Acela and tilting

[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.

[blue streak 1]

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.

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;

1. A train will have a cant deficiency in direct correlation to its speed?.Zero def when stopped?

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? 

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?

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?

Now it gets complicated.

5. If there is a DPU pushing on the rear what happens?

6. add in grades?

7. What are the balancing speeds for different degrees of curves? Any tables?

8. What are good curves for HSR?

Now  you can beat me up!!!

[timz]

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]

blue streak 1

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;

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.

 

[blue streak 1]

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

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.

[BNSFwatcher]

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

[oltmannd]

blue streak 1

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.

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.

[oltmannd]

HarveyK400

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.

If you remember those single axle, single platform intermodal cars from the 1980s (TTOX, TTUX marks), they had a tendency to get popped off the rails when empty and in high buff conditions on curves....which is why they are now history.

[HarveyK400]

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 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.

[timz]

HarveyK400

I think the rule for vertical curves used to be 100 ft for every 1% change in grade at conventional, 60-80 mph speeds.

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.

[HarveyK400]

timz

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.

I have never heard of such a long vertical curve for road or rail; but that doesn't mean what you say is incorrect.  The Williams cutoff example would mean that the change in grade takes almost two miles!  I can tell you that the South Shore goes from about level to a 2.5% grade and back down to level in less than a mile.  Highway vertical curves must be much longer for visibility and safety over a crest for the allowed speeds. 

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. 

[timz]

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".

[blue streak 1]

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.

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.

[HarveyK400]

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.

[HarveyK400]

 

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.

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.

[aegrotatio]

 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.

 

[timz]

HarveyK400

I don't doubt that the TGV has much greater than normal vertical curves.

Actually, they're not so huge. I still say 0.1% change per 100 ft is/was considered sort of standard in the US (maybe Hay is where I read that)-- which you notice is 100000 ft radius.

[timz]

HarveyK400

I suspect the 100 mph curve [east of Providence] is slightly broader, perhaps 1.25-degree.

A reasonable suspicion, but it turns out it is indeed 1.5 degree. No idea why more cant deficiency is allowed there than elsewhere.

[diningcar]

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.