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Determining angles of rings


Troy D.

Hello folks.

I have a ringmaster, and thought it might be very useful in creating bowls from a board. That is after all what it is designed to do. Unlike mounting a blank on the lathe and using a parting tool or using a bandsaw to cut out parts, the ringmaster is capable of precise angles. It would seem a good companion to segment pro.

If you're making up a standard cone-shaped bowl, there is a linear progression as the angle or slope remains constant, as does the thickness of wood.

Once you start getting into nonstandard or non-cone-shaped bowels, then of course the angle changes. Segment Pro does tell you the starting diameter, and the finished diameter of each ring, so I would think with some trigonometry you should be able to determine the angle.

Admittedly, I'm no computer programmer, and it's been many many years since I've done any trigonometry. Could anyone tell me how to determine the angle of each ring based on the starting and finished diameter, as well as thickness of board?

I would think something could be set up in Excel to do this. I think it would be really nice to see segment Pro add this feature as well. I suspect it won't take more than a few lines of code, but then again maybe it's more involved than I think.

Any help appreciated!


I’ve started on a piece of software to do exactly what you ( and I) want. I’m a long way from finishing it, though. I know it would sell well but I just don’t have the time available to focus on it. Contract programmers are just too expensive right now so that is not an option either.

I have a new jig that works like the ringmaster so I definitely have an interest in doing this.

I wish I had a better answer for you but it is what it is, I’m afraid.

Thanks Lloyd.
I would think there must be a way to do this more simply than creating an entire program for the purpose. Even if the angles were slightly off, it would be a huge timesaver, and material saver.

I've got an email out to Peter from ringmaster, as apparently they've been working on this a bit too. If something could be printed out full-size, the easiest solution of course would be to just measure it right off graph paper. While this is a little tedious, is not as though most of us are running off hundreds of bowls per week.

I'm not sure if any of your programs have the ability to print out a design full-scale? Being able to export into a file format that sketch up would recognize would be great as well, as you could actually measure the angle within the program very accurately.

As I mentioned it's been a while since I've done any trigonometry, but your program does tell you the starting and finish diameter of a ring of any segment if I remember correctly.

Let's say for example you've got a ring that's 6 inches in diameter at its starting point, and 5.5 at its finish point . That's a difference of a half inch, and could also be plugged in as one leg of a right triangle. We also know one other variable, namely the thickness or height of each segment. Now you have two legs of a triangle.

So if the wood thicknesses say a half inch, and the difference between the starting and endpoint is a half inch, we would know that that angle is 45°.

I'm just an average Joe and figured that much out. Surely there must be a way to lay this out in excel with the info segment pro give us? Law of cosines? Too many years for me to remember. I would think this would be child's play for a programmer, but makes my head hurt:)




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I'll do a little more research on how to perform the trigonometry equation, since Lloyd is not responding to that. I know it's really not that difficult. What we need right here is an eighth grade student, instead of us old farts who minds don't remember the stuff!

Segment pro list the outside dimensions of each ring in the segment. The difference between each one of these is what we would need. I earlier said the program list the outside and inside (which it does), but those would be the wrong figures to use to determine the angles.

What we really need to know is the diameter of any given ring at its and point, and then the diameter of the next ring in succession at its end point.

So let's say we have a ring that starts at 6 inches, and the next ring on top of it, end at 6.2 inches. The .2 difference is what we're interested in, combined with the thickness of the piece. That gives us the two variables needed to create an equation to determine the angle. It's nothing more than basic multiplication and division once you know the formula.

This type of information would really be invaluable for people using ring masters. When you start combining this with say quarter inch thickness rings, you could really create a wide variety of shapes with very little turning required on the lathe. Not only a huge timesaver in labor, but material as well.

It looks like Lloyd started on something all the way back in 2014, but as I started out saying, I don't think we need an entire computer program for this. Just a simple Excel spreadsheet would help a lot. I'm sure it would be nice to to have all this information in something like segment pro, it's just going to be a little more work to manually type in the numbers in something like Excel.

I'll do a little research here and I'm sure I can figure out the trigonometry equations. It's really not that difficult I just can't remember the precise formula. If nothing else I'll ask my tenant who's a computer programmer, as I'm sure this would be a joke to him.


Okay, just did a little research. It looks like we need to know the length of the hypotenuse created in order to determine the angle using the law of cosines. So, in short we need to know all three lengths of a right triangle to determine the angle.

So let's go back to my original example:

Let's say we have one ring at 6 inches diameter, and a ring sitting on top of that that is 6 1/2 inches in diameter. Let's also assume that the thickness of the wood is 1/2 inch.

So now we know we've got a right triangle who's one side is a half inch, and one leg is also a half inch, and we need to determine the length or hypotenuse of the right triangle.

We do this using the Pythagorean theorem. Remember from your eighth grade trigonometry that Pythagorean theorem states:

that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The theorem can be written as an equation relating the lengths of the sides a, b and c,

a 2 + b 2 = c 2

So... .5 squared is 0.25 +0.25=0.50 and the square root is .7071

Now using the law of cosines we need to determine the angle created between two stacked rings.

Open the attached file to see the equation, and how we know the angle in this case is 45 degrees.

Here's an online calculator link for doing the math:
Title: Law of Cosines Calculator

Maybe we can persuade Lloyd to make up an Excel spreadsheet for this?

If not, I'll see if I can remember how to set up the formulas in a spreadsheet so people can just type in the numbers and get the results without a lot of complex math.

I have no idea if I did all this correctly , so hopefully somebody with a wee bit more intelligence can jump in here and tell me if I'm on track!


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Troy, looks like a great project and learning experience.
If you are going to follow this all the way thru to a finished bowl, alone with all your learning. I would like to move this over to the Follow Along Projects.
What do you think?
I don't really have any objections, but I think it would be good to leave it listed here as well, with perhaps a link at the end that says the thread is continued in "follow along projects".

Hopefully Lloyd will jump in or somebody else and let me know if I'm on the right track, and also provide something we could use in Excel.

I am definitely not a programmer, just an average Joe, so getting out of my comfort zone for sure.

Troy, I don't think there will be any problem with you getting help with the project.

I'll move it over to Follow Along Project, with a link saying it has been moved.
Okay, I played around with a preliminary Excel spreadsheet program. See attached.



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Just checking in. We had a nice day in Oregon (one of the last, I’m sure) and so I spent the entire day working outside.

Your formula is correct and I encourage you to do whatever you like with Excel. My direction is to provide full-blown solutions with user interfaces. Unfortunately, they are a big effort and I have to have a long time available before I start one. I did talk about this a couple years ago but then decided that SegPro was higher on my priority list.

What I have in mind for Bowl from a Board / Dizzy Bowl is the ability to build the thick blank similar to the Laminate Wizard in Lamination PRO. Next, you will create a wall profile or select one similar to the SegPro Profiles. You’ll also specify the thickness of that blank.

You’ll then select how many slices and the thickness of the slices that are to be cut from the blank. At that point the software will let you know if it is possible to make the profile from the number of slices you select using a standard progression through the slices with no waste. If you can’t it will increase the number of slices until it is possible to build the profile using a ‘waste is OK’ method.

The software will then let you specify the assembly rotation of the rings which can either be static or based on a formula and will then create the turning in 3D so you can see the finished result before ever going into the shop. Once you like the design, the software will print out a template for each slice which will show the location of the cut locations and the angle at which it is to be cut. You’ll be able to specify a RingMaster, Band Saw or Scroll Saw template.

I’ll also make it so that you can create a laminated design in Lamination PRO and use that as the laminated block. You’ll also be able to take a picture of a board you have already created and use that as the laminated blank.

About the only think I won’t be able to do is to allow a blank that has has been assembled by slanted cuts instead of perpendicular strips. Without a ‘solid works’ engine, it simply isn’t possible.

So I’m glad to see what you are doing with Excel but I’m going to keep working on my software design so that as soon as I can get the time, I can work full time on it. Having used SketchUp to fully understand the work flow and being able to start with the User Interface Shell and 3D libraries of Segment PRO, I should be able to dramatically shorten the development time for this new software. At least, I hope that is the case.


What you're proposing sounds absolutely wonderful! I can't wait for its completion! I can also say you first talked about this back in 2014, so I'm not going to get my hopes up, unless you have a proposed release date in mine.

I just realized earlier today that you already have an export feature, so that you can take the planner and look at things in Excel. It doesn't seem like it would be that much more difficult to add a function to include angles to that export. I've been looking a little bit at segmented project planner, and it appears you can specify the ringmaster in that program, and it specifies angles. I can also say the interface is not nearly as eloquent as what you have in segment pro. I still need to watch some tutorials to see what he's offering.

Mostly, just trying to find a way to make the process of visualization and cutting easier. I wish you much success with the program.
I came across another software program yesterday called segmented Pro planner. It doesn't have the 3-D capabilities of segment pro, but it did have a section to convert projects into ringmaster projects. The nicest thing I see is it provides the angles from one ring to the next. Take a look at the screenshot of this bowl I created. I'm still working through the tutorials, but it looks like it shows promise until Lloyd can come up with something better. I have a feeling I'm going to be using a combination of Segment pro to help visualize projects in 3D , and segmented project planner for the actual cut out. I would like to use the ringmaster as much is possible to save time and materials.

If anyone has used this program I welcome your feedback.


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I have the program, forgot about the ringmaster part......sorry. I use segment PRO for most of my stuff, I like the 3D part
I too like the 3-D part of Segment Pro. As I mentioned in the last thread, I may end up using a combination of both programs until Lloyd releases his masterpiece:) It's at least nice there is another program that calculates the angles. Wish I would've found it before I spent half the day doing the math! The program also has a way to design around a photograph, so I think it would be quite possible to create something in Segment pro and do a screenshot of it, and then use that as a basis for a bowl in segment planner. I like the fact too it has a fine-tuning section, so if there's an area that's a little bit too thin, you can easily see it visually and make changes. I'm still watching tutorials and leaning, but it looks promising.


Hi Troy,

I was wondering if you pursued the handing of of Segment Pro designs to Segmented Planner Pro? Seems like an excellent idea to me and I would like to try it.
I have made a few B from a B and set my band saw at 45*. I have seen one other person that changed the angle on their BS. That was Malcolm Tibbets. You can buy his book on Amazon.


I came across another software program yesterday called segmented Pro planner. It doesn't have the 3-D capabilities of segment pro, but it did have a section to convert projects into ringmaster projects. The nicest thing I see is it provides the angles from one ring to the next. Take a look at the screenshot of this bowl I created. I'm still working through the tutorials, but it looks like it shows promise until Lloyd can come up with something better. I have a feeling I'm going to be using a combination of Segment pro to help visualize projects in 3D , and segmented project planner for the actual cut out. I would like to use the ringmaster as much is possible to save time and materials.

If anyone has used this program I welcome your feedback.

Hi Troy.
I have used a ringmaster a few times that our club has to make a bowl from a board. In the image you show from the Segment Planner you probably already know it will take more than one blank (board) to make all the rings. That said, I have used WTP summary sheet which can be imported into excel to sort diameters. I can then assign how many rings I can get out of a blank. I cut out the rings, glue up the blank and finish turning on the lathe. The rings are cut out on a scroll saw. So the side cuts are 90 degrees.
My first bowl from a board project Title: SW Dizzy Bowl

I personally found it to much labor intensive to set up possible different sidewall angles for each ring. The lathe does fine for the final shaping.


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