NATIONAL AERONAUTICS AND SPACE ADMINISTRATION TECHNICAL NOTE D-325 AN ANALYTICAL METHOD FOR STUDYING THE LATERAL MOTION OF ATMOSPHERE ENTRY VEHICLES

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP71B00265R000200130003-2
• Release Decision: RIFPUB
• Original Classification: K
• Document Page Count: 19
• Document Creation Date: December 23, 2016
• Document Release Date: November 21, 2013
• Sequence Number: 3
• Publication Date: September 1, 1960
• Content Type: MISC

I TT
Declassified and Approved For Release 2013/11/21 : CIA-RDP71600265R000200130003-2
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
TECHNICAL NOTE D-325
AN ANALYTICAL METHOD FOR STUDYING THE LATERAL
MOTION OF ATMOSPHERE ENTRY VEHICLES
By Robert E. Slye
SUMMARY
An analytical method for studying the lateral motion of entry vehicles
is presented. The method is applicable for small entry angles and results
obtained with the method are compared with results from numerical integra-
tion of the complete equations of motion. The method is found useful for
studying maneuvers of vehicles'with aerodynamic lift-drag ratios up to
about 1.5. Thus, the method should be useful for vehicles of current
practical interest. It is found that bank angles of about 45? are
sufficient to utilize the near maximum lateral-range potential of a
vehicle without overly penalizing entry heating effects.
kid
INTRODUCTION
Many authors have investigated the motion and heating of vehicles
entering the earth's atmosphere (see, e.g., refs. 1, 2, 3). In these
investigations, the effects of vehicle aerodynamic and mass characteris-
tics
?
tics on entry heating, deceleration, and range have been studied, and
several convenient 'and useful simplified methods for analyzing entry tra-
jectories have been developed. Primarily, attention has been devoted to
the trajectories of entry vehicles which do not maneuver laterally. How-
ever, for the purposes of recovery or landing of the entry vehicle at a
specified point on the earth's surface, the vehicle should be able to
maneuver laterally. In fact, the lateral range of a vehicle during entry
may be as important as the longitudinal range. The objective of the
present paper is to develop approximate analytical methods which are
useful for studying the lateral motion of entry vehicles.
SYMBOLS
vehicle reference area
bo' CD drag coefficient
drag
1 '
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2
resultant deceleration in g' s
local acceleration of gravity
total heat
vertical componentof lift
lateral displacement
mass of vehicle
distance from the center of the earth
ro radius of the earth
distance along the flight path
time
velocity
Vs local circular satellite velocity
normalized velocity, v'Til
longitudinal displacement
side force
vehicle lift-drag ratio in an unbanked attitude
0 logarithmic rate of decay of density with altitude
7 flight-path angle with respect to local horizontal
side-force parameter
air density
On function defined by equation (l4)
roll angle
lateral deflection angle
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A
3
7
9
0
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3
Subscripts
entry conditions
conditions at initiation of maneuver
ANALYSIS
Equations of Motion
A The equations of motion for a lifting vehicle in unpowered flight
3 are given as
7
9
cfr ..,-diflic : (WI fr mV -- = -D - mg sin y
dV Op -
AC1+ if ii 45 ? ds
H:-.4*-: 0 "PIS = Vdr = ell mV2 Ili = L
ds i (2)
- m cos 7 g - 15)
\ r
mv2 dir = y (3)
ds
In this coordinate system, the drag, D, is opposite in direction to the
instantaneous velocity, the lift, L, lies in the plane containing the
center of the earth, and the side force, Y, is normal to L and D. If
the side force, Y, is developed by banking the lifting vehicle, then for
a vehicle which develops a constant aerodynamic lift-drag ratio of (L/D)0
and for a bank angle T we have
L = (I
cos p
\j510
Y
= \D) (I ? sin T
D o
In general, solution of the above set of equations involves numerical
methods. For trajectories suitable for the entry of manned vehicles,
that is, trajectories which tend to minimize decelerations and heating
rates, the flight path angle, 7, must be restricted to moderate values.
.Thus, the usual approximations made to simplify the above equations are
1mg sin 71