How do I calculate a compound Miter?

[gdemers]

Michael,

Would your formula work for crown moulding? Also, would the slope in your formula be measured in degrees from the horizontal axis? And further, since you seem to be a math whizz, can you explain why the distances between the slope angles in a compound miter chart are not equal?

 

[gdemers]

Michael,
Would your formula work for crown moulding? Also, would the slope in your formula be measured in degrees from the horizontal axis? And also, can you explain why the distances between the slope angles in a compound miter chart are not equal?

 

[Reg]

Other than for "academic interest" there is almost never a "need" to do this.
Just set the saw to the angle you want for each of the parts in each of the planes in which you cut - DONE.

 

[Iplayfarmer]

I think there are actually some good crown moulding charts out there that will give you the answers you need. A google search for "crown moulding charts" came up with a few right off the bat.

Another trick is to fab a jig out of scrap wood that puts the moulding at the correct angle relative to the saw and then just cut at half the angle that you need (I.e. for a 90 degree wall you'd cut a 45 degree angle.) If you need clarification post back, and I'll try to explain more.

 

[gdemers]

Thanks Reg & Iplayfarmer.
You are correct,my question was purely academic, a curiosity about the math. I have a compound miter chart in my toolbox that I refer to regularly as I am an experienced carpenter/ furniture maker. I was glad, however, to see the formula supplied by Gizmo and thought that since he knew that formula he might also be able to answer my crazy question about the miter chart itself.

 

[Iplayfarmer]

Since I first posted this question 4 years ago, I have used the Georgia woodworkers miter calculator a handful of times. I'll be using it again soon as my wife wants strawberry boxes hanging from the porch railing. If I'm going to make them, they're going to look cool. No square boring boxes for me.

 

[jdjllee]

Maybe I see it too simple or missed the issue completely. I've cut some wood but don't see why you seem to think there are mysterious angles to cut for this project. I could be missing something in your description.
Any compound cut can be broken into two cuts which, when combined become a compound cut but you can look at each cut separately to get a brain cell around it.

Keep in mind: If all you do is a bevel cut (0 degrees miter)the sides are cut at the bevel angle and the cuts along the top and bottom will be square to the sides. Similarly, if all you do is a miter cut (0 degrees bevel) the top and bottom are cut at the miter angle and the cuts along the sides are square to the top and bottom.
When you put the two together to cut the compound angle the same ideas will hold true. The miter angle will be cut on top and bottom of the work and the bevel angle will be cut in the sides. If you want to lay this out on your stock, scribe the miter angle across the top side, scribe the bevel angle
on the sides, then the miter angle along the bottom. If you scribe precisely the scribe lines will all connect at the corners.
Does this not work?
For your project I just see this as follows. You have one leg coming off one side of the central square tube with 30 degree bevel angle (no miter) to slope the leg down. The other two legs need this same bevel angle but they also need a 30 degree miter to rotate the legs to get the equal leg spacing.
In the end the bevel angles are seen on the sides of the leg, the miter angles are on top and bottom. What have I missed? What's to calculate?
If you want 30 degree bevel and 30 degree miter these are scribed directly on the stock as above. No need to cut a wooden piece then measure angles and transfer to steel. If you measured 35 degrees on the intermediate wooden model, that's a cutting error you just transferred to your steel.

 

[Iplayfarmer]

Maybe I see it too simple or missed the issue completely. I've cut some wood but don't see why you seem to think there are mysterious angles to cut for this project. I could be missing something in your description.
Any compound cut can be broken into two cuts which, when combined become a compound cut but you can look at each cut separately to get a brain cell around it.

Keep in mind: If all you do is a bevel cut (0 degrees miter)the sides are cut at the bevel angle and the cuts along the top and bottom will be square to the sides. Similarly, if all you do is a miter cut (0 degrees bevel) the top and bottom are cut at the miter angle and the cuts along the sides are square to the top and bottom.
When you put the two together to cut the compound angle the same ideas will hold true. The miter angle will be cut on top and bottom of the work and the bevel angle will be cut in the sides. If you want to lay this out on your stock, scribe the miter angle across the top side, scribe the bevel angle
on the sides, then the miter angle along the bottom. If you scribe precisely the scribe lines will all connect at the corners.
Does this not work?
For your project I just see this as follows. You have one leg coming off one side of the central square tube with 30 degree bevel angle (no miter) to slope the leg down. The other two legs need this same bevel angle but they also need a 30 degree miter to rotate the legs to get the equal leg spacing.
In the end the bevel angles are seen on the sides of the leg, the miter angles are on top and bottom. What have I missed? What's to calculate?
If you want 30 degree bevel and 30 degree miter these are scribed directly on the stock as above. No need to cut a wooden piece then measure angles and transfer to steel. If you measured 35 degrees on the intermediate wooden model, that's a cutting error you just transferred to your steel.

Try it and tell us how it turns out.

 

[jdjllee]

"Try it and tell us how it turns out"

That response made me think I probably have it wrong.

OK, haven't tried it, but realize after fuurther review I have missed a few technical details. Will keep on it.

 

[Iplayfarmer]

"Try it and tell us how it turns out"

That response made me think I probably have it wrong.

OK, haven't tried it, but realize after fuurther review I have missed a few technical details. Will keep on it.

Think of a 90 degree angle made from 2X4's. If you make the angle with the 4" side up, you'll cut a 45 degree angle accross the 4" side and a 90 degree angle accross the 2" side. If you make the angle with the 2" side up you'll cut 45 accross the 2" side and 90 accross the 4" side.

Now picture in your mind the same miter, but with the 2X4's all tilted at a 45 degree angle (Like a fancy picutre frame). The cuts accross the 4" side and the 2" side now have to be somewhere between 45 and 90 degrees. I can't wrap my simple mind around how to calculate what each of those angles needs to be, but others have done it and posted charts, tables, and calculators.