Oops. Vertical easement whatever are you talking about? It's been a long time since I studied Architectural Drafting. Feel free to put in your two cents.
Now I have a better understanding. This illustration shows exactly what you want. You don't need a jump off ramp. Never a spot where your engine can be high centered or hang up on the rails. Trying to remember how I did that. What comes to mind is a 12" transition from flat to the grade desired. Same thing at the summit and so on. Night time is about to overtake me. So I will get back to this tomorrow. Maybe with some pictures.
At the time I built this layout the double stack cars with loads all made it through. No nudging, smudging or scraping going on. I actually think that most of my clearances are taller, higher then the 1.75, as you put it. However, when I measured them today that is what I came up with. There again my vision isn't quite what I'd like for it to be. Double check it in the morning. Yes, I make mistakes.
Well, did I make a mistake? Not on the information I gave you. My measurements are still 1&3/4 inches or 1.75 and that's not M&M's. The rest of my clearances vary from 2.0 to 2.50 inches. No problems with them. Will the double stacks, autoracks or Hi-level types make it through? You asked. Maybe pictures later. I have a busy day ahead of me. I will find and get out and demonstrate the clearances. Gosh, the things I volunteer to do. Considering the layout may have suffered some damage during shipping during the move to Idaho. It's possible something broke or slipped. Will be checking that over as well. Do keep in mind most of the track in the helix is glued directly to particle board. No roadbed until we get back out and in the visible or open areas. Feel free to submit what works for you. No one has answered the question, how wide a radius curve do you need in N scale for a 2% grade? You chew on that for a bit. You will find, discover or learn the tight radius curves some of you have worked with in the past aren't 2%. More like 4% to 5% depending on the variances. I know because I've been there. For now you have my 2 cents. I will be installing "Switch Panels" and getting rid of the "Automated Switch Machines" or as some call them "Solenoids". Installing the Kato Switch Panels with the Automated Switch Machine embedded in the plastic roadbed. Out of sight!!
I think an 18-24 inch radius to be minimal for a 2% grade. That will loosen binding of the wheel sets, and reduce the overall drag to a more reasonable running. Of course larger is always better.
FWIW, the NMRA recommendation for "modern era" vertical clearance is 1.73", as measured from the top of the railhead on the track passing below to the underside of the bridge (or benchwork/supporting structure) for the track passing above. https://www.nmra.org/sites/default/...ck_centers_and_clearance_diagrams_2019.01.pdf
I use Unitrack, so I'm not sure how high the rail head is above the base, if there is no roadbed under the ties. 1/8"? Then there is the thickness of the plywood, etc. upon which the bare track is laid. We can assume that any supports are sufficiently to the side to not interfere. Let's assume 1/2" plywood (which is actually less than 1/2" thick, but we'll buy ourselves some margin by figuring on 1/2" thickness.) If we assume 0.125" for rail height, and 0.5" for plywood thickness, then we need a rise in elevation of 1.73 + 0.625, or 2.355" rise per 360 degree (complete circle) turn. Divide 2.355 by 2% (0.02) grade, and we need a run of 117.75" per turn (centerline distance) to achieve the desired change in height. The radius of a circle (one layer of a helix, more or less) with 117.75" circumference, is 117.75 / 2 / pi = 18.74" centerline radius. Given the assumptions, neglected glue thickness, etc. I would use a minimum of R19 curves. I would use longer radii for the first and last (top and bottom) 90 degrees in the helix (i.e. at top and bottom of the helix), for some vertical and radial easement. If you are double-tracking the helix, and can always run uphill on the outer track, then the inner track can be less radius (and a steeper grade) for the downhill run, and save some room.
Good that you included a factor to account for the rail height, roadbed and supporting benchwork/plywood. However, unless - as noted above - you don't want an abrupt transition to/from level track and the section on a grade, then the length of the circumference should be increased by the length of the transition sections at the bottom and top of the grade.
I stated: "I would use longer radii for the first and last (top and bottom) 90 degrees in the helix (i.e. at top and bottom of the helix), for some vertical and radial easement." This initial/final 90 degrees is to allow easement of the transition from level to incline/decline, and from (assumed) straight track to the ultimate curvature of the helix. A longer radius 90 degree curve preserves the original rotation, while increasing the length (circumference) of the curve, and therefore reducing the slope of that portion of the curve. The 90 degrees is just a stab at it, it could be more or less, as needed. Or perhaps I misunderstand your point?
Assuming that you do "use longer radii for the first and last (top and bottom) 90 degrees in the helix (i.e. at top and bottom of the helix)", then fully half (180 degrees) of the circle is no longer on a 2% grade. Approximately, how much longer/wider would that "longer radii" have to be to ensure that the 2.355" of clearance is achieved?
This isn't a contest, just a discussion. I do appreciate your participation and thoughts on the issue at hand. Big Jake said: I would use longer radii for the first and last (top and bottom) 90 degrees in the helix (i.e. at top and bottom of the helix), for some vertical and radial easement." I couldn't get the quote feature to work. It is what it is. You lost me with "longer radii" Jake said. Can you explain? Are we talking about a curved easement? Then I read vertical easement 90 degrees. Are we talking at the crest of the summit? I stated: Earlier in this discussion that by using the wider radius curves for example 18" curves. The need for a curved easement isn't essential or necessary. Although, I did build into each end of the helix a curved easement, which doesn't amount to much. Now with the vertical easement I need to get my camera out. Other things are taking presidence right now. More later.
The longer radius at lower grade/slope would largely lie 'outside' the remainder of the helix by the time it had reduced the overhead clearance enough to cause an issue. You could use 360 degrees of that increased radius before the reduced slope created clearance issues to itself, and that's discounting the increased circumference that provides more run to make up the difference in clearance. That's a little confusing; let me try it another way: if you use a larger radius helix, the circumference is proportionally longer as well. That results in a lower slope required to achieve the same loop-loop vertical climb/clearance. In a situation where only the top and bottom ring, or portions thereof, have larger radii than the middle rings, the top and bottom ring will also progressively lay outside the smaller radii rings of the middle layers of the helix, so clearance should not be an issue by the time there is anything overhead. Note, you have to "play" with the radii to transition from one ring to a different radius, concentric ring above/below it. That should be relatively easy with flex. Not so much with sectional track (but still doable, with care.)
The entrance/exit of a circular helix, from/to horizontal tangent track, need both vertical (slope) and curvature (radius) easements. Since a larger radius curve section at the entrance/exit of a helix does both (the curve is less sharp, and the circumference of the larger curve is also longer, meaning in will make the same vertical climb/descent in a longer horizontal distance.) That means less slope, or a vertical easement. Since I use Unitrack, I think in terms of sectional track, where curvature easements are accomplished by substituting longer radius sections at the ends of curves (and sometimes shorter radius section(s) at the apex to compensate for the additional space consumed.) Yeah; it ain't perfect, but it's a reasonable compromise. Clear as mud? Great!
Rick had cited, as examples, either Williams or Tehachapi Loop - which are only one turn - to describe the configuration he is attempting to build. The question, then, is does he want all of the grade - including the transitions at the top and bottom - to be contained within that one 360-degree loop? If so, then the radius will have to be quite a bit greater (on average if they are also to include a horizontal easement) in those two transition sections if they are to comprise half of the loop and still achieve the proposed 2.355" gain in height. If not, then the loop can be the constant 19", or so, radius per your calculations as shown above.
