A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Position-Finding
From: Andrés Ruiz
Date: 2018 Mar 12, 15:00 +0100
Jeremy, you wrote:
"I seem to remember Longitude by Chromometer/Time sights were fairly limited by the body needing to be bearing nearly E/W no? "
No. That was a misconception of late 20th century celestial navigation. It was a way for navigators using the intercept method to feel good about the modern methods and leave time sights behind. :)
For any given latitude, the time sight calculation gives you an exact longitude on the circle of position for that sight. Exact. To extend that into a line of position, you can either get an azimuth in some way, or (really much easier!) you can just calculate a second point on the circle by feeding a nearby latitude into the calculation. And there you go: run a line through the two points and you have a line of position with minimal calculation. This is easy to do on a calculator, and it's been the basis of my "Modern Celestial Navigation" for many years. Note that a line of position plotted from two points can be drawn on common graph paper. You don't need plotting sheets, and you don't need to know anything about scaling for longitude. Naturally also there is no "AP" (or you could argue that there are two AL's, assumed latitudes instead of one AP consisting of both a latitude and a longitude --there's no free lunch). In most respects, there's far less baggage than in the traditional intercept method.
Somewhat contrary to what Greg wrote, this calculation works under any circumstance, not limited to some range of meridian angle (time from meridian passage), but a navigator must understand that the resulting longitude is derived from the input latitude. It's exact for that latitude. Historically, this was problematic because navigators often did not understand that a single altitude always yields a circle of position (or a LOP when we zoom in on that circle) regardless of how we get to it mathematically. So a point from an uncertain latitude is still a perfectly valid point on the circle of position, but that doesn't mean it's your position. You're on the circle of position. When in doubt on latitude, you should always run the calculation twice to get two points on the circle so you can draw a line through them. Note that ex-meridian sights add nothing to this except a calculational twist --fun for historical emuation but un-necessary in any modern setting. You never need ex-meridian sights for anything. The only other trick in the toolkit for LOPs by time sight is some rule for selecting the two latitudes. Most of the time you do just fine with a spacing of 0.1°: run the calculation with best estimate latitude and again with that lat+0.1. But if the sight is very near the meridian, you need to reduce the spacing. There's a simple trick for this, but you can worry about that later. Also it's important to understand that the calculation can fail if you pick a latitude that is outside the high/low limits of the circle of position. So if the sight is anywhere near the meridian, you work out Lat = z.d.+dec for the sight with both signs on z.d. and then you limit your latitudes that go into the time sight calculation to values between those limits.
By the way, even in the 19th and early 20th centuries when navigators commonly worked up single longitudes based on the best estimate latitude for that time, there was nothing like that obsession over sights on the prime vertical, exactly east/west, that's sometimes suggested in modern "quick" histories of navigation. Typically historical navigators took the longitude sight at some convenient local time everyday, like 3:00pm. That's what you often see in the original logbooks and other primary source evidence. An interesting practical benefit of this is that you know the answer reasonably well before you do the computation. The time sight will yield a local time, and if you set a pocket watch at high noon and waited until 3:00pm for the sight, then the calculation for the time sight will yield something rather close to three hours elapse time (different, of course, if you have travelled east or west in those three hours and also different because the time of high noon was only an approximate call).
But that's history. For modern usage, run it twice and get an LOP! The line of position is the "underlying reality" --working it up by the intercept method or by this time sight procedure is just mathematical analysis.