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Let’s try this again.
I’m making a lamp, the lampshade of which is going to be made from oak scant. The shape will be square, with the corners compound-mitred to form a shape like a pyramid with the top half cut off. For example, I could use a 45-degree mitre with a 22.5-degree bevel. The problem is that the angle of the lampshade is not steep enough using this combination of cuts.
I could increase the bevel to make the angle steeper, but then the mitre needs to change also, in order to keep the corners at 90 degrees. Is there a formula (magic trick?) to figure out which two angles to use? Thanks.
Replies
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Yes, there is a formula.
Dave
(I don't know it, though)
*Try this.Take a piece of milled stock,any convenient diminsion.Be sure that the edges are 90 degrees to the top and bottom and that all edges are straight and parallel.Tilt the saw blade to 45 degrees and make a cut on one end of the block.Now put a bevel on the long side of the block equal to the desired angle of slope of your shade.This surface of the block represents the outside face of your detail part.Now all required angles can be measured directly from this sample An auld patternmakers trick. No math required.For any other number of sides,change the first angle (45)accordinglyI hope that this helps.I do not have the equipment to post a sketch.¬¬¬¬PAT¬¬¬¬
*This was a good brain teaser for a lazy Thanksgiving day:Let N represent the number of sides of the box (4 in your case).Let A be the vertical angle a panel makes with the floor, looking from the size (in other words, 90 degrees for a cylindrical shape that never comes to a point; A is always between 0 and 90).Let B be the miter angle to cut a panel, where 90 degrees would be a rectangular panel; B is always between 0 and 90.Let C be the bevel angle, where 0 degrees is a square edge panel; C is always between 0 and 90.Then:B = arctan[1/cos(A) * 1/tan(180/N)]C= arctan[sin(A)* tan(180/N)]'pretty sure this is right; when I get back home I'll try to make a seven-sided box.
*In high school drafting (27 years ago) we were taught to find answers to questions like yours on the drafting board, with t-square, triangles, scale, and pencil. Fairly quick process, too, if your drafting table was handy and set up.Lately, I've always got a computer nearby, AutoCAD installed, and can get the same results. It's somehow harder to do and suspiciously complicated in AutoCAD. So I suspect AutoCAD is not the best way to calculate angles.Then there was that amazing user-manual that came with our dewalt compound miter saw. There were tables in there for every kind of wierd box. You'd just look up #of sides across the side, then angle of sides across the bottom. Where they intersected the angle between them was listed. Of course, all really useful things in the university shop quickly get "borrowed", then lost. I guess I've got a calculator around here somewhere though. Now if I could just remember the formulas!Poor sad Dave. ;-(
*Try this link. It works for dummies like me.Peace.-Robhttp://www.woodworking.org/WC/mitercalc.html
*For another source, look at the Dec 2000 entry for a downloadable Excel spreadsheet that calculates the bevel and miter angles.http://www.popularwoodworking.com/new/calc.xls
*Now I know why I don't make lampshades out of wood. My hat's off to you, friend.I wonder how this got done before Excel spreadsheets, scientific calculators, and AutoCad?Try Major's method.......
*hey, it may be too late, but...if your shade is rectangular (or square) in plan view, and remains so at any section in plan view, then the angle on the edge at any given point is 45 degrees. so, if you decide on, and cut your bevel first (the one seen in side/front elevation), then you simply have to find a way to cut the edge 45 degrees to the face. you could use a sacrificial fence on the table saw and run the edge against the fence with the blade set at 45, or one of those 45 degree router bits with a similar set up. sorry I can't draw the pictures for you either, but I do all kinds of things to avoid math...SB
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