On most model railroads, including my own, curves don’t have easements; straight track suddenly curves into whatever minimum radius the curve is without any gradual adjustment. Are there any curves like that on real railroads or do all curves start out gradually and then become progressively steeper?
Sometimes - but not very often. I am a land surveyor in Western Colorado. I have surveyed along the ROW of the North Fork Branch of The Union Pacific ( formerly the Denver & Rio Grande Western ) I have a copy of the ROW sheets of the railroad coming into Delta Colorado from Grand Junction. ( Signed by Arthur Ridgway, Engineer, dated June 1919, and up-dated 1927 ) and I see 7 curves to be simple curves with no easements. This branch is mostly low speed traffic. I don’t think I have seen any posted speed limits above 30 MPH. On the ROW sheets of the track going up to the mines in Somerset most of the curves do have easements even though most of the posted speed limits are around 20 MPH. I doubt that on high speed track there would be curves without easements.
Steve
The correct term is SPIRAL, not easement. A spiral is a cubic parabola. All railroads (and highways) utilize spirals to transition from tangent to the simple curve, and back again to tangent as the simple curve is exited, when speed is a factor. The railroads constructed in the late 19th century were designed with simple curves but it soon became necessary to modify them with spirals and super elevation so that greater speed could safely be attained. The greater the proposed speed the longer the spiral. This is a simple explanation that others may choose to elaborate on.
A cubic parabola is an approximation to the sort-of-ideal spiral shape; railroads used to use it instead of the harder-to-calculate clothoid. Nowadays the clothoid is easy to calculate, but I guess high-speed RRs look down on it? A linear increase in lateral acceleration isn’t considered good enough any more?
Streetcar lines seldom used spirals. Some modern ones do use spirals and so do most modern light rail lines.
From my Civil Engineering Hand Book -
Railway Spiral Curves. Transition or easement curves are used between tangents and circular curves on main-line railroad track to provide a satisfactory means of attaining the super elevation and to avoid an abrupt change in alinement. The Spiral curve, defined by the A.R.E.A. as “a form of easement curve in which the change of degree is uniform throughout its length” has been generally adopted.
So - yes a Spiral curve is an easement. You can call it either one. Easement curves are spirals.
On the D+RGRR drawings I have the centerline points are described as-
PS - point of spiral
PSC - point spiral to curve
PCS - point curve to spiral
PT - point of tangent
But on one the drawing I have there are simple curves with just a PC and PT, point of curve and point of tangent.
Steve
Excellent responses… learned something from each one, thank you…
Try looking up Klauder Spiral.
Pencil geeks can calculate spirals all kinds of ways, especially with all the computers and calculating power we have out there. Now just try to actually build it and then reasonably maintain it - there’s the challenge. (and don’t get me started on that clown from Purdue in 1884, Searles.)
Steve, being a surveyor you may encounter some ROW which is not defined by a legal description, ie., Act of Congress Grants and several other means. When it is “understood” that the ROW is 100ft or 200ft wide then it may frequently be “assumed” that the ROW lines are 50 or 100 feet from the track center. But when the original main track was built w/o spirals and then spirals added at some future date the track center beyond the spirals (the simple curve) will be offset by the “O” distance specified by those particular spirals and thus the ROW lines cannot be assumed as 50 or 100 feet from the track center. When we constructed new railroad in AZ in the 1960’s we placed the ROW fences as if they were established W/O spirals; and so the track center through the simple curve portion of the complete curve is offset from the ROW fences by “O” distance for the spiral being established. Thus replicating what was done when the 19th century curves were reconstructed with spirals.
Simple answer to OP and to further my Team-Chico teammates response:
(1) In yards and backtracks, think simple curve.
(2) In switches, think kinked simple curves. Kinked between the switch curve and the lead curve [DC- Is Leo Rekusch’s ghost watching? [angel]]
(3) On main tracks and important industrial leads/secondaries , think spiral.
(4) Track machinery cannot lay out tangent to simple curve, there has to be a spiral (however short) to transition between tangent to curve. Track machinery cannot lay out perfect geometry, it has to be helped along if you want that. Team Chico (Santa Fe) was VERY good at that.
(5) Stringlining does NOT generate perfect geometry (track liners work on the same principal, albeit skewed chords) …DC and I dealt with plenty of track engineers that had zero clues how track machines worked. The curve in the field isn’t the same as the one on da’ map. (plenty of Cap’n Hook stories there.)
(6) Don’t say “easement” around a railroad surveyor or a track engineer unless you are ready to run for your life. (“Easement” is a dirty word in railroad technical circles. Incredibly abused term.)
Who needs that Arc Definition crap anyhow?. Chord definition rules on the railroads!
Don’t make me come over the continental divide and wash out your brain with soap. (Oh wait, we’re already over there…including right now in Delta[:-,])
If all Steve has is the Val Map for the North Fork Branch, he’s already in trouble (0. 855 feet off because of the narrow gage shift from when it was built between 1902 and 1906)- Better know where the GLO filing map is. We’ve seen plenty of blunders by surveyors all three directions out of Delta, including Delta to Sommerset.
AREA (It’s been AREMA since 1996) started because the civil engineers (ASCE), including that Searles clown, lost their grip on practical reality. That AREA 10-Chord spiral was adopted from the Talbot 10-Chord Spiral (Talbot’s books and reports are an AREMA staple to this present day)
Arthur Ridgeway (sharp cookie) was more of an operating bubba by the time he signed that Val Map. (His RGS and Moffat Road engineering days
No argument with most of the previous posts, but I will point out that as a practical matter - even as flexible as real rails are - their inherent stiffness precludes an instantaneous change from a tangent to a perfectly circular alignment at the Point of Curvature (“PC”) and the reverse at the point of tangent (“PT”) in 0 (zero) feet. How long that transition is depends on the rail section and the degree of curvature of the body of the curve, but for curves that matter - say, anything over 8 degrees - it’s probably in the range of 20 feet (1/2 rail length) or so. The effect is more noticeable in jointed rail than welded - the joints tend to ‘kick out’ more - and especially if the tie condition is poor and allows gauge widening at the joints (an inherent weak spot anyway). Curves like that (8 deg.) are in lower-speed tracks, so that short de facto spiral may be more effective than one would think.
Also, some posts above alluded to it, but I’ll restate this point to make it crystal clear: Spirals are as much about providing a place to “run-in” (increase) and “run-off” (decrease) the super-elevation at an acceptable rate with a matching curve, as they are to provide a gradual transition from tangent to curve and back. Since super-elevation can’t go from 0" (level) to say, 4" instantly, that has to occur over some distance (how long depends on the track speed). To try to do that in either a tangent or constant curve will result in a varying unbalance one way or the other (or both). The compromise was to adopt a spiral with continually sharpening curvature, which the super-elevation can then match as it increases gradually, and then everything is in balance, proportion, and harmony (or close enough).
- Paul North.
The standard on CPRail was to require a spiral into curves of 1 degree and higher. A spiral was also required in compound curves where the difference in degree of curvature was greater than 1 degree. The latter are a bit ugly to calculate and then lay out in the field, but sometimes you don’t have any alternative.
The length of the spiral could vary, longer for higher degrees of curvature and/or train speeds.
John
Mudchicken -
I just came back from the County courthouse, I ran into a fellow surveyor and we wound up having a discussion about the Railroad Row / Easement. ( He brought up the subject - not me ) He was talking about a recent US Supreme Court ruling that railroads for the most part have a easement - not fee ownership. The term Right of Way and Easement are thrown around but mean quite different things.
Here is a link to that Supreme Court decision:
http://www.supremecourt.gov/opinions/13pdf/12-1173_nlio.pdf
Yes - know about the change over from narrow gauge to standard gauge, but did not think that was what this discussion was about. I also have some Railroad maps of the D+RGRR between Grand Junction that show the original ROW / Easement and show the changes to the track alignment inside the original ROW / Easement . They show the track centerline was changed from the original centerline location but still inside the original width ( which alternates from 100 ft to 200 Ft ) I assume the changes were made for higher speed.
What did you mean when you said " Oh wait, we are already over there … including right now in Delta" Are you refering to the railroad re-alignment for the Delta Bypass ?
Steve
US-50
Well aware of the SCOTUS decision. (and also aware that there are people that didn’t read the decision making all kinds of bizarre claims)
Another aspect of spirals not yet mentioned here is that they minimize the coupler/ draft gear mis-alignment, which is worst when one long car - or a car with a long drawbar extension, etc. - is on a tangent and another similar car is in a sharp curve, with the couplers right about at the PC (Point of Curve, where the tangent meets the curve). The problem is that the coupler of the car in the curve has already swung far to the outside, but the coupler of the car on the tangent is still on the tangent centerline (more correctly, the 2-1/2" off-center to one side, or whatever the standard dimension for that is). As the latter car moves into the curve, its coupler swings outward too, and although there’s a considerable angle between them, at least they’re close to touching at the same point towards the outside of the curve. All this is very well-illustrated by a diagram in the late John H. Armstrong’s Track Planning for Realistic Operation.(3rd edition, Kalmbach Publishing - see: http://www.kalmbachstore.com/12148.html ).
- Paul North.
Link to 2001 AREMA paper (Copyright © 2001 by Louis T Klauder Jr. - found it by a Google search without inputting any of my AREMA ID info) by Louis T. Klauder, Jr., PhD, PE, dated May 25, 2001, titled “A Better Way to Design Railroad Transition Spirals” (48 pages, 886 KB electronic file size in 'PDF" format):
https://www.arema.org/files/comm/c17/Milwaukee_22.PDF
Some excerpts to give a flavor of it:
ABSTRACT
The traditional rules for geometrical design of railroad track stipulate that when the curvature of the track needs to change (as, for example, when a section of tangent track is followed by a curve), the curvature should not change abruptly but rather should change linearly with distance. The geometrical curve shape in which the curvature changes linearly with distance along the curve is a form of spiral that is generally referred to by railroad track designers as a clothoid spiral. The present paper observes that the clothoid spiral is not a good form of spiral fro
I believe the actual patent was US 7027966, granted in April of 2006. (The .pdf has much better illustration quality and is typeset more legibly than the application.)
If anyone wants to download a .pdf of the application, it is available via the link to espacenet. Select ‘whole document’ and then right-click on the ‘download’ option (which will bring up the ‘captcha’ EPO uses to validate the request).
Another aspect of this, which is that spirals reduce the rate of “jerk”. Similarly, Armstrong called it - at the point where a tangent met a constant circular curve - the “coefficient of lurch”. A brief explanation:
(*I’ll leave the inevitable jokes to others . . . [swg] ).
Curves cause centripetal (centrifugal) acceleration inwards, perpendicular (always) to the instantaneous (or local) direction of motion. Circular curves - and the lateral position - are defined by a radius, or by a pair of coordinates, e.g., R (squared) = X (squared) + Y (squared).
The following is from https://answers.yahoo.com/question/index?qid=20080516010236AAQXCM9 , with some added comments:
Velocity is the rate of change of distance [location, or position - PDN] with time. [1st derivative of location, in terms of just X and Y - PDN]
Acceleration is the rate of change of velocity with time. [2nd derivative of location, in terms of just a constant. - PDN]
Jerk is the rate of change of acceleration with time. [3rd derivative of location, which would be zero in a circular curve, but which would have an actual value at the transition from a tangent to a curve - PDN]
For even more info than you probably wanted to know, see also:
“Determination of Minimum Horizontal Curve Radius Used in the Design of Transportation Structures, Depending on the Limit Value of Comfort Criterion Lateral Jerk” (11 pages, 265 KB electronic file size in ‘PDF’ format) at: http://www.fig.net/pub/fig2012/papers/ts06g/TS06G_kilinc_baybura_5563.pdf
http://en.wikipedia.org/wiki/Jerk_(physics)
Principl
(*I’ll leave the inevitable jokes to others . . . ).
Thanks Paul - I needed a good giggle today after dealing with the pipeline tribe. (something akin to Steve Martin going railroading)