Segmenting an ellipse

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Forum topic by ken_c posted 01-04-2015 04:16 AM 1546 views 0 times favorited 11 replies Add to Favorites Watch
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323 posts in 3158 days

01-04-2015 04:16 AM

OK Lumberjocks here is a tough question, it involves segments of an ellipse. I needed to make an ellipse and I wanted to make it out of segments rather than use an entire panel of maple and my Archimedes trammel. I will use the trammel on the glue up of segments. I was hoping that there was an easy way to calculate 8 segments (2 sets of 4 identical ones). I consulted my “circular work in carpentry and joinery” book but did not find that info. Then Google, but I only found things well above my mathematical understanding. So I resorted to cad, drew it, divided it into 8 segments and measured the angles and lengths of the strait stock needed. That method works but I was hoping to just run some calculations like I do for a segmented circular turning. Has anyone out there got the info needed for the calculation task? Thanks

There are 3 angles, two segment lengths and one width as a result of cad work. in this case 17, 19, 38, 6 13/32, 4 9/16 and 3 1/4…

here is the first stage of the resulting cad work:

11 replies so far

View pjones46's profile


1001 posts in 2639 days

#1 posted 01-04-2015 07:04 AM

To calculate the perimeter of an Ellipse is very difficult as it uses an infinite sum formula. Then to cut it into a specified number of equal parts would be equally as difficult as the lengths between points equally spaced along the perimeter of the curved elliptical surface would equally difficult.

All that being said; there may be an old boat builder trick to approximate the segments which I have no clue if it exists.

-- Respectfully, Paul

View Kelly's profile


2025 posts in 2940 days

#2 posted 01-04-2015 08:15 AM

You can’t just put a circle in it and divide the 360 by eight, then mark them off on the inside and outside?

View pjones46's profile


1001 posts in 2639 days

#3 posted 01-04-2015 08:46 AM


You will not get equal segments as the center of the Ellipse is not equidistant from it’s perimeter.

-- Respectfully, Paul

View AlaskaGuy's profile


4127 posts in 2305 days

#4 posted 01-04-2015 10:52 AM

Why make it harder than it needs to be? If your cad program works why not use it?

-- Alaskan's for Global warming!

View ken_c's profile


323 posts in 3158 days

#5 posted 01-04-2015 12:50 PM

Thanks for the replies.
@kelly – the method you describe give a great octagon.
@Alaska, the reason for the mathematical quest is time and curiosity – CAD is fine and gets the job done but from making segmented rings for round turning I know the math way is faster
@PJ – it is definitely a difficult question and problem – I wish I knew a boat builder…

View hhhopks's profile


651 posts in 2373 days

#6 posted 01-04-2015 01:20 PM

Yes, you should draw it up in CAD. I think it is a lot easier. I happen to have completed a CAD exercise recently similar to your requirement.

You will able to slice it so that only two segments are needed to create the eight pieces. The segment will need to mirrored to create other parts of the ellipse. I doesn’t matter how you slice them (radially, orthgonally & segment length). The hard question really should go back to “how to draw an ellipse?”.

So that works great in CAD, but will the two patterns that you make will allow your to create the pieces with perfect fit? More likely, one or more pieces will have to be “hand” fitted to ensure that there are no gaps and maintain the smooth curves.

I would consider laying the pieces such that the gaps are uniformly spaced and have gap filled.

-- I'll be a woodworker when I grow up. HHHOPKS

View Kelly's profile


2025 posts in 2940 days

#7 posted 01-04-2015 11:29 PM

I was confused as to why you need “two sets of identical ones” for your segments. I presume you are going to still be making forty-fives, rather than a mix match to end up with segments having about the same area, so requiring different angles (e.g., twenty-five degree to thirty degrees, fifty-five to sixty-five and forty-fives).

Why not just make a pattern from card board or paper (like typing sheets taped together). You’d then know about what dimension your boards need to be without producing the waste you [reasonably] were concerned with.

In the end, it shouldn’t be too far off the octagon you posted. Four boards might have to be elongated.

This all presumes you are making more of a frame than a plaque, table top or some other thingamajig.

View Dark_Lightning's profile


3159 posts in 3105 days

#8 posted 01-05-2015 01:03 AM

Another option is to use the cut out portion of the panel for another, smaller ellipse. When I make a large bowl for turning (I have one that is 14” OD, for example), I drill and use the scroll saw or a jig saw to cut out the central “waste” except for the bottom and I make another bowl from the cut out material. I’ve made as many as four bowls from one purchase of wood. Mahogany wasn’t cheap, even in 1974, when I made that particular bowl and its derivatives. I seem to be able to find only two now- the ones I gave to my parents and got back, later.

-- Random Orbital Nailer

View ken_c's profile


323 posts in 3158 days

#9 posted 01-05-2015 02:14 AM

thanks for the thoughts and responses – if I ever do it again I will use CAD again – it worked out just fine and the energy spent doing it that way was less than all the trouble I have caused posting the question.

Thanks again:

View Yonak's profile


986 posts in 1517 days

#10 posted 01-05-2015 05:09 AM

Here’s how I solved it. I had flats at the top, bottom and sides :

View realcowtown_eric's profile


608 posts in 1933 days

#11 posted 01-05-2015 05:34 AM

I;m not suprised that Hodgsons tome would’t have provided the solution, but a simple cabinetmakers elipsograph would have.

Every few years a contractor buddy calls me up and asks me if I still have mine. Borrows it to cut openings for elliptical windows

Cad don’t connect to my bandsaw anyway, but a pencil does and one heck of a lot easier and quicker

Not so hard to make


-- Real_cowtown_eric

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