The backstaff is a navigational instrument that was used to measure the altitude of a celestial body, in particular the Sun or Moon. When observing the Sun, users kept the Sun to their back (hence the name) and observed the shadow cast by the upper vane on a horizon vane. It was invented by the English navigator John Davis, who described it in his book Seaman's Secrets in 1594.
Types of backstaffs
Backstaff is the name given to any instrument that measures the altitude of the sun by the projection of a shadow. It appears that the idea for measuring the sun's altitude using back observations originated with Thomas Harriot. Many types of instruments evolved from the cross-staff that can be classified as backstaffs. Only the Davis quadrant remains dominant in the history of navigation instruments. Indeed, the Davis quadrant is essentially synonymous with backstaff. However, Davis was neither the first nor the last to design such an instrument and others are considered here as well.
Davis quadrant
thumb|Davis quadrant, made in 1765 by Johannes Van Keulen. On display at the [[Musée national de la Marine in Paris.]]
Captain John Davis invented a version of the backstaff in 1594. Davis was a navigator who was quite familiar with the instruments of the day such as the mariner's astrolabe, the quadrant and the cross-staff. He recognized the inherent drawbacks of each and endeavoured to create a new instrument that could reduce those problems and increase the ease and accuracy of obtaining solar elevations.
One early version of the quadrant staff is shown in Figure 1. It had an arc affixed to a staff so that it could slide along the staff (the shape is not critical, though the curved shape was chosen). The arc (A) was placed so that it would cast its shadow on the horizon vane (B). The navigator would look along the staff and observe the horizon through a slit in the horizon vane. By sliding the arc so that the shadow aligned with the horizon, the angle of the sun could be read on the graduated staff. This was a simple quadrant, but it was not as accurate as one might like. The accuracy in the instrument is dependent on the length of the staff, but a long staff made the instrument more unwieldy. The maximum altitude that could be measured with this instrument was 45°.
The next version of his quadrant is shown in Figure 2.
Thus Davis was able to optimize the construction of the quadrant to have both a small and a large arc, allowing the effective accuracy of a single arc quadrant of large radius without making the entire instrument so large. This form of the instrument became synonymous with the backstaff. It was one of the most widely used forms of the backstaff. Continental European navigators called it the English Quadrant.
A later modification of the Davis quadrant was to use a Flamsteed glass in place of the shadow vane; this was suggested by John Flamsteed. This placed a lens on the vane that projected an image of the sun on the horizon vane instead of a shadow. It was useful under conditions where the sky was hazy or lightly overcast; the dim image of the sun was shown more brightly on the horizon vane where a shadow could not be seen.). By setting the shadow vane height, the range of angles that could be measured was set. The transom could be slid along the staff and the angle read from one of the graduated scales on the staff.
The sight vane (C) and horizon vane (B) were aligned visually with the horizon. With the shadow vane's shadow cast on the horizon vane and aligned with the horizon, the angle was determined. In practice, the instrument was accurate but more unwieldy than the Davis quadrant.
Initially, the transom and yard are set so that the two are joined at their respective 45° settings. The instrument is held so that the yard is horizontal (the navigator can view the horizon along the yard to assist in this). The socket is loosened so that the transom is moved vertically until the shadow of the vane is cast at the yard's 90° setting. If the movement of just the transom can accomplish this, the altitude is given by the transom's graduations. If the sun is too high for this, the yard horizontal opening in the socket is loosened and the yard is moved to allow the shadow to land on the 90° mark. The yard then yields the altitude.
It was a fairly accurate instrument, as the graduations were well spaced compared to a conventional cross-staff. However, it was a bit unwieldy and difficult to handle in wind.
Benjamin Cole quadrant
thumb|Figure 7 – Cole quadrant from 1748.
A late addition to the collection of backstaves in the navigation world, this device was invented by Benjamin Cole in 1748.
Cross bow quadrant
thumb|Figure 8 – Drawing of a cross bow quadrant. The 120° arc was graduated as a 90° arc, resulting in divisions that are slightly greater than their nominal arc size.
Edmund Gunter invented the cross bow quadrant, also called the mariner's bow, around 1623.