Tables for Calculating Spiral Helix Dimensions

Several people have asked me about determining various heights, lengths, and footprints for spiral helixes. I’ve attached an Excel table for calculating the dimensions of bowl-shaped spiral helixes with circular or oval footprints. This table is NOT designed to provide numbers for a traditional stacked helix used in many track plans.

This is a work in progress. I am starting this as a separate thread to obtain feedback on how the table works for spiral helixes. If you have questions or comments, please post them. If you discover glitches, please post about them so I may repair them. If there are other values you would like to have determined to facilitate the design or construction of a spiral helix, let me know in a post.

The purpose of this thread is not to debate the relative merits of spiral helixes, stacked helixes, nolixes, etc. Such debate belongs in a different thread, and if someone starts a different thread of that topic, there’s a good chance I’ll add my $0.02 on the pros (and cons!) of a spiral helix to their thread.

Please play with values and see what might work for your layouts. Select an orange cell, and type in the value preferred for the layout. Press <Enter> and the Excel program automatically calculates a number of specific values for the spiral helix. Presently, all lengths are calculated in inches expressed in decimal form or fraction form. (Eventually, I plan to develop a table that expresses lengths in metric values.) This application is interactive and, by playing with a variety of values, a modeler can experiment to determine what values will work best to include a spiral helix on his layout.

Minimum Radius (Cell A5). This value represents the smallest track centerline radius within the helix. While this value can theoretically be extremely small, the practical limits are about 24 inches on an HO-scale helix, 14 inches on an N-scale layout, and perhaps 9 inches on a Z-scale layout. These limits are approximations and are significantly influenced by the grade, the total length of the first loop, and the thickness of the subroadbed supporting the track for each loop: a steeper grade yields more rise in a single loop; an oval helix loop is longer than a circular helix loop of the same radius; and thicker roadbed requires a larger rise between railheads from one loop to the next. These three factors combine to affect the amount of clearance between the first track railheads as they enter the bottom of a bowl- shaped helix and the underside of the subroadbed for the 2nd loop. That clearance is a major factor in establishing the practical limits of a spiral helix.

Maximum Slope (Cell C5). Slope is determined mathematically by the formula:
Slope = Rise divided by Run
where Rise is a vertical distance and Run is a horizontal distance.
Modelers referring to a 2 percent Grade on their layouts are referring to a Slope that is 0.02:
2% Grade = 2 per cent (100) Grade = 2 units of rise per every 100 units of run = 2 units of rise over 100 units of run = 2 divided by 100 = Slope of 0.02
As with Minimum Radius, the Maximum Slope could theoretically be straight up, but practical limits are influenced by locomotive pulling power, weight of all cars being pulled, amount of curve on the helix (tighter curves are harder to pull cars around), and how freely the wheel sets roll. Many modelers choose a Slope value around 0.02 (about a 2% Grade), but setting the Maximum Slope or Grade on a layout is strongly tied to personal preference and the practical limits mentioned above, so testing what works on your layout with your equipment and track is HIGHLY recommended.
It is important to note that the Maximum Slope value to be entered in Cell C5 is expressed in 100th or 1000th, not percents, integers and fractions (0.0225, not 2 and ¼)

Ramp Width (Cell E5). The width of the ramp (subroadbed) of the helix must be at least as wide as the track plus space to clear supports for the next bigger loop which is higher and of a larger radius. I used 1 inch on one of my spiral helixes, but had to shave off some of my supports to ensure proper clearance throughout the helix. Most of my ramps have been 1.5 inches wide. Loops with double track would, of course, need to be wider.
The width of the ramp (subroadbed) affects the overall footprint of the helix and how many loops can be fit into the available space.
For example, if the ramp is 1 inch wide, then the radius will increase by 1 inch in one loop (15, 16, 17, 18 inches at the start of each loop) and track centerline diameter will be 2 inches bigger for each additional loop (30.5, 32.5, 34.5, and 36.5 for the diameter of each of the 4 loops). When calculating the helix footprint, you will need to add .5 inches from the track centerline (which is what the above figures are based on) to the outside edge of the ramp—on both sides of each loop. This will add 1 inch to the outside diameter of each loop’s ramp to give the total footprint of each loop. For a 1 inch wide ramp with 15 inch minimum radius on loop 1, the outside footprint for each loop will be 31.5, 33.5, 35.5, and 37.5 inches.
With a 1.5 inch wide ramp (radii of 15, 16.5, 18, and 19.5 at the start of each loop), then diameter across the track centerlines of each loop will increase by 3 inches for each additional loop (30.75, 33.75, 36.75, and 39.75). Overall outside footprint for each loop’s ramp will be 32.25, 35.25, 38.25, and 41.25.

Maximum Helix Footprint (Cell G5). This value represents the largest outside diameter of loop ramp that is allowed in the track plan (Note: loop ramp outside diameter…not track center diameter). In the table, this value will determine which Helix Footprint cells (Shown in Column M) are highlighted in red when they exceed the Maximum Helix Footprint value in the orange cell at G5. It will also determine which track centerline radii will be highlighted in red when they will be on a support that extends beyond the Maximum Helix Footprint.

Length of grade Before Entering Base of the Helix (Cell I5). This value represents the horizontal distance in inches covered by track on a grade prior to entering the base of the helix. Some track plans may have tracks climb a grade for a certain distance before entering the base of the helix to reduce the number of helix loops needed to rise from the lower deck to the upper deck. If there is no distance covered on a grade before the track enters the base of the helix, then this value would be set at 0. If the grade starts 4 feet before the helix, then this value would be set at 48”.

For the purposes of all calculations in these tables, it is assumed that the grade outside the helix matches the grade inside the helix. Re-calibrations are possible when there is a different grade outside the helix than in it…contact me by PM for the adjustments.

It is critical to accurately enter this value because the calculated values for all elevations within the helix are determined by the elevation where the track crosses the first support in the helix. If the track has risen any height above the 0 elevation of the lower deck, then the values where every loop crosses every support need to be adjusted, accordingly, in order to have the track exit the top of the helix at the proper elevation for the upper deck. The table does this automatically, but accurate measurement of the distance from the start of the grade at 0 elevation to the point at which the helix actually starts, will ensure the automatic calculations actually reflect the proper support heights.

Length of Grade After Exiting the Top of the Helix (Cell K5). This value represents the horizontal distance in inches covered by track on a grade after exiting the top of the helix and before coming to the 0 elevation of the upper deck. It is critical to accurately enter this value because the top elevation of the helix must match the 0 elevation of the upper deck or else move along a grade until it does.

NOTE: The attached Oval Helix Tables are designed to provide dimensions for both circular and oval spiral helixes. Circular spiral helixes are just oval spiral helixes whose straight sides are 0 inches long.

 

I can attest to Dave's engineering prowess--he did just about everything but draw, cut, and install my helix, and it works fantastic!
He helped me figure out all sorts of issues, very helpful, and patient--I had a heck of a time understanding a couple things, and he calmly and rationally explained them to me, in very well-thought-out PM's and posts. A true expert!

 

:embarassed: :embarassed: Gosh-a-golly, Hemi...'Tweren't nothing!! You did all the heavy lifting!!

BTW: Was it you who Stickied the thread?...Thanks!

 

Not I, but thanks to whoever did!
If it weren't for your assistance, I'd be trying to build a stacked helix..... And cussing while I attempted to lay track in it!

 

There are lots of ways up the mountain...each with their own advantages and disadvantages.

Easy Helix offers a stacked, cylindrical-shaped helix in kit form. I believe theirs is intended for HO but could easily be used for N scale. The one on their website has a 68" outside diameter with 2.1 and 2.3 percent grades that rise 2, 6, 10, 14, or 18 inches (more in 4 inch increments). Their stacked helix takes up 32 square feet of real estate and, at 4.5 turns for $230 + shipping, might seem too pricey to some modelers, but worth it for others who don't want to do their own design and component construction.

This calculator is designed to help N-scalers who want to build their own bowl-shaped helix to fit their personal givens and druthers. It automatically determines critical dimensions for a bowl-shaped helix as a function of the specific preferences entered by the modeler. With judicious use of grades before and after the helix, it is possible to rise a considerable distance without going beyond a 48 inch diameter (i.e., the helix footprint could fit in a 4 ft by 4 ft space--16 sq ft). The entire ramp and a 4x4 ft support base panel could potentially be cut from a single 4x8 sheet of plywood and the vertical supports and tangent ramps from another 4x8 sheet...perhaps $100 for a 5 or 6 loop bowl-shaped helix.

Take a look at my blog entries on bowl-shaped helix construction and at Hemi's and Cleggie's threads on their layout construction.