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John Lock
07-06-2004, 12:02 PM
I've been asked to build a new stand to hold flowers in celebration of misc events at my church. In order to match the existing furniture the piece needs to taper from 5 1/2" wide at the top to 4 1/2 " at the base (height of 11 1/2 "). I made a jig for cutting the tapers but cutting the mitres so the pieces form a square has gotten me lost. Normally, making a box is a basic 45' angle, but the taper has me worried that 45 would cause problems with getting the pieces to fit correctly. Any suggestions on the best way to cut these on a table saw?

RANDY PAULK
07-06-2004, 12:48 PM
The Angle Will Still Be 45 Degrees. You Don't Have To Worry About The Taper.

Chris Padilla
07-06-2004, 1:11 PM
Jack,

You have two angles to cut:

The 45 degree one is the easy one to calculate. A 10 or 12" sliding compund miter saw will make your life easier but let's assume you don't have one.

To calculate the second angle, you need to make up a right triangle that is 11.5" tall by (5.5 - 4.5) 1" wide. This triangle will yield two angles:

arctan (11.5) = 85.03 degrees
arctan (1/11.5) = 4.97 degrees

Notice they add up to 90 degrees as they should. :)

Tilt your TS to 45 degrees and then make a jig or use your miter gauge to cut at 5 degrees

Todd Burch
07-06-2004, 1:56 PM
John, you do have to worry about the angles, as it is not 45°, but a tad bit less.

These are what are called dihedral angles. I made a cradle several years ago, and some trash cans since that were all tapered sides.

Sorry I can't offer the formula, but an internet search will probably produce results.

Chris Padilla
07-06-2004, 2:41 PM
Todd,

I beg to differ. One of the angles will be precisely 45 degrees. You are joining 4 pieces to form a box.

Now we flare the box out slightly. That first 45 degrees still remains the same because you aren't changing this dimension of the box...it is still a square if you look at it from above. Now look at it from the side as you taper it out you'll see another angle changing but this doesn't impact the other one...it still must be at 45 degrees.

It is like joining crown moulding in a corner that is perfectly orthogonal. One cut will be precisely 45 degrees but the other one depends on the dimensions of the crown molding--how far it is away from the wall and ceiling where it meets.

These two angles are independent of each other...one doesn't affect the other.

John Lock
07-06-2004, 4:25 PM
Todd,

I beg to differ. One of the angles will be precisely 45 degrees. You are joining 4 pieces to form a box.

Now we flare the box out slightly. That first 45 degrees still remains the same because you aren't changing this dimension of the box...it is still a square if you look at it from above. Now look at it from the side as you taper it out you'll see another angle changing but this doesn't impact the other one...it still must be at 45 degrees.

It is like joining crown moulding in a corner that is perfectly orthogonal. One cut will be precisely 45 degrees but the other one depends on the dimensions of the crown molding--how far it is away from the wall and ceiling where it meets.

These two angles are independent of each other...one doesn't affect the other.

I have to agree with Todd on this one. If you think of the 2 corner pieces of your box, then draw the bottoms in, the interior side of the boxes will rotate updward and the bevel edges converge. That's why I'm having trouble with the angles. I tried it with a straight 45 cut (4 pieces of scrap for another day), and found that the sides won't match up.

John Lock
07-06-2004, 4:27 PM
Jack,

You have two angles to cut:

The 45 degree one is the easy one to calculate. A 10 or 12" sliding compund miter saw will make your life easier but let's assume you don't have one.

To calculate the second angle, you need to make up a right triangle that is 11.5" tall by (5.5 - 4.5) 1" wide. This triangle will yield two angles:

arctan (11.5) = 85.03 degrees
arctan (1/11.5) = 4.97 degrees

Notice they add up to 90 degrees as they should. :)

Tilt your TS to 45 degrees and then make a jig or use your miter gauge to cut at 5 degrees

Chris, are you sure about the 1" wide triangle? If the top is 5.5 and the top 4.5 centered to the top, shouldn't that be a triangle with a 1/2" x 11.5"? That gives me my exterior taper, but the interior corner angles are what is giving me the most trouble.

BTW, how did you know my nickname is Jack?

Chris Padilla
07-06-2004, 5:14 PM
John, I didn't...dumb luck mistake on my part using Jack for some reason! :)

You are right about the 1/2"...my bad. However, if you have a jig for the taper already built then this part is fine.

You are basically bulding a pyramid with the top lopped off and then inverted.

Think about the pyramids in Egypt and the fly above them and look down. All the corners could be cut at 45 degrees because the base is a square. If you removed the top third (for example) of the pyramid, you would see a square within a square from the plane. The angles are all 90 degrees hence 45 degree miters would work to connect them nicely. This 45 degrees is irrespective of the angle or slope of the sides of the pyramid. In this 2-d view of the pyramid, all you have are squares to deal with. Imagine making a simple square frame for a picture. Now make another one but just a tad smaller than the first. Keep going and you'll eventually reach a pyramid if you stack the frames on top of one another. Notice that the 45 degree angle is maintained here. However, the slopes of the sides of the pyramid will depend on how much smaller you made each successive frame.

Now look at the lopped off pyramid from the side. In this 2-d view, all you see are trapezoids. Try to igore the fact that the trapezoid slopes away from you as it moves from the bottom to the top. All you care about at this point is the 2-d trapezoid. Now calculate your angle and you'll get about 2.5 degrees (arctan of (0.5/11.5).

You also realize that you will need to cut the same 2.5 degree angle so that the pyramid will sit flat on your work bench, too.

Double-check your 45 degree cut to make sure you are on. If you are off, it will not line up well. If the 2.5 degrees is also off, everything will be messed up.

This *should* work...I just can't see how it wouldn't or someone much smarter than me should post here and tell me what I'm doing wrong in my thinking. Shoot, I'm all anxious to go home and try stuff out now! All your stock is the same thickness, right? That could throw things off, too.

Steve Jenkins
07-06-2004, 5:49 PM
Looks like the taper should be about 87.5 degrees and the blade tilt about 45 1/2. the chart I have is in whole degrees. I don't use trig to figure it out exactly. There are a bunch of people here who do that. I'm surprised that no one has chimed in yet.
compund angles can really get your head messed up. Just think about crown molding. basically the same thing you are doing but with a different angle. If you cut the crown like it sits on the wall and at 45 deg. miter it's no-where close.
I've seen charts somewhere on the "net" that lists the taper and blade angles for any angles and nuymber of sides .Just can't put my finger on it right now. Steve

Todd Burch
07-06-2004, 7:02 PM
Chris, Chris, Chris. :)

The lean-out angle is 2.5°. This is the angle that the bottom and top edges will be cut at to get them to sit flat.

The miter angle is something just under 45°. I drew it in Sketchup to check, but SketchUp doesn't provide precision on angles to this degree, but it's not 45°. The taper is so slight though (2½°) that it might be close enough for a gap filling glue. I would try 44.8° or 44.9° - probably 44.9°. Scrap test cuts might be in order.

When I made the cradle, it was a 15° splay on all sides, and the miter angle was 43.5°.

When assembled, and viewed from the top, after the 2½° is cut, yes, it will measure 45°, but that's not the angle it is cut at. Dihedral man, dihedral.

Todd

Chris Padilla
07-06-2004, 7:33 PM
Hold on, hold on...I see the error of my ways.

For my above diatribe(s), I did not take into account the thickness of the material!! I assumed zero thickness although I didn't intend to at the time. The thickness of the material is what causes the joint to go from 45 degrees to something other than 45 degrees.

I'll post my results later but I am now happy I've figured out my error...now to figure out the formula and correct number!! :D :D

Jim Tobias
07-06-2004, 10:29 PM
John,
Here is a link to a chart that will solve your problems. I have recently(in the past year) built several small items that dealt with the same "angle dilemma".
Hope this helps.

http://www.woodcentral.com/bparticles/miterangle.shtml


Jim

John Lock
07-08-2004, 12:00 PM
Thanks to all for the feedback and guidance on finding the angles I needed. I redesigned my piece to use the same angles as those listed in the chart on woodcentral that Jim posted. Now I'm double-checking my angles and making some prototype pieces to avoid more scrap.

Once again, thanks for the help.

John Lock
07-20-2004, 10:42 PM
After all the help in trying to figure out the angles for this project, I thought it only appropriate to share what I ended up with. It's made of solid oak with minwax stain (forget which one right now) and wipe-on poly finish. There's actually a vase which fits flush in the hole in the top to hold flowers or a separate cover which forms a flush top for larger arrangements.

Ken Garlock
07-21-2004, 11:04 AM
Nice work John.

Just in case you run into another exercise on figuring miter angles, take a look at these two sites. With a little careful reading, you can figure any slope and angle you might need.

DeWalt Cutting Crown Molding & table of cuts (http://www.dewalt.com/us/articles/article.asp?ID=2)

How to compute compund miter cuts (http://home.att.net/~waterfront-woods/Articles/Compoundangles.htm)

I like the second web page, it gives a nice step by step process. I used this reference just yesterday to calculate a "hip roof" for a dust plenum I am working on. When you see the angles you come up with, you will think it can't possibly work, but it does. :cool:

Jerry Heiser
07-22-2004, 2:21 PM
Nice work John.

Just in case you run into another exercise on figuring miter angles, take a look at these two sites. With a little careful reading, you can figure any slope and angle you might need.

DeWalt Cutting Crown Molding & table of cuts (http://www.dewalt.com/us/articles/article.asp?ID=2)

How to compute compund miter cuts (http://www.dewalt.com/us/articles/article.asp?ID=2)

I like the second web page, it gives a nice step by step process. I used this reference just yesterday to calculate a "hip roof" for a dust plenum I am working on. When you see the angles you come up with, you will think it can't possibly work, but it does. :cool:
Ken,
It seems when I click on the second web link, it takes me to the same DeWalt link as the first. ?? Or do I find the second link once I'm at the DeWalt site? I was getting ready to make a couple dust hods myself and this would be handy.

Jerry

Ken Garlock
07-22-2004, 5:23 PM
Ken,
It seems when I click on the second web link, it takes me to the same DeWalt link as the first. ?? Or do I find the second link once I'm at the DeWalt site? I was getting ready to make a couple dust hods myself and this would be handy.

Jerry

Sorry Jerry, and all, I have corrected the URL on the original post.

There is what it should have been
compound Miter angles (http://home.att.net/~waterfront-woods/Articles/Compoundangles.htm)

Thanks for keeping me straight. Some days I think I need a keeper, and I guess this was one of them. :)

Jerry Heiser
07-22-2004, 5:31 PM
That's better. This will give me something to ponder. Thanks, Ken.