33 THE PLANNING OF SIGHTS AND PREPARATION FOR OBSERVATIONS
125. SIGHT PLANNING
The navigator who chooses his sights with a commonsense eye on the information he really wants will achieve infinitely better practical results than the one who just takes sights haphazardly. This is especially true in respect of Sun sights, which are most used by small craft navigators even though simultaneous star sights are more accurate. Inexperienced navigators tend to think in terms of sights which will give a Lat. or approximately so (sights on or near the meridian) and those which will give a Longitude (sights on or near the prime vertical) and these sights have already been discussed. In practice, however, it is the exception rather than the rule to want position lines as parallels and meridians – it is the odd-angled position lines which are generally the most useful.
In general, the two things the navigator wants to know are:-
i. Am I on my chosen track and, if not, how much am I off it? And
ii. How far have I progressed along the track? – in other words, the two sights which are generally most useful are track checking and progress checking sights.
Bearing in mind that a position line is always at right angles to the direction of the body observed, for a track check observing-a body abeam or nearly so, for if the azimuth is abeam the position line will run parallel to the fore-and-aft line of the vessel. For progress, check and observe a body either ahead or astern or nearly so, for then the position line runs parallel or nearly parallel to the vessel’s athwartship direction.
Providing the Lat. and the time of year are right for the Sun to be well up for a good many hours each day, Sun sights can easily be selected to give the most useful position lines. In summer in the Lat’s of the British Isles, both track checking and progress checking Sun sights can be obtained on any day, whatever the track, and even in winter one or the other of the two forms of sight can usually be observed.
In order to determine the time to observe the Sun for a track check, convert the vessel’s abeam direction into an azimuth, naming it according to the method adopted for the tabulated azimuths in the Sight Reduction Tables. Enter the tables with the E.P. Lat. to the nearest whole degree and the Sun’s Dec. to the nearest tabulated value, and subtract the hour angle for which the nearest value to the abeam azimuth is obtained. Apply the E.P. Longitude to this L.H.A. to convert it into G.H.A. and then look in the N.A. to find the G.M.T. at which the Sun’s G.H.A. is about this value. A Sun sight taken at this time will give a track check.
For a progress check the only difference is that the tables are examined for an ahead or astern azimuth, instead of an abeam azimuth.
The same method of choosing a sight to give a position line which suits the momentary needs of the navigator can be extended to clear a danger by a desired amount or to decide when to alter course from one course to the next, or to get on to a desired course which leads into a harbour. Suppose that in fig. 33-1. a vessel wishes to pass 10 miles from the lighthouse on the headland and proceed up the channel to the eastwards on the Course DB.
The most useful Astronomical observation to take would be one which gave a position line parallel to the required new course DB when the vessel was in the vicinity of C on the southerly approach to the headland. To achieve this, and using the above method, the navigator would calculate the time to observe a suitable celestial body when its azimuth was at right angles to the required new course DB. This would give the position line at C.
The line AB would then be drawn on the chart, tangential to the 10-mile circle round the lighthouse and parallel to the position line. The vessel would then be run on from C by dead reckoning until the new track was reached, when she would then be turned on to the new course DB.
Although crossed and simultaneous Sun and Moon sights can often be obtained in daylight, and crossed simultaneous sights of the Sun and Venus ♀ are sometimes available, the usual daylight observed position is by two Sun sights with a run between, in other words a running fix on the Sun.
The sun between sights always introduces an unknown error, for here the navigator depends on his assumptions regarding distance run, leeway, tidal stream or current. Consequently, the less the interval between sights the better, and for this reason they should be taken, if possible, at the beginning and end of a period when the azimuth is changing most rapidly. With very few exceptions, azimuth changes more and more rapidly as altitude increases, reaching a maximum when the body is on the meridian. It follows therefore, that the period for a running fix on the Sun should be centred about solar noon and that the best sights for this purpose will be those taken at about equal intervals on either side of the solar noon, i.e., on either side of the time of the Sun’s Mer. Pass..
It is a common error in choosing sights for a running fix on the Sun, to take the first sight too long before noon and the second too long after, in an attempt to get near a right-angle cut. The table in fig. 33-2 shows, to the nearest tenth of a mile, the relation between angle of cut and error (in miles) caused in the resultant observed position for 1′ of error in one of the altitudes. From this it will be seen that an angle of cut of 50º is not much inferior to one at 90º) and that 40º is still acceptable. 30º or thereabouts may, for practical purposes, be regarded as the smallest angle of cut the navigator will accept.
An angle of cut of 50º corresponds to Sun sights taken with azimuths at 25º either side of the solar noon azimuth, i.e. N.55º E and N.55º W. in northern latitudes. A glance at the Sight Reduction Tables will show that in Lat. 50º with a Dec. of 20º contrary name (winter conditions) this corresponds to hour angles of 25º before and after noon, while a 90º cut could not be obtained at all with reasonable altitudes. In summer, in the same Lat. with Dec. 20º same name, a 50º cut can be obtained with hour angles of only 14º each side of noon (under one hour each side of noon) whereas the 90º cut means hour angles of 27º (i.e. about 1¾ hours each side of noon). Thus, in the summer example given, the navigator who picked the 50º cut would have a run of under 2 hours between his sights while the navigator who insists on a right angle cut has a run of nearly 4 hours with consequent doubled liability to error, not to mention the longer wait to obtain an observed position.
EX. No. 03: A vessel whose estimated noon position will be Lat. 50º N., Long. 030º W. on a day when the Sun’s Dec. is 4º S. requires the approximate G.M.T. of Sun sights for double sights with an angle of cut of about 60º.
Taking the Sun’s transit of the Greenwich meridian as 1200 G.M.T.. (which is always within a few minutes of the actual time and near enough for the present purposes) the time of solar noon in Longitude 30º W. is about 14:00 hrs G.M.T.. An angle of cut of about 60º means a tabulated azimuth of 180º – 30º = 150º for the morning sight (where Zn = Z). Entering Vol. 4 of the S.R.T. with Lat. 50º and Dec. 4º, inspection of the right-hand pages (contrary name) reveals that the L.H.A. for azimuth Z 150.2 is 25º = lh. 40m. in time, therefore: –
sights at about 14:00 + lh.40m. = 12:20 and 15:40 G.M.T. will be about right.
Purists will note that in the above example the vessel’s Longitude is assumed to be her noon Longitude for both sights. In practice, except in a fast ship in high latitudes on a course which changes the Longitude rapidly, this assumption may be safely made because, after all, only approximate times are required. When for any reason, closer accuracy is required, allowance for change of Longitude between the two sights may be made by applying the estimated longitudes for the two sights when converting the hour angles from the tables into G.M.T..
126. THE PRACTICE OF AVERAGING SIGHTS
In the case of a body which is rising or falling throughout the period of observation, the experienced navigator either takes only one sight of the body or, more usually and better, he takes three and finds the average by adding together his three altitudes and dividing by three, similarly adding together the three times at which they were taken and dividing by three. He then works the resultant averaged sight. The assumption behind this practice, which, like most professional navigators’ practice, is not lightly to be discarded by any amateur, is that sights taken by a skilled man are not likely to be individually erratic so the average of three is probably more accurate than any one of them. This unfortunately is often not true of the beginner and he needs to watch himself, at any rate in the learning stages, much more carefully.
It is not easy to find any reliable test against erratic and erroneous observations by a beginner and the only final cure is to cease to be a beginner, i.e. to practice frequently. The advice commonly given by amateurs, to plot sights on squared paper with altitudes against times and then draw a straight line through the majority of them, rejecting those which lie off the line and picking one of the others is obviously quite useless unless more than three sights are plotted and not a lot better even if four or five are taken.
If an observer who has a considerably varying personal error takes five sights of the same body one after another, and after plotting, them on squared paper, finds that a straight line will go through three of them leaving two off that line, he has very little justification for assuming that the three are good and the two are bad, for a straight line can be put through any two of the five, and the two he has rejected are nearly as likely to be the best as the three he has adopted.
There is, however, one check which the amateur can apply easily to his own observations if he uses the N.P. 401 Sight Reduction Tables, and that is the rate of change of altitude.
Except when a body is on or near the meridian, its rate of increase or decrease of altitude may be assumed to be constant over a short period of time such as the few minutes required to observe three or four sights. This rate of change of altitude is obtainable direct from the Sight Reduction Tables. The only practical difference between successive hour angles tabulated in the tables, for present purposes, is that the 1º higher L.H.A.. corresponds to a time 4 minutes later than the L.H.A.. 1º lower, because the vessel’s position may be taken as unchanged during the short time here in question. Suppose a number of sights were taken in the four minutes between a time when the tables would be entered with L.H.A.. 317º and a time when the tables would be entered with an L.H.A.. of 318º in Lat. 50º N. with a Dec. of 20º N. The Tab. Alt. for L.H.A.. 317º in these circumstances is 44º 43.8 and for L.H.A.. 318º the Tab. Alt. is 45º 18.4.
The rate of change of altitude is, therefore, 45º 18.4 – 44º 43.9 = 34.6 (increasing).in 4 minutes = + 8.65 per minute. If the sights are correct they should show an increase of altitude at the rate of 8.65 per minute. The navigator should, therefore, select any two or more sights whose altitudes and their differences give this rate of change and either take one of them or average them as described above.
127. THE PREPARATION FOR TAKING SIGHTS
It has already been mentioned in the Astro-navigation study that it is a strongly recommended practice to work out in advance the approximate altitude and azimuth to be expected from the chosen celestial body, and this is one of the most important operations in the preparation for taking sights. By so doing, the navigator will be able to set the pre-calculated altitude on his sextant before going out on deck and thus facilitate the easy identification of the required body, particularly in the case of stars and planets. There is, however, another reason for the pre-calculation of altitudes.
There are both upper and lower limits to the altitudes which can be observed without introducing chances of error which are unacceptable unless the navigator is so anxious for a position line that he is prepared to be grateful even for a doubtful one. The lower limit, which is the more important, is set by refraction.
As was shown in § 09-13, this is one of the corrections which has to be applied to the Obs. Alt.. The less the altitude the larger the correction necessary. Refraction is caused by the pressure and temperature of the Earth’s atmosphere through which the light from the observed body reaches the observer’s eye, and the less the altitude the more likely are abnormalities and variations in refraction to introduce unknown, and possibly substantial errors. Accordingly, navigators should regard altitudes of below about 15º suspect, and should endeavour whenever possible, to take altitudes of 20º and above.
The upper limit of reliable altitude observation is less important but worthy of note. As was explained in § 18-20, an Astro position line is tangent to the position circle of which the G.P. of the observed body is the centre and the zenith distance is the radius, and one of the basic assumptions of the theory is that, for practical purposes, the tangent is the same as the adjacent arc of the circle.
As the altitude increases, however, and the zenith distance becomes smaller, this assumption becomes less true and for very small zenith distances it gives rise to appreciable error.
In fig. 33-3 AP is an assumed position adopted for a sight taken with a body of very small zenith distance (large altitude) whose G.P. is at X. the position line resulting from the sight being PL. If the true position is at Z on the azimuth line AZ there is clearly no error involved in regarding the tangent PL as part of the position circle PC. If however, the true position is on the radius AZ1 for example, an error equal to Z1 – Z2 will be introduced, because the sight gives the position as on the tangent PL where it is in fact on the circle PC. Obviously, the greater the length Z – Z1, (and this means in practice, the more the E.P. is in doubt) and the less the zenith distance ZX, the greater will be the error. This error is always such as putting the observed position too far away from the G.P. of the body.
Altitudes must be very high indeed before any appreciable error arises from this cause, but if Z – Z1 is 20 miles the error is about ½ mile for an altitude of 85º. About the same error is obtained if Z-Z1, is 25 miles and the altitude is 80º and where Z-Z1, is 30 miles and the altitude is 75º. If a mile error is acceptable, the navigator can go up to 85º for a Z-Z1, a distance of 25 miles, while the same altitude gives about 1½ miles error when Z-Z1, is 30 miles.
Apart from the pre-calculation of altitudes and azimuths and, in the case of multiple star and planet sights at morning or evening twilight, a rough diagram showing the approximate altitudes and azimuths together with the direction of the vessel’s head (as recommended in § 24-28), preparation for taking sights should include the following: –
A sextant should always be kept in its case with (if possible when the lid is closed) the telescope in the collar and the draw-piece focussed so that the instrument is ready for immediate use. It is a good plan for the navigator to find the focussing adjustment which suits his eyes and to mark it on the draw tube with a fine file so that he can adjust it rapidly for use. An efficient navigator will then be able to observe a sight at a few seconds notice; it is extremely important not to lose valuable sights through un-preparedness.
When waiting for celestial bodies to appear from behind cloud banks, the sextant should be kept handy in a position where it will not slide about with the vessel’s motion. In a small craft probably a bunk is best, and in a larger vessel on the chart room settee.
Before taking sights, the sextant should have been checked for perpendicularity, side error and I.E.. The first two should be removed but if the I.E. is under 3′, it is advisable to leave it in and allow for it arithmetically when reducing the sights. Do not forget that both the observed I.E. (if any) and the error for the particular altitude shown on the sextant certificate (if any). must be applied to every altitude taken with the sextant. Following any adjustments to the index or horizon glass, see that the glass is firm in its mount and that none of the adjusting screws is loose. After adjusting it is a good plan to flick the glass with the finger-nail and then note if any change in adjustment ensues.
It is also desirable to know in advance the height of the observer’s eye at each point on board where observations are likely to be taken. This should be measured periodically when the vessel is lying in still water in her home berth and the results entered on a card pinned above the chart-table or inside the chronometer locker lid. If the sight is being taken away from the observer’s customary position, he should remember to use the appropriate H. of. E. (if it is different from the usual one).
It is important to make sure that the minute and second hands of a Deck Watch are lined up so that there can be no possibility of error in the reading of the minute hand when sights are being taken. This error cannot occur with a chronometer (where the minute and second hands are synchronised) but when a Deck Watch is set initially it is vitally important to see that when the second hand is at 0. the minute hand is exactly on a minute graduation. Figure 32-5 (a) shows the wrong way to set a Deck Watch with the minute hand exactly on the hour when the second hand is well away from 0. Figure 32-5 (b) shows that this Deck watch is liable to cause errors when recording the time of sights, since here there is uncertainty about whether the time is 8h. 49m.55s. or 8h. 50m. 55s. Attention to details such as this can make all the difference between good navigation and bad navigation, since a minute error in the timing of a sight can mean an error of 15 miles in the resultant position line.
Immediately prior to taking sights, the cover or lid of the chronometer or deck watch should be removed or lifted. The Sight Record Book (mentioned earlier) and the pre-calculated list (or diagram) of altitudes and azimuths laid out ready near the chronometer together with a pen or pencil.
*** The navigator is now ready to take his sextant on deck to make his observations ***