Model Railway Helix Grade Calculator

A helix is one long curve with the grade fixed by two numbers: how far around a turn is, and how far up you have to be by the end of it. The circumference sets the first, and the clearance you need to get a train under the deck above sets the second. Neither is negotiable by much, which is why almost every helix ends up steeper than its builder wanted and why the radius has more to do with the grade than the curve does.

To the track centreline. On a multi-track helix use the radius of the track you care about, usually the inner one, because that is the steepest.
Railhead to the underside of the deck above, measured against the tallest thing you run and whatever margin you want for a hand. Your figure, not one from this page.
Subroadbed plus roadbed plus the track, measured on the sample you built.
Used only when the select above is set to it.
Curve drag expressed as added grade. Get it from your own drawbar or pull test on this radius with these cars — it is not a constant and this page does not supply one. 0 leaves it out.
The page reports the radius and the rise that would hold it. 0 skips that block.
Used only to turn scale miles per hour into real inches per second for the run time.
For the outside diameter the helix needs on the benchwork.
Model Railway Helix Grade and Train Length CalculatorBuildFigure

The grade is circumference against rise

Everything else is decoration. An 18 in radius has a circumference of 113.10 in, and if the deck above has to sit 3.5 in higher than the one below, the train climbs 3.5 in over 113.10 in of track. That is 3.09 percent. There is no arrangement of the woodwork that changes it.

The 3.5 in in that sum is not a free choice either. It is the clearance you need above the railhead plus the thickness of the deck itself, and with the defaults it is 2.6 in of clearance under 0.9 in of deck. Shaving it means either running shorter stock or building a thinner deck, and the deck is holding up a spiral of track.

Radius is the only real lever

Circumference is proportional to radius, so at a fixed rise the grade goes down in exact proportion as the radius goes up. Move the default helix from 18 in to 22.5 in and the grade falls from 3.09 percent to 2.48 percent with nothing else touched. It also takes the outside diameter from 39 in to 48 in, and that nine inches is usually the reason the helix stays at 18.

The other direction is worth knowing too. Holding 2.5 percent at 18 in radius would need the rise cut to 2.83 in a turn, which is 0.67 in less headroom than the defaults give. That is most of the margin between a boxcar and a double stack.

The whole train is on the grade at once

This is the part that separates a helix from a grade out on the layout. A 20 car train of 6.5 in cars behind a 12 in locomotive is 142 in long, which at 18 in radius is 1.26 turns. Once it is inside, every axle is on the curve and on the grade simultaneously, with no crest to lift part of the load off and no straight to let the couplers line up. The drawbar sees the full compensated figure, 3.49 percent with the default allowance, for as long as it takes to get through.

At 25 scale mph, that is a while. The 14 in climb is 4 turns and 37.7 ft of track, which at 5.05 in per second takes a minute and a half. Nobody watching sees any of it, which is the other well known thing about helixes.

The curve allowance is yours to measure

Curve drag is real and is not a constant. It depends on the radius, on the cars, on how free the trucks are and on how well the track is laid, and published figures for it are prototype figures for prototype curves. The field takes a number you measured, by pulling a train up a test grade of known percentage and finding where it stalls, then doing the same on the curve. If you have not measured it, leave the field at zero and read the uncompensated grade rather than trusting a number somebody else measured on a different layout.

What the page will not do

It will not tell you how many cars your locomotive pulls. That is a question about a specific model on specific track on a specific day, and the answer moves with the weather. It also will not tell you the helix is too steep, because too steep is defined by what you run and what you are willing to watch.

Questions people ask

What grade does a helix have?

Rise per turn divided by circumference. At 18 in radius the circumference is 113.10 in, so a 3.5 in rise per turn is 3.09 percent. The radius is the dominant term, because circumference is proportional to it: the same 3.5 in rise at 22.5 in radius is 2.48 percent.

How do I work out the rise per turn?

Clearance above the railhead plus the thickness of the deck above. The clearance is set by the tallest stock you run and whatever room you want to get a hand in, and the deck thickness is whatever your subroadbed sample actually measures. Both are yours; the defaults here are placeholders. With 2.6 in of clearance and a 0.9 in deck the rise is 3.5 in.

How much track is in a helix?

Turns times circumference. Climbing 14 in at 3.5 in a turn is 4 turns, and at 18 in radius that is 37.7 ft of track, which stands for 0.62 of a scale mile at 1 to 87.1. At 25 scale mph a train takes about a minute and a half to get through it, out of sight the whole way.

Why does a train struggle more in a helix than on the same grade outside it?

Because there is no relief anywhere in it. The whole train is on the curve and on the grade at the same time, with no crest to unload part of it and no straight to let the couplers line up. A 142 in train fills 1.26 turns of an 18 in helix, so from the moment it is in to the moment it is out the drawbar sees the full grade plus whatever the curve adds.

How much grade does the curve add?

Whatever you measure, which is why the field takes your number rather than supplying one. Curve drag varies with radius, with how free the trucks roll, with how the track is laid and with the cars themselves. Pull a train up a straight test grade until it stalls, do the same on the curve, and the difference in percentage is your figure for that combination.

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