With help from my you all I have found answers to a good number of my questions. Now I am thinking about lead in for grades. What type of rates do I need?
What I imagine to find out is if a hypothetical 4% grade needs one longest railcar you run length of 1%, one of 2% and one of 3% to keep railcars from high centering on down hills or lifting wheels on the ups?
Hi Mark,
the drawing above is not to scale.
Anyway when you think a 17% grade is possible you might be in for surprises.
The extra required length should be ideally the length of your longest piece of equipment for every 2% of change of grade. Both at the top and the bottom of the grade. The resulting grade will be much steeper then the original17%.
(of course a 17% grade is not possible, it is only used for making a clear drawing. According to John Armstrong any grade above 4% will be an attraction by itself.)
BTW doing the math is needed in the planning stages. So you will be sure beforehand if the grades easements and the needed vertical clearance are up to your standards. When building the subroadbed in cookie cutter style the plywood itself will form beautiful easements. You only need lots of C-clamps and a last check before you can finally fasten the subroadbed.
Paul
That’s a great diagramme, Paulus. It should help to make it clear that, as you insist upon rising to greater heights in a defined space/length, you impose insurmountable geometric difficulties on yourself because the actual consistent part of the grade must necessarily be steeper than if you had been able to just place a sharp kink and angle at each end of a fully consistent grade. However, if you do use a kink, you are probably going to cause your locomotive’s couplers to dip down out of a couple from the coupler on the head end of the car behind it. And that’s assuming the coupler pin or pilot at the front of the locomotive can get over the sharp rise in front of it.
So, think of it this way: the steeper the grade, the shorter the distance of the actual steady grade you will have because as you increase steepness you will also have to increase the length the rolling stock needs to stay railed and coupled…the vertical curves on either end must be even longer! Forgetting the traction problems, it just keeps getting worse and worse as you demand a higher elevation change in a given length.
What you should do is to make up what seems to be a reasonable vertical curve length for the minimum height change you can live with (or else you need a new design entirely). A good formula for most applications is 5" of vertical curvature for every 1% change in grade. If you need 4% grades, you will need about 20" in vertical curvature. At each end. Remember, though, it won’t be a 4% grade between those curves, and that is always the rub. It will be closer to 4.8% Can your locomotive do it with the trailing tonnage you hope it will take up the grades?
Crandell
Great topic that I too need to learn from and adjust plans for! [tup]
I generally use about a car length for each per cent of grade.
Second the motion - with the caveat that it has to be your longest car…
Paul, those grades in your drawings look perfectly prototypical - for the mule' tracks alongside the locks of the Panama Canal. Of course, those mules’ are rack locos…
Chuck (Modeling Central Japan in September, 1964 - with a rack railway branch on the cutting room floor)
Hi Byron and Chuck and others,
i have 2 questions:
When you are talking about one carlength for every percent of change of grade, are you referring to the total length of the easement or the required extra length only? ( I did the latter) Of course the length of your longest piece of equipment should be used.
Is clearance the height needed for your highest car only or the railhead to railhead distance? (included some airspace, the rail and road- and subroadbed)
Anyway two compensations are needed when planning slopes. One for curves and one for vertical easements. The resulting “run” will turn out to be very long when going for moderate grades; often more then 13 ft is needed for a simple non-level crossing. On a small 8x4 you will hardly find that kind of length. Running very short trains is the only option to climb steeper grades.
Paul
Hi!
My current and previous layout had long winding 2 percent grades leading to/from a lower level. The lead in to the grade was accomplished with the cookie cutter method. Basically I sawed about two feet in on either side of the horizontal road bed, and then gently moved this up or down to meet the 2 percent grade. For HO, this worked beautifully and has never been a problem.
I do believe that for mainline “regular” railroading, 2 - 2 1/2 percent is pretty much the maximum that will work and look like it belongs. Yes, if you are doing narrow gauge or unusual circumstances, a steeper grade is OK. But I would try to do what it takes to keep it at 2 percent or below.
Hey, that’s just me, and the beauty of the hobby is we can all do just as we please!
Edit: For me, it’s the total length of one easement. So it would be doubled in a typical grade, where there is an easement on each end.
For me, it depends on the context. On a drawn plan, I use railhead-to-railhead, which is the convention. When talking about clearances (within a helix, for example), I might be talking about actual physical clearance for the tallest car. I try to make this clear when posting, perhaps I don’t always.
Agree – people on forums toss around suggestions for steep grades through tight curves and right through switching areas (as they are doing on another thread right now) without taking into account the physics involved.
The "lead in"you refer to is called a vertical curve in civil engineering. In Paulus’ sketch, you would need two vertical curves. A “sag” curve at the left of the sketch and a “crest” curve on the right.
The formula for finding the height of the cure at any point from where the curve starts is as follows:
for a “crest” curve: Elevation = PC elev. + g1 * (x) - A*(x)squared / 200* L
Where: Elevation = the elevation of the curve at a distance (x) from the beginning of the curve
PC elev.= the elevation at the beginning of the curve (Point of Cuvature)
g1 = the grade going forward in unit per unit. ( a grade that is 2 feet per 100 feet, 2 inches per 100 inches, (2%) is expressed as 0.02 feet/feet, inch/inch meter/meter, etc.)
x = the distance from the beginning of the curve (PC)
A = the agebraic difference in grade of the two intersecting grades (for example, a 2% uphill grade (+2%) meets a 2% downhill grade (-2%) for a difference of 4 (2 - -2).
L = the length of the curve.
As an example, let’s say you have a flat grade (0%) going into a 17% grade. This is a “sag” curve.
Let’s use an elevation of 0 for the PC elev.
g1 = 0.00 A = 17
For this exercise, let us say th
My typical grade is 1/4" per foot which is just over 2%. For the first foot I raise it an 1/8" then the next foot starts the 1/4" per foot. Pretty simple and I’ve had no problems with it.
My $.02
Mark