Replies

1. 
   SgianDubh | Dec 10, 2002 04:01am | #1

   Roly, an 8 sided polyhedron, where each face slopes in from the base line to the narrow end at 10° viewing each of the eight faces perpendicular from an edge, i.e., your bucket forms an eight sided 'hopper' where each of the eight sides slopes from the top towards the base 10°, then aim for the following to form the mitred join.

   The dihedral angle is 172.38°. Halve the dihedral angle to establish the bevel cut = 86.19°. Tilt the saw blade a bo'hair less than 4° from vertical (or 3.81° to be precise.)

   The angle that each long edge of each stave describes to the wide end of the stave as viewing the face of the stave perpendicular, is 67.81°.  You need to set the mitre cut to 22.19, or thereabouts. Slainte.

   Some stuff I've made.
1. 
   roly94 | Dec 10, 2002 07:53pm | #3

   Thanks Donald and Richard.

    Donald I don't have excel,unfortunately,so can't read the file I have downloaded from the pond.I really need to get Excel.It is so ubiquitous.Thanks for the link.

    Richard thanks for the help.Are you sure that is correct?The reason I ask is that a tapered octagonal bucket that cants a mere 10 degrees is pretty close to being a non-tapered staved octagon whose bevel angle is 22.5 degrees.If I set the bevel of the blade to 4 degrees that makes a difference of 18.5 degrees.That seems a bit much doesn't it.

   Same argument applies to the taper of the staves.68 degrees is alot of angle relative to 90 degrees isn't it,which is what the staves would be if it were a staved octagonal cylinder,90 degrees.

    The angles(both bevel and taper) wouldn't be that different from a regular staved octagon(22.5 degrees,90 degrees) would they,i.e., in this instance.Thanks tons for the help everyone.Roland.

1. 
   DonaldCBrown | Dec 10, 2002 09:01pm | #4

   Roly-

   Don't get Excel simply for that program. There are other free programs out there; I'll see if I can find another.

   If you really want a spread sheet program, take a look at Star Office from Sun. It's a full-featured suite of seven programs, including a spread sheet fully as capable as Excel and capable of reading Excel files. Well less than a hundred bucks for the whole shebang, including an excellent manual. It will run on Windows, Linux, and Solaris. I'm sure Microsoft will eventually make their programs incompatible with Star Office, but at least for the moment S. O. will read files from MS's comparable programs.

2. 
   DonaldCBrown | Dec 10, 2002 10:23pm | #5

   roly-

   Maybe the attachment will clarify Sgian's angles. My numbers are slightly different from his because I didn't use a metric abacus.

   
1. 
   roly94 | Dec 10, 2002 11:39pm | #6

   Donald,thanks tons for that image.That is exactly what I did.I think I screwed up in having the tilt off a degree or two.But those are the theoretical numbers I used anyway.See ya.Roland.

3. 
   SgianDubh | Dec 11, 2002 01:28am | #7

   Roly, whoops. You are correct. I input the wrong numbers by mistake into my calculator, using 10° instead of the complementary 80° which is the way I work the numbers. Darn it. We all make mistakes, and there was one of mine I guess. I'd have surely spotted it right away on some test pieces at the saw, and corrected the error, but I wasn't in the workshop. Good job you questioned me. I hope it hasn't screwed up your job. My apologies are extended.

   Okay. Correct numbers are-- dihedral = 135.72°/2= 67.86°. Tilt the sawblade from vertical to form this angle, or use its complementary angle, 22.14° (depending on how your protractor is set up.)

   85.89° is the correct angle to taper each long edge of the the stave from the wide end to the narrow end. Set your mitre gauge to just over 4° (4.11° is the actual figure.)

   Apologies again for screwing up, but the figures supplied above I am pretty certain are correct. Slainte.

   Some stuff I've made.

1. 
   roly94 | Dec 11, 2002 02:33am | #8

   Richard no problem.You're are Scottish.You have the right to screw up.Me grandmum is Scottish,from Grenoch.You even speak a little gaelic like her.

    Anyway Donald was very helpful also.He sent me a little program,a freebie,that automatically calculates the required parameters.One imputs the desired number of staves and cant angle or slope and this little Vector drawing modifies itself in real time showing the visual relationships.Neater than all get out!

    E-mail me([email protected]) if you would like a copy.It is freeware.Perhaps you already have a program like this.Thanks tons again all,Roland.

1. 
   SgianDubh | Dec 11, 2002 03:41am | #9

   I don't have that programme, roly, but I do have a couple of formulae and a calculator which I use, and a friend who is both a maths whizz, and sharp at setting up formulae in Excel. In practice, I can calculate any of the angles required for a polyhedron from 3 sided to, well, infinity, either in my workshop or on my computer. The only information I need to know is how many sides, and at what angle the sides lean in from the 'base' plane. The only practical limitations for swift execution after making the calculations are what angles can be set on the power saw being used. Beyond what the powered saws can achieve is down to hand work, where it's worth it.

   I tend to think in 'pyramids', i.e., with the sides leaning in from a base plane by X°, and your 'hopper', i.e., an inverted pyramid threw me. I simply forgot to plug in the complementary angle (80°) where you said the sides lean 10°.  Slainte.Some stuff I've made.

2. 
   DonaldCBrown | Dec 10, 2002 04:05am | #2

   Sgian has answered your immediate question. Here's a reference for the general case of N sides and arbitrary tilt.

   http://www.wwforum.com/faqs_articles/index.html Find Downloads, then Compouond Miter Angles.