Terminal Velocity for Incline Runaway

[Nick Holliday]

I recently got hold of a fascinating book on the Rosedale Mines and Railway, from the Scarborough Archaeological and Historical Society.  The line itself was built by the NER in 1871 to serve ironstone mining,  and was about fourteen miles long, mainly running along the top of a ridge in the Yorkshire Dales at over 1,000 feet, connected to the main network at Battersby by the Ingleby Incline, some 1,430 yards long, and, for most of its length, around 1 in 5 in gradient.  The line was worked at high level by various 0-6-0 tender locos, and a full shed and workshop was available at the end of the branch, at Bank Top.  The incline was so precipitous that the centre driving wheels had to be removed from locos when they were moved up or down the incline, and the works at Bank Top had shear legs to carry out this operation.

What I found interesting was an appendix that calculated the possible terminal velocity of wagons if the cable were to break as they started their downward journey. This was no finger in the air bit of inspired guesswork, but three pages of formulae that would have been at home in "The Big Bang Theory" and which, with a bit of computer assistance, came up with the impressive answer of 113 m.p.h.! There were plenty of runaways on the line, but I suspect none actually achieved this speed, meeting their ultimate fate before they reached it.

It would be interesting to see similar calculations for the various cable operated inclines in Britain, especially the ones in the Welsh slate quarries, but I don't suppose they were as long as Ingleby, but perhaps steeper.

[The Lurker]

About 15 years ago we stayed in Rosedale Abbey and the cottage had a book about the railway, which I had never heard of before. It certainly didn’t have the details you are mentioning but did talk about the engines and the incline at Battersby and the story of a train being snowed in for IIRC 6 weeks. The book mentioned that there were unofficial passengers on the incline which makes sense given the general nature of the area- hopefully they were never caught up with a runaway 

[Paul H Vigor]

2 hours ago, Nick Holliday said:

I recently got hold of a fascinating book on the Rosedale Mines and Railway, from the Scarborough Archaeological and Historical Society.  The line itself was built by the NER in 1871 to serve ironstone mining,  and was about fourteen miles long, mainly running along the top of a ridge in the Yorkshire Dales at over 1,000 feet, connected to the main network at Battersby by the Ingleby Incline, some 1,430 yards long, and, for most of its length, around 1 in 5 in gradient.  The line was worked at high level by various 0-6-0 tender locos, and a full shed and workshop was available at the end of the branch, at Bank Top.  The incline was so precipitous that the centre driving wheels had to be removed from locos when they were moved up or down the incline, and the works at Bank Top had shear legs to carry out this operation.

What I found interesting was an appendix that calculated the possible terminal velocity of wagons if the cable were to break as they started their downward journey. This was no finger in the air bit of inspired guesswork, but three pages of formulae that would have been at home in "The Big Bang Theory" and which, with a bit of computer assistance, came up with the impressive answer of 113 m.p.h.! There were plenty of runaways on the line, but I suspect none actually achieved this speed, meeting their ultimate fate before they reached it.

It would be interesting to see similar calculations for the various cable operated inclines in Britain, especially the ones in the Welsh slate quarries, but I don't suppose they were as long as Ingleby, but perhaps steeper.

For a REALLY savage inclined plane, see the Denniston Incline in New Zealand!

[Nick Holliday]

On 07/05/2022 at 00:22, The Lurker said:

About 15 years ago we stayed in Rosedale Abbey and the cottage had a book about the railway, which I had never heard of before. It certainly didn’t have the details you are mentioning but did talk about the engines and the incline at Battersby and the story of a train being snowed in for IIRC 6 weeks. The book mentioned that there were unofficial passengers on the incline which makes sense given the general nature of the area- hopefully they were never caught up with a runaway 

The book I acquired is the 2021 updated version, and much expanded.  Excellent value, thanks, probably, to having Heritage Funding, with over 150 pages and plenty of photographs and maps, many in colour. No connection, just a happy purchaser.

https://sahs.sumup.link/product/rosedale-mines-and-railway-2021-updated-edition

PS If the line had not been lifted in 1929, and had survived into BR days, I'm sure it would have been as well known as the Cromford & High Peak.

Edited May 9, 2022 by Nick Holliday
Note re CHPR added

[The Lurker]

thanks for the link - I am quite tempted by that. A quick search on Amazon suggests the original 1984 version had just 32 pages, which chimes with my holiday memories.

[Reorte]

There was a runaway once on Sheep Pasture Incline that was estimated to have reached that sort of speed. I'll try to remember to dig out the book when I get home.

[The Stationmaster]

23 hours ago, The Lurker said:

thanks for the link - I am quite tempted by that. A quick search on Amazon suggests the original 1984 version had just 32 pages, which chimes with my holiday memories.

32 pages sounds about right - without digging out my copy to count them!

[woodenhead]

The Deniston video was interesting, the hoppers were not fixed into the wagons, to load in to a ship the simply lifted the hopper clear of the chassis, over the ship and opened it (by hand).

[Boris]

There's information at the Cromford and High Peak railc/anal interchange that a train naffed off on its own down the incline there and a good amount of it ended up in the canal having reached estimates approaching 100mph.  I mean the stuff is all designed for relatively low rolling resistance, and you can move an empty wagon by hand with a couple of fellas.  Air resistance isn't going to be a huge factor until you reach about180mph apparently, although I am treating that figure with a pinch of salt.

[Edwin_m]

On 06/05/2022 at 21:47, Nick Holliday said:

I recently got hold of a fascinating book on the Rosedale Mines and Railway, from the Scarborough Archaeological and Historical Society.  The line itself was built by the NER in 1871 to serve ironstone mining,  and was about fourteen miles long, mainly running along the top of a ridge in the Yorkshire Dales at over 1,000 feet, connected to the main network at Battersby by the Ingleby Incline, some 1,430 yards long, and, for most of its length, around 1 in 5 in gradient.  The line was worked at high level by various 0-6-0 tender locos, and a full shed and workshop was available at the end of the branch, at Bank Top.  The incline was so precipitous that the centre driving wheels had to be removed from locos when they were moved up or down the incline, and the works at Bank Top had shear legs to carry out this operation.

What I found interesting was an appendix that calculated the possible terminal velocity of wagons if the cable were to break as they started their downward journey. This was no finger in the air bit of inspired guesswork, but three pages of formulae that would have been at home in "The Big Bang Theory" and which, with a bit of computer assistance, came up with the impressive answer of 113 m.p.h.! There were plenty of runaways on the line, but I suspect none actually achieved this speed, meeting their ultimate fate before they reached it.

It would be interesting to see similar calculations for the various cable operated inclines in Britain, especially the ones in the Welsh slate quarries, but I don't suppose they were as long as Ingleby, but perhaps steeper.

That might depend on whether aerodynamic and other resistance forces have been considered.  I seem to recall Dionysius Lardner ignoring these and predicting an improbably high exit speed if a the brakes of a train were to fail in Box Tunnel.  I make the speed without resistance to be around 170mph, in a lot less than three pages, so I assume the calculation allowed for these resistances.  

[John-Miles]

Air resistance, more correctly called drag, goes up as a square of the velocity so would become appreciable well before 180 mph. Try driving your car at different constant speeds and see how the fuel consumption varies. A small change between say 60 and 70 mph makes a significant difference.

[Bernard Lamb]

Searching my brain for obscure information that  I came across long ago, I seem to remember a figure of about 110mph for people falling off of mountains. That makes the figure quoted of 113mph look about right. I never did put it to the test when I did climb mountains though. SWMBO reckons about 120mph for parachutists but I leave that sort of thing to her.

Bernard

[KeithHC]

There would have to other factors to consider. How much cable might be dragged down as well. Also how would the axel boxes stand considering that normal speed was about 30 to 40mph. Would the bearings disintegrate and set up wheel wobble derailing the wagon at a lower speed. 
 

Keith

[doilum]

On 10/05/2022 at 15:28, The Stationmaster said:

32 pages sounds about right - without digging out my copy to count them!

For those with the original version, the new one is well worth adding to the library.

[jamie92208]

I believe that there are still the remains of some wagons in one of the catch pits on the Cromford and High Peak.  120mph for parachutists sounds about right.  Just as an aside a Union Pacific 4-8-4 ran away from Buford near the top of Sherman Hill and went merrily down 20 miles of 1 in 65 under light steam, in I think, 1956.  All 450 tons of it derailed at the east end of Cheyenne yard demolishing a diesel.  The terminal speed was estimated at over 130mph from the track circuits. It had been left unmanned at Buford, whilst the crew chatted to the signalman and was returning light engine after a banking turn.  It was repaired and running again within 3 months but the diesel was a write off.

 

Jamie

[Fen End Pit]

On 09/05/2022 at 11:41, Nick Holliday said:

The book I acquired is the 2021 updated version, and much expanded.  Excellent value, thanks, probably, to having Heritage Funding, with over 150 pages and plenty of photographs and maps, many in colour. No connection, just a happy purchaser.

https://sahs.sumup.link/product/rosedale-mines-and-railway-2021-updated-edition

PS If the line had not been lifted in 1929, and had survived into BR days, I'm sure it would have been as well known as the Cromford & High Peak.

I purchased a copy of this book based on your recommendation. I must thoroughly agree, an excellent book and very good value. Arrived in 3 days from Scarborough.

David

[The Lurker]

I got around to ordering a copy as well

[Nick Holliday]

On 10/05/2022 at 18:25, Edwin_m said:

That might depend on whether aerodynamic and other resistance forces have been considered.  I seem to recall Dionysius Lardner ignoring these and predicting an improbably high exit speed if a the brakes of a train were to fail in Box Tunnel.  I make the speed without resistance to be around 170mph, in a lot less than three pages, so I assume the calculation allowed for these resistances.  

The writer has taken both kinetic friction and air resistance into account in his calculations. He has also allowed for the different gradients on the incline itself, and explains each step carefully, hence the three pages. Thankfully, he avoids the calculus method of solution, espousing a form of finite element analysis instead, using a loop technique where the velocity is recalculated every 0.001 seconds.

If you want to carry out the calculation yourself, the writer assumed that kinetic friction reduced the effect of gravitational  acceleration by a third, and used a unitless drag coefficient of 2.02 based upon work published in the Journal of Wind Engineering and Industrial Aerodynamics.