i was curious about what values above resulted in. the drawing shows the 30" circular curve in red and the 30" easement coordinates in blue.
I eventually figured out that values are the vertical (downard in my image) offset from the tangent rail that starts 5.99" to the left and 0.2 above the start of the curve (leftmost red point). I hadn't realized that the easement starts both outside the curve and earlier than where the curve starts.
greg - Philadelphia & Reading / Reading
BNSF UP and others modeler In an effort to steer this back on course... Does anyone know the exact numbers (raduis and length) for easements into 30" raduis track? And 28" raduis too?
In an effort to steer this back on course...
Does anyone know the exact numbers (raduis and length) for easements into 30" raduis track? And 28" raduis too?
Using the calculator on the link:
With a 12" easement (that's 12" along the straight track) for each of the two radii above, the offset at every 1.20" along the straight track (10 points total--10 x 1.20" = 12") is:
For 30": .001, .006, .022, .051, .100, .173, .274, .409, .582, .798
For 28": .001, .007, .023, .055, .107, .185, .294, .438, .623, .854
If you have laid out the straight and non-eased curves on your "plywood", the new starting point for the eased curve will be 5.99" farther down the straight track (away from the curve).
Incidentally, if the 30" and 28" represent curved double track, the NMRA recommends a wider spacing in the curves.
Ed
A 12" easement is appropriate for an 18" radius curve, with longer easements for wider radius. If you don't want any of your easements longer than 12" then probably all your easements should be 12" long.
You should make an easement as long or as short as it needs to be.
Rich
Alton Junction
I am sorry. I probably did. I don't know how long I want my easement to be. I am just getting into this. All I can tell you is that I don't want it over a foot long...
I'm beginning to realize that Windows 10 and sound decoders have a lot in common. There are so many things you have to change in order to get them to work the way you want.
I provided a link to do just that earlier. Perhaps you skipped over it.
Anyway, I'll be glad to run the formula for you if you tell me how long you want the easement to be.
Doughless dknelson In the (unlikely) event that anyone wants to bone up on the actual engineering principles and forumulas behind all of this, the classic text is "Railroad Curves and Earthwork, With Tables" by C. Frank Allen. My copy is the 7th edition (1931). The original was 1889. For the FULL flavor of what a railroad practical engineer would need to lay out easement curves, then you'd need "Smoley's Combined Tables, Logarithms and Squares, Slopes and Rises." Mine is the 10th edition (1953). In the alternative you could just enjoy another martini. Holy Smoley, thats a lot of reading!
dknelson In the (unlikely) event that anyone wants to bone up on the actual engineering principles and forumulas behind all of this, the classic text is "Railroad Curves and Earthwork, With Tables" by C. Frank Allen. My copy is the 7th edition (1931). The original was 1889. For the FULL flavor of what a railroad practical engineer would need to lay out easement curves, then you'd need "Smoley's Combined Tables, Logarithms and Squares, Slopes and Rises." Mine is the 10th edition (1953). In the alternative you could just enjoy another martini.
In the (unlikely) event that anyone wants to bone up on the actual engineering principles and forumulas behind all of this, the classic text is "Railroad Curves and Earthwork, With Tables" by C. Frank Allen. My copy is the 7th edition (1931). The original was 1889. For the FULL flavor of what a railroad practical engineer would need to lay out easement curves, then you'd need "Smoley's Combined Tables, Logarithms and Squares, Slopes and Rises." Mine is the 10th edition (1953).
In the alternative you could just enjoy another martini.
Holy Smoley, thats a lot of reading!
this slide presentation on Curves and Superelevation answered my questions, that superelevation counters centripedal forces at a specific speed.
dknelson In the (unlikely) event that anyone wants to bone up on the actual engineering principles and forumulas behind all of this, the classic text is "Railroad Curves and Earthwork, With Tables" by C. Frank Allen. My copy is the 7th edition (1931). The original was 1889. For the FULL flavor of what a railroad practical engineer would need to lay out easement curves, then you'd need "Smoley's Combined Tables, Logarithms and Squares, Slopes and Rises." Mine is the 10th edition (1953). In the alternative you could just enjoy another martini. Dave Nelson
Dave Nelson
- Douglas
BNSF UP and others modelerDoes anyone know the exact numbers (raduis and length) for easements into 30" raduis track? And 28" raduis too?
One good answer is in the first post in this thread in reply to your question.
cuyamaAn Internet search for "model railroad easement" will yield lots of results, many of them useful. Here's one from our hosts:http://mrr.trains.com/how-to/track-planning-operation/2017/05/easy-easements-for-model-train-track
From that linked web page:
Note the upper-right-hand corner.
As has been discussed multiple times in this thread, there is no fixed "radius" for a spiral easement -- it is continuously variable.
Layout Design GalleryLayout Design Special Interest Group
Easement: a gradual change from one steady state to another--frequently from straight track to constant radius curve, or back.
In a flat curve, that would be a section of track between straight and constant radius.
In a superelevated curve, that would be a section of track, usually the same section noted above, that is between the straight track and the superelevated constant radius.
You CAN have an eased flat (without superelevation) curve. An example is in the trackage for a terminal passenger station. There is no need for superelevation because the speeds are so slow. Curves can be tight, though, since such terminals tend to be in large cities. So flat easements are essential.
gregc i found Track transition curve helpful. It includes the following as an explanation for easements Such difference in the elevation of the rails is intended to compensate for the centripetal accelerationneeded for an object to move along a curved path, so that the lateral acceleration experienced by passengers/the cargo load will be minimized, which enhances passenger comfort/reduces the chance of load shifting (movement of cargo during transit, causing accidents and damage). but i think Sheldon's explanation that it provides time for the trucks to change alignment and avoid flange contact more correct.
i found Track transition curve helpful. It includes the following as an explanation for easements
Such difference in the elevation of the rails is intended to compensate for the centripetal accelerationneeded for an object to move along a curved path, so that the lateral acceleration experienced by passengers/the cargo load will be minimized, which enhances passenger comfort/reduces the chance of load shifting (movement of cargo during transit, causing accidents and damage).
but i think Sheldon's explanation that it provides time for the trucks to change alignment and avoid flange contact more correct.
Except that that quote is talking about superelevation. Not easements. They are NOT the same thing.
When setting up a superelevation, one DOES use a vertical easement. THAT happens, approximately, in the same section as the horizontal easement.
Note that the quote (and article, I believe) never talks about vertical easement, and confuses easement with superelevation.
7j43k I will suggest that the length of easement needed to keep the flange from striking the rail when entering a curve is far shorter than those that are actually used. The page on Euler spiral explains that easement became more important as rail speeds increased. if the lack of easements wasn't noticable for low train speeds, then presumably the length of the easement depends on the train speed. if super elevation helps counter the centripedal force of a train going around a curve at speed, i wonder what happens if a train is going slower than the speed the super elevation is designed for -- do the wheel flanges rub against the innder rail? (how much force do the tapered wheel produce)? what happens if a train is stopped on a super elevated curve? do the flanges rub against the inner rail until the train gets up to speed?
7j43k I will suggest that the length of easement needed to keep the flange from striking the rail when entering a curve is far shorter than those that are actually used.
The page on Euler spiral explains that easement became more important as rail speeds increased.
if the lack of easements wasn't noticable for low train speeds, then presumably the length of the easement depends on the train speed.
if super elevation helps counter the centripedal force of a train going around a curve at speed, i wonder what happens if a train is going slower than the speed the super elevation is designed for -- do the wheel flanges rub against the innder rail? (how much force do the tapered wheel produce)?
what happens if a train is stopped on a super elevated curve? do the flanges rub against the inner rail until the train gets up to speed?
Here, again, the terms "easement" and "superelevation" are incorrectly used interchangeably.
There will be a component that will try to "slide" the equipment into the lower rail. When that happens, the difference in tread circumference will have a corrective effect. Just as in a flat curve.
It would be interesting to design a section of track where the train WOULD slide into the flanges. Included in the work would be the difference between static friction (when the train is truly stopped) and rolling/sliding friction (after it starts moving).
gregc dknelson In the (unlikely) event that anyone wants to bone up on the actual engineering principles and forumulas behind all of this, the classic text is "Railroad Curves and Earthwork, With Tables" by C. Frank Allen. i always find the engineering interesting. i found Track transition curve helpful. It includes the following as an explanation for easements Such difference in the elevation of the rails is intended to compensate for the centripetal accelerationneeded for an object to move along a curved path, so that the lateral acceleration experienced by passengers/the cargo load will be minimized, which enhances passenger comfort/reduces the chance of load shifting (movement of cargo during transit, causing accidents and damage). but i think Sheldon's explanation that it provides time for the trucks to change alignment and avoid flange contact more correct. 7j43k I will suggest that the length of easement needed to keep the flange from striking the rail when entering a curve is far shorter than those that are actually used. The page on Euler spiral explains that easement became more important as rail speeds increased. if the lack of easements wasn't noticable for low train speeds, then presumably the length of the easement depends on the train speed. if super elevation helps counter the centripedal force of a train going around a curve at speed, i wonder what happens if a train is going slower than the speed the super elevation is designed for -- do the wheel flanges rub against the innder rail? (how much force do the tapered wheel produce)? what happens if a train is stopped on a super elevated curve? do the flanges rub against the inner rail until the train gets up to speed? engineering is full of compromises and is often only optimal for a single situation (which is better than no compensation).
dknelson In the (unlikely) event that anyone wants to bone up on the actual engineering principles and forumulas behind all of this, the classic text is "Railroad Curves and Earthwork, With Tables" by C. Frank Allen.
i always find the engineering interesting.
engineering is full of compromises and is often only optimal for a single situation (which is better than no compensation).
Yes, there can be too much superelevation for slow train speeds. The biggest effects there are too much drag in the inside flange/taper, and possible string line derailments of long, heavy, slow freight traffic.
And yes, higher speeds require longer easments, and more superelevation, but that needs to be balanced with slow speeds needs as well.
Engineers must consider all factors and balance the outcomes.
Sheldon
dknelsonIn the (unlikely) event that anyone wants to bone up on the actual engineering principles and forumulas behind all of this, the classic text is "Railroad Curves and Earthwork, With Tables" by C. Frank Allen.
7j43kI will suggest that the length of easement needed to keep the flange from striking the rail when entering a curve is far shorter than those that are actually used.
My text is Route Location and Design by Felix Hickerson. About 1960.
It deals with highway engineering. I know, blasphemous on a railroad forum. But nevertheless, the principles and mathematics are applicable.
Martini, anyone?
Robert
LINK to SNSR Blog
gregcis this saying that super elevation changes gradually during in the easement and remains failrly constant when the curve radius remains relatively constant?
That is my understanding of the real thing, but I don't have a prototype engineering reference.
7j43k I will suggest that the length of easement needed to keep the flange from striking the rail when entering a curve is far shorter than those that are actually used. Ed
I will suggest that the length of easement needed to keep the flange from striking the rail when entering a curve is far shorter than those that are actually used.
Agreed, but the prototype is also concerned with wheel and rail wear, stress on spikes, keepers, tie plates, as well as worst case operating conditions.
And as you suggested, there are other reasons for easements, not the least of which in minimizing pulling force offsets, especially with long cars.
The wheel/rail relationship at a given speed may require one thing, but the desired pulling force alignment may require a more gentle easement, especially for passenger cars.
Here is some light reading on this topic:
http://webspace.webring.com/people/ib/budb3/arts/tech/ease.html
http://webspace.webring.com/people/ib/budb3/arts/tech/curv.html
ATLANTIC CENTRALThe inner part of the wheel near the flange is the larger diameter part of the wheel, not the smaller diameter.
yes. thanks for the correction
gregc ATLANTIC CENTRAL Wheel direction does not change until forward motion forces the wheel taper up the outside rail, then the larger diameter speeds up the outside wheel, steering the axle in the new direction. seems to me, that a truck encountering a curve will continue to go straight causing the the outside wheels to rest on the inner and smaller radius part of the wheel causing it turn in the opposite direction of the curve. seems that super elevation is needed to cause the truck and wheels to follow the curve allowing gravity to help pull the wheels toward the center of the curve.
ATLANTIC CENTRAL Wheel direction does not change until forward motion forces the wheel taper up the outside rail, then the larger diameter speeds up the outside wheel, steering the axle in the new direction.
seems to me, that a truck encountering a curve will continue to go straight causing the the outside wheels to rest on the inner and smaller radius part of the wheel causing it turn in the opposite direction of the curve.
seems that super elevation is needed to cause the truck and wheels to follow the curve allowing gravity to help pull the wheels toward the center of the curve.
The inner part of the wheel near the flange is the larger diameter part of the wheel, not the smaller diameter.
As the rail curves under the wheel, the wheel rides closer to the flange on the outside, farther from the flange on the inside. The larger diameter outside riding surface covers more distance per revolution, causing the wheelset to change direction with the wheel.
Did you look at the video on the link I posted above? You should, here it is again.
Note: the static picture on that site is wrong, but the video shows the correct action of the wheels in a curve.
https://www.scienceabc.com/eyeopeners/how-do-train-wheels-turn.html
ATLANTIC CENTRALWheel direction does not change until forward motion forces the wheel taper up the outside rail, then the larger diameter speeds up the outside wheel, steering the axle in the new direction.
seems that super elevation can help is needed to cause the truck and wheels to follow the curve by allowing gravity to help pull the wheels toward the center of the curve.
ATLANTIC CENTRALMost prototype curves actually have no fixed radius, they are often just two long spiral easements back to back, like a section out of the small end of an ellipse. Especially if the change in direction is 90 degrees or less.
the lateral forces on the train will be maximum on the tightest part of the curve. seems that an easement allows these forces to increase gradually.
i agree. why should the easement be for a limited distance except to limit the minimum radius of the curve and the maximum lateral forces (of course these forces can be minimized by limiting the speed of the train).
cuyamaOn the prototype (and well-designed large layouts), the easement between superelevated curve and tangent also provides the running length for the superelevation to decrease back to level.
is this saying that super elevation changes gradually during in the easement and remains failrly constant when the curve radius remains relatively constant?
7j43k gregc 7j43k For a train at speed, the change in lateral acceleration will not be abrupt. Meaning that both equipment and load will have a lessened "feeling" of getting kicking in the head as they enter the turn. Or leave. Or, put another way, their Martini glasses are less likely to tip over. are you saying this is just for passenger comfort and there's no mechanical benefit? No. I was attempting to describe mechanical stresses for equipment. And loads. I agree with Sheldon. But there are reasons beyond those he describes. Ed
gregc 7j43k For a train at speed, the change in lateral acceleration will not be abrupt. Meaning that both equipment and load will have a lessened "feeling" of getting kicking in the head as they enter the turn. Or leave. Or, put another way, their Martini glasses are less likely to tip over. are you saying this is just for passenger comfort and there's no mechanical benefit?
7j43k For a train at speed, the change in lateral acceleration will not be abrupt. Meaning that both equipment and load will have a lessened "feeling" of getting kicking in the head as they enter the turn. Or leave. Or, put another way, their Martini glasses are less likely to tip over.
are you saying this is just for passenger comfort and there's no mechanical benefit?
No.
I was attempting to describe mechanical stresses for equipment. And loads.
I agree with Sheldon. But there are reasons beyond those he describes.
Yes, but I am trying to avoid writing the whole engineering manual....
On the prototype (and well-designed large layouts), the easement between superelevated curve and tangent also provides the running length for the superelevation to decrease back to level.
gregc ATLANTIC CENTRAL Easements allow gravity, forward motion, and the wheel taper to change the direction of wheel set gradually, without the flanges crashing into the rail. not sure about wheel direction because it is constantly changing on a curve. it sounds like you're saying an easement provides time for wheels to shift to one side (inward) so that the taper causes the truck to follow a curved path. (the outer wheel rides on the larger radius part of the wheel and the inner wheel the smaller radius). presumably the easement also does the opposite when the train comes out of the curve. is superelevation also required, at least for a higher speed train?
ATLANTIC CENTRAL Easements allow gravity, forward motion, and the wheel taper to change the direction of wheel set gradually, without the flanges crashing into the rail.
not sure about wheel direction because it is constantly changing on a curve.
it sounds like you're saying an easement provides time for wheels to shift to one side (inward) so that the taper causes the truck to follow a curved path. (the outer wheel rides on the larger radius part of the wheel and the inner wheel the smaller radius).
presumably the easement also does the opposite when the train comes out of the curve.
is superelevation also required, at least for a higher speed train?
Yes it does the opposite on the way out.
Wheel direction does not change until forward motion forces the wheel taper up the outside rail, then the larger diameter speeds up the outside wheel, steering the axle in the new direction.
Again, done too suddenly, failure results.
Super elevation allows even higher speeds for any given radius. Super elevation begins at the beginning of the easement, increasing gradually as the radius gets sharper.
Most prototype curves actually have no fixed radius, they are often just two long spiral easements back to back, like a section out of the small end of an ellipse. Especially if the change in direction is 90 degrees or less.
Your car steers this way too for similar reasons........
Only toy trains (like LIONEL or an HO set with snap track) crash into curves, all others vehicles make elliptical turns.......
ATLANTIC CENTRALEasements allow gravity, forward motion, and the wheel taper to change the direction of wheel set gradually, without the flanges crashing into the rail.
And friction means wear on wheels and track. There are actually anti-friction products used to decrease wear. How railroads decide where to use these products is a mystery to me.
Henry
COB Potomac & Northern
Shenandoah Valley
It is actually a mechanical necessity.
In theory, trains would work without flanges on the wheels. The wheel taper centers the wheelsets between the rails. Then the wheel taper allows the rigid axle to go around the curve.
The value of rail travel is the very low rolling resistance per ton. As soon as the flange hits the rail, that advantage is lost.
Easements allow gravity, forward motion, and the wheel taper to change the direction of the wheel set gradually, without the flanges crashing into the rail. This keeps the ride smooth, and the friction low, so the locomotive can pull a similar load around the curve as compared to what in can pull in a straight line.
At any high speed, trains would simply derail if thrust into a curve without an easement. They would continue going straight (basic physics) and the flange would be no match for the forces, the wheel would simply climb the rail.