# Making an 8-segment arc while restricting its segment length

I have a given arc chord C=98.695955 mm and I want to create an 8-segment arc on it where each segment’s length is 12.7 mm. How can I do this?

8 times 12,7 gives 101,6? If each vertice needs to be on the mathematical arc, it won’t work.

It works, I just don’t know how to get the radius.
Here’s a visual figure: (WARNING: it’s obviously not to scale because if so, I wouldn’t be asking this question)

A bulge of 10,412931747 will do the trick, but that was with my trial-gonom-error-y

That’s odd, I brute-forced it also ( in meters) and got different numbers. Bulge= 10.4967 and a radius of 121.247801. And the chord length and arc segments worked out.

Without any trig… , just plain SketchUp.
Draw the chord of desired length, draw an arc of 8 segments ontop.
Dimension one segment.
Drag the middle cardinal point out or in and watch the dimension changing.
“In” the ‘Measurements’ field adjust the value (trial and error) till you get the desired segment length,

Don’t click in the ‘Measurements’ field, just type after dragging the cardinal point and [Enter], adjust your value, typing a new value and [Enter] etc.

bulge value incuded:

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I decided to go for the Arc length, also plain SketchUp,(total length should be 8*12.7) by typing the bulge
Why do I get a different result?

Arc length is the same for 8 segments or any number of segments in SketchUp. Itś the real arc length, not the sum of segment lengths. Is that your problem?
I used the ‘Arc’ tool, not the ‘Polygon’ tool.

p.s. see the difference between curve lengths of an arc and a polygon when changing the number of segments.

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I’ve already tried the trial-and-error method, but the radius of the ‘arc’ is so long that the chord length and the segment length may measure the same, but the radius will have discrepancies.

the difference between chord length/segment length and the radius is so large that a 0.0000001 deviation of the former (which SU cannot display) can produce a radius with a possible deviation of at least 5 mm, and I need an exact radius as I’ll be attaching this arc to my model through the radial center point.

My answer nailed it to the results you wanted to 8 digits, granted it was meters. Provided you are willing to accept lines for arcs. And actually the tolerances you seem to be looking for are probably unattainable in the real world. So divide by 1000

I scaled it up so that each segment measures 12700000000.000000 mm, then I scaled it back down.
I achieved a radius of 121.247742 mm, which is tolerantly close enough to yours. (I have a maximum tolerance/deviation of 0.01 mm)

I do wish SU adds additional features to drawing arcs and polygons where you can restrict the segment/side length. Or even at least an extension capable of the same thing.

A classic ‘instinker’ …

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Tig has a plugin Arc By that allows you to specify segment length.

This is a good extension but it has too large tolerances/discrepancies. Maybe refining the unit precision in the plugin will do the job.

I ‘trial and errored’ down the chord length to be 12.700000mm instead of 12.700001mm, (previous image)
In nex image you see this result: the earlier radius (121.247646mm) in red, the new values in green.

In the closeup in next image you see both centers (before and after the change in bulge), and the difference between both centers. This is by far much smaller than 5mm as you say.
The black value (0.000439mm) is just a dummie edge situation to show get a sense of the distance between both center points.
I later managed to get the coordinates of both centers in text (both in different drawing contexts).
It’s all in the range of making it impossible to draw anything this close.

The ‘trial and error’ method is good for a one time solution
And I imagine TIG’s extention will be very useful if it provides this case of construction.
Or a little spreadsheet program to calculate your input would also do if you need to do this often.

How do you dimension the third segment of the arc? I can only dimension the first!

Good question, I could only snap tho the first one also, unless a line was drawn?

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Like this:

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In what manual did you read that?

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