I do not have the technology or experitse to post drawings so I hope I can be clear. Here’s what happend.
I wanted to make a four sided pyramid with the top cut off ( for a bird feeder but that’s irrelevant). I machined the stock in to 2 X 12″ squares 3/4″ thick. I then cut the squares into two on the diaganol resulting in 4 triangles that made up a square. I then cut the apex of each triangle off resultng in a large square (cuts on the diaganols of course) with a square hole in the center. I then chamfered all edges at 45 degrees. I assumed that doing that would enable the sides to stand on end leaning into eack other, the top hole to have vertical sides and the sides to mate up as a four sided box. Wrong! The first two things worked out BUT the sides mated as a triangle! The external faces are at 90 degrees to each other but the inside faces are at 60 degrees to each other.
So, my questions are: What is the math that causes this and at what angle sould I chamfer the mating edges to result in a 4 sided “pyramid” ? I now have a three sided bird feeder but would like to build a four sided one!
Replies
non-
Unless you really want to understand the math, there's a nice calculator at
http://www.woodworking.org/WC/mitercalc.html
You provide the number of sides and the slope of the faces you want, and it will specify the miter and bevel angles you need.
Don
Thank you, I will save this site but I'd still like to understand the calculations behind the outcome.
Thank you, I will save this site but I'd still like to understand the calculations behind the outcome.I agree BUT I found that if I had the answer to a Math question and worked for many days and somehow came up with the same I could backtrack and then understand it.. Make sense? I did to me!I have passed many Math classes in my life with a A grade.. NO... I did not understand what I was doing.. I just answered the questions..I was not that smart! Just enough to do the 'drill'..I understand where you are coming from..
If I understand correctly, you're measuring the angles of the exterior edges in a plane parallel to the base. Instead you should measure the angle in a plane perpendicular to the relevant edge. The angle between the sides will be greater than 90 degrees if the sides tilt in (or out). The extreme case is when the sides tilt in so much that they lie flat. Then the angle between the sides will be 180 degrees.
You've entered the world of compound angles. Search the internet for 'compound angles' to locate many articles on the subject. Here's one which includes the underlying math:
http://www.waterfront-woods.com/Articles/Compoundangles.htm
Ed
This should give you a leg up on the topic.
http://www.josephfusco.org/Articles/Dihedral/Dihedral.html
http://joes-stuff1960.blogspot.com/
Almost forget, here is another calculator as well.http://www.josephfusco.org/Calculators/Advanced_Box_Cutter.htmlhttp://www.josephfusco.org
http://joes-stuff1960.blogspot.com/
Other's have posted the "how" -- here's the "why".
Imagine you are joining two edges of a box, like you did. If the edges are perpendicular to the bottom, like a normal box, the cut will be 90 deg. (straight crosscut) and the edges will meet with a 45deg. miter (bevel) on each. Now, lay those sides down flat one the bottom. Now you need a 45 deg cut and no bevel (which is 90 deg to the face of the board). Like a simple mitered picture frame.
As the sides gradually go from straight up to laying down, the cut (miter) angle gradually goes from 0 to 45 deg, and the bevel gradually goes from 45 deg to 0. Both these settings are dependent, tho' "in reverse", to the angle the sides make with the bottom. That's what trig is all about -- how changing one angle affects the others. I used to be able to do this by looking at the tables in the back of the book, and figgerin' it out on paper, or by using a slide rule. (Remember those? Do they still make them?) Now, I use a computer or calculator. (Who doesn't?)
Mike Hennessy
Pittsburgh, PA
Welcome to the world of compound miters. The math involves Trigonometry which can get a little complicated. - lol
Very generally speaking, you're thinking in one dimension and you need to think in two dimensions - simultaneously. (Did someone say Calculus??) - lol
The best reference I know of is a book on cutting crown molding. It does a good job of explaining compound angles and has loads of tables giving the necessary saw settings. I don't remember the title, but I got mine at Home Depot.
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