THE NORTH STEAMING ERROR
The source of error which we have just discussed affects the
gyro-compass whether it is on land or on a ship. We have now to discuss
certain errors which are only met with when the compass is mounted on
board a moving ship.
The first of these errors to which we will refer is sometimes called
the “north steaming error,” although it is equally associated with
a due south course. Imagine the vessel on which the gyro-compass is
fitted to be sailing due east along the equator. If its speed is,
say, 20 knots it would, if it could, circumnavigate the globe in 45
days. Its velocity round the earth’s axis apart from the rotation
of the earth is thus 0.000015 revolution per minute. As the speed
of the earth on its polar axis is 0.0007 revolution per minute, the
actual rate at which the gyro-axle is being carried round in space is
0.000715 revolution per minute. If the vessel is sailing due west its
speed opposes that of the earth, so that the actual rate at which the
gyro-axle is being carried round in space is 0.000685 revolution per
minute. As compared with the same gyro-compass on land, the only effect
of the ship’s speed on these courses is in the one case to increase the
magnitude of the directive force and in the other case to reduce it,
the increase and reduction both being quite small--about 2 per cent.
actually. Sailing due east or west in latitude 60 deg. north or south,
its speed would cause the vessel to circumnavigate the globe in 22½
days. On these courses in either of these latitudes, therefore, the
directive force would be increased or diminished respectively by about
4 per cent.
[Illustration: FIG. 24. The North Steaming Error at 0 Deg. and 60 Deg.
N.]
If, now, the vessel starts at the equator and sails due north, its
speed is at right angles to the speed with which the rotation of the
earth is carrying the gyro-compass round in space. The speed of the
ship--2026 ft. per minute--may be represented by A B (Fig. 24) and the
speed of rotation of the earth--92,400 ft. per minute--by A C. The
actual speed and direction in which the gyro-compass is being carried
round in space is A D, and the actual axis about which it is being
carried round is not the earth’s polar axis N S, but an axis N´ S´ at
right angles to A D. The gyro-axle will settle, therefore, on the line
N´ S´, and not on the true north and south meridian. The true north
will be to the east of the indicated north by the angle N´ A N, which
for the ship speed in question--20 knots--will be 1.25 deg. If the
ship starting from the equator sails due south, the deviation will be
towards the opposite side, the true north lying 1.25 deg. to the west
of that indicated by the compass. If the course is neither due north or
south nor due east or west, the deviation will have some intermediate
value between zero and 1.25 deg., the true north lying to the east of
the indicated on all courses with a northern component and to the west
on all courses with a southern component.
If the ship is in latitude 60 deg. north, and is steaming north, its
speed will carry it, as before, 2026 ft. northward per minute, as at
E F, but, as its distance from the earth’s polar axis is now only
half what it was at the equator, the earth’s rotation is carrying it
round at only half the equatorial speed, namely, with a velocity E G
of 46,200 ft. per minute. The compass is therefore being carried round
in space with a velocity represented in magnitude and direction by
E H--that is to say, it is being rotated not actually about the earth’s
polar axis N S, but about an axis N´´ S´´ at right angles to the
resultant velocity E H. The axle will therefore align itself parallel
with N´´ S´´, and not with N´ S´. Thus in that latitude at the given
speed the true north will lie 2.5 deg. eastward of that indicated by
the compass. On north-easterly or north-westerly courses at 60 deg.
north latitude the deviation will lie between zero and 2.5 deg., while
on all courses with a southerly component the true north will be to
the west of the indicated north by some amount between the same two
limits. Our demonstration is not strictly accurate, for, arising from
the rotundity of the earth, the speed E F of the ship is not really
in the plane of the paper, but should be drawn inclined with the end
F below the level of E. Accurate analysis, however, shows that the
deviation arrived at by neglecting this fact is substantially correct.
In the tables issued in connection with the early Anschütz compass the
deviation at 20 knots due north or south in latitude 60 deg. N. is
given as 2.5 deg., while those issued by the Sperry Company give it, by
interpolation, as 2.41 deg.
It will be seen that this error is a natural one--that is to say, it is
not caused by any peculiarity in the design of the compass in use. The
table of deviations on various courses, at various speeds, in various
latitudes, compiled for one type of compass would be equally applicable
to any other design. In the case of the early type of Anschütz compass
the “north steaming error” was corrected solely by means of such
tables--that is to say, to find the exact bearing on which the ship
was sailing the compass was read, and from its reading there was
subtracted, or to it there was added, arithmetically, the appropriate
figure taken from the tables, the uncorrected reading being a
sufficiently accurate indication of the true course to permit it to be
assumed as the true course for the purpose of extracting the correction
from the tables.
In the Sperry design the use of similar tables in a similar way is
permissible and is provided for. In addition, however, provision
is made whereby the tables may be entirely dispensed with and the
correction applied by moving the lubber line relatively to the ship’s
fore and aft direction. In the case of the early Anschütz compass the
lubber line could be moved through 4 deg. on each side of the position
in which it was parallel with the ship’s fore and aft centre line.
This movement was, however, for the purpose of correcting the latitude
error, and not the north steaming error. In the Sperry compass
provision is made for moving the lubber line so as to correct for both
errors. The latitude error depends upon the design of the compass and
the latitude. The north steaming error is independent of the design of
the compass, and is determined by the speed of the ship, the latitude
in which it is sailing, and the course which it is following. Latitude
thus comes into both errors, being the sole variable causing one,
and one of the three variables causing the other. It is eliminated
simultaneously for both errors, by operating one dial. A second dial is
set to suit the speed of the ship, while the third factor in the north
steaming error, the bearing of the ship’s course, is automatically
brought into the movement of the lubber line by means of an inclined
ring carried round with the compass card.
A diagram of the Sperry correction mechanism is given in Fig. 25. The
lubber ring on which the lubber line is engraved is shown at A. The
latitude corrector dial B is mounted to rotate about its centre and to
read against a fixed scale. It is slotted radially to engage a pin C
on a rod D E, one end of which can slide in a fixed guide F, while the
other is pivoted to a link E G pinned at H to the lubber ring. If the
end G of this link be imagined pivoted to some fixed point it is clear
that rotation of the dial B will communicate a corresponding rotation
to the lubber ring. The proportions of the parts and the positions of
the pivots and pins are such that by setting the dial to the latitude
in which the vessel is sailing the lubber ring is rotated through the
angle by which the local latitude error causes the gyro-axle to deviate
in its resting position from the true north and south direction.[3]
[Illustration: FIG. 25. Sperry Correction Mechanism for Latitude and
North Steaming Errors.]
If the end G of the link E G were pivoted, as we have supposed it to
be, to some fixed point, then the latitude Error could be applied by
itself to the lubber ring. It is not, however, so fixed, but is pivoted
to a link, the end J of which carries a pin working in a curved slot
extending from the centre of the speed corrector dial K to its edge.
The radius of this curved slot is struck from the point G as centre. It
follows, therefore, that with the speed corrector dial in the position
shown the end J of the link G J may be fixed at any point in the curved
slot without affecting the position of the point G. If, however, the
speed corrector dial be rotated about its centre, the movement of the
point G will vary in magnitude with the position at which the pin J
is fixed in the curved slot. This position is set against the scale
of speed in knots on the edge of the slot, but the setting is without
effect until the speed corrector dial is rotated from the position
shown in the diagram. When it is so rotated a corresponding movement
is communicated to the lubber ring through the link G E, the end E of
which is now to be regarded as the fixed fulcrum.
The two dials B K are connected by means of a link L M of length equal
to the distance between the dial centres. The end L of this link is
pivoted to a fixed point on the dial B, but the end M is provided with
a pin which works within a slot in the dial K. Thus the setting of the
dial B to any latitude will not produce rotation of the dial K, but
will merely cause the pin M to slide in its slot. If, however, the
link M N is moved upwards, the angle through which such movement will
rotate the dial K will depend upon the exact position of the pin M in
its slot--that is to say, upon the setting of the latitude dial. Thus
a movement of the link M N will rotate the lubber ring by an amount
proportional to the movement of M N, to the setting of the pin J in the
curved slot of the speed dial, and to the setting of the latitude dial.
The link M N is pinned to a lever P Q, the end P of which is pivoted
to a fixed point. The end Q carries a roller, which engages within the
flanges of a ring R permanently fixed in an inclined position on the
phantom ring of the compass. The higher end of this ring is situated
directly above the north-seeking end of the gyro-axle, and the lower
end directly above the south-seeking end, its east and west diameter
being aligned horizontally.
In the position shown in the diagram the ship is supposed to be sailing
due west. Under this condition, as we know, no north steaming error is
involved, the latitude error only applying. The dial B can therefore
be set to the latitude in which the vessel is sailing so as to apply
the latitude correction by itself to the lubber ring. At the same time
the pin J can be set to read the ship’s speed--17 knots in the case
shown. The movement of the link J G involved in this setting will,
as we have seen, not alter the setting of the lubber ring, nor will
the setting of the dial B rotate the dial K from the position shown.
The two settings are, however, ready to modify the adjustment of the
lubber ring as soon as any movement of the link M N occurs. Such a
movement arises if the vessel alters course towards the north or south
or intermediately, for when the course is altered the links, dials, and
lubber ring move with the ship, while the compass card and the course
corrector ring R remain stationary. The roller at Q therefore rises
or falls towards the north or south end of the ring, and produces a
rotation of the dial K. The amount of the modification thus produced
in the setting of the lubber ring relatively to the ship’s centre line
will depend upon (1) the setting of the pin M--that is to say, the
setting of the latitude dial; (2) the setting of the pin J on the speed
dial; and (3) the extent of the turn towards the north or south. In
this way the correction for the north steaming error is automatically
added to or subtracted from the correction for the latitude error to
the correct amount on all occasions when the ship’s course is altered
so as to have a northerly or southerly component, the adjustment for
the error being automatically wiped out in all latitudes when the
ship’s course is again brought east and west. The mechanism, it will
be seen, merely by the setting of two dials, takes cognisance of three
independent variables, of which one enters into the required adjustment
in a twofold way.[4] The total correction is indicated on the corrector
scale S attached to the binnacle independently of the lubber ring.
It will be seen, then, that neither the latitude error nor the north
steaming error is in the strict sense of the word eliminated, but is
only allowed for, automatically or arithmetically, when the compass is
read--that is to say, no attempt is made to force the gyro-axle to rest
in the true north and south position in all latitudes at all speeds
on all courses. The crucial angle by which the ship is navigated is
the angle between its longitudinal centre line and the true meridian.
A constant straight course will be held if this angle is maintained
constant. If the indicated meridian on the compass is open to error,
the constancy of the navigating angle may be preserved by introducing
a similar error into the degree of coincidence between the lubber line
and the longitudinal centre line of the ship. The readings of the
master compass may therefore be used for the purpose of maintaining
the ship on a given course or for setting it on a new one. But for
taking the bearing of some passing object, the fact that it may not
be indicating true north may render the observation somewhat more
troublesome than it need be. To overcome the difficulty here involved
the repeaters served by the master compass are arranged to indicate
true north under all conditions, provided the latitude and speed dials
on the master compass are correctly set. The repeaters are operated
electrically, the first element in the transmission system between
them and the master compass being a pinion meshing with the gear wheel
attached to the phantom ring beneath the master compass card. This
pinion is mounted on the lubber ring, and therefore rotates with the
ship round the card when the course is altered. But, as it is mounted
on the lubber ring, it also partakes of the movement of this ring
relatively to the ship produced by the correction mechanism. Thus the
net indication transmitted to the repeaters when the ship changes
course or latitude or speed is compounded of the relative motion of
the master compass card and of the lubber ring. The reading of the
repeaters thus shows the true north. A pelorus or dummy compass may be
combined with the repeaters to facilitate the taking of bearings. In
war vessels the actual navigation of the ship is preferably conducted
from a repeater, the master compass for safety in action being disposed
below the armoured deck.
The Sperry compass is peculiarly complete in the provision made for
taking account of the latitude and north steaming errors. The Brown
compass, as we have seen, is free from latitude error, so that the
north steaming error alone has to be dealt with. This error may be
allowed for arithmetically in the usual way by means of tables of
corrections to be applied to the readings of the master compass. As
regards the repeaters, the error is eliminated by a method involving
the mounting of the repeater cards excentrically, the excentricity
being varied to suit the latitude, speed, and course.