[TheForge] Re: helical railing calculations

[Mike Spencer]

Bruce:

> "what do you MEAN by an elliptical helix"

Make an elliptical well in the building, one which in plan, is an
ellipse.  Put "suitably spaced" stair treads around the outside of
this well.

> For a staircase, the risers should be uniform, and the steps should
> be more-or-less uniform.

See how cleverly I evaded that with the word "suitable".  Ordinary
"spiral" stairs aren't actually very good stairs unless they're quite
large (with a stairwell instead of a center support) because the
treads are too narrow near the center and not uniform in width in any
case.  A grand staircase built to an elliptical plan couldn't help but
be better.

I'm sure I've seen a spectacular stair like this in somewhere.  Maybe
just a photo.  Also stairs based (in plan) on Piet Hein's "super
ellipse" or "superegg" [1] but I can't recall where I might have seen that,
either.

Based on:

    X^n       Y^m
    --     +  --- = 1
    a^n       b^n

for n and m greater than 2.  It's an elegant shape when tweaked to
suit the dimensions of what yr building.  (And with n < 1 and m > 2,
you can make interesting arches resembling but more elegant than the
traditional ogee arch.  I haven't seen any place where anybody else
has used this particular form.  Did I think it up?  Dunno.)

- Mike

[1] See: http://www.mathsyear2000.org/resources/slice/superegg.html
         http://www.2dcurves.com/power/powerse.html
         http://c2.com/cgi/wiki?PietHein
-- 
Michael Spencer                  Nova Scotia, Canada       .~. 
                                                           /V\ 
mspencer at tallships.ca                                     /( )\
http://home.tallships.ca/mspencer/                        ^^-^^

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