Module : 9A

grades

Grades, Slopes, Inclines, Declines & Descents

No matter how you choose to describe this particular feature grades are one of the most important aspect of model railways and merit a complete module all on their own.

Few prototype railways are level as they have to follow the contours of the landscape and that can mean going over hills and mountains rather than tunnelling through them which might prove very expensive to accomplish, both in time, and overall cost.

In fact, given a choice, railway companies will always tend to follow as a straight and level route as possible since locomotives use less energy, speeds are frequently higher, and there's less wear on rolling stock and permanent way. But the terrain rarely offers this luxury and the landscape rises and falls, both natural and man-made obstructions must be negotiated, and all manner of contingencies allowed for.

This means that changes in elevation and the introduction of curves are often unavoidable in order to reorientate the direction of the tracks around these obstacles by means of slopes (gradients in UK/Europe) or grades (in the USA) and elevated sections. Even when grades are unavoidable real railways have very smooth, gradual changes in elevation wherever possible. On main lines, for instance, grades are generally 1 percent or less, and inclines steeper than about 2.2 percent are relatively rare. rare. Suffice it to say your model railway will look more realistic if it does the same.

When engineering ways around or over these physical features great care has to be taken to ensure that the planned locomotive roster for the line has sufficient power to successfully traverse these undulations.

For an explanation as to why trains are not actually very good at going up hills (or decending them) I suggest you watch this excellent video by James May appropriately entitled "Why Can't Trains Go Uphill":

Grade Measurement Terminology

Around the world, inclines are expressed in slightly different nomenclature but in essence they all arrive at the same answer portrayed in different ways.

In the UK, and places with heavy British influence, gradients are expressed in terms of the horizontal distance required to achieve a 1 foot rise. For example a gradient where track rises one foot over a distance of 100 feet would be expressed as ‘1 in a 100’. Similarly a much steeper rise might be referred to as a ratio of ‘1 in 40’.

The terminology in Europe is much the same but may use the metric “per mille” parts per thousand system expressed as ‰ (similar to a percentage sign but with an extra 0 in the divisor).

In North America, gradient is expressed in terms of the number of feet of rise per 100 feet of horizontal distance. Thus a track rises 1 foot over a distance of 100 feet, the gradient is said to be "1 percent;" whereas a rise of 2‘6” would be a grade of "2.5 percent” and so on. In many ways this method is probably the easiest to comprehend and I have used this nomenclature later in these pages.

Real Railway Practice

Inclines on prototype railways tend to be much gentler than one might find on a large scale model railway. On modern main lines, grades are typically 1 percent or even less whilst grades steeper than about 2.0 percent are quite rare.

For the most part the factors described in the video tends to limit grades on most major railways to a maximum of 4% (4’ in 100’) for high speed express trains tracks and a much less daunting 1.5% (1’6” in 100’) for slow moving freight trains.

Notable Exceptions

Needless to say there are numerous exceptions of even steeper railways around the world using the conventional ‘adhesion system’ (as opposed to those based on rack, cog or cable) which demonstrate that there is a prototype for everything.

The most notable example in the UK is the Lickey Incline in the UK at 1 in 37.7 (2.65%) , and the Docklands Light Railway, London, UK at 1 in 17 (5.88%)h pictured below.

In the USA the steepest grade on a major railroad's standard gauge mainline track (as opposed to industrial spurs, narrow gauge lines, etc.) is reputed to be on the Pennsylvania Railroad north of Madison, Indiana.

The Madison Incline is said to rise 416 feet over a distance of 7012 feet – equivalent to a 5.89-percent grade.

This video clip recreates a ride on the section as alas, the incline has not been in operational use since 1992.

Three popular tourist lines incorporating steep inclines are the Cumbres & Toltec Scenic Railroad in Colorado, USA with 4% grades ( 1in 25), the White Pass & Yukon Railroad with a severe maximum of 3.9% (1 in 26) and notably the Cass Scenic Railway, West Virginia, USA at an incredible 11.1% (1 in 9) and The railroad is home to the worlds largest collection of geared Shay steam locomotives, but these are very much the exceptions.

Impact of Grades

The effect of grades or inclines on train operations is significant. It is estimated that for each percent of ascending grade, there is an additional resistance to constant-speed movement of 20 lbs. per ton of train. This compares with a resistance on level, straight track of about 5 lbs. per ton of train. In the real world a given locomotive can haul only half the tonnage up a 0.25% (1 in 400) grade than it can on the level.

Descending grades carry their own penalties in the form of equipment wear and tear and increased fuel consumption. In practice this degradation in pulling power is why few prototype railways employ gradients in excess of 2%.

As a real-life example imagine a fully-loaded train comprising 40 modern coal wagons, each one with a tare weight of 28 tonnes (empty) + a coal load of say 75 tonnes gives a combined weight of 103 tonnes. Even 40 such cars x 103 tonnes equates to a massive 4120 tonnes. Take into consideration the weight of the actual locomotive pulling this consist (say 200 tons) and the combined weight of the train in total is likely to be around 5,800 tons!

With this weight burden it is easy to see that too steep a slope will severely limit what you can be feasibly run on a real railway.

These are staggering figures, and much the same rules of physics apply on a model layout.

A model train locomotive will need enough power to safely pull its cars up (or down) a grade without slowing to a stop or a derailment happening. An underpowered engine won’t be able to haul many wagons up a steep grade, so if you want precipitous grades, you’ll require substantial locomotives. As a 'rule of thumb' any given locomotive is only likley to be able to pull only half the cars on a 4% slope than on level track.

In general, more weight means greater wheel traction. A heavier loco might be able to climb a steep grade, whereas the steel wheels on a lighter weight loco might start to slip. Following this logic; a larger scale locomotive might cope better on steeper grades than would a smaller scale locomotive.

Model Train Grades

However, railroad grades demand very careful consideration if you are to avoid operational problems such as stalling or even derailments. It’s not just the loco that will need to safely navigate up or down the raised track, it is also the fully laden cars carrying coal, timber, metal, refrigerated foods, fuels, vehicles, livestock, or even people (well, plastic models of people). A long train can be very heavy and this needs to be taken into consideration when going up or down a gradient of a real railroad, or on a scaled down model railroad.

Model trains can be expected to perform in similar fashion so you would expect to observe a “no grade more than 2%” rule. But a lot depends on the power and weight of you locomotives and the number and weight of the rolling stock they will have to pull. The advice on grades appears to apply to all model railway scales but the mass and substance of large-scale locomotives suggests that they might have the advantage over their small and lighter bretheren.

In simple terms the more powerful the locomotive the more coaches or wagons (cars) it can haul up hills. The weight of the locomotive is also a key factor as the heavier it is the greater the traction. Lighter locomotives have a tendency to slip on inclines. This is why many modellers add additional weight to their engines to improve tractive effort.

As a ‘rule of thumb’ you will often read that the tried and tested ratio for determining maximum grades on model trains is 1 in 50 (2%).The consensus amongst experienced large-scale modellers is that one should not generally go above 1 in 40 (2.5%) with 1 in 30 (3.33%) as the absolute maxima unless you plan to use other methods of getting you trains up hills such as banker engines, double heading or split trains.

These boundaries may appear overly rigid particularly when you realise that even a fairly modest 1% (1 per cent or '1 in a 100') grade will require a considerable length of track run ( a mind-boggling 83 feet 4“ inches to be exact!) to enable it to pass comfortably over another track allowing the recommended vertical clearance of 10” (measured from the top of the rail-head to the bottom of the bridge (or other obstruction)). Needless to say, you also need to check that this clearance is sufficient to accommodate your tallest locomotive or rolling stock allowing 'a little bit more' just in case.

Few model railways, even garden installations, are likely to revel in the luxury of this amount of space so some compromises usually have to be made in order to condense the run.

If the problem is resolved by making the climbs (and descents) more demanding the track runs can be proprotionately reduced, viz.

• To achieve the same elevation of 10” using a 2% (1 in 50) grade would only require around 42’ of track which is more manageable.

• Alternatively the use of an even more severe 3% (1 in 33) grade takes just over 27’of track to achieve.

My own Durango Wells & Crystal Springs layout measures approximately 24’ x 16’ so I would need at least a complete circuit to achieve the required elevation and the same again to return to datum level.

Had I listened to my own advice I would possibly have designed the layout slightly differently with a higher datum level to allow tracks to descend by 5” and rise by 5” to make the inclines much gentler. As things stand I have somewhat compromised by creating a flat ‘mezzanine’ level at 5” higher than base level, ostensibly to accommodate a second station, but also serving as a level run before ascending the gare once more. I have not yet calculated the resultant grades yet but i suspect that they are very testing and almost certainly closer to 4% than I would wish.

One can always be wise after the event! Fortunately most of my locomotives have so far, managed to surmount the challenge but I shall still keep my fingers crossed each time my valuable Bachmann K-27, coupled to a rake of yellow Jackson-Sharpe Passenger Cars, (an appropriate adjective given that "rake" is a synonymous with the nouns grade and slope), actually commences its journey around the layout.

Ruling Grade

The term "ruling grade" is used to describe the limiting grade between two terminals. It determines the maximum load that can be pulled over that portion of line by a given locomotive. The concept is analogous to that of the weakest link in a chain; no matter how many lesser grades a train can handle, if it can't make the ruling grade, it won't be able to complete the run.

A ruling grade is also not necessarily the absolute steepest grade between two endpoints; it is assumed that trains will surmount certain steeper grades with momentum from descending grades or with the aid of helper locomotives.

For grades that are short relative to the total length of a train's run, helper engines - extra locomotives added to the front, rear, or even middle of a train - are employed. While the superior power of diesel locomotives has eliminated many helper districts, dieselisation has brought helpers for use on trains going downhill, where dynamic braking is used to control speed on the descent.

If a train cannot make a grade, and no helpers are available, it may have to "double the hill," a practice in which the train is taken up the grade in two separate pieces. On some hills, "tripling" is necessary considerably adding to the total journey time.

(Reference from “Grades & Curves” by Robert S. McGonigal | May 1, 2006)

Garden Railway Considerations

These practical limits on full-size railways are also best observed when building a garden railway layout as there is usually less room to accommodate a realistic incline. According to the experts one should always aim for as level a track as possible to avoid putting too much strain on your model motive power.

Notwithstanding this sage advice as to the acknowledged benefits of maintaining a horizontal plane for optimum running performance many model railway enthusiasts will still entertain a yearning to incorporate some measure of variation in height on their layouts even if the space available is somewhat restrictive. This may be to simply to add interest or perhaps more accurately represent the railway prototype they are seeking to reproduce.

To be honest a flat railway can sometimes appear a little boring so if you are determined to integrate some ‘rise and fall’ there are ways in which this can be achieved without causing undue wear and tear on your cherished motive power.

First we need to learn a little bit more about grades or inclines.

"Grade" — in railway terms, as we have already learned, this is the extent to which track rises or descends from one level to another. This can be expressed in a number of ways according to which country you reside in but essentially the formula is usually expressed as:

Calculating Grade

The formula for calculating grade is:

Grade (%) =

Rise

Run

x 100

Rise and Run must use the same units of measurement. You can use inches, millimetres, feet, miles, etc., as long as both rise and run use identical units of measure. However, if you use inches it is a good idea to convert fractions to decimals unless you are a wizard at mathematics!

Example: 2 3/4 inches = 2. 75 inches.

The formula above divides the rise by the run, yielding a small and apparnt insignificant number but you then need to multiply that result by 100 to convert the number to a percent.

For example: Grade (%) = 3.5” rise divided by 150” run = 2.33%

Grade (%) = 2.0’ rise divided by 200’ run = 1.00%

Thus:

A Rise of 4” divided by Run of 200” = 0.02 x 100 = 2% or 1in50 (said to be the 'proven ratio' for model railways as it is the optimum ratio for rate of climb that trains can manage while covering the minimum distance of track but I have been unable to establish the science which underpins this claim).

Indeed, the consensus among experienced railway modellers is not to go beyond 1 in 40 in any circumstances with 1 in 30 being the absolute maximum considered by modellers on Model Railway Forum and the Anyrail forum (here and here).

Just to put things in perspective a 1 in 30 grade equates to 3.33% – which far exceeds the 2.65% Lickey incline figure h gives you some idea as to how model railways compare to the real thing.

In the USA, the steepness of grades (inclines) is usually expressed as a percentage of rise so a rise of 1" in every 100" (or any other unit) is equal to a 1% grade; 2 in 100 = 2%, and so forth.

In many other countries, such as the UK and Australia), steepness is traditionally expressed as a ratio of one part rise to so many parts run. For example, a slope that has a rise of 5 feet for every 100 feet of run would have a slope ratio of 1 in 20. (The word "in" is normally used rather than the mathematical ratio notation of "1:20").

Examples:

1% Grade = 1 in 100 feet

2% Grade = 2 in 100 feet

3% Grade = 3 in 100 feet

4% Grade = 4 in 100 feet

and so on.

Naturally, modellers tend to ask related questions such as how long does my track have to be to raise the level by 4" with a grade of 1%? This can be calculated by re-arranging the above formula thus:

Run (Length) = Rise (Height) / % Grade Sum: Length = 4" divided by 0.01 = 100"

The formula to determine the Rise (height) you could achieve with a 2" grade over a 200" Run is as follows:

Rise (Height) = Run (Length) x % Grade Sum: Height = 200" x 2% = 4"

If all this is just too much to information to process why not take the easy way out, as I often do, and use a Grade Calculator available on Youtube courtesy of modelbuildings.org. Access via the video clip below:

Model Train Grades

The importance of paying close attention to getting railroad grades 'right' cannot be over-emphasised if you are to avoid operational problems such as stalling or even derailments. It’s not just the loco that will need to safely navigate up or down the raised track, it is also the fully laden cars carrying coal, timber, metal, refrigerated foods, fuels, vehicles, livestock, or even people (well, plastic models of people). A long train can be very heavy and this needs to be taken into consideration when going up or down a gradient of a real railroad, or on a scaled down model railroad.

Model trains can be expected to perform in similar fashion so you would expect to observe a “no grade more than 2%” rule in the majority of situations. and certainly if you plan to use live steam where you would be well advised to limit any incline to 1%. However, a lot depends on the power and weight of your locomotives and the number and weight of the rolling stock they will have to pull.

In simple terms the more powerful the locomotive the more coaches or wagons (cars) it can haul up hills. The weight of the locomotive is also a key factor as the heavier it is the greater the traction. Lighter locomotives have a tendency to slip on inclines. This is why many modellers add additional weight to their engines to improve tractive effort.

Model Railway Exceptions

I will now undo all the good work set out in the preceding text by showing you some modelling exceptions which somehow work but really shouldn't.

This Regner Lumber Jack live steamer locomotive seems to be making easy work of pulling 3 Bachmann cars up a slope of 11.5% (1 in 8.5). The engine weighs 2.4 Kilo and generates 3 bars of pressure to cope with these empty Bachmann 20' Gondola cars (weighing approximately 1.5 kilos).

Another steamer tackling a hill in confident manner. The actual grade is not known.

Potential Locomotive Damage

Always bear in mind, when contemplating grades, is that the more you place repetitive strain on the locomotive and the harder it has to work, the more current it will draw and the hotter the motor will get. Ultimately these exertions are likely to result in mechanism burn-out which could prove a costly to repair so always err onthe safe side by having less demanding slopes wherever possible.

By all means test the principle by creating “test runs” up various inclines with various configurations of your locomotives and stock (if you are lucky enough to have a large roster) and see what would work best on your planned layout. If problems do arise I’m afraid it’s back to the drawing board but at least you didn’t the snags after laying out all you track!

Trial Runs

Curves on Grades

Another rule of garden railroading is that the effect of grades can be exacerbated if the slope includes a section of curved track which further increases the drag factor causing the locomotive to work even harder. A fairly modest 1% gradient around a curve could produce the same effect as a 2% on a straight incline.

On the descent gravity can also have the unfortunate effect of causing the locomotive to accelerate and if the speed is not controlled is likely to result in your favourite wagons or coaches being hurled off the track.
This is another good reason for not only having the most gentle slopes but also installing the widest possible curves on your layout, especially on inclines.

Vertical Easements, Grade Transitions or Transitional Slopes

We have already established that a grade (or incline) is normally measured in percent based on a rise in elevation over a certain length (ie. 1 ft up over 100ft length is 1%) but can sometimes be expressed as a fraction or simply "1 in 100". Just as "lateral easements" are recommended when tracks progress from a tangent (straight) to a curve (See Module 9) there is also a strong case for adding similar "vertical easements" (or grade transitions, or transitional slopes) at both ends of a grade in order to achieve a smooth flow from level to grade and grade to level without any sudden jumps or drops - especially whwer long-wheelbase rolling stock is invloved.

We have already encountered the use of precisely calculated "hyperbolic" curves in establishing the smoothest way into and out of a horizontal curve when driving a racing car. Vertical curves are essentially the same in that they 'ease out' the abrupt changes of level at the entry and exit points of a grade in order to smooth the passage of locomotive and rolling stock.

Such "vertical transitions" (apparently termed "vertical curves" in the civil engineering parlance) are critical to smooth, reliable operation as without them, couplers are likely to disengage and locomotive wheels can even lift off of the rails, either of which could cause a disrailment. These are just a few of the possible bad things that can happen when vertical curves are missing or not done used correctly.

Essentially, a vertical easement (or grade transition, etc.) observes the same principle as for an ‘easement curve’ but in a vertical, as opposed to a lateral, plane. In order to smooth the entry of a train approaching a rising grade from a level track the nominal grade percentage is ‘softened’ so that locomotives, coaches or wagons with a long wheel-base are “eased” into the next stretch of line without experiencing a sudden hump or hollow. The same easing process is also followed at the exit of the grade to its new level. This has the effect of extending the overall length of the actual incline compared to a raw calculation but achieves a much smoother passage.

On a model railway this can sometimes simply be achieved by trial and error but there are a few helpful hints naccessible via the "Vertical Easements" button link below.

This diagram illustrates the theory:

Vertical transitions, using cut-out marine plywood, or similar weather-resistant roadbed, are actually pretty easy to accomplish, with not much math involved. If you have known upper and lower elevations and also know the length of the run between them, then you can easily determine your grade percentage (see Module 9). While the grade percentage with vertical easements won't be constant, for the purposes of establishing the easements, we'll assume that it is.

Fasten the roadbed in place at both the top and the bottom of the grade, then find the mid-point of that run and, using a riser, fasten the roadbed there at a height one half that of the total climb - you may need to raise or lower the roadbed at that point to accomplish this. Next, without raising or lowering the remaining unsupported roadbed, add sufficient risers for proper support, simply setting their tops at a height equal to that of the bottom of the unsupported roadbed.

For long grades, after adding the riser at the mid-point, subdivide the two halves of the grade again, and raise those new mid-points to 1/4 and 3/4 of the total rise, and you can further subdivide as necessary for especially long climbs. To avoid negating the natural vertical easements which will have formed at the top and bottom, though, don't overdo this procedure - you only need to remove any obvious snags.

Irrespective of what method you use,the key essential is to try and ensure that your inclines are as gentle as possible as any sudden change in gradient can place a considerable strain on your motive power. In simple terms the steeper the incline the greater the load on the locomotive, especially on the motor and gears which can prove costly to replace. It is one of those tasks where it is probably better to abandon any attempt at making detailed calculations and simply install your track on a solid base using shims and, supports and piers at regular intervals to spread the load and adjust these until it "looks about right". Test with a locomotive pulling a reasonable load and check for any "jumps". Make adjustments and test again until everything runs smooth.

One tip I came across is that if it proves difficult to measure the actual run simply measure the track length. It can sometimes be awkward to measure the run. Scenery and structures may interfere. Fortunately, your grade calculation will be accurate enough if you simply measure the actual track length from the beginning to the end of the grade. This results in a relatively small inaccuracy but in not enough to seriously matter in the context of model railways.

Remember, if the grades are still too steep you might also consider adjusting the rise and fall of the surrounding scenic terrain to create the illusion of an incline whilst keeping your track fairly level.

Articles dealing with application of these principles to large-scale rack are few and far between but the following links are recommended for further enlightenment:

Model Railroader "Vertical Easements"

Sprucecrafts Model Train Track Grades and Maximum Grade Issues

Vertical Easements

Grading Runs

Finally, on the question of grades, I am prompted to include this piece of shrewd advice from a model railway forum:

" To enable one track to cross over another in a short space, the oldest trick in the book is to incorporate inclines on both tracks - half below datum level and half above datum. That effectively halves the gradient. This shows a 3D helix version which shows 20" height differential (+10" to -10" ) at the rear give a clearer representation but in practical terms you would probably only need a 10" differential on most layouts."