Figuring Angles for a Curve....Help! -PICS

[Dennis Peacock]

Greetings,

I'm starting to work on a kitchen table that will have rounded end. The radius of the skirt ARCH is 15" for a total of 30" wide where the arch meets the table legs. I've tried 30º for the 6 pieces that will make up the arch in brick stack form and that doesn't seem to work. I've tried 20º and that gets a little closer but still way off once I get to the other 1/2 of one end.

Each piece is 4" wide.
I need to cut a total of 6 pieces to make up the 180º arch.
The ends closest to the table will have to be at 90º so I can put a tenon on the ends to enable me to insert them into the mortises in each table leg.

I've cut up a LOT of scrap stock trying to figure this out, but how does one figure out the angle AND the length without cutting up 100 board feet of wood just trying to make it all work and fit properly?

Needless to say......I need your HELP!!!!!! :D

[Derek Tuchscherer]

Hey Dennis,

I am not sure about the lengths, still working on that part but your angle, if I understand what you ar doing correct should be 18 degrees. You want to cover 180 degrees with 6 sections, therefore divide the 180 degrees by 5 to get 36 degrees for each joint, then divide this by two to get each side of the joint for 18 degrees. 18 deg X 2 angles/joint X 5 joints = 180 degree coverage.

Probably clear as mud.

Derek

[Derek Tuchscherer]

OK, after some further figuring, I think that each of your sections should be 9.42". The Formula used is Arc Length=pi x R x angle
180

In simpler form 0.01745 x R (15") x angle (36 deg) = 9.423"

I think this should be correct, this would be the long side of each piece.

Derek

[Richard Wolf]

In essense you are only working with 4 pieces because the first two are 90 degrees to the apron. Each joint is 30 degrees so the mitre angle will be 15 degrees. It is always easier if you can lay it out full size.

Richard

[Derek Tuchscherer]

Hi Richard, I see where you are coming from, but to cover 180 degrees that must be the sum of all of your angles, the way you are saying it there would be a total of 10 cuts at 15 degrees for a total of 150 degrees. Or am I way off....Head is starting to hurt now.

[Ralph Barhorst]

Dennis,

According to my calculations each of the six boards should be 7-3/4" long with a 15 degree angle. The problem is that with 6 sides the first and last side will be at 75 degrees from the table leg (90-15). You need it to be 90 degrees for the mortise.

If it were me I would make it with nine boards. Seven of the nine boards would be 5-3/4" long and the two that meet up with the table legs would be 2-7/8" long. The angles would be cut at 11-1/2 degrees. Th 5-3/4" dimension will vary depending on where you measure the radius (inside or outside).

Let me know if you have any questions.

[Dan Barr]

i think there are enough ideas here. its like monkeys and typewriters. one of em' has to be right. :D

Dan

[Derek Tuchscherer]

In essence you are using a portion of a ten sided polygon, 360 degrees divided by ten sides = 36 degrees per angle. And yes this is with two of the angle ending at 90 degrees to the legs. On the picture you would use the six right most or left most sides. Does it make sense now?:D

http://upload.wikimedia.org/wikipedia/commons/thumb/9/90/Decagon.svg/150px-Decagon.svg.png

[Ken Fitzgerald]

Have you folks noticed that Dennis has gone offline........?

[Lee Schierer]

Here is a drawing of what I understand you are trying to do. You would tilt your saw to 15 degrees to make the cuts on each end.

[Dennis Peacock]

Ouch!!!!! I've created quiet a stir now haven't I?? :confused:

I've been tinkering in the shop with these angles some more. I've got a fairly close fit with this:

1st piece - 90º to the table leg and one end cut at 30º
Pieces 2 thru 4 being cut on both ends at 15º
6th piece - 90º to the table leg and one end cut at 30º

I don't remember the actual length of each piece according to the outside dimension, but I believe it's.....just over 7-1/2"??? I don't remember exactly now. I was stressing out more with the angle than the length.

Here's a picture to show what I've gotten done on a Trial & Error routine.

I forgot to add.....

This is a "brick stack" glue up (the stack of pieces on the upper right will stack on top of the previous layer via glue, thus a "brick stack") for cutting the arched skirt for the table top support. Each end will require 36 pieces to make the 4" in height and then bandsawn to form the outside and inside faces for the arch. According to Tod Evans, this is the most solid method for making an arched piece that has No spring-back.

[Dennis Peacock]

Here is a drawing of what I understand you are trying to do. You would tilt your saw to 15 degrees to make the cuts on each end.

Lee,

Excellent drawing you have there. :D
I tried cutting the first piece at 15 degrees but that threw everything outta whack. I tried 30 degrees and that seemed to make it work better.

I'm just checking with everyone here to see if there's a way to do this "close" the first time without cutting 30 - 40 pieces like I just did while cutting, testing, fitting, cutting, testing, fitting, cutting.......well.....you get the picture. ;)

[Dennis Peacock]

OK...I've got the first layer down as you can see in the previous post. Here's a shot of Layer #2 and I'm wondering if it's supposed to be so bad "out" like it is in the pic. :confused: :confused:

Does anybody really understand what I'm trying to do here?
I'm trying to build "up" the thickness in order to bandsaw the 4" tall arched table skirt and a brick stack is the only way I've been told in order to not have to figure out how to deal with "spring-back"....like in steam bending.

Help me out here and tell me if I'm way off base.

[Scott Rongey]

Hi Dennis,

Maybe this will help. I've made the calculations assuming the arch will be 4 inches wide once it is cut out, but I've also tried to show how it can be generalized for other sizes. For the case considered, the odd numbered layers would need 6 pieces 4 7/8 wide and 8.172 inches long on the long side; each end would be cut at 15 degrees. For the even numbered layers, I would use 7 pieces (although the 7th could be a half piece if desired). Imagine glueing up the 7-piece arch and then rotating the whole thing 1/2 a segment so that the joints of one layer are in the middled of the segments of the other layer.

Note, this doesn't have the ends at 90 like your sample. However, the arch will still end up perpendicular at the end so the mortise/tenon would still be at 90 to the face of the edge.

Edit: if you really need the ends to be at 90 degrees in the rough form you can do a few things to this setup:
(1) use a slightly wider piece for the end piece and cut the sides at a 15 degree angle (imagine how you could square up the current end pice by adding triangular pieces to both the inside and outside parts of the arch
(2) using a wider piece, cut the ends at 30 and 0 degrees instead of both at 15 degrees
(3) cut the end piece in half using a 15 degree cut and then there would be another short piece for the 90 end that would be cut at 15 degrees on one end and 0 degrees on the other (similar to option #2 but doesn't require as wide a piece).

Scott

[Alan Turner]

Dennis,
I can't help with the math, but to square the ends of the stack after the glue up, and before or after cutting the arc on the bandsaw, tack a piece of plywood to the glued up stack, and run the edge of the plywood against the fence of the TS. Unless you have a 12" TS, you will probably need to flip it over, cutting the square edge from both sides. Might need to use a tall fence setup. You could cut the length at 15", plus the length of your tenons, and then lower the blade, shorten the plywood by the length of your tenon (being careful with the kerf width to get it right on), and cut the top and bottom tenon shoulders. You could then bandsaw the tenon cheeks, or cut them by hand.

But, you probably already figured all of this out anyway.

Since you can scribe the arc in the stack, make the stach sufficiently wide and long enough, and the angles and lengths will not matter much, esp. if you are veneering the face of the brick stack. If not, you may want the pattern of the joints to be symetrical, at which point the math of the other posters will be of importance.

Good luck, and don't let this get your goat. With all of the long grain glue surfaces, it will be quite strong.

[Dennis Peacock]

Scott and Alan,

Great help there guys. I guess you can tell that this is a learning experience for me and my frustration level is quiet short right now. :o

Funky angles and such as that have never really been my strong point, but now is as good a time as any to get something like this under my belt. :) Besides that? I'm also putting down and learning Gloss Black Lacquer finishing on a customers computer desk all the while I'm trying to get the commissioned kitchen table started!!!! :eek: :eek: :rolleyes:

I like a lot of your ideas Scott and may just tinker with some of those suggestions to night after work. I'll post an update and more pics later tonight. Thank You for all your help.....so far. :D

[Chris Mire]

dennis,
to me, it looks like in that pic that you made the first two cuts on the "straight" pieces 15 degrees like the others, in the first layer these were cut at 30 degrees.

good luck
chris

[Barry Beech]

Dennis,

How wide with the apron be? I understand what you're trying to do, but if the apron will only be 3/4in wide just as long as the joints are tight you will be able to cut off a lot of excess.

Oh, and I agree with Chris. I think your end angles are off.

[Dennis Peacock]

dennis,
to me, it looks like in that pic that you made the first two cuts on the "straight" pieces 15 degrees like the others, in the first layer these were cut at 30 degrees.

good luck
chris

Cuts on the first "straight" pieces are at 30º...all other cuts are at 15º.

[Dennis Peacock]

Dennis,

How wide with the apron be? I understand what you're trying to do, but if the apron will only be 3/4in wide just as long as the joints are tight you will be able to cut off a lot of excess.

Oh, and I agree with Chris. I think your end angles are off.

Apron will be 3/4" Thick by 4" tall...this why it will take 6 layers to make up the "height" of the table skirt.

[Chris Mire]

dennis,

i now see what you are trying to do, and it makes sense now. you are obviously using a different number of sections in each layer, therefore overlapping any joints on each layer. which totally makes sense. i didn't realize that at first. in that respect i think the 2 layers are as close as you can get them for the number of sections you are using.

good luck
chris

[Dennis Peacock]

dennis,

i now see what you are trying to do, and it makes sense now. you are obviously using a different number of sections in each layer, therefore overlapping any joints on each layer. which totally makes sense. i didn't realize that at first. in that respect i think the 2 layers are as close as you can get them for the number of sections you are using.

good luck
chris

Chris,

Thanks. The hardest part for me is figuring out how to cut each piece so that when the material is cut away, I wind up with a 3/4" thick arch that is 4" tall for the actual table skirt. I know there will be a lot of waist on this, but it's the only way I know for now without buying a bunch of stuff to try steam bending for the first time. :eek: Maybe steam bending will come one day when I'm not under the "gun" to get something finished for a customer.

I've already said that I will NOT take on any commission work next year as I'm turning down more work than I care to take, plus I want and need to extend my expertise in woodworking in other areas for now.:D

[Greg Funk]

Dennis,

Unless I am missing something wouldn't it be easier to make the skirt by laminating 4" wide strips of 1/16 to 1/8" thick strips?

Greg

[Dennis Peacock]

Dennis,

Unless I am missing something wouldn't it be easier to make the skirt by laminating 4" wide strips of 1/16 to 1/8" thick strips?

Greg

Easier? Yes....but then you have to calculate how much "spring-back" will be in the glue lamination in order to prevent excess side pressure on the overall table skirt and legs. With a brickstack? There's ZERO spring-back. :)

[Greg Funk]

I guess I'm just lazy but I would laminate the two skirt boards and space the legs according to the glued up skirts. Unless of course you've already built the leg assemblies. In any case I think the one spring-back calculation might be easier than figuring out all the angles for the brick-stack. ;)

Greg

[John Schreiber]

I'm sure you've already got this worked out, but it was in the back of my head and I've been playing with SketchUp a lot so I wanted to try it out.

I didn't read all the posts above, so I based it on a 3" tall apron with three 1" thick layers. It wouldn't be hard to adapt to six 3/4" layers to get a 4" apron.


53156
I figure it would look roughly like that.



53155
That's the parts list for half of what you would need since I was picturing it differently when I was drawing. I also realized I forgot a very important dimension in the drawing above. The width of each piece would be 1 1/2" assuming a 1/8" allowance. I also see I had x-ray view on when I produced that. Sorry about the extra confusing lines.


I can see that others came up with similar solutions, but I had fun doing the drawing and wanted to share. If you'd like the SU file, let me know.