Degree of Curve/ Chord Definition is extremely simple and you can backfigure radius with simple trig and geometry. The method and definition came from our military engineers (artillery) who were in abundance, especially post civil war via West Point & Jefferson Barracks. Calculating curve length is much easier using degree of curve than using radius and the laying out of curves in the field is also much quicker.
John WR:
For your information, there are still more misleading issues in the railroad industry at the present, I think.
You mentioned why no one knows it. I don't know why. However, there are thousands of trains running everyday. Railroad people depend heavily on testing to determine the speed of a train. So defects in design can be compensated by lowing the running speed of a train. Thus, a train can run but with low efficiency, such as high maintenance cost, high energy consumption, etc.
Thanks, Mud Chicken. I looked up "degree of curve" on the internet and now I can see that the calculation can be done. I have to say I wouldn't call it "extremely simple" but perhaps that is because I am extremely simple.
John
workerFor your information, there are still more misleading issues in the railroad industry at the present, I think.
I think there are misleading issues in just about every aspect of our lives. By "misleading issues" I mean issues that seem simple but in fact are more complicated than they appear to be. However, to say that an issue is more complicated than it appears to be does not mean that it is incapable of resolution.
mudchicken Degree of Curve/ Chord Definition is extremely simple and you can backfigure radius with simple trig and geometry. The method and definition came from our military engineers (artillery) who were in abundance, especially post civil war via West Point & Jefferson Barracks. Calculating curve length is much easier using degree of curve than using radius and the laying out of curves in the field is also much quicker.
Exactly!
I found a couple of old texts on railroad surveying in Google Books which enlightened me on tried and true techniques, which is something which might help our new poster get some insight into "how it's done" and why it's not really magic like it seems, but just the systematic application of fairly fundamental mathematical principles. That, of course, is one good definition of what engineers do, or at least that's been my take for a long time. In fact, I probably cannot take credit for the expression, as I am sure I heard it early on in one or more engineering classes oh so long ago.
I might suggest to him or her the getting hold of a good text on railroad engineering, which doesn't have to even be all that recent. I have a 60-year-old book by William Hay of the U of Ill Railway CE department that I have had for over 30 years which is an interesting read for a retired EE (yes, we had to take the same fundamentals courses that the other disciplines did then, plus two upper-division electives in CE or ME, something that seems to have gone by the way for EEs these days, I am told). Perhaps the poster could find some illuminating discussions of spiral easement sections of curves.
Surveyors and those polite engineers have certainly refined the art of track alignment over the years and it is my impression that at this point it is mostly settled art (not a reference to dirt engineering) and has been probably for quite some time. It is, to say, at least presumptuous in any engineering field to try to re-invent the wheel without first knowing how wheels have been made before. (Not a new concept, as Henry Petroski in one of his fine books quotes a Roman engineer on that exact topic from about 200 BC.) Of course, I had steady income for a few years correcting those reinventions, so maybe I shouldn't complain too much.
Curve surveying practices might make an interesting thread, going into frequency of survey, events making a survey necessary, reasons for such frequent surveys (kinks come to mind with respect to an Amtrak derailment a few years ago).
ChuckCobleigh,
As I said, I am not a surveyor, and I don’t want to dig into the survey area to re-invent the wheel. However, I did invent a device to measure the radius of curvature for the curves and spirals. You make me wonder how many curved rails (spirals) constructed for the railroad would have the radius as specified in the design if I measure them with my device. We trust you but we need to check. That is what they say.
You also mentioned: “Perhaps the poster could find some illuminating discussions of spiral easement sections of curves.”
I did re-invent the wheel in spirals. I encourage you to challenge my invention. After digging into that many historical files, do you find anything wrong in my invention? If so, come to challenge me.
I will gladly defer to the engineers on this thread, but I don't think that any rail was ever rolled or cast in a curve of specific radius. The rail would be spiked into place at one end and pulled into the desired curve and then spiked into place.
workerI did invent a device to measure the radius of curvature for the curves and spirals.
Worker,
Why don't you show us the device that you invented, explain how it works, and tell us what benefit it provides?
Worker seems very confused, even if he feels certain in his own mind.
It is very easy to determine the degree of curve. You need three people, a piece of string 62 feet long, and a short ruler measured in inches. Hold each end of the string against the gauge side of the rail and pull it tight. The distance from the center of the string (31' from each end) to the gauge in inches is the degree of curve. No need to head half a mile off in the trees to find the center of the curve. If you check several places along the curve there will almost certainly be minor variations. Occasionally you might also find compound curves when the alignment was constrained by outside obstacles.
Nor do I understand what he thinks the spiral easements are. When travelling at any speed you don't want to suddenly change from going straight to turning. Same when driving a car - you don't instantly yank the steering wheel over. The spiral easement is also where the superelevation transitions from nil to whatever is specified for the train speeds and degree of curve. On compound curves another connecting spiral may be required if the respective degrees of curve are significantly different.
The degree of curve and spirals that the railroads use are slightly different from those used by the highway engineers.
CSSHEGEWISCH I will gladly defer to the engineers on this thread, but I don't think that any rail was ever rolled or cast in a curve of specific radius. The rail would be spiked into place at one end and pulled into the desired curve and then spiked into place.
Rolled straight, for sure, and in regular heavy rail, just laid down and spiked in place, unless there is a rare exception. Transit, though, with high-degree curves, has been known to put rail through a portable curve bender to get those tight alignments. I'm not able to find the site referenced in a much earlier forum post, but the machines are definitely out there. As I recall, we are talking a three-roller tube bender on megasteroids.
John cx500:
You said:“ The distance from the center of the string (31' from each end) to the gauge in inches is the degree of curve.”
For a curve with R = 100ft, this curve is a 60 degree curve. Your measurement shows a 59.116 degree curve. Is this good enough? Not sure about the accuracy for other different curves. Also, you need three people to perform the testing. My device has zero theoretical error and only needs one man to operate.
You said: “When travelling at any speed you don't want to suddenly change from going straight to turning. Same when driving a car - you don't instantly yank the steering wheel over. The spiral easement is also where the superelevation transitions from nil to whatever is specified for the train speeds and degree of curve. On compound curves another connecting spiral may be required if the respective degrees of curve are significantly different.”
John, I have been through all those stuff you mentioned before I made the invention. Again, there is on jump in radius from tangent to curve. So the centrifugal force increases smoothly from tangent to curve, no yank. There is an impact force due to change in vehicle moving direction from tangent to curve, but my calculation shows the impact force is only about 5% of the centrifugal force in one typical case.
As I said before, spirals would cause two problems per my calculations. My statement is further supported by a test, presented in a paper by Louis T. Klauder Jr., PhD, PE., “A Better Way to Design Railroad Transition Spirals”, Preprint submitted to ASCE Journal of Transportation Engineering, May 25, 2001. It says “A 1998 paper by the Austrian engineers Gerard Presle and Herbert Hasslinger (ref. 6) reports measurements of rail vehicle ride motion disturbance and of damaging systematic lateral force on the track structure caused by the clothoid spiral even when the linear ramp profile is deliberately “rounded” at each end.”
Easiest way I know of to find the answer is to look at the track charts I have on my external hard drive.
Norm
I pregnantly waiting to view 'Worker's invention?
Never too old to have a happy childhood!
I will point out that a 60 degree curve might be found on a streetcar line, but freight railroads don't get anywhere close. Most of today's equipment will have trouble above 20 degrees. There are very few places where a mainline curve is greater than 10 degrees.
Your calculation may show that the impact force is only about 5% of the centrifugal force. The reason for the spiral easement is to eliminate that impact force. It may not sound much, assuming your calculation is correct, but repeated 200 times every time a freight goes by it will start to shift the track slightly out of alignment. And then the impact force will be higher, and the shifting more pronounced.
The whole idea of superelevating curves anyway is to keep the combined gravitational and centrifugal force at the design speed normal to the track, so there is no centrifugal force acting on the track. The spiral easement matches a gradual increase in superelevation to a gradual increase in degree of curve. You can't simply lift one rail 3 or 4 inches immediately.
As to your claim " there is on(sic) [no] jump in radius from tangent to curve", that is completely ridiculous. A tangent has, mathematically, an infinite radius. A curve radius is considerably less than infinity, only 5730 feet for a broad one degree curve. So from tangent to curve it is a substantial (infinite in fact) reduction in radius rather than a jump.
I have no idea what the paper you cite is talking about. There are several types of spirals. The traditional American 10 chord spiral is quite suitable for normal speeds and is easy to calculate and lay out in the field. I have heard that other types of spirals have been found to be slightly better, and especially for very high speeds. The paper's title suggests this is the topic, determining the best spiral, not showing them to be unnecessary as you seem to have somehow interpreted.
And as others have noted, rather than measuring the degree of curve it is much easier to just look it up in the railroad track charts. It could be done fairly easily by one person using a transit. The stringline method requires no special device, just some simple materials readily available from the local stores to anyone.
worker I did re-invent the wheel in spirals. I encourage you to challenge my invention. After digging into that many historical files, do you find anything wrong in my invention? If so, come to challenge me.
Patent number? You wouldn't otherwise want to disclose the details publicly otherwise as that starts a very short clock running which prevents patent protection if filing is not done before the buzzer goes off.
Actually, I doubt if I could summon much interest at this point and wouldn't bother to critique something which is mercifully completely undefined.
ChuckCobleigh CSSHEGEWISCH I will gladly defer to the engineers on this thread, but I don't think that any rail was ever rolled or cast in a curve of specific radius. The rail would be spiked into place at one end and pulled into the desired curve and then spiked into place. Rolled straight, for sure, and in regular heavy rail, just laid down and spiked in place, unless there is a rare exception. Transit, though, with high-degree curves, has been known to put rail through a portable curve bender to get those tight alignments. I'm not able to find the site referenced in a much earlier forum post, but the machines are definitely out there. As I recall, we are talking a three-roller tube bender on megasteroids.
The machines do exist. On one of my summer jobs back in my college days, I worked in a steel service center that supplied rebar for construction jobs. The machine operator and I were assigned one day to a job in another building which involved running rebar through a machine which bent them in a large-radius curve. I'm sure that a rail bender would work on a similar principle.
Ring rail in a turntable pit is about the only place the freight railroads would use pre-curved rail. They will, however, for shorter turnouts put a single bend in the turnout side stock rail just before the switch point.
mudchickenDegree of Curve/ Chord Definition is extremely simple and you can backfigure radius with simple trig and geometry.
I sat down with a pencil and graph paper to see what I could remember from my school days. Working a very simple example made it clear to me that it is quite possible to lay out curves even if the center would be inside a mountain or a lake. To simplify things I assumed the curve would be a segment of a circle. No doubt railroads have their own methods of doing this along with specialized equipment.
The only question I have is what about actual curves in nature? Wouldn't curves often be irregular so they would not lie on a circle or an ellipse or even a cycloid? What then?
cx500 Ring rail in a turntable pit is about the only place the freight railroads would use pre-curved rail. They will, however, for shorter turnouts put a single bend in the turnout side stock rail just before the switch point.
Paul D North did a calculation on how sharp a curve would need to be in order to exceed the elastic limit. My recollection was that it was sharper than 15 degrees. Pre-curved rail may be used on some light rail lines.
- Erik
John WRThe only question I have is what about actual curves in nature? Wouldn't curves often be irregular so they would not lie on a circle or an ellipse or even a cycloid? What then?
I'm not sure I understand the point of the question. I was staying out of this, but have to ask.
The purpose for transition spiraling is the same basic logic as using modified-trapezoid profile on cams. Essentially you want to modulate the acceleration rate smoothly, first going from tangent into curve entry, and finishing up at the constant lateral (radial) acceleration corresponding to a curve radius. Any curve that does not do this will not be 'as effective' -- and a railroad curve is not a form 'found in nature' but an optimized construct.
Note that you do not start such an analysis by reference to the 'radius' of the curve. That is merely an artifact of the maximal value of lateral acceleration necessary to get properly through the angle from one straight length of track to another (note how I avoid using 'tangent' to mean 'straight' in this very limited context). You can also understand why a spiral is used as a transition, rather than being used entirely through the curve; there is a point where lateral acceleration is reached after which a simple circular curve matching that rate does the business.
On the other hand, the actual shape the rail assumes on a transitioned superelevated curve is a resultant, between the transition appropriate for lateral curving and the vertical transition used to accommodate superelevation. This is no more 'irregular' than any other resultant.
My understanding of current geometry determination is that you have a beam of known length, with a laser at one end and a target at the other. This lets you determine the offset from any number of station points, not just 100' intervals with fixed chords, if that is something you want or need to do.
My grandfather taught me when I was six that there were ways of laying out a curve that did not require the equivalent of a compass or trammel. I'm a bit surprised to find that there are people speaking magisterially (if a bit obliquely) here that seem to think such a thing is not common knowledge and a Bold New Device is needed to perform such magic. But perhaps I misunderstand what the device does, and I continue to await a technical explanation in clear English, without further ad hominem distractions or ... well, precisely the sort of approach and language that Angus Sinclair was describing with Eli Gilderfluke's design thinking and method of 'description'...
You said: “Most of today's equipment will have trouble above 20 degrees. There are very few places where a mainline curve is greater than 10 degrees.”
For a 20 degree curve (R=285ft), your measurement is 20.290 degree. A 5 degree curve, your measurement is 5.034 degree. For 3 degree curve (R =1910ft), your measurement is 3.0195 degree. The measurement errors decrease significantly for low degree curves. However, the radius of curvature increases significantly in low degree curves. Therefore, the deviation in determining the curve decreases in low degree curves but not significantly. That is, the deviations in high degree curves and low degree ones are still comparable.
You said: “You can't simply lift one rail 3 or 4 inches immediately”
The super-elevation can be lifted up smoothly from tangent to curve without the spirals, I think.
You said: “So from tangent to curve it is a substantial (infinite in fact) reduction in radius rather than a jump.”
As far as I know, I believe this the reason why they want a spiral. So they think there will be a smooth transition without yank with a spiral. My calculation shows that the centrifugal force increases smoothly from tangent to curve because the radius decreases smoothly from ∞ to R smoothly.
You can drive your car to a crossing and take a turn, to finish a tangent-curve-tangent process. But in the whole process, you must keep the same velocity, no stop, no brake and no slip. You can measure the centrifugal force (using a pendulum, etc). You will see the centrifugal force increases and disappears smoothly.
Centripital (not centrifugal)
Railroad spiral curves (except Klauder) are cubic parabolas of some form. Except for HSR, Klauder has little practical application.
Grade line in a spiral curve is the low/inside rail.
If you believe the curve on the map is exactly the same as the curve on the ground, I've got some beachfront property for you in Colorado's San Luis Valley.
"The super-elevation can be lifted up smoothly from tangent to curve without the spirals, I think." - the tonnage will spiral it for you and several railroads tried to do that (pre- Searles, Hood and Talbot) with disastrous results before 1900. Anything with a high center of gravity or non-uniform loading is doomed. L/V forces [ unballance] at the PSC are [is] not to be ignored. (The technical side of AREA/AREMA split away from ASCE (circa 1898-1905) because the ASCE folks were somewhat obtuse and not always practical/pragmatic - same holds true today in a railroad sense) . You are entitled to your opinion, but you have not sold me.
My point, Overmod, is that I just tried to see what I could learn from looking at a very simple example using what I remember from plane geometry and trigonometry. I had no text of any kind but just used what I remembered. And what I did learn is that these problems certainly can be solved.
But I don't want to even remotely suggest that my own figuring is all that there is to even planning a curve much less to transferring that plan to the actual terrain a railroad track must actually run over. All of that is completely outside of my understanding. However, I do know that neither perfect planes nor perfect smooth curves occur in nature but railroads have been dealing with nature for quite a while now. And I was thinking on my computer about how they might do it.
I hope this answers your question.
PS. I'm sure that you are aware we have electronic gadgets today that used to do what many people can still do by hand fairly easily. A friend of mine is in graduate school studying economics, a field where calculus used to be required. He tells me that some of his fellow students do not understand per centages. It seems to be a whole new world.
mudchicken If you believe the curve on the map is exactly the same as the curve on the ground, I've got some beach-front property for you in Colorado's San Luis Valley.
If you believe the curve on the map is exactly the same as the curve on the ground, I've got some beach-front property for you in Colorado's San Luis Valley.
About 16 miles NNE of Alamosa, maybe? Looks great from the air, as I recall.
Or maybe just jump in the old time machine and go back about 100 million years.
worker As far as I know, I believe this the reason why they want a spiral. So they think there will be a smooth transition without yank with a spiral. My calculation shows that the centrifugal force increases smoothly from tangent to curve because the radius decreases smoothly from ∞ to R smoothly.
That's a pretty good definition of a spiral, the distance where the radius decreases smoothly to the desired "R". You can't have that smooth decrease without one. Sorry.
On a separate topic in this thread, I have seen a curve of about 33 degrees put in to serve a warehouse, and there was no need to pre-curve the rails. That was while Alco switchers and 40' boxcars still served the industrial areas, and I expect the siding was short lived. (The building was built at a different angle and closer to the tracks than original plans showed, so it was that or nothing.)
ChuckCobleigh mudchicken If you believe the curve on the map is exactly the same as the curve on the ground, I've got some beach-front property for you in Colorado's San Luis Valley. About 16 miles NNE of Alamosa, maybe? Looks great from the air, as I recall. Or maybe just jump in the old time machine and go back about 100 million years.
Don't try coupling or switching in that 33 degree curve - you need a chain. Tightest freight curve I ever remember laid out was 38 degrees at Pueblo (Target Warehouse - Architect pulled an incredibly stupid stunt)
Help? "You need a chain".....
As usual, I am lost....
She who has no signature! cinscocom-tmw
mudchicken Tightest freight curve I ever remember laid out was 38 degrees at Pueblo (Target Warehouse - Architect pulled an incredibly stupid stunt)
Tightest freight curve I ever remember laid out was 38 degrees at Pueblo (Target Warehouse - Architect pulled an incredibly stupid stunt)
Looks like they "erased" that mistake some time ago, as the spur has been nipped off about half way through the curve.
mudchicken Don't try coupling or switching in that 33 degree curve - you need a chain. Tightest freight curve I ever remember laid out was 38 degrees at Pueblo (Target Warehouse - Architect pulled an incredibly stupid stunt)
Sounds like the same guy. The original concept from the architect showed two tracks inside the building with a crossover between them half way down. Might have worked with the old Lionel model equipment and track, but not in the real world. I think there was just enough room so if the first switch point was at the door the opposite was at the bumping post! He got just a single track.
Just checked on Google earth; it seems to be all gone now, including the building. Not too surprising some 40 years later.
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