[TheForge] helical railing calculations

[Andy Vida]

Andy Vida wrote:

>         ...I think what you need is an arc
>         whose chord depth is equal to the radius of the cylinder
>         you intend to wrap the steel around.

	I just relised that this is quite completely wrong.  The
	chord depth will vary we the pitch of the helix varies.
	My bad.  Chord depth will be a function of the helical
	angle.  I just cannot quite see the precise relationship
	in my head at the moment.  The delta-z is constant in
	relation to the delta-y	and delta-x.  This is really a
	rather simple relationship in three dimensions  smoething
	like dz = sin(theta) ((x + dx)**2 + (y + dy)**2) where
	theta is the spiral angle.  I'm sure this is wrong in the
	particulars, but my notion is correct, I think. :)  

	As the spiral angle approaches zero, the radius of the 
	flat iron would approach that of the wrapping cylinder.
	As the spiral approaches 90*, the radius approaches infinity.
	How is that relationship precisely expressed in mathematical
	terms?