So, a friend recently asked me about calculating the miters
for if you want to build a box like this, but you want to
taper the sides out a little bit. What he realized is,
because it didn't quite fit, is that the miter angles in here
have to change a little bit. So, I thought about this problem
a fair bit and I worked up the math for it and I made
a table for working out these angles using tons of
trigonometry. And I even made a test piece on how to make
one of these. And in this video I'll cover that a bit more.
So to give you an idea why these angles need recalculating
for different angles of tapering out this shape.
So I've got this miter gauge set to 45 degrees.
And that follows nicely on here. But now if I actually look on it
along like this, you'll notice
this is not the same angle anymore, because these things,
as we move them out, they actually flatten out.
And a good way to illustrate that is, imagine if we
make just an octagon that is straight and as we
tilt these out further and further, imagine we tilt them
all the way out until we just have a flat octagon.
We don't actually have a double cut on here at all anymore.
So the cut goes from a full 45 degrees for the joint,
or 22 and a half on each side for an octagon.
And as we splay it out completely
by 90 degrees, it goes
gradually to zero. but how and how fast.
And that's where a lot of trig comes in.
So you can download that spreadsheet off my website
woodgears.ca, but gluing those shapes together
is pretty tricky so that's what I'll cover in this video.
had just cut the pieces off the end of a 2 by 4
with my miter saw. And the cool thing about that
is you only need one setting because when you cut
the one piece off you can just take your stock,
flip it 180 and then make the next cut.
But with everything in the miter
saw being in such close quarters,
I didn't feel that was a very safe way of making the cuts.
And I can never get a super clean cut on any sort
of miter saw because they're too much flex in the saw.
So for this next one, I'm gonna cut these on the table saw.
So this time I want to make one that’s 10-sided
and I want to tilt the sides out, not by 30
like I did on this one, but by 40 degrees.
So I look on here and it's calling for 10
And then 40 across, for 40 degrees.
The miter is 11.8.
And the tilt of the saw is gonna be 13.69.
Now I also want the next one to be a little bit larger
than this one. This one is 27 across
and I think I want about 30 centimeters across
for this one. And so that would mean
the radius from the middle to the edge from here to here
would be 15 centimeters, so I want an R
or 15 centimeters and looking over here
the R over L ratio here
that means I have to take 15 centimeters times
.649, times .649,
So I want my sides to be 9.7
centimeters long.
So I need to set my miter to 11.8 degrees
Now this miter gauge has the right angle at 90 degrees
and I need to be 11.8 from 90.
But, so just go from 95 10
And I need to go to almost 12, just shy of it.
Now you may say, Oh these things
aren't really trustworthy. But I've always second guessed
this miter gauge and every time I set it
precisely using other means when I check this pointer.
It always points at exactly the right number.
Now I have to tilt this saw by 13.69 degrees
10 - 11 - 12
13 and then let's call that
.69 here.
If you like to second guess your angles.
One of these rafter gauges is really good
because they have a really large scale on here
and they're 1 piece so there's very little to go
wrong with them. So let's check
my 13.69 degree angle so
this would be 90 degrees here and it's come in by
10 - 11 - 12 - 13
And let's call that .69 here.
And that's about as accurate as I can check it
against this cheap little blade.
I'm just gonna add a sacrificial fence to the miter gauge.
Because I want to be able to support the work piece
on both sides. So I'm gonna cut through this fence.
So, I want all my pieces to be 9.74 centimeters long.
So, I've marked that here.
And I've marked that same angle on here.
And transferred the mark to the other side.
So, that means I need to take this piece
to about here.
And I'm gonna need all these pieces that same size.
So I can just clamp a stop to my fence.
So I can now just cut all these pieces one at a time.
So, next we need to glue these things
together, like that. But where to clamp
them and how.
So I figure it's easier to just glue them together
in pairs but I still have the question of
how the heck do I clamp these.
So I want to figure out the center of the area
of the joint, so I'm just going to trace out the
outline of my joint on the work bench.
And here's basically the glue area.
And I want the force to be applied
right about this point, with my clamps
so that it's even along everything.
So, let's try to figure out how to project that down
to pieces of wood.
And let's get this piece of wood, right over
the corner, the center that I want to clamp.
And, let's put this piece of wood back on here.
And I can tell the center of clamping
should be right about this point here
so, this is gonna be tricky to clamp it just like that.
So what I'm gonna do is, I'm gonna clamp
some bits of wood to here.
So if I clamp this piece of wood on here like so
then that center of clamping ends up here
and I can have a place to put the clamp.
Now you may wonder, for this scrap,
I've got a beveled edge on here. What's the ideal
angle for this? Well the ideal angle is actually the same
as this bevel down here. So it ends up parallel.
So basically, I just use a saw
with the tilt set to it and cut these scraps out here.
So let's put that on here with this C-clamp.
Now its still really tricky to clamp one of these together.
If I used one of these quick-grip clamps
that would certainly make it easier because
I can operate that clamp one-handed.
The problem is these clamps don't
really apply a lot of force.
So I don't like to use them for gluing.
So, this ermin clamp works fairly well
because the ratchet tends to stay put.
So, if I just put that on here
and now...Whoops.
So I could just force it together.
And tighten the screw, and I got it.
So now to try this with glue.
OK, let's put these together.
Now with glue it's trickier because the glue
is a lubricant.
Let's line these up.
And we can see glue squeezing out.
So I hope I have enough glue in everything.
So the thing I'm making has got 10 sides
and I've got 4 of these pairs already glued together.
And I was about to glue the 5th one together
when I realized, that's a bad idea because
I want to be able to assemble these in halves,
which means I need to add 1 extra segment
to 2 pairs to get 2 pieces of 5.
I just unclamped all of my pairs
and 2 of those pairs I used the same method
to glue another segment on there.
So now I just need to glue the segment of 2
to a segment of 3.
And, as usual, this is tricky.
So now I just need to put those 2 segments of 5 together
to get a bowl shape.
Unfortunately it's not that simple because
these joints don't quite close.
With 20 miter cuts all around
the errors accumulate and even if I'm only a
fraction of a degree off, by the time I get to the last miter,
that's 10 times as much.
So the best way to fix that is to
flatten the 2 joints on the belt sander.
So with these sanded into 1 plane on both parts
they now fit together pretty good.
And I'm ready to start clamping.
This is, of course, frustrating as always.
Well, got it aligned at last.
So here's my finished shape.
I'm not sure what I'm gonna do with it.
Maybe try to trim a bowl out of it.