The whys and wherefores of navigation

by Gershom Bradford

It was the master’s intention to pass through the South Channel, between Georges Bank and Nantucket Shoals, but as he had lost his reckoning to such an extent he hesitated about laying a course through such a danger-strewn locality.

In the late twilight immediately following the clearing sky, the master succeeded in catching the altitude of a star bearing 300° and established a line, the direction of which led close westward of Cultivator Shoal (a 6-foot spot on Georges Bank). So to be on the side of prudence and give this shoal a good berth, the master steamed 8 miles at right angles to this position line. The course or direction of the new position parallel to the first was found to lead directly into the range of visibility of Nantucket Lightship. So the master’s mind was put at rest as he laid his course along the second position line, knowing he would at length make the lightship.

It often happens that a distant mountain peak is visible and the sun is in a suitable position to establish a set of cross bearings, using the mountain for one object and the sun for the other. Now with what has previously been stated, it is hardly necessary to remind the reader that a “line of position” obtained from observations of the sun will be at right angles to the sun’s true bearing; therefore, in order to judge whether these objects are properly placed to give a good intersection, due consideration must be given to the relative bearings of the objects. It is evident that the sun must bear by compass nearly in the direction of the mountain or in the opposite direction to have the position line and the line of bearing of the mountain cut at nearly right angles. Of course, as with any set of cross bearings the angle of intersection may still be effectual if the lines cut at 50° to 60°, but the nearer a 90° cut the more accurate the resulting position.

A position line is liable to displacement through a variety of causes among which is an inaccurate altitude and through incorrect Greenwich mean time. In the former instance, an error of 1´ will displace the position one mile; if the altitude is 1´ too large, the correct position of the line will be 1 mile directly away from the bearing of the body and vice versa. The effect of an error in time upon a position line is to displace it bodily eastward or westward the amount of arc corresponding to the error in the chronometer; the direction of the line is, however, unaltered. The sun carries his system of circles of equal altitude with him from east to west as he travels along a certain parallel of latitude corresponding to his declination (neglecting the slight change in declination). It is quite evident that any arc of a selected circle, will, if its position is plotted on a small scale chart—say every 20 minutes—be found continuously parallel with itself. And the intervals between each two plotted positions of the arc will be 5° (of arc) the corresponding value of 20 minutes. Thus the displacement of the position line due to an error of time is explained. If the time was slow, the line was too far to the eastward, if fast, it was too far to the westward.

The value of a position line has been demonstrated, yet with all it does not positively establish the position of a vessel. The mariner in locating his vessel in a harbor does not usually stop after he has taken one bearing, but proceeds to find another object whose bearing will make a favorable “cut” with the first, and thus at their intersection determines his position. As a further check against possible error a third object may be chosen and, if the three bearings plot without forming a triangle at their intersection, a very reliable fix will be obtained.

What applies to terrestrial objects thus employed may be used as an illustration to be followed in taking celestial bearings. If the mariner establishes a position line and knows his vessel is located at a point somewhere along it, let him look about for another body so placed that the position line derived from it will make a good intersection with the first line; if all data are correct this point will indicate the position of the vessel.

When the sun is used this is seldom possible but in lieu of another body the sun can again be employed to establish the second position line after it has moved sufficiently in azimuth to make a good cut. The thought no doubt immediately arises as to the effect of the vessel’s change in position during the interval. This is easily taken care of by means of the course and distance run during the interval between the sights.

The first position line must be considered carried bodily by the vessel without change of bearing from its first position to the position of the second observation. That is, if at 9 A.M. a position line was established bearing in a 15°-195° direction, and the vessel then steamed and made good a 40°-course for 6 hours and 10 knots an hour, when another position line was established, the 15°-195° line of 9 A.M. would be moved bodily in a 40° direction 60 miles; where its intersection with the second line would indicate the position of the vessel at 3 P.M. The determination of position at sea by employing two position lines of a body with the run between sights is called Sumner’s double altitude problem.

It has already been shown that one body, notably the sun, can be used to get an intersection of two of its lines of position by waiting a sufficient time between observations for the body to change its bearing at least 30°, the nearer 90° the better. The relationship between the interval of time and the amount of change of bearing varies greatly, depending upon the latitude of the observer and declination of the body. For example, let us consider the two extreme cases: Suppose a mariner to be observing the sun on the equator on March 21st, he will note practically no change in azimuth during the whole forenoon. Yet another mariner in the Polar sea, whose latitude differs about 90° from that of the former, will have the sun encircling his horizon making the whole amount of the sun’s movement a corresponding change in azimuth.

Therefore it will be seen that with a low-riding sun (or other body) the change of azimuth is greater in a given time, and for this reason the position lines derived from the sun are more advantageously practiced in higher latitudes, especially in winter. This is a point of great value in view of the fact that the sun’s diurnal course is such that it is never on the prime vertical in northern latitudes during the winter months, making longitudes derived from chronometer sights very unreliable.