Octagonal Tower

[jasonB]

I agree with the 2degree cut on the eight sides which is what I said in my first post but the saw blade also needs to be altered , for the 5degree slope the bevel neds to be 22.25, 10 degree slope 22bevel, 15 degree slope 21.5 bevel and so on. Its a bit like setting a chop saw to 31.5 degrees to cut crown moulding when you lay it flat to get a 45deg mitre

Its a while since I have had to work out true lengths of line, true angles etc, but I do have a "compount mitre chart" for 4,6 & 8 sided cones that gives the bevel for each 5 degree increment in slope

Jason

 

[jasonB]

A bit of googling turns up several results for "compound mitre calculator" this oneseems easy to use.

For our chosen example of an eight sided tower with 5 degree slope it gives the mitre angle of 2.07 quite close to the 2 that we have said but the bevel angle is 22.4, probably OK for the 5deg slope to use 22.5 unless you have a wixey to set your saw by 0.1deg increments but try altering the slope and see how the bevel angle needs to change. This may be why people are suggesting seting the saw to 22.5 which really only works for a parallel sided shape.

JAson

 

[Lord Nibbo]

A bit of googling turns up several results for "compound mitre calculator" this oneseems easy to use.


JAson

Many thanks Jason, that is easy to use, it's bookmarked now

 

[Shultzy]

Having read all the posts I think its getting too complicated. We are working in wood and cutting compound angles accurately is difficult. I think Steve Maskery's idea is the best starting point, but use boards instead of solid. Cut boards to the desired width and length and twice the thickness of the taper. Plane each board down to the correct taper, then set table saw to 22.5 degs and cut the mitres. Cut the window apertures out before gluing.

 

[Woody Alan]

Ok I have to admit this is doing my head in a little, but I am confused with the relationship with a compound mitre saw calculator thingy. It doesn't seem to relate to the idea in my head on a tablesaw. To put it in perspective I have never made any of these things except some planters with sloping sides, but I just can't see how my idea needs some degrees adding in to it, that is done by the sled raising the piece of square timber to the slope angle . I did last year drag out trigonometry SOHCAHTOA to cut a piece of plasterboard for my gable end on my summerhouse, that I couldn't measure into the angles of, and that worked so I am not a totally lost cause. Damn it I suppose when I get time I am going to have to try it. Excellent question by the OP and enjoying reading the reasoned discussion. expecting light bulb moment to still occur at 03.00AM
cheers Alan

 

[Sgian Dubh]

For our chosen example of an eight sided tower with 5 degree slope it gives the mitre angle of 2.07 quite close to the 2 that we have said but the bevel angle is 22.4, probably OK for the 5deg slope to use 22.5 unless you have a wixey to set your saw by 0.1deg increments but try altering the slope and see how the bevel angle needs to change. This may be why people are suggesting seting the saw to 22.5 which really only works for a parallel sided shape.JAson

You are correct on all counts Jason. In the earlier calculations I simply rounded to the nearest half degree. The bevel (saw tilt) should really be, as you say, 22.41º and the mitre 2.07º. And again, as you rightly point out who can set a saw that accurately?

Certainly as the slope of the sides gets more acute to the base line, eg, let's say a 61º slope, but still with eight sides, then the saw bevel setting is 19.55º and the mitre setting is 11.35º. By the time we get to these sorts of angles that simple 22.5º bevel setting for an eight sided column is disappearing fast over the horizon.

Similarly the numbers change if you add or remove a side. If we revert back to sides sloping in 5º from vertical, but with only 7 sides, then the dihedral angle is 128.78º leading to a saw tilt bevel setting of 25.61º for a mitred join, and the mitre gauge setting is 2.4º.

The 25.61º bevel setting I've just mentioned is not far from the 25.71º setting that would be used on a seven sided column where, as it is a column, all the sides are vertical from the base line. This, as I've realised you know but I'm working through here for anyone that may not have caught on, is found simply by dividing the number of sides into the 360º in a circle and dividing the result by 2, viz, (360º/7)/2 = 25.71º.

I think I've done enough calculating for one day, and probably far too much for this thread, ha, ha. Slainte.

 

[Steve Maskery]

who can set a saw that accurately?

I can, I can!

Well, at least I can set it that precisely, and I think it would probably be accurately to 2 dp, certainly to one. 2 decimal places is achievable with a good shooting board and digital calipers.

I use a 10" sine bar (it's one of the operations for which I prefer inches to mm). The sine of 22.41 is 0.381 and 10x that is 3.81. So I'd make a spacer 3.81" long and us it to set the angle of a sliding bevel and transfer that to the tilt of the table. Or use a Wixey.

The taper is done the same way, set a board up with a fence at 2.07deg which requires a spacer 0.36" long.

I think the more important point here though is this.

Whichever way you do it, glue up two halves separately first, then joint them to fit. That way any aerrors are cancelled out.

Sgian - if you can find time to do little sketch of your logic, which I don't doubt for a moment, I for one would find it valuable, I'd like to follow your explanation better than I do.

Cheers
Steve

 

[shinobi]

Guys

Thanks for all your responses - clearly a lot of thought has gone into this. There was me thinking it would be straightforward!

Am going to read through the posts in more detail to understand what's going on - though I suspect this job needs the right tools to be done well, which might make things tricky for me.

Thanks again!!

 

[Fecn]

I was thinking about this one last night as I was lying in bed half asleep... There seems to be a lot of effort in trying to get 22.5 degrees...

45 degrees on one face and 0 degrees on the other would work just as well... as long as the angles on each join add up to 45 degrees (22.5 * 2 ) then everything looks right when it's glued up.

... or am I missing something here and therefore wrong?

 

[Sgian Dubh]

...if you can find time to do little sketch of your logic.. I for one would find it valuable, I'd like to follow your explanation better than I do. Cheers. Steve

The calculations I do Steve are to find the two requisite angles that determine the blade and mitre gauge setting.

Refer to the sketch below. I need to know the dihedral angle in order to set the bevel cut, ie, the blade angle of the table saw, or chop saw, etc. The dihedral angle is found, in the sketch, by looking down from the top point of the pyramid to one of the corners.

The second calculation determines the mitre gauge setting of the sliding table saw, chop saw, etc. This is the angle the rising sides form to the base line (of the sketched pyramid.) To do this you have to look at the side perpendicularly. This is not the same as looking at the pyramid from the side. This view is deceptive because the rising side slopes away from you making the angle appear more acute than it actually is.

The sketch shows a pyramid, but the same basic rules apply no matter how many sides there are in a polyhedron. I used to draw out the solution, but it's very inaccurate. The solution is that used for roof structures.

Nowadays I use a spreadsheet that crunches the numbers for me for any polyhedron with a minimum of 3 sides up to 11 sides. More sides than that in the thing and I pull out the scientific calculator. Slainte.