Sagitta Rule

by Daris A Nevil

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.


 * Sagitta calculator spreadsheet (XLSX)

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.

Note: Paul Havasi pointed out that it is quite easy to set one's printer at a slightly different scale to make things fit, then forget to reset it. You can easily verify that the sagitta rule below prints to the correct scale by measuring the distance for 120' (feet) and validating it is 1.25 inches.

Paul Havasi


 * Sagitta Rule for 10 Foot Rail (PDF)



Use
Using a Sagitta Rule is as simple as following these steps.