In its ordinary definition, a gyroscope is an instrument for illustrating the laws of rotation, and consists essentially of a heavy rotating wheel, the axis of which is free to turn in any direction, and may be acted upon by external couples or forces.
Such an instrument is shown in Fig. I.
The gyro wheel A is capable of spinning on its axis, xx, which axis is supported by the frame BB. Frame BB is at the same time capable of rotating around the axis, yy, which axis is supported by the frame CC. Frame CC is at the same time capable of being rotated around the axis ZZ. The above construction permits the axis of spin xx of the gyro wheel to turn, or point, in any direction in space.
The gyro wheel A has some peculiar characteristics. For example, suppose we start it spinning around its axis, xx, and then, while it spins, lift it out of its mounting, holding it between the thumb and first finger thus: Fig. 2.
We may move the wheel in space in any direction, and so long as the axis, xx, remains parallel to its original position and the wheel is spinning no special results of any kind will be noted.
Fig. 3
Fig. 4
For example, the axis of the wheel while spinning may be moved to the successive positions 1, 2, 3, 4, 5, 6, 7 as in Fig. 3, and so long as each movement carries the spinning axis through space parallel to itself no special phenomena present themselves. If, however, the spinning wheel be moved in such a way as to produce rotation of the spinning axis as in Figs. 4 and 5, instead of mere translation, most curious and striking results occur.
There is felt first a definite, positive, resistance to this rotating movement of the axis accompanied, at the same time, by a curious wriggle and tilting of the wheel and its axis xx. This resistance, and its accompanying wriggle, follow definite laws and possess the secret of the gyroscope and the gyroscopic compass. Unless this cause and effect is remembered in its physical sense, it is useless to attempt to understand the principles of the gyro compass.
The “Wriggle ’’-Precession
Suppose (in Fig. 6) while the wheel is spinning in the direction shown by the arrow, a, we put a light, steady pressure on each end of the axle of spin, xx, so as to tilt this axis by the couple PP. The result is astonishing in that the axis of the spin, xx, will resist
being tilted, and will move off in the direction RR at right angles to the plane of action of the couple PP, which is producing the tilting. Suppose in Fig. 7 we apply a couple tending to rotate xx as shown by the arrows PP. What is the result? It is equally astonishing—xx will resist rotation by the couple PP, and will at once tilt in the vertical plane in the direction RR at right angles to the plane of the couple PP. This effect in the spinning gyroscope always follows this cause, or this cause always produces the above-noted effect, and it is the application of this principle which permits the gyroscopic compass.
It is not necessary for the dabbler in applied science to be able to understand the mathematics of the gyroscope, but he must be able to remember the physical phenomena here presented as “cause and effect,” if he desires to understand the principle of the gyroscopic compass.
Referring to the conditions represented in Figs. 6 and 7, the movement of the axis of spin, xx, in a plane perpendicular to that of the couple applied to it is called a “precessional motion” or “precession.” The application of the couple is said to cause the spinning wheel to “precess.”
It doesn’t matter whether the initial position of the spinning axis in space is horizontal, vertical or tilted, the relations of the directions of the precession and its producing couple are the same.
Again, referring to Fig. 3, it is recalled that moving the spinning axis, xx, parallel to itself in space does not produce precession. Conversely, unless the gyroscopic system of Fig. 1 is acted upon by external forces tending to produce precession the spinning axis always points in the same direction in space, i. e., remains parallel to itself in space.
A gyroscope suspended so as to be able to rotate around three axes as those of xx, YY and ZZ, of Fig. 1, is said to possess three degrees of freedom. If motion around one axis is denied by reason of rigid construction, that motion is said to be suppressed and the gyroscope is said to possess but two degrees of freedom.
Effect of Earth’s Rotation and of Gravity on a Gyro Located at the Equator
In Fig. 8, let AB represent the earth as seen from above the North Pole. Let C be a gyroscope spinning at the celestial equator, at the end of the radius, NG, with its axis, xx, horizontal and standing east and west, the gyro being so far away, in space, from the earth that it is not affected by gravity.
After a certain length of time, the earth will have rotated until the gyro is at the position G1, Fig. 9, then in the case of the gyro with three degrees of freedom, i. e., uniformly suspended and free to turn in all directions in space, the axis of spin, xx, -would no longer be horizontal as regards the surface of the earth, but the condition would be as shown at G1, Fig. 9, the gyro having kept its spinning axis parallel in space to the original position which it occupied when at G in Fig. 8. Under this assumption there would be no precession.
Suppose now, Fig. 10, the gyro be moved in towards the earth’s center, along the radius. As it approaches the earth’s surface, the force of gravity is caused to act in the gyro compass to make the axis of spin, xx, take a horizontal position x'x’ relative to the earth’s surface, and in so doing will cause this axle to tilt through the angle 9. Recalling the discussion of Figs. 6 and 7, we see that the rotation of xx to x'x', will cause precession of this axis so that the gyro finally occupies the position of G1 in which the plane
of the spinning wheel coincides with the plane of the equator, while the axis of spin lies in the vertical plane through the earth’s axis, i. e., the axis of the spinning wheel lies in a meridian plane and thus points true north and south.
Fig. io
So long as the force of gravity acts in this manner to tilt and keep the gyro’s spinning axis horizontal to the earth’s surface, just so long will the precession caused by the resultant of this and the earth’s rotation cause the gyro’s spinning axis to point true north and south, unless acted upon by some force tending to throw it away from the meridian. A compass card may be so mounted on this axis as to show true compass readings.
OSCILLATION-DAMPING
But the mass of the gyro wheel possesses inertia, and as the wheel passes from the position G2 to G3 its inertia will carry the axis, xx, past the horizontal and meridian planes. When this occurs, a reverse process will take place and in time the axis, xx, be brought back to the meridian plane, only to again swing past it. This process, unless restrained, will continue for a very long time before the oscillations finally disappear as the forces come into final equilibrium.
Practically, in order to use a compass card on a gyro, mechanical processes are used to check this oscillation and produce equilibrium sooner than would otherwise occur. This is called damping.
In all of the foregoing, the gyro has been considered as stationary on shore at the equator.
The Action of the Gyroscope at Another Place than the Equator
If the gyro be at some parallel of latitude other than the equator, the force of gravity is caused to keep the axis of rotation
of the gyro horizontal to the earth’s surface and turned into the meridian line, i. e., pointing to the earth’s poles, in a manner similar to that discussed in Figs. 8, 9 and 10. For illustration: Assume
Note.—Figures 11 and 12 of the original manuscript are combined in Figure 24A.
the gyro of three degrees of freedom at A, Fig. 13, to be not acted upon by gravity. Then as the earth rotates, the spinning axis, xx, under this assumption would move through space parallel to itself as indicated in the successive positions 1, 2, 3, 4 of Figs. 13 and 14.
However, as a matter of fact, with gravity acting, the gyro would not arrive at 3 in the position shown in Fig. 13 for its spinning axis, xx, would be held, by gravity, horizontal to the
earth’s surface so that it would arrive at position 3 as shown in Fig. 15. In reaching position 3 from position 1 (see Fig. 15) the spinning axis, xx, will have been tilted through an angle of 83°. This tilting will have been gradual and continuous during the movement from (1) to (3) and such a tilt would produce continuous “precession” tending to keep the spinning axis in the meridian plane, i. e., pointing true north, as shown in Fig. 16.
Further Latitude Considerations
Suppose the gyro instead of being located at a place whose latitude was A, as in Fig. 15, was located at latitude B or C as shown in Figs. 17 and 18, respectively. A study of the figures will show that the angle ?, through which the spinning axis, xx, must tilt in order to remain horizontal to the earth’s surface, is less for latitude D, and greater for latitude C, than it was for the place whose
latitude was A. Furthermore, as the earth rotates around its own axis once in 24 hours, each gyro has required the same absolute amount of time, i.e. 12 hours, to move from position (I) to position (3) regardless of whether its latitude is that of A, B or C.
But in this same length of time, one spinning axis has tilted through an angle ?1°, the other through angle of ?2°, the third through an angle ?3°, each differing from the other and dependent upon the latitude. Thus the rate of tilting of xx must vary for different latitudes, and as precession results from this tilting, it follows that each particular latitude must have its own rate of tilting, and resulting rate of precession, if the gyro’s spinning axis is to be kept turned into the meridian, i. e., kept constantly pointing true north.
Damping
Suppose, in Fig. 19, G be a weight hanging quietly at rest suspended by the spring S. Suppose this weight be lifted by hand to the position 1, Fig. 20, and then suddenly released. Under the influence of gravity the weight will fall from (1) towards its previous position of rest, but upon arrival there will not stop but
Fig. 19
Fig. 20
will be carried to position 2. At this point the weight will stop and begin to travel upwards towards O but again by virtue of its inertia will pass O and continue to travel towards (1). There will thus be set up a series of oscillations of G, and, if it so happens that the mass of G and the length and character of the spring N are just right for it, the oscillation of G will continue for a very long time unless they are checked or “damped” by the application of some outside force.
Under the conditions of Fig. 20, the path followed by any point a, of G, would be the vertical straight line of be. Now, in Fig. 21, let a slot be cut in G and in this slot one end of the axis of spin, xx, of a spinning gyro wheel be inserted as at a, position O, Fig. 21. Let G now be started oscillating in the same manner as described for Fig. 20. As G rises and falls in the vertical plane, it will cause xx to rise and fall (tilt) with it, but recalling the principle of precession explained by Fig. 6, we see that xx will not only rise and fall with G but will precess right and left as illustrated at positions (1) and (2), Fig. 21, so that while the end of xx travels in a vertical oscillation equal to be of Fig. 20 it has also a horizontal oscillation equal to dc of Fig. 21. The result is that any point on the end of the axis of spin, xx, is oscillating both vertically and horizontally at the same time and, in consequence, describes a path which is an ellipse.
Fig. 21
Now a careful study of Figs. 15 to 18, inclusive, with the text relating thereto shows that the gravity couple (force of gravity) is constantly tilting the axis of spin, xx, of the gyros therein shown, to keep them in the horizontal plane. Also there exists the fact that the inertia of the mass of the gyro tends to force xx on past the horizontal plane, just as G of Fig. 20 was forced past its middle, 0, position, and that when forced past gravity tends to return it. So, in reality, in a spinning gyroscope there may be the same kind of vertical oscillations and corresponding precessions as indicated in Fig. 21 and these will continue unless checked or “damped.”
In a gyroscope in which the oscillations just referred to are allowed to take place unchecked or undamped, the end of the axis
Fig. 23
of spin is constantly describing a curve similar to that of Fig. 22.1
In a gyroscope in which such oscillations are unchecked or undamped, the oscillations continue for a very long time and render such a gyro useless for carrying a compass card, since such a card would be constantly oscillating (precessing) through a wide range on each side of the meridian thus producing a compass whose error was constantly changing from one instant to the next.
Hence, before a gyroscope can be used for mounting upon it a compass card that will be of any practical value whatsoever, mechanical arrangements, of otic kind or another, for damping oscillations must be incorporated in the design of such a compass.
An undamped gyro’s axis when acted upon by gravity and the earth’s rotation will constantly travel around the path of Fig. 22, but when this compass has a damping force applied to it, its oscillations get less and less and the axis finally settles down at some point N (settling point) at which it remains practically constant for the place (the latitude). See Fig. 23.
Explanation of the Principle of the Application of the Damping Force of Couple
In Fig. 24 let A be a gyroscopic wheel with the usual axes YY, ZZ, and axis of spin xx. Let the horizontal and vertical planes through the meridian be as indicated. Let xx be tilting downward under the influence of gravity g. Let gi represent the continuation of the downward tilt past the horizontal because of the wheel A’s inertia. The resulting precession around axis ZZ due to the tilt g + gi would be pg + pi as shown in the figure and the end of xx would tend to take the position (2). Suppose, however, as xx approaches the meridian and tends to pass it to go on to (2) we forcibly turn it back around the axis ZZ by applying to it an external couple or force d. This rotation of A by d around the axis ZZ will cause tilting of xx around YY (the amount of tilt t being indicated in the figure), with the result that under the combined action of the gravity and damping forces the axis of the wheel will settle at some point N (called the settling point), very close to the meridian and horizontal planes and, in a properly designed, constructed and operated machine, will, for all practical purposes, remain at N. Any condition and direction of forces might have been taken for illustration and A might be either above or below the horizontal, or east or west of the meridian, but in any
case very small and practically constant so long as the gravity and damping couples (forces) act as just described.
In the earlier German compass the damping force or couple consisted in the action of an air blast tending to turn the wheel A around the axis ZZ; in the Sperry compass a connection or bearing eccentric to the axis, ZZ, produces a similar effect. But in each compass damping must be produced if the compass is to be of any use to the mariner.1
The diagrams below show the character of the curves of damped and undamped oscillations in a gyro compass.
In Figs. 15, 17 and 18 it is shown that the spinning axis has tilted through 37°, 83° and 108°, respectively and that in each case it required the same amount of time, 12 hours, to do it.
The rate of tilting in each case is 3.00, 6.9° and 9.00 per hour, respectively, and this rate is different for each and every position
in latitude. Or, to put it in another way, each and every latitude requires its own particular rate of tilting, and resulting precession, in order to turn the axis, xx, into the meridian and to keep the compass pointing true north.
1The following explanation of damping is by Mr. H. L. Tanner, of the Sperry Company:
“As the connection between the bail and wheel case is eccentric (see e Fig. 26), the torque applied to the wheel case is about a line inclined to the horizontal by an angle equal to the angle of eccentricity of the above connection. This causes precession about a line inclined the same amount to the vertical, i. e., a line passing through the eccentric connection and the center of the wheel. This precession may be resolved into two components, one in a horizontal plane and one in a vertical, and it will always be found that the component in the vertical plane is in such direction as to decrease the angle of tilt of the wheel’s axis, thus de-energizing it and reducing the amplitude of its oscillations about the meridian.”
Bearing this in mind, and referring to the damping force d of Fig. 24, we see that d has to balance a rate of precession that varies with every change in latitude, and that unless this balance is absolutely exact for each latitude the compass will change the position of its settling point, S, upon a change of latitude so that while in one latitude it might settle at S, in other latitudes it might settle at S1 or S2 relative to the meridian plane. This balance is very difficult to accomplish in the actual building of a compass.
In practice, it is customary to mechanically construct a material compass which is exactly balanced or adjusted for one latitude, then calculate the error of the settling points (relative to the meridian) for other latitudes and correct for them by moving the lubber’s line. In the German compass, this is done by loosening a couple of set screws and shifting the plate which has the lubber’s line marked on it. In the Sperry compass a similar result is obtained by different mechanism described later.
The German compasses of 1910 were all adjusted for a mean latitude of 50° north. In going to other latitudes the errors due to change in latitude, which error is corrected in each case by shifting the lubber’s line, are given in the following table:
For a Compass Adjusted To Be Correct in Latitude 50° N.
Error required to be corrected by shifting lubber’s line (German Compass)
Latitude of Place
60° N ………….. 0° 36' easterly.
50° N None, compass designed for this latitude.
40° N. …… 0° 30' westerly.
20° N. ... 1° 06' westerly.
0° …......... 1° 36' westerly.
20° S. .... 2° 06' westerly.
40° S. .... 2° 42' westerly.
60° S. 3° 48' westerly.
How the Gravity Couple or Force of Gravity is Applied in the Gyroscopic Compass to Keep Tilting the Spinning Axis, xx, into the Horizontal Plane
Throughout this paper the expression “gravity keeps the spinning axis turned into the horizontal plane” has been repeatedly used. (Study Figs. 10, 15, 17, 18 and 24.) Gravity is utilized to accomplish this as follows:
In the German compass of 1910 the casing carrying the gyro wheel is suspended from a hollow circular ring, rr, floating in a bowl of mercury mm. The gyro wheel casing is rigidly connected to 'rr by H and Z, and as rr floats horizontally on the surface of the mercury at every latitude, then xx, by the construction, is constrained to remain horizontal at every latitude.
In the Sperry compass, a similar result is obtained by a different construction.
In Fig. 26, A is the casing carrying the gyro wheel, xx its spinning axis; the horizontal and vertical axes, YY and ZZ being
shown also. Between the ring C and the wheel casing A is a weight B (called the “bail”) supported at points ff outside of the gyroscope proper. Under the influence of gravity, this weight hangs in the vertical plane through ff whatever may be the latitude of the place. There are slots in C which allow B to do this. Between the wheel casing A and the weight or bail B there is at c a pin connection or bearing.
Now the bail B constantly hangs in the vertical plane, but the plane of the gyro wheel A tending to keep its position in space as the earth revolves will tend to separate from B. The flexible pin connection c prevents this and thus gravity acting by means of B through e constantly tends to keep the plane of the spinning wheel, A, vertical and its spinning axis horizontal.
The Damping Couple
A study of Fig. 26 will show that when A and B tend to separate not only is the gyro wheel rotated around the YY axis, but if e be set off to one side of the axis ZZ, A will receive from B through e rotation around ZZ. This brings into play the damping force d as explained in Fig. 24. In this compass, e, of Fig. 26, is called the “eccentric bearing.”
Summary of Preceding Notes
So far, all that has been written refers entirely to a compass mounted on a stationary base on shore. The notes have indicated the following points:
- The axis of the gyroscope, with three degrees of freedom, tends to remain pointed in one and the same direction in space unless acted upon by an external force.
- That in the gyroscopic compass the tendency of paragraph 1 is constantly overcome by a mechanical application of the force of gravity, which constantly tends to pull the axis of the spinning wheel into a horizontal position relative to the earth’s surface.
- That the pull of paragraph 2 causes the axis to tilt and this tilt results in precession which tends to make the spinning axis of the gyro always lie in a meridian plane (tends to set itself parallel to the earth’s axis), i. e., always point towards the earth’s true poles, i. e., true north.
- That because of the material gyroscopic wheel possessing mass and inertia, the foregoing combined causes produce oscillations in the spinning wheel, rendering it useless for carrying a compass card unless these oscillations are checked or damped.
- That damping is an essential feature of every practical gyroscopic compass.
- That a compass may be built to read correctly for' one latitude but will be in error in another latitude.
- That the error in any latitude, other than that for which the compass was designed, is allowed for by moving the zero point (lubber’s line) to compensate for the error due to difference in latitude. This correction which is dependent upon the latitude alone is known as the “latitude correction.”
The Compass Mounted on a Moving Ship1
The gyroscopic compass on a moving ship does not point exactly to the true north but constantly requires the introduction of some three positive, or negative, correction factors before one can ascertain the true location of the meridian.
1 The following explanation of the deflection due to the actual movement of the ship north, or south, is due to the courtesy of Mr. Harry L. Tanner, Engineer of the Sperry Gyroscope Co.:
“If we assume the ship to be at rest and the earth rotating, the compass will assume a position with its axis in the plane of the earth’s axis; then if we assume the earth to be standing and the ship to be moving north over the earth’s surface, it will be moving in a great circle, the axis of which lies in the plane of the equator and the end of the compass wheel which is normally the north end will point west. It is evident that if we combine the movement of the ship and the rotation of the earth the compass will assume an intermediate position, and as the velocity due to the rotation of the earth is many times that due to the movement of the ship, this position will deviate but slightly from the plane of the earth’s axis. The amount of this deviation may be computed as follows:
In Fig. 1 let ab represent the linear velocity of the compass due to the rotation of the earth (this velocity of course will vary with the latitude,
FIG. 1
FIG. 2
being proportional to the cosine of the latitude) and be the velocity of the ship with respect to the earth the resultant velocity will then be ac and the deviation of the compass will be equal to the angle cab.
In Fig. 2 the ship is shown with an easterly velocity be and as ac coincides with be, no deviation of the compass will be produced.
Fig. 3 shows the ship moving northeast and the angle cab is intermediate between that of Figs. 1 and 2. In practice, line ab is so long with respect to line be that the easterly component of be may be neglected and only ' the northerly component, which is equal to be cosine ship’s heading, need be considered.
Referring to Figs. 17 and 18, suppose we take the compass at latitude B° of Fig. 17, mount it on board ship and steam true north at a speed of 10 knots per hour to the place whose latitude is C° of Fig. 18.
By so doing we have steamed directly from a place at which the rate of tilting of xx was 370 in 12 hours to a point at which the rate is 108° in 12 hours. Suppose in starting from B, we had steamed 20 knots per hour instead of 10 knots. We would thus arrive at C in one-half the time it would have taken us at 10 knots and the rate at which this change in the tilt of xx takes place, as due to differences in speed, would be twice as great in the second case as in the first case. Thus speed is introduced as a factor.
Suppose, starting from any point, we steam true east at either 10 or 20 knots. As we do not change our latitude, the rate of tilting of xx is the same at every point at which we arrive as it was at any point we left. There is no appreciable disturbance of the compass from this case because the ships speed is merely additive to that of the surface of the earth, as the earth revolves on its axis, and is negligible.
Suppose we steam NE. true. Then the true northerly component of the ship’s speed will have an effect, because it changes the rate of tilting of xx and as this northerly component depends upon the ship’s course, the course is thus introduced as a factor.
The relative effects of moving the compass in north and south directions, i. e., steaming on these courses, compared with movement in easterly or westerly directions is indicated very simply in Figs. 27 and 28.
In Fig. 27 let A be a gyro at the equator, the projection in Fig. 27 being on a meridian plane. If we steam true north or south from A to B, or to C, we do not transport xx parallel to itself in space but by introducing gravity cause it to tilt as shown, and this tilting of xx causes precession, the rate of which is affected, not only by the latitude we happen to be in, but by the speed with which we steam from A to B, or to C.
In Fig. 28 we have a projection on the plane of the equator. From A let us steam true east, or west, to B or to C. In so doing we have transported the spinning axis xx of the gyroscopic wheel parallel to itself in space, in consequence of which there is no resulting precession. See Figs. 2 to 5 and the text thereon. If we steam east or west from any other latitude we do not change the rate of tilting of xx, hence there is no change in precession due to an east or west course alone.
The Sperry Compass
Fig. 29 is a diagrammatic sketch of the Sperry compass. It is only intended to illustrate certain principles of construction and operation.
The gyroscope wheel A is mounted to spin on a horizontal axis, xx, within the casing B, which is pivoted on the horizontal axis Y Y through its center of gravity and carried by the frame or vertical ring D. The ring D is suspended by the tortionless strand E and guided by bearings ZZ' to allow a free oscillation of limited amount about its vertical axis ZZ' within the frame or phantom G.
The phantom G has a hollow stem H to which the strand E is attached at its upper end, and the stem forms a journal for rotation in azimuth with respect to the supporting base frame I. The frame J is mounted in gimbal rings K'K' on the binnacle in the same or similar manner as the ordinary magnetic compass is mounted in its binnacle stand.
Secured rigidly to the stem H of the phantom is a large gear wheel, NN, having 360 teeth, one tooth for each degree of azimuth. This gear wheel can only move with the phantom and conversely when the gear wheel, NN, is moved the phantom must move.
Rigidly secured to the frame J, and thus fixed relatively to the ship is a motor, M, whose small spur wheel w engages with the teeth of NN. Mounted rigidly on NN is the compass card CC graduated to 360°. Flush with the surface of the compass card
FIG. 29.—Partial diagram of section in an east and west line illustrating mounting and the follow up system.
is a flat ring, FF, on which is engraved the lubber’s line. FF is supported by brackets, QQ, on the frame J. Rigidly secured to the lubber’s ring, FF, is a transmitter P whose function is to transmit electrically to the repeater compass at the helmsman, or to the pelorus repeaters, any movement made by the compass card CC.
z*
Fig. 30.—Wheel Casing and Vertical Supporting Ring, North End.
The wheel A together with the wheel casing B and the ring D is called the sensitive element. As a matter of fact, and most important, the sensitive element is the real gyroscopic compass, and all the other mechanism is installed simply to reproduce the exact movement, headings, or readings of the sensitive element in azimuth without interfering with it. Attached to the sensitive element, on the vertical posts, a, a, as shown, are two electrical trolley contact, a, a, which make a light electrical contact with double stationary contacts bb', bb' carried by the phantom. The object of this mechanism is to make the phantom carrying the compass
Fig. 31.—Wheel Casing and Vertical Supporting Ring, East Side.
card follow exactly every movement in azimuth of the axis of the gyro wheel and thus register in degrees either the heading (course) of the ship or the direction in which the gyro axis, xx, is pointing relative to the meridian. Furthermore, this movement, by means of the repeating transmitter, P, is sent to every steering
Fig. 32.—Phantom Card, Azimuth Gear and Cam for automatic Correction Mechanism.
compass, bridge pelorus, and repeater compass in the ship. This work is performed without any interference with the freedom of action of the sensitive element except that of the very light touch of the electrical contacts aa and bb' bb'.
Illustrations of the sensitive element and phantom are shown in Figs. 30, 31 and 32. Compare them with Fig. 29.
The method of operation follows:
Referring to Fig. 29, let us assume that the compass has been shut down and stopped for several days, that the ship is tied up to the dock and is stationary, heading say SE and that the sensitive element has stopped so that its axis happens to be pointing in the direction of the keel line, SE. and NW., which is perpendicular to the plane of the paper upon which Fig. 29 is drawn. Now start the up compass. As the wheel A gathers speed, it will tend to move out of the plane of the paper upon which Fig. 29 is drawn and the axis, xx, will tend to turn into the meridian to point north and south, carrying with it the sensitive element. As the sensitive element moves in azimuth to seek the meridian the contacts aa come in touch with the contacts bb' bb' and send current through the azimuth motor M which in turn rotates NN (and the phantom and compass card) through exactly the same number of degrees in azimuth through which xx has turned. In other words the compass card is forced to register exactly the movement in azimuth of the gyroscopic wheel.
As NN is revolved by M it turns the spur wheel nf of the repeater transmitter P. This wheel carries a commutator or contact maker S which energizes the motors of the compass cards of each and every repeater compass in the ship and makes them, too, register exactly as the compass card, CC, of the master compass shown in Fig. 29.
The conception and construction of this “follow up” and repeating system is very pretty.
The Automatic Correction System
Fig- 33 is a diagrammatic sketch of this mechanism. In studying this figure it must be borne in mind that it is a sketch made solely for the purpose of illustrating principles and is not a mechanical drawing of a machine. It merely illustrates how the operations may be carried on but does not show the exact mechanical details of the construction. In Fig. 33 and in Fig. 29 the same parts have the same letters.
As stated previously in these notes, the gyroscopic compass on moving ships does not point north as has been supposed, but constantly requires the introduction of some three positive, or negative, correction factors before one can ascertain the true location of the meridian. While on land a gyro compass will point to the absolute north, yet when mounted upon a moving body, as a ship, which has a northerly or southerly course, or component of course, the gyroscope no longer receives simple easterly motion (from the earth’s rotation) but a mixed motion, and is accord-
ingly deflected from the meridian to correspond with the new relative axis in space. The amount of this deflection depends upon three variables, namely, the course of the ship, the speed upon such course and the latitude. The latitude also introduces a second correction, due to certain characteristics of the compass. The formula for the total deflection is as follows:
D=aK cos H / cos L – b tan L.
Where D=total correction for the deflection of the gyro compass from true geographical north; H=ship’s heading or direction of travel on course figured in degrees from the geographical north; K=speed in knots; L = latitude; and a and b are constant reduction factors for the units employed and certain dimensions of the instrument.
Heretofore it has been necessary to make simultaneous readings of these three independent factors and compute the total correction, or else consult elaborate printed tables to determine the positive or negative correction necessary, in some cases to make various adjustments by the addition or removal of weights with changes of latitude. Mr. Sperry has produced an automatic correction apparatus which constitutes a simple part of the compass structure, by means of which all of the above components of deflection and exactly compensated for and automatically entered, so that all readings of the master compass, together with repeating compasses and other auxiliary apparatus are always held dead upon the meridian. The indication of each repeater located at remote parts of the ship is always held true and found to read exactly upon the sun without any of the troublesome correcting factors mentioned above.
In Fig. 33, the compass card CC, the phantom G, sensitive element BD, lubber’s line ring FF, azimuth motor M, repeater transmitter Pw', etc., are all shown, lettered and indicated as in Fig. 29.
Referring to Fig. 33, the lubber’s line ring, FF, carries a smalltoothed rack r, engaging in the teeth of the arm s, the arm s being pivoted at i. Rotation of s around i causes the lubber’s line ring, FF, to slide around in its bearings QQQQ.
An arm l connects j to the latitude correction dial L, which in turn is connected to the speed correction dial K by the arm m, and K in turn is connected by the arms n and o to a roller bearing t which engages in the slot of the cosine cam T. (See also Fig. 29.)
It will be seen that this construction is in effect a system of link work such that as t moves in accordance with the guide slot of the cam T, its motion is transmitted through o, n, m, I, s and r to the lubber’s line ring, FF, and moves it to the right or left by an amount which is necessary to make the desired correction. The cosine cam T is designed to correct for the course of the ship, i. c., when the ship changes her heading (or course) T automatically introduces that correction referred to where it stated “thus the course is introduced as a factor.” When FF is moved by s, the repeating transmitter wheel w' rolls around CC which remains fixed, and thus each repeater compass in the ship is made to read exactly as the master compass. For example, if the lubber’s line were moved 30 to the right of its position of 0° as shown in Fig. 33, the course by the master compass would then read N. 30 E. But while FF moved to the right 30 it would carry the repeater wheel wf with in and cause ?</ to roll around on CC and this movement of 30 would thus be electrically transmitted to, and simultaneously, registered on every repeater compass in the ship so that they, too, would read N. 30 E. exactly the same as the master compass.
The cosine cam T thus regulates the amount the lubber’s line is moved to correct the error introduced by the ship steaming on any course between north and south, east and west.
For any specific course, the amount of correction introduced by the link work /, m, n, o will be always the same, provided the length and relative positions of the link work arms l, m, n, etc., remain unchanged.
The speed correction dials K, and the latitude correction dial L are a complicated series of disc cams, so constructed that by loosening up the set screws on either dial the proportional arrangement of the arms of the link work system connected to that dial may be altered without changing the relative effect of the link arms attached to the other dial. (The diagram does not show the mechanical details of this construction.)
Thus, to set the latitude dial so as to introduce its correction, slack up on the latitude dial set screw, turn the dial L to the proper latitude reading and then clamp the set screw again. The link work system now has the latitude correction combined with the course correction. To add the speed correction to the foregoing, slack up the set screw on the speed correction dial, K, turn this dial until it is set for the speed at which the ship is steaming, then clamp the set screw. The proportion of the arms of the link work system have now been so adjusted that the corrections for speed is automatically added to that for the latitude and course, and the
Fig. 34.—Portion of Master Compass Card, Showing Exact Meridianal Course, also the Amount of Correction being Automatically Introduced at the Moment.
Fig. 35
lubber’s line indicates, on the master compass card CC, the exact true course the ship is steering and all other repeater compasses in the ship indicate the same course as the master compass. See Fig. 34-
Fig. 35 shows a setting for 15 knots speed in latitude 40° N.
As the factor introduced by the cosine cam T is constant, this cam is so designed that when once installed no further adjustment of the cam itself is necessary.
When the compass is running normally and the dials are set for the correct latitude and speed there should be no error and this should be shown by the fact that true bearings or azimuths of the sun as observed by an azimuth circle on a repeater should be the same as the true bearing of the sun worked out by the azimuth tables. If these agree exactly there is no error in the compass and all bearings taken, or courses steered, by it are true.
If azimuths of the sun indicate an error in the compass in spite of the fact that the dials are correctly set for the correct speed and
Fig. 35A.—Cosine cam engages here.
latitude, the presence of such an error indicates one of two things, viz.: (1) The presence of an oscillation, during which the error passes slowly to a maximum easterly error, then back to a corresponding maximum westerly error, and so continues for some time until the oscillation subsides; or (2) The compass may have changed its settling point so that it has a constant easterly, or westerly, error.
To Correct a Constant Error.—Loosen the small set screws jj (Fig. 33) found on each side of the lubber’s line aft. Loosening these screws allows the lubber’s line ring to be turned independently of the short rack r driven by s. By means of the thumb and forefinger of each hand, turn FF through the number of degrees measured on the scale h (Fig. 33) as an azimuth of the sun has shown the compass to be in error, then clamp or set up tightly on
jj. Now if the dials are correctly set for speed and latitude the master compass and all repeaters should show no error, by observation of the sun, under all conditions of service.
To Determine if the Compass has an Oscillation
The period of the compass, i. e., the time it takes to make one complete oscillation varies from 70 to 80 minutes, hence observations of the sun, or Polaris, for azimuth, taken every 10 or 15 minutes apart, extending over a period of 70 to 80 minutes, will show whether the compass is oscillating and, if so, the amount of such oscillation.
Or if the sea is calm and smooth, 10- to 15-minute comparisons of the ship’s head per gyro compass with that per standard magnetic compass will disclose the oscillation.
Or if the ship is at rest, as at anchor in a smooth harbor, and no sun is available, the rise and fall of the axis due to an oscillation is indicated by the travel of the bubble in the spirit levels attached to the compass.
A Query
To the reader not quite familiar with the principles of operation of the compass the thought may arise that the lubber’s line on FF has been indiscriminately moved around CC and then said to give a true reading. How can this be so? The keel of the ship has not changed! The lubber’s line on the steering compass and pelorus dials on the bridge are absolutely fixed and installed parallel to the keel of the ship and cannot be changed, yet you are constantly shifting the lubber’s line on the master compass and say this gives true courses and bearings on the bridge! How can this be so?
The answer is simply this: The compass cards of each and every repeater compass are controlled and moved by the lubber’s line ring FF. They move with it and not with the compass card CC of the master compass. The compass card of the master compass by virtue of its association and connection with the sensitive element, serves as a scale upon which to indicate the true bearing of the meridian. Hence, if we move the lubber’s line, FF, around CC to a point reading, say, 346° on CC, then each repeater compass card will move around to register 346° by the fixed lubbers’ (keel) lines on the bridge compass, and will show the ship to be steaming a true course of 346°. If 346° be not the course to be steered to reach port, then the keel of the ship is altered by the rudder to such a course as will bring her to the desired destination.
In other words, in the master compass we have the lubber’s line travel around the master compass card, but in the repeater compass the card travels around under the lubber's line. As the movement in azimuth is identical in each case, each compass will read the same number of degrees.
Rolling and Pitching
All of the foregoing notes upon the principle of operation of this compass have referred (1) to a compass mounted on shore and (2) to a compass mounted on board a ship moving in a smooth, calm sea.
When the ship rolls and pitches, new forces and conditions arise. The forces due to the rolling and pitching of the ship may be resolved into two components; (1) the accelerating forces due to reversal of direction, and, (2) centrifugal forces due to the fact that the parts of the compass have an angular motion in addition to the motion of translation.
In the Sperry compass the effect of the acceleration forces on the compass is overcome by means of the stabilizer gyro shown in Figs. 36 and 36a while the centrifugal forces are overcome by means of the compensating weights shown in Figs. 36a and 36b.
The Sperry compass in service aboard the Montana gave us great comfort and satisfaction and we relied upon it. We considered it a wonderful instrument and one of the most valuable additions of modern science to the sea-going world. In the conning-tower, and below decks, its freedom from magnetic influence is most valuable.
It requires for its proper functioning the intelligent care and supervision of officers and electricians who know how to run it, but it did not require greater specialization along its particular lines than did guns, torpedoes, chronometers or any other mechanical devices installed in a modern ship.
I have only praise for it. Like everything else, though, success with it depends upon intelligent care and operation.
Fig. 36.—Floating Ballistic or Stabilizer.
Fig. 36A.—Master Compass, North West Elevation; Showing Stabilizer or Floating Ballistic B, and compensating weight WIV.
Fig. 36B.—Compensator Weight and Frame.
APPENDIX
The following explanation of the deviations due to accelerating and centrifugal forces and their correction is by Mr. Harry L. Tanner, engineer of the Sperry Gyroscope Company, to whom acknowledgment is here made:
Compass Deviations Due to Acceleration Forces
The compass wheel, wheel case and bail may be represented diagrammatically by a rotating disk A, Fig. 37, rotating on bear-
Fig. 37
ings B in a U-shaped frame C, which is in turn suspended by means of a flexible cord D.
The ballistic factor of the compass is represented by the weight of the disk A, multiplied by the distance from center of the disk to point E when flexible cord D is attached to frame C.
Now suppose, for instance, that the compass be accelerated alternately NE. and SW., Fig. 38. The whole compass will act as a pendulum and will take up a position such that the cord D will be parallel to the line of the force F, which is the resultant of the acceleration force and gravity.
The frame C will respond to the ElV. component of this force, but not to the NS. component on account of being stabilized in this direction by the disk A.
Let a, shown in projection in Fig. 38 as a, represent the angle between force F and the horizontal plane, then the horizontal component of F will be F cos a. When the acceleration force is NE. the NS. component of this force will produce a torque about xy,
which lies in the plane of the disk. This torque may be resolved into a component about the vertical axis zy and a component about the horizontal xz. Similarly, when the acceleration force is SW. the arrows z'y' and x'd represent components of torque about the vertical and horizontal axes respectively. It will be seen that the torques about xz and x'z' are equal and opposite and therefore cancel, but that the torque about zy and z'y' are in the same direction and therefore add, giving a torque about the vertical axis of the disk which, acting through a cycle of precessions, will cause a movement of the disk in the direction of the torque.
Similarly, it may be shown that alternate NW. and SE. accelerations will produce a torque in the opposite direction about the vertical axis.
As the direction of the acceleration pressures approaches the EW. line it is evident that the NS. component of the force F cos a will approach zero and as the acceleration pressures approach the ATS. line, the lever arm of these forces about the vertical axis will approach zero, in either case resulting in zero torque about the vertical axis.
As explained; the compass deviations, due to accelerating forces, are due to the fact that the force and lever arm reverse at the same instant, giving a torque in a constant direction about the vertical axis of the compass. By reducing either of these components to zero or making the direction of either constant while the other changes, we shall have either zero torque about the vertical axis or equal positive and negative torques, which would give a resultant zero torque. The latter method is made use of in the compass.
As all of the forces acting upon the wheel in the compass are introduced through the bail, it is only necessary to hold the point of connection between the bail and wheel case fixed with respect to a vertical line passing through the center of the wheel. As far as the effect of the acceleration force goes, it makes no difference what this position is so long as it is fixed, but to secure damping it is nearly one-fourth inch to the east of the center of the wheel.
Referring to Figs. 39 and 40 it will be noted that the stabilizer is mounted on the north side of the compass wheel case, the bearings at point A leaving it free to swing about an axis parallel to that about which the main compass wheel spins.
The small gyroscope, B, spins upon an EW. axis and is free to precess about a vertical axis, the bearings being shown at CC.
Due to the stabilizing effect of the gyroscope B, the frame D will be held in a fixed relation to a vertical line passing through the center of the main compass wheel, and the small rollers,.EE, are therefore held a fixed distance from a plane passing through the axis of the main wheel. These rollers run in tracks, F, attached to the wheel case and G attached to the bail.
Fig. 40
Compass Deviations Due to Centrifugal Force
Cause of Deviations.—If a bar A, Fig. 41, be suspended by means of a wire loop B, and a thread C, and be swung as a pendulum about an axis passing through D it will take up a position such that the bar A, and thread C, will lie in a plane perpendicular to the axis of swing through D. This is illustrated in Figs. 42 and 42a in which A represents the bar and ab the axis about which the
Fig. 44
pendulum is swung. The arrows represent the direction in which the bar would turn. This has been determined mathematically and later verified by actually constructing the apparatus as illustrated and testing. Application to Compass.—It will at once be seen from Figs. 43 and 44 that the vertical ring, wheel case and stator of the compass, i. e., the entire sensitive element with the exception of the rotor (which does not enter in any way on account of being free to turn on its bearings about an axis perpendicular to the plane of horizontal bearings of the case) may be replaced by a weightless rod H, a weightless support J and thread K and two weights I, 1.
Theory.—Fig. 45 shows the apparatus of Fig. 41 swinging about an axis which makes an angle of about 45° with the bar A. It is evident that any point in the bar will swing in a plane perpendicular to the axis ab and in the arc of a circle of which the center lies in the axis ab. Thus the particle c would move in an arc of a circle of radius cd and in a plane perpendicular to ab. The centrifugal force then would be directed along the line dc. This force
Side Elevation Front Elevation
can be resolved, as shown, into components cf and eg. Then eg can be again resolved into components eh and ci. It will be seen that all components such as ci have no effect other than to produce tension in the bar A but that all components such as eh produce a couple tending to rotate the bar toward a position perpendicular to ab.
Remedy.—From Figs. 42 and 42a it will be seen that two like bars which are 90° apart have equal torques in opposite directions. Therefore, if we should fasten two of these bars together the forces would exactly neutralize each other. This would be true when the cross is placed in any position so long as the bars are at right angles to each other, as the torque is proportional to the product of the sine and cosine of the angle with the axis of swing so conies up to a maximum at 45° and drops to zero at 0° or 90°.
It will be evident from Fig. 46 (or Fig. 46a) that the effect of the crossed bars may be secured in the compass by attaching
arms MM to the north and south sides of the vertical ring and attaching weights LL to them at points in line with the center of the wheel. These weights must be attached to the vertical ring as they would have no effect if attached to the stabilized case. See Figures 36a and 36b.