Abstract
The aim of this paper is to examine the extent to which detailed empirical analysis of the metrology and proportional systems used in the design of Irish ecclesiastical architecture can be analysed to provide historical information not otherwise available. Focussing on a relatively limited sample of window tracery designs as a case study, it will first set out to establish what, if any, systems were in use, and then what light these might shed on the background, training and work practices of the masons, and, by association, the patrons responsible for employing them.
First published as: Avril Behan and Rachel Moss , “Metrology and Proportion in the Ecclesiastical Architecture of Medieval Ireland”, pp. 171–183 in Nexus VII: Architecture and Mathematics, Kim Williams, ed. Turin: Kim Williams Books, 2008.
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Notes
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The original manuscript text of the law is in Trinity College Dublin MS H.3.17. The most comprehensive of the texts is in Long (1996: 141–164).
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Other options include terrestrial laser scanning and discrete point/line measurement using a reflectorless total station. The total station option was rejected because the required field time was prohibitive for the number of sites being visited for the ongoing project. Terrestrial laser scanning was not used due to the unavailability of equipment, because there would be no gain in accuracy, and because significantly more field time would be required without a commensurate reduction in processing time.
- 5.
Photogrammetry is the science of generating measurements from imagery. Stereo photogrammetry uses two photographs captured and viewed in a simulation of the way human eyes achieve depth perception from offset images.
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This is to be compared with the results of terrestrial laser scanning, which although usually accompanied by supporting photographs, requires a detailed understanding of the handling of point clouds (set of 3D points) to ensure the best results.
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Suitable digital cameras cost between €500 and €1,000; reflectorless total stations of sufficient accuracy cost about €12,000. This is still inexpensive when compared to a terrestrial laser scanner price of more than €80,000.
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The reflectorless total station generates a 3D coordinate for any point, identified by the operator with the crosshairs of a telescope, using horizontal and vertical angle measurements and a distance measured using a time-of-flight laser. The calculation is based on trigonometric formulae and is a standard surveying technique.
- 9.
This level of redundancy was required mainly because the chosen control points were naturally occurring (e.g., sharp corners on stonework or patterns caused by lichens) or pre-existing features (e.g., screws holding protective grilles or metal bars used to prevent unauthorised entry to sites). To generate the highest accuracy photogrammetric products it is advisable to use man-made targets (typically plastic cards or reflective stickers) but these could not be used in this survey because of the delicate nature of some of the sites (and the potential damage that the targets might cause) and the inaccessibility of the features (lifting or hoisting equipment could not have been used in many of the locations because of issues of topography and the position of the features in very close proximity to modern graves). The extra points enabled detailed accuracy checking after the modelling procedure.
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This is a Computer Aided Drafting package with a number of enhancements for the better handling of survey generated data and the manipulation and visualisation of three-dimensional models.
- 11.
Image matching involves automatically checking the levels of similarity between pixels in the overlapping images to find the best correspondence. Once identikit pixels have been found, a space intersection can be carried out using the orientation information previously calculated from the control information to generate a 3D coordinate for the matched point.
- 12.
While image-matching techniques are relatively robust the LPS software was primarily designed for aerial photogrammetric work and, thus, needs operator input to ensure the highest quality of the resultant 3D model.
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- 14.
<3, <2 and <1Â mm respectively: It is acknowledged that this level of accuracy is not possible from the original measurement method but the results are analysed here relative to the other measurements in the group, rather than in their absolute form.
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Behan, A., Moss, R. (2015). Metrology and Proportion in the Ecclesiastical Architecture of Medieval Ireland. In: Williams, K., Ostwald, M. (eds) Architecture and Mathematics from Antiquity to the Future. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-00137-1_30
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