[TheForge] Re: Length of a Spiral Railing

[DaveS]

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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