Tuesday, June 22, 2010

The Navigational Cross-Staff

For over 20 years I have been heavy into historical re-creation and research. The following piece details the construction and testing of a navigational cross-staff that I entered into an SCA Arts and Sciences competition years ago.
Period/Culture: The navigational cross-staff, sometimes called the forestaff, was first developed in the fifteenth century. The cross-staff was initially used by astronomers as early as the ancient Greeks to measure the angles between celestial bodies. A German mathematician named Martin Behaim is credited with first using this instrument as a navigational tool while sailing with the Portuguese explorer Diogo Cao on his voyages down the coast of Africa in 1485. The cross-staff was used by every seafaring culture in western Europe. It did not fall completely out of use as a navigator's tool until the late eighteenth century.

The cross-staff consisted of a square-cut wooden staff, 30 - 36 inches in length. Affixed to this at a right angle was a much shorter cross-piece that could run smoothly up and down the main staff. The cross-staff is used by placing one end on your cheek just under your strong eye and moving the cross-piece until it is in a position that just spans the distance between the heavenly body you are taking a sighting of (generally the north star or the sun) and the horizon. The ratio between one-half of the cross-piece length and its distance along the staff from your eye defines one-half of the angle of elevation for the object observed. The staff is graduated in such a way that you read the full value of the angle you require.
The cross-staff has many different names. The early Portuguese and Spanish ship's pilots were taught to aim this instrument towards the sky like a cross-bowman. Thus they called it a 'balestilja' or cross-bow. The later invention of another navigational instrument called the back-staff led to the name cross-staff fading out of use. The instrument then became known as the forestaff because you faced forward to use it. To use the back-staff you put your back toward the heavenly body that you wish to take your reading from.

Wider use of the cross-staff led to many changes in its basic form. Fairly quickly sailors realized that the closer you came to the equator the less useful the cross-staff became due to the fact that the single cross-piece was too large to be used at lower latitudes. This was because you could never move the single cross-piece to any location that did not block the north star if you lined the bottom up with the horizon line. This problem was solved in the sixteenth century by the addition of 3 smaller cross-pieces for use at lower latitudes. Another innovation came about from the same problem. In the sixteenth century latitude could be determined by applying simple mathematics to readings of the sun at noon. The pilots had in their rutters a list of the solar zenith distance as computed by astronomers. The zenith distance minus the declination reading taken with the cross-staff equalled the latitude. This innovation added to some cross-staves smoked lenses at the ends of the cross-pieces so that the sun would be less blinding to the pilot and he would be able to take a better reading.

Compared to modern methods of navigation the cross-staff is, of course, laughable. In period however, the instruments in the hands of a trained pilot often provided accuracy to within less than 1 degree.

Period Materials and Methods: In period the cross-staff was usually constructed out of hardwood. They were often constructed of oak, rosewood, or ebony. The construction methods were quite simple. Some cross-staves were constructed by simply tying the cross piece to the staff in a manner allowing the cross piece to slide. Finer examples had cross pieces that slipped over the end of the staff. In late period use, smoked glass was added to ends of the cross piece to ease the strain on the eye when taking solar sightings. The method for making the angle markings involved using a protractor to measure angles and drawing lines from the angles into a rectangle whose size was determined by the staff and the cross piece used with it. This method is the one I used and it is explained more fully below. The length of the cross pieces developed as needed and were simply a matter of record among period ship's pilots. The markings along the staff were carved into the wood and inked or painted.

My Materials and Methods: I attempted to duplicate as closely as possible known period materials and methods. My cross-staff is constructed of red oak. The cross pieces are held together with brass wood screws. The markings were made originally with pencil and then engraved and marked with a wood burner. My cross piece lengths were taken from the book Latitude Hooks and Azimuth Rings. My angle measurements were deduced using the period method explained below.

How I Constructed the Cross-staff: I cut the main staff to a length of three feet. I cut the cross pieces as described in the table below:

Latitude in Degrees Finished Cross Piece Length Cross Piece Cuts for Construction

0 - 10 2 inches 2 @ 5/8 "

10 - 20 4 inches 2 @ 1 5/8"

20 - 30 6 inches 2 @ 2 5/8"

30 - 40 8 inches 2 @ 3 5/8"

The cross piece cuts for construction had to account for the 3/4" thickness of the main staff to reach the finished cross piece length measurements.

The cross pieces were assembled on the main staff by using 1/4" x 3/4" pieces of oak at lengths to bridge the distance of the main staff. After the cross pieces were assembled I sanded the main staff to make them slide easier up and down the staff.

The angle measurements were determined graphically by using 4 pieces of poster board and a protractor. A series of rectangles were laid out on the poster board matching the size of the staff with the various cross pieces. Thus there were four rectangles (2" x 36", 4" x 36", 6" x 36", and 8" x 36") on four different poster boards all divided down their center line. The protractor was taped in place just inside the defined rectangle and radial lines were drawn from each side. The radials were connected with lines that crossed the center line and were perpendicular to it. These lines show where on the staff a certain angle marking should be located. For example, radial lines drawn through the 50 degree mark on each side of the protractor define an angle of 80 degrees or twice the difference between 90 degrees and 50 degrees.

Next, the main staff was made square along the center line and the markings were made with pencil. This technique was repeated with all of the poster boards using a different side to mark the angles each time. Next, the inch measurement scale to 1/4" marks were added on the 0 - 10 edge. Finally, the marks were etched with a hot iron to burn them into the wood.

How I Tested my Cross-Staff: In period a cross-staff was used for three basic tasks relating to navigation: 1) It was used to take readings from the pole star and the sun to determine the latitude of the ship; 2) It was used to measure the distance away from an object given that the height or length of that object was known; 3) It was used as a straight edge for plotting a course on a chart. After finishing my cross-staff I decided to test it against the first two of the three tasks listed above. I believe its usefulness as a straight edge is apparent.

For the first test I quickly discovered that I could not properly test the instrument because it is designed to be used on the open sea where a horizon line is evident. I live in the middle of a modern city and could not find an open horizon to properly test the instrument. However, my luck changed once I reached Lumberton Mississippi, the site for Gulf Wars. On a clear night I was easily able to find the north star and I proceeded to take six readings, three from the 20 - 30 degree scale and three from the 30 - 40 degree scale. My first three readings were 32 degrees, 31.5 degrees, and 33 degrees. My second three readings were 31.5 degrees, 32 degrees, and 31.5 degrees. Unfortunately, all I could do at the time was record this information for later because I did not know the real latitude for Lumberton. Later in the week, during a class on Elizabethan Shipboard Life taught by William MacArthur, the Meridies Patron for the Known World Nautical Guild, he had his wife demonstrate the use of the cross-staff. She had researched the latitude of Lumberton Mississsippi for her demonstration. It is 31.60 degrees.

For the second test I measured the height of a fence in my subdivision that I could see from some distance. The height of the fence was 66". I walked some distance away and used the cross-staff with its 4" crosspiece to determine a measurement on the staff of 25 1/2". By applying the trigonometric relationship between the cross-staff and the 90 degree angle between the ground and the known wall height (A:B = C:D), I was able to determine my distance from the wall. The calculation worked out to be 34.72 feet. I then measured with a tape measure to determine the true distance. It was 34' 7 3/8" or 34.61 feet. Two other measurements from the same location produced results of 34.59 feet and 34.79 feet. The average of these results was 34.66 feet.


Cameron, Ian. Magellan and the First Circumnavigation of the World. New York: Saturday Review Press, 1973.

Davis, John. The Seaman's Secrets (December 21, 2000)

Fisher, Dennis. Latitude Hooks and Azimuth Rings. Camden, Maine: International Marine, 1995

Johansen, Jan. The History of Navigation. (February 25, 2001)

Phillips-Birt, Douglas. A History of Seamanship. New York: Doubleday, 1971.

Taylor, E.G.R. & Richey, M.W. The Geometrical Seaman. London: Hollis and Carter, Ltd, 1962.

Copyright 2001, Mark S. Cookman

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