THE DAMPING SYSTEM OF THE ANSCHÜTZ (1910) COMPASS
In the preceding chapter we demonstrated the necessity for damping the
horizontal oscillatory movement of the gyro-compass axle and discussed
the nature of damped vibrations in general. We now turn to describe the
damping means provided in each of the practical forms of gyro-compass
so far evolved.
Turning to the early (1910) form of Anschütz compass, we find that, as
shown in the purely diagrammatic sketch given in Fig. 16, the spinning
wheel is enclosed within a metallic case formed with tubular journals
B C for the axle, and provided with trunnions E F, whereby it is
supported within the vertical ring, which, as before, is free to turn
on a vertical axis H J. The casing, it will be seen is, so far as the
support of the wheel is concerned, exactly equivalent to the horizontal
inner ring of our preceding illustrations. In the actual instrument
the method of supporting the casing so as to permit it to turn about a
horizontal and a vertical axis is not in the least like that shown in
our sketch.
The wheel, running at 20,000 revolutions per minute, although it
is quite plain, has a powerful blower-like action. On one side of
the casing an orifice D is formed for the inlet of air, and on the
periphery below an outlet duct K, directing the air blast tangentially
away from the casing, is provided. The exact value of the pressure of
the blast in the early Anschütz compass is not known to us, but in the
Brown compass, wherein a similar blast is developed, the wheel, running
at 15,000 revolutions per minute, gives an air pressure equal to some 3
in. of water.
[Illustration: FIG. 16. Air Blast Damping System of Anschütz (1910)
Compass.]
The mouth of the outlet duct K is partially closed by a plate L fixed
at the end of a pendulum arm suspended frictionlessly, or practically
so, from some convenient point on the casing, so that when the casing
turns on the vertical axis H J the arm and plate turn with it. The
pendulum arm is carefully balanced in such a way that when the axle
of the spinning wheel is horizontal the plate L exactly divides the
orifice K, leaving equal passages for the air blast on each side. In
this condition the two passages M N being equal in area, the air blast
is divided by the plate into two streams of equal volume and momentum,
so that if their free discharge is not influenced by surrounding
objects their reactions on the casing, one on the one side of the
vertical axis H J, the other on the opposite side, will be equal.
Let the compass be deflected until its axle points east and west, the
end B being towards the east. Then, as we have seen, the tendency of
the axle to remain parallel with its original position, combined with
the rotation of the earth, will cause the axle to assume an inclined
position relatively to the earth’s horizontal surface. Gravity acting
on the pendulous weight S as thus displaced from the plumb line will,
as we know, set up a precession about the vertical axis H J, so as
to cause the end B of the axle to move towards the north. When,
however, the axle tilts in this manner about the horizontal axis E F,
the pendulum plate L, hanging freely, remains in the plumb line.
Consequently the equal areas M N become unequal, as at P Q, the larger
P being towards that end of the axle which has tilted upwards, namely,
the north-seeking end B. The reaction on the casing of the portion of
the air blast issuing from P is now greater than that of the portion
emitted through Q. This inequality results in the application to the
sensitive element of a force acting about the vertical axis H J. The
reaction of a jet of air or water or other fluid being opposed to the
direction in which the jet is issuing, the force applied to the casing
is such as to drive P into the plane of the paper and to bring Q out of
it--that is to say, to tend to rotate the casing on the vertical axis
in the direction of the arrow R.
The force thus applied clearly tends to oppose the return of the
axle from the east towards the north. On the other hand, if the axle
succeeds in turning round until the end B points to the west, the
rotation of the earth will result in the axle tilting as before, but
with the end B downwards. Consequently the area M diminishes and the
area N increases, and the reaction applied to the casing is such as
to tend to turn it in the reverse direction to R. The applied force
in this case therefore opposes the return of the axle from the west
towards the north. The exact manner in which the opposition acts is to
be noted. A force applied to a simple gyroscope, so as to tend to make
it turn about the vertical axis H J in the direction R (Fig. 16) will,
as was stated in our second chapter, cause the wheel to precess about
the horizontal axis E F, the end B of the axle going down and the end
C up. If the force about H J is reversed, the movement produced will
be a precession of the wheel on E F such that the end B of the axle
rises and the end C falls. The opposition between the moment applied
to the sensitive element by the air blast and the moment applied to it
by the directive force is therefore not quite direct. When the end B
of the axle is deflected towards the east a directive force is called
into being by virtue of the tendency of this end to rise. The air blast
reaction about H J induces precession on the axis E F, causing the
end B to fall. By the amount by which the air blast reaction succeeds
in lowering the end B of the axle, by that amount will it reduce the
normal magnitude of the directive force. When the axle swings through
the meridian towards the west a reversed directive force is called into
play by virtue of the tendency of the end B to fall. The opposition of
the air blast reaction arises from the fact that its tendency now is to
make the end B rise. Thus on both sides of the meridian the opposition
of the air blast reaction is effective because it tends to precess the
wheel on the axis E F in the direction opposed to that in which the
rotation of the earth is trying to tilt the axle. The tilt moves the
pendulous weight S away from the vertical, so producing the directive
force; the air blast reaction reduces the tilt and so opposes the
directive force.
The reaction applied to the sensitive element by the air blast thus
fulfils one requirement of a satisfactory damping force; its effect at
all times is opposed in direction to the direction in which the axle
is moving. The second requirement is that the magnitude of its effect
should always be proportional to the velocity with which the axle is
moving.
In connection with this second requirement it is assumed that the
momenta of the air jets issuing from the openings P Q (Fig. 16) are at
all angles of tilt equivalent to the momentum of a single jet issuing
from an imaginary orifice U situated at some distance _d_ from the axis
H J on the side of the larger opening P, the area of the imaginary
orifice R and the velocity of the air through it being constant at all
angles of tilt. If this assumption is correct, then the moment about
H J applied by the reaction of the air blast is proportional to the
distance _d_--that is to say, to the angle of the tilt.
The assumption here made is, we believe, substantially justified if
the angle of tilt is never very great. In actual practice it is always
small. Various considerations, however, suggest that the reactions
of the two jets P Q are not equivalent strictly to the reaction of a
single jet through an orifice R of constant area. Thus from geometrical
considerations we can show that the sum of the areas P Q is not equal
to the sum of the areas M N. Again, the total weight of air drawn in
per minute through the orifice D may be constant, and therefore the
total weight of air delivered per minute through the combined openings
P Q may be unaffected by the tilt. But the ratio in which the total
volume divides itself between the two openings P Q and the velocity
through each certainly vary with the tilt. A peculiar practical
phenomenon also has to be considered in this connection. In the 1910
form of Anschütz compass the peripheral speed of the spinning wheel
was 500 ft. per second, or 340 miles an hour. The air friction at
this speed was so very great that after the wheel had been run a few
thousand hours its surface was found to be noticeably smoother than it
was when the wheel left the grinding machine on which it was finished.
As a result of this polishing effect, we should expect that even though
the speed of the wheel remained perfectly constant, its blower-like
action would decrease somewhat until the compass had been in use for
a certain length of time. If the blower action does so decrease the
magnitude of the air blast reaction on the sensitive element at any
given angle of tilt must diminish with time. We do not know whether the
diminution would be sufficiently great to introduce a serious error in
the reading of the compass.
Taking the assumption to be correct, at least for small angles of tilt,
we have next to study how the angle of tilt varies as the axle swings
from the east side of the meridian over to the west and back again.
When the axle is pointed due east the rotation of the earth, as we have
seen, tends to make the end B rise. If it is pointed due west, the
end B tends to fall. If it is lying dead on the meridian, the earth’s
rotation has no tilting effect at all on the axle. If the axle is
pointed in some direction between due east and due north, the tilting
effect is less than it would be if it were pointed due east, but it
is in the same direction; the end B tends to rise. Similarly, in any
position in the north-west quadrant the end B tends to tilt downwards
under a tilting influence which is somewhat less than that experienced
in the due west position. Let, then, the axle be turned to point due
east. The end B begins at once to rise, but immediately the axle thus
leaves the horizontal position it begins to feel the directive force,
and it commences to turn towards the north. Until it reaches the north
the tilting influence of the earth’s rotation continues so that during
the whole time the axle is swinging through the north-east quadrant the
tilt is increasing and the end B is rising, higher and higher. When the
north direction is reached the tilting influence vanishes and the end
B of the axle tends to travel horizontally in its elevated position
over into the north-west quadrant under the influence of the momentum
acquired in that direction during its movement through the north-east
quadrant. But on passing to the west side of the meridian it again
comes under the tilting influence of the earth’s rotation, which this
time tends to make the end B fall. When the axle reaches the due west
position, the tilting influence being equal to that acting over the
north-east quadrant and reversed in direction, and having acted for the
same length of time, will just have wiped out the elevation of the end
B, and the axle will again be horizontal. On the return journey through
the north-west quadrant the tilting influence is still reversed, so
that on reaching the north position again the end B is as far below the
horizontal as it was above it on the swing from east to west. Passing
to the east side of the meridian, the tilting action assumes its former
direction, the end B begins to rise, and when the due east position is
reached again the axle is once more horizontal. The path traced out
by the end B during a complete vibration from east to west and back
again is thus in the nature of an ellipse--or, in extreme cases, a
circle--such as that shown at _a b c d e_ in Fig. 17.
[Illustration: FIG. 17. Free and Damped Motion of Axle.]
On an east-to-west swing, then, the end B of the axle in Fig. 16, if
the air blast is out of action, tilts upwards from zero to a maximum
in the mid position and then again falls to zero. If the air blast is
brought into play, the reaction, being, as we have seen--at least for
all small angles of tilt--proportional to the angle of tilt of the
axle, will correspondingly increase from zero to a maximum and again
fall to zero. On the west-to-east swing the reaction will similarly
rise and fall in the reversed direction. The unrestrained movement
of the sensitive element under the influence of the directive force
is, as we know, analogous to that of a simple pendulum, so that the
velocity with which the axle moves is zero in the extreme positions
and a maximum in the mid position. Thus we see that the air blast
reaction not only constantly opposes the movement of the axle, with
the variation in the velocity with which the axle moves. The air
blast reaction therefore completely fulfils the requirements of a
satisfactory damping force. When it is brought into play the end B
of the axle, instead of vibrating indefinitely in a closed elliptical
path _a b ... e_ (Fig. 17) moves spirally, as indicated at _f g h_ ...,
until in a relatively short period of time it comes virtually to rest
at _m_ pointing towards the north.
[Illustration: FIG. 18. Damping Curve from Anschütz (1910) Compass.]
An actual curve taken from an Anschütz (1910) compass while it was
settling down on the meridian after the gyro-axle had been deflected
nearly 45 deg. to one side is given in Fig. 18. The crests A B C occur
at 70-minute intervals--the period of vibration of the system when
damped, as we have already stated. The oscillations are, it will be
seen, damped down very effectively, being entirely eliminated in less
than three hours in the course of the third complete vibration. It
follows that if the wheel of a gyro-compass is started spinning with
the axle pointing elsewhere than due north, several hours must be
allowed to elapse before readings are taken from the card. During the
period of settling down, and especially during the later portions, the
movement of the axle towards its resting position is extremely slow,
and cannot be detected by direct observation. It can, however, be
inferred from the readings of a spirit level placed on the card, for,
as we have seen, the oscillations are accompanied by a tilting of the
wheel case on its horizontal axis.