Low Energy Navigation

The subject of this post was prompted by another post in the Archdruid Report nearly a month back, and by the follow-up discussion. The Archdruid had reported that he had passed his Amateur Extra FCC examination, which entitles him to the highest level of amateur radio privileges. It is quite an achievement. Some how the follow up discussion included a thread or a mention of GPS, and the question was asked about pre-GPS navigation, and how that could be carried out.

GPS has somewhat trivialized navigation for the user, making precision navigation accessible to anyone who can operate a receiver. (True story -- I was in Sacramento last year traveling with another engineer. We had just landed at the airport and had just rented a car, as well as a hand held receiver. I gave the printout with the address of the hotel and the receiver to my colleague, and asked him to direct us to the hotel. Although he had never used a receiver before, he had the address entered into the device and guiding us to the hotel before I hit the freeway. No instructions, no help from me) My concern is what happens if any one of the three legs of the Global Positioning System fail. It would seem that the weakest parts of the triad are the control and the space system, but no doubt others have come to this conclusion as well, and contingencies have been prepared. The user segment is as strong in the near term as the various power supplies, but in the longer term even batteries run down. In any case, I'm concerned with how to determine one's position on the earth without electronic navigation aids.

The principal method has been celestial navigation, using the predictable motion of the earth and planets to triangulate on the sphere one's position. The tools to do this are still readily available. To obtain a fairly precise location (perhaps one to two decimal places after the minute), you'll need a sextant of some sort and an almanac. The traditional marine sextant is a wonderful solution, but requires an artificial horizon when using the sextant in-land, like here in Tucson. There is an aviation sextant that has some compensation for the horizon built-in but I don't believe aviation sextants have been manufactured for some time. The second item, an almanac, can be filed through the acquisition of a current Nautical Almanac. This document, jointly published by the US and UK governments, costs about thirty dollars. There is also an almanac published by McGraw-Hill and written by George G. Bennett. This is a compressed almanac that carries data for five or so years, but lacks the precision of the Nautical Almanac.

I've forgotten the third element required for a celestial navigation solution: an accurate time piece. Just about any quartz wristwatch is accurate once the error from UTC is known.

Using a sextant and the Nautical Almanac, I've been able to determine my location to about 5 miles, which I don't think is bad given what I'm using for a horizon. I've used the reduction equations documented in the back of the Nautical Almanac, and programmed them into a calculator. However, there are a number of documents that provide for other reduction of the sextant and chronometer measurements, but reduction is essentially the solution of the navigation triangle for the unknown quantities. Before the advent of calculators solving this triangle was not trivial; although closed-form solutions exists, computing of those solutions is involved.

The next steps in achieving a low energy navigation solution for me is to first determine a replacement for the various almanacs. Essentially, this requires generating an almanac from local astronomical measurements. The final step would be to create a low-cost, reproducable, but sufficiently accurate sextant. I doubt if I get to this last step, but that would create a totally local and independent navigation system.