Gradients

[peterfgf]

I originally posted this in the Heljan GWR 47xx thread in response to 71000 (post 567) who had carried out a very comprehensive series of tests on model locomotive haulage. His article is worth reading.  I've decided to post my reply here as it is more relevant to this section.

 

I did some less comprehensive tests, varying the gradient (by using shims) and varying the number of coaches. The test track occupied a length of about 4.5 metres and incorporated a 1.0 meter radius curves at the beginning and end, with a further level section of 2 metres at each end (imagine a flattened "U" shape).  Trains were started from stationary at the beginning of the first curve at the bottom of the slope.  This is quite a hard test, incorporating a slope, two curves and a standing start, but resembles the space in which I have to build a layout.  All locos were DCC chipped and control was by a handheld Roco Multimaus.

 

The results are shown in the attached graph and can be summarised as follows:

• 1 in 100 (or 0.010 radians) is the maximum slope for full length trains of 8-10 coaches. 
• Haulage capacity rapidly falls off at steeper slopes, roughly by 2 or 3 coaches for every 0.015 radian increase in slope. At 1 in 50 haulage capacity was reduced severely. 
• The performance of model steam locomotives is not as good as might be expected but can be improved by extra weight.  An additional trial weight of 100g increased haulage capacity by as much as 3-4 coaches.
• As in real life, haulage capacity roughly corresponds to loco size and weight: a 4-6-2 Pacific (heavy) can manage 8-10 coaches, 0-4-4Ts (light) can only manage 2 or 3 coaches.
• The haulage capacity of Bachmann Pacifics was surprisingly poor.
• The haulage capacity of Hornby 2P 4-4-0 and 4F 0-6-0, both with rubber tyres, was impressive and both took 10 coaches up 1 in 50 (0.02 rads).
• The performance of model diesel and electric locomotives is very good in comparison to steam locomotives. A limit was not met with 12 coaches even on 1 in 50 (0.02 rads).

 

Peterfgf

Edited April 3, 2018 by peterfgf

[gordon s]

Thanks Peter for confirming my own findings re 1:50 and 1:100 gradients.  At the time, I didn't undertake the range of tests you have done, so it's good to see some factual data.

 

Good information for those contemplating the dark side of railway modelling....

[peterfgf]

Thanks Peter for confirming my own findings re 1:50 and 1:100 gradients.  At the time, I didn't undertake the range of tests you have done, so it's good to see some factual data.

 

Good information for those contemplating the dark side of railway modelling....

Glad to have helped. 

I couldn't find any very definitive answers when I started looking around, so decided the only way was to do some measurements myself.

Peterfgf

[gordon s]

The problem as always is that 20 guys will say 20 different things and definitive info is hard to come by.  There are still so many plans that appear on here with horrendous gradients to get round multi level requirements and no matter how many times you try to explain the difficulties involved, people will always say they run 10 coach trains up 1:25 gradients......

 

Maybe one of us has got the calculations wrong.....

[Silver Sidelines]

Interesting that you single out Bachmann pacifics as being poor performers - I am presuming A1s. When suitabley tweaked I think these are superb machines. Depending on the model there are a number of checks that you need to carry out.  Most importantly you need to stop the rear of the engine resting on the tender.  There are some details in an old Blog Post:

 

http://www.rmweb.co.uk/community/index.php?/blog/880/entry-10439-is-your-Bachmann-a1%E2%80%93-a-follow-up-to-adding-weight-to-Bachmann-a4s/

 

The A4s can also be made to haul a decent load. 

 

http://www.rmweb.co.uk/community/index.php?/blog/880/entry-10376-streaks-and-highlights-%E2%80%93-weighing-up-Bachmann-a4s/

 

Unlike Hornby who simply add weight to bogies and pony trucks, Bachmann use springing which if not properly adjusted can lift the driving wheels with obvious consequences for haulage.

 

Ray

Edited April 3, 2018 by Silver Sidelines

[peterfgf]

Interesting that you single out Bachmann pacifics as being poor performers - I am presuming A1s. When suitabley tweaked I think these are superb machines. Depending on the model there are a number of checks that you need to carry out.  Most importantly you need to stop the rear of the engine resting on the tender.  There are some details in an old Blog Post:

 

http://www.rmweb.co.uk/community/index.php?/blog/880/entry-10439-is-your-Bachmann-a1%E2%80%93-a-follow-up-to-adding-weight-to-Bachmann-a4s/

 

The A4s can also be made to haul a decent load. 

 

http://www.rmweb.co.uk/community/index.php?/blog/880/entry-10376-streaks-and-highlights-%E2%80%93-weighing-up-Bachmann-a4s/

 

Unlike Hornby who simply add weight to bogies and pony trucks, Bachmann use springing which if not properly adjusted can lift the driving wheels with obvious consequences for haulage.

 

Ray

Ray,

 

Many thanks for those suggestions. I was expecting better things from both the A1s and the A2s I tested and will follow up the links you mention.

 

I didn't test a Bachmann A4 but I did try an old Hornby tender drive A4.  This was absolutely atrocious to begin with.  The tender drive is designed as an 0-6-2 with the rear wheels are arranged as a trailing bogie.  Unfortunately the tolerances were wrong and the rear of the bogie lifted the rear of the tender off the track, resulting in an 0-2-2 drive.  A slight bit of filing cured it and performance was good, if somewhat noisey.  I didn't modify it until after I had completed the tests but would expect it to be similar to the old Hornby R033 Morning Star which is in the tests.

 

Additional: I've just looked at your excellent articles and I'll follow your suggestions.  Your blog looks like worthwhile reading too. Thanks again.

 

Peterfgf

Edited April 4, 2018 by peterfgf

[JST]

It seems to me that this is not an exact science as so much depends on the state of the loco and maybe it's individual idiosyncrasies. There is also the state of the track to think about. I have two Bachman pannier tanks both maintained to the same standard but they have differing running tendencies. I have a gradient on my layout (00 Peco code 100 track) which starts with a 1 in 67 over 1.5 metres, followed by a level 180 degree 4th radius curve and then an 8 metre straight climb at 1 in 90. Both Bachman tanks will happily drag 5 coaches up the gradient but only one of them will take 7 coaches without slipping. My Hornby Castle and Bachman class 47 will go up it with 8 coaches without slowing or slipping.

 

Seems to be too many variables to be dogmatic.

[Silver Sidelines]

Thanks Peter

 

. I was expecting better things from both the A1s and the A2s..

 

I had forgotten about A2s (how could I) - they have smaller diameter wheels and should perform better than the A1s.  Just as the prototypes that were built for the lines with steeper gradients north of Newcastle.

 

Regards

 

Ray

[Flying Pig]

 

I had forgotten about A2s (how could I) - they have smaller diameter wheels and should perform better than the A1s.  Just as the prototypes that were built for the lines with steeper gradients north of Newcastle.

 

 

Why? Surely adhesion is the limiting factor here, not tractive effort?

[Silver Sidelines]

Well done Peter, PhD topic? 

 

The problem as always is that 20 guys will say 20 different things and definitive info is hard to come by.  There are still so many plans that appear on here with horrendous gradients to get round multi level requirements and no matter how many times you try to explain the difficulties involved, people will always say they run 10 coach trains up 1:25 gradients......

 

Maybe one of us has got the calculations wrong.....

 

As Gordon said at the top of the thread - everybody has their own opinion.  Then there are all the variables, known and unknown - Donald Rumsfeld comes to mind.

 

When I was building my layout I made a number of videos of engines struggling with seven Bachmann Mks1s.  There is one here with a Bachmann A1 in the early days.

 

 

and another with a Bachmann A4

 

 

but no A2!

 

I settled on seven coach trains and nominally 1 in 60 gradients - which in reality turned out to be 1 in 56.  These are too steep but there is no way that I could have fitted in the number of features that I wanted if I had flattened the gradients to 1 in 100.  I think 1 in 60 still needs around 11 feet to rise the minimum 2 1/2 inches.

 

Regards

Ray

Edited April 4, 2018 by Silver Sidelines

[Pete the Elaner]

I am intrigued by your choice to describe gradient in radians.

Is there a particular reason? Maybe we should all be working in radians to make our lives easier?

[DCB]

poor tractive effort is the curse of modern modelling   50 years ago it wasn't an issue, a Hornby Dublo Castle will pull 10 kitmasters and probably 10 Triang Mk1s up a 1 in 36 which is about what the real thing will do.    Likewise the modern Hornby Black 5 will manage 3 coaches up a 1 in 35 which is all the real thing was allowed to haul up the Lickey without a Banker.  Equally huge amounts of nonsense are talked about small loco haulage, Even 14XX will haul 5 coaches, M7s were regularly rostered to long ECS rakes 10/12 coaches.  I would put the decoder in the tender and stuff the loco with lead if you must use DCC or simply stuff it with lead, but really a Pacific should haul 10 coaches up a 1 in 36 or thereabouts, Duchesses, A4s, MNs Royal Scots all did it in the 1948 loco exchanges and GW 4-6-0s did it every day for 60 years.

[peterfgf]

I am intrigued by your choice to describe gradient in radians.

Is there a particular reason? Maybe we should all be working in radians to make our lives easier?

 

It made my life easier! 

When I was calculated the various heights of the spacers or shims needed to support the plywood to give the different slopes I used an Excel spread sheet and the easiest formula used radians (height = distance from reference point x angle in radians).  I could equally well have used the tangent.  Looking back at the spreadsheet, I did start with the traditional way of describing gradients, and the first two columns read:

 

Gradient     Angle  

                  (radians)

1:100         0.0100

1:66.7        0.0150

1:50           0.0200

 

I also think quantifying the angle in radians allows a better and more immediate comparison of the quantities.

 

I was also strongly influenced by my professional life where I was often involved in investigating main propulsion shaft alignment problems on ships.  Slopes of shafts and bearing were always described in radians and I am familiar with their use.

 

Perhaps a longer answer than you might have expected!

 

Peterfgf

Edited April 5, 2018 by peterfgf

[peterfgf]

The problem as always is that 20 guys will say 20 different things and definitive info is hard to come by.  There are still so many plans that appear on here with horrendous gradients to get round multi level requirements and no matter how many times you try to explain the difficulties involved, people will always say they run 10 coach trains up 1:25 gradients......

 

Maybe one of us has got the calculations wrong.....

 

That is exactly why I did the tests as there is not a lot of good information around.  There is a bit of advice from Lord Kelvin which I found useful professionally:

 

  “when you can measure what you are speaking about, and express it in numbers, you know something about it”. 

Peterfgf

[peterfgf]

It might have been useful to include a photograph of the test track.

 

The whole of the train is on the gradient, except the last coach which is still on the horizontal.  The locomotive is about to go round the curve leading to the upper horizontal section. The spacers to build up and vary the height can be seen, as can the connecting pieces of plywood under the plywood supporting the track.  The track is Peco Code 100, temporarily  fixed to the plywood with double-sided adhesive tape.

 

Peterfgf

 

[peterfgf]

Why? Surely adhesion is the limiting factor here, not tractive effort?

 

Indeed adhesion is the problem.  At the wheel and rail it comes down to (copied from https://www.engineeringtoolbox.com/friction-coefficients-d_778.html):

 

       F_f = μ N                     (1)

where

F_f = frictional force (N, lb)

μ = static (μ_s) or kinetic (μ_k) frictional coefficient

N = normal force between the surfaces (N, lb)

 

Or in terms more relevant here:

 

     Pulling power = (coefficient of friction) x (weight of locomotive)

 

One can either increase the weight of the locomotive or increase the coefficient of friction. 

• Increasing the weight is often difficult, but I did find that as little as 100g was worthwhile (photo shows method of temporarily attaching weight to Bachmann A2 for trial purposes!)
• Traction tyres are very effective in increasing the coefficient of friction as I found with the Hornby 2P and 4F. Years ago Triang used "Magnetadhesion" or ridged wheels (diabolical); DCC Conept has Powerbase; real-life has sand.

One of the problems is that most model locomotives have (nickel-plated?) wheels which both look nice and are rather smooth.  This was demonstrated rather clearly to me during the trials.  I have two nominally identical Hornby 8Fs: one which I bought new and still has nice shiny driving wheels; and a second one I bought second-hand which has seen some running and lost some of the shine from the driving wheels. 

• My new-bought with shiny wheels one will only pull 4 coaches at full speed on the level (6 at half-speed) and this tailed off to two at a slope of 0.02 radians (1 in 50).
• The second-hand one pulled 10 coaches at full speed on the level and 12 at half speed.  Unfortunately I didn't bother to test this loco on steeper slopes.

The coaches were a mixture of Bachmann (first five) and Hornby (second five), detached and replaced in the same order for each trial.

 

 

Peterfgf

[JST]

Important point about the state of the wheels. Probably why my Pannier tanks give different results. I guess the same applies to the track in as much as old dirty track is not good for electrical contact but grips better.

[Allegheny1600]

A fascinating subject, thanks for starting it.

I can only relate a story from my old American layout where I had some hidden sidings accessed from a fairly stiff gradient, probably better than 1 in 30. I had an older Athearn 'Trainmaster' 6 axle diesel that was heavy to start with and I lined the interior of its shell with lead sheet, it then weighed an impressive 541 grams and hauled anything I put behind it.

 

Although I still have the loco, that layout was two houses ago so I cannot offer further data, except to say this loco has 'sintered metal' wheels that seem to really grip the track well. Other locos with either plated brass or nickel-silver wheels don't seem to grip as well.

Cheers,

John.

[Chuffer Davies]

Hi,

I’m particularly interested in this topic because our new exhibition layout - Clayton - in build incorporates the gradients of the prototype but with the added challenge that the steepest gradient 1:50 has had to be put on a 54” radius unlike the prototype which is pretty much straight. At the other end of the layout we have installed a spiral on a 1:60 gradient to return the line back down to the fiddle yard and in places the radius on this drops to 48”. Early tests with a couple of our kit built loco’s indicated that they both had a maximum of around 19 wagons (vans) before losing traction. We made up the train from a variety of plastic, brass and white metal kit built vans in an attempt to reproduce a representative train on the layout. The two loco’s tested have already been ballasted with lead to the max and so adding further weight is not an option. One of these pulled the equivalent of 60 wagons around Retford with no sign of losing traction. The equivalent prototype loco’s were permitted to pull around 30 vans on the Queensbury line before requiring banking and so we are already falling short on our model.

 

Do your tests indicate what we are likely to see on the 1:60? Will the same loco’s pull a longer train on the 1:60 or will the tighter radius have a bigger negative impact than the positive effect of the easier gradient?

 

It will be another few months before we have the track laid on the spiral and can actually run tests to check this out and so if you have a scientific way of predicting the outcome it would be appreciated if you could share this with us.

 

Regards,

Frank

(Shipley MRS)

[brianusa]

One word Magnadhesion, or perhaps Magnatraction depending on your side of the pond!  Certainly helps!

 

Brian.

[peterfgf]

I did some calculations a couple of years ago and for optimum performance it is advantageous to carve away as much Mazak as you can and substitute it with either lead or tungsten.  The densities are as follows:

 

Mazak          6.6  g/cc

Lead            11.3 g/cc

Tungsten     19.3 g/cc

 

It is interesting that the ratio of lead to Mazak is the same as that of tungsten to lead: 1.7:1, or 70% denser if you prefer percentages.

 

And just to complete the picture, substituting tungsten for Mazak gives a whopping factor of 3:1 improvement (almost).

 

Tungsten is available in small weights, but it is expensive, and really only suitable for cubic locations, such as tank locomotive side tanks.

 

John

That's an interesting comparison of mazak and lead.  I hadn't realised that the density of tungsten was so high. It is very similar to that of depleted uranium (19.1 g/cc) which weapon makers seem to like.  Tungsten is probably more readily available (but not as much as scrap lead off my old roof)!

Peterfgf

[peterfgf]

Hi,

I’m particularly interested in this topic because our new exhibition layout - Clayton - in build incorporates the gradients of the prototype but with the added challenge that the steepest gradient 1:50 has had to be put on a 54” radius unlike the prototype which is pretty much straight. At the other end of the layout we have installed a spiral on a 1:60 gradient to return the line back down to the fiddle yard and in places the radius on this drops to 48”. Early tests with a couple of our kit built loco’s indicated that they both had a maximum of around 19 wagons (vans) before losing traction. We made up the train from a variety of plastic, brass and white metal kit built vans in an attempt to reproduce a representative train on the layout. The two loco’s tested have already been ballasted with lead to the max and so adding further weight is not an option. One of these pulled the equivalent of 60 wagons around Retford with no sign of losing traction. The equivalent prototype loco’s were permitted to pull around 30 vans on the Queensbury line before requiring banking and so we are already falling short on our model.

 

Do your tests indicate what we are likely to see on the 1:60? Will the same loco’s pull a longer train on the 1:60 or will the tighter radius have a bigger negative impact than the positive effect of the easier gradient?

 

It will be another few months before we have the track laid on the spiral and can actually run tests to check this out and so if you have a scientific way of predicting the outcome it would be appreciated if you could share this with us.

 

Regards,

Frank

(Shipley MRS)

Frank

 

That is more or less the same problem I was trying to sort out: I wanted to put storage sidings below the main running line and needed some reliable data before designing the layout.

 

I think it would be difficult to come up with a formula which would predict performance with an acceptable degree of repeatability/accuracy.  Gradients, curves, locomotive weight, coefficient of friction are probably the main factors but you can probably add motor performance, gearing, rolling resistance and a few other things.  I concluded that it was quicker, and more repeatable, to quickly construct a test track which would represent my intended layout and using the locomotives and rolling stock I have. 

 

I may be able to differentiate between the effects of gradients and curves. I did some other trials on a straight slope which I discontinued as not being representative of what  I what I needed.  I'll dig the results out and see if I can make anything of them.

 

Adding a note of encouragement, Hattons did a rather good video of their new Andrew Barclay which can be seen in full on YouTube at https://www.youtube.com/watch?v=vCjtZ00aPK0. Further information about their test track is available in the topic on these locos on this site at http://www.rmweb.co.uk/community/index.php?/topic/126141-andrew-barclay-14-16-0-4-0st-in-oo-gauge/page-23&do=findComment&comment=3035895 in posts 567 and 568. The loco is shown hauling 11 4-wheel models of 16-ton mineral wagons up a slope of 3% (0.03 radians or 1 in 33) which includes a curve.  Not bad at all.

 

Peterfgf

[Chuffer Davies]

Frank

 

That is more or less the same problem I was trying to sort out: I wanted to put storage sidings below the main running line and needed some reliable data before designing the layout.

 

I think it would be difficult to come up with a formula which would predict performance with an acceptable degree of repeatability/accuracy.  Gradients, curves, locomotive weight, coefficient of friction are probably the main factors but you can probably add motor performance, gearing, rolling resistance and a few other things.  I concluded that it was quicker, and more repeatable, to quickly construct a test track which would represent my intended layout and using the locomotives and rolling stock I have. 

 

I may be able to differentiate between the effects of gradients and curves. I did some other trials on a straight slope which I discontinued as not being representative of what  I what I needed.  I'll dig the results out and see if I can make anything of them.

 

Adding a note of encouragement, Hattons did a rather good video of their new Andrew Barclay which can be seen in full on YouTube at https://www.youtube.com/watch?v=vCjtZ00aPK0. Further information about their test track is available in the topic on these locos on this site at http://www.rmweb.co.uk/community/index.php?/topic/126141-andrew-barclay-14-16-0-4-0st-in-oo-gauge/page-23&do=findComment&comment=3035895 in posts 567 and 568. The loco is shown hauling 11 4-wheel models of 16-ton mineral wagons up a slope of 3% (0.03 radians or 1 in 33) which includes a curve.  Not bad at all.

 

Peterfgf

Hi Peter,

Thanks for taking time out to respond. If you can’t make a prediction from your knowledge thus far I may just have to bite the bullet and give priority to laying the track on the spiral so we can run some tests. We made a decision early on not to resort to gadgets such as Magnahesion to increase the drawbar pull so we may end up banking shorter trains than would have been found on the prototype but this adds to the operational interest and so is not necessarily a bad thing.

If we run tests I’ll post the results on here.

Frank

[peterfgf]

Hi,

I’m particularly interested in this topic because our new exhibition layout - Clayton - in build incorporates the gradients of the prototype but with the added challenge that the steepest gradient 1:50 has had to be put on a 54” radius unlike the prototype which is pretty much straight. At the other end of the layout we have installed a spiral on a 1:60 gradient to return the line back down to the fiddle yard and in places the radius on this drops to 48”. Early tests with a couple of our kit built loco’s indicated that they both had a maximum of around 19 wagons (vans) before losing traction. We made up the train from a variety of plastic, brass and white metal kit built vans in an attempt to reproduce a representative train on the layout. The two loco’s tested have already been ballasted with lead to the max and so adding further weight is not an option. One of these pulled the equivalent of 60 wagons around Retford with no sign of losing traction. The equivalent prototype loco’s were permitted to pull around 30 vans on the Queensbury line before requiring banking and so we are already falling short on our model.

 

Do your tests indicate what we are likely to see on the 1:60? Will the same loco’s pull a longer train on the 1:60 or will the tighter radius have a bigger negative impact than the positive effect of the easier gradient?

 

It will be another few months before we have the track laid on the spiral and can actually run tests to check this out and so if you have a scientific way of predicting the outcome it would be appreciated if you could share this with us.

 

Regards,

Frank

(Shipley MRS)

Frank,

 

Very roughly I think you could make the following generalisations:

 

1. Whatever the number of coaches a steam model locomotive (with metal tyres) can haul on the level, it reduces by two coaches for every 0.005 radians (0.05%) increase in gradient (including curves).
2. Diesel and electric model locomotives, and steam models with rubber traction tyres, can take the same number of coaches up gradients as on the level (limit not reached at 0.02 radians (2%).

I didn't do any comparative tests with wagons and I've dismantled the test track now.  However, I compared the weights of two coaches and a wagon as follows:

 

• Hornby R4714 Mk.I Corridor second class M24912                    140 g
• Bachmann 39-475 LMS 60' Porthole open vestibule M7481M    160g
• Bachmann 37-377B 16 ton pressed end door mineral wagon      27g

Very roughly, the average weight of a coach is 150g and is equivalent to the weight of about 5 4-wheel wagons, . So perhaps one could add a third point, neglecting friction in the bearings:

 

      3.  Whatever the number of wagons a steam model locomotive (with metal tyres) can haul on the level, it reduces by ten wagons for every 0.005 radians (0.05%) increase in gradient (including curves).

 

Peterfgf

Edited April 7, 2018 by peterfgf

[NIK]

I originally posted this in the Heljan GWR 47xx thread in response to 71000 (post 567) who had carried out a very comprehensive series of tests on model locomotive haulage. His article is worth reading.  I've decided to post my reply here as it is more relevant to this section.

 

I did some less comprehensive tests, varying the gradient (by using shims) and varying the number of coaches. The test track occupied a length of about 4.5 metres and incorporated a 1.0 meter radius curves at the beginning and end, with a further level section of 2 metres at each end (imagine a flattened "U" shape).  Trains were started from stationary at the beginning of the first curve at the bottom of the slope.  This is quite a hard test, incorporating a slope, two curves and a standing start, but resembles the space in which I have to build a layout.  All locos were DCC chipped and control was by a handheld Roco Multimaus.

 

The results are shown in the attached graph and can be summarised as follows:

• 1 in 100 (or 0.010 radians) is the maximum slope for full length trains of 8-10 coaches. 
• Haulage capacity rapidly falls off at steeper slopes, roughly by 2 or 3 coaches for every 0.015 radian increase in slope. At 1 in 50 haulage capacity was reduced severely. 
• The performance of model steam locomotives is not as good as might be expected but can be improved by extra weight.  An additional trial weight of 100g increased haulage capacity by as much as 3-4 coaches.
• As in real life, haulage capacity roughly corresponds to loco size and weight: a 4-6-2 Pacific (heavy) can manage 8-10 coaches, 0-4-4Ts (light) can only manage 2 or 3 coaches.
• The haulage capacity of Bachmann Pacifics was surprisingly poor.
• The haulage capacity of Hornby 2P 4-4-0 and 4F 0-6-0, both with rubber tyres, was impressive and both took 10 coaches up 1 in 50 (0.02 rads).
• The performance of model diesel and electric locomotives is very good in comparison to steam locomotives. A limit was not met with 12 coaches even on 1 in 50 (0.02 rads).

Coach haulage on gradients 01.png

 

Peterfgf

 

Hi,

 

I've just done some tests on a Bachmann Jubilee I've been lent for conversion to DCC. I tested the tractive effort on a slip track with the coupling connected to a load cell. I then weighed the loco.

 

I put the tractive effort and loco weight into my experimental gradient and curve calculator.

 

I then took the number of coaches your Jubilee could haul on the flat from your graph in post #1 of this topic in order to estimate the friction of the coaches.

 

I put the estimated friction of the coaches into my calculator.

 

The calculator predicted that my Jubilee would haul 4 of your coaches up a 1 in 50 gradient but not 6 coaches.

Above shows 4 coaches, calc was run again with 6 coaches and at 1 in 50 the loco traction was less than drag due gradient and friction.

 

I haven't tested any other locos on your graph but I was relieved my calculator/predictor wasn't way out.

 

Could you send a link if possible for 71000's article on gradient tests as I couldn't find it under post #567.

 

 

Many thanks

 

Nick