Rolling Resistance

[Lucan]

To settle an argument, how far would a loaded eight coach train doing 125mph on level track roll freely if the traction were cut off? I'm guessing about 2 miles.

 

[contrex]

Do you mean 8 trailers that have become decoupled from their loco, or a complete train with driver, with traction gear on some axles? You must mean the latter, since the uncoupled trailers/LHCS would brake automatically. For free rolling unbraked vehicles, I suspect the answer might be a lot more than 2 miles. More like dozens. I'll might dp some sums in Excel in a bit, but here are some figures on an American web site I found to be going on with (I think it assumes no head or tail winds):

Empty Acela weighs 624 American tons; we'll guess that due to rotational inertia its effective inertial tonnage is 650. Assuming all that:

Coasting on level track-- start at 150 mph
100 mph reached in 5.18 minutes 10.58 miles
25 mph in 26.87 minutes 30.07 miles
0 mph in 45.88 minutes 33.66 miles

 

[100andthirty]

There's an issue of gradient too. Trains will stop pretty readily if left to coast uphill. But when they do stop, if no one puts the brake on, the train will set off backwards.

I recall a train on the West Coast Main Line that lost power just south of Watford Junction and apparently it made it to Euston.

There was an unfortunate incident on the Underground some years ago when a train of some sort ran away somewhere on the Northern line and it ran southbound on the ruling down gradient until getting to the bottom of the slope around Warren St and then up towards Goodge St (locations approximate). It them acted like a yo-yo until it eventually stopped and could then be rescued.

 

[Stigy]

To settle an argument, how far would a loaded eight coach train doing 125mph on level track roll freely if the traction were cut off? I'm guessing about 2 miles.

A lot further than 2 miles.

 

[Watershed]

To settle an argument, how far would a loaded eight coach train doing 125mph on level track roll freely if the traction were cut off? I'm guessing about 2 miles.

It depends on the rolling resistance of the stock in question, but probably more on the order of 10 or 20 miles. You'd have to engage noticeable braking to stop from 125mph in 2 miles (an emergency stop can be done in around 1 mile), so if you're rolling there's no way you'd stop that quickly.

 

[contrex]

It depends on the rolling resistance of the stock in question, but probably more on the order of 10 or 20 miles.

I think this is as good an answer as the OP can reasonably expect. If a rolling train stopped in 2 miles on level track, the power requirements to run at useful speeds would make rail transport impossible.

 

[Nottingham59]

I did a quick Google search and got "the energy consumption of an Atlantic TGV trainset cruising at 300 kilometers per hour on the new high-speed line is 20 kWh per kilometer."

Ignoring hotel power and transmission losses, the retardation force on such a train will be 20x3600 kWs/km (=J/m) = 72kN. Google says a TGV weighs 444,000kg, so the initial deceleration would be 72/444 m/s/s=0.16m/s/s. In real life, this deceleration would tail off as the train slowed down. But assuming it didn't, a TGV going at 300km/h=83m/s would take 520s to stop, and travel 21.5km. Does that help at all?

EDIT: In real life, I'd expect the TGV to roll at much further than this. Wind resistance should vary with the square of the speed, so will drop off sharply as the train slows.

I would expect an HST doing 125mph (200kph) would initially decelerate at around 0.16x4/9 = 0.07m/s/s. (This is 0.7% of g: does that sounds about right?). That deceleration would ease off as the train slowed down, to perhaps 0.1%g (=0.01m/s/s) when all you get is rolling resistance of the wheels. (This implies that an unbraked train on a gradient of 1 in a 1000 won't roll away under gravity. Sounds about right?). So with an average deceleration of 0.04m/s/s, an HST going at 55m/s would stop after 1375s, and travel 38km.

So the best answer I can come up with is "tens of miles", without modelling it properly.

 

[DeparturesBeck]

See this post for some coasting examples: RailUK Forums Regular coasting

 

[Lucan]

probably more on the order of 10 or 20 miles

Wow, that's impressive.

on the Underground some years ago when a train of some sort ran away somewhere on the Northern line and it ran southbound on the ruling down gradient until getting to the bottom of the slope around Warren St and then up towards Goodge St (locations approximate). It them acted like a yo-yo

Yes, I have heard of that one. It was an unbraked PW department wagon that broke away from a battery loco train somewhere near Archway, which is is on a northward rising gradient. Fortunately there were no service trains around at the early hour. Must have been spectacular going through the pointwork at Camden Town.

In one of Adrian Vaughan's books he describes an incident where some wagons broke off the back of a goods train on the then Farringdon branch. There was quite a dip in the line and the wagons yo-yo-ed a few times time. I guess there must have been a brake van in that portion, but perhaps its brakes were not that good, or the guard was enjoying it

 

[contrex]

It was an unbraked PW department wagon that broke away from a battery loco train somewhere near Archway, which is is on a northward rising gradient. Fortunately there were no service trains around at the early hour.

If you mean the Friday 13 August 2010 Northern Line incident, it was a a self-propelled three-car diesel powered on-track grinding machine weighing about 37 tonnes. It became defective shortly before 07.00 hrs between Highgate and Archway on the southbound. To enable removal, it was attached to a train of 1996 stock, using an emergency coupling device. The braking system of the grinding unit was de-activated to allow it to be towed. The combined trains then set out to run wrong-line to East Finchley. After passing through Highgate, an emergency brake application was triggered on the 1996 train and the coupling device fractured. The grinding unit first collided with the rear of the towing train and then began to run back southwards. The crew jumped out at Highgate. The unbraked and unmanned grinder took 16 minutes to roll about 4 miles to Warren Street, where the gradient change made it stop and roll back a short distance before coming to a stand. There were service trains about. Before the coupling broke, passenger carrying services had started to run from both Archway and Edgware. Some of these trains were directly in front of the runaway RGU. The operator of a train standing at Archway was ordered to start immediately, and when it got to Tufnell Park the operator was ordered to leave without opening the doors, to drive quickly, and omit station stops (as were all trains on the Charing Cross branch). At one point this train was only 46 seconds ahead of the runaway.

 

[edwin_m]

If you mean the August 2010 Northern Line incident, it was a a self-propelled three-car diesel powered on-track grinding machine weighing about 37 tonnes, which had become defective between Highgate and Archway on the southbound. Shortly before 07.00 hrs on Friday 13th August 2010. It was coupled to a train of 1996 stock, using an emergency coupling device. The braking system of the grinding unit was de-activated to allow it to be towed. The combined trains then set out to run wrong-line to East Finchley. After passing through Highgate, the coupling device fractured and the grinding unit began to run back southwards. The crew jumped out at Highgate. Due to the gradient, the unbraked and unmanned grinder took 16 minutes to run about 4 miles to Warren Street, where the gradient change made it stop and roll back a short distance before coming to a stand. There were service trains about. Before the coupling broke, passenger carrying services had started to run from both Archway and Edgware. Some of these trains were directly in front of the runaway RGU. The operator of a train standing at Archway was ordered to start immediately, and when it got to Tufnell Park the operator was ordered to leave without opening the doors, to drive quickly, and omit station stops (as were all trains on the Charing Cross branch). At one point this train was only 46 seconds ahead of the runaway.

Here's the report: https://www.gov.uk/raib-reports/runaway-of-an-engineering-train-from-highgate-13-august-2010
Above post renders a further quote unnecessary.

In one of Adrian Vaughan's books he describes an incident where some wagons broke off the back of a goods train on the then Farringdon branch. There was quite a dip in the line and the wagons yo-yo-ed a few times time. I guess there must have been a brake van in that portion, but perhaps its brakes were not that good, or the guard was enjoying it

That happened more recently too: https://www.gov.uk/raib-reports/locomotive-runaway-near-east-didsbury

On Sunday 27 August 2006 an unmanned locomotive became uncoupled from the rear of a freight train as it approached Heald Green station, between Manchester Piccadilly and Manchester Airport. The locomotive then ran back northwards in the direction the train had come from for around 3 miles, and through a worksite at East Didsbury station. The locomotive then paused momentarily at Burnage station, before returning back southwards because of the gradient and through the worksite again. The train was brought to a stop by a combination of the gradient and workers wedging a wooden post in front of one of the locomotive’s wheels.

The brakes had been set up wrongly for "top and tail" working, so that when its on-board reservoir was exhausted the locomotive was unbraked. It then separated when a coupling broke.

 

[SansHache]

Drivers also like to explore the rolling resistance characteristics of their trains. 390013 coasted 32 miles from Tring into Euston on 6th October 2009, arriving on schedule. The train was still running at more than 70mph when the brakes were applied at Kilburn.

Clearly the gradient works very much in your favour in this example but steel wheel on steel rail remains a very efficient mode of transport.

 

[edwin_m]

To give an idea, safety guidance assumes that an unbraked train might roll away on a gradient as shallow as 1 in 500.

 

[hooverboy]

To settle an argument, how far would a loaded eight coach train doing 125mph on level track roll freely if the traction were cut off? I'm guessing about 2 miles.

It would be a lot more than 2 miles for sure.
Your load 8 train would have several determining factors though.Assuming level ground, does the unit have some kind of regenerative system?
That would slowly brake due to the motors acting as a generator,therefore converting kinetic energy back into electrical energy.

Also, is your unit aerodynamic?. The lower the drag coefficient,the further it will coast.So a slab front will stop in a shorter distance than a pendolino for instance.

Then,how fully loaded is your unit?. The overall tonnage in excess of tare will add to the distance.

 

[niggill617@gma]

To settle an argument, how far would a loaded eight coach train doing 125mph on level track roll freely if the traction were cut off? I'm guessing about 2 miles.

Two miles would be a typical braking point on level gradient 125 mph, for class 800 braking at 40 percent, about 4.9 percent g, allowing 2 seconds freewheel.

 

[satisnek]

This is something I've always wondered: if a train (choose your own) was driven over the summit at Blackwell at walking pace and no further power or braking was applied, then (a) how fast would it be going through Bromsgrove and (b) where would it come to rest (assuming the points aren't set for the Droitwich route in which case the answer would most likely be 'in a field')?

 

[furnessvale]

Wow, that's impressive.

Which is one of the reasons that rail is so much more efficient in fuel use compared to road haulage.

 

[niggill617@gma]

To settle an argument, how far would a loaded eight coach train doing 125mph on level track roll freely if the traction were cut off? I'm guessing about 2 miles.

I would estimate about 30 miles, given a 480 tonne passenger consist ?

 

[Nottingham59]

how fast would it be going through Bromsgrove?

It's about 90mph. The rule of thumb is 100mph equates to 100 metres of height gained. The Lickey incline is about 300feet.

 

[edwin_m]

It's about 90mph. The rule of thumb is 100mph equates to 100 metres of height gained. The Lickey incline is about 300feet.

However, kinetic energy is proportional to the square of speed, so descending twice the distance only increases the speed by a factor of about 1.4. In fact it will be less than that because air resistance increases with the square of speed too.

 

[king_walnut]

OP asked how far an eight coach train doing 125mph on a level track might travel if it was left to coast down to 0.

The first poster started theorising about any coaches becoming uncoupled. Then someone else said about uphill gradients. Then someone else wanted the comprehensive list of variables. Why?

I'll try and ask the same question again on behalf of OP:


Imagine a hypothetical stretch of track. This stretch of track is completely level, it's impossibly level. The train is an 8 coach Intercity 125. It's empty apart from one driver who weighs 75kg. Its fuel tanks are full. The weather is very calm and it's a clear day. Doing 125mph to start with, how far does that train coast for?

 

[Nottingham59]

Doing 125mph to start with, how far does that train coast for?

Tens of miles. I estimated 38km in post #7, but we would have to model the non-linear wind resistance to get a more accurate answer. I doubt if anyone has actual relevant experience of that situation in Britain, but there may be real-life examples from places like the Nullabor plain in Australia (though not from 125mph).

== Doublepost prevention - post automatically merged: 21 Mar 2022 ==

kinetic energy is proportional to the square of speed

True. But I remember I got 90mph when I worked it out a couple of years ago.

EDIT: I previously used Barnt Green (at 175m elevation) and Bromsgrove at 79m, giving the Lickey Incline at about 96m, just over 300ft. Someone else on here will be able to give us more accurate figures.

 

[satisnek]

Tens of miles. I estimated 38km in post #7, but we would have to model the non-linear wind resistance to get a more accurate answer. I doubt if anyone has actual relevant experience of that situation in Britain, but there may be real-life examples from places like the Nullabor plain in Australia (though not from 125mph).

== Doublepost prevention - post automatically merged: 21 Mar 2022 ==


True. But I remember I got 90mph when I worked it out a couple of years ago.

EDIT: I previously used Barnt Green (at 175m elevation) and Bromsgrove at 79m, giving the Lickey Incline at about 96m, just over 300ft. Someone else on here will be able to give us more accurate figures.

And the line continues on a general descent south of Bromsgrove, although I'm sure it undulates a bit. So, using the figures mentioned upthread, the train would roll for at least 20 miles from here?

 

[Nottingham59]

And the line continues on a general descent south of Bromsgrove, although I'm sure it undulates a bit. So, using the figures mentioned upthread, the train would roll for at least 20 miles from here?

38km is 24m, but the speed at bromsgrove will be less than 125mph. My best guess would be around 20, say 15-25 miles. What would help would be any real life experiences from class 91s having to coast through sections of damaged OHLE on the East Coast route. i.e. how much speed loss over how many miles?