How do I calculate a compound Miter?

[Iplayfarmer]

This has vexed me for some time. Any time I try to figure out the angles to set my saw and miter guage at to make compound miter cuts I end up wrong. I've always had to resort to the cut, test, cut, test method for compound miters. Now I'm working on putting together a couple of roller stands from spare pieces I've had laying around. I've given up trying to figure it out. I'm swallowing my pride and asking for help.

I know someone out there has a great trick for determining the cut angles for a compound miter. Please share.

In this specific situation I have a square tube and I am putting three legs off of it. One will come straight off the back of the square tube angled down 60 degrees. That cut is easy...60 degrees along both sides of the leg and 90 degrees accross the top and bottom. Same thing for the base of the leg that will touch the ground.

The other two legs will come off of each side of the square tube. They will be angled 60 degrees from the tube to accomplish the 120 degree split between all three legs and they will be angled down the same 60 degrees as the leg coming off the back. The cuts along the sides of these legs will be at 60 degrees, but the top and bottom cut will be something between 60 degrees and 90 degrees.

How do I figure out what the angles of these top and bottom cuts will be?

 

[Spiveyman]

Howdy. Any chance you could sketch out what you are talking about so we can see it?

 

[MrJimi]

Sounds like a three legged stool with the legs spread some, I have wondered the same thing, I hope we get good answers for this, just picture a 3 leg stool and what are the top and bottom angles to make it sit level
thanks in advance

 

[Renze]

not sure if my comments are of any use, because i'm not sure what youre asking but:

The three angles of a triangle ALLWAYS make a total of 180 degrees.

So if you want to brace the stool stand with square pieces, the stand will stand upright, 90ï½°
Then the other angles should add up to 90ï½° like 45ï½° and 45ï½° or 20ï½° and 70ï½° or 30ï½° and 60ï½°

Not sure if that's what you meant to ask though....

==============

edit: i think i get what you mean, you mean multi axis, or 2 dimensional mitre. Like when you have, let's say, a 2x4 tube, you want to make a mitre on the 2" as well as on the 4" side....

hmm over here in Holland, right now its too late to punish my brains to think of how i'm going to explain that.... I'll have to think hard because i dont do that very often, i usually try to avoid this when making construction drawings, because it takes more effort for me to make a sawing list for the guys on the floor, and for the guys on the floor, its allways a tricky job to get it right on a standard Kaltenbach circular saw... there are some band saws that are set up for it but they are expensive and not very common...

 

[GT2]

If I'm understanding correctly; Why dont you just cut them 60d and then v notch them so they will fit the corners of the center tube?

 

[Iplayfarmer]

If I'm understanding correctly; Why dont you just cut them 60d and then v notch them so they will fit the corners of the center tube?

That's cheating.

I've thought about just notching. I still may end up doing that, but this has come up before in projects I've done, and I'm sure it will come up again. I'd really like to figure it out.

 

[Iplayfarmer]

Howdy. Any chance you could sketch out what you are talking about so we can see it?

Below are my rough attempts to sketch out what I'm talking about. The first picture is a 3D sketch so you can get the basic idea of what I'm trying to accomplish. The second pic shows detail from a top view and a side view. At the bottom of the second picture is an example of the stock from which I'm planning to cut the leg. What I'm trying to figure out is what angle I have to scribe on the stock to cut a leg that will weld onto the square tubing at 60 degrees from vertical and 60 degrees from perpedicular to the side of the square tubing.

 

[Reg]

I don't see it as a problem.
Just set the mitre cut to (60 degrees or whatever) and the bevel cut to (60 degrees or whatever) and cut. Do the (90 minus your whatever) at the end where they touch the ground.

I tried to figure the dihedral angle of that dodecahedron thang a couple of months ago - gave up.

 

[GuglioLS]

According to my calculations it should be a 60/30 compound angle.
60* you got, cuz that's what you want.
I came up with 30* because.....you want all three legs to be roughly equal "distance" or angles apart, so thats 360 / 3 = 120* since you are using a square (4x4?)to mount the legs to they are 90* apart, so one leg is mounted and the others are referenced to the starting point. The next leg is already 90* away so add 30* to that 90 to get to the 120*.

To Compound matters
There is a bit of a "problem" in that "perfect" 30/60 compound angle theory -The vertical center-post is Square!

Now,if you were to cut that post to a 3 sided 120* triangle or if it were round, your legs would fit perfect without a compound angle.

K.I.S.S.

Good luck.


Larry

 

[gizmo]

In your case I think you are talking about a 'three sided pyramid'

These formulas should solve just about any miter problem. Start by getting a value for 'A' based on the number of sides. Then figure the miter and bevel. Ensure you calculator is in degrees mode and the value for 'SLOPE' is in degrees. If you load these into a spreadsheet program you can create a chart.
A=90-(180/#SIDES)
MITER=90-(ARCTAN(SINE(SLOPE)/TAN(A)))
BEVEL=ARCSIN(COS(A)COS(SLOPE))