How to Calculate Height With Sextant

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Historically, measuring the distances between celestial and marine objects beyond the naked eye has relied on instruments that take advantage of the Earth in relation to those objects like planets and stars. Knowing basic principles of geometry and physics, scholars invented tools like the sextant for measuring angular distance between these objects. That's where sextants come into play.

Sextant Principle

Sextants measure angles. They do this by reflecting incoming rays of light from the environment or objects they're studying such that the angle of the ray of the incoming light equals the angle of the ray reflected. This occurs naturally in all cases of light incident on surfaces due to the nature of reflection, but, in practice, the material and density of the mirror slightly alter the angle at which light leaves the surface.

This means you can use two plane mirrors in succession with one another such that the light leaves both of the mirrors with double the incidence angle. The sextant uses this with the index mirror and the horizon mirror for measuring angles between the horizon and a visible object such as a ship at sea or a planet in the solar system.

By measuring these changes in angles of light, a sextant can tell you the relative altitude of a far away object (referred to as the "unknown" object) with respect to the horizon or another object with an altitude you already know such as the altitude of the sun from an almanac. Because the altitude represents the line that intersects with the Earth, you can determine how far away the object is using trigonometry.

This means forming a right angle between the unknown object, the known object and your own position, and using the angle between the two objects to determine the length of the triangle's side that represents the distance to the unknown object. Historically, people would use sextants to measure distances between any two points on the Earth's surface. When dealing with objects at sea, you can measure the angle of difference between two objects by turning the sextant on its side.

Sextant Calculator

Modern technology provides a new way of understanding the quantities sextants measure. Online sextant calculators, such as the one from Nautical Calculators, use the location of the observer by latitude and the angle at which you observe some celestial body to determine the error due to the compass bearer.

These online applications can also correct for other factors like air temperature and slight variations in the Earth's curvature. This makes their calculations more accurate.

Using a Nautical Almanac can give you the numbers of distances between objects to use when performing measurements using a sextant. They also offer information on calculators that are more appropriate for various calculations and methods of calculating other quantities.

Other Helpful Quantities

This includes the azimuth, the direction of a celestial object from the observer on the Earth's surface, and angle of refraction, the process by which an angle deflects when it enters a medium, that are involved in the sextant's use. You can even account for other factors that may plague the readings of a sextant instrument itself such as more precise values of the dip and index error.

The former is a measurement of the angle between the horizontal plane through the observer's eye and plane through the visible horizon from the observer's location. The latter is the difference between the zero as denoted on the sextant, and the graduated zero of the observation itself.

Sextant Apparatus

The sextant uses two mirrors in combination with one another. When you look through a sextant, you can see an index mirror, one of the mirrors that lets some of the light pass through, and it changes based on the angle of the mirror. If you want to determine the location of objects when navigating the oceans, you can look at the horizon as a fixed point through this mirror. The horizon mirror lies in front of part of your view that works with the index mirror in this double-mirror effect.

If you were to change the angle of the index by a certain amount, your view would change by double that amount in degrees. This is because changing the index angle mirror changes both incident and reflection angles that are part of the process of light bouncing upon it.

Aligning the sextant along the horizon, you can observe the change of the ray of light through changing the angle when looking at objects at great distances away. When you look through the eyepiece of the sextant, the images of the objects should rest upon the horizon if you aligned it properly. Then, you can read the appropriate angle off the scale of the sextant. Degrees are generally used for distances between celestial bodies.

Sextants are known for their precision. The material and design of sextants can rid them of sources of error that would otherwise plague sextant measurements. Metal sextants in particular don't have to deal with issues of refraction, oblateness (a measurement of curvature) of the Earth and data tabulation.

Sextant Practical Applications

As discussed, researchers or other professionals studying vessels at sea and objects in space need the precise measurements of angles and distances that they observe. This helps navigation across oceans, and sextants were historically important in making these calculations during navigation.

Though modern navigation methods now use technology such as GPS, sextants are still useful for understanding historical data such as the research work of scientists and researchers like explorer Bartholomew Gosnold.

Devices that investigate features of the ocean such as drifters, tools that take measurements of current and other features like temperature and salinity, would have their locations accurately recorded using the features of sextants in the early 1900s. When radio direction technologies began seeing increased used in these areas of research, they displaced sextants and gave more precise readings of drifter trajectories.

These sextant practical applications extend to land surveying equipment to projects that would look for the locations of reservoirs alongside sounding poles to determine the depths of waters. Alongside compasses, echo sounders and other tools, historic researchers would find sextants handy among their tools.

Errors in Sextant Readings

Other errors in sextant readings can come about through their design. The error of perpendicularity occurs when the index mirror isn't perpendicular to the plane of the sextant instrument itself. Individuals who use sextants should press the index bar around the middle of the arc that the sextant creates and hold the sextant horizontally with the arc facing away from them.

When the objects you can see through the mirror are aligned properly, this error can be reduced. You can also adjust the screws at the back of the index glass to align the images properly through the sextant.

The side error is caused by the horizon glass not remaining perpendicular to the plane of the instrument. You can press the index bar at 0 degrees and hold the sextant vertically to view celestial objects. If you turn the micrometer in one direction and then the other, the reflected image you see through the sextant can move above and below the direct image.

If it moves left or right, then the side error is occurring. Using the adjustment screws to find the true and reflected horizons in the same line with one another can mitigate this.

References

About the Author

S. Hussain Ather is a Master's student in Science Communications the University of California, Santa Cruz. After studying physics and philosophy as an undergraduate at Indiana University-Bloomington, he worked as a scientist at the National Institutes of Health for two years. He primarily performs research in and write about neuroscience and philosophy, however, his interests span ethics, policy, and other areas relevant to science.

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