Circular Arcs with a large radius (5th December 2002)

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In the construction/engineering industry you often need to set-out or mark-out circular arcs, especially for a one-off or new job, until jigs and templates can be made to make the construction process more economical. Examples include sheet metal pattern development, shuttering for reinforced concrete arches, and so on. These skills are highly regarded and very few books document practical techniques. CAD drawings often do not show the dimensions that the tradesman would need build the circular arch. It is common to see the chord length and the centre height of the arc. The radius is often given with CAD drawings but a large radius is almost impossible to layout on the floor of the workshop even with a string trammel. I find it is often necessary to calculate heights to the arc which are square to the chord line. Applying a rectangular co-ordinate system where the chord line is placed parallel to the x axis and the perpendicular heights to the arc lie in the y direction. By knowing only the chord length,c, and the height at the centre of the arc, h, we can calculate the radius,R, and the constant theta.





The above formula then allows us to find the height {h(x)} at any position on the x axis. The full derivation can be found http://www.tyharness.co.uk/gates/arc/carch.htm

Another important part of workshop life is that of making a cutting list so it is often important to know the length of the arc, s is given by



I recently needed the above formula to form an arc on the tops of some iron-work gates and also prepare a cutting list for all the railings. Other example include a 25m radius for a bus station canopy.
Gates
Canopy

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