THE LATITUDE ERROR
Having explained the necessity for damping the horizontal vibrations
of the gyro-compass axle and how the damping force is generated and
applied in the Anschütz, Sperry, and Brown compasses, we are now in
a position to discuss the various errors to which the gyro-compass
is open and how those errors are in practice eliminated, reduced, or
allowed for.
The first error to which we shall turn our attention is that known as
the latitude error. This error is a direct consequence of the necessity
we are under of damping the horizontal vibrations of the compass axle.
It will be recalled that in any latitude other than the equator the
compass rests on the north with a slight tilt up or down of the axle,
the tilt increasing progressively as the poles are approached and being
upwards in northern latitudes and downwards in southern. The tilt
acquired in any latitude is perforce and automatically just sufficient
to precess the axle westwardly or eastwardly at the rate required at
that latitude to keep the axle on the north once it has found it.
Let us suppose, then, that a compass of the early Anschütz type is
stationed in some degree of northern latitude. The axle in acquiring
the appropriate tilt will clearly disturb the equilibrium between
the two sections of the air blast. As the axle tilts its north end
B upwards the north section of the air blast will enlarge and the
southern diminish in area. Thus the tilting of the axle brings into
play an air blast reaction which is applied as a moment tending to
turn the sensitive element about the vertical axis H J in such a way
as to make the north end move eastwardly. The actual movement produced
will, in accordance with the fundamental rule, be a precession of the
axle about the horizontal axis, the end B going down. Thus the tilt
upwards of the axle required for the correct working of the compass is
opposed. It is not allowed to acquire the full value which it should
have, but instead stops at the point at which a balance is struck
between the upward moving tendency of the axle resulting from the
earth’s rotation and the downward moving tendency caused by the uneven
air blast reaction. The westerly precession of the axle about the
vertical axis is now that arising from the reduced angle of tilt, and
is less than the rate required to keep the end B pointing to the north.
The resulting deviation is known as the latitude error. Its magnitude
depends upon the latitude and upon such factors as the speed of the
wheel, its efficiency as a blower and other items incidental to the
particular design of the compass.
In the Sperry compass the latitude error arises from an exactly similar
cause. Thus the tilt of the axle is transmitted through the excentric
pin to the casing as a moment about the vertical axis H J, tending to
make the north end of the axle move over to the east, and therefore
causing the axle to precess vertically downwards until the position of
balance is reached.
In the Brown compass, on the other hand, it is claimed that there is no
latitude error. Thus when in northern latitudes the north end of the
axle tilts upwards under its unsatisfied desire to set itself parallel
with the earth’s polar axis, the air blast is divided unequally between
the two partitions of the box. Excess pressure is exerted inside the
damping bottle attached to the northern face of the wheel casing, and
as a result an excess of oil accumulates in the damping bottle on the
south side. The weight of the excess oil applies a turning moment to
the spinning wheel about the horizontal axis, and tends to lift the
north end of the axle upwards in opposition to the pendulum weight,
which tends to turn it downwards about the same axis. Thus in this
compass the natural tilt of the axle is not interfered with by the
action of the damping arrangement, for that action is applied about the
horizontal axis E F, and not, as in the Anschütz and Sperry compasses,
about the vertical axis H J. The damping action in the Brown compass is
virtually equivalent to a subtraction from the weight of the pendulum
bob, and is not applied, as in the other compasses, to the reduction of
the tilt of the axle. It tends, therefore, to reduce the natural rate
of westerly precession required at the given latitude to keep the axle
on the north. Actually, however, the tilt acquired by the axle will
take cognisance of the reduction in the weight of the bob caused by the
weight of the excess oil. The north end of the axle will rise until the
effective moment of the bob--that is, the moment due to its own actual
weight less the moment due to the excess oil in the southern damping
bottle--is such as will automatically generate the required rate of
westerly precession for the given latitude.
In the Anschütz and Sperry compasses the latitude error can be allowed
for by shifting the position of the lubber line relatively to the
ship’s longitudinal centre line in accordance with calculated tables
of the error. The exact value of the error depends upon the design of
the compass, but in both types it increases with the latitude. Analysis
shows that--at least in the early Anschütz compass--the latitude error
may be neglected if the change of latitude is less than 10 deg. In the
Sperry compass, as we shall see presently, the movement of the lubber
line to correct the latitude error is effected by a very pretty piece
of mechanism, which also can control the position of the lubber line
to allow for a second error to which the compass is open, to wit, the
so-called “north steaming error.”
In some respects as an alternative to moving the lubber line,
the latitude error may be completely eliminated for a particular
latitude--the latitude of most frequent use would naturally be
chosen--by attaching a small weight to the north side of the wheel
casing. In the early Anschütz compass such a weight was provided
as indicated at T in Fig. 16. This weight and its position were so
chosen that at 50 deg. north of the equator its moment about the
horizontal axis E F, when the axle of the compass was horizontal,
was just sufficient to supply to the wheel the amount of westerly
precession required to keep the axle pointing to the north. The axle
being horizontal in that latitude, the air blast was equally divided by
the pendulum shutter, and as a result the rate of westerly precession
produced by the weight T was not affected by the existence of the
damping system. At other latitudes, of course, the latitude error
arose, and at the equator--where ordinarily there should be no latitude
error--and south of the equator, the error became worse than it would
have been without the addition of the weight, unless the weight and
its position were adjusted. With the compass corrected for 50 deg. N.
latitude the error had the following values:
Latitude Error
60° N. .6° E.
50° N. Zero
40° N. .5° W.
20° N. 1.1° W.
0° 1.6° W.
20° S. 2.1° W.
40° S. 2.7° W.
60° S. 3.8° W.
In the Sperry compass no attempt is made to eliminate the latitude
error at any particular latitude, the correction applied to the lubber
line being solely relied upon to allow for it. In this compass,
therefore, the latitude error is zero at the equator. At 50 deg. north
or south it amounts to 2 deg., easterly and westerly respectively.
A feature found in this type of gyro-compass of a connected nature
calls, however, for mention at this point. This feature consists of
mounting the pivots M N (Fig. 19), on which the bail swings, within
excentric housings and graduating the edge of the housings with a scale
of latitudes. In this way the pivots can be displaced to one side or
the other of the vertical plane containing the axis H J by an amount
proportional to the latitude. When the spinning wheel is at rest, this
displacement makes the angle between the axle of the wheel and the
plumb line through the centre of gravity of the bail a little less
or a little more than a right angle, and in northern latitudes makes
the north end of the axle dip below the horizontal and in southern
latitudes rise above it. The scale is so graduated that the dip of the
axle or its rise when the wheel is not running is just equal to the
natural rise or dip which the axle would acquire at any given latitude
with the wheel running and with the bail pivots in the mean position.
As a result, when the compass is in service and the bail pivots are
adjusted for the latitude of the station, the natural rise or dip of
the axle leaves the axle horizontal, but deflects the bail weight from
the vertical by the amount required to generate the correct degree of
easterly or westerly precession.
Thus in the Sperry compass the axle, if the latitude bail correction
is applied, is at all latitudes horizontal when resting on the north.
Several advantages are thus secured, the chief being that the effect
of any change in the speed of the spinning wheel or of a complete
failure of the electric supply driving the wheel is greatly reduced
or spread over a longer interval. Were the axle as well as the bail
allowed to acquire the rise or dip proper to the latitude, the axle
during a change of speed of the wheel would tend to deviate and develop
an error which might prove misleading. If, however, the axle is not
allowed to acquire the rise or dip appropriate to the latitude, the
error introduced by a change in the speed of the wheel takes longer
to manifest itself, and is reduced in magnitude. As it is difficult
to guarantee that the voltage of the current supplied to the compass
will not vary, this feature of the Sperry compass is undoubtedly of
practical advantage.