[TheForge] eliptical rings on a cone mandrel?

[Bruce Freeman]

An ellipse is by definition symmetrical. 
If it ain't symmetrical, it's some form other than an ellipse.
I'll have to review the math...
Bruce

>>> wmullett at bright.net 11/17/2006 4:23 PM >>>
The ellipse formed by a cone is not symmetrical.

> 
> From: "Bruce Freeman" <FREEMAB at pt.fdah.com>
> Date: Fri Nov 17, 9:45 AM
> To: <theforge at mailman.qth.net>
> Subject: [TheForge] eliptical rings on a cone mandrel?
> 
> 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
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