Exceedingly rough guess
Dear Paul,
It (the answered questions) does help, although there's still a lot of "fudge factor" to work around.
Let's start with some basic givens:
(Warning : Maths ahead! While not overly complex, if the maths below starts to make your head swim,
then I would seriously suggest considering a layout design that does _not_ use a helix.
The below is the _minimum_mandatory_ to calc a helix).
- based on one of Joe's earliest articles, a curve radii which is 3x the length of the longest piece of equipment in-play is a nice ballpark place to start. From the gear you've mentioned, a SD40 is around 65' long, or around 130mm in N scale.
130mm loco length x 3 = 390mm curve radii
= 15 1/4" curve radii.
We _may_ be able to go tighter, but this would be a good radii to aim for so everything stays coupled and runs reasonably.
Keep that in mind as we move on...
- I just checked a LifeLike SW1200, which tops out at just under 1 1/2" tall, roadbed surface --> top of cab
(That includes the track the loco is sitting on)
For the sake of the maths, lets say 2" roadbed --> "clearance" height
(might be worth checking if you intend to run excess-height cars or double-stacks!)
- Let's assume you have some known helix-compatible roadbed technique which allows all the strength the helix requires, in less-than 1" of thickness
- For no reason more than a flat-out guess, let's allow 2" between the top of the equipment and the bottom of the "next turn of the helix Up" for fingers, and to rerail cars which may come adrift in the helix.
(I have Roadie/"loader"/Sound-System-Engineer hands, and would find 2" a bit tight... )
Total = 5"
That means, each "circle" or "turn" of the helix has to achieve 5" of lift over whatever linear track distance 1x lap of the helix is.
- let's assume, for no better reason than it's a round number, that the grade is 4%, or, said another way,
1" of "up" for every 25" of linear travel.
(to keep the maths simple, we're working with sheer constant grade, and not easing it to compensate for the tightness of the curve in the helix. The tighter the helix, the more significant the drag of the train).
- Right, back to the curve maths. With our guess-timated target radii of 15-and-some inches, we get around 94" of linear run per "lap" of the helix.
(15" radii x 2 = diameter of 30"
Circumference, or "distance per lap of the helix" = diameter x Pi
Circumference = 30" x 3.14
Circumference = 94" approx)
IE for every lap of a 15" radii helix, the train travels approx 94"
- now we get to choose how we work things.
Assuming 15" radii and having to achieve 5" of "rise" per lap, the resulting grade = ???
15" radii gives 94" linear run
(see above)
94" linear run (per lap) / 5" rise = 1-in-18.8 grade, or 5.3%
(Ouch! That's starting to look like Saluda Grade territory!)
So, if we strictly stick to our desired 4% grade, (still steep, but much more acceptable),
and keep the 15" radii curves, How much "lift" or "rise" _can_ we get per lap?
Linear run / grade = rise-per-lap
94" / 25" (for every 1" of "rise") = 3 3/4"
Hmm, only 3 3/4" worth of "rise" per lap, that's _barely_ enough to allow the track, loco, and the next layer of helix, and leaves _no_ room to get your fingers in should anything go wrong!!!
(we kinda knew that already, based on the previous calc, but just to prove the point... ).
Sooo, what can we do? We obviously need more "linear run per lap of the helix" in order to get the desired 5" rise-per-lap, at a grade (estimated 4%) that the locos may actually have some chance of pulling...
There's 1 obvious, and 1 maybe-not-so obvious solution.
Obvious Solution 1 - make the helix curve bigger, so that we _do_ get the required linear-run-per-lap,
(given 5" rise and a desired grade of 4% or "1-in-25",
that calcs out to a linear run of 125" per lap of the helix,
and an extrapolated curve radii near enough to 20")
OR
Not-So-Obvious Solution 2 - keep the 15" radii curves, but cut the "circle" into 2x 180 degree "curves", and stretch the helix from a circle to an oval, effectively adding straight track and "linear run" distance for each loop.
It'd make construction of the helix a bit more challenging, but by adding a pair of 16" straights into each "lap" of the helix, you get the tight curves _and_ the required "linear run per lap" you need to make a 4% grade work...
Now, please note that all of the above "givens" are completely up for grabs. As long as you were able to follow the maths, you should be able to adjust for your preferred roadbed thicknesses, "hand space" clearance, etc etc,
and still extrapolate out a meaningful set of results...
I hope this helps!!!
Happy Modelling,
Aim to Improve,
Prof Klyzlr