15 LATITUDE BY MERIDIAN ALTITUDE

62. UPPER AND LOWER MERIDIAN PASSAGE.

We are now in a position to discuss and describe the shortest and simplest of all Astro-navigational sights – that for obtaining the vessel’s Lat. by meridian altitude.

From the description of figure drawing in the preceding section it will have been noted that any celestial body, in performing its apparent diurnal motion in the sky, attain its greatest altitude when it bears due N. or S.. When a body bears due N., or S., it lies on the observer’s celestial meridian, at which time it is said to culminate or transit, or to be at Mer. Pass.

The observation of the altitude of any navigational celestial body when that body is on the observer’s meridian, i.e., at Mer. Pass., is known as a meridian altitude observation (often abbreviated to mer. alt) and this affords an easy method of finding the observer’s Lat., using the simple formulae described earlier in this chapter. Because the direction of an Astronomical position line is at right angles to the azimuth of a body at the time of observation, and the azimuth of a body on the meridian is either N. or S., the position line obtained from a meridian altitude runs E.-W., i.e., it lies through the vessel’s position along a parallel of Latitude.

We have seen in figs. 14-6 & 14-7 that the Latitude (QZ) of an observer is equivalent to the altitude of the celestial pole (NP in the northern hemisphere – fig. 14-6 and SP in the southern hemisphere – fig. 14-7). A body which crosses the observer’s upper celestial meridian is said to be at upper transit or upper meridian passage or to be on the meridian above the pole.

Occasionally, however, the observer’s Lat. (QZ) is greater than the polar distance (PX) of the body under observation, and in this case the body is continuously above the observer’s horizon, it does not rise or set and has, therefore no amplitude. Such a body, called a circumpolar body, has two meridian altitudes, one when it crosses the meridian above the pole (called, as above the upper transit or upper Mer. Pass.), and the other when it crosses the meridian below the pole, called its lower transit or lower Mer. Pass., when it is said to be on the meridian below the pole.

All celestial bodies are, of course, circumpolar in the sense that they describe a circle round the pole, but the name circumpolar is generally used to designate those bodies which are visible at their lower transit across the observer’s meridian.

Fig. 15-1 is drawn on the equidistant projection showing the plane of the celestial horizon for an observer in Lat. 50° N. and a body whose Dec. is 56° N. (so that its polar distance is 34° – less than the observer’s Lat.). The dotted circle represents the body’s diurnal path around the pole, which lies entirely above the observer’s horizon so that the body is continuously visible, and neither rises nor sets. The body is therefore circumpolar, with its upper Mer. Pass. at X (when the body is between the pole and the zenith), and its lower Mer. Pass. at X1 (when the body is between the pole and the horizon).

Note that when a circumpolar body is at lower transit, its L.H.A. is 180°, whereas the L.H.A. of all bodies at upper transit is 0° 00.0. Also that circumpolar bodies at lower transit always bear N. in N. Lat. and S. in S. Lat. no matter whether the Dec. or the Lat. is the greater.

Except in high Latitudes, and even then for only part of the year, the Sun’s lower Mer. Pass. cannot be observed. Furthermore, the number of stars visible at lower Mer. Pass. is small. For these reasons the navigator is chiefly concerned with upper Mer. Pass., and unless otherwise stated the term Mer. Pass. always refers to the upper transit.

63. THE TIME OF MERIDIAN PASSAGE.

The best way of taking a meridian altitude is to calculate the time the celestial body will be on the observer’s meridian and then to observe the altitude at that moment. The time of meridian passage of any celestial body can be calculated quite easily and quickly by one simple method. This method is simply the reversed process to that described in the first Chapters of this study for finding the LHA of a body for a given GMT. In this case, the LHA of the body is known since it must always be 00º 00’ (or 360º 00’) when the body is on the meridian. The GHA can be found by applying the observer’s Longitude to the LHA, so that GMT of meridian passage can be found against the tabulated GHA in the ‘Nautical Almanac’.

In the days before chronometers and N.A.’s, the observation of the Sun on the celestial meridian in order to obtain the vessel’s Lat. ranked as the most important of all Astronomical observations. In modern times, the noonday Sun observation has lost some of its former glory since the advent of position-line navigation (to be described later in this study).

Now that an Astronomical position line may be ascertained at any time provided that an altitude observation of any navigational celestial body is possible, there is no reason to rely solely on the meridian altitude observation of the Sun at noon for Latitude. However, the ease with which the Lat. at noon may be found from a meridian altitude observation of the Sun, which can be coupled with a position line obtained earlier in the morning or later in the afternoon, makes this method of position fixing pre-eminent during daylight hours.

Finding the G.M.T. of Mer. Pass. of the Moon. or planet or a star for the purpose of ascertaining Lat. by meridian altitude can hardly be regarded as practical in modern navigation because an observation of any celestial body at any time will yield no more than a simple position line: that obtained from a celestial body at Mer. Pass. differs from other position lines only in respect of direction. In taking stellar observations at morning or evening twilight, if a planet or star happens to be on the meridian during the period of observation it is obviously advantageous to observe it at the time of Mer. Pass., and this possibility will be discussed in a later chapter dealing with stellar observations. In this Lesson we Shall therefore confine our discussion of Mer. Pass. to that of the Sun.

64. LATITUDE POSITION LINE BY MERIDIAN ALTITUDE OBSERVATION

In our description of the Equidistant Projection in Fig 14-11 of this chapter we showed how the formulae for finding the Lat. from the observation of a celestial body on the meridian was: –

Latitude = Zenith Distance or + Declination. 

Where the Lat. is greater than the Dec. and of the same name (i.e. both N or both S), then: –

Lat. = Zenith Distance + Declination.

Where the Lat. and Dec. have opposite names (i.e., one N. and the other S), then: –

Lat. = Zenith Distance – Declination.

Where the Dec. is greater than the Lat. and of the same name (i.e. both N or both S), then: –

Lat. = Declination – Zenith Distance.

There are many aids to memory designed to assist navigators who have little or no knowledge of the principles involved to remember the above rules for combining zenith distance and Dec. to find the Lat.. The rules work if they are applied properly, but the principle is simple, and, if a rough diagram of the conditions is made, they’re in no need either to remember the rules or to resort to a mnemonic.

In this example, the Dec. was subtracted from the zenith distance because the Lat. (N) and the Sun’s Dec. (S) have opposite names, but this problem could have been easily resolved by drawing a rough diagram on the equidistant projection as shown opposite, from which it can readily be seen that Lat. (QZ) = Zenith Distance. (ZX) = Dec. (QX).

The position line would be drawn on the chart in a 090°~ 270° direction through Lat. 29° 51.2 N., Long. 61°W. Note that this is not the vessel’s position since Long. 61°W. is only estimated. The meridian altitude observation has only established that the vessel is somewhere on Lat. 29° 51.2 N.

In this example the Lat. and Dec. both have the same name (S), and the Lat. is greater than the Dec., so the zenith distance is added to the Dec. in order to obtain the Lat. As before, however, the question or the correct application of Dec. to zenith distance is more easily resolved by a simple diagram on the equidistant projection as shown opposite from which it can be seen that Lat. (QZ) = Zenith Dist. (ZX) + Dec. (QX).

The position line would be drawn on the chart in a 090° ~ 270° direction through Lat. 46° 04.2 S., Long. 35° 45.0 E.

In this example, the Lat. and Dec. again both have the same name (N). but in this case the Dec. is greater than the Lat., so the zenith distance is subtracted from the Dec. in order to obtain the Latitude.

The diagram (fig. 15-5) drawn on the equidistant projection for this particular problem shows that: – Lat. (QZ) = Dec. (QX) – Zenith Dist. (ZX) and the position line would be drawn on the chart in a 090° ~ 270° direction through Lat. 10° 42.7 N., Long. 175° 15.0 W.

Note also in this example that the Sun’s upper limb was observed, thus making the correction to apply to the apparent altitude negative. Owing to the Longitude, the zone time of Mer. Pass. differed from the G.M.T. by twelve hours.

65. OBSERVING A SUN MERIDIAN ALTITUDE

It is common practice in the majority of ocean-going vessels to observe the maximum altitude for a meridian altitude observation. The best way of doing this is to start the observation a little before the Sun reaches the meridian (i.e., while its azimuth is still a little easterly) having first calculated the time of meridian passage as shown above. Then follow the Sun up with the sextant while it is still rising, noting the maximum altitude reached just before the Sun starts to fall again. No appreciable error will result from this method in a slow-moving vessel.

When taking the meridian altitude of a celestial body it must then bear either true N. or true S., or be directly overhead in the observer’s zenith. When a celestial body has a low meridian altitude it will appear to remain stationary on the observer’s meridian for several minutes. When the meridian altitude is high however, this apparent stand of the body will be only a second or so, and when the meridian altitude is nearly 90°, the Sun will swoop across the meridian, and appear to touch the horizon all round, so rapidly that it is difficult to decide on an accurate meridian altitude; in this case it is best to pre-calculate the time of Mer. Pass., observe the N. or S. (true) point of the horizon and take the altitude at the precise time of Mer. Pass. This latter method of observing a meridian altitude should always be adopted in fast moving craft.

If there is drifting cloud about which might obscure the Sun at the time of Mer. Pass., it is a wise precaution to take a few readings of the sextant at intervals of, say, 4 minutes or so, while the Sun is still rising and a few more after it has started to fall, noting these observations with their times. By plotting these observations on graph paper and drawing a smooth curve through the plotted points, it is quite easy to read off the maximum altitude from the curve, even it the Sun was obscured at the time of Mer. Pass. The beginner is advised to adopt, this practice even on clear days.

The curve should be symmetrical and of the Shape shown in fig. 15-5. in which the plotted points correspond to the following set of observations, the pre-calculated time of Mer. Pass. being 14h. 09m.

•      13h. 50m.            16° 49.5 5.           14h. 10m.           16° 56.0
•      13h. 55m.            16° 52.7 6.           14h. 14m.           16° 55.4
•      13h. 59m.            16° 54.5 7.           14h. 19m.           16° 53.5
•      14h. 03m            16° 55.6 8.           14h. 23m.           16° 51.6 

Mer. Alt. is at the top of the curve, being 16° 56.1 at 14h. 09m.

66. ASSUMPTION THAT MAXIMUM ALTITUDE = MERIDIAN ALTITUDE.

When the sun bears due S. (or N.), the reduction becomes very simple. Your Lat. is 90° – True. Alt. + Same name Dec. or – Opposite name Dec. Unfortunately, a sextant does not directly indicate the bearing of the sun.  It is the common practice to calculate the time of local noon, and then to observe the altitude of the sun either side of this time, taking the maximum altitude reached as being the meridian altitude.

Maximum altitude may not exactly correspond with meridian altitude, and the difference can be significant in the case of a fast moving vessel steering either N. or S. The difference for a sailing boat is too small to concern the sailor. The difference between maximum and meridian altitude is caused partly by the change of sun’s Dec., and the effect of the vessel sailing either towards the sun, which will make the altitude increase with time, or away, which works in the opposite direction.

If we take the case of the vessel sailing towards the sun, the altitude will be increasing due to ship’s movement, and decreasing as the sun moves off the meridian. When these two effects cancel, maximum altitude is reached, which is more than meridian altitude.

The effect of changing Dec. is small, and can be allowed for by adding the change of Dec. per hour to the ship’s N./S. component, taking due account of sign. (The maximum change is about I’ per hour at the equinox.)

The time difference between maximum and meridian altitude can be found from a formula given in the Admiralty Navigation Manual Vol 3, 1938, p154:

Time = 15.28 X y X (Tan Lat + /- Tan Dec) Where y is the rate of N./S. change in Lat. combined with rate of change of Dec, in minutes of arc per hour (knots). The effect of E./W. movement for a sailing vessel is utterly negligible.

Taking a case in which the effect is large, Lat. = 60° N, Dec = 0°, changing at a rate of l’ per hour (the vernal equinox) and a speed of 9 knots due S., gives: –

Time = 15.28 X 1 0 X Tan (60) = 264.6 4 min 25 sec

Using the Ex. Mer. Alt Tables gives:

Tab Log C         =            9.761

Tab Log H         =            5.968

Sum                   =            5.729

Table 3 gives correction = 0.37′ +, but who takes sights to this accuracy while doing 9 knots in Mar at Lat. 60° N?

If we work it out again for a vessel in Biscay sailing S. at 9 knots at midsummer, the correction becomes 0. 1’+.

The figure, calculated from the spherical triangle, shows how the altitude changes with time around local noon, for a ship moving under the same conditions and a stationary ship in the same position, as that of the first example.