Here are the details for doing the math: I had a 48 inch radius helix on my layout. It was constructed from ¾ inch plywood with 2x4 risers (perhaps overkill but I could walk on it if needed!). To make things easy for myself, I installed the risers center to center at 12 inch spaces and cut the top ends on a chop saw at the proper angle so the plywood helix pieces sat on the 2x4s nicely (did the trigonometry but do not remember what that angle was!). The center of each 2x4 was ¼ inch taller than the previous. (.25/12) x 100 = a grade of 2.083% - not precisely 2% but worked well for me.
Here is the critical math: The circumference of a 2*48 = 96 inch diameter circle = 96*Pi = 96*3.1415 .. = approximately 301.584/12 = 25.13 feet. Since, in my case, the helix rises ¼ every foot of length, the spacing between adjacent levels was 25.13 * ¼ = 6.283 inches ------minus the thickness of the plywood. This easily accommodated the height of any rolling stock I was using. I used the helix to accommodate a mushroom design. There were two layers to my helix so I gained 2 * 6.283 = roughly 12 ½ inches. I needed more spacing between the levels of the mushroom but I had enough straight track between the helix and the mushroom to continue the climb and get to the upper level. For your case, using 46 inch radius but my 2.083% climb rate design, you would get 92*Pi = 289.018/12 = approximately 24 feet per level. 24*1/4 = 6 inch spacing between levels. If you used 3 levels in the helix, instead of only two, you would actually gain 18 inches in height. Or, depending, on where you need the ends of the helix to be, you could get 15 inches with 2 ½ levels in the helix. that is, trains leaving the helix would be traveling at a direction 90 degrees from whence they entered. You could also back calculate the radius if the 15 inch rise is important. That is, for instance, with a 3 layer helix, you need to rise 15/3 = 5 inches (I am not remembering the NASG standard for height clearance is that enough?). Then 5*4*12 = 240 inches of helix track required. 240/Pi = a 76.4 inch helix diameter = a 38.2 inch radius, which is probably smaller than what you would like to use. I hope this has helped. Walt Jopke
