The mariner’s astrolabe was an instrument used to determine the latitude of a ship at sea by measuring the altitude of the sun at noon or a star of known declination at night (in other words any celestial body above the horizon, measured at its maximum altitude – that is on the meridian through your location). The star or sun declination was then looked up in an almanac. The latitude was given by the formula : (90º- measured altitude) + declination (that is the angle between the equator and sun rays. At the equinox this angle is zero, but it goes up to 23,45º during solstices. It is to find in an almanac for the corresponding altitude depending of the date).
Because it was difficult to know for sure if the sun or star was at it’s maximum altitude at the time of measurement, sailors where usually taking several measurements in order to estimate correct altitude.
Mariner’s astrolabe are thus very inaccurate instruments, and errors between 4 or 5 degrees where common at the time. The base plate is simply a graduated ring in degrees with an alidade on top of it. Holes are pierced on the plate to allow wind to come through and stabilize the instrument while sailing. It is also for stabilization issues that the original astrolabes were made of heavy thick brass.
The upper-left and bottom-right quadrants labels already include the (90º-measured altitude) calculation for simplicity (a dimension called Zenith Distance). The upper-left and bottom-right quadrants are labeled in regular degrees (from 0 to 90) in order to easily estimate the altitude of a standing object on ground.
Moreover, measuring longitude was not possible at the time. Therefore the ship was sailed to a known measured latitude, then moved east or west toward the desired location. The instrument could also be used to estimate the height of a tall object.
To determine current latitude:
- Using the horizon as a point of reference, align the base of the astrolabe by firmly holding the instrument’s handle with your hand.
- If measuring the sun’s altitude at noon, rotate the alidade until its shadow appear between the alidade’s notches. The sun will then be correctly aligned and it’s altitude can be measured. DO NOT look directly at the sun, use its shadow !
- If at night, look toward the point of interest by aiming through the alidade’s notches.
- Perform the (90º- measured altitude) operation, if required.
- Correct this angle by adding the declination value by looking in an almanac.
- Walk from the base of the object until you can aim to its top while maintaining a 45º angle on the astrolabe. Measure this distance (or approximate it by estimating your pace-length).
The height of the object is then given by the distance from it’s base plus the height of your eye from the ground while aiming with the astrolabe.
- If it is not possible to aim to the object with a forced 45º angle, the distance will then be given by the expression: D•Tan(measured angle) + the height of your eyes from the ground, where D is the distance from the base of the object of interest.
Download the full paper here [pdf]. Astrolabe