[TheForge] eliptical rings on a cone mandrel?

[Bruce Freeman]

I don't happen to have a cone mandrel, so can't try this myself.  I'm
hoping someone can give it a quick try and let the rest of us know how
it works:

Those of you who suffered through algebra are aware of the "conic
sections" - shapes that can be derived mathematically from a cone.  The
circle, for example is a horizontal slice through a cone.  Blacksmiths
make use of this by using a cone mandrel to make perfectly circular
rings.

What is not so obvious is that the elipse, the parabola, and the
hyperbola are all also conic sections.  If look at a cone from the side,
it's a triangle.  (Mathematically, it's two triangles, one upside down
atop the other, but we don't have to bother about that.  One "half-cone"
will do.)  Draw a horizontal line through this triangle (i.e., of the
cone), and, as I said above, you've got a circle on the cone.  Draw
vertical line through this triangle and you have a parabolic curve on
the cone - interesting, but probably not too useful.  (And the hyperbola
is even worse.)

But an elipse is also possible.  An elipse arises from an angle between
horzontal and vertical.  And they're really cool shapes.

So, make a ring.  Round it up on the cone.  Then take it off the cone
and hammer it from the side to make it somewhat oblong.  Put it back on
the cone and hold it at an angle (say, 30 to 60 degrees from horizontal)
and "elipse" it up on the cone.  Got that?

If some interested folk could try this out and report back, I'd like to
hear about it. 

(I suspect the trick to make this practical might be to make it
narrower than wanted on the anvil, as the thing will tend back to round
on the cone.  It also may be necessary to take it off the cone
occassionally to flatten the plane of the ring against the anvil.)

Bruce
NJ