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The collinearity equations as a helpful tool in the design and construction of sundials

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Abstract In the past, designing sundials implied graphical procedures which, though ingenious, were in general cumbersome and time-consuming. Difficulties increased even more if, instead of solar time, civil time was required. For positions of the dial plate other than the classical horizontal and vertical, these procedures became extremely complicated. By applying the collinearity equations familiar in photogrammetry, this problem is greatly simplified and computer programs can be readily written for any position of the dial plate. Some examples of sundials telling the official time of a country are shown.


La conception de cadrans solaires exigeait autrefois des procédures graphiques ingénieuses certes, mais complexes et laborieuses. Les difficultés étaient encore plus grandes si, au lieu du temps solaire, on demandait le temps solaire moyen. Pour des positions du plan du cadran autres que les classiques horizontale et verticale, ces procédés devenaient extrêmement complexes. En appliquant les équations de colinéarité, bien connues en photogrammétrie, on simplifie considérablement le problème, et on peut facilement écrire un programme d’ordinateur pour n’importe quelle position du plan du cadran. Quelques exemples de cadrans solaires donnant l’heure légale d’un pays sont présentés.

Keywords: civil time; collinearity equations; computation and plotting of dial plates; placement of gnomon; sundial design

Document Type: Research Article


Publication date: 2011-03-01

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