CelNav Zero - Course Preliminaries

[HenryC]

CelNav Zero  (Edited 10/27/14 for the 2015 Nautical Almanac)

This is the first article in a series on the fundamentals of celestial navigation. Future articles will require that the reader have the following:

1) Simple plotting tools, parallels and dividers
2) A nautical chart of his area, or a Universal Plotting Sheet
3) A Current Nautical Almanac
4) "Celestial Navigation with the S Table", by Mike Pepperday (Paradise Cay Publications)
This publication can be ordered from Celestaire, Inc.  They are on the internet.
An alternative to Pepperday is a trig-capable scientific calculator.
5) An accurate timepiece and the means to set it to Universal Time.  (WWV time signals or
GPS receiver).
6) A pocket calculator with trig capability (for those who prefer not to use the Pepperday sight reduction tables.

All navigation is done by the intersection of Lines of Position (LOP).  It doesn't matter whether it is Piloting, Radar, RDF, LORAN, or even GPS.  The ship's position is always somewhere on an LOP, and  if it is on two or more LOPs, then the intersection point of those LOPs is where you are. If the LOPs don't all intersect at one spot on the earth's surface, then the uncertainty of where those lines cross is a measure of the possible error of the position.  The LOPs may come from different methods or devices, or be even derived at different times, but your position will always be at the intersection of two or more of them.

In piloting, the LOPs are lines plotted on a chart from the ship to some visible landmark on shore.  With radar, the LOPs are arcs of constant range to the ship's radar from some distant target.  In GPS and LORAN, the LOPs are radio signal arrival delay times calculated and "drawn" inside the circuits and processors of your receiver; with earlier versions of LORAN, the LOPs used to be actually printed on the chart as multicolored lines. 

Celestial navigation is no different.  Your ship's position will be at the intersection of two or more LOPs, and the more LOPs a navigator can collect the more accurate his final position will be.  After all, if one LOP is in error, for whatever reason,  a "good" LOP will not cross it at your position.  If you have two LOPs, you'll have no way of knowing if one of them is in error. If you have three LOPs and one is off, you'll know it because they won't cross at the same spot, but you won't know which one is incorrect. With four or more LOPs, if one is wrong, you will be able to identify it and ignore it. You can't have too many LOPs, and to get a good position it is nice to have at least five.  This way two of them can be in error and you can still get a good fix.

If you're a sailor you already know all this, but the important thing to remember about celestial navigation is that you are still navigating with LOPs, the only difference is that now your LOPs are determined by observing distant objects in the Solar System or the Galaxy.  For every body you observe with your sextant, you will have one LOP, and several LOPs will give you your fix.  That's all there is to it: a celestial navigator will observe several bodies with his sextant, draw an LOP on the chart  for each one, and where all the LOPs cross is where he is. 

So just what IS a celestial LOP?  It isn't a bearing to a star or planet, because you simply can't measure bearings very accurately aboard ship. The earth is so big, even if your bearing is off by half a degree (about as close as you can read a compass), you could be hundreds of miles off.  The only thing a human being can read to any high level of accuracy (with the help of a sextant) is an angle.  The human eye working with the mechanism of a sextant can read (with a little practice) an angle to an accuracy of about a minute of arc, that is 1/60th of a degree. One minute of arc on the earth's surface is equivalent to a nautical mile, or 1/60th of a degree of latitude. To give you some idea of what a tiny angle this is, the full moon is about half a degree, or 30 minutes of arc in diameter. A nautical mile is roughly 6076 feet, and from now on in this course, when I say "mile" I will always mean a nautical mile.  (Now you know why sailors will never go metric!). The rest of this course will be dedicated to how to convert one sextant observation to one Line of Position and where to locate that LOP on a chart.

The procedures to do this are not magic, and they do not involve high level math on your part (the actual math has already been done for you by some very clever folks and computers, a long time ago and very far away).  But it is rather involved and tedious, and it requires lots of practice and a true understanding of what you're doing.  The purpose of this course is to show you how to do this.  Think of it as a recipe, you don't have to know the chemistry, but you need to follow directions and use the right ingredients in the correct order.  The entire practice of celestial navigation has evolved over the centuries so that it is a set of steps which if followed in order will give you the answers you seek. It has been designed by geniuses to be used by idiots... All you really need to know is how to add and subtract angles and time (which is why they use the same units (degrees, minutes and seconds AND hours, minutes and seconds).  You don't have to memorize anything, you will be working off pre-printed forms which guide you from one step to the next.  This is why I ask you to use Pepperday's S-Table and his forms.

Creating an LOP is a procedure called a transformation.  You start with certain numbers, and follow a set of steps, and it transforms them to certain other numbers.  The items you bring to the party are

1) The exact time of the celestial observation.
2) The altitude angle you measure with your sextant between the object and the horizon.
3) Your Assumed Position (AP), a rough guess of your Latitude and Longitude; anywhere within a   few hundred miles of your true (but unknown) position is good enough.

Using these figures, you go into the Nautical Almanac and look up some information on the body you will need, as well as some corrections you will have to apply to your observation.

With this information, you go into the Sight Reduction Tables and "Reduce" your observation to an

1) Azimuth ( a bearing to the Celestial body) drawn through the Assumed Position (AP)
2) An Intercept (A distance from the AP along the Azimuth line through which the LOP will be drawn (at right angles to the Azimuth).

Putting this another way each LOP is derived like this: Time, Altitude, AP ---> (Almanac, Sight Reduction Tables) --->  Azimuth, Intercept--->Plotting the LOP on the chart.

The celestial LOP is not actually a straight line, but a tiny piece of a huge circle drawn on the earth's surface where that celestial body would have been at that altitude if observed at that moment in time.  But in the tiny piece of the earth's surface on your chart, that little piece of the circle looks like a straight line. The Intercept is the distance you are from the AP.   The Azimuth is not from your position, it's from the AP, but the earth is so big the two angles differ very little at your chart scale.  So to a very close approximation, you are somewhere on the LOP drawn on the chart.  Now just repeat the whole process for a few more LOPs...

I think that's enough for today, folks.    I may come back to this page in the future and make additions or corrections, so check the date of last edit next to the title.

Good Luck,
Hank

[Andrew]

Henry...your Celnav 101 is a great idea and very generous.  I was a bit shocked when doing a search for the almanac and about the best price is about $30 bucks to the door. Any good suggestions for cheap skate like me for a book that will be out of date in a year.

thanks Andrew

[HenryC]

Celestaire, Inc sells the "Commercial Edition" for about $27 + shipping, which seems to be pretty much standard (the publisher sets the wholesale price).  It is rather scandalous, considering, all they do is photocopy  the US Gov Pub which has already done all the work of observation, calculating, development and typesetting at taxpayer  expense.  And on top of that, they fill it with  advertising (which I methodically rip out when I get my copy of the commercial edition every year, just out of spite). When I become dictator I'm going to instruct the Naval Observatory to give it away for free (instead of selling at the cost of production) and put all these copycats out of business.

There is another Almanac out there called "Reed's", which carries the data, but I suspect it is in a different format and not suitable for my exercises.  The other alternative is to go to the public library and use their copy (if they carry the NA, my library has canceled their subscription).  I also have a copy of the 2010 N. A., so I can simply do each example problem twice, once using the 2010, the other with the 2011.  You might be able to pick up a 2010 edition at a discount, now that the 2011s have come out. Let me know if this is the case so I can "double up" on the exercises.

I've rejected the idea of just reproducing the pages I'm using and publishing them with the exercises.  The examples alone aren't enough; you must have your own copy so you can read it cover to cover and get thoroughly familiar with all its features.  And you need to do your own practicing, too, over and above my examples.  This is why it's a good idea to get your copy as soon as its available so you can practice with it for more than a year and get thoroughly checked out.  Once you are familiar with the layout of the book, you can quickly locate anything you need.  For this reason, the Almanac always uses the exact same format (at least since 1990 when I first start using it frequently). They've got something that works and they are not messing around with the layout, so you don't have to re-learn it every year. Fortunately, Sight Reduction tables like Pepperday's don't have to be replaced every year.  They are like a paper calculator, except they never wear out or need batteries.

The Almanac is a wonderful thing, it has evolved over the centuries so that every single page is crammed full of very useful information, with no fluff, all arranged in just the right way so that it is as convenient as possible for the navigator (and geographers, mapmakers,  surveyors, astronomers, and even architects and planners). It may look confusing and cluttered at first, but when you get used to it it is a masterpiece of economical design. Some of this information is ephemeral, that is, it changes every year.  This is particularly the case for the astronomical data.  But many of the tables, instructions, examples, etc are reprinted verbatim every year, so you don't have to refamiliarize yourself with it. After a few years of use it becomes an indispensable tool. Your tax dollars are very well spent on the Almanac.

It's a wonderful book, with an unbroken history that goes back to the medieval Arab world (almost all technical terms in navigation, as well as most star names, have an Arabic origin).  Knowing how to use this book puts you in the historic line of navigators going all the way back to the  ancient Phoenicians. Some people honor their history by dressing up in old uniforms and reenacting ancient battles. I do it it every time I use the Nautical Almanac.

[Bob23]

Henry:
  Quick question about CelNav zero. On the very first page you state we need a Nautical Almanac for 2011. Don't you mean 2010? Maybe I missed something basic here.
Bob23