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.

Calculating

The following spreadsheet is provided to calculate the sagitta value for different radius curves for 10 foot and 20 foot rail lengths.

Here are the values provided by the spreadsheet above.

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.

A sagitta rule for directly measuring the radius of 10 foot sections of rail.

Use