Kamal
Among some of the oldest tools used in navigational history is the arabian tool, kamal. The kamal was in its simplest form just a piece of wood and a line of string; however, it was used by Arabian sailors to determine their latitudes. As such, sailors would be able to use knots on the string of the kamal to ‘remember’ specific latitudes. For example, if a specific knot was known to be the latitude of a town, sailors would use the kamal to return to that latitude and then sail directly east/west back to the town. What was particularly useful about the kamal at the time was the ease of use and the fact that it could be used by the illiterate.
To use a kamal, sailors would use their arm to extend the kamal with it being parallel to the ground and with the string also being perpendicular to the string. Often to ensure the string remains taut during measurement, the user may use their teeth to hold onto the knot. If the user was on the latitude that matches the latitude of the knot, the user would find that the Polaris star would fall exactly atop the edge of the kamal. The usage of the kamal is dependent on the mathematics of trigonometry and the relative position of the Polaris star. Fundamentally, the kamal allows for the measurement of latitudes through trigonometry with reference to Polaris and this latitude is stored physically on the rope through the position of the knot.
Astrolabe
The astrolabe is another ancient navigational tool that we decided to research. We found that the mathematics behind this instrument include many more applications beyond navigation.
In ancient Greece, it was a combination of a planisphere (a map of the stars) and a dioptra (an ancient version of a protractor). At this time it was used to calculate time and date using the position of the stars and planets. Hypatica of Alexandra (~400 AD) is sometimes incorrectly credited to their invention, although they were invented at least 3 centuries prior to her birth. She did however teach others how to construct them.
In the 8th century mathematician, Muhammad al-Fazari, created the first astrolabe in the Islamic world. This time period is where astrolabes really took off as a navigation device, as well as an important tool in Islamic religion. In the 10th century astronomer, al-Safi, listed about 1000 different uses of the astrolabe with most applications related to astronomy, astrology, navigation, surveying, when to plant crops, when to raise taxes, rising and falling of tides, timekeeping, prayer, Salat (type of prayer), and Qibla (direction of Mecca).
It has a ring on the top to keep it held directly upright. The largest circle part, called the Mater, in Latin, has all kinds of information, such as zodiacs and times, and keeps the astrolabe together. Within the Mater, are multiple changeable plates that are made for particular latitudes which are often double sided. In the Islamic world plates would often be made for Mecca, Cairo, and Cordoba. On the top would be a map of the stars. Then on the back there would be a straightedge that you would align with the sun, which would then translate into various information. These different parts are highlighted in our rendition of the astrolabe.
References
astrolabe (2018). In James Evans (Ed.), (1st ed.). Oxford University Press.
Bennett, Jim, Navigation: A Very Short Introduction (Oxford, 2017; online edn, Very Short Introductions online, Feb. 2017), http://dx.doi.org/10.1093/actrade/9780198733713.001.0001, accessed 29 Nov. 2021.
Booth, C. (2017). Hypatia: Mathematician, Philosopher, Myth. Fonthill Media.
Ives, R. L. (1961). Navigating with the kamal. Journal of Geography, 60(6), 268. Retrieved from https://www.proquest.com/scholarly-journals/navigating-with-kamal/docview/1290486548/se-2?accountid=14656
Kolev, R. (2013). The babylonian astrolabe: The calendar of creation. Neo-Assyrian Text Corpus Project.
Martin, L. C. (1923). Surveying and navigational instruments from the historical standpoint. Transactions of the Optical Society, 24(5), 289.
Nielbock, M. (2017). Navigating with the Kamal. arXiv preprint arXiv:1710.04482
SciShow. [SciShow]. (2017, February 27). 6 Creative Ways People Used to Navigate the Oceans [Video]. YouTube. https://www.youtube.com/watch?v=2Bv8dc19HQ0&t=145s&ab_channel=SciShow
Staples, E. Indian Ocean navigation in Islamic sources 850–1560 CE. History Compass. 2018; 16:e12485. https://doi.org/10.1111/hic3.12485
The British Museum. [The British Museum]. (2018, June 28). How to use an astrolabe I Curator's Corner S3 Ep1 #CuratorsCorner [Video]. YouTube. https://www.youtube.com/watch?v=N8oWGwcdFmA&ab_channel=TheBritishMuseum
Also the slides we used.
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