Finding UTC of LAN with the Starpath Custom Sun Almanac

We published a short book last year that is intended to be the bare minimum celestial navigation training that will serve as a backup to a loss of GPS. In keeping with the backup concept, the book is presented in such a way that it is totally self-contained, which means the book also covers how to use the simple Davis Mark 3 sextant. This is a small device, for under $50, that could be used to safely circumnavigate the world.

Our promise is that this book could be opened up and read for the first time when it was actually needed, and it would be adequate to teach how to take the sights, and then find your position from them using only data in this small book—a large part of which is a custom Sun Almanac designed to make the position solutions especially easy.

GPS Backup with a Mark 3 Sextant

The techniques taught in this book are finding Lat and Lon from "noon sights" (local apparent noon,  LAN) as well as Lat by Polaris in the Northern Hemisphere. What we forgot to include in this first printing was a way to determine an efficient time to start taking the sights near midday. LAN occurs when the sun crosses our meridian, bearing due north or due south at its peak height in the sky.

When the sun is less than halfway up the sky at noon, we can approximate its motion along the horizon as a bearing change of 15º per hour.  So if we want to start about 30 min before the sun reaches the horizon, we would start taking sights when the sun was bearing about 173 T.  After that first round of sights, we will know the time of LAN and the next day we can fine tune the starting time.

When the noon sun is much higher in the sky it is more difficult to predict its bearing change rate as it approaches noon, and as we head off toward the tropics the sun will indeed be much higher at noon, so it is valuable to have a systematic way to predict the time of LAN to plan around. The custom Sun Almanac offers an easy way to do this. In fact, it is easier than the standard methods we use when teaching the "full cel nav" course.  The full theory is in the picture below from our textbook Celestial Navigation: A Complete Home Study Course.

As the earth rotates toward the east, the position on earth directly below the sun (its geographical position, GP) moves west at the rate we are rotating, namely 360º of Lon in 24h = 15º of Lon per hour.

The custom Sun Almanac tells us the longitude of the GP (called its Greenwich hour angle, GHA) every hour of every day. So we can go into Sun Almanac on the right day to see which whole hour of UTC has the sun's GHA just east of our location.  Then we subtract that GHA from our DR-Lon to see how far it has to go (as an angle) to get to us, and then we just covert this angle to time at the rate we are turning, which can be derived from 15º = 1 hr, 1º = 60 min/15 = 4 min, etc.

                      1º = 4 min

                      1' = 4 sec.

Here are two practice problems from our textbook (page 33.)

Example 1.  July 25 from DR-Lon = 122º 18'W.

DR  = 122º 18'   =  121º 78.0'
20h = 118º 21.7' = -118º 21.7'
            diff =    3º 56.3'

3º = 3º x 4m/1º                 = 12m
56.3' = 56.3' x 4s/1' = 225.2 s =  3m 45s
                            SUM = 15m 45s

Final time is 20h 15m 45s, which we would round to 2016 UTC, as we never need to know these times more precise than that, not to mention that the DR position that it is based on has some uncertainty.

This is the UTC of LAN observed from 122º 18' W. If we wanted the watch time (WT) of the event for a watch set to zone description (ZD) + 7, then we would have to back out that ZD.

Recall the definition of ZD, which comes from this equation UTC = WT + ZD, where WT is the watch time being used for navigation. Thus if the ZD = +7 and the WT = 1200, then the UTC = 1900. Likewise if we know the UTC is 1900 on a watch with ZD = +7, then the WT = 1200. 

In the above example, LAN = 2016 UTC would correspond to WT = 1316 for a watch set to ZD = +7.

Example 2. Find  UTC of LAN on October 27 viewed from 136º 10.5' E.

This is an eastern longitude. In east longitudes the GP of the sun is still moving west with increasing time, so the longitude it crosses gets smaller as it passes across the eastern half of the globe. But that does not matter to us, because, unlike longitude, GHA does not decrease on the eastern half of the globe. GHA is defined as 0º to 360º, measured west from  Greenwich.  Our job is to determine what GHA does 136º 10.5' E correspond to. Starting at Greenwich we head west to 180º W (the dateline), and then proceed from 180º E to 136º 10.5' E, or we cover 180º - 136º 10.5'  =  179 60 - 136 10.5 = 43º 49.5', which is what we must add to 180º to get the GHA equivalent of this eastern longitude. The answer is 223º 49.5'.

Now we are back to solving the problem just as we did for western longitudes.

 "DR" = 223º 49.5'E 
  02h = 214º  1.7'  
 diff =   9º 47.8'

9º = 9º x 4m/1º                  =  36m 00s
47.8' = 47.8' x 4s/1' =    191.2s =  3m 11s
                              SUM = 39m 11s

We add this to 02h to get 02h 39m = 0239 UTC,

If we need to convert back to WT, we refer to the definition: UTC = WT + ZD, or with ZD = -9, we WT = UTC +9h = 1139 WT. 

For those who might like extra practice, you can use the USNO sun data computer (Form B) to randomly select locations and dates to compute UTC of LAN (they call it "sun transit"), and compare that with what you get from the custom Sun Almanac.

In principle the answer depends on the year, but our custom Sun Almanac averages out yearly differences, but even with this, the time of LAN found from the these tables will always be right to well within one minute.

Notes: 
• the USNO site is down until April 30, 2020
• the new printing of this backup book now includes an arc to time table as well as an analemma as an alternative means of finding time of LAN.

New PDF Edition of a Classic NWS Pub... With Related Notes on FTPmail

There is a new edition just out, dated April 11, 2019 of the long standing publication, now called 

WORLDWIDE MARINE RADIOFACSIMILE BROADCAST SCHEDULES

We refer to this document in our teaching by its file name "rfax.pdf" rather than its title for a couple reasons. First, even though the content and title of the book have changed over the years, the filename since it was first put online has not changed; you can always find this with a search for "rfax.pdf." 

This is now a free PDF, but back before internet it was a must-have nav pub for ocean navigation. In those days, in keeping with its earlier title (below), the pub included the voice broadcast schedules as well as radio fax schedules, including valuable global diagrams of the forecast regions. 

Oldtimers with memory of ocean sailing before the internet will recognize this book that everyone had on board. For historical interest, old versions are online.

Secondly, beyond containing all the radiofacsimile schedules from around the world, it has also for many years now included the best of all of the official references to the FTPmail service offered by NOAA. This part of the publication has been hidden in this pub since it was added some years ago by not being mentioned on the title page or bookmarks. It was at the end of the document as "Appendix B," but the only bookmark was to Appendix A-8, without a title. 

Granted, if you did read to the end of the Table of Contents you would see it listed as Appendix B. In this new edition, the FTPmail instructions are in the same place, and they have minimized the confusion by removing any reference to any appendix in the bookmarks.

Appendix A is also valuable for mariners including contact info for all branches of NWS as well as a detailed list of all weather resources online. 

Appendix A and B are major resources, not implied by the title of the document, so we just have to know they are there... which you would know from our weather book as we have stressed the value of this reference of years.

I am hoping that if anyone from NOAA sees this note they might consider reissuing this latest version of rfax.pdf to include a mention of these important references in a subtitle of the document (such as "and Related NWS Resources"), and add bookmarks with real titles.

Also if they do make a new one, I hope they will also update the section at the end on the Voluntary Observing Ship (VOS) information, including the links to Port Meteorological Officers (PMO) listed. PMOs are the key liaison between participating ships and the weather service, and their personnel and contact information in this April 2019 issue is a year or two out of date. Having that data wrong is incongruous in that the book starts out on the first page of text praising the VOS program and how important it is to mariners. 

There is another subtle reason modern mariners have an interest in this rfax.pdf document, even if they do not receive weather maps by rfax, but instead get their maps by email request. What we learn from this document is which nations actually produce synoptic weather charts. If such maps exist, they are the products of professional meteorologists, and not just reprints of a GRIB presentation of a pure model output. As such, they add much to our confidence in forecasts compared to using pure model data alone.

Once we know these maps exist, we can go about finding out how to get them by email request. We have compiled a list of Southern Hemisphere sources, and we can find international sources in the FTPmail folder on line—see, for example, the file called otherfax.txt.

The rfax.pdf also tells us when these maps are available for email request, as they must certainly exist at the time the rfax version is broadcast.

One possible reason why these valuable FTPmail instructions in rfax.pdf are not being stressed as much as I think they should be, is the NWS is working on new publications devoted to FTPmail.

Historically, the most often referred to instructions for FTPmail is a file called FTPmail.txt, which is pretty much unchanged since the system was developed many years ago. It is an introduction to conventions, along with a list of links to more detailed product lists, i.e., otherfax.txt. 

One version of the developing new instructions can be found at a link at the Ocean Prediction Center (OPC) under menu: INFORMATION / Receiving Products / FTPMail: Products via Email, which is a more convenient version of FTPmail.txt.

Another version is attributed to the VOS. Find this one at the OPC menu: INFORMATION / Product Information / Product Guides / Marine Radiofax Chart FTP Email Procedures.  This one has the valuable feature of showing not just a list of map file names, but also includes samples of each of the maps. But this document is maps only, whereas FTPmail can be used to obtain just about any product made by the NWS, including all reports and observations, and such important ones for offshore as the Metarea forecasts and tropical storm advisories.  Also, none of the files are actually linked in this presentation.

In short, both of these alternative discussions of FTPmail are better than the simple FTPmail.txt, but neither one of them, nor both together, is as good as the set of hidden instructions in the back of rfax.pdf, which stand out first because they provide live links to the data and second they specify the broadest range of products, directly without reference to other documents.

For that reason and others mentioned, it seems navigators will want to download this file and store it on one of their their devices they will have when underway.

Starpath News — April 2019

• Tracking Jacob Adoram 

We are in contact with  former Starpath Student Jacob Adoram as he rows from Seattle to Cairns AU. He left on July 7 and now, after some 6,000 miles of rowing, he is just over 1,000 miles from Cairns. To make this event into a marine weather study project we have created a series of Google Earth overlays so you can see live conditions of wind, current, pressure, and sea state. We have an ongoing series of short articles introducing short video discussions of his progress. Start at the first post to get an overview of what we are doing, and check the index of overlays.  Even disregarding the factor there is a row boat somewhere around where we are covering, it is very interesting to see the ASCAT live satellite wind measurements.  For a jumpstart, if you have Google Earth installed you can click here to load the KML file. 

Our original goal was to try to get live measurements of ocean currents to compare with the RTOFS and the OSCAR predictions. This has not produced much fruit. First these two models do not often agree (they are totally different kinds of products) and second it is difficult for such a large boat with so little control to measure accurate boat speed and compass heading to compare with COG and SOG from GPS. The difference between these two vectors is the current we want to measure. In cases where both models did agree there was notable current (ie > 1 kt) and more or less aligned with the wind, then we do indeed see him make more progress than he would without the current, but that is about it.

On the other hand, we have had much more success in testing new simulated radar reflectivity forecasts of the FV3 GFS model. We discuss this new breakthrough in marine weather technology in Modern Marine Weather  (see pages 112 to 115), but now we see it live. Namely we can forecast to the hour when he should be in squalls and how severe they are using a GRIB format of the combined reflectivity,  and then compare that to his observations. These are easy to measure events so the data are good. We have just started this study but it does look promising in the cases we have had.  We use the program LuckGrib to download the FV3GFS data and display the reflectivity

• New Regiment of the Pole

In keeping with one of our unpunished mottos "Always old; always new," we have revamped the late 16th century celestial navigation tool called a Regiment of the Pole. This will be written up in  more detail shortly in our Navigation Blog. It is a way to read from the orientation of stars near the pole the correction to a Polaris sight needed to find latitude.  We had originally developed a prescription for this in the mid 80s for the book Emergency Navigation, and now we are fine tuning that one. It is the same general principle, but with a relatively easy addition we get more accurate results.  This new method is used in our new book GPS Backup with a Mark 3 Sextant.  With this rule and a sextant, you can find your latitude in the Northern Hemisphere to within a few miles on any date without any further tables.

• Weather Trainer Live Updates

Over the past few months we have updated Weather Trainer in several ways. We have updated the content and reorganized several of the sections.  We also now have the Mac and PC versions working in the same manner, and we have changed the general structure of this cloud based service and training tool. The initial activation period remains at one year, but at the end of one year the subscription does not end if users have an active starpath web card of any kind, which includes being registered in any course. If you sign up for a second course after the weather course, for example, then the Weather Trainer is active for another year at no charge. After your web card expires, you could come back in a year or two and reactivate a web card for as low as $17 and have full access to the Weather Trainer to check out all the latest resources.

• Looking into live online lectures

We have done a few short test runs on offering live online lectures. This looks promising and we will be pursuing that shortly. We will announce the courses in the Discussion Forums and in our Facebook page.

• You could call it experimentation… or you could call it tinkering.

We have experimenting with use of pitot tubes for anemometers. The idea came from a new product from Ireland that apparently works well at least for stronger winds.  It is nicely called the Wind Urchin.  This is too big for the mast head, but I do not see why it could not be made much smaller and then we read honest 3d wind direction and correct vector speed.  We now have a real pitot tube and a differential barometer for testing. All seems to work very simply, but to get accurate values at low wind speed will be challenging. The first application of this type we know about is in an observatory on Mt. Washington.

We are also experimenting with a new style of artificial horizon suitable for use with stars. It has a lot of promise but needs some work. Seems it is best tested during daylight with a low daytime moon so testing times are limited. As spring approaches we also gain the number one factor for good cel nav studies of any kind, namely warm weather!