[TheForge] eliptical rings on a cone mandrel?

[David E. Smucker]

While on this subject here is an interesting variation.  You can make a cone 
which appears elliptical in cross section when looking down on the cone from 
above -- but cut at the correct angle its cross section will be a circle. 
With the help of my father who was a very good woodworker we shaped such a 
cone when I was in high school -- and presented it to my math teacher.  He 
loved it and always showed it to his advanced math classes.  Place on this 
circular base the cone would sit at an angle.

Dave Smucker


----- Original Message ----- 
From: "Rick" <rick at smokyforge.com>
To: "Sponsored by ABANA" <theforge at mailman.qth.net>
Sent: Saturday, November 18, 2006 8:44 AM
Subject: Re: [TheForge] eliptical rings on a cone mandrel?


> 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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