Weights, Gradients & Tractive Effort

As I run a 00 garden railway with gradients of up to 1 in 50, I have developed a bit of a preoccupation with the weight of rolling stock and the pulling power of locomotives. This has led to the building of a simple locomotive test rig, and the generation of a spreadsheet to convert the test results into "number of coaches up 1 in 50" for each of my locomotives. I have later compared the results with the actual performance achieved in the garden, and - purely out of scientific interest - the tractive efforts  and weights of full-size locomotives and stock. It also allows me to try to improve poor performers by trial and error, wihout having to keep taking 10 coaches into the garden to see if it has worked.

First the test rig. A short length of track (1m is more than enough) is attached to a level base with a vertical drop of at least 25cm at one end. The edge of the drop is rounded, and covered with smooth tape. A length of cotton running over the edge has a loop at one end, and to the other end is attached a cradle weighing between 5 and 10 grammes. (I used a plastic lid from an aerosol can.) You also need up to 10 identical weights of between 5 and 10 grammes. (I used 8g steel balls from a bearing.)

Place the loco on the track, and attach the cotton loop to its coupling hook. Start it running so that it lifts the cradle off the ground. Keep repeating, each time adding another ball, until the loco can't lift it. Take out  one ball, and the weight of the cradle plus balls is the loco's maximum tractive force. In some models this can be improved by adding or moving weight within the loco, or adjusting bogie springing, to optimise the weight on the driving wheels

To convert this figure into "coaches up 1 in 50", first decide on the average weight of a coach. I use a figure of 150g per coach, which seems fairly typical. The number the loco can pull up a 1 in 50 gradient is then

[(tractive force x 50) -(weight of loco & tender)] / coach weight

assuming that losses due to rolling resistance and track curvature can be ignored. If your steepest gradient is 1 in 80, replace the 50 with an 80. I have found in practice that the results usually agree to within one coach with what is achieved in the garden, though I suspect that curves of radius less than about 4ft might start to have a significant effect.

Before proceeding to a comparison with full-size equipment, let me introduce the concept of "scale weight". If a full-size item weighs 35 tons, the "scale weight" of its 00 model is

35 x 1000000 / (76 x 76 x 76) grammes, = 80g.

This assumes 1 ton = 1 tonne, and 00 is 1/76 scale, both of which are true within the accuracy of our measurements. Thus the scale weight of an 87 ton 9F 2-10-0 is 198g, and the scale weight of a 55 ton Midland 2P 4-4-0 is 126g. This compares with an actual weight of 395g for the Bachmann 9F, and 170g for the Hornby (loco-drive) 2P, which is 2x the scale weight for the 9F, and 1.3x the scale weight for the 2P.  Similarly, a typical 35 ton loaded mk1 coach weighs about 35 tons, giving a scale weight of 80g, yet a typical 00 model weighs 150g, almost twice the weight.

Why are the models so much heavier? There are several reasons.

1. A model has to survive handling by "giants", so the thickness of materials is much greater.
2. Stock must stay on rough track with no wheel springs or compensation, so weight is added.
3. Uncompensated locos need more weight to prevent wheel-spin with heavy trains.

The 2P can afford to be proportionately lighter than the 9F because it has rubber traction tyres.

The final concept to get our heads round is Tractive Effort. The figure we measured earlier using the test rig is effectively the tractive effort of the model loco - the force with which it can pull a train. Tractive Effort in the world of real railways, as anyone who has owned an Ian Allan ABC of steam locomotives will know, has the same meaning, but is usually quoted as a theoretical figure calculated from certain characteristics of a class of loco. I won't go into any more details here; it is explained in full in the front of the said ABC books, and the tractive effort of each class is given in the data tables in the same books. I will however use the same two locos, the 9F and the 2P, to make a comparison between the "scale" of the theoretical T.E. of the full-size engine, and the measurements made on my test rig. The 9F has a T.E. of 39670lb, which to 00 scale is 41g, compared with 35g, 39g, and 43g for the three Bachmann 9Fs I have measurements for. The 2P has a T.E. of 17730lb, which to scale is 18g, compared with 23g for the Hornby model. Not quite so close, but the model does have the advantage of rubber tyres. A key observation I haven't mentioned before is that I have yet to see the tractive effort of a modern 00 model limited by the power of its motor. In every case, it is because the wheels start to slip, and lose traction on the rails.

Well, what does all that prove? Was it worth the effort of writing it down? I'll leave it for you to judge.

2P or not 2P? That is the question!

Now that winter is here in earnest and the garden is permanently driech and dreary, I have nowhere to pose my models. So when a new Hornby loco-drive 2P came to stay, after a quick test it was placed on the very incomplete "winter project" layout, and an "Elmbridge Cycle Users" display photograph was used as a backdrop.

A Scottish 2P "borrowed" by the Bath shedmaster runs light through Mineries Wood.

Anyone expecting the 2P to be to the same standard as those other Hornby 4-4-0s, the Schools and the T9, will be disappointed. It's certainly an improvement on the old tender-drive version, running smoothly and quietly. But those Hornby steam-roller bogie wheels are very obvious on the 2P, and you don't have to be a rivet-counter to spot some of the other compromises carried over from the old version.


On the test rig, the 2P generated a respectable tractive force of 23g before the wheels slipped, which equates to 6 typical coaches up a 1 in 50 gradient; about the same as the prototype, I suspect. The model weighs only 170g (loco only), and achieves its reasonable hauling power with the help of rubber traction tyres on the front driving wheels.

In summary, a good runner, conveying the atmosphere of the prototype, but not reaching the level of detail attained by some of the new models from Hornby and Bachmann. And I think I might be tempted to put "new bogie wheels" on my list of things to do ......

Inactivity

December hasn't been a good month for activity in model-land. Apart from a bit of time spent building a platform and shelter, the time I should have spent on layout-building has mostly gone on dealing with the investigation, repair, and secondary effects of a leaking bathroom down-pipe and a non-working central heating boiler. Oh, and a defective garage door.

So it was quite pleasant this evening to sit down for a couple of hours and do a bit of identity-changing and weathering, as a way of getting back into the mood. Here's one of them; a very old Bachmann pannier tank. It's now 8745, which worked at Yeovil and Bath (S&D) in its latter years. It's had its first pass with the dry-brush, but needs a little more work. The brake tie-rod could also do with some attention; I think it's always been bent like that, so I presume it's a moulding fault.

The piece of track on which the engine is standing was made by my father in the early 1950s. I haven't done it any favours by getting in so close.

I also did some weathering on 9F 92220 and 4F 44560, but there's more work to do before they are ready to be photographed.

Mineries Halt takes shape.

The basic structure of a platform and waiting shelter for Mineries Halt have now been assembled. The platform design is similar to Bason Bridge, Somerset and the shelter is broadly based on Cole, with features from other similar shelters. The fencing will also be based on Cole, which used reclaimed bullhead rail for the posts. There's still lots of tidying up, detailing, and painting to be done!

Really Nice Trams

I'm out of Model-land at the moment, in Nice, southern France. While there, we travelled by double-deck train from Nice to Monte Carlo, Monaco and Ventemiglia, Italy.

Monaco / Monte Carlo station is in a hollow hill.

The trams in Nice are interesting, in that they lower their pantographs and (presumably) use battery power over certain sections such as the town square, where overhead wires would be undesirable.

A Nice tram with pantograph raised ...

... and with pantograph lowered, on battery power.

Back home tomorrow, so I can get back to the important business of layout-building.

The Winter Project

Although there's plenty of indoor maintenance and repair work to do for the garden railway, work has now started in earnest on the Winter Project, "Priddy Mineries". This is set on the branch line running from Masbury Junction to serve the farming and mining community of Priddy, on the Mendip Hills. Mineries Halt is not much more than a mile from the terminus at Priddy Green, at the junction with the spur to the old St Cuthbert's Lead Mine, the site of which is now a limestone quarry. As well as serving the mineries, the halt is on the old coaching route from Wells to Bristol and near to two pubs, one of which, the Mineries Inn, is just across the road from the crossing-keeper's cottage.

All of this is is of course a product of an over-active imagination, but it does give a sort of a reason and purpose to the track-covered board in the spare bedroom and the strange smells of solvent and hot resin pervading the house.

The track-layer's clutter.

Almost ready for the scenery ....

This is my family's first venture into hand-made track since my father's in the early 1950s, and the results look remarkably similar. The sleeper appearance, length and spacing, and the rail profile, are all about the same.  The main difference is that my chairs are not made of solder.

Railway Apprentices

It's three weeks now since the garden railway had a proper run (rather than just being used as a stage for photographs), and as the weather was good I decided to fire it up and see if any corrective maintenance was needed before the winter proper. Little Lucy (nearly four) from down the road was disappointed last time she visited as the railway wasn't running, so she was invited along to assist, as were Holly & Ella (nearly two) from across the road, who also like trains. After Thomas the Tank Engine had run past a few times with Annie & Clarabel, and Lucy had had her first driving lesson, I brought out some real trains for the grown-ups to play with.

"Evening Star" pounds up the 1 in 50 reverse curves with an easy 7 coaches.

Note that in the first two pictures, the engines are leaning towards the inside of the curve. This is not due to a sloping camera; the track is banked on the curves (I think the correct term is "supelevated") by up to 1mm. During tracklaying, a narrow strip of 1mm thick neoprene rubber is placed under the sleepers at the outside rail, with a transition through 0.5mm to none at all at the end of each curve and where the curve reverses. Those of you with a firm grasp of elementary geometry will already have calculated that the trains lean by up to 3.5 degrees (nominally) from the vertical.

The 1mm maximum was not arrived at scientifically; It is within the range said to be used in the real world of 12" to the foot scale, for which a 6" maximum difference is often stated. And it looks about right at low to medium speeds.

4F 44417 coasts down the hill with a local train, as "Evening Star" thunders up.

A short local train coasts past the quarry, slowing for the station.

I think that "Evening Star" must take priority for a gentle weathering, to lessen the appearance of having just left the sales showroom.

British Bulldog

The postman this morning thrust two parcels into my expectant hand. The first was a Static Grass Applicator from Finescale Model Railways. It's exactly like the one I've been meaning to make for nearly a year now. I bought a £3 high-voltage insect swatter and a metal tea-strainer for the purpose. The swatter was so effective as a swatter that it was retained for that purpose and another one purchased. This was immediately requisitioned as the "upstairs swatter", so I bought a third, which went to the summer-house ..... Eventually I reserved one for grass-making. But there's always something better to do than designing and building a tool so that it will work reliably, when you know that you won't need until some time in the future. So when someone comes along who has a proven design in quantity production at a reasonable price, I am more than happy to part with a few pounds and take one off his hands. And we have a spare swatter and a smart new tea-strainer into the bargain.

The second parcel was even more exciting; my Bachmann 3F 0-6-0 had arrived from Hattons. It was soon on the test track and "running in" on the rollers. And it was a dry, sunny day, so as the trackwork on my indoor layout currently has more rails in ink than in nickel-silver, I cleared a section of garden track and fired up the controller.

Bachmann's new Midland 3F 0-6-0.

The 3F ambles up the 1 in 50 past the quarry.

The excellent cab detail is visible in this view.

And as well as looking beautiful, it runs beautifully too! I also like the infinitely variable tender-spacing adjustment (though care is needed dressing the cables under the tender to avoid them jamming the wheels) and the working fall plate. Bachmann have also moved level with Hornby in the quality of the dummy screw coupling in the accessory bag. The only thing missing is the option of a Whitaker tablet catcher on the tender (though even on the S&D only a few if the class were fitted with them). No doubt it will appear in the future, with a suitable running number.

As usual, I'll enjoy the model for a few weeks in its current ex-works condition (at least until I'm reasonably confident it won't need to go back under warranty), then it will be given a characteristic coat of grime and coupled to a suitable train of equally grimy wagons.

Ivatt in the garden.

'Twas a beautifully sunny day today, so after our walk I did some emergency maintenance on the garden railway. Some of the solder joints for the wire jumpers linking sections of track were not painted, and were corroding into a white powder. Out with the wire brush, the fibreglass brush, and the paintbrush and the job was soon done.

Of course a test run was essential, so newly-painted 41249 had a few runs up and down the curves by the wall.

41249 lets off steam impatiently while posing for photographs.

41249 coasts down the bank past a Pyrocanthus bush, with a short local train.

Another engine hits the brush!

The damp weather this week means that any railway time has been spent indoors, on updating the plans for the "Mineries" layout, and in work on engines and rolling stock. In the latter category is 41249, which has had its numbers applied, crew, steps, couplings and pipes added, and a layer of grime drybrushed on using a 1965 photo as a guide.

41249 after first application of weathering.

The disadvantage (or advantage) of taking photographs of models you have been working on is that they show up any omissions or flaws in the workmanship, and I now have to get out the tools and paintbrushes again to make good.

As a result of an exchange of emails about "the last train from Evercreech to Highbridge", I also made a blue disc bearing the coat of arms of the Somerset & Dorset Joint Railway, which all engines wore on the final day of services on the line, 5th March 1966. The real 41249 was pulling that last train, albeit bunker first.

The real 41249 at Glastonbury with the last Highbridge train, 5th March 1966.

This winter's evening picture raises the question of whether it would be practical to build or adapt a model railway to represent night-time. I think the answer is probably yes - in the privacy of your own home and if you don't mind operating in the dark or half-light. Exhibitions might be more of a problem, and your layout would probably require its own darkened room and all that that entails in ensuring the safety of the public.

3218 goes visiting

Today I went along to the Wycrail model railway exhibition in High Wycombe, where I was kindly invited to do some operating on Chris Nevards inspirational layout "Catcott Burtle". I took along my recent model of Collett 0-6-0 3218, and for light relief Thomas the Tank Engine came too.

3218 arrives at Catcott Burtle on the "Milkie" empties.

3218 at Catcott Burtle

Ian Mellors' hypothetical BR Standard 8MT 2-8-2 runs through Catcott. 

I would hate to shatter Chris's unsullied reputation by posting a picture of Catcott Burtle with evidence that Thomas had visited, so you'll have to wait until the next exhibition and see for yourself.

Running the Railway

The unusually warm, dry weather in October meant that construction work continued longer than expected. It also means that there have been more opportunities to run the railway.

A recently-acquired "bargain" Collett 0-6-0 is tried out with a train before going into the workshop for refurbishment and a change of identity.

The Collett 0-6-0 comes off the viaduct past the planned station site.

A Beattie Well tank has a short test run ...

... including a passage hrough the tunnel.

Another Collett 0-6-0, this one a very old "Mainline" model of number 3210, has just been "weathered" into the condition in which I knew its prototype the 1960s. We would have regarded this as a very "clean" engine!

The quarry has acquired a Hunslet 0-6-0ST to cope with the steep bank up from the quarry floor. It is named "Penelope Jane" in honour of the quarry engineer's wife. When she saw it recently she was not best pleased with its state of cleanliness, and the engineer has paid a girl from the village to come and give it a scrub while the driver has his lunch.

It's not only in India where illicit passengers ride on the coach roof.

Collett no 3210 runs light engine past a Jinty, waiting in the quarry spur.

"Playing trains" again today (2/11), mainly for test and photographic purposes. This is the "bargain" engine that appeared in GWR colours at the top of this post. It had clearly been rattling around in someone's toybox, was liberally spattered with food residue, and had lost any vulnerable protrusions. After a clean, a bit of repair work, a tender swop, a repaint and a new identity as 3218, this is how it looks. Not perfect, but much as I remember its prototype in 1965.

 

The figure with a camera on the loco represents me as a teenager, having blagged a ride from Glastonbury to Highbridge. The only non-authentic aspect of the tableau is that in reality I was so terrified by the rolling and lurching of the engine that I held on firmly with both hands and didn't take a single photograph on the footplate!

Relaying the double track

Last Sunday, I plucked up courage and started relaying the double-track section downhill from the viaduct. The original trackbed of this section of track was found to be too steep. Fortunately I found this out before I had laid too much track, and over the past two weeks I have lifted the track and remade the trackbed at a constant gradient of 1 in 50. I now have the first 6ft of double track down from the viaduct.

A ballast train on the new section of double track.

The ballast train.

The first passenger train over the new track, running wrong-line.

Next day, a further 6ft of double track was laid. It was then extended down the trackbed with temporary track, and tested with several locomotives and long trains.

Tangmere with 8 coaches is piloted by a 2P.

The train has crossed the viaduct and is starting the climb to the tunnel.
The gradient change through the station is evident on the coaches

The Quarry

After a break of several weeks and two demonstration sessions, work started again this week on the quarry. The final trackwork was laid for the exchange siding and shunter refuge spur, and the quarry floor was completed and given a steeply-descending line down to the lowest point.

The first picture shows one of the shunting engines with some wagons in the quarry bottom. It is clear from the angles of the wagons that the track is very uneven here, possibly damaged either by subsidence or a rockfall.

On another occasion, a Sentinel 0-4-0 is seen propelling three wagons up the short stretch of 1 in 15 from the deepest part of the quarry.

Sixty years later, a class 08 shunter lifts a ballast train out of the quarry...

... and propells it into the exchange siding.

The shunter then waits in the refuge spur until a main line loco comes to collect the train. On this occasion it was most unusually a Yeoman class 59.

The class 59 then leaves the quarry and heads over the viaduct ...

... and through the tunnel.

Back in time again, and a L&Y "Pug" storms out of the quarry with a single loaded wagon.



After the wagon has been added to the those in the exchange siding, the "Pug" returns to the refuge spur. The driver sounds his whistle in greeting as a train approaches on the main line.





Phase 1 Inspection

On 6th September 2011, a distinguished team of railway specialists was assembled to carry out the formal inspection of Phase 1 of the Garden Railway Project (GRP). The evening started with a tour of the railway in the inspection saloon, followed by a lineside viewing of several trains running specially for the occasion.

34067 "Tangmere" with a Phase 1 Inspection special.

The inspectors were given a copy of the Chief Engineer's pre-inspection report, and after satisfactory responses to several more questions, deemed the Railway to have passed its phase 1 inspection. The team then repaired to the house for a celebratory dinner.

It was pointed out that the loco that had pulled one of the GRP Phase 1 Inspection trains had earlier in the week pulled the "Atlantic Coast Express " on the big railway at the end of the garden, only a few yards from the GRP railway.

34067 "Tangmere" passes our garden.

For the Chief Engineer's report, see Annex 1 at the end of this post.



Quarry Siding

The trackbed is now in place for the main quarry siding. This leaves the main line just above the station, and is parallel with the main line for the length of the quarry. The gradient is level, so by the end of the siding, the main line is well above it. Track was laid temporarily to check levels and clearances, and this provided a photo-opportunity as a light engine on the main line passed our test engine.

A BR class 4 runs light down the main line from the tunnel past 37406, sitting simmering in the new siding.

There are two additional turnouts at the entrance to the siding. The first will lead to a short spur, long enough for a shunting engine and 2 or 3 stone trucks. This will allow the quarry shunter to transfer wagons between the main siding and the quarry without the need for access to the main line. The second turnout will lead down to the quarry floor on a steep gradient.

The arrangement of turnouts at the quarry.

As the shunting spur is unlikely ever to be used in model-land, I considered several alternative layouts including that shown below. I think I'll stick with the original though. 

An alternative turnout arrangement, considered but rejected.

Annex 1

GRP Phase 1 Inspection

Chief Engineer's Report.

The Garden Railway Project

The Garden Railway Project (GRP) is a project to construct a 00 scale railway in the garden of our house.

It was decided early in the project to divide the construction into phases. Phase 1 covers the section of track between the Bean Wigwam and the Oak Tree. Construction should then cease until the Chief Engineer is confident that the construction techniques have been seen to meet the environmental and other critical requirements. 

During phase 1, the content of phase 2 will be defined.

Objectives for Phase 1

1. Complete the detailed design of the phase 1 facilities.
2. Construct trackbed from the Bean Wigwam to the gate, and lay track.
3. Construct a removable section of track past the gate.
4. Construct a trackbed past the Oak Tree, with space for a station platform, and lay track.
5. Provide an electrical infrastructure for safe operation.
6. Provide a plan for phase 2, and an initial outline for the entire project.

Requirements

1. It shall be possible to run long trains, up to 12 coaches of the equivalent length in freight wagons.
2. The removable section past the gate shall allow passage of items at least as wide as the gate itself.
3. It shall be possible to open the gate with the removable section in place.
4. The railway shall be safe
5. The railway shall survive the annual climate with the minimum of maintenance.

 Design Decisions

1. The railway will be broadly based on the Somerset & Dorset around Midford, south of Bath.
2. The removable section will be a viaduct, based on the one at Midford.
3. There will be double track from the Bean Wigwam to the viaduct, becoming single on the viaduct and continuing single through the station.
4. The station will be based on Midford.
5. The rail will be Peco Streamline code 100, with “wood” sleepers.
6. The line will use DC control for the locomotives. The wiring shall not preclude future conversion to DCC if so required.
7. The topology of the garden necessitates gradients. The gradient shall not exceed 1 in 50 at any point on the main line
8. There will be no curves sharper than 48” radius on the main line, and wherever possible the radius will be greater than 72”. Any turnouts on the main line will be Peco Streamline “large” radius (1524mm).

Achievement of Phase 1 Objectives

1. The Requirements and Design Decisions are listed in the relevant sections of this document. Detailed design data and calculations are recorded in the Chief Engineer’s log book.
2. The basic trackbed is in place from the Bean Wigwam to the gate, and about 4 metres of track is laid (single only). However, some sections are steeper than 1 in 50, the worst being short sections of 1 in 30. This severely limits the hauling capacity of the locomotives, and is not acceptable. Some sections of trackbed are also very uneven, and have been levelled with unsuitable materials (B&Q window frame sealant). The contractor has been instructed to relay at his own expense this entire section of trackbed, with a maximum gradient of 1 in 50 and using shuttered rubbercrete to provide an even trackbed
3. The viaduct is complete with the exception of some detail painting, and the fitting of fencing. It has been designed and built, but not yet tested, to be weatherproof. It is reasonably easy to fit and remove. Electrical contact is currently through the fishplates, but ultimately a connector will be needed. The turnout is currently manually operated.
4. The track is laid past the Oak Tree, and the basic structure of a station platform constructed but not yet fitted. In view of the delays in construction of the section downhill from the viaduct, the Board agreed to go ahead with constructing a section uphill from the Oak Tree, and a tunnel under the path. This work necessitated the removal of about six cubic metres of earth and construction of a rockery garden (quarry).
5. A 230V mains to 16V AC transformer is fitted in the summer house. The 16V supply is taken to a weatherproof junction box on the Oak Tree, containing a DIN 6-way connector for a controller, and an output cable to the track just above the viaduct.
6. The plans for phase 2 and beyond are given in the sections below.

Plans for Phase 2

The following activities will occur during Phase 2:

1. Complete any unfinished Phase 1 work.
2. Continue the track down the “end” (south) fence and the east fence of the garden (bordering next-door's garden).  It should revert to double track soon after the tunnel. The proposed trackbed is pre-cast concrete lintels (Wickes).
3. Provide a long siding and a quarry siding in the “quarry” (rockery). This was partially completed as extra work during Phase 1.
4. Provide any necessary additional electrical infrastructure.
5. Investigate the feasibility of remotely controlling the turnouts, and implement if practical.
6. Design and implement a method for pre-assembling trains and “plugging in” to either end of the track. Ideally up to 12 coaches plus 2 locos, but it would be acceptable if a train this long was in two sections for transport.
7. Operation and maintenance of the railway would greatly benefit from an “indoor” or under-cover section, where trains can be stored between uses during an operating session, and easily “put on” and “taken off” the running lines. It would also provide somewhere to store the removable sections, control equipment, tools, etc. The minimum requirement is a shed 8ft  long, and sufficiently wide to provide the necessary access and storage. A review of potential locations concluded that the optimum location would be replacing the deep hedge behind the washing line, but other options are available. This should be investigated further during phase 2.
8. Provide a plan for phase 3, and refine the outline plans for the entire project.

The target date for completion of phase 2 is Spring 2012.

Plans beyond Phase 2

It is an aspiration to complete a circuit of track around the garden. Preliminary surveys have shown that the two most likely options are:

1. Complete the circuit with a removable section across the lawn, from just below the pond to just above the washing-line trellis
2. Complete the circuit with a removable section across the lawn, in the vicinity of the cherry blossom shrub planted in an island in the lawn. This would connect along a raised track in front of the raised beds, following the stone slab path, and a raised track in the hedge behind the border on the east side of the garden.

A decision on which option to take will be needed during phase 3, or possibly late phase 2.

Conclusions

Phase 1 is largely complete, but is now undergoing major rework on the double-track section. Significant extra work was completed beyond the original Phase 1 objectives, including the quarry bank and the tunnel. Plans for phase 2 and beyond have been defined.

It is proposed that work commence on phase 2 at the discretion of the Chief Engineer, with immediate effect.