How do I calculate the length of the railing for a spiral
You need to know three things:
(1) The distance from the railing to the axis of the staircase (the radius
(2) The rise of the staircase in one revolution (H), and
(3) The number of revolutions (or the total height) of the staircase.
What you do is envision the railing as a helical line traced out on a
cylinder. If you unroll the cylinder, this becomes a sloping line (or
several identical sloping lines) on a plane. This line (or each of these
lines) is the hypoteneuse of a right triangle with a height of the repeat
distance and a base length of the circumference of the circle. The square
of the length of this hypoteneuse is equal to the sum of the squares of the
other two sides. So,
L = (H^2 + C^2)^(0.5),
L is the length of railing in one turn of the staircase,
H is the height of one turn of the staircase, and
C is the circumference of the cylinder = 2 pi r.
All you then need to get the total length of the railing is the number of
turns N. The total length of the railing is NL.
Richard E. Barrans Jr., Ph.D.
PG Research Foundation, Darien, Illinois
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Update: June 2012