SEL formula

[JYALBERT]

Given the notion that the number of segments divided into the circumference of a bowl gives you the Segment Edge Length, I'd like to understand why there's a difference in the SELs in Segment Pro vs a plain calculation. For example: for a 6" 12 segment bowl the formula would be (3.1416 * 6 ) / 12. That, rounded, equals to 1.571", yet the SEL in Segment Pro returns 1.608". Anyone know why that is? Is my "notion" incorrect? I have a attached a .json of a straight walled bowl to test this calculation and I do get 1.608 SEL for the above bowl.

Another question is why did the segments get automatically wider when the outside profile is vertical? And more interestingly, if the SELs for all rings are 1.608 why would the board length be different from one to the next? I have a suspicion it is due to the fact that the segment widths are different which makes the savings in length when flipped at cut time (or using the alternate fence) vary because of the width change... if that made sense. TIA

 

[mfisher]

Given the notion that the number of segments divided into the circumference of a bowl gives you the Segment Edge Length, I'd like to understand why there's a difference in the SELs in Segment Pro vs a plain calculation. For example: for a 6" 12 segment bowl the formula would be (3.1416 * 6 ) / 12. That, rounded, equals to 1.571", yet the SEL in Segment Pro returns 1.608". Anyone know why that is? Is my "notion" incorrect? I have a attached a .json of a straight walled bowl to test this calculation and I do get 1.608 SEL for the above bowl.

You are showing the simple method of calculating SEL. That is SEL = Pi * dia.) / number of segments. For most woodworkers that is close enough.

SP uses the true trig formula of SEL = tan(miter angle) * radius * 2

tangent of 15 degrees is 0.26794919243
radius = 3
0.26794919243 * 3 * 2 = 1.60769514 or rounded to 1.608 per SP.

The slight difference is in what formula is being used.

Another question is why did the segments get automatically wider when the outside profile is vertical?

Because the inside diameter of the ring are not the same between the rings. This is to allow for a transition from the side profile to the bottom of the vessel. If you want the same inside ring diameter you could use WTP.

And more interestingly, if the SELs for all rings are 1.608 why would the board length be different from one to the next? I have a suspicion it is due to the fact that the segment widths are different which makes the savings in length when flipped at cut time (or using the alternate fence) vary because of the width change... if that made sense. TIA

Lloyd would have to address the math on this question.

When I looked at the json file summary sheet the longest was 16.6 board length. Keep in mind that is the minimum. For safety reason I would add about 3.5 inches. making the needed board 20" long. You need a bit extra to safely hold onto the stock while cutting.

 

[JYALBERT]

Thanks, I totally get the Trig function change.

Is WTP WoodTurnerPro? So SegmentPro automatically gives these width to the segments. If so, that's OK, I was just testing the SEL calculation.

Yes on the board length, I would include some length for the kerf and finger protection when I get to the end of the board. And I hope Lloyd will validate/invalidate my suspicion on the width of the board impacting the length of the board. I'd like to understand that formula too...

 

[mfisher]

Thanks, I totally get the Trig function change.

Is WTP WoodTurnerPro? So SegmentPro automatically gives these width to the segments. If so, that's OK, I was just testing the SEL calculation.

Pretty sure WTP uses the same formula. One difference in WTP you can set calculations to the nearest. (1/16th, /1/32, 1/64, imperial inch or metric)
When you use the fraction options it rounds based on your choice. I tend to use the imperial decimal inch in WTP.

Yes on the board length, I would include some length for the kerf and finger protection when I get to the end of the board. And I hope Lloyd will validate/invalidate my suspicion on the width of the board impacting the length of the board. I'd like to understand that formula too...

 

[Lloyd Johnson]

The Segment Edge Length trig formula uses the Outside Diameter, number of segments and the angled saw kerf to determine the OUTSIDE SEL. The difference between the outside diameter and the inside diameter determines the board width. A third formula calculates the INSIDE SEL from the outside SEL, board width and cutting angle. All of these formulas are based on the Unit Circle.

The formula for board length for 12 segments is 6 times the oustside SEL plus 6 times the inside SEL plus 11 times the angled saw kerf. This calculates the exact minimum board length that willl yield 12 segments with zero waste.

So yes, the board width does affect the board length but not in the way you would expect. The narrower the board width, the longer the board must be. It does make sense, though, because the wider the board, the smaller the inside SEL will be.

Both Woodturner PRO and Segment PRO use the exact same formulas.

 

[JYALBERT]

I get the 6 OD SEL + 6 ID SEL as you flip the board or use the second fence. I also get the 11 saw kerf addition. I couldn't get the Segment Pro software to give me a straight sided bowl with a 6" OD and a 6" ID so I couldn't see the base numbers for the hypothetical bowl in the Summary. A couple questions, what is the kerf width being used in the total length calculation. And, why does Segment Pro override my Wall width entry? Try as I might, I would always get an ID in the Summary that would have made the Wall width greater than 1". I managed to force just one ring by making the bowl height less than the Row Thickness. TIA

 

[mfisher]

I get the 6 OD SEL + 6 ID SEL as you flip the board or use the second fence. I also get the 11 saw kerf addition. I couldn't get the Segment Pro software to give me a straight sided bowl with a 6" OD and a 6" ID so I couldn't see the base numbers for the hypothetical bowl in the Summary.

If you have WTP use it. You can build your straight sided bowl.

A couple questions, what is the kerf width being used in the total length calculation.

Yes, saw kerf is taken into consideration when calculating board length. What is not included is a fudge factor for safety.
Saw kerf in STP is 0.125.
In WTP you can input the blade width (kerf) under options.

And, why does Segment Pro override my Wall width entry? Try as I might, I would always get an ID in the Summary that would have made the Wall width greater than 1". I managed to force just one ring by making the bowl height less than the Row Thickness. TIA

Attached is a 3 inch high straight wall plan done in SP. Looks like it can be done with having the taper done on ring 1 the disk.

1" is the max wall thickness in SP.
If you want a larger wall thickness build your vessel in WTP.

 

[Lloyd Johnson]

If you want complete control over the outside and inside wall profile, use Woodturner PRO as it follows your instructions completely. With Segment PRO, the software makes your inside wall profile for you and it does that only with standard segmented bowls so it transitions the lower rows to the base the way a standard bowl would be designed.

But, if you want to use Segment PRO to make a cylinder, just use three dots to make a vertical line at the width you want and set the wall width to whatever you want. Print out the summary and select the row you want as the cylinder and make every ring with the calculations from that row. I’m not going to show it to you on the screen since you don’t need me to.

When you start a new project, determine if you can make it as s standard segmented vessel. If you can, use Segment PRO and if you can’t, use Woodturner PRO. Woodturner PRO is slow and powerful and Segment PRO is fast but restrictive. If I were to start from scratch today, I would build the two programs exactly as they are today.

I won’t be adding additional capabilities to Segment PRO as I’ve run out of real estate on the screen and would have to add additional pages and that would give me two programs that are difficult to use.

Once you spend time with Woodturner PRO, you can get much faster with it, but never as fast as Segment PRO. Having said that, to make a cylinder in Woodturner PRO, add a single row above the base and change the outside diameter of both rows the same number and then set the inside diameter of the segmented row to whatever you want and then start pressing the New Row button until it gets to the height you want and it will display a true cylinder. In less than 20 seconds, you’ll have your project done.

Easy. Peasy.

Lloyd

 

[JYALBERT]

Not that I didn't believe you Lloyd, but I am a visual guy, so I used a a product called Visio and drew up the attached. The reason for my digging into this is that I am building a spreadsheet which will answer the following question: If I have a stick of wood that is "x" inches long, how many segments can I get for a "y" segmented bowl for a ring at "z" outer diameter and "w" inner diameter? Of course, the difference between "z" and "w" has to be less than or equal to the width of my stick of wood.

 

[mfisher]

If you are flipping your stock this is more of what you are calculating . Just remember to add saw kerf + a fudge safety factor.

 

[JYALBERT]

Yup, I ignored the saw kerf in my drawing but it is 1 less than the number of segments times the kerf width. I use 3/32" blades, so .09375. Absolutely on the safety factor, I arbitrarily add a couple inches even if I'm using a clamp to hold that last piece.

 

[Lloyd Johnson]

I also model my calculations using a graphics program but I use SketchUp because it is so much more powerful than Visio. Anytime I make a change to a formula, I test it against two other segment calculators and then I draw a manual rendering using the calculations from my software. That’s why I guarantee that my calculations are 100% correct. There was a time when people would challenge me on calculations and I would take the time (sometimes a LOT of time) to prove my numbers were correct. With my guarantee, I haven’t had to prove my calculations for fifteen years. Now I require the challenger to prove my numbers are wrong. That brings the discussion to a halt immediately. :->

Yours will be an interesting spreadsheet, although I think you’re going to find it to be far harder than you’d like. I take the exact opposite approach. I help you design a bowl and when you’re done, I show you exactly how much wood you will need. Working backwards as you suggest will move the decimal place in terms of difficulty and when you’re done, you’ll still have to design the bowl.

 

[mfisher]

I have used WTP and SP for years. I have never found the board length calculation to be wrong. As far as that goes, have not found the SEL to be wrong.

I have used the export to a spreadsheet when constructing a dizzy bowl. I use the Outside and Inside diameter information to determine which rings I can cut out of a laminate blank.

I pretty much rely on the summary sheet as my guide in the shop. This thread may be of interest to you regarding segment edge length and how to measure.

SEL versus actual blade to stop distance

Have you ever considered adding the actual distance between the blade and the stop used on the saw to get the correct SEL for the angle the of the segment being cut. I have watched many videos of people using the SEL to set the saw stop. This gives a segment that is actually longer than the SEL...

woodturnerpro.com

 

[JYALBERT]

In fact, I was in that thread and have a much better understanding of the SEL being used to set the stop block. I don't measure straight across now, I measure at the angle of the wedge to set the stop block. One way or the other, it really it has a minor effect on the total length of material required or the diameter of the ring created.

Lloyd, in order to dispel the notion that I am "checking" the calculations in SP, rest assured I am only trying to back into them to make my spreadsheet. The purpose being, without having to build a bowl in SP, I can determine the usefulness of a stick of wood for future use. Sometimes, I just make the maximum ring possible and set it aside for inclusion in some project later.

 

[mfisher]

JYalbert
If you have WTP you can use it to build just a single ring. So, if you have some stock and wondering if it is long enough to build the ring. Just enter the dimensions of the ring you want to build. WTP will give you the economy and grain match board length needed.

Years ago I went down the path you seem to be on to build a spreadsheet to do some basic segment ring calculations. Then I discovered Lloyd's software. Now I only use excel for doing bowl from a board calculation.

WTP is my go to software. While you cannot import a SP file into WTP or WTP into SP, I have found it takes very little time to design a bowl in SP. Then using the summary sheet recreate the bowl in WTP. In WTP I can make tweaks to the bowl that SP does not allow you to do. SP has a great paint feature for designing patterns.

Both are very good tools for what they were designed for. Sometimes thinking outside the box allows for more creativity.

 

[mcjayjay]

What your simple math is doing is taking the circumference of circle and divided by the number of segments, in fact when you cut you're using a straight line from corner to corner of your segment which is defined as SEL (Segment Edge Length) which is really called a chord. A chord of a circle is a straight line segment whose endpoints both lie on a circular arc. 12 chords will NOT match 1/12 of a circumference.

 

[JYALBERT]

What your simple math is doing is taking the circumference of circle and divided by the number of segments, in fact when you cut you're using a straight line from corner to corner of your segment which is defined as SEL (Segment Edge Length) which is really called a chord. A chord of a circle is a straight line segment whose endpoints both lie on a circular arc. 12 chords will NOT match 1/12 of a circumference.

True, and as you increase the number of segments (chords), you approach the true aggregate circumference. I'd like to know, based on the number of sides how much should be allotted in the length of the board to cover that error. Then, when turned, that longer segment would result in the desired circumference. I am sure there is a trig formula that would provide that. I have now started using the tangent function, but it too, when doubled only gives you a chord length.

 

[mfisher]

In my experience in cutting segments if I take the board length identified in the Summary sheet of either WTP or SP and add 3 to 5 inches to the total is enough of a safety factor.

I have never found the need to calculate down to the two or three decimal points the board length. Most turners I know build slightly larger rings and turn down to the final diameter. Even if that larger ring is only 1/8 or 1/16th larger. It allows for some forgiveness in the rings not being perfectly centered or round.

Bottom line. the calculations in WTP or SP are more than adequate to know the material needed to build the vessel. One just needs to add whatever fudge factor one is comfortable with in holding/clamping the stock when cutting segments.

 

[mcjayjay]

Like mfisher I teach my students to add about 6" to the economy board length.

Remember , using fractions there is rounding, even if you use 1/32" setting if you use decimal it is more precise but try to measure 1.6345 and you go nuts without even thinking about eyesight tolerance and pencil line thickness.

If you are trying to get to 'surgical' precision you should think of a different hobby.

I have made over 300 bowls and taught over 400 students who in turn made bowls and found WTPro to be superbly accurate 100% of the time.

 

[Ken Sherwin]

"If you are trying to get to 'surgical' precision you should think of a different hobby."
Exactly. Have you noticed there is no cross slide, compound, or leadscrew on a wood lathe? There's just no need for that level of precision. Even if you turned a piece to that level, it's going to change and move next spring anyway.