I posted a question a couple months ago about framing cross vaults. Does anyone know if when laying out cross vault all arches need to be elliptical?
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Check out this link http://forums.jlconline.com/forums/showthread.php?t=27721&highlight=Groin
and Prof. Bartok should be around soon :-)
Groin Vault Math
The geometry and numbers say that a groin vault may be based on any conic section. I don't know about calculating other curves such as cycloids, sinusoids, catenaries, etc. The safest way to determine the Valley curve in these cases would be by projection.
The vault barrels may be segmented (parts of the ellipse) or the full semi-ellipse. In either event, always start by solving the dimensions of one barrel and base the Valley and remaining barrel measurements on those of the first barrel.
You cannot "mix" different types curves. The barrels must all be ellipses (combinations of circles and ellipses are O.K., since a circle is a special case of the ellipse), or all parabolas, or all hyperbolas.
Joe Bartok
Edited 4/18/2007 10:36 am ET by JoeBartok