnout. Nothing i s l o s t , however, i f the chosen endpoint i s beyond t h e s e n s i t i v e range. Each m i s s i l e must be t r e a t e d i n d i v i d u a l l y t o determine the s e n s i t i v e region of t h e t r a j e c t o r y t o be considered. Configurations vary so much t h a t there i s no r u l e which can be used i n a l l cases.
There are s e v e r a l schemes f o r determining s e n s i t i v i t y . The method used here c o n s i s t s of programming a sharp-edged h o r i z o n t a l gust t o h i t t h e vehicle a t various a l t i t u d e s along i t s nominal no-wind t r a j e c t o r y . A constant s i d e wind of 50 f t / s e c , which was allowed t o remain e f f e c t i v e u n t i l burnout, w a s used f o r a l l cases considered. I n other words, the vehicle is' flying the nominal trajectory until the gust a l t i t u d e i s reached and t h e n remains under t h e e f f e c t o f t h e wind until burnout. The a l t i t u d e s chosen f o r t h e wind t o become e f f e c t i v e were a r b i t r a r y , b u t most were a t t h e lower a l t i t u d e s where the s e n s i t i v i t y i s g r e a t e r .
The wind causes t h e m i s s i l e t o yaw through an angle yY which i s evident a t t e . By knowing t h e value of yY a t t e and by assuming that t h e p i t c h angle a t t h i s p o i n t w i l l be the nominal value a f t e r wind compensation, it i s possible t o use equation (8) t o determine the values

A comparison of the r e s u l t i n g

for different altitudes is

a measure of wind s e n s i t i v i t y . A t y p i c a l plot showing t h e change of
with gust altitude is given f o r the Shotput i n figure l3(a).
k Y t ) te Note t h a t t h e a l t i t u d e s are t h e a l t i t u d e s a t which t h e vehicle e n t e r s
the gust.

From t h e f i g u r e , it i s seen t h a t t h e r e i s no noticeable change i n
( ) % p a s t an a l t i t u d e of 42,000 f e e t . This i s t h e end of t h e sent te

s i t i v e range and the wind p r o f i l e s f o r Shotput were c u t a t t h i s p o i n t . The corresponding time of f l i g h t w a s 25 seconds which determined t e .

The d a t a of f i g u r e l 3 ( a ) can be put i n a more useful form by dividing

each value of

by t h e maximum value occurring, as shown i n f i g -

(Yyl)te

ure 13(b). The maximum value w i l l usually occur a t zero a l t i t u d e , but

t h i s i s not a n e c e s s i t y . This curve i s a representation of r e l a t i v e

s e n s i t i v i t y s i n c e it i s a comparison of

values as a function

of a l t i t u d e . A change i n the r a t i o

of 0.01 repre-

s e n t s a 1-percent change i n s e n s i t i v i t y , and t h e corresponding a l t i t u d e bracket i s t h e l a y e r over which t h e change occurs.

18
8
The a l t i t u d e f o r each 0.07 change w a s read and l i s t e d i n t a b l e 11. These a l t i t u d e s d e f i n e t h e boundaries of wind l a y e r s which have a weight f a c t o r of 0.05 assigned t o them. Thus, a t o t a l of 20 l a y e r s w a s obtained
but more or less may be used depending on t h e v e h i c l e c h a r a c t e r i s t i c s and t h e shape of t h e s e n s i t i v i t y curve. Note t h a t 55 percent of s e n s i t i v i t y
OCCUTS i n t h e f i r s t 1,000 f e e t .
The boundaries defining t h e wind l a y e r s w e r e drawn on a p l o t of t h e
wind p r o f i l e s as i l l u s t r a t e d i n f i g u r e 14. For any reasonable a l t i t u d e
scale, the small l a y e r s below 1,000 feet would be i n d i s t i n c t ; t h e r e f o r e , a logarithmic s c a l e w a s used which tends t o make t h e l a y e r s e q u a l l y important. A disadvantage i n using t h e logarithmic s c a l e i s t h e imposs i b i l i t y of having an exact zero a l t i t u d e , but t h i s u s u a l l y c r e a t e s no problem since t h e vehicle c e n t e r of g r a v i t y i s not a t zero a l t i t u d e a t take-off. (The Shotput center of g r a v i t y w a s about 25 f e e t off t h e ground while s t i l l on t h e launcher.)
As an example of t h e wind-weighting procedure, consider t h e wind
d a t a p l o t t e d i n f i g u r e 14. These d a t a were measured before t h e f i r i n g of a Shotput vehicle on October 28, 1959 a t NASA Wallops S t a t i o n using
aerovanes and radar-tracked chaff balloons. Table I1 includes t h e wind v e l o c i t y and d i r e c t i o n readings for each l a y e r . For example, i n l a y e r 20
t h e wind v e l o c i t y read was 30 f t / s e c which w a s i n t e r p o l a t e d from t h e
assumed constant gradient p r o f i l e s . The wind azimuth i s read d i r e c t l y s i n c e no p r o f i l e s e x i s t f o r t h e wind azimuth.
After the velocity and azimuth values a r e tabulated f o r each layer, t h e e a s t and n o r t h components a r e determined by using t h e following expressions :

The components are added a l g e b r a i c a l l y and t h e weighted wind v e l o c i t y

and azimuth a r e obtained from t h e s e summations as shown i n t a b l e 11. Note

E( that t h e weighted north and east components are determined by dividing

(Vw,h)* and

vw,h)E by 20. The value 20 must be used s i n c e each

l a y e r has a weight of 0.05 as explained previously. The weighted wind
v e l o c i t y and d i r e c t i o n f o r t h i s p a r t i c u l a r wind was computed t o be
16.4 f t / s e c and 305O, respectively. Hence, t h e a c t u a l wind i s represented by a constant gradient with a surface v e l o c i t y of 16.4 f t / s e c and a direc-
t i o n of 305O.

a

I

Using t h e s e values i n f i g u r e 12 gives 74.7' f o r t h e launch elevat i o n and 9 9 O f o r t h e launch azimuth. A discussion of t h e r e s u l t s with
the use of these angles i s presented i n the next section.

DISCUSSION

Check of Analysis and Assumptions

The previously described wind a n a l y s i s w a s checked by using two d i f f e r e n t schemes which w i l l be discussed i n t h i s section. I n t h e f i r s t of these, t r a j e c t o r i e s were computed by using t h e assumed p r o f i l e s while holding t h e wind d i r e c t i o n constant i n each simulation and by using t h e derived launch corrections discussed previously and presented i n f i g ure 12. By t h i s procedure it w a s possible t o check t h e b a s i c assumptions\ of t h e wind analysis up t o t h e point of the wind-weighting procedure. The second scheme consisted of computing t r a j e c t o r i e s with wind data having varying v e l o c i t y and d i r e c t i o n , part of which were measured a t NASA Wallops S t a t i o n on t h e days of Shotput f i r i n g s and the remainder of which were a r b i t r a r i l y s e l e c t e d . This procedure checks t h e b a s i c assumpt i o n s again but, i n addition, it checks the wind-weighting procedure.
The r e s u l t s f o r t h e f i r s t scheme of checking are shown i n f i g ure l 5 ( a ) . Various wind p r o f i l e s and wind d i r e c t i o n s were considered
which a r e l i s t e d i n t h e f i g u r e . P i t c h and yaw compensation angles were read from f i g u r e 12 for each of t h e s e conditions and were used i n t h e t r a j e c t o r y analysis. It can be seen from the f i g u r e t h a t t h e compensat i o n values a r e i n excellent agreement w i t h t h e t o t a l change produced by t h e wind i n each case. It w a s concluded from t h i s study t h a t t h e assumptions made i n developing t h e wind-compensation graphs a r e v a l i d .

The r e s u l t s f o r varying wind v e l o c i t y and d i r e c t i o n a r e shown i n

f i g u r e 1 5 ( b ) . Actual wind d a t a measured on t h e day of f i r i n g of f o u r

Shotput vehicles were used i n this study i n a d d i t i o n t o one a r b i t r a r i l y
s e l e c t e d wind p r o f i l e . Winds measured on October 28, 1959, a r e pre-
sented i n figure 14, and the remaining wind data a r e presented i n fig-

ure 16. These winds were weighted using the procedure described under

t h e previous s e c t i o n of t h i s report and t h e compensation angles were

read from f i g u r e L2 using t h e weighted values. These weighted values

a r e a l s o l i s t e d i n f i g u r e l 5 ( b ) with t h e date t h e wind was measured.

Here again, t h e compensation values agree very w e l l with t h e t o t a l

change produced by t h e wind. "he average e r r o r i n p i t c h was 0.3' and

t h e average e r r o r i n y a w was 1.3'.

It was concluded from t h e s e r e s u l t s

that the weighting procedure i s sufficiently accurate.

An e r r o r a n a l y s i s similar t o t h e one discussed previously was c a r r i e d out f o r t h e wind-compensation system f o r the unguided Scout-SX-1

I

I

20
missile. This system w a s developed by using t h e assumptions and methods described i n t h i s paper and i s presented i n t h e appendix. The e r r o r s obtained were of about t h e same magnitude as those found f o r t h e Shotput system y e t t h e m i s s i l e configurations and performance h i s t o r i e s a r e very different.
Significance of Limitations Imposed on
Previous Wind-Compensation Methods
Several other wind-compensation methods were described i n t h e Introduction of t h i s paper w i t h t h e l i m i t a t i o n s imposed on them. I n t h e following paragraphs, an attempt w i l l be made t o show t h e e f f e c t s of t h e s e l i m i t a t i o n s f o r t h e type of v e h i c l e and launch conditions cons i d e r e d h e r e i n . The assumptions made i n r e f e r e n c e s 1 and 2 were given as :
1. Vehicle motions i n p i t c h and yaw a r e independent.
2. Linear aerodynamic c o e f f i c i e n t s with respect t o t h e flow incidence angle and small angular p e r t u r b a t i o n s a r e used.
3 . Launch angles f o r wind compensation are t h e d i s p e r s i o n angles
computed using t h e weighted wind.
4. F a c t o r s used t o determine azimuth c o r r e c t i o n are computed f o r
the standard launch-elevation angle.
The e r r o r caused by t h e f i r s t assumption can r e a d i l y be seen i n the wind-compensation graph of f i g u r e 12. A pure side-wind p r o f i l e
( & = Oo, 180°, o r 3600) with a v e l o c i t y of 40 f t / s e c r e q u i r e s a
yP, Q
f o r wind compensation of 74.5O which i s 3.5O beiow t h e nominal launch
angle of 7 8 O . I n t h e previous methods, no p i t c h c o r r e c t i o n i s made f o r p u r e s i d e winds so t h i s would be a 3 . 5 O e r r o r i n e l e v a t i o n under these conditions.
The second assumption i s poor because t h e flow incidence angle 7 i s very l a r g e during the e a r l y p o r t i o n of f l i g h t . If t h e Shotput vehi-
cle were subjected t o a 40 f t / s e c wind a t launch, it would t r a v e l about 63 f e e t t o an a l t i t u d e of 90 f e e t before q decreased t o a value of loo. As can be seen i n f i g u r e 14, t h e r e a r e almost f o u r wind l a y e r s i n t h i s
a l t i t u d e region which comprise 20 percent of t h e t o t a l wind e f f e c t . Since t h i s i s a large portion of t h e t o t a l e f f e c t , it i s concluded t h a t nonlinear aerodynamic coefficients should be used.

1

I

21
The e f f e c t of t h e t h i r d assumption can be seen by r e f e r r i n g t o
f i g u r e 11. Suppose t h e r e were a pure side-wind p r o f i l e of 40 f t / s e c (qw = 90") a c t i n g on the m i s s i l e . It can be seen i n the f i g u r e t h a t
t h e v e h i c l e would yaw ?lo under t h e s e conditions. Now, i f t h e f u l l ?lo
were used as the launch-azimuth correction, the new value of qw would
be 90° + 51° or 141'. The m i s s i l e would then yaw only 33' and the a z i muth e r r o r would be 18' which i s very l a r g e . The same argument can be
applied t o t h e p i t c h case as w a s shown previously i n t h e s e c t i o n e n t i t l e d "Derivation of Wind-Compensation Graphs."
E r r o r s introduced by assumption 4 can be shown by considering equat i o n (8) which w a s stated a s

Now, l e t y ' be a reasonable value of 5O and l e t y be TO0 and 80°.

Y

P

Then, yY corresponding t o these values would be 14.8O and 3O.2O, respec-

t i v e l y . Thus, a d i f f e r e n c e by f a c t o r of approximately 2 i s obtained f o r

t h e two launch angles. Obviously, using t h e same wind c o r r e c t i o n f o r each

launch angle can produce intolerable e r r o r s .

The main l i m i t a t i o n imposed on t h e wind-compensation method of r e f -
erence 7 f o r t h e L i t t l e Joe i s t h e maximum a l t i t u d e . The author p o i n t s
out t h e e r r o r s t h a t could be obtained with the Little Joe vehicle f o r
various wind conditions under t h i s assumption. For t h e Shotput, i t i s
i n t e r e s t i n g t o note i n f i g u r e 1 4 that 60 percent of t h e wind weighting remains a t an a l t i t u d e above 455 feet which i s about t h e a l t i t u d e t h a t
t h e L l t t l e Joe analysis was discontinued. It i s concluded that t h e l i m i t a -
t i o n of r e f e r e n c e 7 can not g e n e r a l l y be made without causing e r r o r .

CONCLUDING FilWUKS

A method f o r c a l c u l a t i n g wind compensation f o r unguided m i s s i l e s has been derived which has a g r e a t e r degree of f l e x i b i l i t y than previously proposed methods. Most of t h e e a r l i e r t h e o r i e s were based on a common set of assumptions which are: (1)vehicle motions i n p i t c h and yaw a r e independent, ( 2 ) l i n e a r aerodynamic c o e f f i c i e n t s with r e s p e c t
t o flow incidence angle and small perturbations a r e used, ( 3 ) launch
angles f o r wind compensation a r e t h e dispersion angles computed using
t h e weighted wind, ( 4 ) f a c t o r s used t o determine azimuth correction are
computed f o r t h e standard launch-elevation angle.

22
Elimination of the first two limitations resulted from using a three-dimensional trajectory simulation with arbitrary wind and nonlinear aerodynamic coefficients with respect to flow incidence angle. The last two limitations are removed by the unique analytical methods which are presented.
Use of the wind-compensation technique was demonstrated by using the Shotput vehicle as a model. Postflight simulations of four of these missiles with the use of measured winds showed that, if the winds were known, very good accuracy could be obtained using the proposed method.
A wind-compensation system for the unguided Scout-SX-1 is presented in the appendix. This system was developed by using the assumptions and methods presented in this paper. The errors obtained are of about the same magnitude as those found for the Shotput system; yet the missile configurations and performance histories are very different.
A more detailed preflight trajectory analysis is required for the use of this technique than is necessary with the use of conventional methods. However, in order to obtain the desired missile performance with minimum wind dispersion, a wind-compensation scheme having the capabilities of the one presented must be used.
Langley Research Center, National Aeronautics and Space Administration,
Langley Field, Va., October 17, 1960.

APPENDIX

WIND COMPENSATION FOR TH2 SCOUT-SX-1

The Scout-SX-1 vehicle w a s t h e f i r s t t e s t of t h e Scout s e r i e s . This missile w a s f i r e d without guidance; thus it w a s necessary t o use a wind-compensation procedure. The procedure described i n t h i s paper w a s s e l e c t e d and t h e compensation graphs and r e s u l t s a r e presented.

The Scout-SX-1 e x t e r n a l c h a r a c t e r i s t i c s are presented i n f i g u r e 17.
This i s t h e configuration that e x i s t s a t launch and during f i r s t - s t a g e
burning. The f i r s t - s t a g e propulsion system i s an A l g o l solid-propellant
rocket motor. The missile i s 760.1 inches long and has a maximum diam-
e t e r of 40 inches. Four 8' wedge f i n s having an area of 4.5 square f e e t
per panel provide aerodynamic s t a b i l i t y .

The aerodynamic parameters f o r t h i s missile a r e presented i n f i g -

ure 18. Figure 18(a) shows t h e aerodynamic c o e f f i c i e n t s as functions

of Mach number, errii t h e time varying parameters are shown i n f i g u r e 1 8 ( b ) .

These are t h e same terms as previously presented f o r t h e Shotput vehicle

except that

w a s small arid assumed t o be zero f o r t h i s m i s s i l e . R o l l

Cmi

symmetry was again assumed and t h e reference area S and length D a r e

1 square f o o t and 1f o o t , respectively.

The nominal performance of t h e Scout-SB-1 vehicle i s shown i n f i g -
ure 19 as p l o t s of a l t i t u d e and v e l o c i t y v a r i a t i o n s with range. The launch angle w a s 81O and t h e ICAO standard atmosphere ( r e f . 9 ) w a s assumed. It can be seen by comparing figures 3 and 19 t h a t t h e launch
a c c e l e r a t i o n i s much smaller f o r Scout-SX-1 than f o r Shotput. The Shotput
launch a c c e l e r a t i o n was ll.9g; whereas f o r Scout-SX-1 t h i s value w a s 2.7g.
The combination of lower a c c e l e r a t i o n a t take-off and t h e s t e e p e r launch e l e v a t i o n (81O f o r Scout, 7 8 O f o r Shotput) are f a c t o r s which make t h e
Scout vehicle more s e n s i t i v e t o wind than the Shotput.

A s e n s i t i v i t y curve yas computed using t h e method previously

described. The p l o t of

i s presented i n figure 20.

This curve i s very similar t o t h e one presented f o r Shotput i n f i g u r e 13,
which i s reasonable since t h i s curve only shows t h e r e l a t i v e s e n s i t i v i t y for different altitudes.

The wind-compensation graph f o r t h e Scout-SX-1 i s shown as f i g u r e 21. When compared with t h e Shotput curve of f i g u r e 12, it can be seen t h a t t h e p i t c h c o r r e c t i o n s are very similar f o r t h e same wind v e l o c i t y and d i r e c t i o n . (Note t h a t Scout curve has a maximum wind v e l o c i t y p r o f i l e of

24

30 f t / s e c . ) The azimuth c o r r e c t i o n s are q u i t e d i f f e r e n t , however. The
maximum correction for Scout with a 30 f t / s e c p r o f i l e i s about 48' but t h i s value f o r Shotput i s 38'. Since t h e s e n s i t i v i t y i n p i t c h i s almost the same for t h e two vehicles, t h e lower a c c e l e r a t i o n of t h e Scout must
be somewhat compensated f o r by i t s smaller r a t i o of aerodynamic moment
t o p i t c h i n e r t i a . The increased yaw s e n s i t i v i t y must then be mostly due t o t h e higher launch angle of t h e Scout.

Wind b t a measured on t h e day of f i r i n g f o r t h e Scout-SX-1 are pre-
sented i n f i g u r e 16. These data were weighted which gave 26.9 f t / s e c and
310° f o r t h e weighted wind v e l o c i t y and d i r e c t i o n , r e s p e c t i v e l y . The
compensation angles were obtained from f i g u r e 2 1 using t h e s e values.

I

For t h e p o s t f l i g h t simulation, it was found that t h e yP change

obtained i n simulation was 4.6' as compared with t h e 4.8' a c t u a l l y

used and t h a t t h e yy change obtained i n simulation was 17.2' compared with t h e 17.8' a c t u a l l y used. The data show a 0.2' e r r o r i n

8. p i t c h and a 0 . 6 ~e r r o r i n yaw as
obtained f o r Shotput of 0.3' and

c1o.m3

ared

with

the

average

errors

1

L

25
REFERENCES
1. L e w i s , J. V.:, The Effect of Wind and Rotation of t h e Earth on
Unguided Rockets. Rep. NO. 685, B a l l i s t i c Res. Labs., Aberdeen Proving Ground, Mar. 1949.
2. Daw, Harold A.: A Wind Weighting Theory f o r Sounding Rockets Derivable From t h e Rocket Equations of Motion. Contract NgONR-9530 1, Phys. Sci. Lab., New Mexico College of Agric. and Mechanic Arts,
Nov. 5 , 1958.
3. Rachele, Henry (revised by W i l l i a m H. Hatch): The Effect of Wind and Tower T i l t on Unguided Rockets. Rev. Prog. Rep. N r 6, Missile Geophys. Div., U.S. Army White Sands Signal Agency, Feb. 1958.
4. Webb, W i l l i s L., Jenkins, Kenneth R., and Clark, George Q. : F l i g h t
Testing of t h e Arcas. Tech. Memo. 623, Missile Geophys. Div.,
U.S. Army White Sands Signal Agency, May 1959.
., 5. Zaroodny, Serge J., Mylin, Donald C and McIntosh, Fred H. : Spin - of an Honest-John-Type Rocket Experimental Data and Their Impli-
cations f o r the Design. Rep. No. 1090, B a l l i s t i c Res. Labs.,
Aberdeen Proving Ground, Dec. 1959.
6. Anon.: Dispersion Analysis Journeyman Sounding Rocket. Rep. No. 8411-1, Aerolab Dev. Co., Inc. (Pasadena), Sept. 16, 1959.
7. Rose, James T., and Rose, Rodney G.: ARapid Method of Estimating
Launcher Setting t o Correct f o r the Effects of Wind on the T r a jectory of an Unguided Fin-Stabilized Rocket Vehicle. NASA
!I’M X-492, 1961.
8. James, Robert I,., Jr. (With Appendix B by Norman L. C r a b i l l ) : A
Three-Dimensional Trajectory Simulation Using Six Degrees of Free-
dom With Arbitrary Wind. NASA TN D-641, 1961.
- 9. Anon.: Standard Atmosphere Tables and Data f o r Altitudes t o
65,800 Feet. NACA Rep. 1235, 1955. (Supersedes NACA TN 3182.)
10. Anon.: Wind Distributions as a Function of Altitude f o r P a t r i c k Air Force Base, Cocoa, Florida. Rep. No. ~ ~ - m - 1 2 - 5 8 ,Dev. Operat i o n s Div., Army B a l l i s t i c Missile Agency (Redstone Arsenal, A l a . ),
Aw* 5 9 1958.

26

TAI3I.E I
e
COMPUTER RUNS USED IN SHOTPUT WIND ANALYSIS

Run number

Launch elevation,
deg

1

78

2

78

3

78

4

78

5

78

6

78

7

78

8

78

9

78

10

58

11

68

12

88

13

58

14

68

15

88

16

58

17

68

18

88

19

78

20

78

21

78

22

78

23

78

24

78

25

78

26

78

27

78

28

78

29

78

30

78

Wind velocity profile, ft/sec

0

0

0

10

0

20

0'

30

0

40

180

10

180

20

180

30

180

40

0

0

0

0

0

0

0

40

0

40

0

40

180

40

180

40

180

40

45

10

45

20

45

30

45

40

90

10

90

x)

90

30

90

40

135

10

135

20

135 135

43O0 -

67.3 63.2 59 .O 54.8 50.9
71.8 76.4
82.2
85.4 33.4
50.1
86.2 22.5 36.0 68.0
47.0 66.5 105.2 63.7
60.2
56.7 54.3 66.2 64.7 63.7
62.7 69.5 72.1 74.2 75.7

0 0 0 0 0
0 0 0 0
0
0 0 0 0 0
0 0 0
-3.1 -6.0
-8.8 -11.4
-5 .o -8.6 -13.4
-17.6 -3.3 -6.5
-10.0
-13.4

27

28
Q
8
rr) Y

I

i

I
O'l€
! I
+O*€€ c In rr)' I1 ti a

t

J

Cmt;
‘A,O
%
X CP’
ft
Mach number
(a) Variation of ,C , Cm., CA,O~ CN, and 9 7 x w i t h Mach number. CP Figure 2.- Shotput aerodynamic parameters.

1
30

12
10
c
3 '
&6
L
%+ 4
d
g2
0

c, 22
c
& 21
&"
20

140

120
m 5
E: 100
. a 80
c,
m
2 60
E
40

20

n

I

o 5 i o 15 20 25 30 3 5

J5

Time, sec

(b) Variation of w e i g h t , xcg, t h r u s t , Iy, Ix, and My with time.
9
Figure 2.- Concluded.

t

I

3 . - Nominal Shotput performance during f i r s t - s t a g e burning.

32
80
64

16
a

0

0

80

120 160

200

Wind. v e l o c i t y , f t / s e c .

Figure 4.- Velocity profiles used in wind analysis.

t
33
40 30 20 i o o 10 20 30 40
P r o f i l e surface v e l o c i t y , ft/sec Figure 5.- E f f e c t of head and t a i l winds on p i t c h f l i g h t - p a t h angle a t
. t, f o r t h e Shotput vehicle. yp,o = 78

I

t

34

Figure 6.- Change i n f l i g h t - p a t h angle i n p i t c h due t o launch e l e v a t i o n
f o r head and t a i l winds. Shotput vehicle.

35

60

50

40

20

0

20

40

Profile surface velocity, ft/sec

Figure 7.- Launch elevation for compensation of various head and tail
winds. Shotput vehicle.

I

t

u h

37

0

a

38

0 m

0
a3

0 r-

oo
a

39

-100
0 '0
c
f
-80
I 5

/
,

Figure 11.- Yaw angle i n the e a r t h plane due t o winds from various
directions. Shotput vehicle.

I
Q 0 rn 0
2
N 0 rn
0 0 c\
m 0
\0 N o 0
73 ow
NN VO 3
e
000 N”
C 0:
me
d e 0,
L e ov QV dE b
3
N 0
r0 0l
W 0
\0o
f 0
N 0
0

. I
41
44
40
36
32
26
c, k
24
3
L, d
c, d
a c, 2 0
$ 0
16
12
8
4
0
Figure 13.- Shotput vehicle sensitivity variation with altitude.

.
I
40
36
32 28
*
", 24
0) '0
c5 ,
d
f: 20
4
16
12
8
4
0
Variation of 7y l / ( ~ y ' ) with a l t i t u d e .
max
Figure 13. - Concluded.

43

100000
20 19 18 10000 17 16

.+,
Fc 1000
as0
c, rl c,
2
100

12
11 $
10
9'3 8
;I!!t
5-
4
3
2
1

1--0 o
L
o

25 50 75 loo 125 150 175 200 225 250

I

- -wind

VOIOCitgJ

t

I

vwJh, ft/sec
~ _ _-

I

-~

+

30 60 90 120 150 180 210 240 270 300 330 360

Wind direction, 6 w~ deg

Figure 14.- Wind-weighting graph and wind data measured October 28, 1939, at NASA Wallops Station.

. D

44

.

10

5

uU 00

5

10

yp change o b t a i n e d from t r a j e c t o r y s i m u l a t i o n , deg

0

10

20

30

40

50

60

yg change o b t a i n e d f r o m t r a j e c t o r y s i m u l a t i o n , deg

(a) Correlation between wind-compensation angles used and change obtained for assumed profiles.
Figure 15.- Wind analysis check.

45

-0

5

0
Yp change obtained from trajectory simulation, deg
I I III III I

Weighted Weighted

Velocity direction,

ft/sec

deg

0

10

20

30

40

50

60

YY change obtained from trajectory simulation, deg

( b ) Correlation between wind-compensation angles used and change

I

obtained for measured winds.

- Figure 15. Concluded.

46

LP

0

f

In
M

0 In

cIn u

c0u

0
a
M
c0u
M 0
CcUu
0
0 0
cu
0 u3 rl

0
73

0
c0u

c,

0

G-l

u3

4 rl

.>c
0

2 A 42

4

0

0

0
II)

0 ;t

47

-
f-
a
F
v)
-
0
a¶ m
2
8
a
t7;

7

a
2

0
I

-1

0

(3

-1
2

Q) rl

I

k

t c-

0

f

5
M)
d Frc

i

48

Mach number

ems, (a) Variation of

c A , ~ , CN, and xcp with Mach number.

Figure 18.- Aerodynamic parameters for Scout-SX-1.

49
30
25 20
15
cu .Q k I bo ? ,-I m a x H

o i o 20 30 40 50
Time, s e c

o i o 20 30 40 50
Time, s e c

(b) Variation of weight, x c g , t h r u s t , Iy, Ix, and Mycl with time.
- Figure 18. Concluded.

70 x lo3
I
60-
50
c,
cc 40

Time, sec
I
744.5
/
I '
,/40

30

/

7, 30

20

Velocity

/

/ , '

i2i 10 ;(20 /

41
Q)
3 0

f510

Of-

3

Figure

Figure

52