Sagitta Rule

From IBLS
Jump to navigation Jump to search
Visualization of the sagitta. The red line marked with s is the sagitta of the arc.

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.

Here are the values provided by the spreadsheet above.

Sagitta Computations for Rail Radius
Rail Length (feet) Radius (feet) Sagitta (inches)
10 30 4.988
10 35 4.278
10 40 3.745
10 45 3.330
10 50 2.998
10 55 2.725
10 60 2.499
10 65 2.307
10 70 2.142
10 75 1.999
10 80 1.874
10 85 1.764
10 90 1.666
10 95 1.579
10 100 1.500
10 105 1.428
10 110 1.363
10 115 1.304
10 120 1.250
20 30 19.815
20 35 17.027
20 40 14.922
20 45 13.279
20 50 11.960
20 55 10.879
20 60 9.977
20 65 9.213
20 70 8.557
20 75 7.988
20 80 7.490
20 85 7.051
20 90 6.660
20 95 6.310
20 100 5.995
20 105 5.710
20 110 5.451
20 115 5.214
20 120 4.997

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

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