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 www.starpath.com/usno.  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 www.starpath.com/celnavbook, along with other tools of interest.

Procedure:
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.

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.

Available from Starpath Publications

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.

MSLP vs. MSLP

Someone has to care about the details of marine navigation and weather, or things slip by, which might one day show up and cause confusion, and we don't want confusion. Indeed, a hallmark of good navigation and seamanship is clarity in communications. Today, we ran across a gold nugget of doublespeak: MSLP.

We have published a book called the Mariners Pressure Atlas, which contains pressure statistics that are difficult to find, despite their great value for weather tactics in tropical storm prone waters of the world. The book contains global plots of the mean values of the sea level pressure, called mean sea level pressure  (MSLP) patterns (isobars) along with the standard deviations (SD) of these pressures on a month to month basis. The SD are a measure of the variation of the pressure we can expect purely from a statistical spread around the mean value. Sample sections are below.

These are the mean sea level pressures (MSLP) in this part of the world in July. Below are the SD values.

For example, in the tropics with a MSLP of 1012 mb and an SD of 2.0 mb, we know that an observed pressure of 1010 is one SD below the mean and a pressure of 1008 is 2 SD below the mean. When we observe an average pressure of 1007 mb, we are 2.5 SD below the mean. That takes on special meaning when we look at the probabilities.

In other words, the probability of normal pressure fluctuations being down 2.5 SD is 0.6%. A pressure that low is almost certainly (99.4%) not normal fluctuation—that is the approach of a tropical storm! The wind will for sure not warn of that at this point, and maybe the clouds on the horizon might not either, but there is indeed a tropical storm headed your way.

This powerful storm warning technique was well known in the late 1700s, early 1800s when ships carried accurate mercury barometers, but unfortunately with the advent of aneroids, by1860 or so this knowledge slipped away because they were not accurate enough then to do this job.  Eventually even the textbooks stopped talking about absolute pressures and just started preaching up or down, fast or slow, which is useless for this type of long range storm forecasting.  Now we have accurate barometers (including accurate aneroids), which is why we rejuvenated this classic method... mentioned in Bowditch, but sadly without a link to the crucial MSLP and SD data.

There are spot values of mean sea level pressures in Appendix B of the Coast Pilots.

But that is not the point at hand. What we are dealing with in the above is the mean value of the sea level pressure, which we periodically see abbreviated MSLP in weather and navigation documents.

Now, however, look at these weather maps from Australia and Canada.  The UK Met Office also uses the MSLP notation to describe a surface analysis map.

Now we have an all new meaning of MSLP.  This cannot be the mean sea level pressure we discussed above;  these are the actual values of the pressure at sea level at the valid map time. What is going on here is they are not calling the reference plane "sea level," which we often see, i.e., sea level pressure (SLP), but instead they are calling the reference datum "mean sea level."  MSLP in this context is the same as SLP.

Here is an example of aviation weather (METARs) using SLP; it is also used in some numerical model outputs.

Here is another example that shows the fluidity of the terminology.  The ECMWF defines

"MSLP is the surface pressure reduced to sea level." 

So they know that "sea level" is the same as "mean sea level," but they choose to help us make our point!

It is not unreasonable to tack on the "M"; the sea level does change with the tides (to a good approximation mean sea level, MSL, is halfway between MLW and MHW), not to mention that it varies with the pressure above it (called the reverse barometer effect). In fact, MSL is an even more complex concept, but in ways that do not at all effect our use of it as a pressure reference. For present context, this just reminds us to think through the terms we use.  We might note that on nautical charts building, towers, lights, bridge clearances are referenced to MHW, but spot elevations on the land and elevation contours are actually referenced to MSL.

We thus have in common navigation conversation both:

     MSLP = M - SLP,   being the mean value of the sea level pressure, and

     MSLP = MSL - P,   being the pressure at mean sea level.

If you found this abbreviation in some context of your work, and then went to a navigation or weather glossary to look it up, chances are probably only 50% that the glossary will come back with the appropriate answer for your inquiry. Put another way, you will not find an official glossary that has both definitions; they will have one, or the other.

... which I thought we should document, so no one gets the impression we are sitting around the office all day working on trivial matters.

PS. Just ran across this at the Navy site (FNMOC):

Sea Level Pressure (MSLP): The model-estimated pressure reduced to sea level. Units are in millibars; contour intervals are 4 mb. 

Maybe the "M" stands for "model-estimated"?     

Global Warming and Tropical Cyclone Statistics

We happen to be updating some of our training materials today and thought to check the latest stats of tropical storms and hurricanes... there is much talk these days in the news about the various implications of global warming, including affects on tropical storms. Partial results are shown below.

These storms may be getting more severe on average, and maybe wandering off to higher latitudes more often, we have not checked that. All we did is compare what Bowditch reported in 1977 compared to what they report in the brand new 2017 edition as to the total number of systems.  In 1977 there were not many convenient sources of this data. Now we have all the detail we could ever want about every system, and we get it directly from the primary sources, but it is not clear that the new Bowditch data might need updated itself.

The statistics shown below are all data up to 1977 compared with the latest systematic study in the 2017 Bowditch, described as 1981 to 2010. You can click the pic for better view.

The values are average number of incidents per month. "S" is number of tropical storms, meaning sustained (> 1 minute) winds ≥ 34 kts. "H" is number of hurricane-force systems, also sustained.

Note that the storms include the hurricanes... all hurricanes start out as storms.  So of the 12.1 storms per year average in the North Atlantic, only 6.4 of these on average proceeded to become hurricanes. (If you happen to look at the 1977 Bowditch data, they used a different convention on presenting this information; we regrouped that early data to make this comparison.)

The North Atlantic region (including Caribbean and Gulf of Mexico) definitely has more storms (we have about 29% higher chance of seeing storm force winds), but there is a slightly lower chance according to this data that these become hurricanes—but this still leaves us with slightly more hurricanes than earlier, about 20%.

But these are statistics. We could have 10 hurricanes this year (as we did), then 2 the next year, and we are back on the average of 6. The question is, how likely is that, just 2? If we have 10 next year as well, we better have zero the next year, just to approach the average.  In short it could be that these Bowditch stats need to include more recent data, ie 2011 to 2017.

For example, here are the recent data from the NHC.

For the North Atlantic, over the past 7 years (not included in Bowditch 2017) we see 13.8 and 7.1, which is higher than 12.1 and 6.4, but not that much.

Over the past 7 years we see higher numbers for East Pacific: 15.9 and 9.4 compared to 16.6 and 8.9, which is about the same... but both notably higher hurricanes than in 1977 (15.2 and 5.8).

With our check of the recent data we can compute the standard deviations (SD), which are:

East Pacific:  15.9 ( 4.6) and 9.4 (3.0)
North Atlantic: 13.8 (4.8) and 7.1 (3.4)

We do not have a lot of data here, but these are large SDs, which means we can expect large variations of these numbers from year to year. Below is the distribution of events if the variation is indeed random.

This means that 68% of the values should be within 1 SD of the mean, or we can look at it as shown  below

With, say, 7 hurricanes per year with an SD of 3 it means that there is only roughly 16% chance of having 4, or put the other way, there is also a 16% chance of having 10, but if we have 13 events (2 SD above the average) then we are down to 2.3% chance by random, which raises more the issue of looking toward trends.  It would be nice if we had the SD for the 2017 Bowditch data. That was not given in the book, but it is fairly easy to look up the actual values and compute it as we did here.

Without an in depth analysis, it seems we can likely rely on the numbers in 2017 Bowditch values, with the awareness that these do appear to be rising slightly still, beyond that 2010 data sample.  Other notable changes can be seen in the other zones.

It is likely a more interesting study for climatologists to look at severity, but this has little interest to mariners, i.e., we would obviously treat a 150 kts forecast the same as we would a 115 kts... but we might want to keep an eye on storm size. With all the data that is available, one could do a very precise study as a home project on, say, the average area covered by 34-kt winds from inception up to hurricane strength, and then the area covered by 50-64 kts and then >64 kt winds after that.

The other study would be how far north do they go, and indeed how long do they last.  If you have a student with a science project on the horizon, this is very easy data to get online and the analysis would be a good exercise in using numbers.  Furthermore, this has much value to mariners and we cannot count on anyone without a maritime interest in putting these specific values together. (If a student is interested they can call us and we will help.)

Check out the 2017 Bowditch, Chapter 39. They have very good coverage of tropical systems, that even include QR-codes to go directly to the various Regional Specialized Meteorological Centers (RSMC) that do the job of our National Hurricane Center for other tropical cyclone zones.

If you plan to be sailing in a hurricane zone, a mandatory reference is:

Mariner’s Guide For Hurricane Awareness

Noting especially the Mariners 34-kt Rule and the Mariners 1-2-3 rule on storm track uncertainty.  I would also like to think that our own book would be helpful

Modern Marine Weather.

Here is a sample of the 2017 Bowditch's extensive use of QR-codes, which is pretty techy,  but all the links in the pdf are interactive in the first place.