Replies

1. 
   Floss | Mar 23, 2006 02:10am | #1

   sawdust1,

   You are basically cutting 4 hip rafters. Here is a site that has the angles you want for any pitch. I suppose you want a 12/12. However if you want to know how to do it with a framing square the Swansons blue book has all the information you need to do it. I think the big boxes sell the little blue books now.

   http://www.josephfusco.org/Tips/tip0011.html

   J.P.

   http://www.jpkfinefurniture.com
1. 
   WillGeorge | Mar 24, 2006 02:08am | #3

   GREAT TIP!

1. 
   Floss | Mar 24, 2006 02:49am | #4

   That guy has an excellent site. Probably the most informative one ,to all types of hacks and butchers of wood, I have come across on the internet.J.P.http://www.jpkfinefurniture.com

1. 
   WillGeorge | Mar 31, 2006 04:53pm | #12

   to all types of hacks and butchers of wood??Geeeee. Good thing I don't have a web page on the internet! I'd be the worstest..

1. 
   Floss | Mar 31, 2006 05:02pm | #13

   You have posted your work here. From what I can recall it was fine.I'll always be hackin away.Too much to learn to be too proud.J.P.PS. Even if I do have a websitehttp://www.jpkfinefurniture.com

2. 
   WillGeorge | Apr 02, 2006 07:57pm | #14

   I'll always be hackin away.Too much to learn to be too proud.I hear ya! I have made MANY things folks liked.. I AM ALWAYS critical of my work as I'd bet most woodworkers are.. Just Us/Me?I think we all want to do it better.. We see some flaw.. and IF WE SMART NEVER TELL!

2. 
   hammer1 | Mar 23, 2006 05:43am | #2

   How are you doing it now? Will the roof be covered? Are you having problems with rafters or are you just cutting plywood? If the roof will be covered, good idea for longevity, you don't have to miter the plywood on the corners. It would be much easier to make square edge cuts and screw the pieces together at the corners. A small roof probably doesn't need any framing, just some 3/4" ply should be fine. Essentially you cut two triangles the same and two triangles larger than the first, by two thicknesses of the plywood used. Screw/nail them together and plop it on the cupola. You must know what the base size is, the larger triangles will match the base. How far up you measure for the peak depends on how steep you want the roof. On the large triangles the top will not come to a point, it will be two thicknesses of plywood wide.

   Beat it to fit / Paint it to match

1. 
   sawdust1 | Mar 27, 2006 04:09am | #5

   I have tried your method and it does not seem to work.  I am using 3/4 inch ply without any additional support underneeth.  I cut four triangles two of which are larger by twice the thickness.  As I lean them in to assemble the pyrimid the square cut sides of the triangle do not match at all.  It looks like the sides of each triangle still need an angled bevel cut.

                                               Thanks: formally sawdust1 now woodchips

1. 
   storme | Mar 27, 2006 06:21am | #6

   hmm,here's a page that explains the math: http://www.slyman.org/right_projects_math.phpIf the pyramid has all equal sides the angle you need to bisect, (if I haven't read it through too quickly) is 70.53° making your bevel 35.27°better read through it yourself though.-s

2. 
   SgianDubh | Mar 27, 2006 06:46am | #7

   Tell me what angle the sides lean in from the base line and I'll tell you what the relevant dihedral angle is, and the angle the side edges of the triangular panels form at the base line. Slainte.Richard Jones Furniture

1. 
   sawdust1 | Mar 29, 2006 05:14am | #8

   I need 21 inches for the base of the triangle.  I can make it an equilateral triangle which will make the side angles 60 degs. however using a perpendicular line going from the base to the top of the triangle gives me a height of 18 1/4 inches.  This is acceptable but a bit high.  A 50 or 55 deg. angle would bring down the height and that would give a more appealing look.  May I impose upon you to give me the bevel cut for all three different angles.  Also I read an ad in the Woodshop News Library a new book called Compound Miter: The Bevel and Miter Answer Book.  Do you think it would be worth getting.

   Thanks in advance.

1. 
   byhammerandhand | Mar 29, 2006 05:36am | #9

   Here is a compound miter calculator. You will need MS Excel or something that will read its files:http://www.popularwoodworking.com/new/calc.xls

2. 
   SgianDubh | Mar 29, 2006 08:37am | #11

   sawdust1, here are the relevant figures.

   Lean in of side to base, 60º. Dihedral angle is 104.48º. Angle the two side edges of the triangular part describe to their base line, 63.43º

   Lean in of side to base, 55º. Dihedral angle is 109.21º. Angle the two side edges of the triangular part describe to their base line, 60.16º

   Lean in of side to base, 50º. Dihedral angle is 114.40º. Angle the two side edges of the triangular part describe to their base line, 57.27º

   To work out what to cut to form a mitre at the corner divide the dihedral angle by half and tilt the sawblade of a table saw to cut an appropriate bevel angle, i.e., for a pyramid with sides sloping in at 60º calculate, 104.48º / 2 = 52.24º. Find the complementary angle to suit your saws protractor, viz., 90º - 52.24º = 37.76º. Tilt the saw blade over to 37.5º as near as you can judge. To cut the appropriate angle of the side edges as measured from the bottom edge of each triangular side part set the mitre gauge to 63.43º, or its complement, 26.57º.

   Naturally enough it's hard to set a saw this precisely. If you can get it to the nearest half a degree it's my experience that that is usually plenty good enough.

   If, instead of mitreing the corners, you wish to do a locking joint such as biscuits, splines, dovetails, etc., you'll need to cut the edges of the wood so that they'll butt up accurately together. The mitre setting remains the same, but you subtract the dihedral angle from 180º, e.g., 180º- 104.48º = 75.52º This is the correct angle to work around for a pyramid with sides leaning in at 60º from the base line.

   Edit. I forgot to answer your question about the book. Unfortunately I haven't seen it (although I have heard of it, I think) so I don't know how useful it would be to you. Slainte. 

   Richard Jones Furniture

   Edited 3/29/2006 6:08 pm by SgianDubh

3. 
   hammer1 | Mar 29, 2006 07:00am | #10

   Sorry, Sawdust1. I didn't think it would be much on a small roof, but it's probably worse. Here are a couple sites that may help. These are for cutting the bisected angle so all pieces come together with a miter. If you have one with square edges made up, you can lay a straight edge across the high corners and get a pretty close "guesstimate" for the bevel if you want the overlaying sides. You may be able to just skim an angle on the pieces you already have.http://www.josephfusco.org/Articles/Dihedral/Dihedral.html
   http://www.1728.com/volpyrmd.htmBeat it to fit / Paint it to match

1. 
   mrbird90 | Apr 03, 2006 06:09am | #15

   Do you have a similar chart for 4 sided boxes with slanted sides? The only chart I have is for convenient angles of slant such as 15, 30 45 60 degrees. It would be nice to have one where you could put in the angle of slant and the miter and blade tilt angles are calculated.

1. 
   hammer1 | Apr 03, 2006 07:35am | #16

   I just checked my bookmarks and found this one.
   http://www.csgnetwork.com/sawmitercalc.htmlBeat it to fit / Paint it to match

2. 
   mrbird90 | Apr 04, 2006 12:15am | #17

   Thanks.