Minimum Train Rollaway Gradient?

[00crashtest]

For any type of train or railcar on any type of railway, be it mainline freight or light rail, what are typically the respective minimum rollaway gradients when all brakes are fully released and no power is applied, in the absence of any external forces besides gravity and friction such as wind, seismic activity, or other objects pushing or pulling on it? If you have any personal experience, please also comment. It is okay that you are dealing with UK trains, because this is regarding any train in the world, as indicated by the inclusion of gradients in UK format and also the inclusion of Indian Railways. That is because the laws of physics act very similarly to all due to the coefficients of rolling resistance being similar, including those of the bearings. I'm only listing US railroads here because I'm most geographically familiar with them.

Most mainline railroads (more accurately railways) and metros in the world limit the exceptional maximum gradient to 1% = 1:100 at station platforms, with 0.5% = 1:200 being the normal maximum, 0.35% = 1:285.7̅1̅4̅2̅8̅5̅ being the preferred maximum (which is also the standard minimum in underground and aerial structures for drainage purposes for the WMATA Metrorail), and 0.3% = 1:333.3̅ being the normal minimum in underground and aerial structures (including stations) for drainage purposes for some of the other metro systems. Most light rails and monorails limit the exceptional maximum gradient to 2% = 1:50 at station platforms, with 1% = 1:100 being the normal maximum, 0.5% = 1:200 being the preferred maximum (which is also the standard minimum for Sound Transit Link), and 0.3% = 1:333.3 being the normal minimum in underground and aerial structures (including stations) for drainage purposes.

Most mainline railways limit the exceptional maximum gradient in parking and coupling/decoupling areas to 0.25% = 1:400, with the normal maximum being 0.2% = 1:500 and the preferred maximum being 0.1% = 1:1000, with India Railways even limiting the preferred maximum to 1/1200 = 0.083̅ %. Most metros limit the exceptional maximum gradient to 0.5% = 1:200 in parking and coupling/decoupling areas, with 0.3% = 1:333.3̅ being the normal maximum and the preferred maximum being 0.15% = 1:666.6̅ or 1:660 = 0.1̅5̅ %, which are almost identical to each other. Most light rails and monorails limit the exceptional maximum gradient to 0.5% = 1:200 in parking and coupling/decoupling areas, with 0.3% = 1:333.3̅ being the normal maximum and the preferred maximum being 0.25% = 1:400.

Obviously, trains have been known to run away at exactly a 1% grade, with the Federal Express train collision in Washington Union Station on the Pennsylvania Railroad (now defunct) in 1953 happening with its brake failure on the approach with a grade as little as -0.73% (≈ -1:137 gradient), so that isn't a gradient that will prevent a train from rolling away. So, will a 0.5% grade prevent an unpowered, unbraked train from beginning to roll in the absence of external forces? Also, Pennsylvania Station in New York has a constant grade of +/- 0.4% = 1:250 on either side of the crest at the center of the station. So, for curiousity purposes, if any type of train or railcar (even those that do not operate in those tracks such as MTA subway or NJTransit River Line light rail vehicles) is parked entirely on either side of the change in grade, will that be gentle enough to prevent the same train from beginning to roll into the tunnels under the rivers? How about 0.35%, or even 0.3%?

 

[hexagon789]

For any type of train or railcar on any type of railway, be it mainline freight or light rail, what are typically the respective minimum rollaway gradients when all brakes are fully released and no power is applied, in the absence of any external forces besides gravity and friction such as wind, seismic activity, or other objects pushing or pulling on it? If you have any personal experience, please also comment. It is okay that you are dealing with UK trains, because this is regarding any train in the world, as indicated by the inclusion of gradients in UK format and also the inclusion of Indian Railways. That is because the laws of physics act very similarly to all due to the coefficients of rolling resistance being similar, including those of the bearings. I'm only listing US railroads here because I'm most geographically familiar with them.

Most mainline railroads (more accurately railways) and metros in the world limit the exceptional maximum gradient to 1% = 1:100 at station platforms, with 0.5% = 1:200 being the normal maximum, 0.35% = 1:285.7̅1̅4̅2̅8̅5̅ being the preferred maximum (which is also the standard minimum in underground and aerial structures for drainage purposes for the WMATA Metrorail), and 0.3% = 1:333.3̅ being the normal minimum in underground and aerial structures (including stations) for drainage purposes for some of the other metro systems. Most light rails and monorails limit the exceptional maximum gradient to 2% = 1:50 at station platforms, with 1% = 1:100 being the normal maximum, 0.5% = 1:200 being the preferred maximum (which is also the standard minimum for Sound Transit Link), and 0.3% = 1:333.3 being the normal minimum in underground and aerial structures (including stations) for drainage purposes.

Most mainline railways limit the exceptional maximum gradient in parking and coupling/decoupling areas to 0.25% = 1:400, with the normal maximum being 0.2% = 1:500 and the preferred maximum being 0.1% = 1:1000, with India Railways even limiting the preferred maximum to 1/1200 = 0.083̅ %. Most metros limit the exceptional maximum gradient to 0.5% = 1:200 in parking and coupling/decoupling areas, with 0.3% = 1:333.3̅ being the normal maximum and the preferred maximum being 0.15% = 1:666.6̅ or 1:660 = 0.1̅5̅ %, which are almost identical to each other. Most light rails and monorails limit the exceptional maximum gradient to 0.5% = 1:200 in parking and coupling/decoupling areas, with 0.3% = 1:333.3̅ being the normal maximum and the preferred maximum being 0.25% = 1:400.

Obviously, trains have been known to run away at exactly a 1% grade, with the Federal Express train collision in Washington Union Station on the Pennsylvania Railroad (now defunct) in 1953 happening with its brake failure on the approach with a grade as little as -0.73% (≈ -1:137 gradient), so that isn't a gradient that will prevent a train from rolling away. So, will a 0.5% grade prevent an unpowered, unbraked train from beginning to roll in the absence of external forces? Also, Pennsylvania Station in New York has a constant grade of +/- 0.4% = 1:250 on either side of the crest at the center of the station. So, for curiousity purposes, if any type of train or railcar (even those that do not operate in those tracks such as MTA subway or NJTransit River Line light rail vehicles) is parked entirely on either side of the change in grade, will that be gentle enough to prevent the same train from beginning to roll into the tunnels under the rivers? How about 0.35%, or even 0.3%?

On the ECML certain stations have signs stating: "HST/Mk4 trains "hold" here".

The hold means a "holding" brake allocation of at least Step 2 brake should be applied as the 1 in 200 or greater gradients at those stations are sufficient enough that a Step 1 brake application isn't always enough to hold a train against the effects of gravity.

 

[krus_aragon]

Wikipedia's page on Rolling Resistance helpfully gives a typical coefficient of rolling resistance (Crr) for rail vehicles (steel wheel on steel rail) as 0.0003 to 0.0004. This is one of five elements of rolling resistance listed, but the other four only apply to a rolling object, so the coefficient is all we need to look at getting something moving.

Taking a class 153 railcar as an example ('cause it's conveniently a single car unit), a mass of 41.2t, or 41200kg, is under a force of roughly 404 kilonewtons. The above coefficient gives us the force needed to get that vehicle moving (404000 * 0.0004) 161 newtons.

Applying trigonometry, we can find the angle our 404kn of gravitational force need to be at to have a horizontal component of at least 161 newtons? The inverse sine of 161/404,000 is 0.0228 degrees. To interpret this in the traditional form as a ratio, the tangent of this angle gives the ratio of opposite (drop) over adjacent (distance). I make that 0.000399, or a gradient of 4:10000 = 1:2500.

I'm new to this area of physics, so please feel free to check my reasoning and calculations. But I've read of accounts of strong winds blowing wagons up gradients out of sidings and onto the mainline, so the low force calculated above doesn't feel that out-of-kilter to me.

 

[GC class B1]

Wikipedia's page on Rolling Resistance helpfully gives a typical coefficient of rolling resistance (Crr) for rail vehicles (steel wheel on steel rail) as 0.0003 to 0.0004. This is one of five elements of rolling resistance listed, but the other four only apply to a rolling object, so the coefficient is all we need to look at getting something moving.

Taking a class 153 railcar as an example ('cause it's conveniently a single car unit), a mass of 41.2t, or 41200kg, is under a force of roughly 404 kilonewtons. The above coefficient gives us the force needed to get that vehicle moving (404000 * 0.0004) 161 newtons.

Applying trigonometry, we can find the angle our 404kn of gravitational force need to be at to have a horizontal component of at least 161 newtons? The inverse sine of 161/404,000 is 0.0228 degrees. To interpret this in the traditional form as a ratio, the tangent of this angle gives the ratio of opposite (drop) over adjacent (distance). I make that 0.000399, or a gradient of 4:10000 = 1:2500.

I'm new to this area of physics, so please feel free to check my reasoning and calculations. But I've read of accounts of strong winds blowing wagons up gradients out of sidings and onto the mainline, so the low force calculated above doesn't feel that out-of-kilter to me.

I have a different understanding of the force required to get a railway vehicle moving from stationery. I understand this will be the force needed to overcome the static friction on the bearings and to accelerate the rotating elements from rest. (wheelsets, brake discs, final drives etc).

I suspect that this force will be significantly more than the 161 Newtons in your example which is only about 36 lbf.

 

[contrex]

get a railway vehicle moving from stationery.

Paperclips? Ball-point pens? Post-its? Notebooks?

 

[edwin_m]

Wikipedia's page on Rolling Resistance helpfully gives a typical coefficient of rolling resistance (Crr) for rail vehicles (steel wheel on steel rail) as 0.0003 to 0.0004. This is one of five elements of rolling resistance listed, but the other four only apply to a rolling object, so the coefficient is all we need to look at getting something moving.

Taking a class 153 railcar as an example ('cause it's conveniently a single car unit), a mass of 41.2t, or 41200kg, is under a force of roughly 404 kilonewtons. The above coefficient gives us the force needed to get that vehicle moving (404000 * 0.0004) 161 newtons.

Applying trigonometry, we can find the angle our 404kn of gravitational force need to be at to have a horizontal component of at least 161 newtons? The inverse sine of 161/404,000 is 0.0228 degrees. To interpret this in the traditional form as a ratio, the tangent of this angle gives the ratio of opposite (drop) over adjacent (distance). I make that 0.000399, or a gradient of 4:10000 = 1:2500.

I'm new to this area of physics, so please feel free to check my reasoning and calculations. But I've read of accounts of strong winds blowing wagons up gradients out of sidings and onto the mainline, so the low force calculated above doesn't feel that out-of-kilter to me.

With this analysis the gradient to roll away will be equal to the coefficient of rolling resistance - everything else cancels out.

However there is also the effect of "stiction" - it's harder to get a standing body moving than to keep it moving at a very low speed. And I suspect the resistance to motion of a Class 153 is somewhat higher, because two of its axles have hydrostatic drives on them.

I have a different understanding of the force required to get a railway vehicle moving from stationery. I understand this will be the force needed to overcome the static friction on the bearings and to accelerate the rotating elements from rest. (wheelsets and brake discs).

I think the static friction is the "stiction" I referred to above. The acceleration force isn't relevant here - as soon as the vehicle gets moving the stiction is no longer relevant and any resultant force will act to accelerate it, until increasing speed causes the increasing resistance to balance it out.

Paperclips? Ball-point pens? Post-its? Notebooks?

These days it does take a lot of paperwork to move a train.

 

[GC class B1]

The force operating on a railway vehicle has to accelerate both the vehicle body in a forward motion and the wheelsets and rotating parts in a rotary motion. When moving the vehicle has both kinetic energy of forward motion and kinetic energy of rotation. The applied force must therefore be sufficient to accelerate the vehicle body along the rail and cause the wheelsets to spin.
The same situation applies when braking as the retardation force must decelerate both the vehicle forward motion and the rotating parts.

The coefficient of rolling resistance mentioned in krus_aragons post may be the resistance at a steady speed. The force to accelerate a vehicle from stationery will be higher than that required just to maintain a steady speed for two reasons. 1. The resistance of bearings etc when stationery is higher than when moving (stiction), and 2. the vehicle must be accelerated from rest. While moving at a steady speed only the resistance to motion needs to be overcome by the force but when accelerating from rest the force must both overcome the resistance to motion and accelerate the vehicle (probably very slowly).

 

[Elecman]

Something in my memory says 1 in 280 was a BR rule for a maximum gradient to prevent runaways

 

[GC class B1]

Something in my memory says 1 in 280 was a BR rule for a maximum gradient to prevent runaways

That sounds about right. I think the force should be about 10 times the value suggested by @krus_aragon.

 

[krus_aragon]

Thanks for the constructive feedback: my day-to-day engineering is in the world of electronics, not mechanics.

 

[edwin_m]

I recall something about the current UK standard of 1 in 500 for places where trains can be left unattended being tightened up at some point in the past due to the advent of roller bearings, which suggests that the characteristics of the bearing are a significant factor and the rolling resistance alone doesn't answer the question.

 

[Ken H]

With regard to stiction, i think this is when you have a big load on a small area causing deformation. So where the wheel touches the rail, where up to 8 tons on an area of a 5p piece, the rail and the wheel deform a little. When the wheel moves, the bit of rail and wheel that was deformed will recover but a new bit of wheel and rail will deform - and that takes energy.

Kraus-aragon says he is a sparky. He will know that when you first apply power to a resistance, you get a short. spike in amps. This is similar.

 

[GC class B1]

I recall something about the current UK standard of 1 in 500 for places where trains can be left unattended being tightened up at some point in the past due to the advent of roller bearings, which suggests that the characteristics of the bearing are a significant factor and the rolling resistance alone doesn't answer the question.

Total Rolling resistance includes bearing friction and wheel to rail contact rolling resistance. There will also be aerodynamic effects including wind so some factors will be variable. The increased use of roller bearings will have had an effect as they will offer less friction than plain bearings.

I would expect that contact rolling resistance would be much smaller than other elements of rolling resistance.

 

[edwin_m]

With regard to stiction, i think this is when you have a big load on a small area causing deformation. So where the wheel touches the rail, where up to 8 tons on an area of a 5p piece, the rail and the wheel deform a little. When the wheel moves, the bit of rail and wheel that was deformed will recover but a new bit of wheel and rail will deform - and that takes energy.

Kraus-aragon says he is a sparky. He will know that when you first apply power to a resistance, you get a short. spike in amps. This is similar.

That's actually "pure" rolling resistance, and the fact that rubber deforms a lot more than steel basically explains why trains are much more energy-efficient than road vehicles. Stiction is the extra force needed to get something moving, that reduces as soon as motion starts.

 

[Ken H]

That's actually "pure" rolling resistance, and the fact that rubber deforms a lot more than steel basically explains why trains are much more energy-efficient than road vehicles. Stiction is the extra force needed to get something moving, that reduces as soon as motion starts.

so what is the physics for stiction. It seems to go against newton. F=ma

 

[snowball]

so what is the physics for stiction. It seems to go against newton. F=ma

It's just that the factors determining F are very complicated in the case of stiction. That doesn't contradict F=ma.

 

[Ken H]

It's just that the factors determining F are very complicated in the case of stiction. That doesn't contradict F=ma.

Whre can i gen up on what causes stiction

 

[edwin_m]

There are extra effects that come into play when two objects are in contact but not moving, which effectively increase the coefficient of friction.

 

[TheSeeker]

Paperclips? Ball-point pens? Post-its? Notebooks?

A friend always says "e for envelopes, a for all other meanings".

 

[contrex]

A friend always says "e for envelopes, a for all other meanings".

My line manager asked me, by email, to get someone to do a 'stationary order' and I was really tempted to say 'this isn't going anywhere' but restrained myself. She has been to university, apparently.

 

[GC class B1]

I don’t know what happened but my iPad often does this. I wrote stationary and it changed without me noticing.

 

[d9009alycidon]

Would atmospheric conditions make a difference? Wet rail vs dry rail, frost/ice, even if there was a strong wind blowing in the direction of the downgrade?

 

[ac6000cw]

Re. bearing stiction/friction, on page 16 of this (research paper) PDF is a graph (Fig. 10) for a wagon with tapered roller bearings of friction versus speed - https://www.mdpi.com/2075-4442/10/2/26/pdf

Basically the friction at very low speed or stationary is about twice that at 20 km/h.

 

[The Lad]

Do wet rails reduce friction on curves?

 

[d9009alycidon]

Would atmospheric conditions make a difference? Wet rail vs dry rail, frost/ice, even if there was a strong wind blowing in the direction of the downgrade?

Just to justify my question, there was this freak accident at Chelford https://en.wikipedia.org/wiki/Chelford_rail_accident where a strong wind caused a stationary unbraked van to move.

​

 

[Taunton]

Wikipedia's page on Rolling Resistance helpfully gives a typical coefficient of rolling resistance (Crr) for rail vehicles (steel wheel on steel rail) as 0.0003 to 0.0004. This is one of five elements of rolling resistance listed, but the other four only apply to a rolling object, so the coefficient is all we need to look at getting something moving.

Taking a class 153 railcar as an example ('cause it's conveniently a single car unit), a mass of 41.2t, or 41200kg, is under a force of roughly 404 kilonewtons. The above coefficient gives us the force needed to get that vehicle moving (404000 * 0.0004) 161 newtons.

Applying trigonometry, we can find the angle our 404kn of gravitational force need to be at to have a horizontal component of at least 161 newtons? The inverse sine of 161/404,000 is 0.0228 degrees. To interpret this in the traditional form as a ratio, the tangent of this angle gives the ratio of opposite (drop) over adjacent (distance). I make that 0.000399, or a gradient of 4:10000 = 1:2500.

I'm new to this area of physics, so please feel free to check my reasoning and calculations. But I've read of accounts of strong winds blowing wagons up gradients out of sidings and onto the mainline, so the low force calculated above doesn't feel that out-of-kilter to me.

The night the Tay Bridge collapsed in 1878 there were accounts of wagons being blown uphill by the wind at Dundee station.

Key is the rolling resistance of the bearings. I was surprised to learn that old-style "plain" oil-box bearings had a lower rolling resistance than the taper/roller bearings that replaced them. It was the far less likelihood of overheating, etc, that led to the universal adoption of the latter.

There must be a large number of variables. Smooth rails will be easier to run away on than rusty rails. There are numerous accounts of runaways where the vehicles have stood still for hours before they do so, it's not always wind but something must change.

 

[GC class B1]

The night the Tay Bridge collapsed in 1878 there were accounts of wagons being blown uphill by the wind at Dundee station.

Key is the rolling resistance of the bearings. I was surprised to learn that old-style "plain" oil-box bearings had a lower rolling resistance than the taper/roller bearings that replaced them. It was the far less likelihood of overheating, etc, that led to the universal adoption of the latter.

There must be a large number of variables. Smooth rails will be easier to run away on than rusty rails. There are numerous accounts of runaways where the vehicles have stood still for hours before they do so, it's not always wind but something must change.

The reason the wagons didn’t run away straight away is probably because the power brake that was holding them leaked off after this time.

 

[hexagon789]

The reason the wagons didn’t run away straight away is probably because the power brake that was holding them leaked off after this time.

1878, I doubt the wagons would've had a continuous brake, probably single shoe handbrakes.

 

[GC class B1]

1878, I doubt the wagons would've had a continuous brake, probably single shoe handbrakes.

The recent Toton runaway occurred because the wagons hadn’t been secured correctly and the power brake leaked off.

 

[hexagon789]

The recent Toton runaway occurred because the wagons hadn’t been secured correctly and the power brake leaked off.

Sorry, I thought we were talking about wagons being blown uphill in Dundee in 1878