In my quest to develop a practical and pragmatic approach to celestial navigation, I have been exploring the use of a calculator to perform sight reductions. This doesn't eliminate the need for worksheets yet but does open further opportunities to get into the mathematical background of celestial navigation. I don't intend to become a mathematician but to understand as much as I can the workings and solutions of the navigational triangle. So far two formulas form the basis of sight reductions by calculator. They are...
sin Hc = (sin d x sin L) + (cos L x cos d x cos LHA)
and
cos A = (sin d - (sin L x sin Hc)) / (cos L x cos Hc)
where...
Hc = Computed Altitude
d = declination
L = Latitude
LHA = Local Hour Angle
A programmable scientific calculator is needed to store programs and retrieve the variables. Not too expensive - if you end up going this way on a long ocean passage, a backup or two would be wanted.
These two formulas are just the tip of the spherical trigonometry ice berg. I will explore others that are at least as approachable - remember I'm not a mathematician, or an astrophysicist - yet.
The results have been interested and add another dimension to all of this. In my wish to be able to take real sights and perform real navigation on the water during a passage, the following benefits are observations come to bear:
- Need only the Nautical Almanac
- No need to carry Pub 249 (Vol 2 and 3) Tables
- Vol 1 is needed for preplanning of star sights
- No need to carry Pub 229 Tables
- No need to apply Precession and Nutation corrections
- Assumed position can be the exact DR for Lat and Long - which allows for an increased level of accuracy because whole numbers for Lat and LHA are no longer required
- Azimuth correction is achieved
- Must use a stars SHA to determine the stars LHA for Hc
- Accuracy of fixes can be better by calculator - but by tables could sometimes be more accurate than calculator - I will need to do a bunch to see how this holds up and possibly to determine why
Sight reduction by calculator doesn't dismiss the paperwork done by worksheet but it does allow you to be a bit quicker in performing the work to arrive at a fix - without having to leaf through multiple pages of tables and entries. There are lots of opportunities to make a mistake and the calculator takes away a few of these opportunities.
The worksheets are still key to arriving at Ho, LHA and dec - which are the entry points to the Pub 249 and 229 tables.
I accept the use of a calculator as part of the 'acoustic' environment because the calculator doesn't rely totally on battery power but is also solar powered. Exposure to salt water spray or being dropped overboard will negate any attempt to be entirely self reliant in the goal of navigating through human and natural power.
