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A sextant is a classic navigational instrument designed to measure angular distances, allowing you to calculate the elevation of celestial objects like the sun, moon, or stars above the horizon. By using this information, you can determine your latitude, or your position on Earth in relation to the equator. While sextants provide highly accurate location data, adjustments may be needed to account for variables such as the time of year and the specific celestial body you’re referencing. Despite its seemingly complex design, with some practice and a solid understanding of how it works, you’ll be able to use a sextant with confidence to pinpoint your location!
Procedure
Measuring the Angle of Elevation for a Celestial Object
Consult a map to determine your elevation above sea level. If you aren’t using the sextant on a ship at sea, you’ll need to adjust your reading for the difference between your height and the level of the horizon. Refer to a map that provides elevation data or use a tool like Google Maps to check your elevation. Make a note of this value for later correction.
- Since the sextant measures the angle between the horizon and an observed celestial body, the accuracy of your reading will decrease if you're not measuring from sea level or a similar reference. You’ll need to adjust the reading to account for this discrepancy in altitude.
- This variation in height is known as the “dip.”
- Even if you are at sea level, a dip correction is still required to account for the height of your eyes relative to the horizon.
Did you know? A sextant is made up of a sighting scope, two mirrors that allow simultaneous viewing of both the horizon and an object in the sky (like the sun or a star), and a movable arm that measures angles along a 60° arc. This arc covers 1/6 of a full circle, which is the source of the name 'sextant.'
Align the horizon by looking through the scope at the horizon mirror. Focus the sighting scope on the horizon line, which you’ll see reflected through the horizon mirror. The mirror is only partially silvered, so it lets you view both the horizon and the object in the sky at the same time.
- The horizon line serves as the reference for the object’s angle of elevation.
- If the sextant doesn't treat the horizon line as 0 degrees, you will need to adjust the angle of the object by the same amount of the horizon line's error. This is known as index error.
Move the index arm until the object you're measuring comes into view. The index mirror, attached to the adjustable arm, reflects the object you're measuring (like the sun or moon) onto the horizon mirror.
- Adjusting the arm rotates the index mirror, directing light to reflect off the horizon mirror. This causes the object to appear aligned with the horizon.
- Sextants built for solar observations come with shade glasses to shield your eyes from the sun’s intense light.
Important: When measuring the altitude of the sun, always ensure you use the sun shade to protect your eyes from harmful rays.
Fine-tune the arm until the object appears close to the horizon. Once you spot the object on the horizon mirror, gently adjust the arm to position the index mirror until the object aligns with the horizon. Look through the scope to ensure the object is nearly level with the horizon.
- If your sextant has a clamp, use it to secure the arm in place after positioning the object.
- Some models feature levers that allow for larger adjustments of the arm; release them when the arm is in the desired position.
Turn the micrometer knob to bring the object into alignment with the horizon. Locate the micrometer knob or screw on your sextant and use it to make precise adjustments to the position of the index mirror. Gradually turn the knob while gently swaying the sextant from side to side until the object appears to rest perfectly on the horizon.
- For example, if you're sighting the sun, make fine adjustments with the micrometer knob until the bottom curve (or 'lower limb') of the sun just touches the horizon.
Record the exact time of your sighting. As soon as the object is in place, quickly check the time on your watch or phone. Write down the time in hours, minutes, and seconds, starting with seconds to avoid mistakes.
- For example, if you're measuring the sun’s altitude at 7:35:16 AM, you would note down '7:35:16 AM.'
- Recording the time accurately is especially crucial in marine navigation, as both your position and the position of celestial bodies are constantly changing.
Observe the index arm and micrometer knob to determine the angle. Your sextant provides elevation readings in degrees and fractions of degrees (known as 'minutes'). Look at the window over the sextant arc at the bottom of the index arm to read the degree measurement, then check the micrometer knob’s position for the minutes. Some sextants feature a smaller scale called a Vernier, located next to the micrometer, which shows fractions of a minute. Record these measurements along with the time.
- For example, you may record a reading of 25° 6.40’, which is 25 degrees and 6.4 minutes.
- The index bar may include a small magnifying lens to help you read the graduations on the sextant arc more easily.
- A minute is 1/60 of a degree, and a second is 1/60 of a minute. Most sextants offer accuracy down to 10 seconds.
Making Corrections to Your Measurement
Correct for index error if your sextant shows a horizon reading greater or less than 0°. Sometimes, due to slight misalignments, a sextant may produce a horizon reading that is either greater or less than 0°. This is called 'index error.' Before measuring an object’s altitude, check for this error. If your sextant shows the horizon angle as greater than 0 (a positive value), subtract this number from the object’s angle. If the horizon angle is less than 0 (a negative value), add the difference to the object’s angle.
- This error occurs when the index and horizon mirrors fail to align properly when the index arm and minute scale are both set to 0. When this happens, the horizon will appear crooked in the mirrors when viewed through the scope.
- Turn the micrometer knob until the horizon line appears straight to measure the index error. If it exceeds 1.5’, adjustments to the sextant are necessary. Refer to the user manual for guidance if you have one.
Adjust for dip to account for your height above sea level. 'Dip' is the difference between your elevation and the actual horizon level. To correct for this, multiply 1.7725' by the square root of your elevation (including the height of your eye) in meters. Subtract this value from your observed altitude (the reading you got on the sextant when you measured an object’s elevation).
- The ‘ symbol in this formula represents minutes (1/60 of a degree). 1.7725’ is a constant that represents a small fraction of a degree.
- For instance, if you’re 25 meters (82 feet) above sea level and your eye level is 1.7 meters (5.6 feet), your total elevation would be 26.7 meters (88 feet). Your dip would be calculated as 1.7725’ x √26.7 = 9.16’.
- If your sun’s altitude was 38° 10.60’, after correcting for dip, it would be 38° 10.60’ - 9.16’ = 38° 1.44’.
Refer to the Nautical Almanac to correct for refraction errors. Refraction is the bending of light as it passes through Earth’s atmosphere, which distorts the appearance of objects in the sky. This effect causes celestial bodies to seem slightly out of place, much like how a straw appears bent when submerged in water. Since refraction varies with conditions and the celestial body observed, it’s easiest to use a correction table. You can find the refraction correction tables on page A2 of the Nautical Almanac.
- The Nautical Almanac can be purchased from online bookstores, and many of its tables are also available for free on various navigation and sailing websites.
- Refraction always causes objects to appear higher than they actually are, meaning the correction will be negative. Subtract this correction from the apparent altitude.
- The amount of refraction correction depends on your apparent altitude.
Apply a semi-diameter correction when observing the sun or moon. The apparent sizes of the sun and moon fluctuate throughout the year (for the sun) or month (for the moon). These changes can affect your elevation readings, so it’s important to adjust for accuracy. Consult the back of your Nautical Almanac to determine the required semi-diameter correction based on the time of year or moon phase.
- Once you’ve corrected for index error, dip, and refraction, add the semi-diameter correction to your observed altitude.
- For example, if you’re measuring the sun’s altitude in April, the semi-diameter correction would be 15.9’.
- This correction is only relevant for objects that appear circular in the sextant, like the sun and moon. Distant stars and planets, which appear as points of light, do not require this adjustment.
Apply a parallax correction using your Nautical Almanac. Parallax is the apparent shift in an object’s position when viewed from different vantage points. The parallax correction varies depending on which celestial body you are observing (such as the sun, moon, or a planet) and the altitude you measured. Check the parallax correction tables on page A2 of your Nautical Almanac and add the correction after adjusting for index error, dip, refraction, and semi-diameter to determine the true altitude of your observed object.
- Parallax accounts for the difference in viewing positions on Earth’s surface compared to viewing from Earth’s center.
- The combination of corrections for parallax, semi-diameter, and refraction is often referred to as the 'third correction.'
- For example, if your sun altitude reading was 38° 10.60’ and you made the following corrections:
- 38° 10.60’ + 1.2’ (index error) = 38° 11.8’
- 38° 11.8’ - 9.16’ (dip) = 38° 2.64’
- 38° 2.64’ - 1.1’ (refraction) = 38° 1.54’
- 38° 1.54’ + 15.9’ (semi-diameter) = 38° 17.44’
- 38° 17.44’ + 0.1’ (parallax) = 38° 17.45’ (true altitude)
Finding Your Latitude in the Daytime
Measure the sun’s angle of elevation at noon. At exactly noon (12:00 PM local time), use your sextant to record the sun’s altitude. The height of the sun at this time will vary based on both your geographic location and the time of year.
- For instance, if you’re standing at the equator during the spring or autumn equinox, the sun will be directly overhead at 90°. If you’re at one of the poles, the sun will be right at the horizon, at 0°.
Tip: The spring and autumn equinoxes generally occur around March 20th and September 23rd. However, the exact date shifts slightly each year. To find the precise dates, check online or consult the Farmer’s Almanac.
Apply corrections for index error, dip, refraction, semi-diameter, and parallax. For an accurate latitude measurement, you must adjust your reading of the sun’s altitude for standard factors. Account for any index error (the discrepancy between the horizon reading and 0°), and apply the dip correction by using the formula 1.7725’ x √ht (with ht being your height above sea level, including eye level). Finally, consult the Nautical Almanac for adjustments regarding refraction, semi-diameter, and parallax.
- Apply the corrections as follows:
- Observed altitude of the sun
- +/- index error (add if negative, subtract if positive)
- - dip
- - refraction
- + semi-diameter
- + parallax
- = true altitude of the sun
Subtract your corrected altitude from 90°. Once you’ve adjusted the sun’s altitude, you need to determine how far it differs from its position at the equator. Use 90° as the starting point, since this is the sun’s altitude at noon during the equinox.
- For example, if your corrected reading is 82° 17.3’, subtract this from 90° to find the difference: 7° 42.7’.
Consult the Nautical Almanac to find the sun’s declination. The declination refers to the sun’s altitude change throughout the year compared to its position at the equinoxes. Depending on the date, the sun will either be higher or lower in the sky. To determine the correct declination, check the tables in your Nautical Almanac for the appropriate date.
- For example, on February 1st, the sun’s declination is 17° 12’ south of the equator.
- The sun reaches its highest declination of 23° north of the equator during the June solstice, and its lowest declination of 23° south during the winter solstice.
Adjust the declination of the sun to determine your latitude. Based on the sun's position relative to the equator, you will either add or subtract the declination from your previous calculation to find your latitude. If the sun is located north of the equator, you add the declination; if it's south, subtract it.
- For example, if after subtracting the sun’s altitude from 90° you get a reading of 7° 42.7’, and it's April 13, the sun is north of the equator with a declination of 8° 54’. Add 7° 42.7’ + 8° 54’ to get a latitude of 16° 36.57°.
Items You’ll Need
- Sextant
- Nautical Almanac (or equivalent tables)
- Map or app with elevation information
- Watch or smartphone
- Pencil and paper to record your readings
