i understand the concept that a 100' chain can be used to create a chord thru a curved line that intersects at the radial lines over a specific angle in order to lay a curve with a specific radius.
it's not clear to me how a single chain can be used. Is there a 2nd chain perpendicular to the midpoint of the chain between the chain and existing curve?
and how does the curve get started to that enough of the curve is in place to extend the curve?
greg - Philadelphia & Reading / Reading
I knew nothing about this. But found this one explanation, of several.
http://trn.trains.com/railroads/abcs-of-railroading/2006/05/grades-and-curves
It includes the following:
"Curvature can be expressed in terms of the number of degrees traversed by 100 feet of track. For example, a relatively gentle 5-degree curve encompasses 5 degrees of a circle for each 100 feet of track; a sharper 15-degree curve covers 15 degrees in each 100 feet. The radius (distance from center point to edge) of a curve is obtained with the following conversion equation: radius in feet = 5729 divided by the degrees of curvature. This is known as the "arc" definition of curvature, which is normally used by highway designers. Railroad designers use the "chord" definition of curvature, which is based on the degrees encompassed by a 100-foot line segment whose endpoints fall on the arc described by the curved track. An approximate method of determining curvature this way involves stretching a 62-foot-long string between two points on the inside face of the outer rail head. The number of inches between the center point of the string and the rail corresponds to the degrees of curvature: 1 inch equals 1 degree, 2 inches equals 2 degrees, and so on. For the purposes of the casual observer, the difference between the arc and chord methods of measurement are small: the radius of a 15-degree arc-definition (highway) curve is approximately 382 feet, while the radius of a 15-degree chord-definition (railroad) curve is about 383 feet. Curves of 1 or 2 degrees are the most common on mainline railroads; the sharpest curve a common four-axle diesel can take is about 20 degrees when coupled to other rolling stock, more than 40 degrees when by itself. Mountainous territory, however, generally dictates curves of 5 to 10 degrees, or even sharper. Branch lines and minor spurs may have an even greater number of sharper curves."
Paul
Modeling HO with a transition era UP bent
i understand the math
wondering, literally, how the "chain gang" applied it
Assume we are going to layout a completely new line.
Start at the PC (point of curvature.)
Set up the transit on the PC, sight back along the tangent, then extend that line forward 100 ft using the chain, measure an offset, and set station 100.
Move the transit up to station 100. Sight back to the PC, then extend that line forward 100 ft using the chain, measure an offset, and set station 200.
Move the transit up to station 200. Sight back to station 100, then extend that line forward 100 ft using the chain, measure an offset, and set station 300.
Move the transit up to station 300. Sight back to station 200, then extend that line forward 100 ft using the chain, measure an offset, and set station 400.
Etc.
Dave H. Painted side goes up. My website : wnbranch.com
Assume we don't have a transit and are going to layout a completely new line.
Go back 100 ft from the PC, sight from that point to the PC, then extend that line forward 100 ft using the chain, measure an offset, and set station 100.
Move up to the PC. Sight from that point to station 100, then extend that line forward 100 ft using the chain, measure an offset, and set station 200.
Move up to station 100. Sight from station 100 to station 200, then extend that line forward 100 ft using the chain, measure an offset, and set station 300.
Move up to station 200. Sight from station 200 to station 300, then extend that line forward 100 ft using the chain, measure an offset, and set station 400.
Not as accurate as with a transit.
from the PC, presumably the "offset" is measured from the line extending the straight track leading to the curved.
at station 100, where is the offset measured from? the tangent to the curve at station 100?
gregc from the PC, presumably the "offset" is measured from the line extending the straight track leading to the curved. at station 100, where is the offset measured from? the tangent to the curve at station 100?
Yes, that is why the transit is more accurate. 100 feet is not very far when you are bending steel rail. Like a bent stick, it is not really necessary to have too many intermediate measurements. The rail bends evenly between the stations.
Ties are placed roughly and pushed left or right a needed as the curve is established.
So in practice station 100 may be layed out at 2 degrees, station 200 at 4 degrees and station 300 at 6 degrees to create an easement. From there the curve might stay at 6 degrees..... until it starts to straighten out.
Today with big machines, or years ago with men and bars, final adjustments are made after the track is going together.
Sheldon
i confused by the mention of use of a transit. I thought the use of a chain was simple enough not to require any special equipment. (think mid 1800s)
of course more than just a 100' chain is needed. The diagram below shows a how a length of chain with an additional length of chain (red) attached to it's midpoint (an offset) and pulled perpendicular can be used overlapping the existing curve to extend it.
the initial curve segment can be located using offsets (blue) by extending the straight section
part of my interest is could this approach be used on a layout where it's not possible to locate a center and draw a curve using a compass/beam. Wondering if a triangular template could be slid around to locate a curve.
The transit was invented in 1831 by William Young. I believe he invented the transit specifically for the burgeoning railroad construction. I doubt few lines after 1831 were laid out without a transit.
http://www.surveyhistory.org/evolution_of_the_transit1.htm
Ray
Greg,
Read Dave's post more carefully.
Greg, you are missing the point. Your method won't work because there is no way to know where to put the other end of the chain. You can do it on your drawing because you know where the curve is. Doesn't work that way when surveying.
The offest isn't in the middle, its at the end. What they are laying out isn't a curve, its actually a polygon. It becomes a curve AFTER the track is laid. Then you can use the midpoint offset to adjust the curvature of the track. Real track is just like flex track, you can move it side to side.
That's why you have to sight off the previous station to establish a line from which you will measure your offset. You don't use a chain for measuring the offset, just a tape measure or a rule.
Yes, railroads would use a transit because if they were on a tangent they would need that accuracy to keep going straight over miles and miles.
If you want an easy way to lay out model curves, get a 4x4 piece of 1/8 masonite.
Use a trammel to draw arcs on 2" spacing starting with an even radius.
Then use the trammel to draw arcs in a different spot on the masonite (not overlapping the even radius arcs) on a 2" spacing starting with an odd radius.
Cut along the lines.
You will not have a set of radius templates in inch increments. Takes maybe an hour or so to do with a less than $100 investment in hardboard.
Google this:
"laying out railroad curves by offset of tangents"
Also, keep in mind, the prototype does not use much "constant radius" trackage. Most curves are really two easements back to back. So the degree of curvature for each station will likely be different until the apex is reached, then it "unwinds".
gregc
The answer to the original question is yes, curves can be laid out using just a chain.
The ancient Greeks worked out principles of geometry (that are still valid today) using nothing but a straight edge and a compass. Yes, the same compass you know about, but used differently than you think.
There are a dozen or so dimensions regarding curves that can be directly calculated knowing only the radius and the central angle. The central angle is called the delta, and for a curve that has a chord of 100 feet it is called the degree of curve by the railroad definition.
The red line on the sketch above is called the mid-ordinate. If that red line is extended beyond the curve until it intersects the point of intersection of the forward- and reverse tangents (PI), the distance from the curve to the PI is called the external. One way (there are several) to lay out a curve is from the tangents. The chain gang would almost certainly not know this, but the foreman of the crew or the surveyor almost certainly would.
BTW, ancient Greeks did not use rulers. They would open the legs of their compass to a certain distance and stick the pointy end on a point and make little sweep marks in what they estimate is their area of interest. Then they'd move the pointy end to another point, change the distance of the compass, and make a sweep that crosses the first sweep. All of the properties of modern geometry are based on this simple process.
Start by Googleing 'external' and see where that goes.
Good luck.
Robert
PS This only applies to circular curves. Spiral transitions are a whole 'nother matter.
PPS Sheldon typed in something very interesting while I was fidgeting with my post. He's right.
LINK to SNSR Blog
Well Greg,
I found a drawing that shows exactly how it is done, exactly as Dave described. But, my scanner function is not working on my 12 year old printer - and this drawing is on paper, imagine that, in my 1968 set of NMRA Data Sheets which I recieved when I joined......
Update: The drawing in question, and the formulas and info, are on the new updated NMRA data sheets online - but it requires member access. Data sheet D3a - properties of curves, originally issued by the NMRA in 1946.......
Yes, I am a NMRA member, have been continiously since 1968.
ATLANTIC CENTRAL Well Greg, I found a drawing that shows exactly how it is done, exactly as Dave described. But, my scanner function is not working on my 12 year old printer - and this drawing is on paper, imagine that, in my 1968 set of NMRA Data Sheets which I recieved when I joined...... Sheldon
Hey Greg, DaveH, and Sheldon-
I haven't seen Sheldon's scan, but DaveH's method would only work in the wide open plains of Nebraska where you could extend the rear tangent those hundreds of feet. Very long curves could require very large offsets even for large-radius low-degree-of-curve curves. And those offsets have to be laid out and measured perpendicular to the (extended straightaway) tangent line.
The work flow is like this: start at PC, measure to PI, move chain to PI, intersect tangent length from PI to PT with 100' chain from PC. This establishes point on curve at Station 1+00. Repeat.
It's obvious no one here knows anything about railroad surveying so here is the straight dope from someone who staked out plenty of curves.
First, offsets are not normally used to lay out a curve.
Instead, the transit is set up at the beginning of the curve (PC, for point of curve), set to a zero angle, and sighted back along the track centerline. The barrel (the telescope-like tube that you look through) is then flopped over vertically 180 degrees so the eyepiece is now facing the opposite direction.
We now looking ahead at where the curve is to be laid out. Depending on the degree of curve and the desired spacing of centerline stakes (we usually set stakes every 50 or 100 feet; every 25 feet for a very sharp curve) a deflection angle is computed, and the transit is "turned" to that angle (as shown on the angle scale). The instrumentman then puts the person setting stakes "on line" by having him move the stake right or left as needed while also holding the chain or steel tape for the correct distance. The stake is then driven into the ground, a new sight is taken, and a small nail or surveyor's tack is placed in the top of the stake at the exact angle and distance.
For the next stake a new deflection angle is computed, and the process is repeated; with the same distance between stakes being used as previously.
Many times the curve is too long or is obstructed so the entire curve can't be staked from one transit setup; here the instrumentman "moves up" on the curve to one of the stakes set already. After the instrument is set up, it is sighted (with a zero angle) on the PC, and flopped over as before. A new deflection angle is then turned (the previous deflection angle from the PC to the new location PLUS the deflection angle from the new setup to the next stake) and the next stake is set.
The person setting stakes is looking back at the stakes previously set; if all is well they make a smooth curve, and an incorrect angle will make a stake stand out from the curve.
Usually the end of curve (PT, or point of tangent) has been set already and can be used to verify if the curve has been staked correctly. Here, the deflection angle and distance from the last curve stake to the PT is computed; if the turned angle and measured distance match the computed values the curve said to "close."
Curves on higher speed main lines usually have "easements" or "spirals" on the beginning and end of the curve; these gradually increase curvature from zero degrees (tangent) to the curvature of the main curve. Most curves are long enough that the spirals on each end are only a small portion of the total curve. There are various formulas to compute spirals; typically they approximate a cubic parabola. Curves on lower speed track are usually not spiraled.
Kurt Hayek
Hi All,
Being in Australia and having grown up in the imperial age (we are now a metric country) I understood a "chain" to be an old English measurement equal to 66 feet. Curves on the South Line out of Adelaide had the measurement expressed in "chains" and were mostly 10 chain (660 feet) radius curves. This coupled to 1 in 45 (2.2% in US terms) and 1 in 40 (2.5% in US terms) made for difficult operating conditons, something that still provides difficulties today.
I must admit I understand the concept of degrees of curvature ( higher degrees equals a sharper curve etc) but unlike my converting percentages to gradients, i really have a problem readily converting degrees as a radius with a mental calculation.
Just a different slant,
Cheers from Australia
Trevor
ok, all descriptions imply that the use of a transit is essential to laying out the curve, along with something to measure distance.
while i have no doubt this is how it has always been done during my lifetime, i was curious how it was done in the early days of railroads before the existence of a transit. I can't imagine a need for constant radius curves before railroads existed.
dehusmanGreg, you are missing the point. Your method won't work because there is no way to know where to put the other end of the chain.
the diagram shows a series of "T"s composed of a long length and a short perpendicular bisector. If the left tip of the long length and tip of the bisector lie on an existing curve, the right hand tip of the long length locates the next point. It's physically extending the line and using an offset to locate the next point instead of optical using a transit.
another approach would be to "L" shaped arrangement where the long length partially overlaps the previous segment and extends that line and the short length is the offset locating the next point.
i believe this approach ("T") can work because it uses a triangle, 2 pts located on an existing segment of the curve to determine the next (3rd) point on the curve. Each point can be as close to the previous point as desired.
of course, once a line is extended using a transit, multiple points on the curve can be located perpendicular to the extension and appropriate offsets. of course, the radius does not need to be constant.
thanks for the explanations
Be it a highway or a railroad, there are a number of actual field methods depending on the site conditions and the amount of advanced planning and survey work that has been done.
Yes, modern methods make greater use of the transit.
Yes, you can lay out the curve from the inside or the outside.
But the outside offset method Dave described works without a transit and generally works in narrow rights of way.
NMRA Data sheet group D3 goes into great detail about prototype track geometry. The newly refreshed and digitally available Data sheets alone are worth the price of membership........
Including answers and explanations to this question.
It is really very simple: You buiild the tunnel first and then you lay the tracks in the center of it.
The Route of the Broadway Lion The Largest Subway Layout in North Dakota.
Here there be cats. LIONS with CAMERAS
Whether you want to call the instrument a "transit" or not, George Washington was a surveyor, so instruments to layout or lines and angles have existed since before the 1800's.
The predecessor of the transit was the theodolite. It existed from the 1600s. It makes no sense to talk about laying out a railway line without the proper instruments. This work was done by the professionals of their time and they would have had the necessary equipment.
seems that a transit theodolite is used not only to lay a curve, but also to measure the grade.
The term transit theodolite, or transit for short, refers to a type of theodolite that was developed in the early 19th century. It was popular with American railroad engineers pushing west, and it replaced the railroad compass, sextant anid octant.
As a response to those asking why a transit is even necessary at all?
I have had to reproduce the alignment of sections of the PA Turnpike that were laid out originally during the 1950's using "30 second transits" ie transits with angular accuracy allegedly down to the nearest 30 seconds.
Even when flipping the scope to assure angle accuracy, there is still some error that creeps into all the actual point layouts, for a multitude of reasons (that are covered in a college level route and construction surveying class).
The long and the short of it is this: If, sitting at a cadd station in the office, I take an actual aerial survey of a section of PA Turnpike, and I attempt to layout the old plan alignment (using the center point of bridges that can be located graphically today and doing a "best fit") it is very easy to be off line (lateral shift from current centerline of median barrier) by as much as 15 feet in just a couple miles.
I would hate to see the inaccuracy of methods without using 30 second instruments.
John