THE THEORY OF FORCED GYROSCOPIC HORIZONS

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP82-00039R000100020071-1
• Release Decision: RIPPUB
• Original Classification: C
• Document Page Count: 8
• Document Creation Date: December 22, 2016
• Document Release Date: April 6, 2012
• Sequence Number: 71
• Publication Date: November 3, 1948
• Content Type: REPORT

THE THEO T r.F FCRCED GYROSCOPIC HORIZ2
-'~. . of Sci. U~Sn
B. V. Bulga]-.ov and Ya. N. Roytenberg
The 'Principle of .Forcwd G~;rosdopic Stabilisation
In designing ~rroscope supports and general construction, one
employs two different principles to t ake off readings frog gyros-
copic apparatus and stabilizers. The first of these principles
consists of the maximurm "load-relieving" of the grroacopic sensitive
element from the disturbi71g forces which may have caused the element's
declination from the noeit~lon to be maintained. To do this, one
employe various, often rather intricate anti-frictional devices and
the readings 'e taken off from the minimum mechanical load of the
sensitive element. Both problems are often solved with the help
of a tracking system, which reproduces all the sensitive element's
movements relative to the ship or airplane in which the apparatus
h onsists in the fact that
Is net up. One of the difficulties ere c
the errors in the sensitive element are accumulated along with
the errors in the tracking system and the high stability of-gsrroa.-
. 1
copic system cannot be fully utilized.
Declassified
The other principle may be called the principle of forced
stabilizers and consists of employing a "load-relieving" servomotor
or electromagnets which contribute forces that compensate for the
frictional forces in the supports and the slow reaction of the
apparatus in transmitting the readings. In order to control
or regulate automatically the "load-relieving" of the appare~tus;
small reiat::ve movements are utilized in the system of the gtia-
scopic eenaitive. element, which movements beingoauaed by the
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disturbing forces. Suring the ovmcnts, =^reo!er, groaconic momenta
arise which react againat the disturbing force and govern the stabili-
zation at the firat moment eo long as the "load-relieving" apparatus
ie not operating. In this oase there is no need, either for the
tr 4ng system or for a super delicate designing of the external
A
supports of the;eenaitive element, and the readings can be ken
immediately with it. Here the frame of the gyrosoopie
sjeitive element assumes at the same ti:'e the role of the
tracking system.
J
An example of a forced stabilizer'to the well known gyroscopiv
"1.odometer", the description of which is in E. ? Sperry'a book 25,7.
The book also shows that with the aid of two such Sperry stabilizers
it iN possible to obtain an artificial horizon; that is, a plat-
form able to be maintained in a pneition close to the
horizontal.
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The $quationa of Notion of a lbrced Qyroecopic Horizon
seible achemea ie preeented in the flat diagr8Jfl1fl'tie
Oae of the po
\ I tehf a h. Y axis of the Cardan wheel ie directed along the
1ongitudineS axia of the ship. The atabilizanle platform a efl be
e.
rotated .relative to the wheel around the second Cardan
The anglee of rotation around these axea are denoted by alpha fiL,
and beta and are assumed to be small. S, and Sy are the "load-
relieving" motors. The plane of the true coordinate system
' `rhich is connected with the ship, is assumed to be horiZOnta1.
7 ~.~
The xy plane of the second coordinate system xyz is the plane of the
platform. The housings of the four gyroscopea,of nature].
moments Hx, H'x, Hy, H'7, can 'rotate relative to the platform
that the nixes - ? of
around the perpendiculars to their axes,
rotation of the gyroscope remain in the xy plane. S~.nce the housings
are joined in paire as antiparallelograma, then for small angles
r
of preceseion' O Of the firet two ~-roecopee we hav?
.?-~";~ ~alogouely for the other
approximatoly the relations ?
The arrows Hx and B. in the
two gyroscopes we have ' "~ :-?~
diagram represent also the slide runners of the potentiometers,
which control the "load-relieving" motors. The moments, tress
where
ferable by the motors to the Cardan axes, are Sx-7 3y d
S_ and Sy are considered constant. ,In order to create theiegulating
forces, the horizontal pendulums KX and Kyy are employed, which regulate
the motors E and Fy placed on the preceaaional axes of the
c
gyroscopes. Dosing azy movement of the ship of constant velocity $
with respect to the ship course, making a conetant angle with
the direction of the north, the inclin~itiona of tho pendulums are
? and p 8 of the weight g of tho.
na
ti
pendulumebob:UPon the axee'3
proportional to the prolec o
p
 CONFIDENTIAL
ship's trajectory has a radius of curvature p , then the pendulums
are acted upon by other forcee; namely, the forces of inertia
pv2/gpv/g. Therefore the moments generated by the regulating
~'s-
d K
.
), Kx
motors are Kx f ~? M and ~- (1(~ ~' where an
l
it
oc
are eeumed to be constant and So the angular e
ion (ehiP's turning on the arc of radiua ).
of circulation
As for the equations of motion, it is possible to connect
the equations of moments relative to the x, axes for the whole .
system and the equations of moments relative o the whole preceSsion
and
for the g,rroscopic pairs Hx, H'y'
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Designating by ~he angular velocity of the Earth's rotation,
Here A, B are the moments of inertia of the whole system
'S
relative to the x, v axes and the inertial tarTC o o z_
C2 C in the two letter equations are disregarded, in as much ass
the corresponding masses are not largesf, l y, P l' f2
are the gyroscopic moments, whose expressions may be obtained
from the formulas (2.10) in the article by Ta. N. Roytenberg j?7.
by pthe Eerth'e radius, by ' the latitude of the place;
taking, into consideration the various dietinatione in the remaining
designations; end aeeuming that Hx = H'x, Hy B'y then we shall
find than
Substituting in the equations of motion and disregarding the
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Hence it iseen that, if a ship moves with constant velocity iI V
with respect to a oonetart course (v s const, (? conet, v s (,,i s 0),
then the coordinatesCary aperiodica.ly and tend to a
constant limiting value *, *, 0, 0 where:
These quantities are velocity deviations; they are small if K,,
K ire sufficiently large. For v 0 and 0 the apparatus
receives several ballistic deviations which can be studied bgnusual
methods 5].
i
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multiplying by 1 and i and then addixg:
We ere then led to a new unknown:
where the quantity
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(ONFLDENIIAL
The Posaibiiity oP Cvtaining a $4?Minute Period and of ComPenaating
for b Ballistic Deviations
Vie eha11 modify the preceding echeme by uniting the penditm Kx
Li,,, H:y and the pendulw K with the gyroacopia
with the gyroecoPis
BY. H' Y. Egnatione (1) are not modified, but in equatioae (2)
the expressions Ex(~ c- and y( L ' V will, vary elightly
~
in places whexe we perform " onnectione" in such a manner that
the second expression has the minus sign. Aeauming that:
we obtain instead of (R):
or setting:
.,;
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(O'' ~AL
1+.nce we obtain the f ollowirg transformation equations
(ii) Z g L
r
If we select the parametere such that k . JP , then
the equation becomes homogeneous; thin indicates that the apparatus
in this case does not poeeess ballietic deviations. Thus} for
the given system compensation is poesible according to M. 3hu1err
since the system acts during compeneation,as a gyroscopic pendulum
with a period of preceeeions
It does not present any difficulties to provide for ~unpening
of the free procession. In order to do this it is neceeeary
to combine both of the dieeuased variante of the system by joining
each of the pendul'Ze with both gyroscoPio pairs and by selecttt;g
in a suitable manner the transmission ratios of signals.
LITTRATURR
/1.1 R. Sperry. Applied t?Todynamics,. New York. PP 125-128 , 1933.
2. Ta. N. Roytenburg. Polyoscopic Vertical. Applied Math.
i
& Mech. Y No. 1~ 1946?
3. B. V., Bu1gakov. Applied Theory of Gyrroecopes. V.-L. 1939.
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