at least in my opinion, the 9 year how to figure the grade thread had several confusing responses: from "a two percent grade should be two percent for each fraction of that incline" to 'Trains don't "average" the grade'.
While I think we all agree that the grade is simply 100 * the rise over the run (2% is 2" height over 100"), I think it's impractical to build such an incline with a constant grade because of easements, as Lion mentioned. And this can also be confusing.
building a grade with easements inherently results in the grade not being constant over every fraction of the incline. And I believe that for every portion of the grade less than the desired grade, there can be a equal portion greater than the grade by the same amount. The grade doesn't need be constant, it's important that the average grade under the train be what is desired.
For example, a train of ten 50' cars plus engine is roughly 80" long. The the local-grade (measured with an inclinometer over several inches) can vary above or below the desired grade, as long as over every 80" section of the grade, there is never more than a 1" change in height. (yes, the train will average the local-grades under the train). Shorter trains may experience a steeper grade, but they are shorter.
the following plot attempts to show several grade profiles along with the local-grade over each inch of the run. There are two lines of the same color showing the local-grade and height of a grade across a 50" run.
There are two green curves representing a constant 2% grade. The horizontal green line going across the plot indicates that the grade is constant across the entire run. There is also a straight green curve starting at 0 and rising up to a height of 1" over the run of 50". This profile has no easements and every fraction of the incline is 2%.
As Lion pointed out, the abrupt change in grade could cause some unintentional uncoupling or derailments and I believe this is not a good profile to follow.
there are 3 other profiles that have easements allowing the grade to change by 0.25% every inch. They also allow the grade to exceed the desired grade of 2% up to some max.
the yellow curve allows a max local grade of 3%. The height curve shows smooth changes in grade both at the bottom and top. The blue and red curves illustrate profiles with max local grades of 4 and 5%.
Each profile changes in height by 1" over 50" and is therefore a 2% grade, yet the local-grade, over a fraction of the incline, varies from 0.25% to something greater than 2% for all except the green profile.
I believe most modelers inevitably have easements (since wood doesn't bend sharply) and force the endpoints of the grade to match the height over the desired run. Unless the smaller grades of the easements are accounted for by lengthening the run, the result is a profile having local-grades exceeding the desired average grade. And I see no problem with this.
I don't see how a grade with easements that never exceeds a 2% grade over any fraction of the incline can have a change in height of 1" in 50". It must be longer than 50".
I believe that newcomers need to understand the impact of easements, and that local-grades measured with an inclinometer can exceed (w/in limits) the desired grade over the length of the run or need to lengthen the grade. (another pitfall to avoid)
greg - Philadelphia & Reading / Reading
A couple of points.
Your argument that a grade shorter than the length of the train has less effect than a longer grade is supported by John Armstrong on page 42 of the current printing of TPFRO. In a discussion of the flying junction he explains that only the weight of the train actually on the incline is important.
Your "easement" into the grade (which I have always heard referred to as a "vertical curve"), quickly becomes a rounding error when you look at more than short grades that we already know aren't a significant problem. I did some brute force calculations in excel. With a vertical curve at the start and end of the grade equal to one car length, to achieve a 2" rise in 100" the constant part of the grade would be 2.15%. for a 4" rise in 200" it's 2.07% and 8" rise in 400" it's 2.03%.
While I agree with the need to include the vertical curve at both ends of the grade, I don't think it makes a big enough impact on the actual grade to worry about.
I have the right to remain silent. By posting here I have given up that right and accept that anything I say can and will be used as evidence to critique me.
"I don't see how a grade with easements that never exceeds a 2% grade over any fraction of the incline can have a change in height of 1" in 50". It must be longer than 50". -OP
Absolutely so because the easement takes up length at two ends, and doesn't average 2% over its own length! If you have two ends that can't manage to average the same as the grade between them, the total length of the grade must, perforce, be considerably longer than a mere 50".
I have always cautioned, when I have participated in rudimentary queries about grades from newcomers, that if they only have so much room for a grade, they had better settle on less height gain than they may have had in mind if it is going to be rather steep, say in the range of 3%. That's because the easement at both ends of a steep grade must be longer to achieve the effect intended by the easement than the counterpart for a 1% grade. The average may be the intended 3% along the full length, easements plus main grade, but that main part will have to be nearer to 3.6% to achieve the height differential.
Very interesting discussion! I understood the need for vertical easements but I didn't know what the actual effect on the grade would be.
Greg - your chart explains it quite well - thanks.
Dave
I'm just a dude with a bad back having a lot of fun with model trains, and finally building a layout!
Well, since the vertical easements are important enough to not be omitted, the only concern should be the amount of elevation which needs to be gained and the distance available to do so. That the grade is 1.5%, 2.8% or 5.3% matters only in as much as the train you need to get up that grade, and that with which you intend to accomplish the feat.My Y-shaped partially doubledecked layout (picture a Y with the upper arms one atop the other) varies in height from 36" to just over 59", with a lot of up-and-down between those extremes. The continuous climb to 59" begins at a height of about 43" at the crotch of the "Y", but to get to 43" from 36" is done in two separate climbs, one at a nominal 1%-or-so and the other at about 2.5% The first is on two curves, the second on an "S"-bend. Coming from the opposite direction (the foot of the "Y") the line starts at 44", drops to 42", then climbs back to 43", almost all done on curves.The climb from there to the top is a continuous 2.5% (not taking the vertical easements into the calculation), but not constant, as there's a short stretch of about 2.8% near the bottom. This is deliberate, and meant to stall any train which is underpowered, as the climb is about 45' long, with two horseshoe-type curves and a wide radius "S"-bend.The upper level's position was set at an arbitrary height based on what I deemed comfortable, and that height determined that the area below it should be at 36".The height at the foot of the "Y" is a compromise driven by the two end-points. Increasing or decreasing the height at the foot lessens grades to one, but increases them to the other.
Without a trackplan to show, the foregoing may be a lot of pointless typing, but my point is that if you want to include grades for whatever reason, do use vertical easements to ensure reliable operation and do adjust your train lengths and/or motive power useage to ensure that you can operate the layout in the manner you intended. That a grade exceeds recommended practice shouldn't deter you from using it if it suits your needs.
My trains are usually short - 10-24 cars for freights, and all doubleheaded. Some trains are even shorter, but if I'm using smaller locomotives, they're doubleheaded, too. If I want to run longer trains (not normally practical, since most passing sidings will accommodate only 12 cars and two locomotives), then I simply add more locomotives.I think there's too much hand-wringing over this business of grades: if you don't have the room to keep them "reasonable", then either forego them or work with whatcha got.
Wayne
Thanks to everyone who has provided information in this thread. I don't know how much detail is needed, but making sure us beginners are at least aware of vertical easements/progressive grading or whatever is useful. I realize anybody may choose to use Woodland Scenics inclines, but I kind of seem as being for beginners. People like me buy a couple of sets of 4% inclines and think we're good to go. I realize you could buy a few 1% or 2% pieces for the beginning and ending of the grade and piece together a workable system, but they sell those kits and it really makes you think that's all you need to do. I went with WS inclines because I saw it as A) lighter and B) easier for beginners. Funny how a set for beginners leads us right into a problem you all are trying to help us avoid.
In the real world, grade is calculated over miles and within the average grade are many variations because grading goes with the territory. To make the perfect climb it would take far more grading of the roadbed than the accounts are willing to pay for. Some mountain passes actually have sections where they go downhill while eventually climbing over the pass.
On my layout, the pass has two different grades, most of it is 2% however the last little climb where the mountains are the steepest is 4%. This means that helpers are required to push east bound trains over the summit when they hit the 4% section. I guess the reality is that it is a 3% average grade but it is a 2% grade and a 4% grade depending on the location.
Re-designs are sort of fun (my opinion) and I don’t know if the average model railroader can design a layout without there being a need for a re-design. It certainly shouldn’t be something to dread!
NP 2626 "Northern Pacific, really terrific"
Northern Pacific Railway Historical Association: http://www.nprha.org/
Is the math really this simple?
I measured the distance from the center of the rear truck to the face of the coupler on a SD40-2 (my longest piece of equipment) to be 1.95". It seems to me that this represents the length of the grade we have to worry about since this is where the mismatch in coupler heights is created. The face of the coupler is .15" high. Since .15/1.95 = .077, this implies that the difference in grade between the track where the locomotive is sitting and the car following needs to be 7.7% before one coupler drops below the other and they come uncoupled. Can this be right?
Assuming all our coupler heights are perfect, this tells us when the cars WILL come uncoupled. I wonder where the point is where they MIGHT come uncoupled. I'm thinking that you don't need one coupler to drop 100% of the knuckle height to cause an uncoupling. How much contact do we need to maintain? 50%?
I won't bother with the math, other than to say it can be misleading in terms of real world performances outcomes. I've spent time over the last year easing a number of grades I designed in. Some small amount of this was simply settling and small arrors in getting easements right. The biggest factor/problem area has been steam.
Steam locos generally have a longer rigid wheelbase than diesels and far less flexibility in adjusting to changes underfoot. Differences of as little as .010" can cause things to stall with steam. Diesels just take it in stride. Essentially, while the grade is important, it's often the unevenness in the track that causes a steamer to "fall in a hole." That where the averaging that some do let's them down. Switch to diesels and you'll be OK, but that doesn't work so well if you're prototype is 1929, for instances.
Then there is the quest to push things to the limit to squeeze more in. It's at the limits of adhesion that these problems show. Leave yourself some slack and you'll be much happier down the track in terms of performance. The prototype rarely ran trains at the absolute limits of adhesion. Sure, they did when they had to, but the preference was to keep things moving and not risk a stall. That's why tonnage ratings came into being, as they are usually formulated to leave enough slack so trains can reliably operate.
Mike Lehman
Urbana, IL
mlehman....Then there is the quest to push things to the limit to squeeze more in. It's at the limits of adhesion that these problems show. Leave yourself some slack and you'll be much happier down the track in terms of performance. The prototype rarely ran trains at the absolute limits of adhesion. Sure, they did when they had to, but the preference was to keep things moving and not risk a stall. That's why tonnage ratings came into being, as they are usually formulated to leave enough slack so trains can reliably operate.
Yeah, if you have grades and especially if they're steep, it's a good idea to determine tonnage ratings for all of your locomotives. I found it to be a lot of fun, and it should increase the enjoyment of your operations, too.
My locos are all steamers, and my rolling stock has variable rolling qualities - most roll well, some too well, and a few not well at all. To add to this, I run "live" loads in open cars: scrap or gravel in gondolas and coal or gravel in hoppers. These loaded cars may weigh in excess of 8oz.I used loaded hoppers and an Athearn caboose to create a test train, then ran each loco up the 2.5% grade with the "S"-bend, adding 8oz. loaded hoppers until the loco slipped its drivers. I arbitrarily chose to designate a loaded 34' hopper as weighing 85 tons (which probably is a bit too high) and the caboose as 50 tons - this is too high, but since it's about the same weight as most house cars, it seemed appropriate.Tests showed that one loco could move 6 loaded cars plus the caboose, giving it a tonnage rating of 550 tons (rounded down).The only regularly scheduled freight trains on my layout are coal trains, which run from an unmodelled point on Lake Erie (accessed by an interchange in staging) and running to a power plant, also unmodelled, on the upper level of the layout. I found that any two road locomotives (I run DC) can move 12 loaded hoppers and the caboose over all grades on the layout, so I let that train-length dictate the minimum length of passing sidings.House cars sorta screwed-up the equation, though, as each of those same road locos can move at least 16 of them (one is the caboose) over the entire layout. I assigned each such car a nominal weight of 50 tons (same as that fat caboose), which resulted in the tonnage rating jumping to 800 tons per loco.I seldom run trains of that length (remember those passing sidings?) and since most of these cars are longer than those 34' hoppers, even 12 of 'em won't fit into some sidings.Since I operate alone, and only one train at a time, I decided that freights would normally be 12 cars (600 tons) or less, but could expand to 16 cars if necessary - usually a through train which does no en-route switching. If a loaded open car is among those making up the train, it's considered to be the same tonnage as the house cars. However, two or more loaded open cars within the train count for their full 85 tons, with train length adjusted accordingly.
This scheme seems to work quite well (at least I don't have to teach anyone else how to figure it out ). However, many trains end-up being doubleheaded anyway: locals, which switch industries along their routes, often pick up enough cars to exceed their tonnage rating. Eastbound and northbound trains are uphill runs, and even though the direction of car movement is fairly balanced, locos have to be returned to where they'll next be needed.