Sagitta Rule

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Visualization of the sagitta. The red line marked with s is the sagitta of the arc.

From Wikipedia:

In geometry, the sagitta of a circular arc is the distance from the center of the arc to the center of its base. It is used extensively in architecture when calculating the arc necessary to span a certain height and distance.

In Live Steam a Sagitta Rule is used to directly measure the radius of a curved section of track.

Construction

It is easy to construct a Sagitta Rule. Obtain a large paint stir stick (for 5 gallon buckets of paint) from a big box store or where paint is sold. Print the following paper rule. Cut out and tape or glue to the end of the paint stir stick.

Use