The method, which is here to be described, has worked successfully for two years with the compasses of the Castine and all the submarine flotilla. The German and Greek letters, ordinarily used, are here done away with, and thus the biggest bugbear of compass work is eliminated, the constant A being the only coefficient given real consideration in this method.
We consider that any compass is properly corrected when a distant object can be made to have the same compass bearings for all headings of the ship.
To COMPENSATE THE COMPASS.
Note the change of bearing of the sun for every twenty minutes, using the azimuth tables, the approximate local apparent time, the latitude (correct to a degree), and the date of the month as arguments. A curve of the sun's change of bearing is then plotted on cross-section paper. A reference to the azimuth tables shows that an error of a few minutes in time, of a degree in latitude, or even of a day or so in date, make practically no change in the rate of change of bearing of the sun; though, of course, with such erroneous data there is a decided error in the actual bearing of the sun, but with the actual bearing we are not now concerned.
Problem.—Correct all compasses of a vessel, and swing for residuals in latitude 40° 20' N., A 70° W., about 3.00 p. m. on October 30.
Procedure.—t. Set watch to local apparent time approximately. For example, if watch had been keeping 75th meridian mean time, as would be probable, set it ahead twenty minutes, thus making it 70th meridian mean time, and then apply the equation of time.
2. Pick out from the azimuth tables, using 400 as latitude, and the column nearest the day of month—October 31—bearings of the sun at 20-minute intervals, viz:
Time. | Bearing of sun. | Change of bearing per 20 minutes. |
3.20 | 106° 10’ | …… |
3.40 | 102° 14’ | 3° 56’ |
4.00 | 98° 34’ | 3° 40’ |
4.20 | 95° 05’ | 3° 29’ |
Using cross-section paper, taking ordinates as times, and abscissm as degrees—unnumbered as yet—now draw in the curve ABC (see Fig. A).
3. Now head the ship north. Using the azimuth circle take a very accurate bearing of sun; in this case it equals 246° 30' at 3.22. Put the helm over and swing to south. Plot point X, with this data, on Fig. A, close to the change of bearing curve, now marking the degree line at A as 246°, and also giving values to the abscissae.
4. Steady on south. Bearing of the sun is found to be 245° 30' at 3.29. Plot this as point Y. Draw XX' parallel to ABC. X', therefore, represents the sun's bearing if headed on nor that 3.29. Now draw a curve parallel to ABC and through the point Z, which is halfway between Y and X'.
5. Now, using watch and curve, raise or lower the athwartship magnets until sun bears as it should. Then there will be no deviation, and south by compass will be correct south. All the other compasses are then made to read south in the usual manner.
6. Correct on east, and then on northeast in the same manner.
7. Head the ship north. If there is a difference in bearing from curve, one-half of this is deviation. Plot point, and, swinging on every fourth point, plot differences and draw curve through the mean of points. Those points to the left then are westerly deviation, those to the right being easterly.
If, however, there is a real constant magnetic error, it is not known by the above method, it is not and should not be taken out on one heading, as the error due to it would then be doubled on the opposite heading. The navigator's error is quite frequently the constant which makes the work check.
Now, to find the constant error, compute an actual bearing of sun and compare. For example, if the compass error at 7 a.m., and again at 10.30 a.m., on the same heading, is exactly the same, it is safe to assume that there is no instrumental error and the constant error can be calculated. An instrumental error frequently found is that of the azimuth circle, i.e., the mirror may read accurately on one angle and not on another. When correcting a compass in the usual method by a calculated bearing of the sun, this instrumental error and all errors in calculations give a false constant A. During the short time to correct in the above method less than one hour—the angle of change of the mirror, or change of its error, should be very little, and, even if the mirror were in error ten degrees, the compass would be correct, because the distant object has been made to bear the same all the way around.
Where as we know that in the usual method the compass would be corrected to take out the whole error (true constant A, instrumental and magnetic) on one heading, and on the opposite heading the instrumental error and plus true constant A error which should not have been taken out will be doubled.
It frequently occurs that an azimuth circle is in error by 2° after it has knocked about ship for a few years.
MATHEMATICAL NOTE ON THE ABOVE BY COMMANDER G.R. MARVELL, U.S.N.
tan ? = A’ + B’ sin z + C’ cos z + D’ sin 2z + E’ cos 2z / 1 + B’ cos z – V’ sin z D’ cos 2z – E sin 2z
The above is the strict mathematical formula for the deviation, z being ship's head magnetic. If the deviations are less than 200, this formula can be reduced to (see Muir, p. 121):
? = A + B sin z'+ C cos z' + D sin 2z' + E cos 2z’, where z’ is the ship's head per compass.
Let z’ = 0°, then ?0 = A + C + E
Let z’ = 180°, then ?? = A - C + E
?0 + ??/2 = A – E (1)
Let z’ = 90°, then ?2/? = A + B – E
Let z’ = 270°, then ?3?/2 = A - B + E
?2/? + ?3?/2 /2 = A – E (2)
Let the compass be compensated on N., S., E., and W., and the coefficients B and C have been reduced to zero. Therefore,
? = A + D sin 2z’ + E cos 2z’
Let ? = 45° ??/4 = A + D (3)
Let ? = 135° ?3? /4 = A - D (4)
Let ? = 225° ?5? /4 = A + D (5)
Let ? = 315° ?7? /4 = A - D (4)
An inspection of these last show that to compensate for D,(3) and (4), (3) and (6), (4) and (5), or (5) and (6), are the combinations.
TO SWING FOR RESIDUALS.
If deviations are small, say not over one-half point, then the "lag" of the compass will be constant, if the swing of the ship is constant. Note the change in bearing of sun during 10 minutes.
Plot-curve of the change of bearing of sun for this time. Start vessel swinging and, after it has swung through 8 points, consider the swing constant.
Example.-1. With data, as in first case, we find the change of bearing from 3.50 to 4.00 to be 2°. Plotted curve AB (see Fig. B), and without designating values for ordinates or abscissae.
2. Headed east and put helm hard to starboard. Follow the sun with the azimuth circle. When passing north, took azimuth and time—i.e., 268 ½° at 3:51. Now, in Fig. B, mark 268° for abscissa at point A and 3:51 for ordinate, and plot N.
3. Took bearings every fourth point and plotted NW., W., SW., S., SE., and E. From the mean between N. and S., E. and W., NW. and SE., and NE. and SW., draw curve XY. By mean is here meant the mean of the opposite cardinal points, or adjacent intercardinal points. Or, this may be drawn from the mean of only north and south, and still be approximately correct.
4. The amount the points vary from this line is the deviation, plus any known constant the compass may have. The result is shown in Fig. B.
Thus, in the above method, we did not need to know the magnetic bearing of the sun (any distant object could have been used), because the bearing used was the magnetic plus the lag plus the constant.
The above method has been proved by trial on various ships with corrected compasses, using uniform speed and helm. The bearing of the sun remained constant, or only varied an amount equal to the change of sun bearing due to time, the bearing being in error the lag.
NOTE ON "LAG" OF COMPASS BY COMMANDER G. R. MARVELL, U. S. N.
The mean directive force of earth and ship in terms of earth's horizontal force as unit is represented by X, which depends for its value upon the effect of horizontal soft iron, symmetrically arranged about the compass.
Therefore, for any particular heading of the ship there is a certain pull or force on the needle, tending to draw it away from the magnetic meridian, and to bring it to rest at compass north. On another heading there is a similar force, but of different value. If a ship is swung with a constant change of magnetic azimuth, the compass needle will be acted upon by a varying force, so that at any particular magnetic head the deviation will be different from what it would have been if the ship had been steadied on that magnetic head. This difference in deviation may be called "lag." If the force acting on the compass needle was constant, and the angular velocity of the swing was constant, then the lag would be constant. But in an uncompensated compass the force is variable, therefore the lag is variable.
By the method of compensating described above, the compensation on N. and S. gets rid of C, but leaves A and E; the compensation on E. and W. gets rid of B, but leaves A and E; that on NE. and SE. gets rid of D, but leaves A. The value of the force of earth and ship to magnetic nor this given by the formula
F = ? (1 + B’ cos z – C’ sin z + D’ cos 2s – E’ sin 2z).
This in terms of earth's horizontal force as unit.
Assume that B', C' and D' have been eliminated by compensation, and the value of ? + E' with correctors in place has been found, then the formula reduces to
F = ? (1 – E’ sin 2z).
If E' is very small, as it is in all centrally located compasses, then the value of F practically remains constant, and therefore the lag is constant.
If the compass is out of the midship's line, and the rods d and b have effect, then the method of compensation, and of finding residual deviations given above is faulty and should not be depended upon.
However, if the deviation has not been entirely removed, the lag will not be constant, for there will remain values for B', C', D' and E', which, when substituted in the formula for force, will give varying values of that force.
The amount of difference in the lag cannot be stated; it may, or it may not, affect the finding of the correct deviation.
TO CORRECT COMPASSES—NO INSTRUMENTS EXCEPT AZIMUTH CIRCLE. NOTABLES OF INFORMATION OF ANY KIND.
1. Steady ship on one course; note bearing of sun and, again, about 10 minutes later; from these two bearings one can tell whether the bearing is increasing or decreasing, and approximate rate. In this case it is noted that the bearing is increasing between 1° and 2° every 10 minutes. Call it about 10° for every 7 minutes. If no watch is available, note approximately the number of revolutions for 1° change in bearing. All that is necessary is some very rough method of measuring time, and even this is hardly necessary for accurate work.
2. Procedure: Head north; sun bears 270°; head south, steady about 2 or 3 minutes; sun bears 276°; time interval about 6 minutes. Six minutes sooner the bearing would have been 275°— the average is 272 1/2°—in 6 minutes, therefore, the bearing would increase 10 and the sun should bear 273 1/2°; so raise or lower magnets and, as a little time will be consumed in this operation, make sun bear between 273 1/2° and 274°. Head east and west, same procedure. Head northwest, then southwest, and follow the same procedure.
On southwest or northeast the natural deviation is east; if it is found to be west the compass is over corrected and it is necessary to move balls out. On northwest or southeast natural deviation is west; if found to be east, then compass is over corrected and we must move the balls out. If the above cannot be remembered, simply move the balls and find out what happens.
Now put the helm hard over and, after swinging through eight points, take bearings every fourth point, and proceed as in the method of swinging for residuals, with hard over helm. If the work was accurately performed, it will be found that the bearing all around will be the same, or about 1/2° more by the end of the swing, due to change of bearing of sun in the time interval.
FLINDERS BAR CORRECTION.
1. Being on the magnetic equator correct compasses, after going north, a deviation is observed. Using rectangular method of Flinders bar, take out this deviation. (In general, it will be found that either a very weak or no Flinders correction is required on the side of the compass.)
2. The vertical magnetic force varies as the sine of the magnetic latitude, or, to express it differently, the vertical magnetic force varies as the sine of the dip. In latitude 14° 31' north, corrected compass, sine of 14° 31' equals 1/4 (no Flinders bar in). In latitude 30°, noted deviation on east course equal 2° W. Sine 30°equals%. Place Flinders bar ahead of compass, add rods until deviation is 2° E. Similar procedure on north heading.
3. The pull causing the deviation in latitude 30°, sine is twice as much as the pull in latitude 14° 31, sine 1/2; so the deviation caused by vertical force, or caused by the magnetism in vertical soft iron, is twice as much in latitude 30° as in latitude 14° 31'. The actual deviation caused by vertical soft iron in latitude 14°31' is thus 2° and in latitude 30°is 4°. The compass must then be changed 4° by Flinders bar, but, having been corrected with magnets in latitude 14° 31', there is now a deviation of 2°; this is to be taken out by correcting with magnets in the usual way.
While this method of Flinders bar correction has not been proved by actual trial, it is believed to be correct.
NOTES.
When first beginning compass work the author started with a carefully worked out magnetic curve, but nearly always found that, after compensating on north, the sun's bearing on south was not according to the curve. So, judging this due to mathematical, instrumental variation, or a constant magnetic error, a curve was drawn half way between the worked out curve and the south compass bearing, and it was found that this curve could be followed all the way around. Then a curve of proper shape only was found to be all sufficient.
If the compass tray is immovable, wires can be added, but do not do so by the bundle; magnets can even be nailed to the deck. It has been found beneficial to have the compass balls annealed by heating to a dull red and cooling slowly over night, about every six months, as they collect a little permanent magnetism.
The above methods are certainly simple, easily taught, form a practical method of compass correction, and eliminate the difficulties ordinarily met with in this work.