Spiral curves

[servoguy]

Very clever, Bob.

[lionelsoni]

I just thought of a simple way to compute the size of a spiral curve and thought it might be useful to someone.

Spiral curves are used on railroads to ease the transition from a straight ("tangent") track into a curve.  The spiral starts with a gentle curvature and gradually transitions to a tighter curvature, then back to gentle and then straight.  This also works on a toy-train layout to make our unprototypically sharp curves less sudden; but there are two other advantages to using spirals for toy trains:

o  They make curves seem bigger than they really are, especially when seen from the inside of the curve, as on an around-the-walls layout.

o  They allow us to put track closer to the edge of the layout, because there is less swing-out on the corner until the train has gotten a little clearance from the edge as it goes through the gentler part of the spiral.  This is also more useful on an around-the-walls layout.

With sectional track, we can approximate true spirals by using track sections of two different curvatures.  For example, I have used O72-O34-O72 and O54-O27-O54.  In these cases, the outer sections are 22.5 degrees (1/16 circle) and the middle section is 45 degrees (1/8 circle).  Other combinations are of course possible, perhaps using 3 30-degree (1/12 circle) sections.

Predicting the size of a spiral made this way may seem daunting; but here is a simple way to do it:  Multiply the radius or diameter (to the center rail) of the gentler curves by magic number A and the shaper curves by magic number B.  For any 22.5-45-22.5-degree spiral,

A = .459

B = .541

Then add these prodects together.  This is the radius or diameter of the simple curve that would fit in the place of the spiral.  For example, using my O72-O34-O72 spiral above, where the O72 radius is 35.25 inches and the O34 radius is 15.75 inches,

R = A * r72 + B * r34 = .459 * 35.25 + .541 * 15.75 = 24.7005

This spiral looks very much like a full O72 curve, but takes up no more room than an O51 curve would (if there were such a thing).

For a 30-30-30=degree spiral, A = .634 and B = .366 .