How do I calculate a compound Miter?

[Iplayfarmer]

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*.

Larry

You are right!

I had my references mixed up. I want 30* from perpendicular to the square (60* from parallel). Furthermore I actually only want the leg to be 30* from horizontal (60* from vertical).

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))

This works great for picture frames and situations where two pieces come together to make a corner. The scenarios I'm talking about are where a single piece needs to be mitered to mate with a flat part of something else. I think there's a way to extrapolate the info from the formulas you've posted to get what I want, but I haven't gotten my head around it yet.

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.

This is great in this particular situation if I were cutting wood on a table saw. I'm cutting metal with a skinny wheel. I need to know the actual angle of that second cut in relation to the log axis of the leg in the plane of the side of the leg.

I actually just got out of the garage and did what you had suggested with a piece of wood and then measured the angle I needed. It worked out to be just about 35*.

I consider that cheating. Threre's still got to be some kind of formula or method of calculating.

P.S. I'm pretty pleased with myself for figuring out how to quote multiple people in a single thread.

 

[2manyrocks]

For a roller stand, I'd forget the compound angle and weld one leg to a old car wheel as a base.

 

[Spiveyman]

I just made it back to a computer to check out your drawings. I see that you've already figured out that you need the top view angle to be 30° from the horizontal line you drew, not 60° in order to keep the feet evenly spaced. The cut though would be a 30° cut. The side view is going to be the tricky one, because here you actually do need a 60° cut, but most mitre saws don't do a 60°. Does yours? The only way I know to get that cut is to fix the leg normal to the work surface and cut at 30°, but then that screws up the compounding. Maybe you have a better mitre saw than I do, but I can tell you, I'd be cutting the vertical at 45° - that would save you some time figuring this thing out anyway and the feet end of the legs would be easier as well.

 

[Iplayfarmer]

I just made it back to a computer to check out your drawings. I see that you've already figured out that you need the top view angle to be 30ｰ from the horizontal line you drew, not 60ｰ in order to keep the feet evenly spaced. The cut though would be a 30ｰ cut. The side view is going to be the tricky one, because here you actually do need a 60ｰ cut, but most mitre saws don't do a 60ｰ. Does yours? The only way I know to get that cut is to fix the leg normal to the work surface and cut at 30ｰ, but then that screws up the compounding. Maybe you have a better mitre saw than I do, but I can tell you, I'd be cutting the vertical at 45ｰ - that would save you some time figuring this thing out anyway and the feet end of the legs would be easier as well.

I just came back in from the garage. I had taken some scraps of wood and set my saw and then made cuts. I measured the resulting angles and then stood and scratched my head for at least 20 minutes. I just can't get my little brain to process.

 

[Spiveyman]

Does your mitre do angles greater than 45°? And if so, does it do it in both directions? If not you are going to be severely limited in what you can cut.

 

[Iplayfarmer]

I can do 45 on the bevel and 60 on the miter with my table saw.

Here's the deal, though: I'm not planning to cut the pieces with my table saw. I'm going to mark them out with soapstone and cut with an angle grinder.

 

[Iplayfarmer]

In a temporary fit of despair I gave up the roller stand momentarily to play with Gizmo's equation.

Ten minutes later...Voila! See the pictures.

Now that I've proven to myself that I'm not completely useless, I'm going to bed. Maybe I'll have an epiphany in my sleep and wake up as an engineering genius.

I'm eager to hear what Renze has to say. His post gave me hope that he'd have some additional insight.

 

[Spiveyman]

See if this will help. Here's the first cut, similar to your drawings. I added the plane of the blade so you can see where it needs to be moved from.



To make this cut you would have to do this: (that's supposed to be the mitre saw by the way)


However I suspect you can't do the 60° angle. Is that correct?

Edit: I just saw your posts while I was making my mitre saw drawing. Nice work on that. If you can do the 60° you should be good to go, but my angles are likely backwards.

 

[California]

A real Carpenter lays out compound angles like that before cutting rafters and roof decking for a complex building. Examples would be extending a roof to cover a new room that juts out at an odd angle, or building a gazebo or a whole cathedral. The math for this was worked out centuries ago. Most of it is inscribed on the side of a standard framing square.

What you need to make sense of it is a 'book of rafter tables'. I Googled on that, and hit what I think is the book I used to use. See
Full Length Roof Framer: The Book

After you get the upper half of those feet attached you can cheat to mark the lower ends accurately: take a small precision block of steel and put it on the (flat) floor next to each leg. Scribe a cut line on each face of the legs sliding the scribe along the top of the block. Math and a protractor won't exceed the precision of this method.

 

[Pooh_Bear]

I drew this up in AutoDesk Inventor and this is what I got.

And a top view:

And a side view:

Here is one of the legs with the compound miter:

To cut the compound miter you need to cut these two angles:

Just remember, all this was drawn at 3am by a bear with fluff for brains.

(edited to add: These legs make a 60 degree angle from the floor)

Pooh Bear