Got good answers on easements on the last post. Now I’m thinking about grades.
Background-
a) Planning three 2-1/2% grades(2 curved at 18" and one straight).
b) Using FlexTrack(code 100).
c) Using WS roadbed and risers.
Observations-The track (as you would expect) is stiff in a direction perpendilular to the track surface. So far I’ve read an article in MR where on some locomotives,the pilot for example can short the rails.
So- What’s a good way to transition from a level surface to the grade and back to level at the top of the grade?
Use at least an engine length as a transition grade both at the top and the bottom of the grade. More would be better.
Also note. Curves on a grade, expecially tight turns like 18", increase the drag quite a bit on the train.
Thanks for the input. That’s what I was wondering about because you transition from horizontal immediately to 2-1/2 at the bottom then immediately back to horizontal at the top. The grades are on a branch line which at the most would have about 3 cars using a 2-6-0 Mogul. This railroad never made a lot of money.
You should be able to do 3 cars with a mogul. I make about 4 cars with an old-time mogul on a 3.1% with 18" curves.
I should mention that they are 36" cars.
I have 2.5% grades with 19" radius curves and have no problems pulling 12-15 cars up them with any of my locomotives [2-8-0, 4-8-2, GP9, GP20, GP30, RS2, H16, or various E or F units]. Just avoid having a joint at the point of change. I have 3/8" plywood under the roadbed that forms the easement. By fastening down at least 6" of plywood in a horizontal position at top and bottom of the grade, it is very gradual.
Quick way to figure vertical easements for grade changes is to allow 1 foot of easement for each percent of grade. This starts the easement 6 inches per percent before the theoretical grade change, and ends it six inches beyond. If using pre-cut forms, this means filling in at the foot of the grade and rounding off at the top.
The same formula can be used whether transitioning from level to grade, grade to level, cresting a summit, dipping through a hollow or simply changing gradient on a long climb. Cookie-cut plywood does this automatically; other subgrade systems require special attention.
As far as pulling power is concerned, my lightest loco (brass 2-6-0) handled the equivalent of five US freight cars up a 3% grade. My die-cast diesels easily pulled the same grade with the longest train that could fit into the sidings.
Chuck
The mainstream prototype uses parabolic (not cubic) easements for vertical curves. The prototype uses a gentler easement on the top (from grade to level) than on the bottom (level to grade). On a couple of traction lines, the minimum vertical curve was given as a radius. The minimum vertical curve radius appeared to be about 6.5 to 8 times the minimum horizontal curve radius in these cases.
Another modeler - I’m having a senior moment and can’t give proper credit - did some calculations in HO using flange depths and rigid wheel bases on circular vertical curves. He found that generally a 10ft vertical curve radius would work for most rigid wheel base steam locos. Note that 10ft is 6.7 times the typical 18" minimum radius for these engines. A few, like the UP 4-12-2, would need as much as a 14ft vertical curve (7 times 24" horizontal radius) to ensure flanges would have sufficient depth remaining while on the vertical curve.
The most interesting calculation to me was how short a circular vertical curve segment was needed because of the small angular change to even a 5% grade from level. I am using 6% grades on my HOn3, so the angular change is arctan (6%) = 3.4 degrees. Vertical curve radius (using 10ft) times Sine (3.4 deg) = 7 horizontal inches for transistion. A more reasonable grade, say 2.5%, would need a horizontal distance of 3" for the vertical transistion.
Bottom line: a reasonable minimum vertical radius is 7 times the minimum horizontal radius. Make a cardboard template to that radius - both convex and concave - and check your easements. If you feel uncomfortable with such short transitions, by all means use longer. Longer might be warranted if your couplers are smaller than normal and the trucks on long cars are set in from the end considerably. The calculations did not look at the coupler over/under-ride issue, but it would take some very small couplers to have a problem when the flanges didn’t.
Interesting how the vertical transition
That is very helpful information, Fred W.
Thanks for posting it.
Just got back. Thanks all for the inputs. It’s amazing what you learn in this hobby. Oops-it’s perpendicular. Need to digest all the info. Was wondering about the mathematics too. An X-Y table to plot an easement template maybe. Yes, it’s a 2" foam (with 3/8" plywood backing) bench top with planned WS foam Inclines and Risers. Pretty soon I’m going to be asking about trackwork to/from and on bridges(got four of them).
It will make life easier for you (making and maintaining) if you can avoid any rail joints in the area of the easement curve. If you have length start both rails 4" -6" before the transition and run them the same sort of distance beyond.
This will mean that you don’t have switches near the transition… BUT this will mean that you don’t have derailments there either! [:)]
You can put switches in the grade… just make sure that they are “flat” in the surface of the grade… err…[%-)] …that’s not “level” but in the same plane as the rest of the grade.
Bridges… Micro Engineering do brilliant bridge track… longer ties, guard rails… really good… for older style bridges… but check out pics of the area you want to model and see what the real thing is doing.
Have fun [:P]
Thanks David-Will look for their website.
Without forcing it I let the playwood base I use for the track [cookie cutter style] make the transition for me. I find it smooths it out quite well.
I hope that helps.