How To Use A Sextant

Background

The sextant allows celestial objects to be measured relative to the horizon. This allows for excellent precision. The sextant allows direct observation of stars which allows it to be used at night. For solar observations, filters allow observations of the sun. Since the measurement is relative to the horizon, the measuring pointer is a beam of light that reaches the horizon. The measurement is limited only by the angular accuracy of the instrument. The horizon and celestial object remain steady when viewed through a sextant, even when the user is on a moving ship. This occurs because the sextant views the (unmoving) horizon directly, and views the celestial object through two opposed mirrors that subtract the motion of the sextant from the reflection.

The scale of a sextant has a length of one sixth of a full circle (60°); hence the sextant's name (sextāns, -antis is the Latin word for "one sixth". Sir Isaac Newton (1643-1727) invented the principle of the doubly reflecting navigation instrument (a reflecting quadrant but never published it. Two men independently developed the octant around 1730: John Hadley (1682-1744), an English mathematician, and Thomas Godfrey (1704-1749), a glazier in Philadelphia.

How to Use

The sextant makes use of two mirrors. With this sextant, one of the mirrors (mirror A in diagram B) is half-silvered, which allows some light to pass through. In navigating, you look at the horizon through this mirror.

Diagram A

The other mirror (mirror B in diagram B) is attached to a movable arm. Light from an object, let's say the sun, reflects off this mirror.

The arm can be moved to a position where the sun's reflection off the mirror also reflects off mirror A and through the eyepiece. What you see when this happens is one object (the sun) superimposed on the other (the horizon). The angle between the two objects is then read off the scale. What makes a sextant so useful in navigation is its accuracy.

It can measure an angle with precision to the nearest ten seconds.

(A degree is divided into 60 minutes; a minute is divided into 60 seconds.)

Navigation by Sextant

There's no way around it: Celestial navigation using a sextant is a complex and involved process that involves a fair amount of calculating, correcting, referring to tables, knowledge of the heavens and the Earth, as well as a lot of common sense. (No wonder it's been so quickly replaced by the satellite-dependent Global Positioning System, or GPS)

Diagram B

Diagram B

But the basic principles behind celestial navigation are fairly straightforward. Here are a few examples that show how a sextant can be used to find location...

Diagram C

Finding latitude is easy enough. The first thing you need to do is measure the angle between the horizon and the sun when the sun is at its highest point, which is right around noontime on your watch. A quick look at your trusty tables tells you which line of latitude the sun should be above on that particular day. For example, let's say it's noon on December 21, and the sun is directly overhead. Well, on that day the sun is above the Tropic of Capricorn, so your latitude would have to be 23.5 degrees S.

It's a good thing, if you're a navigator, that the Earth spins around at such an even pace. Every hour it moves 15 degrees. This means that if the sun is above the longitude of 0 degrees at noon, one hour later it will be above 15 degrees West. Now if you have a chronometer (this is just a fancy name meaning "extremely accurate clock"), you can find your longitude. Let's say that the sun is directly overhead and your chronometer, which was set to noon when you were at 0 degrees, says it's 3 o'clock position.

Diagram D

This means that three hours ago the sun was overhead at this latitude at 0 degrees longitude. In those three hours, the sun moved 15 degrees 3 times, or 45 degrees. So you're at 45 degrees West. Of course, the fact that the sun was directly overhead (which very rarely happens) made it especially convenient for finding your longitude, but you could have found your longitude anyway, with the help of your tables.

Celestial navigation is the process whereby angles between objects in the sky (celestial objects) and the horizon are used to locate one's position on the globe. At any given instant of time, any celestial object (e.g. the Moon, Jupiter, navigational star Spica) will be located directly over a particular geographic position on the Earth. This geographic position is known as the celestial object’s sub-point, and its location (e.g. its latitude and longitude) can be determined by referring to tables in a nautical or air almanac.

The measured angle between the celestial object and the horizon is directly related to the distance between the subpoint and the observer, and this measurement is used to define a circle on the surface of the Earth called a celestial line of position (LOP). The size and location of this circular line of position can be determined using mathematical or graphical methods (discussed below). The LOP is significant because the celestial object would be observed to be at the same angle above the horizon from any point along its circumference at that instant.

Celestial Navigation for Dummies

The text in this section was mirrored with permission.

Source: Herb Benavent, 2018. The Rigging Doctor, Celestial Navigation for Dummies

https://www.riggingdoctor.com/life-aboard/2018/8/29/celestial-navigation-for-dummies

Celestial Navigation is an utmost skill needed for any ocean voyager. Compasses can lie, electronic equipment can fail, but the stars will always be there! Yes, a cloudy day or night will obscure your view of the stars, but at some point, something will become visible in the sky and if you know how to use it, you can get a bearing on where you are.

The easiest way to find your position is to take a Noonsite. This will give you your latitude and your longitude with the least amount of math. All you need to get your noon site is a sextant and a clock (which is set at UTC time). A noon site requires you to know how to use a sextant, which is really easy to learn. All you are doing is measuring the angle between the sun and the horizon.

When you take your noon site, you will receive two pieces of information that you will later translate into coordinates on a map. First you will have your time, which gives you your longitude. Second, you will have your sextant measurement, which will give you your latitude.

Longitude

Longitude is a factor of time on Earth. To make this explanation simpler, we need to use an Earthcentric view of the universe.

Remember that the Sun revolves around the Earth once every 24 hours. The Earth can be divided into 360 degrees of longitude, and in 24 hours, 360 degrees will pass by.

360 degrees / 24 hours = 15 degrees per hour.

At noon over Greenwich (where UTC is the time zone) the sun is directly overhead (their local noon).

In one hour, the sun will be directly over 15 degrees W.

In two hours, the sun will be directly over 30 degrees W.

In three hours, the sun will be directly over 45 degrees W, and so on.

This means that the time of your noon site is going to b a cryptic form of your longitude, and with really simple math, can be converted into your East or West coorditantes.

When you take your noon site, look at the time (it is helpful to set a 24 hour clock to UTC so that you don't make any errors in calculation here, as each hour is 15 degrees!). Then you will simply subtract your time by 12, as this will give you the difference in time from Greenwich to your local noon.

Now take your time difference and separate it into two columns, hours and minutes. The hours will be multiplied by 15 and the minutes by 0.25; the answer will then be added to give you your coordinates.

Decimals are easy to convert into minutes by simply multiplying the decimal by 60.

So, for example, say its 4:55 PM UTC when the sun is directly overhead and you take your noon site. The math will be as follows:

Just that simple, you now know that your latitude is 73 degrees and 45 minutes West. Another example would be local noon (when the sun is directly overhead) at 2:38 PM UTC.

The math would be as follows:

Thats all there is too it! Longitude has nothing to do with the actual number that is displayed on your sextant but everything to do with "when" you measured the sun at its highest point in the sky.

Latitude

Ok, latitude is the North & South value of your coordinates and really weighs heavily on the reading you record with your sextant. To properly calculate your latitude using the sun (by day, obviously), you will need to use the tables in the Nautcal Almanac. These tables can seem long and complicated, and very confusing, but they are not all that bad once you learn what to look for. f you don't want to use a book, you can always download the latest Nautical Almanac for free! A simple Google Search will pull up a few options, and you will certainly be able to download your own copy.

I personally use a print version from 2017 (I bought it in late 2016 and have not updated my copy as of late 2018) as the angle of the sun over the horizon doesn't change all that much from one year to the next. Yes, your reading will not be as accurate as possible, but at the same time, you are measuring the sun on a pitching and rolling deck of a boat out in the ocean! There are going to be errors in your measurement, so a few tiny errors in your calculations will only compound into a slight bit of error in your final coordinates.

It is important to keep something in perspective here, the goal of basic celestial navigation is to ind land, not to find your exact position on the earth. Advanced celestial navigation will allow you to pinpoint your exact position by using three distinct celestial bodies and finding their intersected lines of position. That is very accurate and also a lot of work to do, which is why basic celestial navigation is just fine for ocean cruising.

The goal is to be less than 25nm off from your actual position. A GPS will tell you your true position, and you can then do some simple math to figure out how far off you are. It is good to practice that way you can get your error way down to less than 25nm. I personally tend to get us within 4nm of our true position with simple math and an outdated Nautical Almanac, meaning it can be done and it's not difficult to do. A 25nm error or less will allow you to find land, and once you reach land, you can then use visual navigation to get yourself in to port. By constantly practicing, you will know how good you are at celestial navigation should your electronic navigation equipment fail, forcing you to rely solely on your basic celestial navigation skills.

On the other hand, if you do not have a Nautical Almanac, you can also just measure the angle from the horizon to Polaris, the North Star, and that is your latitude; no math involved!

An important factor that your Nautical Almanac will tell you is a value called Declination. This is the angle of the sun relative to the horizon. You know how shadows are taller in the winter and shorter in the summer, this is because the sun is further overhead in the summer and lower on the horizon in the winter.

The Nautical Almanac is nothing more than an overfilled calendar. On the top corner of the page is the date range of that page, so simply leaf until you find today's page. Then look on the left side of the page for today's date. Then in the box of today, look for the hour you took your noon site. Don't worry too hard about the (time) minutes that you took your sight, simply round up or down to the nearest whole hour. Now, the declination will be displayed to you as Degrees, Minutes, and Decimal of Minutes.

Simply write this number down and begin to do your simple math!

You will take your sextant reading and substract it from 90 degrees, as the sun is directly overhead when you took your noon site. Then you will add or substract your declination to this number. The answer will be your coordinates for latitude.

You might be wondering what I mean when I say add or substract; which one is it? Well, it depends. If the sun is between you and the equator, you will add. If you are between the sun and the equator, you will substract. To keep the math and theory here simple, since this is just "Basic Celelstial Navigation" let's suggest that you do both and see which one is closer to where you actually are.

For example, you are sailing through the Bahamas, meaning that your latitude is somewhere between 27N and 22N. You get your sextant reading and you find today in the Nautical Almanac. It says your declination is 23*24.7' That is a pretty accurate value presented to you, but should you add or substract it from your recording? Well do both and see which one fits your assumed position best! One will be close to where you actually are and the other will be wrong by almost 24 degrees! Now you know for your present location that you should either add or substract next time.

This may sound really confusing, but I guarantee you that it is very simple to carry out this calculation. Lets do an example:

Declination is 23*24.7'

Sextant recording is 87*04'

We start by subtracting our reading from 90. Since each degree is 60 minutes, it makes the math easier if you just write out 90* as 89*60'

Now, we aren't sure if we should add or substract, so lets do both!

Being how you are in the Bahamas, the value of 26*20.7'N seems more plausible than 21*31.3S, so you know for the time being that you need to be adding your declination to the value, instead of subtracting it.

Finding Your Coordinates

It is important to know where you are before you leave, that way you have a rough idea of what the answer should be while you are doing your calculations. If you find that you are way off, you know you made some clerical error and can figure out how to make adjustments to erase this error in tomorrows noon site.

Remember, Longitude is a factor of time, Latitude is a factor of the sun at noon with some minor addition or subtraction.

With this, you can figure out where you are in the ocean using only a sextant and a clock!

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