Sagitta Rule: Difference between revisions
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[[Category:Definitions]] | [[Category:Definitions]] | ||
[[File:Sagitta.svg|thumb|right|300px|Visualization of the sagitta. The red line marked with <i>s</i> is the sagitta of the arc.]] | [[File:Sagitta.svg|thumb|right|300px|Visualization of the sagitta. The red line marked with <i>s</i> is the sagitta of the arc.]] | ||
by [[Daris A Nevil]] | |||
[https://en.wikipedia.org/wiki/Sagitta_(geometry) From <i>Wikipedia</i>]: | [https://en.wikipedia.org/wiki/Sagitta_(geometry) From <i>Wikipedia</i>]: | ||
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In Live Steam a [[Sagitta Rule]] is used to directly measure the radius of a curved section of track. | In Live Steam a [[Sagitta Rule]] is used to directly measure the radius of a curved section of track. | ||
See also [[Rail bender]]. | |||
== Calculating == | == Calculating == | ||
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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. | 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. | |||
* [http://ibls.org/files/2020/CharlesField_TrackPanelJig/150_Sagitta_Rule_for_10_Foot_Rail.pdf Sagitta Rule for 10 Foot Rail (PDF)] | * [http://ibls.org/files/2020/CharlesField_TrackPanelJig/150_Sagitta_Rule_for_10_Foot_Rail.pdf Sagitta Rule for 10 Foot Rail (PDF)] | ||
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== Use == | == Use == | ||
Using a [[Sagitta Rule]] is as simple as following these steps. | |||
<gallery widths=300px heights=300px perrow=2> | |||
File:2020-12-03 10.42.26.jpg|Step 1: Place the ends of the rail against a wall or other straight edge. Place the Sagitta Rule at the midpoint of the rail, where the distance from the wall is greatest. | |||
File:2020-12-03 10.42.41.jpg|Step 2: Read the radius of the rail from the Sagitta Rule. In this photo the rail has a curve approximating a 50 foot radius. | |||
</gallery> |
Latest revision as of 12:38, 15 November 2021
- 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.
See also Rail bender.
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.
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.
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.
Use
Using a Sagitta Rule is as simple as following these steps.