[TheForge] Re: Length of a Spiral Railing

[Bruce Freeman]

Agreed.  That is the correct expression for railing length.  Also the
correct approach to determining the expression.  I did not try a doule
integral approach.  Why bother?  If it works correctly, it will just
yield the same expression.

Now, without peeking at my "equations" posting, calculate the radius to
which the railing would have to be rolled on the flat such that, when
raised into helical position, it will give a helix of the proper
radius.

After that, give me you guess as to the amount of "untwisting" the
railing will need to keep the "top" of the railing on top.

Bruce
NJ

>>> dschw at rocketmail.com 9/23/2004 10:04:00 PM >>>

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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