Cutting compound angles?

logwalker · May 15, 2011, 12:35:41 PM

If I want to make a tapered column, what is the best way to determine the angles? The numbers are 14" square at the bottom tapering to 6" at the top, in 58 3/8" of height. So this can be a teaching moment, explain the process. Thanks

Lud · May 15, 2011, 03:30:59 PM

There's probably a math answer but I'd say draw it out fullscale on cardboard or even make a model so you can see it . Four taper joints are still going to be 45 degree cuts from the one perspective but could be a challenge to fit. I'm assuming you'd make a taper jig for the tablesaw, right?

logwalker · May 15, 2011, 03:36:17 PM

I think the taper will result in less than 45 degree miters.

SwampDonkey · May 15, 2011, 03:42:46 PM

Is the base square and the top round?

logwalker · May 15, 2011, 03:56:13 PM

No, it will be a mitered square column, 14" tapering to 8" in 60". It will be setting on a square stone pedestal about 4 ' hight supporting a porch roof.

beenthere · May 15, 2011, 08:03:24 PM

Might be a learning moment too.

Is it now 8" and not 6" at the top?

DouginUtah · May 15, 2011, 09:45:41 PM

I had it all figured out but realized I had used a base of 16" instead of 14" just before posting.

I'll be back with the corrected answer after I get a haircut. (I told my wife give me ten minutes.)

redbeard · May 15, 2011, 09:51:43 PM

How are going to cut it?

DouginUtah · May 15, 2011, 10:26:15 PM

I'm assuming logwalker will be cutting this on his Wood-Mizer--too big for a tablesaw.

The process of determining the angles: Run a CAD program. ;D

Answer: The angle from the centerline is:

If using 58 3/8" and 6" = 3.92°. (If using 60" and 8" = 2.86°.)

However, you don't need to know the angles to cut this column. Lay a 14" cant (cut to correct length--58 3/8") on a 2x base on the mill. Put a 4" block under one end and cut so one end remains at 14". Turn 90° and repeat. Turn 90° and put an 8" block under the narrow end. Turn 90° and repeat with the 8" block. Now you have a column 14" on one end and 6" on the other end.

(For the 60x8 column use 3" and 6" blocks.)

beenthere · May 15, 2011, 10:34:16 PM

Doug-in-utah has the right angles. and the easy method to cut it.

After the first cut, should then have a wedge to use for support.

logwalker · May 16, 2011, 01:48:47 AM

Hold the saw. This is a mitered box around an existing post. If it was non-tapering I would cut 45's on 4 pieces and box the post. But it will be a tapered box with 4 mitered sides and that is where the request comes in. I know it is slightly less than 45 but thought there could be a traditional way to figure the proper angles.

I will cut the 4 pieces on a sliding panel saw.

I did change the taper from my first post to 14 bottom, and 8 at the top in 60".

I hope this is a little clearer than mud. I feel a little sheepish that I didn't make myself understood better.

Joe

WH_Conley · May 16, 2011, 02:07:51 AM

Use some scrap stock. Come in 3 inches from each side on one end, 3 inches to nothing would be what you are cutting off each side. Set your blade at 45 and run each side through, adjust if necessary. The taper from 14 to 8 is going to be what it is going to be. The 45 should be close.

redbeard · May 16, 2011, 11:55:30 AM

If you were to use a glue joint bit on a router and use straps with blocking on corners you will get a much tighter joint and it will give you the look of a solid piece of wood. Good ideas on cutting a tappered column on the mill I want to try it thanks guys.

jamesamd · May 16, 2011, 11:24:39 PM

The angle remains 45 Deg.
The top and bottom will need to be cut at the slope angle of the post.
Jim

DouginUtah · May 17, 2011, 12:16:11 AM

I would have to agree with James.

Lud · May 17, 2011, 07:12:19 PM

Seems like James and Doug got to where I was in the first reply! ;D ;D

I concur with Redbeard about the routered joint. Would be real strong.

logwalker · May 20, 2011, 11:48:56 PM

I have been away from the computer for a few days.

It seems to me that as the taper gets more pronounced the 45 degree angle would have to get smaller. Imagine the angles on a pyramid. they can't be 45 degrees. Can they?

WH_Conley · May 21, 2011, 12:50:33 AM

The angle remains the same.

SwampDonkey · May 21, 2011, 06:41:09 AM

Quote from: logwalker on May 20, 2011, 11:48:56 PM
I have been away from the computer for a few days.

It seems to me that as the taper gets more pronounced the 45 degree angle would have to get smaller. Imagine the angles on a pyramid. they can't be 45 degrees. Can they?

Yup, 4 isosolese triangles, 90 degree to the top, 45's on the bottom corners. Lay them out so the bases form a square, stand them up to lean into one another. Pyramid. ;D

logwalker · May 22, 2011, 12:16:56 AM

The angle does get less as the taper increases. Here is a neat compound angle program that figures the miters and the end cuts. Try it out and watch the angles decrease.

http://www.pdxtex.com/canoe/compound.htm

jamesamd · May 22, 2011, 12:36:30 AM

I don't consider 1/4 of a degree,a change in angle,Logwalker.
If I was able to post a decent picture here,i would show a double taper (wide at the bottom,wide at the top) column.
My Son had the same thought,that the angle would change.
I proved Him miss led in His thoughts.
90 Deg. is always 90 Deg.,only the widths change,and You better be sure,Ya get them Dang,right.
Jim

logwalker · May 22, 2011, 01:06:29 AM

Quote from: jamesamd on May 22, 2011, 12:36:30 AM
I don't consider 1/4 of a degree,a change in angle,Logwalker.
If I was able to post a decent picture here,i would show a double taper (wide at the bottom,wide at the top) column.
My Son had the same thought,that the angle would change.
I proved Him miss led in His thoughts.
90 Deg. is always 90 Deg.,only the widths change,and You better be sure,Ya get them Dang,right.
Jim

What part of this tapered post is 90 degrees? There is not a measurable 90 anywhere on it. As far as a 1/4 degree being inconsequential, I disagree. The problem with that assumption is that there is no longer a good fit for the glue to work properly. Remember that the 1/4 degree becomes a 1/2 degree when fit to it's neighbor. Granted a 1/2 degree could work with the right glue, but if you increase the taper to 10 degrees from the vertical then it becomes almost a degree. Is that a problem? It is for me. What does surprise me is that most replies state that the 45 degree angle doesn't change when the post goes from straight to tapered.

jamesamd · May 22, 2011, 07:30:26 PM

It will be a square tapered column,top to bottom.
Jim

jamesamd · May 22, 2011, 08:13:35 PM

OK here is a pic of the double taper I made to prove My point,for My Son.

Jim

Lud · May 23, 2011, 08:22:35 AM

Not sure what I'm seeing there, Jaames .

Here's another way of thinking about it. Go back in your mind to Jr. High drafting class. Draw Donk's pyramid, square base.....from dead vertical above, it's a square with four lines coming to dead center......and all angles are 45 degrees. ;D

Draw the square based tapered column from above. It's the same as your pyramid drawing only with a smaller square on the inside with lines going from the base (larger, outer) square corners to the top (smaller, inner) square top. The corner angles all stay 45 degrees. ;D

logwalker · May 23, 2011, 11:51:16 AM

You are over simplifieng the problem. Your pyramid when viewed from above will show 45 degree angles but, the miters that are needed to fit the four sides will be 30 degrees.

Radar67 · May 23, 2011, 12:45:34 PM

To get a square or triangle, you have 360 degrees to deal with. A triangle will have 120 degrees at each joint (60 degree miters), a square will have 90 degrees at each joint (45 degree miters). The taper only makes a smaller square at the top of the post, not a triangle. A tapered square post is cut with 45 degree miters. A taper jig on the table saw will cut the best joint for this purpose. Roll the blade over to 45, set the taper jig to the line on your stock and cut. First, cut your board to the length you want, then use a center line to lay out your pieces. Mark your bottom to you width, mark the top to your width, connect the dots and you have the angle of the taper to set your taper jig with. Easy enough?

logwalker · May 23, 2011, 03:59:05 PM

OK, build a tapered column with a 60 degree taper. Cut the miters with a 45 degree angle. Now try and get them to fit tight. I am sorry but they won't. If you don't believe me then try it. You only need to cut two sides to see how far off they will be.

Joe

EDIT: What everyone seems to be missing here is that this is a compound angle. That means two angles coming together and creating a new and different angle.

SwampDonkey · May 23, 2011, 04:09:39 PM

Joe, my response was only to your Pyramid analogy. ;) I've never cut a tapered post so I can't answer this problem.

logwalker · May 23, 2011, 04:24:01 PM

The pyramid is the same problem. If it has 45 degree angled side then the miters on the corners would have to be 30 degrees.

jamesamd · May 23, 2011, 08:35:50 PM

Quote from: Lud on May 23, 2011, 08:22:35 AM
Not sure what I'm seeing there,James

Lud ;D
The front board and the top board both are 5 1/2" on the ends.They were tapered in a gentle curve to 4 1/2" in the center.Both boards have blocks and shims under them to bend the boards on the ends 1" (up/out) the centers are on a square piece of timber,flat against it.
I made a quick template by hand out of MDF,jigsawed=sloppy but it worked.
If My Son want's to make them for His house,Iwill have 1=one=uno=ein template made of 1/4" alum.
at a shop that has a CNC router and then route 45's on each edge. ;)Worked for Me!
Jim