A Sense of Where You Are, Part 1

If you don’t know where you are going, any road will get you there.
—Lewis Carroll

I think there is a sailing and a strategy corollary, “If you don’t know where you are, your course is meaningless.” For those of us who did a lot of driving in the pre-GPS days, you can probably remember being lost but clearly seeing your destination on a paper map. The only problem was…you were lost, and didn’t know where you were. Seeing the destination on a map was not much help until you oriented yourself and determined your location. Although open-ocean navigation is a bit more complex given there are no roads or signs or gas station attendants to ask directions, and you need to account for currents, drift, wind and waves, the concepts are the same.

My consulting firm’s logo is the sextant which is fitting given how we help healthcare organizations chart their business and technology strategies. The intended course only has meaning in the context of the organization’s current position. Two boats, or two organizations, could have the same goal (destination) but vastly different courses to get there if their current positions are different.

Even though we generally take it for granted, GPS technology is pretty amazing. Your phone, or any other GPS device, relies on a network of about 30 satellites maintained by the US Department of Defense orbiting the earth at 12,000 miles. Wherever you are on the planet, at least 4 satellites are visible to you. Each satellite broadcasts its position and time at regular intervals. Your phone/GPS receiver calculates a “Line of Position” from each satellite. When it has 3 or more lines of position, your device triangulates to determine your location.

Although I knew generally how GPS worked, until I did a little research for this post I didn’t realize that the GPS system must also account for the theories of General and Special Relativity. General Relativity predicts that time will appear to run slower under stronger gravitational pull – the clocks on-board the satellites will therefore seem to run faster than clocks on Earth. Special Relativity predicts that because the satellites’ clocks are moving relative to a clock on Earth, they will appear to run slower. The whole GPS network makes allowances for these effects – proof that Relativity has a real impact in our day-to-day lives and not some abstract concept.

Current GPS accuracy is about 12 feet 95% of the time and recalculates once per second assuming a clear view of the sky. Just amazing. While I’m no fan of big government for big government’s sake, I sigh when people bash the government and the good people who devote their careers to civil service as stifling innovation. Think of all the innovation that has spawned off freely available GPS data. No company could afford to build and maintain the system, we all paid for it with our tax dollars. Perhaps there should be some sort of unicorn tax on companies and entrepreneurs that profit greatly by leveraging the technology that we collectively funded.

While GPS is great, I’ve wanted to learn celestial navigation for some time.

With the rather long GPS preamble behind us, I’ll begin to describe the basics of celestial navigation in this and subsequent posts. I’m by no means an expert but learning a lot and having a lot of fun teaching myself.

I’m a big Winslow Homer fan and the painting “Eight Bells” is a beautiful capture of two navigators getting “noon sights” of the sun.

Eight Bells by Winslow Homer

What I’ll summarize in these posts is the process to determine your position from a noon sight of the sun (a.k.a., the meridian passage). Keep in mind that if you are an advanced celestial navigator you can determine position with the sun at any time of the day and also do sights at night using the moon and stars. I’m at the 101 stage though.

To begin with the end in mind, position on the earth’s surface is expressed in latitude (also referred to as “parallels”) and longitude (also referred to as “meridians”). Both latitude and longitude are measured in degrees, minutes and tenths, hundredths and thousandths of minutes. Minutes of distance are sometimes referred to as “arcminutes” to not confuse them with minutes of time.

As the alternate name for latitude suggests, lines of latitude are indeed parallel to each other. They’re measured from zero degrees at the equator to 90 degrees north at the North Pole and 90 degrees south at the South Pole. Conversely, lines of longitude (aka meridians) converge at the poles. If you recall back to high school Euclidean geometry, three points determine a plane. Your meridian, your longitude, is a plane defined by your current position and the north and south poles. Longitude is expressed from zero degrees at Greenwich, England through 180 degrees east and west.

As an example, my home in Florida is 26 degrees, 14 minutes north (latitude), and 80 degrees, 06 minutes west (longitude). My current position in Caneel Bay St. John USVI is 18 degrees, 20 minutes north, and 64 degrees, 48 minutes west.

While a land-based mile is 5,280 feet, a nautical mile is defined as one minute of latitude anywhere on the globe, or one minute of longitude at the equator; it just so happens to equal 6,076 feet. Given that lines of latitude are parallel, they are equidistant from north to south. However, lines of longitude converge at the poles. Since I’m relatively close to the equator, a minute of longitude here I am now equals about 0.9 nautical miles. As an aside, remember that a “knot” is a unit of velocity and is one nautical mile per hour (~ 1.15 MPH).

Now that we have a primer in latitude and longitude, let’s look at the sextant. Besides being beautiful, the sextant is an optical tool for precisely measuring the angle between two objects and yourself. In this example, we’re measuring the angle of the sun above the horizon. In the picture below you can see some of the mirrors, filters and scales that make it tick. The filters allow you to look at the sun without burning your eyes. The degrees of elevation are read off the arc. The minutes and tenths of minutes are read off the micrometer drum below the arc.

My Astra III-b sextant

Incidentally the arc on a sextant is 1/6th of a circle (360/6=60 degrees), thus the name sextant.

My sextant uses a semi-transparent mirror to superimpose the sun and the horizon. When you take a “sun sight” you look at the horizon through the telescope and adjust the arm and micrometer until the superimposed sun appears to just float on the horizon, like a sunrise or sunset. You then note the time and read the height of the sun at that time from the arc and micrometer.

Below is an example of me taking a noon sight of the sun. I used this picture before in another post and to respond to a few questions I received, the answer is “Yes”. As in, “Yes the hat and beard actually do improve the accuracy of my sights.”

Me taking a noon sight on a dead calm day

One of the truly amazing things about the sextant is that, unlike a telescope, it does not need to be fixed to a solid surface to be accurate. Although challenging, you can get very accurate sights from a rolling, pitching deck. You just need a clear view of the sun and the southern horizon, thin clouds are OK but thick clouds prevent you from getting a sight.

In our next post we’ll go into the details of determining latitude and longitude from noon sights of the sun.

As I said earlier, I’m in Caneel Bay St. John USVI. Moored just off the beach in front of what was the famous Caneel Bay Resort. It was walloped by hurricanes Irma and Marie in 2017 and still has not reopened. The view from Hazel James’s deck today looks beautiful from a distance but when you zoom in, you can see the destruction.

Caneel Bay Resort

Assuming good weather tomorrow, I plan to sail to the island of Virgin Gorda in the British Virgin Islands and clear customs there. I’m excited about that adventure.

Fair winds and following seas.

14 thoughts on “A Sense of Where You Are, Part 1

  1. Hi Dan – I’ve been greatly enjoying your story – your writing style is clear, engaging and so wonderfully descriptive. I’m looking forward to the book!

  2. Amy and I vacationed at the Caneel Bay Resort. You should check out Mongoose Junction.

    Sent from my iPhone


  3. Very cool post, Dan. I’ve long wondered about how a sextant works so I’m really enjoying your explanations. Also, appreciate the etymology for sextant. And the explanation of a nautical mile. I’m learning so much now. Thanks!

  4. heading to Virgin Gorda – you may regale the locals with the legend of Dave MacNamee.. just don’t lead in with “there once was a man named Dave…” it doesn’t end well

  5. The world is a crazy place now.  You’re probably in one of the safest places on earth my friend.  I’ve been following your blog…..I feel like jumping in my boat and coming down there!

    Sent from Yahoo Mail for iPhone

  6. Dan, this blog is such a great diversion from the craziness here. Equal parts educational, thought provoking and entertaining, I really feel like I am there experiencing it! Beyond writing a book, which you absolutely should, your photography rivals National Geographic (full disclosure, I am now using one as my computer wallpaper since it’s better than any of the professional pics). Bring on the snorkeling pics! Keep it up buddy

    1. Paul, that’s great about the photo. I take some with my iPhone (8) and others with my Cannon Rebel SLR (with regular and telephoto lenses). I have a waterproof case on my iPhone so use it for high-action shots and selfies but try to use the Cannon as much as possible because of the quality and flexibility with it. I don’t have an underwater camera…yet. Perhaps that’s coming. Thanks again for the kind words.

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