[TheForge] helical railing calculations

[RICK KORINEK]

Bruce,
Could you get an equation for the 2-dimensional curve by 
integrating the helix equation?

-Rick


---- Original message ----
>Date: Wed, 22 Sep 2004 13:43:16 -0400
>From: "Bruce Freeman" <FREEMAB at pt.fdah.com>  
>Subject: Re: [TheForge] helical railing calculations  
>To: <theforge at mailman.qth.net>
>
>Mike,
>
>Imagine taking one full "rotation" of a helix of round stock 
(eg. a
>coil spring) and cutting it in quarters.  My (unproven) 
assertion is
>that each quarter-arc segment will ALMOST lie flat.  
>
>If instead of cutting it into quarters, we cut it into a 
large number
>of segements, each segment would lie flat to ANY degree of 
accuracy we
>chose.  That statement is provable.  
>
>This is really no more than saying that if you divide a 
curve up into a
>large enough number of straight line segments, you will not 
be able to
>distinguish the assemblage of straight lines from the 
original curve.
>
>So my real assertion is that four segments per revolution 
around the
>helix is sufficient.  SOME number (six, eight, twelve, ...) 
WILL be
>sufficient, but for practical reasons the smaller the number 
the better.
> (Two or three would be better than four, but I'm not 
convinced these
>would do.)
>
>What I've done - in my preliminary sketches - is to 
determine the
>radius of the arc necessary for each of these flat 
segments.  (I may
>also have to determine the degrees of arc necessary.  I 
don't THINK so,
>but that remains to be seen.)
>
>The above assumes the railing is round in cross-section.  If 
it were
>not round, then a twist would have to be imparted to give 
keep the "top"
>of the railing on top.  I have attempted to calculate the 
degree of
>twist.  (I will have to test my assumptions.)
>
>What I'm shooting for is the following scenario:  Take a 
flat bar of
>the calculated length.  Twist it a the calculated number of 
degrees. 
>Then bend it to the calculated radius.  Do this 4 times the 
number of
>revolutions of the staircase.  Then assemble the quarter-
segments
>together.  Voila', a completed helical railing to the size 
needed.
>
>This is untested.
>
>Bruce
>NJ
>
>>>> Mike Spencer <mspencer at tallships.ca> 9/22/2004 12:40:40 
PM >>>
>
>> played with the geometry of helices, as in helical 
railings for
>> circular staircases....Is this subject of any interest or 
use to
>> anyone on this list?
>
>Yes. Haven't thought about this for some time but I may soon 
break
>down and make a helical staircase for the shop.  Peggy's 
getting tired
>of using a ladder to get to her loom.
>
>> ...feasibility of constructing these railings from four 
FLAT curves,
>> each representing 1/4 rotation.  I think the answer is 
yes, but I
>> haven't tested it yet.  The question I addressed was, what 
would be
>> the radius of such a curved railing.  That, I got an 
answer for.
>
>I don't quite understand what you mean.  And being a night 
owl, right
>this minute I have to go off an try to see some *normal* 
people while
>*they* think it's still daytime. :-)  But I'll get back to 
it tonight.
>
>In the meantime, could you give a little more explanation of
>"constructing these railings from four FLAT curves"?
>
>I did once try to do some calculations for an elliptical 
helical stair
>and, after some pages of scribbling and grovelling through 
books,
>smacked into something called "elliptical integrals" that I 
couldn't
>hack.  Maybe now that I have Maple V [1] it would be less
>impenetrable?
>
>- Mike
>
>[1] [OT]  Anybody have a Maple V Reference Manual they'd 
part with?
>
>-- 
>Michael Spencer                  Nova Scotia, 
Canada       .~. 
>                                                           /V
\ 
>mspencer at tallships.ca                                     /
( )\
>http://home.tallships.ca/mspencer/                        ^^-
^^
>
>-- 
>
>
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Rick Korinek
Emerald City Forge
Framingham, MA