Re: Spirals and track precision on narrow gauge lines
| March 31, 2008 08:08PM |
Good point.
Superelevation (SE) and easements do not have to be used together.
From my college text book (Tangent to Curve point is a TC):
"In high-speed operation over alignment on which the curves are circular arcs, an abrupt change from a tangent path to a circular path is required at the TC of the curve. It is obviously impossible to make this change instantaneously. Smooth safe operation around railroad ... curves requires gradual transition between the uniform operating conditions on tangents and the different (but also uniform) operating conditions on circular curves. Any curve inserted to provide such a transition is called an 'easement' curve." (Route Surveying and Design, page 86).
The SE method you described is one used most typically when track speeds were increased but the alignment left unchanged. It was also used early on when the understanding of interrelationship of using both SE and easements were not well understood.
For live steam, with SE of 1/4" and mathematical spiral easements of 20 feet, trying to keep a 1/80" per foot SE change is extremely difficult. Adding easements to that is even more so. I recommend a 10' easement of constant radius for 10' or one car length (whichever is greater). The fixed radius easement is double the curve radius. At Live Steam speeds of 5 MPH, this is plenty.
By the way, do you realize that the "vertical curve" used when changing grades is actually parabolic in nature? With it being parabolic, there is no fixed curve and therefore nothing but a long varying radius curve.
I have used parabolic curves on occasion for horizontal curves when it was easier to calculate than the standard spiral easement. Of course, it was during the pencil and paper era just about the time of the introduction of the first pocket calculator that cost $395
Doug
Superelevation (SE) and easements do not have to be used together.
From my college text book (Tangent to Curve point is a TC):
"In high-speed operation over alignment on which the curves are circular arcs, an abrupt change from a tangent path to a circular path is required at the TC of the curve. It is obviously impossible to make this change instantaneously. Smooth safe operation around railroad ... curves requires gradual transition between the uniform operating conditions on tangents and the different (but also uniform) operating conditions on circular curves. Any curve inserted to provide such a transition is called an 'easement' curve." (Route Surveying and Design, page 86).
The SE method you described is one used most typically when track speeds were increased but the alignment left unchanged. It was also used early on when the understanding of interrelationship of using both SE and easements were not well understood.
For live steam, with SE of 1/4" and mathematical spiral easements of 20 feet, trying to keep a 1/80" per foot SE change is extremely difficult. Adding easements to that is even more so. I recommend a 10' easement of constant radius for 10' or one car length (whichever is greater). The fixed radius easement is double the curve radius. At Live Steam speeds of 5 MPH, this is plenty.
By the way, do you realize that the "vertical curve" used when changing grades is actually parabolic in nature? With it being parabolic, there is no fixed curve and therefore nothing but a long varying radius curve.
I have used parabolic curves on occasion for horizontal curves when it was easier to calculate than the standard spiral easement. Of course, it was during the pencil and paper era just about the time of the introduction of the first pocket calculator that cost $395
Doug
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488 stops for water at Los Pinos tank on closing day Oct. 1979. Photo courtesy Don Richter
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