(SANITIZED)TECHNICAL TRANSLATION OF UNCLASSIFIED SOVIET PAPER(SANITIZED)

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• Document Creation Date: December 22, 2016
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GYROSCOPE
AND SOME OF ITS TECHNICAL APPLICATIONS
GOSTEKhIZDAT, 1947
STATE PUBLISHING HOUSE
FOR TECHNICAL AND THEORETICAL LITERATURE
i
Moecow 1947 Leningr,d
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Section 1. The Rapidly Spinning Top and Its Utilisation in Technology.$ .,,1
Section 2. The Gyroscope in Cardanic Suspension. Stability of the
Axis of a 1~alanced Gyro Imparted to It by Rapid Rotation
of the Gyro .....................................................3
Section 3. Stability of Rapid Rectilinear notion. Jets Issuing Under
High Pressure. The Law o Inertia. Newton's Second Law of
Motion. .....................o ...................................f
Section 4. Inadequate Explanation of the Stability of a Rapidly Rota-
ting Gyro. Degrees of Freedom of a Gyro.
Loss of Stabil-
ity by a Rapidly Rotating Gyro with Less Degrees ccf Free-
dom ............................................................. 10
Section 5. Action of Forces Applied to the maxis of a Rapidly Rota-
ting Gyro,.... ..................................................12
Section 6, the Rule of Precession. . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . a . . . .21
Section 7. Stability of a Rapidly Rotating Astatic Gyro with Three
Degrees of Freedom,... .................. .24
..Section 8. Nutational Oscillations of the Gyr, -x s ...............
Section 9, Instability of a Gyro with Two iiegrees of Freedom ...............29
Section 10 ; Precession of a Gyro Due to a Continuously Kcting Force
Applied to its Axis.............................................31
Section U. Gyro with Three Degrees o Free doel on a Rotating l$se.
The Foucault Gyro. Experimental Proof of the E,rth's
4 _ Intro.duct3.Qr1.................... a ...............~u ............... - .
-4
3 C Chapter I. PROPERTIES IMPARTED TO A BODY HY Rr'PID ROTATION
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Section 1_Gyro with Two. Degrees ot.reedom on a Ro-tating_Base-.._..
.................................... 38
Foucault~s Rule
1..
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Chapter II. SOME OF THE SIMPLEST APPLICATION3 OF THE GYROSCOPE
Section 14. The Obry Gyroscopic steering Device 52
i
Section 15. Gyro Indicator of Longitudinal Tilt of an Aircraft
and of Deviations From its Course...,......,................... 58
Section lb. The Gyroscopic Semi-Compass .................................... e1
Section 17. Design Features and Operation Details of the Gyro-
0
_ scopic Semi-Compass............................................ 65
n~
Section 18. Aircraft Turn Indicator..' ...................................... 70
Section 19. TheGyroscop 74
_.~ a t;onorail Car .....................................
Section 20. Stability of a notating Projectile in Flight................... 81
Chapter III. TES GYRO COMPASS
Section 21. Foucault's Original Concept.................................... 88
Section 22. Rotation of the Plane of the Horizon About the
Section 23. The Sperry Gyro Compass with Pendulum .......................... 98
- Section 24. Inclination of the Axis of a Gyro Compass in its
4D
Equilibrium Position. . . . . . . ? ? . ? ? . a ? a a a a ? . a a a a a a a a ? . ? . ? . ? . . . . . . 103!
?__
Section 25. Undamped Oscillations of the Axis of the Sperry
ay=. Gyro Compass. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1051
46_i
Section 26. Eccentric Coupling of the Pendulum with the i
SO.J Gyro Chamber. . . . . . . . . . . . . . . . . . .. . .. . . . . . . . . . . . . . a ? . ? ? a ? ? ? ? ? . . 109!
--~ Section 27. Deviations of the Gyro Co pass true to the Eccentric
S2-4
Coupling of the Pendulum with the Gyro Chamber, or
whiwTi iiwYiv fl,er4 . i A.........-.--..-...----..........-.../.. ll~
Section 13. Derivation of the Formula for the Gyroscopic Moment............ 41
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I
26, tamping of the 0scil1atio s of the Gyro .Compas5..
Axis, The to Eccent'^ic Coupling of the Pendulum
.... _._ _._ . .__ ._.._......~.__..... _ _.__ _. _ _..... ______~..~___._.~..._...
with the Gyro Chamber. ...j ...................................... 117
i
Section 24.
Course Deviation of the Gyro Compass ........................... 118
Section 30. The Ballistic Deviation o' the Gyro Compass.
The Schuler Condition. ...i ...................................... 124
Section 31. The Sperry Gyro Compass with T1ercury Reservoirs..........,..... 127
THE GYRO HORIZON AND GYRO VERTICAL
2. The Gyro Pendulum. .......I
133
Section 33. The Fleuriais Marine Gyro]Horizon .............................. 138
Section 3;, The Pendulum Aircraft Course Corrector..,.....,..:........., 140
Section 35, fhe Sperry Aircraft Gyro Horizon ............................... 143
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The properties imparted to a body by its rapid rotation (to which it has been j
16_
_customary to apply the term gyroscopic properties since the time of Foucault, who
18_
--constructed an instrument that he called a gyroscope) are becoming ever more widely
2O
used today in various fields of technology. In this book, the properties of the
22
-$yroscope will be explained in a manner within the reach of all, and on the basis of
nt
c .
-this explanation a brief elementary theory of a few of the most important applica-
N` i ~
-;bons of the gyroscope will be presented.
A fundamental study of gyroscope theory requires an acquaintance with higher
-mathematics and with theoretical mechanics (although only to the extent included in
,-the programs of the higher technical schools). Our scientific textbook literature
includes excellent manuals, some of them giving a detailed exposition of gyro theory
3(I might mention the excellent book by the late Academician A.N.Krylov "Obshchaya
teoriya giroskopov i nekotrykh tekhn. 11h primeneniy(General Theory of the Gyro-
4Q~
sco and Some of Its Technical Applications) 2nd edition, 1936). In compiling the
A)
[resent booklet, however, the author set himself a different task; to provide brief
f6~tformation on the properties of the gyroscope for readers unacquainted with either
-1
, [igher mathematics or theoretical mechanics, but with a certain amount of experience:
production, desiring to understand the mechanism of action of what are known as
scopic instruments, in which the propezties of a rapidly rotating gyro find ap-
ication.
The reading of the main text of this book (in large print) will occasion no
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II
_liifficulty for readers acquainted with the elementary mathetics and elementary
2 ~
_... 1.Q .aas taught in the. middle schools from which they graduated, while_.te...suppla
4aentarymateriai (in small print) may be useful reading for students with more ex-
tersive preparation (being familiar with trigonometry).
8
'
i
--~
The author hopes that this book will be useful in the hands of mechanics work- I
1
Lag in gyroscopic instrument building, and also of a wide group of readers interest-
2
ed in mechanical problems. Those wishing to go more deeply into the study of gyro-
1
_scope theory will find more extensive material in the above-mentioned book by Krylov.':
6
.
Section 20 of this book, "Stability of a Rotating Proje:ti1&' was gone over in
18._
banuscript by Prof. L.G.Loytsinskiy, to whom I e: ress deep gratitude for his vale-
20.
,ble suggestions. I am likewise deeply grateful to V.K.Golttszaan, who carefully read
22J
4hrough the entire manuscript and made a number of valuable suggestions.
r J' Ye.Nikolai
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PROPERTIES IMPARTED TO A FO DY BY RAPID ROTATION
Section 1. The Rapidly Spinning Tom and its Utilization in Technology
it placed in rapid rotation than
^ it comes to life and acquires re-
- properties. Who has not
7 felt satisfaction in watching a
rapidly spinning top maintain its
equilibrium, balancing at the tip
- of its spindle, and watching how
it quietly continues to spin, pre
Fig,l cisely supported by some invisible
crce (,.ig._)?
The surprising stability imparted to a top by rapid rotation has long attracted
the a~tention of inquiring minds. About 200 years ago an attempt was made in the
Who has not played with a top as a child? So long as its young owner has not
placed it in rapid rotation, the top lies lifeless and motionless. But no sooner is
British Navy to utilize this property of a rapidly spinning top to provide a stable
-artificial horizon" on shipboard, capable of replacing, in fog, the visible horizon
i~eguired by the mariner for his astronomical observations. The shipwreck of the fri -
"Ytetcry"; ~a whictrt is-instrument eras being tested (the inventor of the n rtX
S( _ a...__.._ - _._- .. _ .
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tidal horizon", Serson, was lost in this disaster) put an end to this attempt.
During the next century no new attempts at a practical utilization of the-spin-
ning top were made. ~', new impetus in this direction was given by the famous experi-
ments of Foucault, reported to the Paris Academy of Sciences in 1852. Among other r
a
experiments, Foucault demonstrated the instrument constructed by him, called a "gyro
{
'scope", whose primary component consisted of a rapidly rotating rotor (top) and whici,
for the first time, provided a direct laboigtory demonstration of the diurnal rota-
tion of the earth. The term "gyroscope" (in literal translation, "instrument exhib-
iting rotation") has been maintained in the scientific world. Today this term is
used, in the broadest sense, to denote any instrument in which the peculiar proper-
ties of a body in rapid rotation are utilized; these properties are commonly called
gyroscopic properties.
. In the same famous report of 1852, Foucault showed that it was possible (at least
theoretically) to construct a gyroscopic instrument to determine the position of the.
meridian (North-South direction) at a given place. Thus was expressed, for the first
time, the idea of a mechanical (nonmagnetic) compass, constructed on the principle of
the gyroscope, and capable of completely replacing the magnetic compass. The :rob-
lem of replacing the magnetic compass by a mechanical one had become particularly ur-
gent with the appearance of large masses of iron on board warships, and in connection
- with the increasing complexity of the electric equixneni, of these ships, which inter-
fered with operation of the magnetic compass en them. However, there ',ere immense
difficulties in the way of any realization of Foucault's idea; these were surmounted
only fifty years later, at the threshold of the present Century. The exceptional
Hprogress in technology made it possible for highly developed gyro cr.mpasses to a p-
51}Hpear at the beginning of the Twentieth Century, to attain general recognition, and
.,~ tiidespread use in the navies of the whole world.
54 J_._ Today gyroscopic instruments are gaining ever increasing importance in various
_ '
-y - naval~.p+ t"chn^1Cg is > > cqui ,. ppa p with ~ jt ^ a oago numb
G ields of technology. ..
5 ~-- _ -_ 'iSL"v4i a-.d .,,...q,t;r
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of instruments based on the gyroscope pririciple. The gyroscope has found particular
`ly_widespread use in aviation. Confident blind flying in the absence. of. visible
;landmarks, and prolonged distance flights for many hours, without landing, have be~
;come possible, owing to the large number of gyroscopic aviation instruments with
which modern aircraft is equipped.
Who has not mused, in childhood years and perhaps even at a more mature age, on
the question of the cause of the surprising behavior of a rapidly spinning top?
What is the explanation of the remarkable phenomena observed during the rapid rota-
tion of bodies, phenomena to which we give the collective term of gyroscopic phenome-
na? In this book we will try to answer these cuestions. We will also show how gyro,
scopic phenomena have been utilized for various purposes in modern gyroscopic instru-
ments and installations.
Section 2. The Gyroscope in Cardanic Suspension. Stability of the
Axis of a Balanced Gyro Imparted to it by Rapid Potation
of the Gyro
Before beginning our explanation, let us sc.;; u few words on she simplest gyro-
scopic instrument, the gyroscope in a Cardanic suspension, which is the most impor-
tant component of most of the existing gyroscopic devices.
The rotor or top P is suspended in two rings A and B, constituting the Cardanic
suspension (Fig. 2). The outer ring of the suspension A rotates freely about its
vertical diameter ab, which is held in a fixed position. The inner ring B rotates
--about the horizontal diameter cd of the outer ring ~, This inner ring bears the axis
--of rotation of the rotor P, which axis is perpendicular to the axis of rotation cd
- of the inner ring B. 'Thus, this devic, comprises tf,ree axes of rotation which inter-
4ect each other at one point 0: 1) the axis of rotation ab of the outer ring of the
? ',
suspension; 2) the axis of rotation cd of the firmer ring, 3)the axisofrotation_-..
t
.~ AP the ayroscone rotor. The rotation of the rotor xyroacope P about the axis of
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..his customarily termed the proper rotation of the gyroscope
!rotations of the outer
tor, and it is for this reason that it is termed free or, sometimes, astatic. This
- readily indicates that the equilibrium of the gyro in any of its positions must be
- considered neutral' and a light tap on one of the gimbal rings is sufficient to
bring the instrument out of its assigned position, to which it will not return, but
Translators note: In U.S, terminology, this would be a 'tfre&t gyro.
Commercial models of gyroscopes in Cardanic suspension satisfy this condition
with sufficient accuracy.
* Stable,u-stabla and neutral equilibria are distinguished. A ball on a concave spher-
ical surface (Fig.3a) is in stable equilibri'.um. Conversely, its equilibrium
on a convex spherical surface (Fig.3b) is unstable. A sphere on a horizont i
plane (Fig.3c) is in neutral equilibrium.
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 ition#. The gyroscope has no stability at all while its rotor is not in, rapid rota
.i
.._iexecuting a iaore or less marked deviationy will remain in some new epuilibrium post
The
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situation changes completely if we first impart a rapid natural rotation to
rotor of the gyroscope (by means of a thread or string wound around its axis).
now give the gyroscope any arbitrary position and then tap one of the gimbal
It can be felt immediately that, under the influence of the rapid rotation
rings.
the rotor,
4
the gyroscope has acquired the peculiar pro;lerty of energetically re-
- sisting the action of forces tending to chance the direction of its axis. Under the
action of the applied shock, the axis of the gyroscope (we mean the axis of the ro-
t)tlo
or does no markedy changr. its directin, and close observation will show only
,I
i?slight and very rapid vibrations of the axis (which are termed nutational oscilla-
~Jtions). This gives the impression that the rapid rotation of the rotor has impart-
.! ,
_ed to the whole instrument some rigidity, a certain resistance to the action of the
applied tap. We conclude that the rapid rotation of the rotor imparts a peculiar
stability to the axis of a balanced gyroscope.
To make this experimental result convincing, the rotor of the gyro must be given
_ as rapid a rotation as possibleH~.
52--~
The instrument, set in motion by a push, finally stops under the action of the
forces of friction that are unavoidahle in any inat-i.mert, If th ;rare :;c
friction in the instrument (and likewise no air resistance) then, if once set
motion by an impulse applied to one of the gimbal rings, the instrument would
continue its motion for an indefinitely long period.
For this purpose, a strong thread or etring is wound around the axis of the
rotor, pulling it first by its end, at a relatively slow speed and not very
.n.v i.IHa caqult, 4LI.1t7 DlJtltlU ~i'6Q{IZ111y~ LLIiI,1L I#IItl fisiJCUIIUW D(JB80 UI. MAlCI1
54
the hand is capable is reached
56.
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The faster this rotation, the more distinctly will the stability acquired by the
._..gyro axis .be manifested. ! ..-...-
It It must be borne in mind that there is one position of the gyro in which it
looses its property of stability on rapid rotation. This is the position when the
axis of the rotor o o '_
. .. col Ji the aiI'cra.f t. Lt.
U8 assume that the aircraft deviates from its course and the heading varies by the
"J_ l
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quantity (Fig. 42b). This would immediately be detectable from the corresponding
;rariatio:: in the angle -etween the gyro axis and the longitudinal axis of the air- a
craft. The pilot must deflect the rudder and return this angle between the axes of
of the aircraft to ite original salve y .I In this way the pilot could maintain th~
. .. . -.- _._______a. _ _l i 1. _ _ _ L ! _ 1 __...L.&
This would be the_ eihation i[ jh&.. srth.4id. noi....rotate. _Let:ue._nox ..detine_th
s
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To take the simplest case, let us putourselves into the position of the crew of
complication introduced by the diurnal rotation of the earth in the operation of they
instrument.
~I
tithe airplanes that left I.D.Papanin and his companions at the North Pole. At the
Fig. 43
of the meridian without change, the gyro must be
longer maintains a stable direction in space but
plane from right to left, rotating by 15? during
gether with the earth about the axt
is of rotation of the earth, which!
passes through the North and South`
Poles; they rotate from right to
left (counterclockwise), making
one revolution ?er day, During the
period of one hour, each meridian
rotates by 3600 = 15?. If the ax-
is of a gyroscope, installed on an
aircraft flying near the North
Pole, is to maintain the position
so arranged that the gyro axis no
rotates uniformly in a horizontal
the course of each hour.
.'e a 1 rep ^y that this ca.; be done, since the
nenoraenon of urecession of the
gyro, with which we are familiar, is involved here. To induce a precession of the
;gyro in the horizontal plane, it is sufficient to apply an aopropriate vertical
;force to the gyro axis. Let us attach a counterpoise weighing p grams to the inner
't J
ding, along the extension of the rotor axis and precisely at that end of the rotor
464
frow much the proper rotation of the rotor appears to be counterclockwise. Ac=
--~cordi .g to the above-described rule of
hat, under the action of the force p, the gyro will precess ma horizontal plane,
otatin counterclockwise, i.e., from right to left, about a vertical axis.
561
S~
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_The angular velocity of precession i3 expkessed by eq.(4 :
.1 w. , -~~
4__ i i
=Ef
Jwhere J is the moment of inertia of the r')tor, W the angular velocity of its prop
or rotation, and . the distance between the tlie point of application of the force p and
a_
the point of intersection of the Cardanic`axes. The instrument provides means for
_.
1 0
;varying the value of a. Obviously, the value of a can be so selected that the angu-~
jlar velocity of precession of the gyro will have the value we require, corresponding
_ I i
14
Fig.44
to the rotation of the gyro axis through 15? during the course of one hour. This op
o~^}inn n~+^}3?"tes the .# the ;nate:a.
- ~'e have considered the operation of the instrument in the region of the North
)
th ltitdith the single
----Pole. On the whole, the situation is the same at oeraues; w
-difference that, in the middle latitudes
vert1ca1 and turns, during one hour, not through l5 but through a smaller angle*.
# Thie question will be discussed further in Section 22. There it will be demon-
that, at all points of the earth'e surface except the poles, the plane of t
bouLthe-vertical but .leo-about--the.weridi,-...ThSs tart
- 54 fates-trot-onl~-a
4t ..the. rising and .aeti-af.oave~l~ bod3s
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.~ , of Leningrad,; the plane of the horizon rotates through
For example, at the latitude
Ikpproximately_13?. per. hour.. Of courss, tIe instrument must be so_ad3uet-ed to.thia___
f
Jangular velocity of precession that, at the latitude of Leningrad, the axis of the
_Jgyro maintains the direction of the meridian without change.
J This is the principle of action of the gyroscopic course indicator, also known
j
~o
_...!as gyroscopic semi-compass. Obviously, this instrument is not a co;apass in the full
;sense of the word. It cannot completely replace the conventional magnetic compass.
auto-
.Y. The g~rro axis in this instrument does not possess the power of aligning itself
tervention by the observer is required to align the grro axis with the meridian. An
a
."important property of the instrument is that it possesses the power of maintaining
--the direction of the meridian with great stability, once it is set. In this lies
i
-kits immense superiority to the ordinary compass.
Section 17. Design Features and Operation Details of the Gyroscopic Semi-Compass
- Having discussed the operating principle of the a^,rroscopic semi-compass, let us
now give a few details of its design and operation.
-- The instrument is mounted in a hermetically sealed body (box) which is attached
v- to the instrument panel in front of the pilot's seat in the aircraft cabin. The ax
,--is of rotation of the outer ring of the gyro is arranged vertically (both rings in
--our instrument are constructed in the form of rectangular frames which,of course,
t ~ I
riot a point of substantial importance). The pilot follows the apparent displace-
-tents of the instrument in the horizontal plane by observing, through a window in the
4~
11 of the body, the displacement of a horizontal graduated circle attached to the
. -outer ring of the inetrument (the outer framm), ma ~> of the {r trte"'t body (n
window)
of
he
-
o----
o the direction of the longitudinal axis of the aircraft. The divlaion of the. grad
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matically along the meridian as does the magnetic needle of a regular compass. In-
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cc is the course mark. 9
i
tational speed of the gyro rotor be main-'
7
tained for a long time. In the instru- }
f
went we are describing this is done in the
following way;
The air is continuously aspirated fror
the body of the instrument by means of a
Venturi tube, thus producing a pressure
differential within and without the body.
Under the action of this pressure differ-
ence, the outerair is drawn into the body
of the instrument through an opening in
the bottom of the body, and a jet cf air enters the channel a (Fig,46) cut into the
step bearing the outer ring b (outer frame). From there, the air jet enters the
I nozzle c, rich is rigidly connected with the outer frame b. The rim of the rotor d,
-.. w' e axi e is attached to the inner frame f, is n?'^V?aP(? The
air jet impinges with great force on these slots on issuing from the nozzle c; this
ensures uniform rotation of the yro rotor. The air pressure in the boy is brought
to 90 mm Hg; in this case the gyro rotor runs at about 12,000 rpm.
Figure 45 gives an external view of the instrument from the side facing the pilot;
M i a is a round window; the field b beyond the window is covered by an.opaque mask wi
a rectangular opening through which part of the graduated circle can be seen; and
f
ently, also the zero division of the card
H would give the direction of the true meridian, while the reading taken from the car
_I opposite of the course line gould directly determine the course of the ship, How-
Fig.78 Fig.79
northern 1:titudes) of the instrument axis and, consequently, also of the zero read
46 flings connected with the follow-up ring ofjthe card, by the angle x o. This intro-
duces an error into the course reading of the
50.E $ gyro compass. It is easy to show,
however, that this error will be compensated by rotating the course ring with the
5
54 course mark toward the east through the sme angle a b (Fig.79). Now the reading
56-jtaken on the card will again give the ehi~'e true course,
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In the Sperry gyro compass, a simple device was provided which permits without
Iany.prelimnary.calcui4tions a rotation off' the course ring through the_necessary.....__1
_1 angle (the so-called "mechanical correcting device"), in this way compensating the
error in the instrument readings due to to deviation caused by the "eccentric cou-
_4 piing".
Section 28, I roping of the Oscillations of the G
i
rro Corn
ss nxis, Die to Eccentric
Coupling of the Pendulum with the gyro Chamber,
Plane of
the horizon
hi1
t
di
e s
--
an
ng to the north
it. and lacing south (as in Section 25). We mark the position of the north end of
+b i
Below, we will discuss the process of damping the oscillations of the pro-com-
pass axis by using an "eccentric coupling" of a pendulum with a gyro chamber,
the gyro-compass axis on the drawing (Fig;80), on which the plane of the meridian
and the plane of the horizon are shown; tie east will be to our left and the west
our right, Let us mark, on this drawing, the equilibrium Position N of the north
end of .the gyro-compass axis; in this position, it is raised above the level of the
horizon by the angle a o and deviates from the plane of the meridian to the east b,
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Fig 80
viewing the instrument
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that the axis of the gyro co,apass is brought. out. ,oL.,it5._equilib,v
assume, e.g., that its north end is given an sdditional deviation
Let us now leave the instrument to itself. J1e already know (Section 2$) that is
there were no "eccentric coupling" of the pendulum with the gyro chamber of the in-
strument then there would be undamped oscillations of the instrument, in which the
north end of the instrument axis 'odd describe the elliptical path shown in Fig.80
by the broken line,
At the same time we also know (Section 26) that as a result of the "eccentric
coupling"
2iI the north end of the gyro-compass axis, being; raised above the ;Mane of
_ the horizon, is now given a tendenc to sink toward that plane. For this reason, i
the presence of "eccentric coupling", the north end of the gyro- crp? ss axis movin~
1
toward the west will describe, instead of the upper half of its elliptical path, th
lower arc ylAZ in Fig.8U, after which it gill commence its return motion toward the
- east. Detailed investigation (which we will not discuss here) shows that the suc-
cessive sweeps of the rro-compass
a
,
- gradually approach its equilibrium
3 b
axis will gradually diminish and that it will
i
positi?n N, where it will finally stop. The
-:north end of the gyrocompass axis, inste4.d of a closed elliptical path, will de-
3 ~__.1
-?scribe a spiral curve
This constitutes the process of dampijg the oscillations of the gyro-compass ax-i
Y~
i I
-4is due to the "eccentric coupling" of the pendulum with the , vrc chamber.
The gyro compass is designed for instdllation on seagoing ships. In the pre-
54 ceding sections we did not take into account the influence on the instrument read-
561inga exerted by the motions of the s}~p, ;1~ts compass is an instrument possess
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i ~
Section 29. Course Deviation of the Gyro Compass. I
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tivity must very markedly react to any ndtions of the ship on which it is installed'
ing extraordinary sensitivity; it is capable of responding to so slow a rotary mo-
tion of its base as the diurnal motion othe earth itself, This._is_preci~ly.w
the diurnal rotation of the earth imparts to the instrument the ability to t+emain 'I
the plane of the meridian. It is obvioud that an instrument possessing such sensi-
1
The errors in the gyro-compass re dings due to the motion of the ship on which it i
installed are termed its deviations.
ht first glance it may seem that there is one case of the motion of a ship ,chic
should not he acconpanied by any deviati;.ns of the gyro compass whatever; this is
the case of strict1rectilinear an
3' and uni-
form motion. This is true
/ IH
Fig. 81
meridian). However, it
linear motions on the earth's surface at
all. Indeed, this is a simple consequence
Af the spherical shape of the erth. Let
us assume that a ship is sailing strictly i
along the meridian in the direction from
youth to north (Fig.Sl). The motion of th
ship at a given instant appears to be tak-
ing place along the horizontal line na
is obvious that the true path of the ship moving
of the ocean is not thestraight line ns but an arc of a circle
radius equal .o the radius of the earth, whose center is located at the
Thus, any motion on the earth's
surface which appears to take place along a
horizontal straight line is,in fact ,a curvilinear motion.
56 relocity, its motion ie etill accompaniediby the appearance of a certain deviation
For this reason, even
in the case when the ship appears to be mbv
54~.-..._.,~ ing along a straight line at constant
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of the gyro comp 5s; this deviation is
dae to the curvature of the
earths surface.
__(
Of course, in view of the immense size oil the earth, the curvature...oL..its surface_
is very small. Is it possible for such g negligible factor to exert a perceptible
influence on the readings of the gyro compass? It has been found that it can, Let
that it can, Let
earth's surface, during the "rectiiinesr'' and uniform notion of a ship.
Let us assume a s in that the ship is sailing on the surface of the ocean,
tsining the direction of the meridian from s?uth to north (Fi;.82). luring a cAr-
us now consider this deviation of the gyro compass, due to the curvature of the
part rises.
# ~e radius of earth is 6370 km.
the
STAT
th- northern p rt of the plane of the horizon will gradually sink while the southertl
46_i r !
tain time interval, the ship will be dis-
placed from the position 1i~ to the position
M. Let us denote the line so obtained at
the point N1 by nlsl, and the
corresponding
line at the point ifs by It is obvious
I
that, on transition of the ship from the po-i~
stion t4 to the position 1!2, the meridian
1 ~
and together :ith it the ilar,e of the horif
i zon, dill have rotated through the angle
about an axis perpendicular to the plane of
t.ne meridian (Fig.82). fnus, ~rhen the ship
is displaced along the meridian in a north-
4 the horizon is rotated about a horizontal line normal to the meridian; in this cases
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Let us assume now that a gyro compass is installed on the ship and that its ax-'
;
at the instant the ship is at position Ml, is directed along the meridian nisi.
r.J
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j Since, during motion of the ship in a non
_plane of the horizon will gradually sink it, follows that the nortiEndoLtheaxis
_._...
-
y - ---,. t._...ev va ".4'- aaw dW/S~. Vil U14
_j other hand, we already know (Section 23) that if the north end of the ye-compass
0 _1
_~ axis rises above the plane of the horizon then the action of the force of gravity
128 _ of the pendulum will cause the whole instrument to start rotating counterclockwise
I
_' about the vertical. Consequently, if the gyro compass is installed on a ship sail-
Ib.
ing in a northerly direction then the influence of the motion of the ship will
l8
cause the north end of the gyro-compass axis, which was originally directed along
.. the meridian, to deviate gradually westward from the meridian.
?? _~
However, when the north end of the gym-compass axis deviates westward from the
?1--I
plane of the meridian, it will also acquire a tendency to decline toward the horizo
? 6
this is a consequence of the rotation of the plane of the horizon about the meridia
---let us recall the stars which descend toward the horizon in the western part of
_i the celestial vault, at a certain magnitude of the westerly deviation of the gyro-j
'- f
;coma ss axis from the meridian, the mutually opposing tendencies of the instrument
4_._' I
axis to rise and fall due,respectively,to the motion of the ship and the diurnal
36_I i
rotation of the earth, are in equilibrium in this position, the instrument will re-
3
i3 -
main in equilibrium for a long time. This westerly deviation of the instrument
40
_~from the meridian is termed its deviation due to the motion of the ship in a north-
f
erly direction.
44
46
45-
How extensive is this deviation? At first glance, it may seem that the magni-
tude of this deviation, which expresses the influence on the instrument reading of
so insignificant a factor as the curvature
f th
th'
o
e ear
s surface ehcul~ be very
r
,:jsmrll. This is not so. A more detailed.ixamination of the questior. shows that the;
5a--ii
54 !magnitude of the deviation with which we are now concerned depende on the speed of
56 the ahP
i and on the latitude of the place It is found tha+w
: , at the latitude of
.~. ---__.---- ~~
of the gyro-compass rotor, striving to maintain a constant direction of its axis of
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STAT
 J Leningrad (60?) and at a ship speed of l q/hr, which approximately corresponds to
_ La.speed of 30 knots,the gyro compass has. ;a deviation of 3?42' and,-consequently,--r.
f
A ,
1 acts markedly to the curvature of the earthts surface; its sensitivity is almost
_ phenomenal;
Thus the motion of the ship in a northerly direction results in awesterly devi
ation of the gyro compass, It is easy to show that with the ship sailing in the
] `,
opposite direction the deviation should also reverse its direction. Consequently,
14__;
the motion of the ship in a southerly direction produces an easterly deviation of
.Je have assumed, up to now, that the ship is moving in the direction of the
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_ meridian (northward or southward). However, in what way does the motion of the shi
in a direction normal to the meridian (eastward or westward) affect the readings of
the gyro compass? ~Je have seen that the primary cause of the appearance of devi-
ations of the gyro compass, w hen the ship, is moving in the direction of the meridian,
is the rotation of the plane of the horizon about a line normal to the plane of the
_meridian. Such rotation of the plane of the horizon does not occur if the ship is
moving in a direction normal to the meridian, ;Je must conclude that in this case
?4.
_athe motion of the ship exerts no influence whatever on the readings of the gyro com
36
--apass*.
3 B -!
* This is not entirely accurate. As a result of the diurnal rotation of the earth,;
the ship is likewise transferred, together with the points of the earth's surface,
in a direction perpendicular to the plane of the meridian and toward the east.
f ,
Consequently, the motion of the ship along the surface of the ocean toward the ''
east or toward the west does exert the isame influence on the fro compass we woui
be the case if there were a certain indrease or decrease in the angular velocity
of the diurnal rotation of the earth. This influence is insignificant and may be
disregarded.
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Let us now assume that the ship is sailing in sono direction, forming a certain #
(~ - -
,
' angle with the direction of the meridijn NS ~.ig.S3); this angle is termed the
course angle or, for short, 4. and is measured in degrees fromf
the course of the ship
herly latitude the course devlation is airectieu
We recall that the deviation of damping is always directed eastward (in the
northern hemisphere Section 27)? Consequently, the course deviation is compounded
with deviation of damping during any motion of the ship toward amore southerly lat-
c4itude and is subtracted from the deviation of damping when it is moving toward nort4-
the gyro-compass readings while the compo-
nent vl produces the deviation discussed
above.
Thus, in the motion of the ship in any
direction, the deviation of the gyro com-
pass is caused only by the velocity compo-
nent vl; the value of this deviation de-
pends on the~alue of the component vl and
Fig.83 on the latitude of the place. However,
since the value of the velocity component vl depends in turn on the value of the
velocity v and on the relative bearing or course angle y then, in the general
case, the magnitude of the deviation of the instrument due to the motion of the ship
depends on the speed of the ship, on the latitude of the place, and on the course of
the ship. For this reason this deviation is termed the course deviation of the
-gyro compass. In the case when the ship is ascending to more northerly latitudes
..,the course deviation is directed westward; when the ship is descending to a more
ern latitiuies. In Section 27, we mentionbd a simple. device allowing a compensation
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'north to east. Lay off the speed of the ship v in the direction of its motion and
-`resolve it into two components viand v2, namely the direction along the mei'idian NS,!
and the direction perpendicular to it. The component v2 will have no influence on
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of the error in the gyro-compass readings due to the deviation of damping. In the
samc manner, the error due to course deviations which is added (with the plus or --~
minus sign) to the error due to the deviation of damping is also compensated.
Schuler Condition,
In the preceding Section we assumed that the motion of the ship on which the
a
gyro compass was installed took place at constant speed and with a constant course.
1
Let us now consider how any variation in the speed or course of the ship will be re-
flected in the readings of the gyro compass.
Let us inagine that we are in a moving streetcar. So long as the car is moving
I
with constant speed along a rectilinear section of the track, we might entirely fail
to notice the motion of the car if the windows are closed if it were not for the
periodic impacts on the rail joints, to which our attention is involuntarily drawn.
The situation is entirely different when the velocity changes sharply or on a
curved track. At a sudden deceleration, all passengers standing in the car experi-
ence a violent shock which throws them toward the front platform of the car. A
passenger experiences the same shock when the car rounds a curve if the car enters
- the curve at a considerable speed; here the direction of the shock is normal to the
. direction of motion; if the car turns to the right, all passengers standing in the
_-car are thrown violently to the left, i.e., toward the side opposite the side on
- which the center of curvature of the track is located. Consequently, when the car
--moves at variable speed or along a curvilinear section of the track, the passengers
=are subjected to the actiod of a special force which is termed the force of inertia';
i
the car is moving along a curvilinear section of the track at constant speed, this
'`
ajforce of inertia is termed centrifugal force.
The same force of inertia ie applied to all objects on the ship when it is mov-
ing at variable speed or along a
5~ auviliaar path, in particular, the force of finer-~
56 is is also applied to the p~tdulamt cf the gyr; cogpase. No matter hour this force J
STAT
 ready know (Section 6) we conclude
that under the action of the pressure;
F the instrument will precess, ro-
1p tical. Consequently, under the ac-
tion of the force of inertia J1, the
i
north end of the gyro-compass axis
will deviate from the meridian toward
of the gym compass due to thV force of inertia of the j
pendulum when the velocity or couxse of t~e ahip varies 1 termed the ballistic
34
56 deviation of the j'rO cc pass. I
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of inertia J is directed (in all cases, it will be horizontal), it may be resolved
i
into two components J1 and J directed, respectively, along a north-south line -- !
2
(i.e., along the meridian NS) and along an east-west line (OW in Fig.Bla).
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Fig.B4
If the gyro-compass axis is directed
northward, the pendulum can swing on-
ly in the plan of the meridian (Fig.
85). In that case the force J2, di-
rected perpendicularly to the plane
of the meridian; exerts no influence
whatever on the pendulum while the
force J1, transmitted to the gyro-com1-
pass axis, exerts a pressure F on it
In Fig.85, it is assumed that the force
is directed southward; in that case, the pressure F applied to the north end of
the gym-compass axis will be direct
I
ed vertically downward. By applying f
w the rule of precession which we al-
STAT
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arc BC, it goes into the new course 2 and continues to move along the straight
On passing along the curve BC, the
variable ballistic deviation due to
the centrifugal force of the pendu-
lum is added to this constant devi-
ation. Can we consider that at
point C the ship is entering a new
rectilinear section of the route
having a deviation of the gyro com-
pass equal to the course deviation
corresponding to the velocity v and
-- Fig.86 the new course '2? In other words,
can it be considered that at point C the gyro compass will be in a new equilibrium
.position corresponding to the velocity v and the course Y? Of course not. For
- this reason, on completion of the caneuver, oscillations of the gyro-compass axis
must arise which are damped only gradual- d the influence of the "eccentric cou-
- pling" of the pendulum with the gyro chamber.
We reach the conclusion that the variation in speed or course of the ship must
r i 4 5--
SD....ibe accompanied by the generation of oscillations of the ro-compass axis. It is a
Sn~rea:rkable fact, ho*ever, that. it is possible to design an instrument in such a way
Let us assume that the ship proceeds at constant speed v along the straight line;
AB B-and keeps the course -'j; then, maintaining this same speed v and describing they
line CD (Fig.86). How will this maneuver, executed by the ship, affect the readings
of the gyro compass?
So long as the ship was moving along the straight line AB, the gyro compass show-
ed a constant course deviation corresponding to the velocity v and the course
S4 a to avoid the generation of such oacil1~tions. _ For thie, it is necessary to ob-
56 erve the following condition: The elesiente of the insti ent muat be selected in
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such a way that the period of its undamped oscillations (mentioned in Section 25) isj
equal to the period of swing of a pendulum whose length is equal to the radius of.
the earth. The period of such a pendulum (i.ee, the time of two sweeps) would be
84.4 minutes; this must be the period of the undamped oscillations of the gyro corn:
... pass to prevent the maneuver of the ship from causing oscillations of the instrument
This condition, which is often called the Schuler condition from he name of the
scientist who discovered it, is alkay, taken into account in the design of a gyro
compass. However, there are certain difficulties involved in its exact satisfaction')
in view of the fact that the period of the undamped oscillations of a gyro compass
varies with the latitude of the place. At the same time, the reservation ;gust be
made that, even with an exact observation of the Schuler condition, a variation in
the speed of the ship or in its course will fail to result in oscillations of the
gyro-compass axis only where the gyro compass contains no device that might cause
damping of its oscillations, i.e., if there is not "eccentric" coupling of the pendu-
lum with the gyro chamber. For this reason, the naneuver of the ship will still
lead to oscillations of the gyro-compass axis, which will only be damped gradually,
after completion of the maneuver and on passage of the ship to a motion at constant
speed and constant course.
-Section 31. The Sperry Gyro Compass with }ercury Reservoirs.
- The Sperry pendulum gyro compass, considered in the preceding Sections, was de-
signed around the year 1910 and at that time was widely used on naval ships of
--'various countries. It was soon found, however, that this instrument had certain
-faults; particularly, its readings in a fresh wind proved unreliable. This is due
1dIto the fact that, if the ship rolls, its aotion is not strictly rectilinear even if
it maintains a constant course. For this reason the rolling of the ship causes a
deviation of the '
;d~r._..~~gyro compass due to the farces of inertia of the pendulum and bav-
__. .... .
56i ~ag g the character to . eta ballistic deviation. It must, however, be borne in mind that
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--th? forces of inertia due to rolling are alternately directed in diametrically op..
,jposite directions and therefore neutralize each other to a considerable extent..In1
!spite of this, the rolling still has some influence on the readings of the gyro com-~
i
--
_pass.
~
The desire to improve the navigational qualities of the vro compass forced the
i 0
American Sperry firm, toward the end of the
instrument substantially. The designers of
Fig.87
-.axis 0 in such a way that the entire system
_.I
the axis 0 (Fig.87), rte assume further that the system of communicating vessels is
balanced in such a way that its common center of gravity coincides with the point 0.,
this case, the system of communicating vessels will be in a date of neutral equi'
36~
38
ibrium. Let us now fill these reservoirs with a certain quantity of liquid (mercury)
-+uch that its center of gravity will coincide with the point 0. Obviously even now
he entire system will be in a state of equilibrium, as long as the vessels S and N
421
th
+c on
e same level (Flg.87).
4 4_
46~
Now let us change the system of
ig.87, by raising the vessel N and
48
communicating vessels from the position shown inj
World 6Jar I, to modify the design of the
the gyro compass abandoned the use of a
pendulum and replaced this pendulum
by two communicating vessels filled
i
with mercury. Thus originated a
new type of gyro compass, the Sperry
gyro compass with mercury reservoir.
Let us imagine two communicating
vessels S and N, suspended on the
i
is free to roll in a vertical plane about;
correspondingly lowering the vessel S (Fig.88).
56 ~t vessels, trop the equilibrium position, once _' takes place, will have
128
bq
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-low a portion of the mercury will flow frog the vessel N into the vessel e, and the
eavier vessel S will thus acquire a tendency to lower still more, while the lighter
ill to
f
::L
tilt I
N ~
,5,
?
ned
o r:e '
-.. ??w o,,... ;aui-o? ins deviation of the system of liquid-filled
STAT
 a tendency to continue in the same trend.) The system of communicating vessels fill
led with liquid and suspended by. this met~od, has properties similar._ta-those-of-an-
,~ I
_1 "inverted" pendulum, i.e., a pendulum in which the center of gravity is above the
point of suspension (Fig.89). Such an "inverted" pendulum, in the vertical position
8_i
_1 will be in unstable equilibrium; if ever the smallest deviation from the vertical
in
takes place, this trend will increase continuously. In such an unstable equilibri
j are our communicating vessels filled with mercury. These may be termed a "liquid"
I
pendulum. Thus, a "liquid" pendulum of this design resembles in its properties an
Fig.88 Fig.89
"inverted" unstable pendulum (Fig.89).
36~
--~ It was by such a "liquid"
Y pendulum that the ordinary pendulum was replaced in
3a
'the new design of the Sperry
--~ ~ gyro compass Let us imagine that communicating ves-
Hsels, filled with mercury, are attached to the gyro chamber in such a way that one
vessel is located on the north side of th
44~ gyro chamber (the "north" vessel N), and
-.,the other on the south side (the "south" vessel S) (see Fig.90). Let us also assume;
46 i
that the axis of the '
gy
48 ro compass is )scatted horizontal] along the meridian; in
cn
that case the mercury vessels will be on the same level and, conseouently, the en-
---t ire systex will be balanced. We know that the earth's diurnal rotation causes a
:rotation_of the plane of the horizon, together with the meridian, in a counterclock-f
56 wise direction about the vertical, assuming that the gyro compass is 1GCated in the
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?~ northern hemisphere. For this
1
_ing-a _tendency. to maintain its
aR
the horizcn about the meridian,
will cause the north end of the
18-
tyro-compasscaxiury sres ::?::northern mer ansdel Nthu,s {
-- Fi.90 above the horizon (we recall the
star rising in the east ,
8 ); (see Fig.92). The rise of the vessel ~J arad the drop of the 1
vessel S cause mercury to flow from the north-
em vessel N to the southern vessel S. The
n
southern vessel S begins to be heavier than
l
the other vessel and this lead to a gener-I
~ f
r i
I..-L 1%' ation
f th
o
e pressures Ff thhb
oe gyro camer;
pressure F, directed upward, is applied to
the northern end of the rotor axis, and the
pressure F, directed downward, to the
south-
em end. We now assume that the rotation of
45 the rotor is clockwise if viewed from the
48_i ! north-aa shown by the curved arrow in Flg
! .90 !
5D._ 1 8 and Fig.92. By applying the rule or nreces-!
5^ Fig.91 sibn, we see that the gyroscope begins to
54 preeees, rntating ebuntercloclcxiee about he vertical, as ahown by the arrows in
55 Fig.92, eo that its axis has a tendency t be aet in the Mane of the meridian. I
reason, t} e north :arid of the gyro-compasrr axis, hay.-
constant direction in space under tie_.influence....af j
the rapid rotation of the rotor, !
will deviate eastward from the me-~
UN ridian (Fig.91). However, in that
I case, the rotation of the plane of
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-~ Asia clear, the gyro compass with ,ue'cury vessels possesses the same propertie.
Jaaa_. jro..compasa. with pendulum. We remark, however, that in speaking_of_the gyro-.
compass with pendulum as described in Section 23, this instrument was given a di-
rectional force toward the meridian if its rotor was rotating counterclockwise rel-
ative to an observer viewing it from the north. i'Je now see that in a gyro compass
with mercury vessels, the rotation of the rotor must take place in the opposite
ordinary pendulum.
equivalent to an "invert-
I
What then is the advantage of the gyro compass with mercury vessels over the
a
yro com ss with ndulum?
e
a
a
d t
li h
I
< _.J sense, i.e., clockwise viewed from the north. Of course, this is connected with
14 _..
I'l
-i ?ig~92
Sti_ i
the fact that the mercury vessels, in their properties, are
--ithe quantity of mercury flowing from one teasel to the nther whe^ the tr?r crt is
Ig p
p
o
e
v
n g~ es in t e fact that a gyro compass with
lt-
mercury vessels provides greater opportunities for adjusting the instrument.
4)
48 The Sperry gyro compass provides an opportunity for regulating,by special cocks
tilted, We have seen in Section 25 that the period of undamped osciUations of the
compass depends on the latitude of the p1Ace. By regulating the quantity of mercu
ilowiu~ frym one vessel to the other, according to the latitude o+ the place, it is
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of the pendulum gyro compass in world prac-L
tics by this new type of Sperry instrument.
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- possible to make the period of
. ...pendent of the latitude of the
condition with great
accuracy.
reducing the diameter of the tube
through which the mercury flows from one vessel into the other, a certain lag in th~
flow of mercury can be introduced which in turn improves the operation of the
instrument during a roll. The obvious advantages of a rro compass with mercury
undamped oscillation of the instrument almost inde-
place, thin making it possible to .satisfy_.the S
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CHIPTER IV
ThE GYRO hORIZON AND GYRO VERTICAL
The direction of the vertical or the plumb line, at a given place, is determine
very simply by means of the ordinary plumb line, that is, a string held at one end
with a weight at the other end. The direction of this string under equilibrium con)
dition gives the direction of the vertical at a given place. Peculiar difficulties
arise when the direction of the vertical must be determined on some moving object, f
such as a ship or aircraft; these difficulties are due to the fact that an ordinary
pendulum, one type of which is the plumb line, does not possess a sufficient degree
- of stability. The effort to increase this stability naturally leads to the thought
- of replacing the simple weight in the pendulum by a rapidly rotating rotor. In thi9
--- way, we arrive at the idea of a gyro pendulum.
i
-- Let us imagine a pendulum swinging in a vertical plane, alternately rotating
-;about the fixed horizontal axis Ak, now to one side and now to the other, and con-
1L. sisting of the rod A with the ring B at its end. To this ring the ends of the axis
5-of rotation CC of the small top or rotor C are attached (Fig.93). Let us put the
48_4 top C in rapid rotation about the axis cc, and then, by a light tap, let us bring
our pendulum out of the vertical equilibrium position. It will then begin to swing
about the axis aa. The question now arises how the rotation communicated to the to
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 In a gyro compass with three degrees of freedom (Fig.9{ or Fig.95) the stabilize
ing influence of the rotation oi' the rotor on the swinging of the pendulumis clew
ly detected: Let us consider the motion of such a gyro pendulum 4th three degrees;
of freedom.
Fig. 94
Fig.95
Let us give the rotor of the pendulum a rapid rotation (for example, counter-
;clockwise, viewed from above) and let us then cause it to deviate by a certain angle;
t3 -~ from the vertical (Fig.96). Here, the letter 0 denotes the point of intersec-
t
J
I
5O- tion of the Cardanic ax?e, which re"sire :,ti : icso, it tac iez i ium design of
~
53-
ig.94, or the end of the base point in the design of Fig.95. If we now release ourl
54-yr pendulum -tt wf~] nat- meaae begin to ewing its the a v rtIcATprane
13.x.
60
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Let us now proceed, as explained in ~ection 6 when we discussed the action on
_the gyroscope of a force applied at a paint of its axis and directed along a line.-
-1 not normal to the axis. At the center of gravity of the gyro compass (which we
ight of the gyro pendulum
assume to lie on the axis of the rotor) i;s applied the we
P. Let us resolve the force P into two components Pl and P2, of which P2 is direct
ad along the rotor axis of the gyro pendulum and P1 :.s perpendicular to that axis.
The component P2 is balanced by the resistance of the fixed point 0, but the compo-
nent P1 causes a precessional motion of the gyro pendulum about the vertical passin4
through the fixed point 0. the sense of this precessional rotation is easily found;
by the rule of precession, which we already know.
By applying this rule (Fig.96) we see that, in this case, the gyro pendulum wild
describe a cone rotating counterclockwise (when viewed from above) about the verti
___: In Section 10, we described an experiment with a gyro made of a bicycle wheel
_ (Fig.18). In essence, the m^del of the gyro then discussed was nothing but a gyro
pendulum and the precessional rotation of the instrument described in Section 10
_ differs in no way from the uhenomenon of which we are now speaking. We remark mere-
ly that, in Section 10, we assumed the gyrro axis to be horizontal, i.e., normal to
the vertical axis of precession while here we are considering the more general case
_.of a gyro compass deviating by an arbitrary angle from the vertical.
_.._ In Section 10, in speaking of the experiment with the bicycle wheel, we remarked
?4 2.
that the higher the angular velocity of the proper rotation of the wheel, the lower
44_J
151ji1i Le the angular velocity of the precessional motion. This remark still remains'
q valid in the more general case now under discussion. The more rapidly the rotor of j
gyro pendulum rotates about its axis, the mare slowly does the precessional motion
c n~-
5 --lof the gyro pendulum about the vertical take place.
tion and that its rotor ie ced in ra d rotation (Fig
97)
Let us now strJ
.
.
`I
--d
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the gyro compass by hand at its lowest paint h, in a direction perpendicular to the
?~ plane of the paper. How will the pendulum react to this impact?
j
The effect of the shock will be expressed in the application, during the ex-
? tremeiy short time of the impact 2' co th`e point A of the gyro-pendulum, of the im-f
pact force S in the direction of the shock, i.e., in a direction normal to the plan
axis, the result of the action of the force
S is found by the rule of precession (Fig.97).
B~ applying this rule (as before, we assume
' I
ttie rotation of the gyro rotor to be counter
I
clockwise if viewed from above), we note that
as a result of the shock, the gyro pendulum
deviates from the vertical in a plane normal;
i
to the direction of the shock (more specifi
cally, to the right) by a certain angle
which is found from eq.(3) of Section 6:
cL =
Sa:~...
Fig.97 (where a = OA is the distance between the
0
point of application of the force S and the fixed point 0; J is the moment of iner-
tia of the rotor; and w is the angular velocity of its proper rotation).
s!
. rr.
(
-to precess about the vertical under the action of the force of gravity,describing a
!
48
Hcone about the vertical as
50.E explained above.
i
f the paper (Fig.97). Since the force S is applied at a point of the gyro rotor
axis, and since it is directed normal to thi
-- In deviating, during the time 'r , by this angle a , the gyro endulum begins
It la clear from eq.(3) that the angle a by which the gyro pendulum deviates
from the vertical under the action of the shock will be smaller, the higher the an-
56 gular velocity w of the
_ proper rotation of its rotor. It is in the eraallneae of C
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^
was put into practice cal y at
the end of the Nineteenth Cen
i
tury in the instrument of the
Fra:?ch inventor Fleuriais.
The Fleuriais marine gyro
horizon is an additional at-
tachment to the ordinary sex-
tant, which measures the alti>
tude of a heavenly body above;
the horizon. In the sextant,
'i 4_J Fig.98 the star S and the horizon
-line are simultaneously viewed through the sight tube A (Fig.98). In the Fleuriais;
J-
mired by the navigator for astronomic observations. The original idea of Serson
instrument an artificial Syr.. horizon is placed in front of the mirror B. It con-
sists of the rotor C, which rests on a pc4nt somewhat above the center of gravity.
Before beginning the observation, the rotor is em by compressed air from a hand
pump. The jet compressed air enters the instrument through a hollow shaft and
impinges on depresaione in the lateral surface of the rotor; during the time of
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-4 this angle of deviation othat the stabiity, communicated to the gyro
_E..the rapid rotation of its rotor, is expressed.
Section 33. The Fleuriais Marine . Ciro Hdrizon .. _
-- We have an example of the practical e;::ey ent of the gyro pendulum in the
Fleuriais marine gyro horizon.
In Section 1 it was mentioned that the first attempt to utilize the properties
of a rapidly rotating top in practice was mada by Serson as early as the Eighteenth
Centurybrtit ended with the failure of the attempt to r'ssigr a gyroscopic '`.rtfi-
- cial horizon" which would have replaced, in foggy weather, the visible horizon re-
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`...second Since the center of gravity of the rotor is lower than
porting paint, we have here a gyro pendulum and, what is more, one
end of one diameter has a plane-convex
observation, the rotor is spinning at an angular velocity of 50 revolutions per
lens; on the flat surface of each lens is drawn, at the height of the optical axis,+
a fine line perpendicular to the rotor axis. The distance between the lenses is
equal to their focal length; for this reason, the line drawn on saoh of the lenses
is clearly visible in the tube A, at each revolution of the rotor.
If the axis of the rotor is strictly vertical then during each revolution one)
i
line or the other appears to be strictly horizontal and at the same level to the
observer loo',dng into the tube A. All successive images of the lines are merged is
the observer's eye into a single horizontal line, which is able to replace the line;
of the natural horizon invisible in foggy weather.
However, if the rotor axis deviates from the vertical by even an insignificant
angle, a relatively slow precessional rotation of the rotor about the vertical be- j
gins immediately, in the course of which the rotor axis will describe the surface o
!a cone about the vertical. To the observer, looking into the tube A, the line vis-
ible
the tube, replacing the line of the natural horizon, appears to be continu
--- ously changing its position. In Fleuriaia instrument, the period of precession (i.
., the time of a single rotation of the rotor axis about the vertical) is equal to
i
approximately two minutes. During these two minutes, the line visible in the tube
,1
Ijappears to be horizontal twice, at its highest and lowest positions; in all inter-
46_
~
-imediate positions it appears to be inclined, now to one side and now to the other.
this mobility of the artificial horizon does not interfere with the observations;
5o__I
5~the technique of astronomic observation develapedwiththrFleuriaia instrument takes
into account the characteristic oscillations of the artificial gyrc horizon.
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_ Section 34. The Pendulum Aircraft Coursed Corrector
4_J If the
i
center of gravity of a gyro pendulum coincides with its fixed point, thi
netrument is Gonvezrt.ed into .n aetatic gyro and becoies unable_to. align.its..axisr
i
with the vertical. In the Sperry gyro horizon, which will be discussed in the fol-
lowing Section, a very interesting method of aligning thR axis of the astatic gyro
l with the vertical is used.
In the present Section the method of Sperry, which may
14 be termed that of the "air pendulum correction", will be discussed.
e#dee3-they sra_ l~nn-eaat~tl balance,- eo that the gyro exf a ~'emeI
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Fig.99
the outer ring is not shown in th-
diagram; the point of intersection of the
. ru~C:ic axis G(iiii~iuaa
gravity C of the entire
rotation of the chamber
WJ.IL
system (the axes of
are horizontal). The gyro chamber b has a
rounded cross section in its upper part an
a square cross section in its lower part.
ber are provided with similar and symmetr-
i
cally arranged windows a, which are partly
covered by the pendulum shutters b. j
i
In the gyro chamber B an elevated air 1
pressure is maintained (in the following Section we will explain how this is accom-!
48-1
shod in the S
instrument) Tr the svm avin is vertical_ as assumed in Fig
err
SO_ 59, all four windows a will be half covered and permit ejection of the saw' 4tof
p
p
y
compressed air from the chamber. Each jet exerts a reactive pressure in the
i
afte-dircctfofr-on the- tuber; Since aU these pressures-are are-directe'
(F g.99);
The rotor of the astatic gyro It is suspended in a Cardanic suspension, whose
inner ring is designed as the gyro chamber B
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in a vertical position.
_Let us now ,assume that the gyro. axis.deviates from the. vertical_..by_u certain._...
4-i
_angle in a plane parallel to two opposite faces of the lover part of the gyro cham-
ber (Fig.1OO). One of the two opposite 4ndows a in these faces will then be com-
pletely open and the other (not shown in Fig.lOO) will be closed. The reactive pre
sure criuscd by the air jet entering through the open orifice in the front face will
* At a very sell angle of deviation of the gyro axis from the vertical, both these
orifices will remain open, but one orifice will be open more than half and the
other less than half. The reactive pressures corresponding to the opposing air
jets will not be balanced; as a result, even in this case, there is a resultant
ii
reactive pressure on the chamber, directed normal to the plane of the paper and E
away from the reader.
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tive pressure, since the orifice in the back)
face is closed; as a result, a reactive presl
sure directed perpendicularly to the plane ofd
the paper, in the direction away from the
chamber. This reactive pressure, trananittec
to the gyro axis, will produce the force F
applied at the upper end at this axis and di-
the direction toward the reader (Fig.100).
Let us now assume that the rotor of the
v-.roscope rotates counterclockwise, if viewe4
f
the rule of precession, we conclude that under the
axis will precess in the vertical plane and will
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approach the vertical until it coincides with it. In this way, the original devi-
m the vertical will be eliminated
f the
ti
ro ads fr
.
a
on o
gy
o
pie have assumed that the gyro axis originally deviated from the vertical in a
plane parallel to two opposite races of the lower part of the chamber. However,
_ since any deviation of the gyro axis from the vertical can be resolved into two suc
deviations, what has been said now still remains true even in the general case of '
tilled the 'ja pparentvertical, i.e., in the direction of the resultant of the force
--;of gravity and the force of inertia. Consequently, the pendulum shutters, in their
14
-1equilibrium positions, are also located along the "apparent" vertical rather than
,n
--along the true vertical.
any deviation of the gyro axis from the verti-
cal. Thus, the pendulum air correction in I
all cases brings the axis of the astatic gfrO
into a vertical position.
In our discussion we have assumed that
the astatic gyro with "pendulum air correc-
Fig.101 tion becomes more complicated if such a gyro
yet up on a moving base, e.g., in the cabin of an aircraft in flight.
the aircraft is flying with a certain acceleration, then all objects on that
aircraft are subjected, in addition to the force of gravity, to a corresponding
fc) (.' .:.ertia, having a direction opposite to that of the acceleration of the
ai. ,aft.. In this case, the ordinary pendulum suspended in the aircraft cabin, in
-,its ~cuilibrium position, is located not along the true vertical but along what is
The reactive pressures of the air jets issuing from the window, a are ryut'!allr
H'i "ed in the case when all the windows are half covered by the shutters b. This
S4 x1._ take place when all the shutters bare parallel to the axis of the instrumentj
56 i.e., to the axis of the gyro. It follsws from this that, in the equilibrium i
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sition of the instrument, the gyro axis is likewise located not along the true
J vertical but along the "apparent!' vertical; in this way, when the aircraft.moves--
t
J with an acceleration, the shutters of the pendulum correction, which themselves
ent" vertical.
If we take into consideration the fact that, during the flight of an aircraft, {
i
its acceleration and consequently, also the corresponding forces of inertia, are
continuously varying in both magnitude and direction, we are able to say that in the
aircraft cabin, a gyro with a pendulum air correction will be, as it were, a means '.
l of averaging the equilibrium positions of the ordinary pendulum and a damper on
_ .- deviate from the true vertical, will entrain the gyro axis; this will force the gyr
axis to precess slowly in the direction not of the true vertical but of the "apps
18
their oscillations.
Section 35. The Sperry Aircraft Gyro Horizon
_ We mentioned in the preceding Section that the method of the pendulum air cur-
rection was used by Sperry in his design of the aircraft gyro horizon. This is one
of the blind flying instruments. It makes it possible for the pilot, when the natu-
_H ral horizon is invisible, to detect any deviation from horizontal flight (diving or
3R_i
climbing of the aircraft) as Weil ~.s any banking.
y .n astatic , -ro with a pendulur air :orrection is placed in the hermet:.caiiy
-,'sealed case of the instrument A which is attached to the instrument board of the
-.
aircraft in front of the pilot (Fig.102); the direction of flight is indicated on
~H the diagram by the arrow.
454
The inner ring of the Cardanic suspension is designed as
- the gyro chamber B, and the outer ring has the
t$
y f rafne C is coupled to the 'Dint D, obowt
- d
form of the
rectangular frame
I
Ilse
t1 ut lever icr can rotate. :ne
52
54
58
. 60
part. g' of this bent lever is visible to the pilot through the glass G in the form
of Be-
of a white bar; this barplaystherotsof the horizon line in the instrument.
i
tyon4. bar. the pilot also sees, throw the glass G, the cylindrical Surface _H
q
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o
s rumen , th Cardanic axes are horizontal;
It -
f -i l U
which is painted in two colors; the light blue color of the upper part of this back
peer Part of this back
_. j
2 .
_ground merges into the dark-gray of the lower part, corresponding to the color of
the sky and the earth, respectively.
In the normal position of the in t t b
?
Side new
S
t3. Fig.102
sujthe axis of rotation xx of the outer frame C, along the longitudinal. axis of the
`'---aircraft and the axis of rotation of the
yy gyro chamber, transverse to the aircraft'.
54
-j lever-B6~-i ccmg}etxith-the--gyro ehaad er b wane of-the-pin-,1; W
SF t
~s-Mao_~t~he_________ _-entl passes tehrough an arc-shaped elob -in bhe..part D6-
58
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W the outer frame and through a rectilinear slot in the part DE of the bent ever.
In its normal position, the bent lever D~jF is horizontal. ---
In the case of the instrument A, a vacuum is produced by the continuous aspira-
.- tion of air by means of a Venturi tube through the orifice K. On the other hand,
I
the inner cavity of the gyro chamber is connected with the atmosphere by means of a
6-I
-wise stably remains in the horizontal direction. The part EF of the bent lever DEF
i
?.a_-_
-is parallel to the axis yy. Consequently this part of the bent lever is also visi-
2_! i
4 4 - strument and, in its function, actually maintaining the horizontal position.
---? If the airplane is in rectilinear horizontal flight and is not banking, then th
46_
--iinstrument case, attached to the instrument panel of the aircraft, occupies the
48 1
.~ C
S n-position shown in Fig.102. The bent lever DEF likewise occupies the position in
_jble to the pilot through the glass, playing the role of a "horizon bar" in the in-
52-
Fig.102. The"horizon line' ' is visible to the pilot in the canter of the glass G
54: likewise at the level of its center, shows a miniature silhouette of the aircraft
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i unbanked flight, the silhouette of the airplane on the glass of the instrument is
represented as projected on the "horizon ;line" EF (Fig.103).
t Let us now imagine that the airplane is descending along an inclined straight
The instrument case A, rigidly attached to the
instrument board of the aircraft, now occupies th~
inclined position shown in Fig.104; the gyro cham-
ber A maintains its former position, since the
I
gyro axis, as we know, remains vertical; the bent
Fig.103 lever with the "horizon line" EF then occupies the
position shown in Fig.104. It is clear that the "horizon line", remaining horizon-
tal, is now shifted toward the top of the glass G. Consequently, the miniature
4 A L. Side view
e#Toue e-e e-4#rorart-#Jnaged on the $la?ee G will -now appear #~o -the-blot ae---, '
- ;+rsna t? +-oolered background below the nhorisan line" EF (Fig 105). _
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It is easy to understand that, during flight along an inclined straight line upward
:,.,.(climbing), t!;e "horizon line" will shif toward the bottom of the .glass.G,.-and-..the
silhouette of the aircraft will be projegted on the colored background above the
"horizon line". In this way, the pilot will be able to determine, from the indica-
tions of the instrument, whether the flight is horizontal or not.
In exactly the same way, any banking by the aircraft can be determined from the
instrument. If the aircraft is flying with a bank, then the miniature silhouette
Fig.105 Fig.106
of the aircraft imaged on the glass of the instrument will likewise go into such a
bank, while the "horizon line", as we know, will always remain horizontal.. If the
. silhouette of the aircraft on the instrument appears to the pilot to be located be-
-.low the "horizon line" and in addition, to have a right bank (Fig.106), then in rea-
~'
- ity the airplane is descending with a right bank.
The remarks made at the end of Section 314, as to the errors introduced in the
operation of the air pendulum correction by the accelerations in the motions of the,
46__4
-- instrument base, must of course also be applied to the Sperry gyro horizon. The
48
--accelerations in the motions of the aircrft result in corresponding errors in the
instrument readings. Wien an aircraft j: flying with a certain acceleration, the
S4 "horizon line" horizon line in the instrument ceases to be etrictlY horizontal. However, since
I
at not too great an acceleration, the deviation of the "apparent" vertical from they
11
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true vertical remains small, it follows tat the deviation of the "horizon line"
In the instrument from the horizontal is
likewise small.
..RIBLI00RAPMY
1. Tochnaya Industriya (Precision Instrument Industry), :o.5-6, 38 (1932).
2. Spirin,I.T. Polety v Arktike (Flight's in the Arctic). GLAVSEVMORPUT
(Central Administration of the Northern Maritime Route), 1940,
i 4 _.
3. Op.cit., p.80.
~. Tochnaya Industriya, No.3 (1938).
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