Wednesday, December 13, 2017

Pub. 249 Vol. 1, USNO, and OpenCPN

Alert! These notes only make sense to those familiar with cel nav.

The cel nav sight reduction tables Pub 249 comes in 3 volumes. Vol. 2 and 3 are similar to Pub 229, in that you enter with a-Lat, Dec, and LHA and come out with Hc and Zn.  And like 229, there are specific volumes for specific latitude ranges. Also like 229, these are permanent publications. They never change. If you see Vol. 2 or 3 in a swap meet or used book store for a couple bucks (list is $25 each plus shipping) then you have a good buy. But do not buy an old edition of Vol. 1. Despite its symmetric name, Vol. 1 is a totally different kind of sight reduction table. It is not permanent; it is issued every five years (latest is Epoch 2020, which good for ± 4 years).

On the other hand, unlike Pub 229 and the NAO tables, which can be used to sight reduce any sight, Pub 249 Vol. 2 and 3 are intended for sun, moon, and planets... and coincidentally, any star with declination less than 29º, which is the maximum those intended bodies could have. Thus, in part because Vol. 2 and Vol. 3 will not do stars in general, there is a Vol. 1 intended for "selected stars."  I say "in part" because all of Pub 249 was developed for aircraft cel nav, which has inherently less accuracy (and hence less need for more versatility) and also needs a method that is fast and easy to apply. Pub 249 has stayed in print beyond its expected lifetime (aircraft cel nav has been rare now for many decades), because these books became popular with yachtsman. The British Admiralty call these Rapid Sight Reduction Tables; they are $55 per volume, for the identical content. The US versions are online as free PDFs, although you could not print and bind them for the $25 they sell for in print.

Use of Vol. 1 takes a new approach to star sights. We figure twilight time from the Almanac, then we look up the GHA of Aries at that time, and from our DR at that time we find the LHA of Aries at the proposed sight time. Then we round our DR-Lat to nearest whole degree, and we have effectively established the sky that is overhead. Knowing this, Vol. 1 then gives us a selection of 7 stars by name suitable for sights, with the 3 best ones marked with diamonds. Stars in all caps are bright ones. The LHA Aries marked a specific time, so Vol 1 can tell us the Hc and Zn to each of the 7 stars. It has precomputed these stars for us, which we would otherwise have to do with Pub 229 or a calculator.

Next we take sights to the three stars in the normal manner, noting Hs and WT for each sight as in standard practice. Convert Hs to Ho and WT to UTC and we are ready to complete an abbreviated sight reduction to get the a-value.  Don't worry, you do not have to know these stars, nor how to identify them in the sky.  Just go out at about the time you used, set the sextant to the Hc given, and point in the Zn given, and your star will be there.  A point of pure light in a pale blue sky, often not even visible to the naked eye without a telescope pointing in the right place. Bring it to the horizon and you are done.  Indeed, it is not unreasonable to use Vol. 1 just to select the best stars and get this precomputation done for you. After the sights you can reduce them however you like, but Vol. 1 itself can be used as shown below.

We illustrate the use of Vol. 1 with a trick way to practice cel  nav for any type of reduction, namely we use the USNO computation of celestial bodies to tell us what the heights are from a given time and place, then we pretend that is what we measured, and we use our sight reduction method of choice to see if we can reproduce the Lat-Lon we gave to the USNO.  (The only better practice is to use our book Hawaii by Sextant!)

We start by choosing a DR and a date, then figure the twilight times from the almanac as shown below.

Fig.1 Set, civil, and nautical twilight. Sailing from the West Coast, with WT = PDT (ZD=+7)

So this is where we start, and from the almanac we learn sight time will be about 0440 UTC on July 5. Note this is 2018, and today is mid December, 2017, which reminds us we can do this for any time. As we shall see shortly, before an ocean voyage, you can know ahead of time which stars will be best on any night.  This can change with cloud cover, but intentions can all be planned.

To figure the stars, we round to Lat = 35N, and look up in the NA the GHA of Aries at 0440z on 7/5/18, which is 353º 7.9' and subtract from that our DR Lon of 130º 23.4' to get an LHA Aries of 212º 44.5', which for  now we can call 212 or 213 it will not matter for this planning of the practice.

Now we turn to Vol. 1 to see what stars they recommend. Note that DR is fixed, so LHA Aries varies as GHA Aries, which increases at 15º/hr which is 1º per 4 minutes. So the LHA Aries column is essentially a time scale, at 4 minute intervals, with 212.75 or so equal to 0440 UTC. We are looking here at the best choices and heights of the stars over roughly an hour (15 x 4 min). But we also notice that the best 3 stars do not change. The ones with the diamonds, of which Antares and Regulus are magnitude 1 or brighter stars.

So we will chose those three stars to "take sights of" for this practice with Vol 1. At this point we could do the same thing using Pub 229 or the NAO tables.

Fig. 2. Section from Pub 249, Vol 1. (We see later why Antares is marked at the next line.)

It takes a couple minutes per sight, and we would typically take them in sequence and then repeat the sequence 3 or 4 times, or as long as we can see the horizon in the evening, or until the stars disappear in the morning.

We make this choice for practice:

Kochab taken at 04 40 23  (hh mm ss) 
Regulus taken at 04 42 19, and 
Antares taken at 04 45 03. 

I chose this order at random for this exercise, but in practice there can be a preferred order. Ideally we want to get 4 or so rounds of each sight, so the order would not matter, but we should be aware of their bearings relative to sunset. July at 35N the sun is setting pretty far north, around 300º, so the sky will be darkest showing stars earlier opposite to that at about 120º.  So we might learn in practice that we could get a couple sights of Antares earlier than maybe Regulus, but it might not matter much for these particular stars. That is just a side note to think on. As a rule, you want to stretch out the useful sight time as long as possible to get as many rounds of sights as you can.  Do not add more stars! Just get more sights of these three... I wander into details from our textbook.

Now we go to the USNO to get realistic practice sights. We have made a shortcut to it at  This is not related to Starpath; it is just a quick way to navigate to an important place—we call the navigator's dream machine—that is not so easy to find at random.

The input page looks like this:

The output for this first sight is

At this point for practice, we can simply use the USNO Hc for our Ho, or we make practice problems by adding the corrections we are going to take out (IC, dip, and refraction). They even tell us what the refraction is, -0.8'.  We can then assume some watch error if we like, and fill out a real form to look like this, which is a starpath form dedicated to Vol. 1.

The form shows the actual time we "took the sight" and then we find GHA Aries at that time from the Nautical Almanac to enter the form. This has an hours part with a minutes and seconds correction.

Since we are using the same DR for all three sights, we have to assume we are not moving.  This shows what the top of the form would look  like for a real sight.  For the others we dispense with that.

This form is essentially the same as we use for Vol. 2 and Vol. 3, but has several parts removed. Copies of our forms with instructions are available for download at, along with other tools of interest.

Once we know actual time of sight, we figure the actual LHA Aries (using Almanac and DR-Lon) for it and return to Vol. 1 to get Hc and Zn. The first dip into the tables was just to see what stars to shoot, at some approximate time. Now we have real times, so we need real LHA Aries. All the rest of the form is the same as using Vol. 2 and Vol. 3.

Then we repeat the process for the next sight times, and get two more LOPs. Note that you get to double check that you looked up GHA Aries correctly, and to double check that you got the right Zn. We are not using either of these from the USNO, only the heights they give.

With these examples, we now skip the sextant and time corrections and go direct to the meat of using Vol 1.

And finally the Antares sight.

Now we have 3 LOPs and we can plot them for a fix. They are summarized here.

Now we can plot these in the normal way to see if we get back what we started with, namely 34º 56.7' N and 130º 23.4' W.

This is zoomed in solution of the plotting done in OpenCPN. I will add a video on that trick shortly. We just plant a waypoint at the assumed position, draw a route in direction Zn, add a range ring to the mark with radius = the a-value, and where they cross draw a perpendicular route line which is the LOP,

We are looking for 34º 56.7' N and 130º 23.4' W.  We are off by about 1 mile, but I was not as careful as possible with the plotting, and Vol. 1 only has an inherent ± 0.4' accuracy... i.e., it rounds all sights to 1' and it rounds all azimuths to 1º. You can in each case use the USNO data to see how accurate Vol. 1 was on Hc and Zn. In short, the result here is about as good as we could expect, i.e., it all works.

With this method you can practice any cel nav sight reduction, for any ocean, for any time of the year.  You can also get the Vol. 1 forms at our cel nav book support page cited above.

Here is a link to this form alone: Form_111_Pub_49_Vol_1.pdf  This is new as of this post here. We will incorporate this into our full set of forms, which are available as free downloads or as a bound set of perforated sheets.

Sunday, December 10, 2017

Why the Book "Hawaii by Sextant" is Unique

There never has been in the past, nor will there likely be in the future,
        such a thoroughly documented navigation study of a voyage
        relying purely on celestial navigation to cross an ocean.

The future part is easy. It is near impossible to find an ocean going vessel without a GPS on board, or in someone’s cellphone. From a legal point of view, it would likely be considered negligent to make such a voyage without GPS.

One might argue that a voyage could be or was navigated by cel nav without looking at the GPS, but even that does not really count. Knowing you have a backup solution changes the mentality of the navigator and biases the navigation. Not to mention that you are less likely to stand on deck with sextant in hand for hours waiting for the sun to peek out for a few seconds to get a sight. With a GPS in a box somewhere, you can more likely gamble that you will eventually get a sight and not have to work so hard at the moment… nor would you be forced to study limited data for hours to figure the most likely position.

Navigators can certainly document good cel nav practice underway in the ocean with detailed information, and such studies are indeed valuable contributions, but that is different from relying on it as the sole source of navigation, regardless of conditions. This book shows what it was like to navigate by cel nav with nothing else to go by but compass and log. It raises the questions you would have to face, and proposes solutions to analyzing difficult data.

Furthermore, suppose such a voyage were carried out and good records maintained. Then we have to fold in the probability that someone would devote the enormous amount of time and energy required to organize and present the information in a usable manner for students. We venture that this is highly unlikely…. maybe a few days sail, but not across an ocean.  A look into the past treatment of this challenge only reinforces this factor.

Why no such study exists from the past is a more interesting point–especially since we describe our book as being “in the spirit of early Bowditch editions.”  Bowditch’s American Practical Navigator (1802 up until 1900 or so) and also Norie’s Epitome of Practical Navigation (roughly same period) are two classic 19th century texts on navigation.  And sure enough each of these do include very detailed practice voyages with celestial sight data and logbooks. It is curious that they all involve voyages to or from Maderia, Spain, which must have some historic significance, but not an issue now.

The key point is that even though these records list the vessel names, voyage dates, the captain’s names, and the log keeper’s names, they are all fiction when it comes to the celestial navigation. In short, they made up the data to demonstrate what they wanted to teach… which is what all navigation teachers do to this day at some point.

These Bowditch and Norie Journals may have been based on actual voyages made at some time in the past, but the data presented is blatantly artificial. (We leave it as an exercise to confirm this observation. The books are online.)

We agree with these masters of navigation that this is the best way to teach the process. And certainly we do not even approach the skill and seamanship they represent, nor can we hope to emulate the high standards they set in navigation. The only point we make is data in Hawaii by Sextant is real; the comparable data in these classic texts was manufactured… and we know as well as anyone why they might do what they did.  After an ocean passage under sail, it is sometimes difficult to put the pieces back together to present a coherent picture of the full navigation, day to day–not to mention that the many details required to reproduce the results are tedious. Few would consider them worth preserving. As we point out in the text, and you see in our own records, when the going gets tough, the boat gets more attention than the logbook.

In more modern times there have also been a couple books published that present ocean exercises in celestial navigation, but these too have been based on manufactured data.  We thus maintain that Hawaii by Sextant is a unique contribution to the library of navigation textbooks.

It is obviously not at all unique to sail across an ocean by cel nav alone. Thousands of mariners over the years have done so. Bowditch did many times. It is not clear that Norie actually navigated. He was more famous as an author and book publisher at the time. He was the founder of what is now called Imray Nautical Publications in UK. That fact also is not surprising. Many early classic texts on navigation were from scholars who did not have practical experience underway. Bowditch, Lecky, and Thoms were notable exceptions.

PS. We have been told that there are several highly experienced navigators who do still have all the records of their early voyages done by cel nav alone.  We look forward to their publications if they choose to do so.  The more data we have of this type the better our learning will be. If these are from larger vessels (we understand they were commercial ships), then that too will add another perspective.