A Sense of Where You Are, Part 3

My middle and high school friend Paul and I reconnected recently, partially due to this blog which is neat. He recently added a kind comment to the blog that it’s such a welcome diversion from all the Coronovirus craziness. I hope others find the same.

A couple of related items in light of the current situation: In late-January, when I made landfall in the Virgin Islands and got into a marina with wi-fi, I connected to the internet and downloaded the news. I took a deep breath before I looked at it because, with the exception of weather reports and short messages with my son about the weather and routing, I had been totally isolated for 12 days. The first several articles I read were about Coronovirus. I hadn’t heard the term prior to that. In addition, as I’ve said in previous posts, when entering a new country in a vessel, the letter “Q” flag (a solid yellow flag) is to be raised in the starboard rigging. “Q” standing for quarantine.

Hazel James flying the “Q” for quarantine flag on our sail from the USVI to BVI

In most countries, the crew must stay on the vessel and only the master of the ship (the captain) may go directly to customs and immigration with all the crew’s passports and paperwork. Once the vessel is checked-in to the new country, the crew can come ashore. In some countries that get less foreign yacht traffic and—even during normal times—have more strict quarantine protocols, the captain must also stay on the vessel. The vessel anchors well offshore and a customs and immigration official comes by boat to the vessel to inspect and check-in—at-times with a physician to make sure all are healthy.

I’m in the British Virgin Islands (BVI) now and heard yesterday that the BVI is closing its inbound borders today with the exception of BVIslanders and those with valid work papers. I’m in no hurry to get home (although a part of me would like to be home right now). It seems like it makes the most sense to stay here in the Virgin Islands for another month and let things sort out a bit.

My original routing plan for the passage home was to island-hop from the USVI to Puerto Rico to the Dominican Republic to the Turks and Caicos and finally the Bahamas before arriving home in the mainland US. However, given all the closures, I think I’ll need to just sail directly from the USVI or Puerto Rico home. I’m thinking when arriving in the mainland US, it would be helpful if my last passport stamp were from a US Territory with a clear date on it. I’ll also keep my ship’s log assiduously updated to prove that I have been “self-quarantined” on the high-seas for the 8-10 day passage home. Time will tell, I want to be back in the US before hurricane season (~June 1) and have plenty of provisions. As I write this I’m offline and it’s Thursday, March 19 (not sure when I’ll have wi-fi to upload it), the next several days will be interesting as there are an incredible amount of bareboat and captained charters out of the BVI. 80-90% are weekly and they turnover on the weekend. My sense is that, come this Sunday, the BVI will become a ghost town. It’s hard to imagine how difficult it will be for the majority of islanders who make their livings off the tourist economy—and early-April is typically the height of spring break and spring vacations.

Anyway, back to the subject at hand: Part 3 of “A Sense of Where You Are”. In Part 1 we covered general theory, the latitude/longitude coordinate system and the sextant. Part 2 focused on determining latitude. In this post we’ll look at longitude.

If you recall in Part 1 we said that lines of longitude are also called “Meridians”, and a meridian is defined as a spherical line that intersects the North Pole, your position and the South Pole. In Part 2 we introduced the concept of the LAN (Local Apparent Noon), this is the exact time when the sun crosses your meridian. It’s generally within an hour either side of 12:00 PM your local time. This is also the source of the acronyms AM and PM (AM being Ante Meridian and PM Post Meridian). The key to determining an accurate longitude is determining exactly when LAN occurs at your geographic position. The reason I repeated the word “Exact” a couple times in the previous sentences was deliberate…

Consider this: There are 86,400 seconds of time in a day (24 hours x 60 minutes/hour x 60 seconds/hour = 86,400), and 21,600 arc-minutes in a circle (360 degrees x 60 minutes/degree = 21,600) and, at the equator, an arc-minute of longitude equals 1 nautical mile. Obviously the earth rotates through 360 degrees every 24 hours. Dividing 21,600 into 86,400 yields 4 seconds of time per arc-minute of distance. Back to my “Exact” comment, for each 4 seconds of time that you are off in determining your LAN (Local Apparent Noon), your longitude calculation will be off by roughly 1 nautical mile. Being off by a minute, which is easy to do as we’ll soon see, puts you 15 miles off.

You can imagine early navigators, without accurate chronographs or accurate charts, being totally freaked out by longitude—especially when approaching low-lying islands that, at that time, were totally unlit. Thus early ships would have someone posted in the bow as high as possible (thus the “crow’s nest”) 24 x 7 scanning the horizon for land. Imagine sailing from (say) Africa to Florida. Although you might know you are on the proper line of latitude, you didn’t have a good estimate of when you would reach Florida or if landfall would occur at noon on a sunny day or in the midst of a thunderstorm at night. Early navigators (particularly Polynesian and other non-European navigators) were especially attuned to the changes in the ocean as they approached land. The color of the water changes subtly as does the make-up of floating seaweed and other marine life.

Today, even with accurate tables and accurate watches that are synchronized to the second to GMT (Greenwich Mean Time), determining the time of your LAN is a challenge. If you recall in Part 2, we talked about the sun’s height in the sky following a sine curve. This sine curve is what makes finding the height of the sun (to determine latitude) “easy”, you can measure the sun’s height within 5 or 10 minutes of your LAN and have readings that are very close (think about the gentle, rounded top of a sine curve). However, this same effect makes determining the exact time of the LAN so difficult (remember, being off by a minute of time means you are off by 15 miles, 5 minutes is 75 miles). In my early days of learning celestial navigation, when taking sights from my backyard in Southeastern Florida, I’d regularly come up with longitudes in the Bahamas or the West Coast of Florida.

The way we get around this problem is by averaging the sun’s equal-height times during it’s ascent (the AM, or before your LAN) and its descent (the PM, or after your LAN). The drawing below illustrates this concept.

The sun’s sine curve and Local Apparent Noon (LAN)

These measurements take place roughly an hour before your LAN and again an hour after. In the AM measurements, the goal is to catch the sun while it still has solid upward movement. In this example the height of the sun (h1, h2 and h3) was measured in the AM at t1, t2 and t3 respectively and all heights and times carefully documented. Then after the LAN (and in the PM), you reset your sextant for the height of h3 and document the time when the descending sun reaches h3 (indicated as t3’ in this example), and do the same for t2’ and t1’ respectively. You then average the AM times, and average the PM times, then average your averaged AM time and averaged PM time. If this sounds like a lot of math… it is, and it’s all sexagesimal (base-60). I’m not that good with head math so I write is all out and do it twice and compare my answers. The image below are my calculations for the sight I took when I first spotted land in the Virgin Islands.

Once you’ve got your accurate time of LAN for the given day of the year (or what you think is your accurate time of LAN), it’s pretty straightforward to determine longitude from tables in the Nautical Almanac. In this example I was off by ~3.5 nautical miles, a very good result for me (my GPS longitude was 65 degrees 13.0 minutes West and celestial longitude was 65 degrees 17.1 minutes West).

I sincerely hope you enjoyed this three-part mini series and found it an effective diversion from all going on in the world. If you’re interested in reading more on this subject, I highly recommend the book Sextant by David Barrie. In his writing, he brings together parallels between a sea voyage of his, and the history of the sextant and mapping the world’s oceans. I’m grateful to him and for his book as his style inspired my parallel writing of blog entries on this site.

I’ll leave you with with this hopeful photo. There are a tremendous amount of rainbows in the morning and evening in the VI. Take care and talk soon.

A rainbow in the Virgin Islands

7 thoughts on “A Sense of Where You Are, Part 3

  1. Great stuff as always. Glad to hear from you and know you are riding out COVID-19 like the rest of us. Stay safe and healthy. I hope you don’t have any entry/exit issues.

  2. Stay safe and be aware upon your return you may find something resembling a “ghost town” which is how Orchard Park is during the day. Hopefully Pompano will not be shut down as NY is supposed to be shortly!
    love, T

  3. Albert Einstein is credited with the phrase “The definition of genius is taking the complex and making it simple“. I think that applies to your explanation of navigation in this blog. Really cool stuff, and a fun diversion for sure while we are stuck in our homes. Stay safe and keep the entries coming, we are all digital stowaways on Hazel

  4. We miss you. Hate that you have to stay away longer than expected. Ok the other hand, glad you’re not here to experience this dystopian nightmare. I found a picture I want to send you, can I text it?

  5. Hey, Dan…lovin’ the blog, especially the technical aspect of taking a sighting. When I plug in the lat/long, though, I get a spot in open water about 20 miles north of the BVI. Is that right?

    1. Yeah, that’s actually totally right. When I took that noonsight I was still on my passage and sighted land while I was taking the sights. Given how high the Virgins are above sea level, you can see them from 20 miles out.

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