[TheForge] Re: Length of a Spiral Railing

[Bruce Freeman]

I'm not sure I follow you, but it sounds like you're not accounting for
the contraction of the diameter as you pull the helix vertically.
Bruce
NJ

>>> gladish at cnw.com 9/24/2004 10:20:42 AM >>>
Given this info (below), the "hard way curve" of the railing will be
simply:

 rads or degrees/foot of rail length   (not per foot of vertical
travel)

Do that to the straight piece and pull it to height and there it is.

Andy g.

I'm sure you could make this more complicated, but when you think of it
this
way it's plain that there's no need for twisting in two planes.
Or cut it out of a piece of paper, tape the end to the floor and pull
it up.
If you pretwist it the rail won't sit straight on the pickets.
And here goes my standard tagline, never more appropriate than now:

"No, No! You're not thinking, you're just being logical!"     Neils
Bohr



>
> Looking at a circular spiral staircase top railing, I
> visualize the edge of a large screw.  If you agree
> with that, then  the length of the piece should be,
> for one revolution,
>     L = (H**2 + (2*pi*R)**2) **0.5
> where:
>     L = length of top rail for one revolution
>     H = vertical height from starting point to
>         ending point for one revolution
>     pi = 3.1415...........
>     R = radius from center of stairway to the middle
>          of top rail
>     **2 denote squared
>     * is the symbol for times
>     **0.5 denotes the square root
> [ remember that the length for multiple revolutions
> would be the total height divided by the height of one
> revolution times L.]
> This the equation for the length of the hypotenois of
> a right triangle.  Conceptually, if you take a piece
> of paper and draw a line from one corner to the
> diagonal corner, then roll the paper in a cylinder
> with the two edges touching, you see a single
> revolution helix.
>
> Guess I could write the three dimensional formula,
> integrate twice, but I try to avoid all that when
> simple works.
>
> the other dave from Louisiana

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