sextant experiment calculation

What is Sextant, its types, principle and errors ?

A sextant is a doubly reflecting navigation instrument used to measure altitude or the angle between any two visible objects. Sextant is one of the oldest navigation instruments used by mariners, its called sextant because its arc is 1/6 th of a circle i.e. 60° but it can measure angles upto 120° using double reflection principle. 

Types of Sextant

• Micrometer Sextant
• Vernier Sextant

Comparison between the types of Sextants

• Construction and operating principle of both sextants are same. In both sextants, whole degrees are read on the arc of the sextant.
• The only difference lies in the way the fraction of a degree are read.
• As the name suggests, in vernier sextant, it is read by the vernier whereas in Micrometer sextant, it is read on the micrometer screw.
• Currently, vernier sextants are rarely used.
• On the micrometer drum, a degree may be divided into 100 parts or 60 parts.
• The fraction of a degree therefore can either be read in 1/100 th of a degree, or up to 1/60 th of a degree (which comes to one minute of arc).

Principle of Sextant

• When a ray of light is twice reflected by two mirrors in the same plane, the angle between the original incident ray and the final emergent ray is twice the angle between the mirrors. OR we could say that
• When a ray of light is reflected twice by two mirrors in the same plane ,the angle between the incident and reflected ray is twice the angle between the mirrors.
• Sextant has two mirrors, one of them fixed on the body of the sextant and the other is fixed on the index arm which is called the pivot and changes its angle with the fixed mirror.

• In the diagram above, the altitude of object X is angle XEH.
• Which is measured by movement of Mirror H through angle b, which is half the angle XEH.

What is Use of Sextant?

• For measuring altitude of a celestial body to obtain position at sea.
• Obtaining a fix at sea.
• For avoiding danger.
• To measure distance between ships when steaming in convoy
• Hydrographic Surveys

What are errors of sextant?

Adjustable on board ship

• Perpendicularity Error
• Index Error

Adjustable by Instrument Maker

• Collimation Error
• Vernier Error

Non-Adjustable

• Centering Error
• Graduation Error
• Micrometer Error
• Shade Error
• Prismatic Error

The first three adjustable errors should be corrected in the given order –

• First the perpendicularity which is referred as to making the 1st adjustment
• Next the Side error which is , referred as to making the 2 nd
• And finally the index error, referred as to making the 3 rd adjustment.

What is the Perpendicularity Error?

Cause: Index mirror not perpendicular to the plane of the mirror

How to check perpendicularity error of sextant?

• Bring the index arm in the middle of the arc.
• Look obliquely into the index mirror
• If the true arc and its image are not in the same horizontal straight line, it means there is an Perpendicularity error.

About the author

Amit Sharma

Graduated from M.E.R.I. Mumbai (Mumbai University), After a brief sailing founded this website with the idea to bring the maritime education online which must be free and available for all at all times and to find basic solutions that are of extreme importance to a seafarer by our innovative ideas.

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Solar observations – with a sextant

by Rafael C. Caruso, MD

On June 2019, a group of AAAP members met in Peyton Hall to attend a two-day celestial navigation course, which I found most enjoyable. The course was taught by Frank Reed, the navigation instructor who currently teaches all navigation classes offered by the Mystic Seaport in Mystic, Connecticut, a maritime museum well worth visiting.  

The objective of this short article is to describe an attempt to determine local latitude and longitude by an observation of the noon sun, and its elegant theoretical background.   These measurements are, in a way, a type of astrometry, the earliest form of astronomy. As this was my first such measurement, I opted to carry it out on from a stationary position on dry land rather than aboard a moving vessel (the fact that I do not own a yacht also played a role in that decision). The boardwalk in Belmar, New Jersey, provided a very convenient “deck” from which to observe the sun and the horizon on Saturday, November 16, 2019, a sunny and blustery day.  

1. Requirements

This determination required three equally essential pieces of information. The devices used in this case to obtain this information are shown in Figure 1.

1. A measurement of the sun’s altitude (H) above the horizon al local noon.

The nautical sextant allows an observer to align the images of sun and horizon, and measure the angle between them. A Freiberger drum sextant, manufactured in 1984 in what was then East Germany was used.   Its drum micrometer is calibrated in increments of 1 minute of arc, which allows estimating measurements to about 0.1 to 0.2 minutes of arc.

2. Precise timing of these measurements.  

A wristwatch with quartz movement, set to Universal time (UT) earlier on the same day, was used in this case. UT may be obtained from the US Naval Observatory Master Clock by dialing (202) 762-1401.   Since no assistant was at hand, a mechanical stopwatch was used to measure the time elapsed between each sextant measurement and its corresponding wristwatch reading.  

3. A knowledge of the sun’s coordinates at the time of measurement.  

The Nautical Almanac, an annual publication, lists the sun’s coordinates for every hour of every day of a given year, among much other information for celestial navigation. The Almanac is published jointly by the US Naval Observatory and the British Nautical Almanac Office. A free version containing the same information is also available online ( https://thenauticalalmanac.com )

Figure 1. Sextant, timepiece(s), and Nautical Almanac. This triad provides all the information required to find latitude and longitude (photo by the author).

2. Shooting the Sun

At the moment of local noon, when the sun reaches its highest altitude, the sun crosses the observer’s meridian. This fact is reflected in the etymology of the word, which is derived from “meridies”, Latin for “noon”. For an observer is in a mid-northern latitude, the sun is then due south (conversely, for an observer is in a mid-southern latitude, the sun is due north).

Figure 2. Diagram of a vertical section of the Earth, showing the relative locations of an observer and of the sun’s geographic position (GP) when the sun in over the observer’s meridian. Redrawn with modifications from Prinet(1).

Figure 2 shows the position of an observer, depicted as a small circle on the surface of the Earth. Latitude and longitude are unknown to this observer, but we shall assume the observer does know that he or she is north of the equator.   As this measurement takes place in November, the point on the Earth’s surface where the sun is at the zenith (called the geographic position (GP) of the sun), is south of the equator. The blue line tangent to the Earth’s surface is his or her horizon, which is perpendicular to the observer’s zenith. Given the very large distance between the sun and the Earth, all the sun’s rays fall on the Earth essentially parallel to each other, both at the geographic position of the sun and at the observer’s position.  

All the observer does now is to use a sextant to measure the angle of altitude H of the noon sun with respect to the horizon, and to record the exact time of this measurement. As mentioned above, and particularly since the observer may have only an approximate knowledge of the time of local noon, an ideal way to do this to take sun sights starting while the sun’s altitude is still increasing (before noon) and continuing to do so every few minutes until it begins its decline (after noon).

3. Analyzing altitude data

Figure 3. Graph of the sun’s altitude as measured with a sextant (Hs) as a function of coordinated universal time (UT)

A graph of the measurements just obtained is shown in figure 3, a plot of altitude ( Hs , which refers to altitude H measured with sextant s ) as a function of universal time UT . Universal time is equivalent to Greenwich meridian time GMT for a civil day starting at midnight in the prime meridian. In the course of about an hour, from16:15 to 17:15, the sun’s altitude described an arc of an amplitude of 0.5 degrees, with a maximum at local apparent noon. The plot shows that local noon on November 16 occurred slightly before 16:45 hours UT, and that at that moment, the sun’s altitude read from the sextant scale was approximately 30.9 degrees (30° 54’ of arc).  

Celestial navigation textbooks 1-3 recommend tracing a smooth curve through the data points to determine the peak altitude at local noon by inspection. I opted to use a numerical approach, which I have not seen described in navigation manuals, though I assume has been used more than once in the past, since it is quite straightforward. As these data points describe a curve similar to a parabola, one can fit a parabolic function through them and find the function’s equation

Figure 4. Graph of the data points plotted in figure 3, after fitting a quadratic function (a parabola), and its equation. Fractions of UT hours are expressed as decimal fractions.

From the parabola, one can calculate:

a. The time of local noon, obtained from the time value corresponding to the peak or maximum of the curve.   In this case, local noon was at 16.693 hours UT (16h 41m 37s).

b. The sextant reading corresponding to this time, even if the sun’s altitude was not measured exactly then. This is just the highest Hs value of the curve, which is 30.91° (30° 54.5’).

Both values are similar to those estimated by inspection of the graph. The details of this calculation are described in Appendix 1.

Before using this value to calculate a geographic position, some corrections have to be applied to it, to account for the conditions in which the sextant measurement was made. The reasons underlying this requirement are listed in Appendix 2.   After these operations were carried out, the sextant altitude value Hs (30° 54.5’) was corrected to an “observed altitude” value Ho of 31° 6.5’.  

4. Calculating latitude

This calculation relies of the fact that the observer and the sun are on the same meridian at the time of local noon. As mentioned above, the observer knows that he or she is north of the equator, and knows that the November sun is south of the celestial equator. Therefore, their relative positions on opposite hemispheres are as depicted in Figure 5.  

Figure 5. Diagram of a vertical section of the Earth, showing the three angles required for a calculation of latitude (ZD, dec, lat). Redrawn with modifications from Prinet(1).

This figure shows that the known value the sun’s altitude H above the horizon allows us to calculate the angle between the sun’s position and the zenith. This is called the zenith distance ZD , which is simply 90° – H . In our case, ZD is 90° – 31° 6.5’ = 58° 53.5’.  

The angle subtended by the larger arc drawn “inside” the diagram of the earth is also equal to ZD , since the sun’s rays are parallel for our purposes. The figure shows that this angle ZD can be visualized as the sum of two angles, the sun’s declination (dec) and the observer’s latitude (Lat).

(As an aside, it’s worth noting that the configuration of these three angles (ZD, dec, and Lat) may be different for other possible relative positions of observer and noon sun, but the latitude calculation always involves a combination of all three of them. I find that drawing a diagram of these angles is a more intuitive and less error prone approach than using any mnemonic).

Therefore, knowing the sun’s declination at local noon allows calculating the observer’s latitude.   This is where the Nautical Almanac becomes essential.

Figure 6. Excerpt of a page of the Nautical Almanac for 2019, which shows the sun’s coordinates for every hour of Saturday, November 16.

The relevant section of the Nautical Almanac page for Saturday, November 16, 2019 is shown in figure 6. The almanac lists sun declination values for every hour of the day.   Note that declination values are designated by convention as N(orth) or S(outh), rather than as the positive or negative values, the notation used in astronomy.   The table entries outlined in red indicate that declination was S 18° 46.0’ at 16:00 hs and S 18° 46.7’ at 17:00 hs.   What we need to know is the sun’s declination at 16h 41m 37s UT, which may be obtained by interpolation as S 18° 46.5’.   The observer’s latitude is therefore:

Latitude = ZD – dec = 58° 53.5’ – 18° 46.5’ = 40° 7’ North

6. Estimating longitude

Although there are more accurate celestial navigation methods for the calculation longitude, a measurement of the time of local noon may also be used to estimate longitude.   This estimation relies on the fact that the geographic position (GP) of the sun changes during the day (see figure 7). At local noon at longitude 0°, the sun’s GP is at some point on the Greenwich meridian. As the Earth rotates, the sun’s GP moves westward at a rate of 15° per hour, and completes a whole rotation of 360° in 24 hours. The angle between the Greenwich meridian and the meridian over which the sun’s GP has moved is called the Greenwich hour angle (GHA) of the sun.   This angle is measured westward from the Greenwich meridian, from 0° to nearly 360°. In the Western hemisphere, local noon occurs later than at longitude 0°, proportionally to the distance in longitude from the Greenwich meridian. Therefore, longitude is equal to the Greenwich hour angle of the sun at local noon 2 .  

Figure 7. Diagram of the Earth as a sphere, showing the Greenwich hour angle (GHA), increasing as the GP of the sun circles westward from the prime meridian. Redrawn with modifications from Karl (2)

To use this fact to estimate longitude, one also relies on the Nautical Almanac. The Almanac lists the GHA of the sun (and other celestial bodies) for every hour of each day. The Almanac excerpt in figure 6 shows that the sun’s GHA was 63° 49.2’ at 16:00 hours UT.   Since GHA is between 0° and 180°, longitude is West of the Greenwich meridian. What we wish to know is the GHA value at the time of local noon, i.e., at 16h 41m 37s. Since we know that GHA increases at 15° per hour, or 0.25° per minute, it has increased 10° 23.4’ in the 41m 37s after 16:00 hours.   Therefore, we can conclude that

Longitude = 63° 49.2’ + 10° 23.4’ = 73° 72.6’ = 74° 12.6’ West

7. Checking coordinate accuracy

At the end of this exercise, we have reached the conclusion that our coordinates are:

Latitude: North 40° 7’  

Longitude: West 74° 12.6’  

How accurate is this result? In these days, celestial navigation may be used as a backup if satellite navigation systems such as GPS fail, as it relies on different and independent information. But we may also use GPS as a way to check our celestial navigation results, using these more accurate values as the equivalent of “the answer on the back of the book” in a college math textbook.

The National Oceanic and Atmospheric Administration’s online solar calculator 4 lists GPS coordinates of any selected location on Earth, in addition to giving solar position for any time at that location. For our location on the Belmar boardwalk, these coordinates are:

Latitude: North 40° 10.3’  

Longitude: West 74° 0.9’

As one minute of latitude was historically equivalent to one nautical mile, our error of 3.3’ in latitude is approximately equivalent to a distance of 3.3 nautical miles.  

The length of one minute of longitude varies with latitude, from a maximum of about one nautical mile at the equator, to a vanishingly small distance at the poles.   At a latitude of 40°, a minute of arc spans approximately 0.77 nm. This implies that our error of 11.7’ in longitude is approximately equivalent to a distance of 9 nautical miles. The roughly three-fold difference between the longitude error and the latitude error is not surprising, since the method used here to determine longitude is not an ideal one, and gives only an approximate estimate of longitude.

The great circle distance between the celestial navigation coordinates and the GPS coordinates, obtained with a great circle calculator 5 , is 9.56 nautical miles.  

In this way, knowing an angle, a time, and having access to data which relate this angle to this time, it is possible to measure latitude and estimate longitude by the noon sun.   Celestial navigation is no longer the most advanced technique to find one’s position, but remains a beautiful achievement of the human mind, and provides a perception of the motions of the earth and sky that is most appealing for an amateur astronomer.

Appendix 1. Fitting a parabola

Numerical routines for fitting a parabola, or any other polynomial function, to data points are included in spreadsheet programs (e.g., Microsoft Excel, or the open source Libre Office), in graphing programs (e.g., Kaleidagraph), and in numerical analysis packages (e.g., Matlab, or the open source Octave).   The best fitting parabola for our data points is shown in Figure 4, in which fractions of UT hours are expressed not as minutes but as decimal fractions, which are required by the numerical routine used.   The curve-fitting program also yielded the equation of this parabola:

− 1.59 t 2 + 53.02 t – 411.58

This equation may now be used to find the time of local noon, which is the time t for the maximum Hs value.   For this purpose, one can follow the usual approach to find a maximum of a function. This involves calculating the first derivative of the function:  

− 3.18 t + 53.02  

The maximum t value is obtained by setting the first derivative to zero and solving for t .

In this way, one can determine that local noon occurred at 16.693 hours UT (16h 41m 37s). Finally, one can calculate the sextant reading corresponding to the exact time of local noon. This is just the peak Hs value of the curve, and can be obtained by substituting the peak time (16.693) in the equation of the curve. This results in a value of 30.910° (30° 54.5’) for Hs .

Appendix 2. Applying corrections

This altitude value as measured with a sextant needs to be corrected, to account for the following facts:  

• A calibrated sextant may still have a minimal residual error in its angular measurement (which has to be added or subtracted from a reading).
• The observer is not at horizon level, but rather at a variable known height above it (in this case, on a modestly elevated boardwalk, 3.2 m (10.6 ft) above sea level).
• Aligning the lower limb of the sun with the horizon yields a more accurate measurement than aligning its center, which is the almanac-tabulated value.
• The atmosphere refracts rays of light from the sun. This effect is greater if the sun is close to the horizon, and minimal if it is close to the zenith.
• Sun sights are taken from the surface of the Earth rather than from its center. The resulting small parallax error is greater if the sun is close to the horizon.

Performing these corrections is considerably simpler that it may seem after reading this list. The observer is able to determine the angular measurement error (known as the index error) of his or her sextant (in this case, 0.3 min had to be added to the reading). The Nautical Almanac contains tables to perform the remaining four corrections. Alternatively, formulas for the same purpose are readily available, and may be entered on a spreadsheet program for ease of use.  

• Dominique Prinet, Celestial navigation using sight reduction tables Pub. No 249. Friesen Press, Victoria, BC, 2018
• John Karl, Celestial Navigation in the GPS age. Paradise Cay Publications, Arcata, CA, 2011
• David Burch, Celestial Navigation, a complete home study course. Starpath Publications, Seattle, WA, 2019
• NOAA National Oceanic and Atmospheric Administration. Online solar calculator ( https://www.esrl.noaa.gov/gmd/grad/solcalc/ )
• Ed Williams.   Great circle calculator ( http://edwilliams.org/gccalc.htm )

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What Is A Sextant? Explained By A Ship’s Officer

The sextant is a navigational instrument used to measure angles. In celestial navigation, it measures the angle between the horizon and a celestial body (the sun, moon, planets or stars), and in terrestrial navigation, it measures the angle between two charted objects (lighthouses, piers, etc.).

The sextant is essentially a very accurate, scientific version of a protractor. It measures angles.

Protractors measure the angles between lines on a sheet of paper to the closest degree. The sextant can measure angles between distant objects, accurate to the closest 0.002°.

The main difference is that a sextant uses mirrors to measure the angle between different beams of light.

When you angle a sextant’s mirrors correctly, you can visually overlay two objects. In celestial navigation, you would overlay a star with the horizon. In terrestrial navigation, you might overlay a lighthouse with a pier.

As the sextant uses the Double Reflection Principle, the angle between its mirrors is directly proportional to the angle between the objects.

Using the micrometer, you can read a very precise angle straight from the sextant itself.

Having established that the sextant is basically just a very accurate, scientific protractor, we can start to learn a little more about exactly what it is.

Types of sextant

In modern navigation, there are two types of sextants: plastic nautical sextants, and metal nautical sextants.

In the past, there were different sextants used for different tasks so you had three further sub-categories: Nautical Sextants, Box Sextants, and Sounding Sextants.

Today, however, Box Sextants and Sounding Sextants are no longer used because their functions can be accomplished by other means, or performed by the standard nautical sextant. Consequently, the only versions of those still available are historical metallic versions.

This essentially only leaves us with a choice between a plastic nautical sextant, metal nautical sextant, a historical metal box sextant, or a historical metal sounding sextant.

Plastic sextants

A plastic sextant is a nautical sextant with plastic used as its main construction material. They are a relatively recent development, made possible by advancements in the precision and durability of plastic manufacturing techniques.

Commonly, they will be priced lower than their metal counterparts because they are easier and quicker to manufacture.

Their disadvantage, however, is that plastic is still less durable than metal, so you can expect a plastic model to suffer greater deterioration over time.

Despite that, I actually recommend a plastic sextant over a metal sextant for most users. They offer enough accuracy for most use cases, and their lower price point keeps them affordable for more people.

If you are considering buying a plastic sextant, you should read my round-up article looking at your different options: Plastic Sextants: Which One Is Best?

Metal sextants

A metal sextant is a nautical sextant with metal used as its main construction material. Traditionally, sextants were all made from metal because it was possible to manufacture accurate metal instruments much earlier than plastic versions.

Due to the additional resources and work required in the manufacture of metal sextants, you will find most models priced significantly higher than their plastic counterparts.

The additional investment is offset by the gains in durability and subsequent gains in accuracy over time that are possible with a metal sextant.

For users needing to guarantee a higher amount of accuracy, or planning to use their sextant frequently, I will always recommend a metal model. There is no doubt that they are more accurate and durable than plastic versions, so if you would benefit from those then they are worth the additional expense.

Box sextants

Box sextants were a type of metal sextant, sometimes referred to as a pocket sextant. As the name suggests, they were much smaller than nautical sextants.

The idea behind a box sextant is that it is small enough to be carried in your pocket. Its box cover would protect the delicate mechanism when it was carried inside your pocket.

They were popular in the past when all navigators would carry their own sextant as it meant they always had one to hand when required.

Nowadays, it is more common to only have one or two sextants for an entire ship. As such, nautical sextants are always chosen instead, so the box sextant has fallen out of common usage.

Sounding sextants

Sounding sextants are very similar to nautical sextants, except they were designed to be used by hydrographers.

They get their name because they were used to confirm the position of lead-line soundings that were being taken during a survey of the coastline. Accurately plotting your position gave the sounding an accurate position on the chart.

Nowadays, most soundings are taken by single or multi-beam sonars, with positions continuously plotted through the use of GPS.

Additionally, the small differences between sounding sextants and nautical sextants meant that it was not economically viable to continue producing them for the shrinking market.

How does a sextant work?

A sextant works by adjusting the angle between two successive mirrors to superimpose the image of two objects over each other. The angular distance between two objects can then be found by reading the angle between the two mirrors using the sextant principle (described below).

The exact workings of the sextant are quite complicated, so are best illustrated visually. Fortunately, I have written a complete guide if you are interested in the details: How Sextants Work: An Illustrated Guide .

The sextant principle

The principle that the sextant operates under is known as the sextant principle, or the Principle of Double Reflection: “When a ray of light is reflected from two mirrors in succession, the angle between the incident ray and reflected ray is twice the angle between the mirrors.”

In a sextant, the horizon mirror is equivalent to the first mirror and the index mirror is equivalent to the second mirror. The angle, A, is controlled using the micrometer on the end of the index arm, which is fixed rigidly to the index mirror.

You simply adjust the angle, A, until the desired object is clearly visible, at altitude 2A.

To save you from performing additional calculations, the sextant’s arc shows you the readings equivalent to 2A. Essentially, the angle you read from the sextant is twice the angle that you have deflected the index mirror.

This is why a sextant’s arc spans only 60°, yet it can measure angles up to 120°.

Different ways you can use a sextant

The most well-known use of the sextant is in celestial navigation, but there are a surprising number of other ways in which you can use one to help you navigate.

We have already established that a sextant is just a tool for measuring angles. For an experienced navigator, there is a whole range of different ways you can use those angles to help you find your way.

All techniques rely on the same basic operation of the sextant, which I summarise in 6 steps:

• Plan the time of your sights
• Pick up your sextant correctly
• Correct your sextant for the correctable errors
• Locate the body you are measuring using the telescope
• Bring the body in line with the horizon, or other reference position
• Read the altitude from the sextant’s arc and micrometer

Pro Tip: For a complete explanation of these steps to use your sextant, check out: How To Use A Sextant: A Step By Step Guide .

Once you master getting angles using your sextant, it is just a case of implementing it in the way you choose.

Measuring the altitude of celestial bodies for celestial navigation

When you use your sextant to measure the altitude of celestial bodies above the horizon, you can use the readings to obtain a celestial position fix.

The basic principle of the fix is that you make a guess of where you think you are and calculate the precise altitude of stars from that position.

You then measure the true altitude of the stars using your sextant.

If the stars are exactly where you think they should be, it proves that the guess of your position was correct.

If the true altitude of stars is different to the calculated altitudes, you can use the difference to plot a line of position from your best guess.

It does not matter how accurate your guess was, the idea is that comparing the true altitude of stars to their calculated altitude allows you to correct your guess and find your real position.

Measuring the angular height of a charted object to obtain a range

A Vertical Sextant Angle is used to measure the angular height of a charted object with a known height so that you can calculate how far from the object you are.

For example, if you know that a lighthouse has a height of 10m, and you measure its angular height using a sextant and find that it is 1°10.2’, then you can use trigonometry to find the range is 49m.

Height / Tan(Angle) = Distance

10m / Tan(1°10.2’) = 49.0m

You could then plot a line of position on your chart by drawing a ring 49m away from the lighthouse.

Measuring the angular distance between two charted objects to obtain a line of position

A Horizontal Sextant Angle is used to measure the horizontal angular distance between two charted objects so that you can plot a line of position on a chart.

For example, if you measure the angle between a church spire and a lighthouse to be precisely 50°, you can plot a curved line of position around the objects to get a line of position.

The easiest way to do this is to draw two lines on tracing paper, 50° apart. You then overlay it on the chart and make sure both lines continuously touch the charted objects.

You’ll be able to slide the tracing paper around, and your line of the position will be the one following the intersection of the lines as you move it around.

Observing a charted object to monitor a clearing range

In a similar way to finding a range from a charted object, you can also calculate a safe clearing range from danger and use a Vertical Sextant Angle to keep yourself clear.

For example, if you know you want to keep at least 50m off the lighthouse in the previous section, you can set your sextant at 1°10.2’ and observe the lighthouse. If you observe it and the angle is less than 1°10.2’, you know you are further away.

If the angle reaches 1°10.2’, you know you are now 49m away, placing your boat in the previously established dangerous area.

Monitoring the sun at midday to calculate the time of local noon

Local noon occurs when the sun is at its highest point in the sky, viewed from your location.

Glancing up at the sun, it is impossible to detect the exact time that midday occurs.

With a sextant, however, you can take such precise readings that you can observe the sun around midday and monitor it.

All the while it continues rising, you know that it is not yet midday. The moment it stops rising, you can record the time as local noon.

Interestingly, you can compare the time of local noon to the time of noon at Greenwich to determine your longitude. Assuming your watch is accurate, it is possible to get a very accurate longitude using this method.

Buying a sextant

Now that you know what a sextant is, you may be considering purchasing one yourself.

Read More: for a complete guide on buying a sextant, check out: Choosing The Perfect Sextant: Which One Is Best .

As with everything, there are countless options to choose from.

First, you should consider whether you want to use your sextant for navigation or whether you want it to be purely ornamental.

There are a lot of ornamental models out there that cost a lot less than usable ones. That is fine if you are after an ornamental version, but be wary if you are looking for one that you can use yourself.

Next, consider how much you want to use your sextant. If you will be using it a lot, for many years, you may consider a metal version. Otherwise, a more affordable plastic one will do just fine.

In fact, I actually recommend a plastic one for most people, especially for beginners. I explain why in this article: Which Sextant Is Best For A Beginner?

Who invented the sextant?

Around 1730, John Hadley and Thomas Godfrey are both credited with first using the Double Reflection Principle in a navigational application. They both independently invented the octant within a few years of each other, displacing the previously dominant quadrant.

Almost 30 years later, in 1759 a British Royal Naval officer, John Campbell is credited with suggesting modifications to the octant by extending its arc to 60° and using brass for its construction. In doing so, his modifications led to the first sextant as we know it today.

2 minute read

The optical instruments called sextants have been used as navigation aids for centuries, especially by seafarers. In its simplest form, a sextant consists of an eyepiece and an angular scale called the "arc," fitted with an arm to mark degrees. By manipulating the parts, a user can measure the angular distance between two celestial bodies, usually Earth and either the Sun or Moon . The observer can thereby calculate his or her position of latitude by using a trigonometric operation known as triangulation. The word sextant derives from a Latin term for one sixth of a circle , or 60 degrees. This term is applied generally to a variety of instruments today regardless of the spans of their arcs.

One of the earliest precursors to the sextant was referred to as a latitude hook. This invention of the Polynesians could only be used to travel from one place at a particular latitude to another at the same latitude. The hook end of the device served as a frame for the North Star, a fixed celestial body also known as Polaris. By sighting the star through the hook at one tip of the wire, you could discover you were off-course if the horizon line did not exactly intersect the straight tip at the opposite end.

A sextant. Photograph by Gabe/Bikderberg Palmer. Stock Market. Reproduced by permission .

Christopher Columbus used a quadrant during his maiden voyage. The measuring was done by a plumb bob, a little weight hung by a string that was easily disturbed by the pitching or acceleration of a ship. The biggest drawback to such intermediate versions of the sextant was the persistent requirement to look at both the horizon and the chosen celestial body at once. This always introduced a reading error , caused by ocular parallax , which could set a navigator up to 90 mi (145 m) off-course. Inventions such as the cross-staff, backstaff, sea-ring and nocturnal could not ease the tendency towards such errors.

Although Isaac Newton discovered the principle which guides modern sextants, and even designed a prototype in 1700, John Hadley in England and Thomas Godfrey in America simultaneously constructed working models of the double-reflecting sextant 30 years later. These machines depended upon two mirrors placed parallel to each other, as in a periscope. Just the way a transversing line cuts two parallel lines at matching angles, a ray of light bounces on and off first one, then the other mirror. You displace the mirrors by adjusting the measuring arm along the arc , in order to bring a celestial object into view. The number of degrees of this displacement is always half the angular altitude of the body, in relation to the horizon.

Although it has been largely replaced by radar and laser surveillance technology, the sextant is still used by navigators of small craft, and applied to simple physics experiments. Marine sextants depend upon the visible horizon of the sea's surface as a base line. Air sextants were equipped with a liquid, a flat pane of glass , and a pendulum or gyroscope to provide an artificial horizon.

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sextant , instrument for determining the angle between the horizon and a celestial body such as the Sun , the Moon , or a star , used in celestial navigation to determine latitude and longitude . The device consists of an arc of a circle, marked off in degrees, and a movable radial arm pivoted at the centre of the circle. A telescope , mounted rigidly to the framework, is lined up with the horizon. The radial arm, on which a mirror is mounted, is moved until the star is reflected into a half-silvered mirror in line with the telescope and appears, through the telescope, to coincide with the horizon. The angular distance of the star above the horizon is then read from the graduated arc of the sextant. From this angle and the exact time of day as registered by a chronometer, the latitude can be determined (within a few hundred metres) by means of published tables.

The name comes from the Latin sextus, or “one-sixth,” for the sextant’s arc spans 60°, or one-sixth of a circle. Octants, with 45° arcs, were first used to calculate latitude. Sextants were first developed with wider arcs for calculating longitude from lunar observations, and they replaced octants by the second half of the 18th century.

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