HWC it 4995

DEFINITION OF SAFE-SEPARATION CRITERIA

FOR EXTERNAL STORES AND PILOT
t ESCAPE CAPSULES
by
Eugene E. Covert
Massachusetts Institute of Technology
for the
Weapons Devedopment Department

ABSTRACT. It is shown tl~at the early part of the trajectory of ary store or escape capsule
released from a parent aircraft is governed principally by two effects. The first is the relative velocity
between the store and the aircraft at the instant of release. The second is the acceleration acting on the
store at the same instant. This acceleration is due not only to gravity, but also to the aerodynamic forces
and moments acting on the store. The (normalized) relative velocity and (normalized) acceleration, as
the ordinate and a1b ;issa, define a planar coordinate system. A boundary delineating safe from unsafe
separation characteristics can be arawn on this plane. Thus. if the proper data are available, safe
separation conditions can be prewicted in advance. The available data from flight tests strongly support
the predictive aspects of this diagram.

In principle, since the diagram is based on velocity and airloads, no additional information is
needed to define safe-separation characteristics. Moreover, the results fromn this study suggest that
airload data for the store on P rack ca." be directly applied to give valuable results about safe-store
separation.

S2 •:NAVAL WEAPONS CENTER

CHINA LAKE, CALIFORNIA * JUNE 1971

S• v•'d.": d by

NATINALTECHNICAL
INFORMMTION SERVICE
APPROVED FOR PJBI.r RELEASE; USi'H;BUTION UNLIMITED. "

r
 NAVAL WEAPONS CENTER
AN ACTIVITY OF THE NAVAL MATERIAL COMMAND
W. J. Moron. IMDM. USN................................. Comnmander
II. 0, Wilson...................................... Technical Director

FOREWORD

The specifi work unit result reported herein was accomplished under the continuing exploratory
developmnent proprant. managed by William C. Volz of the Naval Air Systems Command (NAVMIR-
320C), pertaining to tL'e fI*( dynamics of air-launched weapons. Ia this report the aulhoi treats the
yang problem of separating stores and capuwles from aircraft in flight. and derives 2rid sets forth a
propo'-d safe-aeparaticn cniterla.

The work was performed for the Navali Weapons Center over the period 20 December ;968 to 20
February 1970, under Contract N00123..69-C.021, by the Ar-rophysics Laboratory, Department of
Acronautics and Astronautics, Massachusetts Institute of Technology. Cambridge, Mass. Funds were
provided by AirTask A3?-320.216/70 F17-323-201.

Technical reviewers were Renard Smith and Leonard Seeley of the Aeromechanics Division,
Weapons Development Department. Release of this report i5made at the working level P . inforiiational
purposes only.

Released by Under authority of

RAY W.VAN AKEN, Head F. H. KNEMEYER, Head
Aeromechanks Division Weapons Development Department
r 27 May 1971

NWC Technical Publication 4995

Published by......................................... Weapons Development Department

Manuscript .......................................................... 40/MS 70-39
collation.................................ý. Cover, 34 leaves, DD Fcrm 1473, abstract cards
First printing ....... ..................... I.................. 175 unnumbered copies
Security classification 'A IO f .e ......................... UNCLASSIFIED

ITITIgajlAWfurSCTONE
DoeT RVi.aUFF
SECTIO

98 ViiETO
 UNCLASSIFIED
DOCUMWENT CONTROL DATA - R D
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ft 600 .1 b.htsw I G~d idxa M.4.N... out be "mWe" -how ON se.asopnl Pa. cl.asiie~d)
I OUGf-A .,.G ACTI.- r(.pAaE 010311SCRTCASFCTO

Massachusetts Institute of Technology UCAS D

Aeronau tics and Astronautics Department
Cmbridge, Massachusetts
31REPORT TITLE

DEFINITION OF SAFE-SRPARATICK CRITERIA FO% ~rERNAML STORES AND PILOT ESCAPE

CAPSULES

A. OESC 3IPT.VE NOTes (T"',e .1pwt MWdinc&i.. dares)

Final (December 20, 1968 to February 28, 1970)

[June 1971
ea.~1
T8
on
N00123-69-C-0821
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d@f mI15*1 I~"
tot
94
62 14
AEFIAOSRPOTH111911

APPOVE
FO PULICRELEASE: DISTRIBUTION UNLIMITED.

I.SUPPLEMENTARV NOTES 2 PNOIGMLTdYATVT

'tis shown that the early part of the trajectory of any store or escape
cpuereleased from a parent aircraft is governed principally by two effects.
Tefirst is the relative velocity between the store and the aircraft at the Instant
ofrelease. The second is the acceleration acting ott the store at the same instant.
Thsacceleration is due not only to gravity, but also to the aerodynamic forces
admomenLs acting on the store. The (normalized) relative velocity and (normalized)
acceleration, as the ordinate and abcissa- define a planar coordinate system. A
bonaydelineating safe from unsafe separation characteristics can be drawn on
this plane. Thus, if the proper data are available, safe separation conditions can
be predicted in advance. The available data from flight tests strongly support the
predictive aspects of this diagram.

In principle, since the diagram is based on velocity and airloads, no additional

information is needed to define safe-separation characteristics. Moreover, the
results from this study suggest that airload data for the store on a rack car. be
directly applied to give valuable results about safe-store separation.

DD
FORM
DD A7 IPAGE 1)
NOV 5147 UNCLASSIFIED
S/N O1IO1.807-6101 scrtclssification
 j ROLC INt *@LSt no-
UOT .

Safe store separation

Airplane dealga
Trajectory amdlyIm
Aerodyamic interfaerence

DD 73 V UNCLASSIFIED
(PAGE 2) Security Classification
 NIC TP 4995

PREFACE

In recent decades, developments in store/carriage/launch systems

have increased tenfold the weapon-loading combinations available to a
single aircraft. It has thus not been possible to certify the launch
and separation adequacy of all possible weapon loadings by flight test
or laboratory investigation, and operational problems have arisen as a
result, principally with free-fall stores. These problems have prolif-
erated commensurately with the growing variety of free-fall hardware,
and have paced in severity the steady increase in jet aircraft
performance.

The present work develops a general separation criteria which may

first find useful application as a screening device for quickly sep-
arating those cases which, by the criteria, clearly are safe from those
wiich are clearly unsafe, thus quickly identifying that vastly reduced
number of cases which are marginal, requiring closer scrutiny. In this
way, boundaries of release envelopes may be established for individual
aircraft with greater facility and confidence.

In Section 2, the criteria are developed and compared with the

results of others. A detailed mathematical derivation of the needed
trajectory information is given in Section 3, which can be skipped with-
out loss of continuity, if desired. A summary is provided at the end
of Section 2 that includes the definition of the several parameters,
and provides a step-by-step outline for the application of the proposed
criteria.

iii
NWC TP 4995

CONTENTS

Preface ....... ............. ........................ iii

Acknowledgment ...................... ............................ v

List of Symbols ................................................... . vi

Section 1. Introduction ........... W

......................... 1
Section 2. Safe-Separation Criteria .................-.... 5
Initial Development of the Safe-Separation Criteria ............. 6
Basis of the Criteria ...................................... 8
Application to Pilot Escape Capsules ........................... 15
Relation to Earlier Results .................................... 16
Proposed SSC ................................................... 20
Concluding Remarks ............ . .............................. 24
Summary and Computational Outline .............................. 24

Section 3. Separation Analysis in Detail .......................... 33

Reference Coordinate System .................................... 33
Position of Store .............................................. 33
Motion of the Store ............................................ 36
Separation Distance ............................................ 41
Aerodynamic Loads on Store ..................................... 45
Primary Wing-Body Interference ................................. 46
Section 4. Conclusions and Recommendations ......................... 49

Appendix: Some Mathematical Details ................................ 52

References ....... ......................................... .. 59

iv
 &WC TP 4995

ACKNOWLEDGMENT

This work on store separation characteristics was sponsored by the

Naval Weapons Center, China Lake, CRlifornia. The project monitor was
Leonard Seeley. In addition to Mr. Seeley and Richard Meeker and
Ray Van Aken of NWC, the author would like to acknowledge the interest
and cooperation of the many engineers he met and conversed with during

Sindus.try.
visits to various government activities and to several companies in
1.1 particular, he would like to acknowledge his indebtedness
t.j John Clark of the F-14 Project, Aerodynamics Group, at the Grumman
Aircraft Engineering Corporation, Bethpage, Long Island, New York, for
calling attention to errors in a prior draft. Finally, the author would
like to thank Dr. L. H. Schindel of the Naval Ordnance Laboratory,
White Oak, and members of his Panel for the Separation of Stores from
Aircraft, a Panel of the Naval Aeroballistic Advisory Committee, for
their patience and useful comments.

The author, in acknowledging this indebtedness, does not wish to

imply either approval or disapproval of his hypothesis by these
engineers. If their comments are misrepresented in this report, he
apologizes in advance. In any event, the ultimate responsibility for
the material in this report is accepted by the author.

V
I,,°

NWC TP 4995

LIST OF SYMBOLS

A vertical fall parameters, see p. 14 (Eq. 24)

CD store drag coefficient

Cxo' store axial force coefficient in aircraft coordinates and

free stream conditions at time t - 0 (+ forward)

C'YI store
time side force coefficient, in aircraft coordinate at
t - 0 (+ starboard)

CZ store vertical force coefficient, in aircraft coordinate

at time t - 0 (+ downward)

CL store lift coefficient

CM'0" store pitching moment coefficient about aircraft y axis at

time t - 0 (+ nose-up)

C ' store yawing moment coefficient about aircraft z axis at

N, time t - 0 (+ nose starboard)

6 Cx'--6CN' change in coefficient due to aerodynamic interference.

Note Cxo' + 6C'' is for example, the coefficient of axial
force acting at the instant of release. The same applies
for the other coefficients.

d 2 rmax - store reference length for moment coefficient

dr relative position of store in reference system

r force

FO rack impulse, see p. 2 (Eq. 3)

F applied force

g acceleration due to gravity

IxIyIz ioments of inertia about store xy,z axis

ky, k2 store radius of gyration about y,z axis Iy - mk, etc.

iJk unit vectors in store coordinates

vi
 NW.C TP 4995

tN length from center of mass to store nose

tT length from center of mass to store tail

m store mass

Ma ~ slope of store pitching moment coefficient

[R] transformation matrix from store coordinate system to

reference coordinate system

distance from origin of reference coordinate system to

aircraft center of mass

r(x) distribution of store radius in store coordinate

rmax: maximum value of store radius

2
S aerodynamic reference area S = 7rr
max
t time seconds

U(O) store velocity in x' direction at t = 0

U1' store velocity in reference syste-n (primed coord) with

respect to earth (Section 2)

V reference velocity with respect to earth (Section 3)

VI aircraft velocity with respect to earth (Section 3)

A/C
w vertical velocity

W store weight

x,y,z store coordinates, origin at center of mass

x'vy',s ' reference coordinates, usually origin is on rack or pylon

6y' initial lateral distance between store and nearest strike

point

az'(xt) distance between store and aircraft in reference coordinates

zc displacement due to constant force

6x,6y, etc. displacement in x,y direction

vii
NIC TP 4995

AJW relative vertical velocity of store at position x with

respect to aircraft, In reference coordinate system at
t - 0 (Section 2)

A2(0) relative vertical acceleration of store at position x with

respect to aircraft, in reference coordinate system at
t - 0 (Section 2)

A3 (x) relative lateral velocity of store at position x with

respect to aircraft, in reference coordinate system at
t - 0 (Section 2)

k(x) relative lateral acceleration of store at position x with

respect to aircraft, in reference coordinate system at
t - 0 (Section 2)

AS(x) relative velocity of store at position x and aircraft in

x direction in reference coordinate system at t 0
(Section 2)

A6 (x) relative acceleration of store at position x and aircraft

in x direction in reference coordinate system at t 0
(Section 2)

£ an arbitrarily small parameter

*o090oo store Euler angles at t - 0

aircraft Euler angles at t - 0

store to earth coordinate transformation

p dir density frr from aircraft at store altitude

ACy,•wz relative angular velocity imparted at ejection by rack,

t = 0

Sw angular velocity of store in store coordinate system

angular velocity of aircraft in reference system

Note: (1) All aerodynamic force coefficients based upon free stream
dynamic pressure, q and S.
(2) All aerodynamic moment coefficients based upon free stream
dynamic pressure, q and Sd.

viii
____NWC TP 4995

Sectior. 1. INTRODUCTION

The goal of the study reported here is the development of general

criteria to enable the designer or operator to estimate a safe store-
separation boundary quickly and relatively accurately. Although it is
likely that no general law exists stating that a successful aircraft will
be put to an increasingly wide set of tasks, there is strong empirical
evidence to suggest such is the case. Thus an aircraft may become an
all-purpose carrier, having been retrofitted with a variety of multi-
purpose racks and pylons for carrying an astonishing variety of shapes
and densities of external stores. In case of emergency the pilot must be
able to jettison safely these stores, pylons, and racks in a great variety
of combinations, without causing damage to the aircraft from the store
striking the aircraft. From an operational viewpoint, the safe-jettison
envelope should be larger than the aircraft operational envelope. Super-
ficially, the safe-jettison requirement would seem to be the most strin-
gent of all the store-separation requirements. Actually, this is not
necessarily true. A low-drag, low-density store, i.e., a droppable fuel
tank, or an empty gun pod suspended near a general-purpose rack, may
represent a more difficult store-separation problem.

These problems of store separation have received ccnsiderable

attention recently. Black (Ref. 1) has shown that in some cases wind
tunnel tests are extremely useful in predicting full-scale separation
characteristics. Larlier work has been summarized by Reed, et a!
(Ref. 2). The question of general scaling has been widely discussed,
and a summary of scaling for free drop tests, the grid method, and
trajectory simulation is discussed in Ref. 3 and 4. Application of
these results to a specific prob]em is contained in Ref. 5, as is a
suggestion for criteria. D. A. Jones (Ref. 6) has presented a straight-
forward analysis of pos3ible criteria. These criteria, and Unge.:'s
suggestions (Ref. 7), are discussed herein in Section 2.

In establishing useful design criteria, it is necessary to be con-

servative tu allow for variations in geometry, performance, and opera-
tional conditions, while still defining a safe separation. Necessarily,
several stringent assumptions are made, but the evidence presented
herein supports their validity. These include assumed aerodynamic loads
and rack ejection characteristics. The former may either be measured or
estimated analytically. These computations must include ways or account-
ing for not only the far field, slowly varying aerodynamic interference
between the store and the aircraft, but more importantly the near field,
rapidly varying aerodynamic interference. The far field problem resolves
to that of determining the aerodynamic characteristics of the store in
NWC TP 4995

a nonuniform field. Results from a comparison between calculations and

wind tunnel tests suggest that slender body theory, scaled to the free-
air-uniform field experimental results, and expressed as follows, is
suitable:1
Lf2 CLa "ES*RFf dS

PU 2 L A sf - T dx
Lft 2 2..S(4N) - S(tT)
• IT x

Moment = 0U2
p S!)F t2 ,z) ( S

Volume • (k 2 - kl) x) (

The notation ct(x,y,z) implies that the flow curvature is spatially

dependent. The remaining notation is standard.

The near field interference has yet to be treated successfully in

an analytical way. In the general case, this interference is due not
only to potential flow interaction between stores and wing, stores and
pylon, or stores themselves, but also to a viscous flow separation and
sometimes shock wave that acts to repel the stores. Usually near inter-
ference is of an attractive nature; its decay rate is strongly shape-
dependent. In the case of a sphere the near fieiL interference, pro-
portional to (rmax/6z') 4 , is down to 0.6 of its initial value in the
distance of one diameter. These near interference effects usually act
over a short time period, say 0.2 second or less. Their time icale is
the same as the time scale of the rack ejector mechanism.

A typical characteristic of ejector racks is shown in Fig. 1 (from

Fig. 13 of Ref. 3). While this characteristic is not that of a true
impulse, which implies a Jump in velocity while a jump in force implies
a jump in acceleration, it can be so treated. Note this force terminates
at about 0.06 to 0.10 second. It will be assumed, in the analysis, that
the actual impulse will be applied at zero time and zero relative motion.
Some care is needed at this point because a flexible rack may deflect
under the impulse rather than accelerate the store. For this calculation
a force distance characteristic is needed, but with a reasonable assump-
tion the force distance curve may be converted into a force time curve.

I _ _

The structure of these equations is based upon linear theory (cf

Nielsen, J. N., Missile Aerodynamics, McGraw Hill 1960, pp. 114-118,
182-201); experimentsl support is based upon the results of Beane and
Durgin (ASD-TDR-61-295 part 2).

2
 NWC TP 4995

2. 4 0 0 - Fi.-
FULL STORF.

2.000

I'. "- ~EXPENDED

-1,200

.00
4

50 0 0.0 0.02 0.03 0.04 0.05 0.05 0.07

REAL TRAJECTORY TIME. t (SEC)

1,600
's-EXPENDED STORE

IL1,200

w
0 END OF, aSTROiCE
U.

0 END OF STROKE
b
W 400
w

0 0,02 0.04 0.06 0.06 0.10

REAL TRAJECTORY TIME, I (SEC)

FIG. 1.Variation of Simulated Ejector Force With Time.

NWC TP 4995

The near fieid interference, as can be shown, aleo has an effect

that acts like the force distance effects discussed above. This Rgain
differs from a true impulse. However, we iill regard the near field
effects as a constant force and moment acting from the release point.
The primary problem is to estimate the size of near field effects with
sufficient accuracy.

The criteria that will be developed may be shown on a plane coord-

inate system whose ordinate is the relative velocity of any selected
point on the surface of the store (i.e., at x) with respect to the rack,
in a rack coordinate system. The abcissa is the acceleration of tho
same point, i.e., the gra&,ity component plus that caused by airloads
acting at the instant of release. It turns out that such planes are
needed for both vertical and lateral motion (and axial motion for pilot
escape capsules and other special iases). It is possible to draw a
line or lines on these planes that separate safe from unsafe store
spearation. The validity of the proposed criteria has been tested
against flight test data.

From a pragmatic point of view, a miss of 1 foot or one radius may

be considered the limit. Rather than specify the details of the rack
and pylon, we shall pass a plane through the lowest point of the rack
parallel to the aircraft lateral plane and define this plane as the
critical plane, then, any store that fails to move one radius awa• and
normal to this plane in 0.25 second will be assumed to be not safe
(Ref. 5). This latter requirement will be expressed more rigorously in
terms of characteristic times and distances, but this definition seems
to be adequate for the purpose of this report.

2 The choice of one radius in 1/4 second is the author's. The

basic idea is David L. Schoch's.

4
 NWC TP 4995

Section 2. SAFE-SEPARATION CRITERIA

The criteria developed for safe store separation will be discussed

in detail in this section, which also contains available data in support
of the usefulness of the criteria. The detailed mathematics supporting
the choice of variables used to define the safe-separation criteria (SSC)
is presented in Section 3.
The set of variables used to define the SSC is based upon one pri-
mary assumption: the trajectory near the aircraft is governed by the
forces and moments acting on the store at the instant of launch and they
continue to act at the same magnitude. This assumption allows aimple
computation of a trajectory in terms of dimensionless variables. Once
the proper variables arc selected, a limiting boundary in a plane defined
by these variables can be drawn either by theory, test data, or some
combination of both. While the variables used in the SSC presented here
are based upon a constant force and moment approximation to the actual
data.

To validate the constant force assumption, one can compare actual

trajectories with trajectories based upon constant forces and moments.
The time dependence of vertical distance as a solution of a second-
order differential equation for z is

z(t) F(T)dTdt (3)

in response to an unsteady force F(T). Suppose F(T) can be represented

by a Taylor series

E dnF T-
F(T) f F(O) +
n=l dTn n! (4)
t=0

Then

Z(t)
)lF(O)t2
([) + nl
ddF
LtF
tn+2
(n+2) jI + w(O) t + z (0) (5)

t =0

5
NWC TP 4995

Clearly the effects of variation of the force upon the displacement

always appear two powers of t higher than in the series for the force.
Thus when the value of z for the constant force approximation (ze) is
arbitrarily close to the actual z, (IZ-Zci< E), there is corresponding to
each c a sufficiently small value of t. The practical problem is whether
or not this small value of t is large enough in practical cases. Detail
examination shows the initial force is the difference of gravity and an
aerodynamic force. Hence the constant force assumption produces trajec-
tories that lie above (smaller z) the actual trajectories. The actual
variation of forces and moments in two cases are shown in Table 1. It
can be seen that the variation of the forces is as high as a factor of
30 in the first 0.2 second. Nevertheless, the vertical trajectories are
in fairly close agreement (Fig. 2). The lateral trajectories seem to be
more sensitive since the lateral forces are small to begin with.

TABLE 1. Variation of Forces and Moments.

Time, FN, lb Fy, lb M, lb-ft N, lb-ft
sec 66 67 66 67 66 67 66 67
0 913 25.4 -25.7 -43.0 -30.6 -38.5 -99.6 -1.34
0.05 33.7 31.7 -33.8 -53.9 -19.6 -20.6 -86.7 -1.10
0.1.0 12.6 -152.0 -61.5 -1.25 -927.8 171.3 -58.2 -72.3
0.15 -579 53.6 -93.4 1.94 -785.3 23.1 -30.8 -18.2
0.20 -35.9 -1.0 -1.25 -2.6 -633.0 30.4 -724.0 37.81

It is remarkable that a position error of only 33% is introduced by

the constant force approximation while (for example) the force varies from
913 to -36 lb. For this reason the parameters were selected on the basis
of the constant force assumption. Figure 2 shows that the constant fcrce
assumption generally underestimates the z displacement, which is conserva-
tive, and also underestimates the y displacement, which is not conservative;
but a method of allowing for lateral errors on the safe-separation envelope
will be given below. The final SSC is felt to be conservative.

INITIAL DEVELOPMENT OF THE SAFE-SEPARATION CRITERIA

The SSC is developed from consideýrations of the distance between

some point on the store and a reference point in the critical plane
described in the Introducticn. The vertical distance is emphasized here
because with a suitable time constraint it can be made to be a sufficient
condition. Schoch (in a private communication) argues that the store
should quickly fall a critical distance equal to the maximum diameter of
the store. In that case a store which moved sideways to the wing tip
without striking the aircraft and then fell one diameter would be considered

6
 NWC TP 4995

0.32

ANGLE
YAW ANGLE
0.28 , A

0.24

0.20 -

RUN 66
O1 aACTUAL
PATH
0 CONSTANT FORCE
0.12 -- PATH
0.82 A -4

0.9 --6
CA 0-

0.4 6,

0 1 2 3 4 0 1 2 3 4

Z DOWN-- Y OUTBOARD--•

0.32 r

0.30

0.24

0.20 RUN 67

A ACTUAL PATH
S0.16 0 CONSTANT FORCE -
[Zz=PATH D

0.12 _ A

0.06

0.04

II I
O
2 3 4 5 0 1 2 3 4
0 1
Z DOWN-- Y OUTBOARD--

FIG. 2. Comparison of Constant Force Trajectories With

Actual Trajectories.

7
NWC TP 4995

unsafe 3 . The initial vertical distance, 6z'(O), is the distance between

the initial contact point and the point on the store in question in a
coordinate system fixed to the rack; z' is thus an aircraft fixed coordi-
nate, positive downward. Generally 6z' is a function of x and t, i.e.,
(from Section 3, Eq. 93)

6z'(x,t) 6z'(O,o) + Al(x)t + A2 (x)-+ ... (6)

BASIS OF THE CRITERIA

To develop the SSC we want to find out the circumstances for which
Eq. 6 has no real positive roots, because a positive root implies that
the store hits the aircraft. Setting
6z'(X,t) a 6z'(OO) (7)

gives for the quadratic (constant force) approximation

t 0(8)( 2 t Al)ý

Thus the roots are t = 0 and t = -2A1 /A2 . If A1 and A 2 each are greater
than zero, there will never be a positive root, so the separation is
safe. A1 and A2 are defined to be the initial velocity and initial
acceleration just at release of the store in the z' direction (note the
case AI<O and A2 <0 has been excluded for stores suspended below the
aircraft). Hence we can say that A1 >O and A2 >0 is a sufficient condition
in the z' direction for SSC. A1 and A2 have dimensions. Usually non-
dimensional parameters are preferable, se we use the characteristic velocity

/ 2 grmax

and the acceleration due to gravity, g. Defining a plane coordinate

system with the ordinate

A1 /l 2grmax

and the abcissa A2 /g, we can say that a store whose initial velocity and
initial acceleration fall in or on the axes of the first quadrant of this

The lateral case will be discussed later.

8
 NWC TP 4995

plane has satisfied the safe-separation criteria. This is indicated in

the sketch below. The line Al - Is included in the safe region on
the right half plane.

A1 /

/
/
/
/ SAFE REGION
SCHOCH% LIMIT DEFINED (VERTICAL DROP)
$Y FALLING TOO SLOWLY /
/

///

/0

A2

t/2
The usefu region of the A1-A2 plane (the first quadrant) is further
restricted by he arbitrary requirement that the store fall one maximum
radius in one-arter second. This limit line is similar to the criteria
used by Schocff This new limit is derived from the distance relation,
which may be :_Xen

Al = tz A (9)

Setting 6z' =frmax and normalizing gives

S= • rmax ~ V T rmax g i0

The term rrmaxit2g times Athe T~t

N/2-is the ratio of the time for the store
9)
1
to fall its own radius at one g to the critical time. This relation
between Al and A2 defines a diagonal line of negative slope that excludes
the region near the origin. This line's location depends upon the radius
(i.e., a store) and a critical time. For a 12-inch store and a quarter
second, for example
NWC TP 4995

A x z0.35 - 0.71 ()()

The broken line shows this boundary on the sketch above. It is seen that
the restriction is not large. Indeed, from the example calculated, the
excluded region corresponds to a small triangle bounded by a velocity of
about 35% of that attained in free fall and by an acceleration of 0.49 g.
This acceleration is equivalent to an airframe pitch angle of greater than
60 degrees, a steep climb or dive. Note further that the slope of this
line is proportional to the critical time and the intercept is propor-
tional to the reciprocal of the critical time. Hence, the shorter this
time, the larger the region of the first Quadrant that is excluded from
the region of operation. Note that, as the location of the characteristics
of the store on this plane are farther from the boundaries, the cleaner
the separation zharacteristic.

Briefly, it seems possible to define a boundary in the velocity-

acceleration plane that delineates those stores that will separate
safely from those that will not. Ultimately, the best boundaries should
be determined by experimental results.

Figure 3 shows typical plots on this vertical SSC plane. The solid
line is taken from computations by Daniel Jones of the Naval Weapons
Laboratory (Ref. 6). This line lies to the left of the ordinate because
the negative acceleration effects considered become smaller as the store
moves away from the aircraft. Hence, high ejection velocities can allow
safe clearance for the store in the left half plane unless they induce
strong restoring aerodynamic forces that cause the store to rise back
to the aircraft.

Before discussing A1 and 62 in detail let us consider the lateral

case. Here we have two alternatives. The first, simplest, and most
conservative alternative is to simply let the store move almost the
distance 6 y'(0) to the nearest store. Again, from Section 3 we find
this implies

(A3/A4) > 0 (12)

10

•mmmI
____ ____
___ ___
___ ______ ___ ____ ___ ___ ___ ___ NWC TP 4995

Ul

ca

r-k.
e d)*r
us~
o
i

I I I
_ _3

xsj~~/I ~'M~1A QLZIVJQ

dig3
NWC TP 9-995

In this case, depending upon the direction of the nearest stora, either
the fir2t or third quadrants are acceptable, as sketched below.

••f i• I _SECOND

AI1I, 1 /AVVEftAT1VE
1 AI

FIRST
ALIEW2AT1VI

I I"4/ -

11111, SAFE

'iI •/ LATERNAL-

'I / UMIT

Note the first quadrant app]es if the store maust move to the left
(6y'(t) < 0) to strike something solid, while the third quadrant applies
to the casp- where movement to the right is dangerous. However, there is
a better alternative to define a boundary in this plane. This boundary
comes about because the lateral motion of a store may be limited. Hence,
we will require a store that moves a distance 6y' (the distance to the
object it may strike) must also fall a distance 6z' in LtKe SaWW time.
Az' is the distan:-e the store must fall to pass under the object at 6 y'.
Arguing as above /,Eq. 9 and 10)

A3 1 y_ max 1 / 4\ (13)

Now, t, the time to fall the distance 6 z', is

.-A1 +VA- + 2,3z'A(

t 1 (14)

12
12
 NWC ITP 4995

Substituting and simplifying,

A3 - (15)
2r 2rmax 2gA

where

A2

(
V + Sz'
rmax
A2
g
2 grmax
A2
9 1

Note if A1 O,A
O +-)-..

This line in the A3 , A4 plane has a negative slope and limits the useful
area. Thus the safe-separation region in the lateral plane is determined
by two slanted lines. The intercept in the A3 axis is determined by
6y'(0). The larger the distance 6 y'(0), the bigger the useful area. For
many practical calculations, 6z' can be taken to be one diameter or one
fin span. Note this bounuary is fixed by a particular store-aircraft
situation. This latter alternative seems to be the better.

So far the fore and aft motion of the store has not been considered.
In every case studied, a store whose fore or aft motion causes trouble
was in trouble from the vertical or lateral criteria. However, if one
writes, for completeness, an x displacement equation
t2
(7
6x' = A5 t + A6 t (17)
with A5 usually zero and A6 < 0. The nondimens7onal relation insuring
that the store falls farther than it moves aft, then, is

Ima 2g A2
A(11

13
NWC TP 4995

and

A6 (1/2)pU2 (0)SCD (19)

g W

This term may be large if the store roý.tes 90 deg, but as indicated
above, usually a store that rotates 90 deg this close to the aircraft is
already suspect. Alternately, a line can be drawn on the A1 , A2 plane to
insure that this limit be met. Using earlier results

I 6z'(t) - 6z'(O) - A2t

2 t (20)

relation
and from the x

•26x' (1
t = ) E6(1

Substituting and nond2mensionalizing gives the relation

_/
_-_1 _z' _6rmax q6x' A2
S2 grma--x 2
rmx g-X A6 rax 2 (222)

In the relation, A6 and 6x' are negative. This line represents a second
lower bound and may be compared with the earlier condition, where the
intercept is

6 A6 rmax
rmax z'
tg2• as compared with 2z Y rmax

____

as compared with V.
I6rmax
272 rmax

14
 NWC TP 4995

Since Sx' is usually large, CD is small and 6z' is small, the aft distance
criteria lies belc-u the time-to-fall criteria as long as

6x' t2
A6 2

Hence this criteria is not usually needed, although it may apply to

items like safe/arm pins and arming wires.

APPLICATION TO PILOT ESCAPE CAPSULES

Application of this result to the pilot escape capsule requires

some minor changes, mostly in definitions. Since the capsule leaves from
inside the aircraft, A,, A2 , A6 will be defined at the instant the capsule
just clears the fuselage. This instant will be taken to be the origin
for time, i.e., t = 0 at this instant. For an upward ejection A1 < 0,
A2 > 0 and surely A6 < 0. If the highest point on the aircraft has
coordinate -xT' -zT' then the safe region in the Al, A2 plane will be
mostly in the third quadrant, below the line

A1 ZT [x 6 /9 1 2 (3
22g h N
A 9h

Here h is the maximum height of the capsule. Thus the safe region for
the upward-ejected pilot escape capsule is below and to the left of the
line as shown below.

<-%...-

SAFE SEPARATION
OF CAPSULE I
(UPWARD EJECTION)

,.BOUNDARY
"-TO S7IRIKE -XT,-ZT

15

L __ ___ ____ ___ ____ ___ ____ ___ ____ ___ ___
NWC TP 4995

Note that even if A2 > 0, there is a domain in the fourth quadrant that
allows safe operation. Previous capsules probably operated in this
domain.

RELATION TO EARLIER RESULTS

All the safe-separation criteria discussed heretofore are based

upon the idea of displacement, either in the complete form given in
Section 3 or in one or another simplification. 4 Jones, Schoch, and
Unger adopted the simplified form. (Schoch has used a better criteria
by using actual stores and actual aircraft shapes.) In general, the
simplified spatial relationship

z'(t) - Ze(t) >• Act) (24)

is employed where e > 0 for the nose and t < 0 for the tail. A slightly
more accurate form

z'(t) - t sin 8 - r(t) cos 0 z M~~t (25)

AC

simply allows for the possibility that there is a store shape change. In
each case that a simple result is sought, as opposed to a detailed numer-
ical result, the aircraft is represented as a plane. Schoch adopted the
reference plane below the store so that 6z'(O), the initial store refer-
ence plane distance, is negative.
The treatment of this basic formula (Eq. 25) varies from investi-
gator to investigator. Jones calculates the displacement at time
t =ty 7T I Mot; although, in the same vein, he could have selected
t = 2-'y/ - Me. Jones then used the constant force equation evaluated
at the half pericd, or the condition of finite downward velocity at the
edge of the lift interference field.

Unger used a more complete solution in the basic condition for safe
separation and simply computed trajectories, isolating those that struck
the aircraft. He also expanded his solutions to the 4th order in time
and substituted into the equation that represents the separation distance,
as well as writing two approximate forms involving trignometric force

The use of constant force and moment analysis has been proposed
also by G.V.R. Rao and B. Jaffee "Study of Generalized Safe-Launch
Bounds for External Stores," submitted to NSRDC Aerodynamics Laboratory,
October 20, 1967, on Contract N00600-67-C-0592. Rao and Jaffee construct
the safe limits in thE P, z plane.

16
 NWC TP 4995

functions. The simplest is a constant Force approximation (the inter-

ferences do not vary), thus

-~LL~t)
-~I - Cos VFc tJ

+ wot + F(O)- > ZAC (26)

reduces to the second-order result described abov,. That is, we have

replaced sin x by x and cos x by 1-x 2 /2. This suggests that the quad-
ratic ap roximation indicates the store will rotate too fast (cos x - 0
at x - r2not
r/2.) The implication is that the quadratic approximation
is conservative, because the store falls relatively more slowly than it

rotates. Hence, any store that is safe by the quadratic or constant

force criteria is likely to always be safe.

Figure 3 shows the SSC computed from the constant force approxima-
tion and a typical lower boundary due to distance-rime limits and the
results from Unger and D. A. Jones. The most striking point is the
difference between the ordinate as a boundary and a boundary derived
from Fig. 7 in D. A. Jones' report.* Equally striking is the effect

*NOTE: A linear approximation gives the Jones boundary the form, for a stable store,

Sr2M(+) 2 1 T A2
A1 ____ - [A ~- -/HO
-(~)
v/2gr,,,x I 2 r
grmax wj-M,(O)I1

Here T is the period of the store in a uniform stream, tc is the critical time. This
line has a slope that is much steeper, in the ratio T/2tc, than Schoch's line and is
the boundary for

"A2 .2126.'Frmax x \/M(O) ___

g ~rmax t2g /

tc
0.354~ _
2 T
rmax tc

Note this line (because of the ratio M(O)/I ia) is not fixed, but rather depends
upon the flight conditions such as q, Mach number and angle of attack. The latter is
dependent upon load factor. These terms are known because they are contained in A2 ,
but nevertheless this is a movable boundary. For T » tc the ratio
"r2 2
A /2(l - -)x t H(O) t
62 = - 2.29 c xM(O)
2 grax I 2grmax I

2
For T << tc, the limiting value of A2 Ig approaches the value 2rmax/t g. The former
case is more likely to be encountered.

17
NWC TP 4995

of the (one radius in 1/4 second) limit in increasing the required ejec-
tion velocity in the region of negative acceleration. The region in the
second quadrant dominated by Jones' results are thosa cases where a stable
store moves down and then up to hit the aircraft. The lack of symmetry
in the vertical plane (A1 , A2 ) when compared with the appearance of the
A3 , A4 plane (Fig. 3 and 4) is due to the geometry of the lateral configur-
ation if they are not mounted on a wing tip or a side body pylon.

Returning to the expressions of A1 , A2 , A3 , and A4 in detail, one

finds that much of the experience gained in the area is supported by this
SSC. There are, however, several features that are worth a detailed
discussion. A1 and A3 are simple, i.e., (from Section 3)

A1 - w - Awy x(cos * 0 sin 60 sin e; + cos Cos

C0 60)

- Aw r(x)(cos *o cos e0 sin eo- sin eO cos eo) (27)

Thus, A1 is just the velocity imparted to a store at position x in the

coordinate system attached to the rack. w is the vertical ejection
velocity of the store with respect to the aircraft rack reference point,
acting at time t = 0. Similarly, Auy is the store angular velocity
about the y' axis with respect to the aircraft rack. w is positive if
it acts downward and &y is positive nose-up. x is positive for stations
ahead of the center of mass and negative for stations aft the center of
mass. r(x) the radius (or fin) distribution is always positive. By the
same arguments,

A3 = v + Awz [x - r(x)] (28)

From Section 3, the acceleration term is, for straight and level
flight,

A2
-- = cos Cos

+ .1 pu2(o). CZ; + 6cZ~ (x + rOd (GMI + 6cM;)j > 0 (29)

y
In this relation, Cz', 6 CzS, CM• and 6Cf are evaluated at the Mach number,
angle of attack appropriate to the lead factor, and angle of side slip
that are imposed by the trajectory. The altitude and flight speed are
characterized by the dynamic pressure, and the aircraft trajectory appears
in cos 61 cos to.

18
 NWC TP 4995

U,

m cc

000

to~ N

- 1 94
NWC TP 4995

The following conclusions may be drawn for stores below the aircraft:

1. The effectiveness of gravity is reduced for any non-straight

and level flight path.

2. If the term inside the brackets is negative, i.e., the aerodyna-

mic loads force the store towards the aircraft, a lightweight store is
more likely not to clear the aircraft. This situation is aggravated as
(1/2)pU2 (0) becomes larger.

3. If the term inside the brackets is positive, a heavy store or

a low dynamic pressure flight is more sensitive to flight path angle,
because the aerodynamic forces and moments are less effective.

4. The constant force and moment approximation suggests that the

some information needed to evaluate the carriage air loads on a store
can also be used to determine the safe-separation criteria. Thus extra
information is not needed, but the needed information may be shared by
different groups of the same design team.

PROPOSED SSC

The SSC is developed on the nondimensional velocity-acceleration

planes by applying every bit of data the author could find for which all
the needed parameters were available. 5 This data is listed in Table 2.
The values of Al, A2, A3., and A4 were computed for both the nose and the
tail, and the results plotted together with the limit lines for the
particular store.

Figures 5 and 6 show the location of nose and tail points on the
nondimensional velocity-acceleration plots (the run numbers are contained
in the circles). The data is for conditions listed in Table 2 of Ref. 1.
All these separations were clear in the vertical plane. The implication
is that the ordinate is far too restrictive, and that even the 1/4-second,
one radius limit is too severe. The nose points all show a positive
acceleration but almost no vertical velocity at ejection, whereas the
tails come down because of their velocity, even though they are accelerated
negatively (upward). The tails of runs 68 and particularly 71 tend to
float, i.e., it takes them a longer time to clear the area. In the
lateral plane, run 67 is out of the safe domain--its nose moves too
far to the left (hits the fuel tank). In run 71 the tail brushes the
pylon. The analysis says it is safe (A 4 /g ' 0.03) but between "hanging
up" and the errors in the measurement (at least that large) the clearance

5
In particular the author is indebted to Charles Matthews (AFATL/ATII
Eglin Air Force Base).

20
 NWC TP 4995

'A- ZA 0~ 0f D 41
0D 0* 2. 1 X wn 'A

11 02

@10 J 0

%-m %D .0

00 0
U
LA 0 0a- r*
X 0 ON 4L -c 10
Ch0 '. n
a~0 4 m1 T'4

IO

ON' co No

0. X: -

0~ C U.

0 0 0

c4-

0 m 0 I

UN

0 01 Ci. i'

4% 0'. 0
0 0
4- z

01 '0

C '

o~C C' U.

cc w

nir

4% 020

6LC i' '. I' '

NWC TP 4995

to

;. La4
9%d

ri 2 0

4 0

Cus 4

LU 0
41
C4ý4J

LUU

- (1)

C. 0 N
('.4
/ V±$43
xswg0 ~IV~t&O

22U)0
* ~NWC Ti' 4995

I s
0 w
I

zzW 0
)1 3
LU.a

ku 0
tLu

w- c
0

z 0

Z cj
0

fa

0 to

xlWjBZ k EV 'A1JI:DO-3A C13ZlI~IVUON

23
.ýC 7P 4995

is uncertain. Run 68, wnich i3 run 67 at a reduced angle of attack

(Mm - 0.7), cleared safely. Figures 5 and 6 world support thete zesults
I
if Jones' criteria a~n the 1/4-second limit were u.ed.

Figures 7 and 86 show the charactcristics of the Mk 4 gun pod on an

A-6 pylon. These characteristics are bazed upon flight test trajectories
and computed trajectories. The lateral separation was clean for these
cases. On test 533 the ta t l hit the pylon, while on tests 553 and 556
*the nore was within Inches of hitting the pylon. The plot shows the nose
on 553 and 556 actually had an upward velocity at release, so it is not
surprising that it.hit, The tail hit on test 533 is also indicated.
ihese flight test results again indicate the utility of the acceleration-
velocity plots.

Figure 96 shows the vertical separation characteristics of the

Sargent-Fletcher fuel tank (empty) from the OV-1D. In every case the
trajectory is clear and the plot of the flight test results shows that
jettison is safe. Similarly Fig. 10 shows the lateral characteristics
are satisfactory. Flight 57 is most interesting, because here the air-
craft was rolled and the hasic values of AWg4 were negative. However,
because of the roll, a gravity component acted to cause the store to fall
in the outboard direction. Note that even a slight negative value of
A4 /g is not serious, because there is 8 ft of distance before there is
anything for the store to strike.

CONCLUDING REMARKS

The results cited in Fig. 3-10 suggest that the background calcula-
tion is quite valid in determining the safe-separation characteristic.
Further, even if the theoreticel basis were unacceptable (although it
seems to be satisfactory), the ordinat- and abcissa displayed here seem
tc describe the data and separation limits adequately.

SUL"IARY AND COMPUTATIONAL OUTLINE

The basic properties needed to compute the separation chalacter-

istics of a given store are the relative velocity of a point with
respect to the rack and the relative acceleration of the same point with
respect to the rack, both evaluated in rack coordinates at the instant
of release. The former may be written

[R.] (Uo + ub x rp) " '- x (Rol • rp)

6 Data courtesy of Charles Dragowitz of Grumman Aircraft Engineering J

Co.

24

It
___________________________NVC TP 4995

/ it
o- 4

I -z

E/

W LU

to t3

LV~~~0 0AD1A03II"O

¾2E25
 NWC TP 4995

/ 0'

0
M 44

(44

Ul 0

C4r7

26t

L
 NWC TP 4995

IL
K0
IIb / 4

T z -Q

> 0m u
U.r

/ 0 u

01 0

4)U s

N N

d 0

03I'I(JHO
XBUAr~xltV'AIOO1A

-'27
 NWC TI' 4995

SARGENT-FLETCHER
EMPTY GAS TANK
OA OV-ID FLIGHT

8y>O
RIGHT LIMIT, FLIGHT

80A
-I
34NS

1-&
.j

4TILI
-1.2
0 -0.
-. 0 0.408 NOSE1.

~
LATERAL
ACEERTINL4
~ ~ 5

a -mte- latr if -at t I 0,e_., IUd

[Ro] *ýU + w-,x _rp) - V11 - Q1j' x ([Ro] "rap)

In the x1, y' z' system, the relative velocity components

and the acceleration components are (A6 ,A ,A ). Because of are (A5 ,A3 ,Al)
4 2 the cumber-
some nature of [R], simplified procedures are useful.

28
 NWC TP 4995

Vertical Motion

The procedures described here are based upon the assumptions:

1. Aircraft motion is steady.

2. The store is rigidly connected to the airframe.

3. The airframe is rigid.

In this case the relative velocity between the store and reference plane
is zero at a time just before the start of the release sequence. With
this simplification

AI= -Ay - x [cos *o sin 0o sin 60 + cos 00 cos efI

+AWy 0 z cos *o cos 60 sin 0o - sin 0o cos e~l

+ w. (30)

w is the ejector velocity and Awy is the difference between its angular
velocity imparted by the ejector Eystem and the aircraft, i.e.,
y •wy(O). The value for z is -r(x), the radius of the store at
position x. To continue,

A2 o Oo cos
[cos o'+ -1 pU2(o)f (C + o) ' O + 6)1times
ky

cos sin 0eo

sin e + cos 00 cos e]__

d(C(x)( +
"+ g- cos 40 sin e' + 1U2(o)U+
y

cos osin 6' cis eo - sin 00 co Ol]

[ 2~Yo
(0 + Y) + ý N. 6CN.) Isin s, e'Cos+6(31)

F 29
NWC TP 4995

where

•'- aircraft roll angle at release

'0
0'0 - aircraft pitch angle at release
o- aircraft yaw angle at release

Lateral Motion

The several terms below have been defined elsewhere, i.e., Uz1 is
the first-order change in store vertical velocity.

A3 - - wy x sin i0 sin 00 + v (32)

A4 - Ux, sin 4o cos 80 +(Uy 1 + wzi X) Cos *o

+ (Uz1 - uy1 x) sin 4'0 sin 60 (33)

L1 f9sin 0 + ~.U2 (o).ýIC +6 + A2 (N+ cN1 (34)

Axial Motion

A5 - Awy x sin 80 - Awz x sin *0 (35)

A6 9 ~U2(O)_i[(X 0 + 6C xo) _ d~r(x)(CM. + 6CM 0 )Jtimes

Vf

cos iOo sin 80 sin 0 + cos 80 cos e

+z+ + '÷ io + oltimes

6C)+k2 I~
L ~yJ

cos i 0 sin C o
0co, - cos 60 sin 8o0

- sin 0 Cos (36)

30
 NWC TP 4995

Comput tional Outline

Tc determine the safe-separation criteria for a given store, rack,

and aircraft combination the following information is needed:

1. Geometr-ic

(a) Store--radius distribution, including fins if any; length;

location of store center of mass.

(b) Rack--foot position with respect to store center of mass;

location of nearest strike point in each direction.

(c) Euler angles of store and rack at launch.

2. Force and Mass Properties

(a) Store--weight; moment of Inertia about each axis.

(b) Rack--force versus distance or time, for ejector foot, if

any, for each rack load and condition. This can be inte-
grated to give impulse. If the details of the rack ejector
impulse are not knowm exactly, the best Dossible approxima-
tion should be used. If possible, this approximation should
underestimate the velocity imparted by the ejection system.

(c) Aircraft flight speed and dynamic pressure.

3. Store Aerodynamic Coefficients in Suspended Position at

Aircraft Maneuver Conditions, Velocity, Mach Nunber, etc.

The calculation proceeds as follows:

1. Given initial values of W, 0, ý and •', 8', •', the Euler angles
of the store and reference (aircraft) coordinate system, re-
spectively, complate the required angular transformations given
in Eq. 30, 31, 32, 34, 35, and 36.

2. Given rack ejection characteristics and store inertial char-

acteristics, compute v, w, and Awy, Awz, the translational and
angular velocity components of the store due to the ejector.

3. Select critical points on the store x and V(x) and compute

A1 , A3 , A5 from Eq. 30, 32, and 35, and normalize with respect
to V2 9 rmax. AI, A3 , and A5 are the required z', y', and x'
component velocities of the critical points.

31
NWC TP 4995

4. Next, given the free stream aerodynamic characteristics of the

store, develop the free stream aerodynamic coefficients (in
body coordinates) Cz , CXo, Cy° and CMo, CN for the aerodynamic
0 0 0~C0
conditions (c, B, q) that exist at t - 0.

5. Develop the aerodynamic interference coefficients (in body

coordinates) 6Cz , 6CXo , SCyo, and e-Mo, SCNo from Eq. 113-119
or from wind tunnel data.

6. Compute A2 , A4 , A6 from Eq. 31, 34, and 36 and normalize with

respect to g. A2 , A4 , and A6 are the component accelerations
of the store critical points in the reference coordinate
sys ten.

7. Prepare charts of normalized velocity (ordinate) and normalized

acceleration (abscissa), using the store radius and a critical
time (say, 1/4 second) to develop the inclined boundary from
Eq. 16.

8. Plot points previously calculated.

Finally, one should evaluate the linear "jones' Limit" for stable
store, i.e.,

. 60
A .70' X LMo() - 2) •
a xj r,-
z', -- •
A2 maIx tc V'-2g ax- =4 (37)

with the comptced A2 /g > A2/gJones.

32
-. i NWC TP 4995

Section 3. SEPARATION ANALYSIS IN DETAIL

REFERENCE COORDINATE SYSTEM

The first problem encountered in studying store separation is the

selection of the most convenient coordinate system. After considerable
experimentation the following selection was made. The origin of the
reference coordinate system is on the rack-store interface waterline;
"located over the store center of mass, in the sense that it is perpendicu-
lar to the aircraft waterline in the buttline plane. The plane defined
in the introduction can be identified with the waterline plane of the
store rack (note each store has its own plane).

The x' axis is forward in the buttline plane, the z' axis is down-
ward in the buttline plane and y' is normal to the buttline plane in the
waterline plane positive in a right-handed sense. The velocity of the
origin with respect to the earth, measured in the coordinate system
described above is denoted

V+ Vy j' + Vz' k' (38)

Further, _he coordinate system has angular motion with respect to the
earth of W'. If the aircraft center of mass is located a distance r'
from the reference origin, the velocity of the center of mass with respect
to the earth in a coordinate system parallel to the reference system is

VA/C = V' + WV x r' (39)

Generally V', W, VA/C are known functions of time. These functions

include the case of the maneuvering aircraft.

POSITICN OF STORE

To define the motion of the store, consider a body-fixed system with

an origin at the center of mass of the store and the axes aligned with the
principal inertial axes. x is forward, z is downward, and y completes a
right-handed system. This cuordinate system is located with respect to
the earth by (1) yawing to the desired heading (+ nose right) (2) pitch-

33
NWC TP 4995

ing to the desired attitude (+ nose up) and rolling (+ right wing down).
These angles are i,8,$, respectively. Transformation matrix from the

xE
x system to the x' system is (see Appendix) quite complicated because
it involves first transforming from the store to earth coordinates
(Appendix).

YE = 9•€ Y (40)

cos 0 coo 0 cos asin sin- sin coo 0 cos asin cos + sin sin

[ sin * coo 0 sin sin 8 sinO + co co sin sin e cos - coso sin (41)
-sin 0 cos e sin 4 cos 0 coo J
and then to the prime coordinate system

y] = ' ,-] V • (42)

z'

which will be denoted

y[ =
M[R] 4 (43)
zi

Similarly, the linear and angular velocities of the store with respect to
t.he earth may be computed in the reference direction

U' = [R] , U (44)

Thus the relative velocity between the store center of mass and the refer-
ence point is

V - U' [I
[]- ' (45)

Thi: can be integrated to give the relative distance

X 1 Lt [-' [R] ]d
dr -dr(O) +fo [V' - [R] Vdt (46)

34

mm
mmm
•~mmm
r• mom
eo
•mmn
~ mnmm
m•
m!I
 NWC TP 4995

Note that in calcula "*n t,8,* we have used the relations

V(t) -0(0) + o(t)dt (47)

and

1 tane6sin~ tan 8cos 1 wx]

" CosB-sin JW (48)

cosO cosf8

A point P away from the origin of the store has a velocity in store
coordinates relative to the earth

U=Up U
U + W x rp (49)

Its relative velocity with respect to a point Q in the reference system

is

V' + S' xrQ- R " I + x rpl (50)

r r=
Xý
Usually we are interested in the image of P in the reference plane,
Z = 0

[R] 'p(51)

thus

d•Ip = dip,(0) -Q' +?' x [R] •

-(R]I UtJ+ w x rJdt (521)

By considering components of d-1 we know the vertical distance 6z'

and horizontal distance 6y' between the store and reference points. The
actual computation is not difficult, but is quite messy because [R] itself

35
NWC TP 4995

is extremely bulky. for our purpose ye will assume the aircraft has
pitching motion only, so *' - f' - 0, and the store has rotatiovel
symmetry, $ - 0. In this simple case,

rcos *os u'0 cos 0 + s$1 B' sin e - co ' @in9 Cos sin S cogS' - sine' c0-
(a) - jsl•n c,, 6 cCoo sin sin (53)
[-cos t cos 0sin 8' - sin 6 coo Sý - sin V coo B vin 9' *'
cc@ * sin a' sin a +CO co Sc

and so for a non-ejecting rac4., with Q - Q= 0 and Wo - 0

6' -6z'(0) v (t. - x l-oi,, o

cog cog e' + s-• sine
e' + f sin ,Co
,y ec
J.

-Uz - (Wy + &•yW)[cos sin 6 sin 0' + cceCos

e8' ] - [Uy + wzat sin * sin .' cos 0

-fz[cos 1 sir e cos 8' -cos 0 SLU 0'! - [us + (P0 + ý )z - times
tzy]

coy * cotB 3.1i:

C' - 0 coo W'I + vijdt (54)

Sy' *6y,(!,: -j'lv;t) - (U,, in ;P Cos 8 t (Ly + uWzx)cos *3 - u. (wy + L)",)x1 sin tr sin 0 dt (55)

MOTION OF THE STORE

The equation of store motion can be written in terms of the body

axis system in follwing form

M d zUV + =UUz
FAERO x FGRAV x(56)

m
[dU -dxz •z J AERO y FGRAY y

dt - WvUx = F + F (58)
1 AERO z GRAV z

36
 _WC _T 4995

dw
1x
- + WY64(Iz - 1y) -t (59)

dw
Iy • + WxWz(Ix - Iz) My AERO
M (60)

dw(
zt Wy4Im(IY - Ix) Mz AERO (61)

The gravity forces are

Fx - -mg sin e (62)

Fy = mg cos 0 sin • (63)
Fz -mg cos 0 cos * (64)
and from above

0 + o(c + tan Osin w + tan Ocos 0 •z)dt (65)

6 = 0(0) + (wycos 4 - wz sin O)dt (6o)

t(o s n W
. ( 6 7)
cosk

The aerodynamic forces are written

Fx AE US Cx + Cxz'z + 6Cx()(68)

y 2 :E c1
2

F z AERO = PU S Cz + Czz'ZI + SCz(0) (70)

37

-'
NUC TP 4995

where p w air deasity at release altitude

-1 Uz
O, - tan
Tx-
Cz - -CL Cos I- CD sin a

Cx W CL sin a - CD cosO

CLCD,CY = lift, drag and side forces coefficient in uniform

air

Czz - rate of normal force due to nonuniform flov

Sc, = incremental value of interference at the suspension

point

Similarly, for the torques

M AEIO .pU2Sd(Ct + Ct.,z' + 6Ct(O)) (71)

y AER 1 U2Sd (C14 z' +6C(O)) (72)

z AER0 "U2,S(cN + CN ZI + dc (0 (73)

These equations are closely coupled and quite nonlinear. Hence, any
analytic solution must involve a simplification of sorts. Consider a
series solution of the form
t2
1!z = Uz(O) + Uzlt + Uz2 + (74)

for each variable, so

dUz
d-t-ff UZ + Uz 2 t+ "' (75)
Recall that ultimately we are interested in displacement, so
t2
z z(O) + Uz(O)t + Uzl t- + ... (76)

38

I
 NWC TP 4995

Hence, a first-order solution in velocity is equivalent to a second-

order in displacement. The variation in the aerodynamic effects with
distance arises only in the third-order terms.

The series for the several terms may be solved to give

Ui- uz(O) + w cos (0' - 0) +l [Ux(O)Wy(O) - Uy(O)Wx(O)J

+ %2(o).ýCZ(o) + 6CzI + g Cos 0(0) Cos 0(O)J . (77)

Ux = Ux(O) + W sin (6' - B) + [JUy(O)Wz(O) - Uz(O)cY(o)I

1 U2(0)- C,(o) + 6C I-sin ( +

- ... (78)

U)+ V + [ -
U Y -vY(O)
+ I~z(OUx(0)
Uy(O)WJO

+ 1U2(o)JCy(O) + 6CyJ + g cos 0(0) sin W(0) t + ... (79)

where w - vertical ejector velocity, v = lateral ejector velocity.

S=Wx(O) + I W.(0)WZ(0) + U2(0)_C(0) + 6Cz)t + ... (80)

S- :,(o) + AW(O) + tWz(O)Wx(o) + 1 u2(0)p (CM(O) + 6cM t + ... (81)

iý -1_ p IY

Wz = Wz(O) + Wx(0)Wy(0) + 2(0) N + t + ... (82)

and

Aw(O) -x > 0. (83)

39
NWC TP 4995

Aw(O) - angular velocity imparted by the ejector. The value of C,(O),

Cx(O) and CH(O), for example, included the maneuvering effects of the
carrier aircraft. Thus Cz and Cx are evaluated at the aircraft angle of
attack at the instant of release plus, of course, any incidence angles
due to the rack and the ejector velocity. Furthe. CM(O) is not only
evaluated at*the same angle of attack, but for a maneuvering aircraft
includes CMVO + CFa also. That is,

CM(O) - CVa(O) + ci(o) + CM&&(o), (84)

a(0) - aAiC(0) + i + w/U(0) + () 85)

i incidence angle > 0.

If the aircraft were rolling, an additional term

b'Qx'IU(0)

would also be needed.

The Euler angles can be computed directly from the formula given
earlier; for example, if 8 - 0,

* = (0) + )X(0)t
[(±--z)uWy(0) (0(O).)+ I 2(-)-§.d (86)

after writing cos 0= cos 0(0) - sin 0(0) Aý(t), etc.

8 =(0) + ['ok/) Cos 0(0) + WoZ() sin 0(0)•t

"+ uCos ÷ cW (O 87)n

+ yd +2 (87)
2 4C 12

40
_NWC TP 4995

A similar expression may be written for *(t),

1 (0)+ sin() + cos . (O)]t + (88)

The second-order terms are quite bulky and, as explained below, are not
needed so they are not presented. Again, if roll is negligible,
* i = 0 and inserting ejection effects

Iw)U2 SdA(C + 2
-
tC)I (89)
0 8(0) + (Wy(o) ++ • (0)(cM +CM)- 2 +...

S= ,P(0) + (wz + Awz) cos 0(O)t

+ -sin 8(O)wy(O)wz(0) + 1U12 Sd(CN( + 6CN) ý2-+ .. (90)

1 2 O)FN(O N' 2

which is a great simplification.

With all these steps completed we can compute 6

y' and 6z' to deter-
mine the fate of the store.

SEPARATION DISTANCE

The previous integral was written in general terms. To make the

calculation more specific we will hold Vz', Vy' and Sy constant during
the calculation. Hence, we write

Co -- Cos e'(o) +' (olt+y+ ••-

Cos 0 -0 Q2'
-'OQt + .. (91)

cos 0 cos 0(0) - (O)w y(O)t

- y (0) + e(0) - u (0) y M+c "

- ~2I0 c)-!u()A + 6C,,$ _2i
+ .. (92)

In this expansion only first-order terms will be retained, which will lead
to an expression for 6 z' with second-order terms. Thus 6z' takes the form
, t2
6z = 6z'(O) + Alt + A2 + (93)

41
NWC TP 4995

Evaluation of A1 and A2 is straightforward but tedious because of the

detail contained in the basic equation. If we assume that (a) the store
is rigidly connected to the airframe, and (b) the airframe is rigid,
then the relative velocity between the store and the reference plane is
zero at a time just before the start of the release sequence. With this
simplification

1 = -- wyx cos ý0 sin 00 sin 6' + cos 00 cos 6

+Awyz cos '0 cos 0o sin O6 - sin 00 cos 80

+ w '94)

where the subscript o implies evaluated at time t 0. Further,

A2 =U' wYlx cos 0o ssin in 6' + cos 0 cos 8

+ [Uxl + U~,zJ [cos 'P0 cos 00 sin 6'; - sin 00 cos 6~

+ U + a)ZX sin 'o sin O + g cos 00 cos (95)

Similarly, if

6 6
y' y(O) + A3 t + A4 t 2 /2 (96)

A3 =-Awyx b.Ln *0 sin 0o + v (97)

A4 (Uy1 + Wzx ) Cos *0 + (Uzi - wyx) sin 'PC sin 00 (98)

The several terms have been defined above, i.e., Uz is the first--
order change in store vertical velocity, w is the ejector velocity, and
Awy is the difference between its angular velocity imparted by the ejector
system a.d the aircraft, i.e., Q y'-uy(Q). The value for z can be r(x), the
radius of the store at position x.

The function 6z'(t) represe:.ts the distance between a point on the

store and the limiting plane. hence, if 6z' = 0, the store is just at
the boundary of being safe. During 2nv rp ease or jettison, then, the
times for which 6z' = 0 are the critica- period of the selaration process.
On the other hand, the criterion 6z' - -ýn be used to define those
characteristics of the store, the rack, ai the carrier airrraft needed -

for safe separation. This criterion can be established by considering

the roots of 6z' = 0, namely values of t, defined by our approximation

42
__NWC TP 4995

t -- •_± A 2 - 2A 26z'(0) (99)

A2

Here two criteria suggest themselves:

(a) no real root for t, which implies

1 2 (100)
(0A2 > 2-M' > 0

or

(b) no positive root for t, which implies

Al>0 (101)

"1>
2A z'(O) 2 (102)
21
To be able to apply these criteria, the expressions for A1 and A2 must be
put in simplest possible form. Substituting the values for A1 and A2 we
7
find the criteria for case a is

-z'(0)VU2(MoIC%0+, 6CZj + g Cos oo

-(VPU2(o))L 2jq,. + 6C,.,] j(cos 'ý sin 80 sin +Cos

-0. 60Cos

I
cos 0o + pu2(0)ý CIo + 6C o

- [2PU2(o) 2CHo + 6CM )(-r(x) J(cos 'o cos 60 sin e0 - sin 80 ces 6o)

U2CC)y + + 1 ( c)C + 6CN sin 4, sin 4

S~mkz

->fw
2 - r(x)&y cos P cos 8 0 sin 8'0 -sin 60 cos 6O

+ X cos ýo sin 60 sin 0' + cos 60 cos (

(103)

(IY mkYIz -mkz

Note the acceleration 0' x V' is not included because it cannot

act on the unrestrained store.

43

1,1a
 95
CT4,9
NWC TP 4995

Note we have used -r(x) for z because we are interested in the "upper"
surface of the store. For case (b) the first criterion is

w + iWy(O)(-r(x)[cos ý 0 cos e0 sinr. 0 - sin 0o cos e~i

- x[cos 'o sin e 0 sin e6 + cos 60 cos O' ) >0 (104)

In examining these criteria, the number of variables seems large.

If one recalls that 00'-00 - i, the incidence angle of the store, and
that for current practice 00 = 0 (i.e., no attempt is made to line the
store with the average lateral wind), the number of variables is reduced.
One is left with the aerodynamic forces and moments acting on the store
at the instant of release, gravity and the airframe pitch angle. Hence,
for case (a) one obtains

6z'(0)1pu (o)i[Czo + 6 c)Cos io + 6C sin

i + C rxo
I(C + )
22
i2 Sd l_
VpU (0) SC~j~ cos i- si i/~x +gCos '2
m 0

y2
2w - cos i + r(x) sin i) (105)

and for case (b)

w - Awy (x cos i + r(x) sin i) > 0 (106)

The nose corresponds to x = 4N, and the rail x = -. T.

For jettison only, i.e., w and Awy 0, - A/C roll angle 0,

one consequently finds for the (a) case

y(•(o)(x cos i + r(x) sin i) 2

Cos 00 Cos U> ow -

2g6z'(0) cos ýO

-!- U2(O)s z + 6Cz) - CM + times

d(x cos i - r(x) sin i) (107)

44
 NWC Tr 4995

or for (b)

w > Awy/O)(x cos i + r(x) sin 1) (108)

For simplicity we have written

Cz, - Cz cos i + Cx sin a. (109)

If the term in (a) in braces is denoted by A, then if one plots

-7r1/2 r/

and locates the value for A, then A1 represents a safe jettison while
A2 is unsafe.

For lateral motion we find, similarly,

[sin 00 + (U+ + (06 L[ + 6CN) /6y'(O < 0

2 W oC 2C 0J

and

I(v + AW X)16y'(o)l < 0 (110)

Note that the effe.-ts of roll angle on the gravity component have
been included. It will be shown below that the effects of the aircraft
maneuver, i.e., load factor, side slip, and rolling rate are implicitly
included in the calculation of the aerodynamic coefficient.

8
AERODYNAMIC LOADS ON STORE

The criteria developed above contain the aerodynamic forces and

moments explicitly. These applied loads appear in two ways: the load
the store would experience if it were at the same angle of attack and

8
This discussion is not meant to be complete, but rather to provide
an outline of some of the methods used to analyze far field interference.
For more detail see Ref. 9-13.

45
NWC TP 4995

side slip angle (including dynamic effects) in a uniform field, and the
load due to aerodynamic interference. For the former the angle of attack
is

aS - aA/C + i + 2U(O) + U(O)

i - rack incidence angle

and if the angle of yaw is 9o, then the side slip angle is
£'C
c Z

•A/C + ýo + u(o" (112)

and cA/C = nW/qSC'C, n = load factor. Ir steady climbing or diving

flight n = cos yo, but in maneuvering flight where mUoy - (n-cos Yo)W the
value of n is not restricted, being either plus or minus and greater than
unity. In general, this value for a is used to estimate the aerodynamic
load in a uniform field.

It will be assumed that results of calculation of uniform field

properties, or wind tunnel data, are available. Similar results are
found for the side force and yawing moment using a rather than a.

PRIMA'P WING-BODY INTERFERENCE

The aerodynamic interference due to the slowly varying fields is

1 2 N dS CE REF
L = U (0) •(x,y,Z)T dx s Z.N) (113)

(+ UPWARDS)

M = MP2-U(0) N axly'.z)x d:'x

e2 dxdxS VLM(k2 SREF
CMaMEAS k)tREF (114)
2 fT dx VOLUME (k 2 k)

(+ NOSE-UP)

46
 NWC TP 4995

where, assuming an elliptic lift distribution, for example,

a(x,y,z) 2C/4 CL 1 - (115)

2
(x-xC/4) + z (2)2AR

for the region x - wing lea.iing edge to x store nose (a(x,y,z) 0

directly below the wing) and
•(x~yz) IX + XT

1 TE
2 2c + XTE
2 A/C (116)

for the region x = store tail to x = wing trailing edge. This is

essentially Multhcpp's procedure (NACA TM 1037) for computing the
induced angle of attack. If the flight Mach number is 0.8 or less, the
Prandtl-Glauert correction may be made.

Similarly, the angle of side slip is

CL (

for the region from the trailing edge to the store tail.

8 =A (118)

for the rest of the store length.

Note the sign on ý is such that the local force is always toward
the wing tip. The side force and yawing moment are particularly st~nsitive
to local configuration changes. The implication from this sensitivity is
that in many cases a more detailed study is needed. Such studies are
available; for examý'ie, Browne and Gallagher (Ref. 8). In general, this
problem has been studied in detail and several references exist that are
of detailed use (Ref. 5-9).

A second kind of slowly varying interference is due to wing thick-

ness t. This increment is, approximately, directly beneath the wing

( dx (119)

and can be deduced from the flow past a Joukowski airframe.

47
NIC TI 4995

The unknovn tnterfereree, at this tLime, Is that due to the win8 in

the st(.re flov iteld or adjacent stores in the store flov field. This
iut~erference factor mast be determined at the present time, frc wind
tunnel or flight testing. it may be optimistic to suggest that these
colticated interfereaces can ever be ccswuted, 1ut ruch a goal is
sitrely desirable.

48
 NWC TP 4995

Secticn 4. CONCLUSIONS &.D RECOM.IMhTAT IONS

The evidence, wvacht is sperse, strongly suggests that a safe-

separation criteria can be expressed in terms Gf the relative velocity
of the store with respect to the aircraft and a(.celeration that acts on
the store at tie instart of release. This a:celeration includes gravity,
in the appropriate direction, the aerodynamic forces divided by the
weight and the aerodynami: nmoents divided by the inertia. Further,
v• locity-acceleration planc contain limit lines determined by each
individual geometry. On the vertical plane one limit line corresponds
:o the requirement tbac the store fall one radius in a certain time
(1/4 second seems adequate). On the lateral plane the line implies the
store must fall the distance necessary to clear the adjacent stcre while
moving laterally the distance necessary to strike it.

The proposed criteria have the advantage that the information

required to define safe-separation limits is the same as that required
to establish air loads and stresses. Hence, no new information is
needed to use the three planes (including axial) ti determine safe-
separation requirements.

The proposed velocity-acceleration diagrams contain a great deal of

information in an extremely compact way. This is a great advantage over
existing schemes. Consider for example the flight characteristics of
an airplane as conventionally represented on a diagram in terms of
altitude (h), Mach number (r), and load factor, as shown in the sketches
that follow--that is, steady flight. This chart may be generalized to
incorporate lines of constant a2/g. This constant is the minimum value
associated with the value of AI!Vl`=. However, this value of A2 /g
involves the dive angle, so an h,M,n diagram. tust be constructed for
each value of n, and roll angle *. A similar curve must be constructed
for each value of 4 at n = 1. Hence, a number of plots must be generated
for the 0, 0 combinations, and this number is increased by virtue of the
number of different load factors.

A similar profusion of charts can be found for the lateral motion.

Thus, it i. difficult to avoid the conclusion that the dimensionless
parameters Al/v 2 rmaxg, A2/g, etc., represent an efficient way to present
safe-separation boundaries.

49
NWC T1699S5
9

FLIGHT

I._____________________________________
50U

m!

I 5
 NWC TP 4995

On the basis of the reaults contained in this report it is recom-

oended that operational e.thods (sw."h as a strain gauge balance in the
rack) of measuring &trloads in flight be developed. Such data would be
of great value in determining detailed correlation. Actua! experience
of this kind in conjunction rith the Al, A2, etc., planes is also
Simportant in determining the sensitivity of store release characteristics
t z-. -: -.•_.-.4%ns in store, rack, and Rircraft geometry and per-
formance. In thi ,iy, itandards for quality control can be determined.

51
AWC TP 4995

Appendix
SOW. MATHEMATICAL DETAILS

GOVERNING EQUATIONS

The governing equations are written in terms cf a pseudo-vector

V Vxi + Vvj + V2k + wxi + atwvj + Wz)k (pseudo-vector)

V Vx+ Vyj + Vzk (linear velocity)

If- wi + Wyj + +7 (angular velocity)

f V(W denotes the velocity at t - t, V(t + 6t) denotes the velocity

at t - t + 6t.

Thus

V(t + 60 vWt + T 6lt

-t

dV
To calculate we may use Newton's second law of motion--

For translation:

dVF
F M -'- ( )E" earth's axes

F ,M + x + (gravity term)
dt

d
dr M- x + (gravity term)

52
 NWC TP 4995

The aerodynamic forces on the body coordinate system are:

Fx- -D co0 c+ S sin 8+ L sin a+ ... g)

Fy- S cos 8+ ... (g)

Fz -- D sin a- L cos a++ ... )

For rot•tion:

d%

dt

where

HE T'24x + Iw + Izwzk *(angular momentum)

dHE dI " dw d'

"-4~ 1~
X + di

dd - dw
wf d
+ Ydt YYd
dI dd
+ kw-z + kIy + Iz k
dtdt
ddi I•. d
X-

dt . x -

dk
dt -W - JWX

Body axes are principal inertial axes.

53
14WC
TP 6995

therefore
dE-
E d- x -+ yw(I - y)
dt ~dt +Ix t1 + I l

,~ rw dI dw
Zjz+I- Zdt+ (Iy --

After some arrangements and simlifications

dv [Htrix A Matrix B
M
dt+

" ,• v_, AS "'t A V%

- N ---
i 0 0 0Wa

-- B 0 0 I 0 Y

,• .. I •-
Ix VV I

N.,ýr !2-_V i ico. a • ) 0

oX o
vX I

LP V VX N0 . 0 a 0 0 0
54 A V V HV A,

1~ Y%

54
I
NWC TP 4995

-where

MZX a sin V Bn * - cos ' sin e cos

Mzy - cos sin + sin sin 8 cos

Mzz -"cos e coe

1
AXD - CD i PS
1
A~sinCS
PS
1
AxL - CL 2 PS

Ay CS 1 PS

AzD - CD PpS
2
AZL - CL 1 PS

where CD is drag coefficient

CS is side force coefficient

CL is lift coefficient

and

()x denotes X axis on the body

( )y denotes Y axis on the body

(.)z denotes Z axis on the body

1

1
Mq - Cm . ps AL
1
Nr - Cn 1 pS AL

where

CL - moment coefficient in roll

Cm - moment coefficient in pitch
Cn- moment coefficient in yaw
AL - length of a store
BL width of a store
[AL - BL for a sphere]

55
NWC TP 4995

EQUATIONS FOR THE EULER ANGLES

The Euler angles *, 0, andA *, developed in the convencioual order

shown in Fig. 11 are presented here as functions of the store.angular
rates wK, w•,, wz (Fig. 12). The relations between 0, e, and * in the
earth coordinate system and ujx w and wz in the store coerdinate
system are
-x w= + tan 0 sin t wy + tan 8 cos wz

0 - cos
C - wz sin

a A + • cos0

:
In matrix form

1 tan 8sir. tan 0 cos ]" 0x1

- 0 Co -sin (*½x

cosO cosz

Therefore, the equations for the Euler angles in terms ol x,

WY , and wz
are

6- + dt
0
0- + St

where ý0, eo, and ýo are the initial conditions for roll, loitch, and
yaw, respectively.

56
 NWC TP 4995

S•E

)Yaw

XE[,21

,X2

(2) Pitch 6 X1

Y1. Y2

z2

zE
z1

x• x

(3) Roll

ZZ

FIG. 11. Euler Angles.

57
NWC TP 4995
r
K1

c-c-!

FIG. 12. Store Coordinate System

58
 __.C TP 4995

REFERENCES

1. Black, R. L. High Speed Store Separation-CorreZationBetween Wing

Tunnel and Flight Test Data. AIAA, No. 68-361.

2. Reed, James, Curry, and Warren. "Comparison Between Transonic Wing

Tunnel and Full Scale Store Separation Characteristics." J AIRCRAFT,
Vol. 6, No. 3, pp. 281-283, May 1969.

3. Arnold Engineering Development Center. Separation Characteristics

of the Tactical Fighter Dispenser from the F-4C Aircraft at Mach
Numbers from 0.50 to 1.22, by L. L. Galigher. Arnold Air Force
Station, Tann., AEDC, July 1969. (AEDC Report TR-69-130.)

4. Covert, E. E. "Wind Tunnel Simulation of Store Jettison." J AIRCRAFT,

Vol. 4, No. 1, p. 48, 1967.

5. McDonnell-Douglas Corporation, St. Louis. "Store Separation from

the McDonnell-"ouglas F-4 Aircraft," by D. L. Schoch. (Paper No. 42
at 8th Nai, S). >osium on Aeroballistics, 8 May 1969, Corona, Calif.)

6. Naval Weapons Laboratory. Some Aspects of the Aircraft Store

Separation Problem, by D. A. Jones, III. Dahlgren, Va., NWL,
September 1968. (14WL Tech. Report TR-2206.)

7. Unger, G. "A Linear Analysis of Aircraft-Store Motion." M. S.

Thesis, Massachusetts Institute of Technology, Department of Aero-
nautics and Astronautics, September 1969.

8. Vought Aircraft Division, Dallas, Texas. "External Stores Air

LonLo Prediction," by R. D. Gallagher and P. E. Brown(;. (Paper
No. 45 at 8th Navy Symposium on Aeroballistics, 8 May 1969,
Ccrona, Calif.)

9. Naval Weapons Center, China Lake, Calif. "Problem of Store

Separation at the Naval Weapons Center," by J. V. Netzer. (Paper
No. 47 at 8th Navy Symposium on Aeroballistics, 8 May 1969, Corona,
Calif.)

10. Air Force Flight Dynamics Laboratory. kethods of Calculating Aero-

dynamic Loads on Structure: Fart I Wing-Body interference Effects,
by C. J. Borland. Wright-Patterson Air Force Base, Ohio, AFFDL.
(AFFDL-TR-66-37, Part I.)

11. Alford, W. J., Jr. Theoretical and Exper~imental Investigation of

the Subsonic Flow Fields Beneath Swept and Unswept Wings oith
Tables of Vortex-Induced Velocities. (NACA Report 1327, 1957.)

59
NWC TP 4995

12. General Dyramics, Convair Division. Prediction of Stores Separa-

tio;: ýTý.zacterin tics for Internally Stowed Weapons, by R. D. Small
and G. F. Campbell. San Diego, Calif., GDC,SD.

13. General Dynamics, Pomona Division. "Effects of Launch Conditions

and Missile Parameters on Air-Launch Trajectories," by B. M.
Niemeier. (Submitted to the Aircraft Stores Compatibility
Symposium, Eglin Air Force Base, Fla., 19-21 November 1969.)

14. "A Method for Predicting Interference Forces and Moments

on Aircraft Stores at Subsonic Speeds," by F. D. Fernandes.
(Submi:ted to the Aircraft Stores Compatibility Symposium, Zglin
Air Focce Base, Fla., 19-21 November 1969.)

60
3 Grumman Aerospace Corporation, Dethpage, New York
F-14 Project Aero. Group
C. J. Dragow, tz (1)
John Clark (1)
Technical Library (i)
1 G. V. R. Rao and Associates, Sherman Oaks
1 Honeywell, Inc., Ordnance Division, Hopkins, Minn. (rechnical Library)
1 Hughes Aircraft Company, Culver City, Calif. (Research and Development
Library)
1 Jet Propulsion Laboratory, CIT, Pasadena (Tecnnical Library)
3 Ling-Temco-Vought, Inc., Vought Aeronautics Division, Dallas
Deane B. Schoelerman (1)
P. E. Browne (1)
Technical Library (1)
1 Lockheed-California Company, Burbank (Technical Library)
3 McDonnell Douglas Aircraft Corporation, St. Louis
David L. Schock (1)
Steve J. Jendras (1)
Technical Library (1)
1 McDonnell Douglas Corporation, Long Beach (Technical Library)
1 McDonnell Dcuglas Corporation, Santa Monica (Technical Library)
2 Massachusetts Institute of Technology, Cambridge
Eugene E. Covert (1)
Aerophysic3 Laboratory (1)
1 Nielsen Engineering & Research, Incorporated, Mountain View, Calif.
3 North American Rock%-ell Corporation, Columbus, Ohio
Dave Reitz (1)
K. 0. Smith (1)
Technical Library (1)
1 North American Rockwell Corporation, Los Angeles (Technical Library)
i Northrop Corporation, Norair Division, Hawthorne, Calif.
(Technical Library)
1 Sandia Corporation, Albuquerque
2 The Boeing Company, Seattle
Military Aircraft Systems Division (1)
Technical Library (1)
1 The Boeing Company, Airplane Division, Wichita Branch (Technical
Library)
2 The Boeing Company, Vetrol Division, Morton, Pa.
Joe Zala (1)
Technical Litrary (1)
1 The Martin Company, Orlando, Fla. (.. Gonzalez)
1.The Rand Corporation, Santa Monica, Calif. (Aero-Astronautics Department)
1 University of Pennsylvania, Institute for Cooperative Research, Eglin
Air Force Base (Reference Center Library)

NWC 1424 (7'71) 175 C