The Sextant and its Corrections
The Sextant is a very accurate and technical device for doing something very simple - measuring angles. You could use a protractor and a piece of string, though accuracy would not be very good!
The Sextant is designed to measure angles very precisely, to an accuracy of Degrees, Minutes and 10th’s of minutes (we call 1/10th of a Nautical Mile a Cable). We normally use the Sextant to measure the angle between the horizon and a vertical object.
In Coastal Navigation we could measure the angle between our horizon and the top of a lighthouse. This can tell us how far we are from the Lighthouse. For those interested, it’s the Tangent Rule, though you don’t need to know this as a table called ‘Vertical Sextant Angles’ is readily available in many marine publications such as ‘Reeds’ Nautical Almanac.
The Tangent Rule;
Imagine we have measured the angle to the top of a lighthouse of height 61m. The angle on the Sextant is 1°43’. The formula is;
(Height of Lighthouse (m) / Tan (Sextant angle)) x 0.00054 (0.00054 is the conversion of meters to Nautical Miles)
(61m / Tan (1°43’)) x 0.00054 = (61/0.0299) x 0.00054 = 1.1 NM
We are just over 1NM from the lighthouse.
This by itself does not give us a position, but gives us a ‘Position Line’ of 1.1 NM which is a circle radius around the Lighthouse. We must be somewhere on this line. To make this a position, we could use our ‘Hand Bearing Compass’ to take a bearing of the Light, to confirm our position on the circle.
In Celestial Navigation, we can measure the angle between our horizon and a celestial body like the Sun. This can be used to tell us how far we are from the Sun’s position on the Earth’s surface (a point called the Geographical Position (GP).
Obviously it’s not quite the same as our lighthouse as the distance to the Suns GP is in most circumstance a long way. Anything up to 5000 miles.
However, the principal is the same in that the angle derived between the horizon and the sun can indeed tell us how far we are from our Sun Lighthouse (it’s GP). 90 degrees minus the True Sextant angle is known as the Zenith Distance (ZD) this is the distance of our position on earth from the Suns GP. Effectively we have a position line, but we will also need to know the bearing of the sun.
Geographical Position (GP)
Simply imagine a line from the centre of the Sun to the centre of the Earth, where this line crosses the surface of the Earth pinpoints the GP.
This position is like the Latitude and Longitude of our Lighthouse. The trouble is, it keeps moving!
Time
You may be aware that when we do Astro-Navigation, we also need a very precise watch, certainly one that is accurate to a few seconds of time. We often call this the Deck Watch or Chronometer however it doesn’t need to be anything fancy, any cheap digital watch will do. The time we use is Universal Time (UT), what was once called Greenwich Mean Time (GMT). When we take our Sextant sight, we (at the same instant) take the time on our accurate watch. This time ‘freezes’ the GP of the Sun.
The Nautical Almanac
This book is produced in collaboration between the British and American Hydrographic departments. It is an annual publication. We enter this book with the date and our UT time of the Sextant sight, and the book gives us the GP of the Sun (or any other Celestial object). Remember, the GP of the sun is its Latitude and Longitude on the Earth’s surface at the time of the sight.
Declination DEC Latitude of the Sun Greenwich Hour Angle GHA Longitude of the Sun
DEC is measured exactly the same as Latitude (Degrees, Minutes, Cables) N&S of the Equator. GHA is similar to Longitude, measured in (Degree, Minutes, Cables), but WEST of Greenwich only.
A Position?
I’m afraid not we only have a position line. The time of the sight gives us the GP of the sun that we could plot onto our ocean chart, the Sextant Angle tell us how far we are from that point (just like the Lighthouse). We are somewhere on this vast position line. To fix our position, let’s use our hand bearing compass to take a bearing on the sun and voila, we know where we are! In practice because this could have errors we use ABC tables to calculate the bearing of the sun or heavenly body.
OK, that’s the theory! However, in practice this is difficult to achieve. Drawing massive circles onto ocean charts is not very accurate and taking a bearing of the sun could easily be out by a few degrees rendering our final position wildly out. In practice we use the ‘Marq-St-Hilaire’ method, but this is about the Sextant.
Reading the Sextant
The sextant measures the angle between the Sun and the horizon, it uses a combination of 2 mirrors, one is fixed (the horizon mirror), one moves on a pivoted arm (index mirror). You look through the telescope, the mirror immediately in view (horizon mirror) is normally split, half is silvered, half is clear. Through the clear section you can see the horizon, through the silvered section you will see a reflected image of the sun.
Your aim is to use the swinging arm (Index Arm, ‘course movement’) and the Micrometer (‘fine movement’) to bring the Sun down to the horizon so that it just touches the surface of the sea. You can now read the Sextant angle you must record the time the moment of the sight.
DIP (Height of Eye)
Ideally, your observations should be taken from sea level; however, it is obvious that this is not only wet but impractical! Imagine yourself standing in the cockpit of a small yacht; your height of eye will be somewhere around 2m and therefore, your local horizon approximately 3 or 4 miles away. Now imagine yourself on the bridge of a tanker, your height of eye may be 50 or 60 metres above the surface of the water, your local horizon may well be 20 or so miles away. This difference in distance to the horizon affects the angle you get on the sextant. The higher up you are, the bigger the angle will be. We need to adjust out sextant angle as though we had measured the sun’s altitude from the surface of the water. This correction is found in the front of the Nautical Almanac. Notice the correction is always negative.
Altitude Correction
This is actually a single correction based on 3 errors. Again, this is found on the ‘loose card’ found in your Nautical Almanac. If you look at the previous page, you will see these corrections on the left hand side. The 3 errors are;
1. Seasonal
2. Refraction
3. Semi-diameter
Seasonal
We live in an ‘average’ world. We assume that a day is 24h (but it’s not!). We assume that a year is 365 days (but it’s not) and we assume the orbit of the earth is around the sun is circular, but in fact it’s elliptical. What this means is that half the year the earth is closer to the sun, and therefore the sun is bigger, the other half of the year the earth is further away from the sun, and is therefore smaller. We don’t notice this with our eyes, but the precision of the sextant will see this difference.
Refraction
Refraction is the bending of light rays through different mediums, in this case the earth’s atmosphere
Semi-diameter
The GP is the imaginary line from the centre of the sun to the centre of the earth. With this in mind, when we take the Sextant sight, we should aim to place the centre of the sun onto the horizon. However, our eyes and brains cannot do this very accurately, so it is better to use one edge of the sun, either the Lower Limb or the Upper Limb depending on cloud cover. Because we have used the edge of the sun, and not the middle, we must adjust our reading to take in effect the ‘thickness’ of half the sun. The Semi-Diameter.
Under normal circumstances, we prefer to bring the ‘Lower’ limb of the Sun down to the horizon