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Oil Trains Cause Track Defects?

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Posted by Electroliner 1935 on Tuesday, October 20, 2015 11:23 PM

Fluids in motion have considerable momentum forces. Best examples are shown in water hammer which is why your plumbing has antihammer arrestors. This is one reason that I think there is merit to the proffered theory's as to CBR trains having dynamics that are not fully understood yet. 

From Wikipedia

https://en.wikipedia.org/wiki/Water_hammer

Water hammer (or, more generally, fluid hammer) is a pressure surge or wave caused when a fluid (usually a liquid but sometimes also a gas) in motion is forced to stop or change direction suddenly (momentum change). A water hammer commonly occurs when a valve closes suddenly at an end of a pipeline system, and a pressure wave propagates in the pipe. It is also called hydraulic shock.

This pressure wave can cause major problems, from noise and vibration to pipe collapse. It is possible to reduce the effects of the water hammer pulses with accumulatorsexpansion tankssurge tanks, and other features.

 End of clip

213,000 LB of Crude can be contained in the tank car, but what does it do to the suspension and the loadings on the trucks, axles and wheels when it wants to move in its direction which may be different than the way the train is going. Does anyone know of any studies of tanker truck dynamics? 

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Posted by M636C on Wednesday, October 21, 2015 4:04 AM

I have carefully explained how oil trains can break rails without needing to invoke any unconventional explanations.

The problem with any "water hammer" explanation is that the oil is not moving relative to the tank as water is in a pipe when a valve closing can cause cause a water hammer event.

As I've said before, most of the oil won't and can't move. What moves is a relatively small bubble of air in the very top of the tank. It will be much more like a bubble in a spirit level and less like a Tsunami....

Now, if we were talking about a train of interconnected cars (as the great majority of trains are not) and the leading car was half full, you might get a significant surge in an emergency stop, but in general, there won't be any significant surge.

There are enough conventional explanations for oil trains breaking rails without needing to find an unconventional one.

It is the results of an oil train derailment and not the cause that attracts attention. A train of boxcars and hoppers breaking a rail is literally a daily occurence but it is regarded as a minor nuisance while exactly the same physics derailing an oil train may be a national disaster.

We don't need to find a different explanation for oil train derailments. Statistics are just simplified summaries. I challenge anyone to read the full report of an oil train derailment and find anything that requires an oil-specific explanation.

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Posted by tree68 on Wednesday, October 21, 2015 8:14 AM

M636C
We don't need to find a different explanation for oil train derailments. Statistics are just simplified summaries. I challenge anyone to read the full report of an oil train derailment and find anything that requires an oil-specific explanation.

Yes

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Posted by schlimm on Wednesday, October 21, 2015 8:24 AM

M636C

I have carefully explained how oil trains can break rails without needing to invoke any unconventional explanations.

The problem with any "water hammer" explanation is that the oil is not moving relative to the tank as water is in a pipe when a valve closing can cause cause a water hammer event.

As I've said before, most of the oil won't and can't move. What moves is a relatively small bubble of air in the very top of the tank. It will be much more like a bubble in a spirit level and less like a Tsunami....

Now, if we were talking about a train of interconnected cars (as the great majority of trains are not) and the leading car was half full, you might get a significant surge in an emergency stop, but in general, there won't be any significant surge.

There are enough conventional explanations for oil trains breaking rails without needing to find an unconventional one.

It is the results of an oil train derailment and not the cause that attracts attention. A train of boxcars and hoppers breaking a rail is literally a daily occurence but it is regarded as a minor nuisance while exactly the same physics derailing an oil train may be a national disaster.

We don't need to find a different explanation for oil train derailments. Statistics are just simplified summaries. I challenge anyone to read the full report of an oil train derailment and find anything that requires an oil-specific explanation.

M636C

 

I'm going to ask a potentially stupid question.  Is it possible some tank cars are exceeding the 286,000# limit?  Are they all weighed?

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Posted by BaltACD on Wednesday, October 21, 2015 8:49 AM

schlimm

I'm going to ask a potentially stupid question.  Is it possible some tank cars are exceeding the 286,000# limit?  Are they all weighed?

I have not seen waybills for oil shipments.  However, I suspect, since the oil being shipped has a known weight per unit of volume it is being shipped under a 'Shippers Weight Agreement' wherein the shipper declares the weight for billing purposes.  The Weight Agreement contract specifies penalties for those who violate the agreement.  While most carriers maintain weighing in motion scales, trains that don't need weights for billing purposes are not routinely weighed to check the accuracy of the shippers agreed weight.

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Posted by schlimm on Wednesday, October 21, 2015 9:06 AM

BaltACD

 

 
schlimm

I'm going to ask a potentially stupid question.  Is it possible some tank cars are exceeding the 286,000# limit?  Are they all weighed?

 

I have not seen waybills for oil shipments.  However, I suspect, since the oil being shipped has a known weight per unit of volume it is being shipped under a 'Shippers Weight Agreement' wherein the shipper declares the weight for billing purposes.  The Weight Agreement contract specifies penalties for those who violate the agreement.  While most carriers maintain weighing in motion scales, trains that don't need weights for billing purposes are not routinely weighed to check the accuracy of the shippers agreed weight.

 

I see.  Given the Bakken and Canadian producers less-than-accurate info about the volatility of their products in the past, can that Agreement be relied upon?  Maybe some cars could be 10% over?

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Posted by Euclid on Wednesday, October 21, 2015 9:49 AM
I find that the oil train anomaly that the article concludes from the statistic it quotes is fallacious.  It contains nothing that shows an unusual in the number of oil trains being derailed by track defects as the tone of the article implies.  The key to the fallacy is in the words, “the overall rate for freight train accidents.”  That overall rate has to include mixed manifest trains.  Therefore what the statistic would illustrate is that any unit train will find more track defects than would a mixed manifest train. 
 
“Track problems were blamed [on for] 59% of the [oil train] crashes, more than double the overall rate for freight train accidents, according to a Times analysis of accident reports. Investigators and rail safety experts are looking at how the weight and movements of oil trains may be causing higher than expected track failures.”
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Posted by BaltACD on Wednesday, October 21, 2015 9:57 AM

schlimm
BaltACD
schlimm

I'm going to ask a potentially stupid question.  Is it possible some tank cars are exceeding the 286,000# limit?  Are they all weighed?

I have not seen waybills for oil shipments.  However, I suspect, since the oil being shipped has a known weight per unit of volume it is being shipped under a 'Shippers Weight Agreement' wherein the shipper declares the weight for billing purposes.  The Weight Agreement contract specifies penalties for those who violate the agreement.  While most carriers maintain weighing in motion scales, trains that don't need weights for billing purposes are not routinely weighed to check the accuracy of the shippers agreed weight.

I see.  Given the Bakken and Canadian producers less-than-accurate info about the volatility of their products in the past, can that Agreement be relied upon?  Maybe some cars could be 10% over?

Each carrier has it's own allowance for permissible overloads from a cars stated gross allowable weight.  Depending on the carrier, these range from 0 to 10 percent.

In my experience, when the weight of a train presented at train handling situation (it stalled when it shouldn't have) - it got weighed at the next opportunity.  I don't know what, if any, actions were taken against the shipper and these occurrences were over 40 years ago and I was never privy to the results of the weighing.

 

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Posted by dehusman on Wednesday, October 21, 2015 10:09 AM

Electroliner 1935
Fluids in motion have considerable momentum forces. Best examples are shown in water hammer which is why your plumbing has antihammer arrestors.

But the contents of a tank car are NOT fluids in motion. In the case of water hammer you are talking about a pipe where the entire crossection of the pipe is in motion and there is a flow through the length of the pipe.  There is NO flow in a tank car, it is a closed container. 

Electroliner 1935
A water hammer commonly occurs when a valve closes suddenly at an end of a pipeline system, and a pressure wave propagates in the pipe. It is also called hydraulic shock

A tank car is not a pipeline system. There is no flow.  There is no valve closing.  There is no pressure wave top propagate through a system that isn't there.

You need a water hammer trap on you home plumbing because it is a pipeline.  You do not need a water hammer trap on a jug of water you buy at the grocery store.   It is a closed container with no flow.

Two completely different sets of circumstances and two completely different environments.

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Posted by dehusman on Wednesday, October 21, 2015 10:37 AM

Once again, really simple math would fix a lot of the speculation.  Any six grader should be able to do this.

Google "DOT 111"  There will be a picture of TILX 290344.

Capy 30110 gal

LD LMT 198000

Lt Wt  65000

Crude oil weighs 7.1 lbs /gal.  30110 x 7.1 = 213,781 lbs if the car is completely full of oil. 

213781-198000= 15781 lbs overloaded if full shell capacity = 7.9 tons.

15781/7.1 lbs/gal = 2,223 gals of void x .13368 cu ft/gal = 297 cu ft of void.

2223/30110 = 7.4% void

Its not that hard.  Find the picture of your favorite crude oil tank car and swap out your numbers for my numbers.

Of course these numbers are bad news for the sloshing kills the track crowd.  The difference between a 263 and a 286 car is 23 tons, or 11.5 tons per truck.  Even if you could magically slosh the entire void to one end of the car, that would only be an increase of 7.9 tons, less than the increase in loading of running a 286 car across the track.

The number don't point to a cause.

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Posted by Euclid on Wednesday, October 21, 2015 10:54 AM
dehusman

Once again, really simple math would fix a lot of the speculation.  Any six grader should be able to do this.

Google "DOT 111"  There will be a picture of TILX 290344.

Capy 30110 gal

LD LMT 198000

Lt Wt  65000

Crude oil weighs 7.1 lbs /gal.  30110 x 7.1 = 213,781 lbs if the car is completely full of oil. 

213781-198000= 15781 lbs overloaded if full shell capacity = 7.9 tons.

15781/7.1 lbs/gal = 2,223 gals of void x .13368 cu ft/gal = 297 cu ft of void.

2223/30110 = 7.4% void

Its not that hard.  Find the picture of your favorite crude oil tank car and swap out your numbers for my numbers.

Of course these numbers are bad news for the sloshing kills the track crowd.  The difference between a 263 and a 286 car is 23 tons, or 11.5 tons per truck.  Even if you could magically slosh the entire void to one end of the car, that would only be an increase of 7.9 tons, less than the increase in loading of running a 286 car across the track.

The number don't point to a cause.

 
No it is not hard, but you are leaving out the dynamic component of the load. the reason your numbers don't point to a cause is that your 7.9 tons is a static load, which is meaningless.  We are not just talking about setting weights on a scale.  Your easy calculation leaves out the dynamic load.  For that, you need the mass of oil that moves, how fast it moves, how quickly it accelerates to that speed, and how quickly it stops.    
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Posted by Paul_D_North_Jr on Wednesday, October 21, 2015 11:28 AM

Load Factor of 1.7 is commonly used in structural analysis and calulations for the impact of a dynamic = moving load on a structure - even and including steel wheels on steel rails on steel bridges (deck-type, not even a ballast deck to attenuate those forces). 

7.9 tons x 1.7 LF = 13.4 tons addditional, at most - since oil is a fluid, it would be less hard and more of a cushioned impact than a solid load.

7.9 tons/ 143 tons (286K car) = 5.5% additional.  That's not significant enough to break rails.  (Dynamic load factor would apply equally to the 143 tons and 7.9 ton portions).

143 tons + 7.9 tons = 150.9 tons.  If that's allegedly breaking rails, then better hope that no 315,000 lb. gross weight cars (157.5 tons) are around . . . Mischief

Finally: "Wheel Impact Load Detectors" ("WILD") and similar devices along main lines are capable of detecting overloaded cars/ trucks/ axles/ wheels, depending on their sophistication / capabilities. 

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Posted by Euclid on Wednesday, October 21, 2015 12:13 PM
Paul,
Nobody is suggesting that an additional 7.9 tons of load is breaking the rails.  I am talking about violent slack run-in accelerating the entire mass of the oil load into motion until it assumes a new shape as a full cylinder occupying the forward portion of the tank; and then its accelerated motion being abruptly arrested when it assumes that new shape.
A 143-ton loaded tank car sitting on the track exerts a static load and everything is supported with no failure.  What happens when you raise that tank car 100 feet in the air and drop it onto the track?     
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Posted by Euclid on Wednesday, October 21, 2015 12:21 PM
Near where I live, the C&NW once loaded a wooden gondola with lead ingots.  The car was in good condition and rated for the load.  The problem was that the car bounced, and the upward acceleration of the ingots increased their loading by adding the dynamic load component resulting from their acceleration. The ingots became heavier than their static load, and therefore broke through the floor and wrecked the train.    
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Posted by dehusman on Wednesday, October 21, 2015 1:25 PM

Euclid
Near where I live, the C&NW once loaded a wooden gondola with lead ingots. The car was in good condition and rated for the load. The problem was that the car bounced, and the upward acceleration of the ingots increased their loading by adding the dynamic load component resulting from their acceleration. The ingots became heavier than their static load, and therefore broke through the floor and wrecked the train.

Dude, we are discussing a tank car.  Its a closed container.  The load can't "bounce up", it constrained inside the tank.  The whole load doesn't impact the ends because there is no movement EXCEPT for the liquid that displaces the void.  If you push more than the void towards the end of the tank car then an equal amount of fluid has to rush to the other end of the car, even at that, the load is moving longitudinally, NOT vertically. 

Crude oil doesn't break through the rotted wood floor of the tank car to cause a derailment.  Your example has absolutely nothing to do with the case in hand or sloshing.  Its not even an example of dynamic load damaging the track.

The dynamic load is not significant.  Whatever the dynamic load of a 263 car is, the dynamic load of a 286 car is more.  Virtually every main track of a class 1 railroad has a structure designed to carry 263 loads (including dynamic loading, since by definition a train is supposed to move, making it a dynamic load), most modern main tracks are designed to carry 286 loads.  If it can carry 286, it certainly can carry the load of a 263, whether it be a static or dynamic load.

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Posted by Norm48327 on Wednesday, October 21, 2015 1:36 PM

Dave,

Yes,but..................

Methinks you are wasting your breath. Bang Head

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Posted by BaltACD on Wednesday, October 21, 2015 1:38 PM

The Laws of Physics, yes but!

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Posted by Euclid on Wednesday, October 21, 2015 1:46 PM

Dave,

The lead ingots are an analogy.  I am stunned that you fail to see that.  Did you really think I was saying the tank cars are full of lead ingots and the tanks have wooden floors?

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Posted by BaltACD on Wednesday, October 21, 2015 1:53 PM

Euclid

Dave,

The lead ingots are an analogy.  I am stunned that you fail to see that.  Did you really think I was saying the tank cars are full of lead ingots and the tanks have wooden floors?

The solid load in a wood floor gon and the liquid load in tank car are in no way analogus.

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Posted by schlimm on Wednesday, October 21, 2015 2:26 PM

dehusman

 

 
Electroliner 1935
Fluids in motion have considerable momentum forces. Best examples are shown in water hammer which is why your plumbing has antihammer arrestors.

 

But the contents of a tank car are NOT fluids in motion. In the case of water hammer you are talking about a pipe where the entire crossection of the pipe is in motion and there is a flow through the length of the pipe.  There is NO flow in a tank car, it is a closed container. 

 

 
Electroliner 1935
A water hammer commonly occurs when a valve closes suddenly at an end of a pipeline system, and a pressure wave propagates in the pipe. It is also called hydraulic shock

 

 

A tank car is not a pipeline system. There is no flow.  There is no valve closing.  There is no pressure wave top propagate through a system that isn't there.

You need a water hammer trap on you home plumbing because it is a pipeline.  You do not need a water hammer trap on a jug of water you buy at the grocery store.   It is a closed container with no flow.

Two completely different sets of circumstances and two completely different environments.

 

Dave H, I'm no physicist or expert in fluid dynamics, but your understanding of the forces of liquid in a partially-filled, closed container (like a tank car) seems a bit amiss.   Are you one of the former?   What are your credentials to always speak so dogmatically?

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Posted by Euclid on Wednesday, October 21, 2015 2:28 PM

 

BaltACD
 
Euclid

Dave,

The lead ingots are an analogy.  I am stunned that you fail to see that.  Did you really think I was saying the tank cars are full of lead ingots and the tanks have wooden floors?

 

The solid load in a wood floor gon and the liquid load in tank car are in no way analogus.

 

[/quote]

They are analogus in terms of the effect of dynamic loading.  The point is mass.  It makes no difference whether it is liquid or solid mass.  It makes no difference whether the dynamic loading impacts wood or steel.

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Posted by BaltACD on Wednesday, October 21, 2015 3:17 PM

Euclid
BaltACD
Euclid

Dave,

The lead ingots are an analogy.  I am stunned that you fail to see that.  Did you really think I was saying the tank cars are full of lead ingots and the tanks have wooden floors?

The solid load in a wood floor gon and the liquid load in tank car are in no way analogus.

They are analogus in terms of the effect of dynamic loading.  The point is mass.  It makes no difference whether it is liquid or solid mass.  It makes no difference whether the dynamic loading impacts wood or steel.[/quote]

Were the lead ingots upwardly restrained?  I suspect not, as if they were secured to the car floor, there would be no resulting dynamic loading.  Just because lead is heavy doesn't mean it is going to remain where it was place.  Liquid loads are upwardly, as well as sidewardly restrained by walls of the tank itself and all dynamic loads act on the monocoque of the tank itself.

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Posted by MidlandMike on Wednesday, October 21, 2015 9:15 PM

Some posters have posed that the oil train routes are on lines that don't have other unit trains.  Recalling the recent CBR derailments in IL, VA, and WV, were all on mainlines that carried unit coal trains.  The 2 recent derailments in northern Ontario were in the winter, which probably also meant unit grain trains.

Additionally, CBR is not the only example of tank car unit trains.  There are also liquid sulfur trains, ethanol trains, and also, at least, less than unit train blocks of propane, chemical and fertilizer tank cars.

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Posted by Paul of Covington on Wednesday, October 21, 2015 11:32 PM

   All this detailed analysis of oil train dynamics might be fun, but it seems to me it's usefulness is dependent on comparison of numbers that someone picked out and came up with "could be" and "suggests that".   I would think that the useful comparisons would be the number of derailments due to track failures per car-mile or ton-mile for oil trains compared to that for other unit trains and for manifest trains.

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Posted by Paul of Covington on Wednesday, October 21, 2015 11:36 PM

Euclid
What happens when you raise that tank car 100 feet in the air and drop it onto the track?

   This seems like a good project for MYTH BUSTERS.   They like to destroy things just for the fun of it.

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Posted by Euclid on Thursday, October 22, 2015 8:53 AM
BaltACD
 
Liquid loads are upwardly, as well as sidewardly restrained by walls of the tank itself...
 

That is true IF there is zero air space inside of the loaded tank.  If that were the case, then the oil is 100% constrained, and so there will be no load shifting.  However, I will speculate that there is never a loaded tank car with zero air space.  Therefore, there is always the ability for some degree of load shifting.  So a good question would be to ask how much air space is actually in the tank cars of specific Bakken oil trains.  Does anybody have the documented answer to that question to share with us?
In order to come to any conclusion as to the degree of load shifting and the force that it transfers, we need to know how much air space there is and how hard the slack runs in.    
Here is the point of the lead ingots analogy: 
Like oil in a partially filled tank, the lead ingots were unrestrained.  The ingots were loaded into a car that was perfectly adequate to handle their static load.  The loading was approved by C&NW.  What the company failed to account for was the ability for the load to shift and acquire dynamic loading in addition to the static load.  It is the same way that Dave Husman has mathematically accounted for the static load of oil in a tank car, but failed to account for the dynamic load. 
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Posted by dehusman on Thursday, October 22, 2015 11:45 AM

Euclid
It is the same way that Dave Husman has mathematically accounted for the static load of oil in a tank car, but failed to account for the dynamic load.

What Euclid has failed to account for is that a tank car is a closed container.  The weight in the video was dropped on the box.  There was air space under the weight and above the object impacted.

In a tank car the oil is in contact with and fills the entire container, except for whatever air space there is generated by the differential between the load limit and the volume of the tank car.  The void will be at the TOP of the container.

Euclid neeeds to explain what force he is going to use to displace several tons (not the entire load, just the volume of the void) of oil up to the top of the tank car which would require the the void to be moved to another part of the car (it would be amusing to see where Euclid thinks the void is going to go, he may think it magically, instananeously materializes at the bottom of the oil.)  If he can figure out how to move all the parts around inside the container, the mazimum lift would be limited to the average height of the void (probably something in the range of 6 inches), then he would have to figure out how to drop that oil, simulataneously moving the void from the bottom of the container to the top of the container near instantaeously (if he used magic to beam it to the bottom I guess he can magically beam it to back to the top).  Now as the oil impacts the bottom of the tank car (assuming he can figure out all the above), since its contacting a curved surface the force will have a horizontal component towards the center (which balances out since the curve is the same on the left and right sides and the forces point towards the middle).  The net result of that is to reduce the downward force.

He will probably say that some sort of track defect or slack action causes one end of the car to "bounce" a foot or more in the air to cause the oil to shift.  I want to read how he plans to explain the mechanics of that happening without derailing the car, disconnecting the air hoses, disconnecting the truck brake connections, and with shelf couplers, whose whole mission in life to to prevent vertical bypasses.

 

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Posted by Euclid on Thursday, October 22, 2015 1:52 PM
dehusman
 
Euclid
It is the same way that Dave Husman has mathematically accounted for the static load of oil in a tank car, but failed to account for the dynamic load.

 

What Euclid has failed to account for is that a tank car is a closed container.  The weight in the video was dropped on the box.  There was air space under the weight and above the object impacted.

In a tank car the oil is in contact with and fills the entire container, except for whatever air space there is generated by the differential between the load limit and the volume of the tank car.  The void will be at the TOP of the container.

Euclid neeeds to explain what force he is going to use to displace several tons (not the entire load, just the volume of the void) of oil up to the top of the tank car which would require the the void to be moved to another part of the car (it would be amusing to see where Euclid thinks the void is going to go, he may think it magically, instananeously materializes at the bottom of the oil.)  If he can figure out how to move all the parts around inside the container, the mazimum lift would be limited to the average height of the void (probably something in the range of 6 inches), then he would have to figure out how to drop that oil, simulataneously moving the void from the bottom of the container to the top of the container near instantaeously (if he used magic to beam it to the bottom I guess he can magically beam it to back to the top).  Now as the oil impacts the bottom of the tank car (assuming he can figure out all the above), since its contacting a curved surface the force will have a horizontal component towards the center (which balances out since the curve is the same on the left and right sides and the forces point towards the middle).  The net result of that is to reduce the downward force.

He will probably say that some sort of track defect or slack action causes one end of the car to "bounce" a foot or more in the air to cause the oil to shift.  I want to read how he plans to explain the mechanics of that happening without derailing the car, disconnecting the air hoses, disconnecting the truck brake connections, and with shelf couplers, whose whole mission in life to to prevent vertical bypasses.

 

 

Dave,
Once again you are constructing an absurdity and attributing it to me.
The force is a reaction to slack run-in.  The force that produces the dynamic load moves forward along the horizontal axis of the tank car.  When it does, the oil moves forward, and the air it displaces moves rearward.  So the impact tends to cause the oil to be separated from the air in a vertical plane.  Whether it actually achieves that vertical separation depends on the dynamic force generated in the impact.  Then after the impact, the oil and air move back to their original positions with the air on top and oil on the bottom.
During the impact, the dynamic load is applied horizontally to the forward head of the tank.  During this impact, all of the oil load moves as part of the dynamic force.  Every single molecule of oil moves as the oil shifts its position and separates from the air in a vertical plane.  The oil molecules move at differing speeds, in different directions, and over differing distances. 
Once the oil and air separate vertically, every molecule of oil is stopped from moving by the blockage of the leading tank head.  That abrupt stopping of the oil is where the kinetic energy that produces the dynamic load comes from.  It comes from the sum total of all molecules being stopped.  However, some molecules will be moving faster than others, so as they are stopped, they will contribute differing individual amounts of kinetic energy to the total dynamic load. 
But the point is that the entire load of oil is involved in producing the dynamic load on the leading tank head.  It is not just the amount of oil that equals part or all of the air space. 
Again, I am not asserting that this is derailing trains, and the theory does require an air space.  The greater the air space, the greater the potential dynamic loading will be.
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Posted by BaltACD on Thursday, October 22, 2015 2:01 PM

Euclid
Again, I am not asserting that this is derailing trains, and the theory does require an air space.  The greater the air space, the greater the potential dynamic loading will be.

An yet the Engineers that have run Oil Trains have said they detect no appreciable differences in train dynamics in handling oil train as opposed to other similar sized trains, both with tank cars and with other type cars.  Worst trains the engineers I have talked to are auto-racks, both loaded and empty, with their cushioning draft gear a 100 car train can have upwards of 400 feet of free running slack working its way throughout the train.

Never too old to have a happy childhood!

              

  • Member since
    May 2005
  • From: S.E. South Dakota
  • 13,569 posts
Posted by Murphy Siding on Thursday, October 22, 2015 2:26 PM

Euclid

 

Dave,
Once again you are constructing an absurdity and attributing it to me.

 

I'll admit that there's certainly enough absurdity in the world to go around, some folks seem to be carriers...Whistling

Thanks to Chris / CopCarSS for my avatar.

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