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Calculating ring segment lengths

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Forum topic by Jack Lewis posted 08-20-2016 06:40 PM 397 views 0 times favorited 7 replies Add to Favorites Watch
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Jack Lewis

78 posts in 546 days


08-20-2016 06:40 PM

I have had success cutting ring segments using Deltacad and brute force measuring. Mainly I drew a circle, cutting it into segments and measuring between the angles for the circle diameter. I then calculated for a “constant” value for each angle and used it in a simple spreadsheet formula of (“constant” times radius of ring equals segment length). This solved many ring values simply by entering ring radius for each ring. I developed a cut sheet with starting material length, segment length, length of required stock for each ring and bd. ft. of each ring including 10% waste. I can use the same basic spread sheet for any size segmented project.

BUT, a very big but, also being a many years in the past math major, I wanted to do the same with math as I did with CAD and spreadsheet doing the calcs. I want use a spreadsheet formula for finding the chord (segment length) of the ring diameter instead of my “constant”. I use Works spreadsheet. My spreadsheet formula is [=sum(2rad(sin{angle/2}))] where rad is one cell and sin{angle/2} is another.

From a web search I got [Chord length=2rsin(c/2) where “c” is central angle]

Anyone have any ideas to help me out?

-- "Now we are getting no where, thanks to me"


7 replies so far

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TheDane

4997 posts in 3130 days


#1 posted 08-20-2016 07:19 PM

Jack … I played with this myself in Excel … never getting the right result.

Then I stumbled onto Woodturner Pro ( http://woodturnerpro.com/ ) and haven’t looked back. It was a little pricey, but when you consider the advantages it has, it was worth it (to me).

-- Gerry -- "I don't plan to ever really grow up ... I'm just going to learn how to act in public!"

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Jack Lewis

78 posts in 546 days


#2 posted 08-20-2016 08:51 PM



Jack … I played with this myself in Excel … never getting the right result.

Then I stumbled onto Woodturner Pro ( http://woodturnerpro.com/ ) and haven t looked back. It was a little pricey, but when you consider the advantages it has, it was worth it (to me).

- TheDane


Don’t get me wrong, and I agree Woodturner Pro is fine, I was just wrestling with the math method rather than brute force method. My DeltaCad and SS program produce very fine results that I believe has been shown with the pics uploaded here. Again, I was asking for a way to incorporate a different formula using

IAW trig math.

-- "Now we are getting no where, thanks to me"

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HapHazzard

92 posts in 335 days


#3 posted 08-21-2016 03:42 AM

Your formula looks right, except I don’t think you need the sum(), and spreadsheets usually use “[asterisk]” for multiplication, but I’m not sure what syntax your spreadsheet uses.In Excel it’d be 2[asterisk]rad[asterisk]sin(angle/2). Functions in Excel use parentheses for their arguments.

In mathspeak it would be c = 2r·sin(θ/2), or “two times the radius times the sine of half the angle.”

Note: Apparently this forum uses asterisks for bold text and bulleted lists. They don’t say what you’re supposed to use for asterisks; that’s why I’m using “[asterisk].”

-- Unix programmers never die; they just > /dev/null

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lew

11348 posts in 3223 days


#4 posted 08-21-2016 04:36 PM

Just in case you haven’t seen this, I’m not sure it will help—
http://www.woodturnersresource.com/extras/projects/segmentcalc/index.html

-- Lew- Time traveler. Purveyor of the Universe's finest custom rolling pins.

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Woodmaster1

738 posts in 2054 days


#5 posted 08-21-2016 08:06 PM

I have a sheet made up for the woodworking club it goes to segment rings bigger than I ever intend to make.

View JBrow's profile

JBrow

819 posts in 387 days


#6 posted 08-22-2016 01:49 AM

Jack Lewis,

I am not exactly sure what ideas you are looking for but since you are looking for formulas on the web I assume it is a set of equations. If in fact you are seeking math equations to determine the inside and outside length of the segments and the formula for determining board feet after applying an allowance for scrape, here is what I came up with. However, since I am like you with my math being pretty rusty, independently deriving or empirically verifying might be a good idea…

I assume you are able to program these formulas in Works. It has been a long time since I used Works, but from what I recall it is similar to Excel.

View OSU55's profile

OSU55

1063 posts in 1457 days


#7 posted 08-22-2016 11:54 AM

When I got into segmented turning I started to find all the equations and build my own spreadsheet, until I found Segmented Project Planner. For $37 it did all the calcs and gave renderings of the project, and is easy to change or update the project. It was just too easy to pass up. Along the lines of “make or buy” discussions about tools, jigs, etc., this was a definite “buy” for me vs make.

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