[TheForge] eliptical rings on a cone mandrel?

[Bruce Freeman]

I've checked the math.  A cylinder OR a cone cut (through its axis)
gives an ellipse.  (A circle is a special case of an ellipse.)

Bruce
NJ

>>> rick at smokyforge.com 11/18/2006 8:44 AM >>>
Sorry, but an ellipse is not an angled cut of a cone, but of a
cylinder. 
The larger lower half would be different than the upper half. An angled
cut 
of a cone would give you an egg shape.

Rick


----- Original Message ----- 
From: "Steve Smith" <sos at alum.mit.edu>
To: "Sponsored by ABANA" <theforge at mailman.qth.net>
Sent: Friday, November 17, 2006 8:06 PM
Subject: Re: [TheForge] eliptical rings on a cone mandrel?


> Why wouldn't it be symmetrical? Not that I've tried it or anything,
but 
> Bruce has it right--an angled plane on a cone makes an ellipse.
>
> Steve
>
> Rick wrote:
>
>> You could form half, the turn it around and form the other half. 
That 
>> should work.
>>
>> |8^)>
>> Rick Crawford at Rafter Lazy C
>>  Home of Smoky Forge and Lem the Wonder Mule
>>   In the middle of Northern Illinois
>>
>>    http://www.smokyforge.com 
>>     rick at smokyforge.com 
>>
>>
>>
>>
>> ----- Original Message ----- From: <wmullett at bright.net>
>> To: "Sponsored by ABANA" <theforge at mailman.qth.net>
>> Sent: Friday, November 17, 2006 3:23 PM
>> Subject: Re: [TheForge] eliptical rings on a cone mandrel?
>>
>>
>>> 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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