The 10,000 foot verticle curve at Eagle Nest, 31 miules west of Williams, AZ, has a 1.00% westward decending grade intercepting a 0.88% ascending grade. The purpose was to mitigate slack action and it certainly was significant foresight given the 10,000 - 15,000 foot freight trains now operating on the TRANSCON.
The observation that Santa Fe was not consistent only tends to supplement Santa fe's foresight because at the other locations between Williams and Crookton gradient percentage disparities were not so pronounced while the 10,000 foot V/C was at the end of a 30 mile decending 1% grade with no intervening ascending grades. The slack action mitigation was unnecessary in those locations and therefore the expense of longer V/C's was avoided.
HarveyK400 I suspect the 100 mph curve [east of Providence] is slightly broader, perhaps 1.25-degree.
HarveyK400 I don't doubt that the TGV has much greater than normal vertical curves.
Seems to me, without realignment through Baltimore, the trip will always be too long. I just finished a depressing story of Baltimore railroads when researching the Howard Street Tunnel fire and Baltimore is the major kink of the NYP-WAS segment.
blue streak 1 So Harvey and Oltmannd: Disregarding all ROW, Utility relocation, and other costs; what are the construction costs of a 2,3,4 track overhead essentially straight elevated structure to avoid curves? Use a height of about 30 ft. Ignore bridges and use whatever track span you feel is reasonable.
So Harvey and Oltmannd: Disregarding all ROW, Utility relocation, and other costs; what are the construction costs of a 2,3,4 track overhead essentially straight elevated structure to avoid curves? Use a height of about 30 ft. Ignore bridges and use whatever track span you feel is reasonable.
I haven't seen any recent average per-mile costs that would do you much good.
The biggest hinderances would be the right of way, relocation, court, and good will costs that you didn't list and the approval you may never get.
Incredible. I don't doubt that the TGV has much greater than normal vertical curves. Nonetheless, a video of the record-breaking TGV-West run showed a long curve and a substantial sag across a valley much less than 10 miles wide even through a telephoto lens that would seem to be a lot less vertical curve than even the 16,000 meter radius.
One reason for long vertical curves may be to keep the catenary at a constant height and not pull up in a sag.
oltmannd[The general rule is for heavy haul, curves are OK, grades are bad. For HSR, grades are OK, curves are bad. Normally, HSR has very high HP/ton and can ascend some pretty significant grades at track speed. I remember reading somewhere that the original TGV line has some significant changes in grade and the roller coaster effect made some passengers queasy. They reduced speed at these points to lessen the effect.
I checked the SFe chart-- they weren't consistent on the vertical curve lengths Williams-Crookton. For some reason they made that one curve long, but some others are at a rate of 2000 ft per percent.
Incidentally: say we do have a parabolic curve 10000 horizontal feet long, joining a 1% upgrade to a 1% downgrade; if we replace it with a circular arc the track will shift less than 0.001 ft at the 2500-5000-7500 ft marks. (I lazily assumed a flat earth, but hopefully changing to spherical will affect the two curves the same.)
A 1975 article in Rwy Gaz Intl on the French high-speed plans says vertical curves were to be at least 16000 meter radius (25000 "wherever possible") except that humps could be 14000 and troughs could be 12000 in the "difficult sections".
timz100 ft for every 0.1% sounds more likely. As somebody mentioned, Santa Fe put in vertical curves 10000 ft long where the 1% upgrade met 1% downgrade on the Williams-Crookton cutoff. I think the standard rule was that grade could change twice as fast in a sag as on a hump-- or maybe the other way around.
100 ft for every 0.1% sounds more likely. As somebody mentioned, Santa Fe put in vertical curves 10000 ft long where the 1% upgrade met 1% downgrade on the Williams-Crookton cutoff.
I think the standard rule was that grade could change twice as fast in a sag as on a hump-- or maybe the other way around.
The differential for a sag (100':1%) and a hump (50':1%) for a rail line sounds familiar; but I may have that confused with the CTA.
HarveyK400I think the rule for vertical curves used to be 100 ft for every 1% change in grade at conventional, 60-80 mph speeds.
oltmanndThe general rule is for heavy haul, curves are OK, grades are bad. For HSR, grades are OK, curves are bad. Normally, HSR has very high HP/ton and can ascend some pretty significant grades at track speed. I remember reading somewhere that the original TGV line has some significant changes in grade and the roller coaster effect made some passengers queasy. They reduced speed at these points to lessen the effect.
I think the rule for vertical curves used to be 100 ft for every 1% change in grade at conventional, 60-80 mph speeds. For 220 mph, the vertical curve (and it's more parabolic than circular) would need to change 1% about every 300 ft to avoid an unsettling roller coaster effect. There may be a more precise equation as with the length of horizontal curve transition spirals.
HarveyK4005. If there is a DPU pushing on the rear what happens?I think the opposite has happened, but rarely - cars can be pushed of the track to the outside of the curve. Only examples I can think of are the result of collisions.
5. If there is a DPU pushing on the rear what happens?
I think the opposite has happened, but rarely - cars can be pushed of the track to the outside of the curve. Only examples I can think of are the result of collisions.
-Don (Random stuff, mostly about trains - what else? http://blerfblog.blogspot.com/)
blue streak 1Wow that is much greater than I imagined. --- Far out question---- Does this mean that it is probably better to go with straight grades than curves if costs are the same? Of course you cannot change grades too fast or you might fly off the rails? If so have some thoughts for the NEC.
I'm sorry I chimed in. I flunked "Pickett/K&E Slide Rule 101" in college. This is getting beyond me. I did, as a kid, sneak into the Concordia College (Bronxville, NY) gym and run on their elevated wooden track. Cool, but I never stopped in the turns! Never did make the Olympics, though. Had to wait until I learned how to play ice hockey...
Bill Hays
HarveyK400 8. What are good curves for HSR? I just did a couple examples. With 3" cant and 3" allowable cant deficiency, a 57,000-ft radius curve (almost 11 miles!) would be necessary. 5" cant and 5" allowable cant deficiency would reduce this to a 19,100-ft radius curve
8. What are good curves for HSR?
I just did a couple examples. With 3" cant and 3" allowable cant deficiency, a 57,000-ft radius curve (almost 11 miles!) would be necessary. 5" cant and 5" allowable cant deficiency would reduce this to a 19,100-ft radius curve
Wow that is much greater than I imagined. --- Far out question---- Does this mean that it is probably better to go with straight grades than curves if costs are the same? Of course you cannot change grades too fast or you might fly off the rails? If so have some thoughts for the NEC.
blue streak 1So Harvey let me see if I can understand cant deficiency. If my ideal RR is located on a piece of flat land with no elevation change, no wind, 10,000 ft train with all power up front when it encounters a curve that has no cant; 1. A train will have a cant deficiency in direct correlation to its speed?.Zero def when stopped?Yes to both. 2. Now the center of gravity affects cant deficiency how? ie single level no tilting passenger train different than a double stack at the same speed?The height of the center of gravity does not affect the cant deficiency or overbalance; but it will affect the roll, or lean, of the vehicle and weight transfer with a more complicated set of equations involving spring deflection and features such as swing hangers. 3. Since there is a constant pulling force exerted by the locos will the stringlining effect balance out the cant deficiency more on the front cars than the rear?Stringlining occurs where the pulling force and trailing resistance at the couplers is sufficient to pull over the car or cars already at an angle or pull the flanges of these cars over the railhead. This is exacerbated in the snap from taking out slack and less likely with a constant pulling force. Stringlining is more likely to occur on a curve near the front of a train where trailing tonnage and rolling resistance is greater. 4. For every inch of cant on a curve there will be a balancing speed for each car dependent on its center of gravity? When stopped all trains on a cant will have a negetive cant defieiency but will be different dependent on center of gravity?See #1 & #2. Now it gets complicated. 5. If there is a DPU pushing on the rear what happens?I think the opposite has happened, but rarely - cars can be pushed of the track to the outside of the curve. Only examples I can think of are the result of collisions. 6. add in grades?Again, more likely with slack action. You may break down a long train to get over the hill, but lifting the train adds comparable train resistance. Another reason for distributed power in the train, especially a long one. 7. What are the balancing speeds for different degrees of curves? Any tables?There are tables and formulas in every railroad engineering textbook and in the FRA regulations Mph=SQRT((Cant+Allow def in inches)/(Deg of curve)/0.0007). There are even protocols for calculating the effective curvature of switch points and resulting allowable speed (3" cant deficiency) if less than the curved rails. 8. What are good curves for HSR?I just did a couple examples. With 3" cant and 3" allowable cant deficiency, a 57,000-ft radius curve (almost 11 miles!) would be necessary. 5" cant and 5" allowable cant deficiency would reduce this to a 19,100-ft radius curve. Now you can beat me up!!!Aint that bad; but I'm missing the "Prisoner of Azkaban" and/or the Olympics.
1. A train will have a cant deficiency in direct correlation to its speed?.Zero def when stopped?
Yes to both.
2. Now the center of gravity affects cant deficiency how? ie single level no tilting passenger train different than a double stack at the same speed?
The height of the center of gravity does not affect the cant deficiency or overbalance; but it will affect the roll, or lean, of the vehicle and weight transfer with a more complicated set of equations involving spring deflection and features such as swing hangers.
3. Since there is a constant pulling force exerted by the locos will the stringlining effect balance out the cant deficiency more on the front cars than the rear?
Stringlining occurs where the pulling force and trailing resistance at the couplers is sufficient to pull over the car or cars already at an angle or pull the flanges of these cars over the railhead. This is exacerbated in the snap from taking out slack and less likely with a constant pulling force. Stringlining is more likely to occur on a curve near the front of a train where trailing tonnage and rolling resistance is greater.
4. For every inch of cant on a curve there will be a balancing speed for each car dependent on its center of gravity? When stopped all trains on a cant will have a negetive cant defieiency but will be different dependent on center of gravity?
See #1 & #2.
Now it gets complicated.
6. add in grades?
Again, more likely with slack action. You may break down a long train to get over the hill, but lifting the train adds comparable train resistance. Another reason for distributed power in the train, especially a long one.
7. What are the balancing speeds for different degrees of curves? Any tables?
There are tables and formulas in every railroad engineering textbook and in the FRA regulations Mph=SQRT((Cant+Allow def in inches)/(Deg of curve)/0.0007). There are even protocols for calculating the effective curvature of switch points and resulting allowable speed (3" cant deficiency) if less than the curved rails.
I just did a couple examples. With 3" cant and 3" allowable cant deficiency, a 57,000-ft radius curve (almost 11 miles!) would be necessary. 5" cant and 5" allowable cant deficiency would reduce this to a 19,100-ft radius curve.
Now you can beat me up!!!
Aint that bad; but I'm missing the "Prisoner of Azkaban" and/or the Olympics.
The term "cant deficiency" has nothing to do with center of gravity, or grades, or DPU. A train's "balance speed" on a curve doesn't depend on any of that. When a train is at its balance speed on a curve, the track's cant (superelevation) exactly matches the centripetal force needed at the train's speed-- so the wheels on the inside of the curve are pressing down on the rail just the same as the wheels on the outside of the curve.
The formula is easy to figure out:
E = 0.0007 times (miles/hour squared) times degree of curve
E is the cant (in inches) needed on standard-gauge track to balance a train at a given speed. So at 100 mph on a 1-degree curve you need 7 inches to balance the centrifugal force.
But with a conventional passenger train you're allowed to do 100 mph around a 1-deg curve that has only 4 inches of cant. The cant deficiency then is 7 - 4 = 3 inches, which is the usual FRA limit.
HarveyK400 Most roads have less cant than 4" so passenger speed is limited to about 60 mph; and that is with the allowable 3" cant deficiency and typical of the UP between Lombard, Illinois and West Chicago. The balance speed is just under 40 mph. 4" cant and 3" cant deficiency for a 2-degree curve would allow 71.8 mph, nominally 70 mph. Rock Island did this. The Santa Fe transcon beat this with a 2-deg curve with 5" cant allowing 75 mph for passenger trains at Ancona, Illinois where the main swings sharply west from the original line, now abandoned, that continued to Peoria in a straight line. Running intermodals and priority trains at 70 mph would result in a 1.64" cant deficiency.
Most roads have less cant than 4" so passenger speed is limited to about 60 mph; and that is with the allowable 3" cant deficiency and typical of the UP between Lombard, Illinois and West Chicago. The balance speed is just under 40 mph.
4" cant and 3" cant deficiency for a 2-degree curve would allow 71.8 mph, nominally 70 mph. Rock Island did this.
The Santa Fe transcon beat this with a 2-deg curve with 5" cant allowing 75 mph for passenger trains at Ancona, Illinois where the main swings sharply west from the original line, now abandoned, that continued to Peoria in a straight line. Running intermodals and priority trains at 70 mph would result in a 1.64" cant deficiency.
So Harvey let me see if I can understand cant deficiency. If my ideal RR is located on a piece of flat land with no elevation change, no wind, 10,000 ft train with all power up front when it encounters a curve that has no cant;
Bus passengers, at least this one, are too busy gripping the arm rest and praying the bus doesn't tip. The OTR cruisers are up so high it's a wonder they don't roll over more often; and a transit bus full of standees is a lot of shifting weight on a hard corner.
For what it's worth, I was dozing off in a Lakeshore bedroom when we it hit a low joint (grade crossing?) at 110 mph between Albany and Schenectady, bottomed out on the springs, and seemingly rode on four wheels. That woke me up and broke a sweat. I thought it better to lie to my wife.
In the interest of fair disclosure, I've had many white-knuckle moments driving and flying too.
The compromises for superelevation (cant) have been made. You are correct in that tilt does not reduce wheel and track wear; but tilt allows faster comfortable passenger speeds where cant (superelevation) already is at the host railroad's limit for freight service. As posted in these forums, NS uses a higher cant for more competitive freight speeds on the former Southern, and of course the NEC uses more cant and accepts the cost consequences with mixed traffic for faster passenger trains.
A vehicle will tip roughly the equivalent of the overbalance in addition to the cant relative to spring travel and height of the center of gravity above top of rail.
First, 286,000 lb cars are pretty much on the edge of metallurgy; so high overbalance for increased passenger speed can shift a significant proportion of freight car weight to the low rail. The weight transfer is aggravated by cars with a higher center of gravity of 90-100 inches (compared to a passenger car's roughly 60 inches). This results in plastic deformation and fissures in the railhead that are a defect that must be addressed with restrictions until replaced and reduces rail life much faster than surface wear. Comparable damage is done to the wheel tread. In overbalance, the wheel flange will be in contact with the inner rail head and wear both to the extent that gauge limits are exceeded.
The second problem is that freight cars had comparatively short spring travel, most four inches or less (I'm not clear on this - best case it's for a loaded car). I'm not familiar with today's status; but spring travel was trending upward. Cant over 3" really affects the softness of the ride with even Class IV and Class V track; so higher cant would be problematic at lower speeds.
Third, high cant and sharper curves leave a train more susceptible to a bow-sting derailment where cars are pulled off the tracks to the inside of the curve.
If my approximation is close, a car with a 90" high c/g and 4" spring travel wouldn't tip over standing still without almost 14" cant; so train dynamics and rail degradation would be more limiting.
I may have missed something; but these are my understanding of the issues.
BNSFwatcherIsn't there a physical limit to the amount of super-elevation that can be employed on lines jointly used by passenger and frieght, especially if the train is not moving? Hays
Isn't there a physical limit to the amount of super-elevation that can be employed on lines jointly used by passenger and frieght, especially if the train is not moving?
Hays
Bill: There must be but oltmann would know. I remember running on some indoor, wooden tracks that had very tight, but banked turns. Running was great but if you stopped you had to be careful or you would feel like falling over.
C&NW, CA&E, MILW, CGW and IC fan
I notice that inner city buses, through buses, and tour buses tilt the wrong way quite a bit on almost any curve. As far as I know, the bus passengers don't complain.
I don't think tilting helps to reduce wheel and track wear as superelevation does. Therefore, my opinion is that tilting introduces additional mechanical parts that we can well do without. We should focus instead on getting the best compromise for superelevation, which will balance the train loads at one selected speed and minimize wear on all the equipment.
I was sloppy - the Fiat Pendolino successors are now built by Alstom, not Siemens
schlimm Harvey: I believe the Fiat and Siemens tilting trains are similar but not the same design.
Harvey: I believe the Fiat and Siemens tilting trains are similar but not the same design.
I also suggest going to the Talgo website. The high-speed Talgos used in Spain have low profile (and center of gravity) integrated power cars at both ends of the train. These are not compatible with high level platforms.
Japanese and the Fiat (Siemens?) tilt trains may have distributed powered coaches with a lower center of gravity and are designed for high level platforms.
schlimmblue streak 1Off subject of this post the need for low center of gravity locos and motors to haul tilt trains is not IMHO being pushed enough. Are the European operators pulling tilt trains using any thing along that line? European and Japanese tilting trains mostly use distributed power. If there are separate power units front and rear, they are matching. Again, the wiki article is quite comprehensive with pics:http://en.wikipedia.org/wiki/Tilting_train
blue streak 1Off subject of this post the need for low center of gravity locos and motors to haul tilt trains is not IMHO being pushed enough. Are the European operators pulling tilt trains using any thing along that line?
European and Japanese tilting trains mostly use distributed power. If there are separate power units front and rear, they are matching. Again, the wiki article is quite comprehensive with pics:
Harvey my point is that the Newark - Phl can become almost straight track with very gentle curves except for the section inside Philidelphia city. The "S" curve at Elizabeth is almost the same direction approaching and leaving, (about 4 -5 degrees) The curve at Lincoln (edison) is a left southbound curve of 10 - 15 degrees around edison yard that is mostly not used for the closed ford plant. This should give a long (34 mile) run for true HSR. (170+)
The straightening of Trenton - PHL will help although I forsee many problems to changing the track from Frankford yard Jct thru Shore and the flyovers needed at 16th st/north Philadelphia jct. That is where the tilt is very important.
Off subject of this post the need for low center of gravity locos and motors to haul tilt trains is not IMHO being pushed enough. Are the European operators pulling tilt trains using any thing along that line?
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