Thursday, March 14, 2024

Special Uses of the Star Finder and Sight Reduction Tables

The 2102-D Star Finder is essentially a hand-held planetarium designed for mariners to assist with celestial navigation. It can be used to plan the best sights as well as its main function which is to identify stars or planets whose sights have already been taken. We have devoted a short book to the many uses of this powerful tool called The Star Finder Book.

Sight reduction tables are permanent mathematical solutions to the Navigational Triangle that form the backbone of celestial navigation carried out in the traditional manner using books and manual plotting — as opposed to modern solutions using computers or calculators with dedicated cel nav apps.

There are several styles of these tables, popular versions are called Pub 229, Pub 249, and the NAO Tables, a copy of which is included in every Nautical Almanac. Complete free copies are available online as free downloads, which are good for practice, but do not make sense for use underway because any device that can read the files can also support a cel nav app that does the full process, sights to fix.

All sight reduction tables, regardless of format, do the same thing. You enter the tables with three angles and come out with two angles. We enter with the declination (dec) and local hour angle (LHA) of the object sighted and the assumed latitude (a-Lat) of the observer, and we come out with the angular height of the object (Hc) and its direction (Zn) as seen from the assumed position.

Put in plainer terms, the Almanac tells us where the sun and moon, stars and planets are located at any time of the year, and the sight reduction tables tells us what the height and bearing of any one would be as seen from any latitude and longitude.... or it tells us the object is below the horizon at that time and place.

The Star Finder does exactly the same thing, but with less accuracy. We look up in the Almanac a number that tells us how to set up the disks for the time and latitude we care about, and then we read the Hc and Zn of the celestial objects from the blue templates.

With that background, I want to point out that either of these tools can also be used to answer more non-conventional cel nav questions such as one that is part of our Emergency Navigation course. Part B of question 6 on quiz 5, asks us what are the conditions that lead to the sun's bearing changing with time at a rate of 45º per hour or faster?

This comes up in the context of using the "Eskimo Clock Method" to get bearings from the sun based on the local time of day, which makes the assumption that the sun's bearing moves along the horizon at the rate of 15º per hour. That condition, we show in the course,  requires the peak height of the sun at noon (Hc) to be less than 45º, which leads to the nick name "Eskimo clock," because at high latitudes the sun is always low.

Here we have a more specific related question, but it can be solved with the Star Finder or with sight reduction tables. 

We know that fast bearing changes means the object is very high and the fastest change will occur when the object passes overhead or near so. Consider sailing at lat 15º N during a time when the declination of the sun is also about N 15º (first few days of May).  [Note latitudes get the label following the value; declinations get the label preceding the value.] In this example, the sun will bear near due east (090) all morning and then change to near due west (270) in a matter of minutes as it passes overhead.  The question we have is, how do we specify the conditions that will lead to this bearing change being ≥ 45º/hr? It will have to be high, but it won't have to cross over head.

This could be worked from any latitude in the tropics, but we stick with 15º N, and look at the star Alnilam (declination about S 1º, which corresponds to the sun's declination in Sept, 19th-21st).  Below is the Star Finder set up for the time Alnilam crosses our meridian bearing due south.

Alnilam crosses the meridian bearing due south (180) at a local hour angle of Aries equal to 84.5º.  We see that the height of the star as it crosses is 74º, which we would expect in that we are at 15N and the star is at S1 so the zenith distance (z) is 15+1 = 16º which makes the Hc (90-z) = 74º. 

The rim scale corresponds to time at the rate of 15º/hr, so 30 min later (LHA Aries = 91.0º (84.5+7.5), we see that the star has descended very slightly but now has moved west.

Thirty minutes later the bearing is 205º, or 25º to the west of 180º. Thus if we imagine this star to be the sun in late Sept, viewed from 15º N, we would see its hourly change in bearing at midday to be about 50º per hour.  This is a bit faster than the exercise asked for, but we could experiment around for a closer answer.

We can also do such studies with sight reduction tables, such as Pub 249. We enter the tables with a-Lat = 15º and dec = 1º. With these tables we do not use North or South labels but just specify if they are both north or both south or is one north and one south. The former condition is called Same Name; the latter is called Contrary Name.  We have Same Name in this example.

We will also start with LHA = 0º, which means the sun is crossing our meridian (bearing 180), and like wise look at 30 min later with LHA = 7.5º. We could look at LHA = 15º, exactly one hour later, but the rate of bearing change at LHA 352.5º to 007.5º, as it crosses our meridian, is a bit faster than the full hour on either side.

In Pub 249, each Lat has a set of pages, LHA is on the side of the page, and declination is across the page. The tabulated values are Hc, d, and Z. The d-value is how much the Hc changes with 1º of declination — for Alnihlin, dec = S 1º 12', so we would reduce the tabulated Hc by 12/60 x 60 = 12' for precise values of Hc, but we can neglect Hc for present study.)

At meridian passage the bearing is 180º, then 30 min later (LHA=7.5), we see the body dropped from 74º high at the meridian to about 72º 20' at which time the relative bearing (Z) is about 154º, from which using the rule provided (Zn=360-Z) to find the new bearing of 206º, which agrees with what we found from the Star Finder.

These terms and procedures become more familiar with a full study of cel nav, but we hope the brief discussion of the principles show how these tools might be used for other questions. Note that LHA is defined as how far west of you the body is, so as it approaches from the east it has large, increasing LHA, which goes from 358, 359, 360, 1, 2, 3 as it crosses the meridian.


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