building a helix in oo

[Ark Royal]

Hi all


I thought I'd add a bit more maths to the thread, just to make you're heads hurt!!!!

to work out the EXACT dimentions of the radius, and therefore the gradient, use the following

r = radius ignoring any vertical change
R = radius including vertical change
G = gradient in the form 1/50
Pi = 3.1415.....
c = circumference not including vertical change
C = circumferenceincluding vertical change
h = height drop between layers
R is the radius of the track, and C is the length of 1 loop of track untill it reaches the point directly over itself

to start with,
c^2 + h^2 = C^2
G = h/c or tan(G) = Sin(h/C)
c = 2*Pi*r
C = 2*Pi*R

combining that lot gives:

(2*Pi*R)^2 = (G*2*Pi*r)^2 + (2*Pi*r)^2
if you are using settrack then you know R, and can work out G by using: G = tan-1(Sin(h/2*Pi*R))
btw, thats supposed to be inverse tan (shift tan on most calculators)
if you are designing it yourself then you know r, and G can be what ever you like, and you should know this provided that you know what size of spiral you want



A worked example:

R = 505mm (Peco second radius curve)
height drop is 50mm per turn(minimum clearence if you dont use underlay and you use thin boards)

G = tan-1(Sin(25/505*Pi)) = 0.015755959 (about 1 in 63)
(1010*Pi)^2 = 10067983.45
(G*2*Pi*r)^2 = 0.009800527r^2
(2*Pi*r)^2 = 39.4784176r^2

therefore
10067983.45 = 39.48821813r^2
r^2 = 10067983.45/39.48821813 = 254961.7057
r = +or- 504.9373285
as we can ignore -504.9373285, the actual radius when viewed from vertically above is 0.062671519mm

I think that means we can safely ignore the difference!!!!

Thanks

Chris