Gradient Design

by Colin Phillips

The following is a symposium on the topic of using gradients on model railway layouts resulting from the questions put to the N-Gauge and Southern E-mail Groups in September 2002. My thanks to all those who have contributed.

The following is a symposium on the topic of using gradients on model railway layouts resulting from the questions put to the N-Gauge and Southern E-mail Groups in September 2002. My thanks to all those who have contributed.

Q1. What is the maximum gradient a train of six bogie coaches can manage?
a) (Mike Boydon, N-Gauge) This depends to a great extent on the loco, e.g. a Grafar 4P out of the box might manage 6 downhill, whereas a Fleischmann 7161 with Langley S15 white metal body kit will manage 30 bogies on 1in30. I would suggest nothing steeper than 1in30.
b) (Ken Howard, N-Gauge) I had gradients of 1in40 on my last layout. No problem with Farish coaches but Minitrix were far too heavy.
c) (John A Arkell, SEmG) It depends on many things not least of which is the tractive effort of the locomotive and the rolling resistance of the coaches. Tractive effort can be affected by the materials used for the wheels and the power developed by the motor. I use steel rimmed wheels (Sharman) on my kit and scratchbuilt locomotives. I think they have a greater friction between wheel and rail than polished nickel plated or nickel rimmed wheels such as Romford or those found on commercial ready to run locomotives. What you will have to do is set up a plank with a length of the track you wish to use and experiment with different locomotives and coaches. You will soon find what your set-up will cope with and what needs banking assistance.
d) (Colin Duff, SEmG) I have gone through a sharp learning curve (gradient??) with my current layout. All my previous layouts, save a Triang-Hornby one I built when I was about 10 years old which had an up and over girder bridge with a frighteningly sharp gradient which relied upon Magnahesion, have been level. However my current layout has three levels. As a general principle any gradient should be as shallow as possible. In other words you need as long a run up as you can achieve to gain the required altitude. Apologies to all who do not like the North American/Continental use of percentages but I am afraid that is what I think in these days. Even 1% ( a vertical rise of 1 inch in 8ft 4in) on the real railway is troublesome. To put this into perspective the gradient from Exeter St Davids to Exeter Central is circa 2.7%. It is much the same with models. Trying to squeeze 3 levels into a 12ft x 8ft space on my layout I have gradients of 4% (a vertical rise of 3.5 inches in 7ft) and most of the rise is on curves with a minimum radius of 2ft . This is of course horrendous but it works, if only because in the space I have I only intend running a maximum of a loco with 5 coaches or up to a 5 car EMU. (By the way I am working in 4mm scale and I am not sure how experience in this scale follows for 2mm, what with locos, etc, being lighter.) I suggest you do what I did and run a series of trials with your rolling stock on a test variable gradient. I used a 4ft strip of plywood 2 inches wide with track on it using various size risers calculated and placed by trigonometry to set particular gradients. That way you can find out what your stock is capable of on various steepnesses. I found within reason the power of a model loco is proportional to its real life capabilities - of course excepting models with really weak or strong motors. Thus up my 4% round a 2ft radius curve a Terrier can manage one mk1 coach, an M7 two, a BR Std class 4 three-four, a WC/LN five-six.
e) (Richard Giles, SEmG) The max gradient depends on the loco!! Farish steam locos have no traction tyres and within the range some locos are worse than others - e.g. 8F, Castle, Hall. Diesel locos will normally pull anything up anything!! 1in30 or 1in35 is about max but reduce to about 1in40 to 1in45 on curves. Remember that in a figure of 8 you can have both an incline and decline thus reducing gradients!!
f) (Paul Severs, SEmG) I had the misfortune some years ago to design an N-gauge layout for my father-in-law, based on Riccarton Jcn. and it had gradients to hidden sidings below. It was designed on the basis of a 4mm design reduced by ½. When he began to build it, we realised that there are greater problems in N-gauge than we envisaged. In spite of using a special Peco gradient track [? is it still available] which had a serated rail head to aid adhesion, only very short trains could manage the gradients, and the particular difficulties were on the curves [which were down to the minimum, ~ 12" radius]. It seems that the increased friction on the curves, together with the lack of weight in typical locos, made hill-climbing too difficult.Now admittedly in the tight space he had available to him - ~ 2'6" x 8'0", the gradients were of the order of 1in30.

Q2. What special precautions (if any) have to be taken with gradients on curves, and what would be the minimum advisable radius on a gradient?
a) (Mike Boydon, N-Gauge) Curves on gradients are best avoided if at all possible, if they have to be included then ease the gradient to 1in45 or better.
b) (Noel Leaver, N-Gauge) I would definitely try to change gradient only on straight track to avoid compounding problems.
c) (Ken Howard, N-Gauge) I had 15" radius curves on the gradients and had one serious problem. Peco wagons would invariably uncouple when going down grade. When the loco entered the curves it would slow and the rest of the train would bunch up and some of the Peco couplers would stand up in the uncoupling position. Then as the loco came out of the curve it would accelerate and the train would pull apart before the couplers could return to the horizontal. I had to fit brakes to the axles of all my brake vans.
d) (John A Arkell, SEmG) I try not to lay curves of less than three feet radius on any layout but that is because I work in EM and some of my locomotives are not designed to go round less.
e) (Colin Duff, SEmG) Curves cause extra resistance which on a rising gradient adds to the force of gravity, thus best to avoid, but again I suggest it is far better to test with your stock than rely on any theory or advice from another. It is best to avoid starting and finishing a gradient on a curve - this is not possible on my layout but I have got away with it by using gradual vertical transitions into and out of the gradients. Just as it is best to use a transition curve into a constant radius curve it is best to do the same with gradient changes. It can now be admitted (and some SEmG'ers already know this) that due to a change of track plan I made whilst construction was underway, and thus it was not thought through properly, I ended up with the middle of a reverse curve happening just as a gradient peaked. Unsurprisingly this was a cause of regular derailments particularly with long wheelbase locos which just wanted to carry straight on, which brings us onto your next question!
f) (Richard Giles, SEmG) Curves should not be less than 15" radius (for N gauge) to be safe. I tend to work with a baseboard width of 2' but if you are doing a figure of 8, you need 30" minimum.
g) (Paul Severs, SEmG) See answer to question 1.

Q3. How do you prevent a 6- 8- or 10-coupled loco without suspension from breaking contact with the rails where there is a change in gradient, ie at the bottom or top?
a) (Mike Boydon, N-Gauge) Even if the change in gradient is gradual the longer wheel base locos will lose contact on some wheels, tender pickups ease the problem as there should be enough play in the loco-tender coupling to allow a couple of loco axles to be in contact and tender also.
b) (Ken Howard, N-Gauge) You need to make the change from level to grade over as long a distance as possible. Anyway in theory a 0-6-0 will only ever have 3 wheels in contact with the rails at any given time unless the chassis is compensated so what you are worried about shouldn't be an issue.
c) (John A Arkell, SEmG) You have to taper the gradient by leading on and off it with a curve in the vertical plane i.e. a transition gradient. Again experiment to find what your stock will accept.
d) (Colin Duff, SEmG) Soft vertical transitions, avoid curves and test thoroughly. Learn from my experience learned the hard way. My trackwork tests during construction were done with a Bo-Bo diesel loco, a coach and a short wheelbase steam loco. These gave no trouble and I thought everything was fine with my track until I tried running my new Hornby MN! Then I tested my Lifelike Proto 2000 0-8-0 with even more disastrous results..... the words "see" and "saw" spring to mind..... (the reverse curve has now been eliminated at this position!). Best to test with the widest range of wheelbases and wheel sizes.

Q4. We all know about transition curves, but what about transition gradients?
a) (Mike Boydon, N-Gauge) Worth trying for.
b) (Noel Leaver, N-Gauge) What I was thinking of doing was to have supports at the correct height for the constant gradient bits each side of the change, then attach some reasonably thick plywood as the track base**, so the natural flexibility of the wood would produce a gentle transition. Have not tried this though. I think if you can make the changes very gradual there won't be many problems.
c) (Peter Towler, N-Gauge) **It works. I did this. Feather the edge that is going to "touch down". Drill, countersink and put a screw through the trackbed into the main base about an inch or two from the end to give the necessary pressure and control to pull the plywood down. Put a spacer (e.g. bit of wood the right thickness) widthways under the plywood a bit further from the end to control the final position of the plywood. Screw down and tweak as required. Smooth off with suitable paste. Put some paste on the baseboard where it touches down first too if you like. I use "plastic wood" sets like rock and never moves (unlike plaster). I have a rather testing gradient made that way. A motor bogie three-car cannot hack it, but a full drive chassis three-car DMU can. A two car motor bogie DMU can 'just' hack it (which was my benchmark when I designed and tested it). I've got points on the gradient-changing slope too. That was a bit of trial and error juggling. obviously you cannot bend points. There is a slight inconsistency where the tail of one point meets the nose of another, but it does not cause serious problems. BoBo bogies float a bit. I don't run CoCo up it, and short wheelbase 0-6-0 shunters and tanks seem to not have a spanning problem over it anyway.
d) (Ken Howard, N-Gauge) I don't know what the angle of a 1in40 is but I suspect it is about 1/2 a degree. A transition gradient wouldn't be practical.
e) (John A Arkell, SEmG) See above.
f) (Colin Duff, SEmG) Already answered.

Q5. How do the standard N & OO gauge couplings cope with changes in gradient?
a) (Mike Boydon, N-Gauge) Should not be a problem unless change in gradient is extreme.
b) (Ken Howard, N-Gauge) Probably better than a lot of other couplers as they are bogie mounted so problems with carriage length and overhang on the ends is not relevant. But never-the-less make the change from level to grade over as long a distance as possible.
c) (John A Arkell, SEmG) My three link standard couplings do not usually fall of the hooks!
d) (Colin Duff, SEmG) I can only answer for Kadees and tension link. No problem as there is sufficient vertical movement. Not so with some of my home made bar couplings and most importantly the bar-type close coupling which comes as an option with Bachmann mk1s.

Q6. Do feedback controllers effectively maintain a constant speed on both rising and falling gradients?
a) (Mike Boydon, N-Gauge) Sorry never used one so can't comment.
b) (Ken Howard, N-Gauge) Never used one.
c) (John A Arkell, SEmG) Pass
d) (Colin Duff, SEmG) They are supposed to, but if your driving is going to be realistic constant speed should not be maintained. My locos sometimes struggle with the gradients, which is after all what would happen in real life. I have a feedback controller but have not used it enough to see how it responds with my 4%. I suspect that using high frequency track "cleaners" - which I can switch into circuit on my layout - negates the feedback effect.
e) (Richard Giles, SEmG) Be very cautious about using feedback controllers with N gauge locos especially Farish motors- Farish motors hate most feedback controllers, especially older locos. I use AGW of Farish controllers, even the old H&M are ok!!

Q7. What else (if anything) is there to know about gradient design before we (or the trains!) take the plunge?
a) (Mike Boydon, N-Gauge) Try not to have stations, sidings or other stopping places on gradients, it's difficult to fit brakes on wagons and coaches in N gauge :-)
b) (Ken Howard, N-Gauge) It takes a lot more length to change from one level to another than you might think when you consider the vertical curves at both the top and bottom plus the thickness of your roadbed etc,etc.
c) (John A Arkell, SEmG) Make the transitions easy and consider super elevation on curves by raising the outer rail gradually upon entering a curve. It looks really good to see a locomotive heeling into the curve. If in doubt go and have a look at any length of curved prototype railway.
d) (Colin Duff, SEmG) It is easy to say don't have gradients at all but real life railways have them and like me it may be the only way to achieve the layout you want in the space you have. As with best running practice check back-to-back measurements, check all wheels rotate freely, bogies pivot freely both vertically and horizontally and that mechanisms do not bind. Also that couplings have sufficient free play in the vertical dimension.
e) (Richard Giles, SEmG) Use flexitrack and keep joins on the straight. Use electrofrog points. Dont get too worried about graduation - if it looks right then it probably is right. Test with you longest stock and loco as you build.
f) (Paul Severs, SEmG) How big is this 'looped-eight' layout to be? My suggestion would be to construct just one reasonable length of trackbed on the ruling radius at the steepest gradient necessary, and see what the trains are capable of. A further suggestion would be to have NO LEVEL LENGTHS, i.e. make use of the whole length of the tracks for the rising and falling gradients - it is only where the tracks cross each other that you need the necessary separation between low and high levels. If the hidden tracks are kept to the inside, behind a hillside, and the visible tracks to the outside of the layout, you should not in N-gauge need more than 2" or so difference in levels between high and low levels - use the thinnest plywood possible to support the flyover tracks.
Another tip for this kind of layout is to make maximum use of the LENGTH of the hidden tracks. If you organise your running schedule into a sequence, you do not need a fan of storage sidings with lots of points, with each train having its own siding - have several isolating sections on each track and store the trains end to end on the same track, and all you need to do is to always runs the three, four, five trains on that track in the same sequence every time.

To conclude, I would like to mention the recommendations that I have found in the few books I have which treat the subject -

  1. The length and/or weight of the train plus the type/condition of the motive power determine the maximum gradient that can be climbed.
  2. Generally speaking, gradients from 1in40 to 1in60 are the most suitable for all-round use, 1in30 is the absolute maximum that should be considered for most situations, nothing steeper than 1in80 is advised for the running of really long trains, and 1in20 should be kept for exceptional cases such as 1-coach trains, coaling ramps, etc.
  3. A transition gradient should be incorporated into the top and bottom ends of the ruling gradient. The minimum length of the transition at each end can be calculated as half the length of the longest coach that will be used on that gradient. Thus, in N gauge, if a rise of 35mm is required with a gradient of 1in30 and a coach-length of 140mm, the total length of the space needed for a straight gradient would be (35x30)+140 = 1190mm (or almost 47in).

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This page was last updated 3 December 2002

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