compound angle question

[Robby Phelps]

Hey everybody,

I had a good friend of mine come by today that is a finish carpenter. He ran into a problem with some tapered columns. He couldn't figure out what angle to run on the edges of the panels so that they would miter together. (see drawing below) Wouldn't it still be at 45 degrees? I have been racking my brain with it and i think it should be 45 but he said he tried that and it left a consistant 1/8 gap on the front of all the corners. As soon as he asked the question I immediatly thought of all you fine folks here at SMC and knew that the answer was here. You all are great by the way. Love being a member.

Any help is appreciated though.

[Kirk (KC) Constable]

I'm not smart about this...so I don't understand why...but I believe the tapering sides change the angle somehow. Somebody will post the mathematical explanation, probably in excruciating detail. ;)

KC

[Chris Padilla]

Some claim/swear up and down that the taper causes what one might think is a 45 degree angle to just be off a bit.

I never got the math to work correctly to prove that it ISN'T 45 degrees. Frankly, I just don't see how it couldn't be...that dimension has zero to do with the taper dimensions...they are independent of each other.

I look at it this way:

Make yourself the top view "picture frame" (imagine out of 1/2" material for the sake of argument). You'll agree that they are 45 degree angles I'll guess.

Now make a slightly larger one...then another...then another...then another...stack 'em all up. See where I'm going? You'll end up with a "stepped" pyramid look but guess what, that joining angle inthe Top view is still 45 degrees and it is totally independent of the angle in the side view.

[Kirk (KC) Constable]

I thought the same thing...but try it yourself.

KC

[Shannon Grizzell]

Robby,

The angle of the sides of a piece do change the angle at which a miter has to be cut. I discovered this the same way as your friend - the first time I tried to make a tapered box, I ended up with gaps in the miter joints. :rolleyes:

If you do a google search on compound angles or compound miters, you'll get several sites that have tables with compound angle combinations already calculated for you. There is also an Excel spreadsheet that someone posted on WoodWeb that will calculate the angles based on your inputs. I've tried it and found it pretty confusing to use. I'd stick with a table unless you need some really unusual angles.

If you want to look at the mathematics involved check out this article from the Wolfram Research web site.

http://library.wolfram.com/infocenter/MathSource/5186/

It's in a proprietary "notebook" format, but I think you can download the reader for free. It goes into considerable depth about the geometry of compound angles. If you're like me, it'll either give you a headache, or put you to sleep. :D

Hope that will help you.
Regards
-sg

[Steve Cox]

No it's not a 45. The whole thing is called a "Frustum" or "Frustrum" (both spellings are used). I discovered the the change in angle like everyone else. I cut a 45 and it didn't work. I don't have the answer to fix it either as I used a handplane until it fit the first time and I haven't built one since.

[Lee DeRaud]

Some claim/swear up and down that the taper causes what one might think is a 45 degree angle to just be off a bit.

I never got the math to work correctly to prove that it ISN'T 45 degrees. Frankly, I just don't see how it couldn't be...that dimension has zero to do with the taper dimensions...they are independent of each other.Nope. They're only independent if you measure the bevel angle on a section parallel with the ground (as your "stepped pyramid" does). But the bevel angle is measured perpendicular to the edge, which you are moving as the taper increases.

With the sides vertical, the bevel is 45 degrees. That gets smaller as the sides taper in, until with the sides flat on the ground ("90 degree taper"), the bevel is 0 degrees (straight butt joints). I don't think it's linear (i.e. 1/2 degree less bevel for each added degree of taper), but for moderate tapers that might work as a first approximation.

[Bill Arnold]

Robby,

Try this calculator: http://www.csgnetwork.com/sawmitercalc.html

Although it is setup for a miter saw, you can use the results to set the bevel and taper angles on a table saw. For instance, if the tilt of your assembly is 15* then the saw blade would be set to 43.08* and the taper cut at 14.5*.

Let me know if this works in your application.

Here's a link to a variety of calculators: http://www.1728.com/indexgeo.htm

Regards,

[Lee DeRaud]

If you want to look at the mathematics involved check out this article from the Wolfram Research web site.

http://library.wolfram.com/infocenter/MathSource/5186/
AAARRGH!! Mathematica!! Lisp!! Run away!! Run away!!

Sorry...having a flashback from an earlier phase of my career. :eek:

[Chris Padilla]

Cool! Thanks for the links and explanations...I think I see things a bit differently now but it does mess with one's mind! :D

[Ralph Barhorst]

Robbie,

I have an Excel spreadsheet that calculates the correct angle for the miter guage and the blade tilt. The most important thing to know is the angle between the bottom and the side. On your drawing it appears to be around 70 degrees.

I will email the spreadsheet if you send your address, or you can tell me the angle and I will send the answers to you.

Here is a chart that shows the angles.

[Alan Turner]

Ralph,
I have no immeditae need for this, but would love to have it in my bag of tricks. Would you mind emailing me a copy? Thx.

aturner@alanturnerfurnituremaker.com

[Robby Phelps]

Ralph,

That spreadsheet looks great. Please email it to me if you would @ rpwoodworks@aol.com.

Thanks

[Ken Kimbrell]

You seem to have started something here Ralph!!!:p

Please add me to your list.
ken@mykimbrell.com

Thanks to Robby for posing the question as I will be faced with the same issue about two-three months from now when doing a new front entry.

[Harry Goodwin]

I knew you fellows would ncome up with the chart. I copy and paste stuff on a word document and save it on puter. Years ago this chart was in a delta band saw book. thanks Harry

[Lee DeRaud]

You seem to have started something here Ralph!!!:p

Please add me to your list.
ken@mykimbrell.com

Thanks to Robby for posing the question as I will be faced with the same issue about two-three months from now when doing a new front entry.Uh, you do realize that '.xls' is a perfectly valid attachment file type for this forum?

[Chris Padilla]

Uh, you do realize that '.xls' is a perfectly valid attachment file type for this forum?

I was about to say that...Ralph, just add that spreadsheet here as an attachment much like you would do a picture.

Then you don't have to email it to anyone...they can just right click on it and "Save Target As" for themselves.

Great little spreadsheet you have there...now I gotta delve into the mathematics of this! :eek: :confused:

:D

[Bill Arnold]

Ralph,

Please send me a copy of your spreadsheet. bill@bbarnold.com

Thanks.

[John Hart]

May I have one too Ralph? johnhart@handykraft.com

[Chris Padilla]

bump (bump up my post)

Ralph, please post again and add the spreadsheet as an attachment.

[Lee DeRaud]

bump (bump up my post)

Ralph, please post again and add the spreadsheet as an attachment.I think he got so many requests to email the spreadsheet, he went into Witness Protection to get away. :cool:

[Ralph Barhorst]

I have attached (I think) two spreadsheets. One will do the calculations for any angle and the other is the chart.

I used these when I made some four sided lampshade frames that had stained glass inserted into them by my brother. The formulas work well.


The attachments don't seem to work. Let me know your email address and I will forward them to anyone who wants them.

[Chris Padilla]

Ralph,

For some odd reason, these didn't get attached properly...dunno why...edit your post and try again? Or, email me (click on my name and choose Email Chris Padilla) and I'll reply, and then you can reply to that email with the two files attached.

[Ken Kimbrell]

Thanks for the Email Ralph. :)

[Alan Turner]

Ralph
Thanks so much for the email. If anyone else wants them, and doesn't want to bother Ralph, let me know and I will forward.

This is a wonderful example of why this is a wonderful forum.

[Chris Padilla]

My attempt to post the illustrious spreadsheets! :)

Edit: I've got an email into Aaron asking what's up with attaching these files...I dunno why it isn't working.

[Bill Arnold]

Ralph, thanks for sending the spreadsheets.

All -- Since there's an issue with uploading *.xls files, I placed the spreadsheets on my website so you can download them. Right-click on the link and 'Save Target As'.

http://bbarnold.com/images/compound_angle_cuts.xls

http://bbarnold.com/images/compound_miter_chart.xls

:)

[Chris Padilla]

Excellent, Bill...muchas gracias!

[Bill Arnold]

Excellent, Bill...muchas gracias!De nada, Chris!
:)

[Chris Padilla]

I don't mean to open the "old wound" again but I was watching Woodworks' tapes this weekend (relaxing you know :) ) and I caught Mr. Marks making a pyramidal umbrella stand. According to the show, David simply cut 45 degree angles to mate the 4 tapered edges.

Check out the posted show on DIY network: http://www.diynetwork.com/diy/shows_wwk/episode/0,2046,DIY_14350_26926,00.html

I dunno...just seeing what y'all think about this compund angle stuff.... I would've thought David would've said something if the angles were different than 45 degrees. Man, one of these days I just gotta cut some scrap and see for myself I guess!! :)

[Greg Mann]

I don't mean to open the "old wound" again but I was watching Woodworks' tapes this weekend (relaxing you know :) ) and I caught Mr. Marks making a pyramidal umbrella stand. According to the show, David simply cut 45 degree angles to mate the 4 tapered edges.

Check out the posted show on DIY network: http://www.diynetwork.com/diy/shows_wwk/episode/0,2046,DIY_14350_26926,00.html

I dunno...just seeing what y'all think about this compund angle stuff.... I would've thought David would've said something if the angles were different than 45 degrees. Man, one of these days I just gotta cut some scrap and see for myself I guess!! :)


Chris, This works because David is making the 45 degree miter cuts while the workpiece is still laying on its base surface, not on a surface that will become a side of the pyramid.

Greg

[Chris Padilla]

Chris, This works because David is making the 45 degree miter cuts while the workpiece is still laying on its base surface, not on a surface that will become a side of the pyramid.

Greg

Greg,

Color me clueless here but I really don't follow at all. Near as I can tell, the umbrella stand is simply an inverted pyramid.

Either I don't understand what this whole thread is about or I'm as thick as they come...probably both! :o

[Randy Moore]

Greg,

Color me clueless here but I really don't follow at all. Near as I can tell, the umbrella stand is simply an inverted pyramid.

Either I don't understand what this whole thread is about or I'm as thick as they come...probably both! :o

Chris,
I was no good in math in H.S. some 30+ years back and now this whole thread has me so confused that I am tempted to get the boat out of the garage and go fishing for the day.
I am with you, Chris. It seems the umbrella stand is the same as what would go up on the ceiling. :confused: I guess someday I will get around to trying this.
Thank you Chris for admitting you are you ain't the smartest person in SAWMILL CREEK. Makes me feel a little better.:)
Randy

[Bill Arnold]

... I dunno...just seeing what y'all think about this compund angle stuff.... I would've thought David would've said something if the angles were different than 45 degrees. Man, one of these days I just gotta cut some scrap and see for myself I guess!! :)The actual angle depends on height and tilt. I ran the numbers on the umbrella stand and got these results:
Height: 24 3/4"
Tilt: 8.5* (approximately)
Actual bevel angle: 44.389*

If the bevel is cut to 45* rather than 44.4 (rounded), the outside of the miters will come together first. Under clamping, the slightly over 1* error will be masked or just go away.

Regards,

[Chris Barton]

Very interesting question but, if you consider the gometry of this there is only one correct answer: 45 degrees to the perpidicular plane of cut. If you were to take the pyramid adn bisect it at any point on the perpidicular plane and look at the cross section (as shown to the right in the original post) the points where perpindicular side meet have to be 45 degrees. Now, usually one slightly over cuts the angle so that the outside of the angle will meet closed first. I would expect the error the finish carpenter is having is with less than perfectly precise tools.


Chris

[Richard Wolf]

Chris, your thinking is correct but to cut the angle at 45 degrees you must hold the piece at the taper angle, unsafe and difficult to do. I suggest that people that don't understand this problem, head into your shop and build a tapered box from scrap. Make the taper servre enough that you don't come away with results like David Marks did. Once you do this exercise you will not forget the need for compound angles!
Its exactly like cutting sprung crown molding flat on your miter saw, sure the corners of the room are at 90 degrees, but when setting the compound angles, neither is at 45.

Richard

P.S. To my friend Per; I know, the corners of the room is never at 90 degrees.

[Chris Barton]

Hi Rich,


I agree. When I have done this sort of thing before I have used the tablesaw to cut the tapers and then have used a 45 degree champhoring bit in my router table to cut the angles. Seems to work every time for me.

Chris

[Ralph Barhorst]

Chris, This works because David is making the 45 degree miter cuts while the workpiece is still laying on its base surface, not on a surface that will become a side of the pyramid.

Greg

I saw that episode of Woodworks and Greg is correct.

One way to look at this is to think of three different four sided boxes.

The first box is a simple square box with mitered corners. In this case the sides are square and the blade is tilted at 45 degrees. No compound angles are required.

The second box uses trapezoidial sides with the angles cut at 45 degrees. With the angles cut at 45 degrees you will end up with a flat box with the height being equal to the thickness of the material. The blade does not get tilted at all (0 degrees).

The third box is half way between the first two. The 2 dimensional side view of this 3 dimensional box shows that the angle of the trapezoid is 45 degrees. However the sides cannot be cut at 45 degrees since the side is also tilted in toward the center of the box. The actual cut would be 54.74 degrees (table saw miter guage setting) with the blade tilted 30 degrees. See the chart that I posted earlier in this thread.

[Keith Christopher]

Well here is my go at illustrating this. I didn't taper the whole thing as I felt it was a more dramatic view this way

[lou sansone]

here is an example of the compound miter in action

http://www.sawmillcreek.org/showthread.php?t=18743

lou

[Carl Eyman]

Yeah, still beautiful, but how did you finish it?

[lou sansone]

Yeah, still beautiful, but how did you finish it?

here is what I have found to work for curly maple, after lots of experimentation - You have to have decent maple or else the rest is not worth a hill of beans.

I call this my "double dye process" I am not sure that I have ever seen anyone else use this exact method, but for all I know every one does but will not tell anyone how they do it.

1. sand to 220 grit
2. use a water base aniline dye - I use a mixture of honey amber maple and pilgram maple. mix to suit your taste. I think darker is better than lighter on the color. I make my dye the strength of very very strong tea. I always wear rubber gloves because it will stain your fingers brown.
3. brush on the dye. lots of it. rub it into the wood with a rag.
4. let it dry overnight
5. sand to get rid of the raised grain. Do not sand off the dye. Some folks do that, but I do not. I also do not play games with using different color dyes and sanding them back. If you have decent wood and the right base color the wood will do the work and not the chemistry lab.
6. brush on the dye again- same strength or possibly a little weaker or stronger depending on the first try
7. let it dry overnight
8. coat the whole piece with BLO thinned with turps or mineral spirits- soak it on and if you want you can use a sanding sponge and make gravy with the dust and BLO. Be carefull here - use super fine sponges
9. wipe off the excess
10. let it dry a few days
11. put 1 or 2 coats of orange or garnet shellac 1/2 lb cut on with a brush and sand between coats carefully - this is where you can ruin the piece by sanding through the dye
12. top coat with what ever you like - tung oil, poly soup mixture, more shellac- but use super blond , nitro lacquer, ....
13 put a few coats on of the top coat until you like the build
14. let the finish set a week
15. rub it out with 0000 steel wool and wax or what ever else you like to rub stuff out with
16. make a nice pot of coffee and sit and look at your piece for a while - think nice thoughts and all of that rot.
17. post a picture for us to look at on SMC