Incline and curves question

JimInMichigan Oct 1, 2014

  1. JimInMichigan

    JimInMichigan TrainBoard Member

    I read somewhere here ( cant find it now ), a member stated that a curve would equal a 2 percent grade on a flat. That adding that same curve to a 2 percent incline would in effect make the incline a 4 percent. I do not remember what radius curve he was talking about.

    I have started a new layout with SCARM, and was able to keep my incline to 4 degree's. But in order to do so, there are 2 curves involved, both 24 radius. Is my end result an 8 percent grade?
  2. glakedylan

    glakedylan TrainBoard Member

    curved track does add to the drag on the train via its wheels.
    I have not heard of a measurement, however, that you note as it being equal to 2% incline
    afterall, all helix designs include, at the very least, 90 degree curves (some making ovals by include straights between those 90 degree curves)
    and in helix design, a 2" rise in 100" of length is considered 2% and that works quite well, as far as I know.

    kindest regards
  3. cuyama

    cuyama TrainBoard Member

    The HO rule-of-thumb first postulated by John Allen is that curves add to the effective grade by the amount of 32/R, where R is the radius of the curve through which the grade runs.

    So for your 24" radius curves, the additional effective grade caused by friction would be 32/24 or 1.3%. Assuming that you mean 4% grade and not 4 degree grade (they are different measurements), the resulting effective grade through the curves would be 5.33% -- pretty steep and beyond what many modelers have found to work well.

    Newcomers to layout design also often forget to allow for transitions to the nominal grade, which are a length of track gradually increasing (or decreasing) from level to the desired grade. One rule-of-thumb for this is one car length for each per cent of grade, although you might be able to get by with less through careful construction.

    Here is a not-to-scale representation of transitions.


    Since trains can't run over track that is angled abruptly like a hockey stick, you'll need some transitions. Once that length is considered, it often makes the remaining length of the grade shorter -- and thus even steeper.
  4. Flash Blackman

    Flash Blackman Staff Member TrainBoard Supporter

    I agree with the idea that a curve adds drag or "weight" to the train. I don't have any idea how much but John Allen's 32/R seems about right. I shoot for a two percent grade, maximum. One percent is a lot better.

    (Of course you can always add engines.)
  5. Shortround

    Shortround TrainBoard Member

    Wouldn't the arc length of the curve and length of the train affect this formula as well?
  6. cuyama

    cuyama TrainBoard Member

    Somewhat, the rule-of-thumb is simplified. But note that the worst section of effective grade is nearly always the limiting factor, so for all but the shortest arc lengths and shortest trains, it's what one needs to be concerned about.
  7. JimInMichigan

    JimInMichigan TrainBoard Member

    Here is a few shots of the layout, keep in mid this is a 10' 7" x 8' square. Direction of travel is counter clockwise.

    Along the front edge, where the incline starts ( which is where the 1st curve starts ):

    And where that curve leads to, 8' side of layout:

    Finishing the incline past the 2nd curve:
  8. Grey One

    Grey One TrainBoard Supporter

    Other Considerations:
    • Visual Aesthetic - If it is too steep it may 'look' wrong
    • On a small layout a five car train pulled by a four axle loco, (Atlas GP), would likely make it up a 2% grade with an 11" curve.
  9. cuyama

    cuyama TrainBoard Member

    Why limit yourself to only run trains in one direction?
  10. JimInMichigan

    JimInMichigan TrainBoard Member

    I can only get it down to 3.8 percent. I'm just about ready to give up...... I don't want a completely flat layout. If 3.8 percent grade over a 10' span is not doable, then I guess I'll sell what I have bought so far.
  11. Mike C

    Mike C TrainBoard Member

    Why can't you start the grade sooner and make it longer ?
  12. JimInMichigan

    JimInMichigan TrainBoard Member

    Cant make it much longer. There is a removable bridge in front. I'd like to keep that section flat.
  13. ppuinn

    ppuinn Staff Member

    It looks like your main travels around relatively close to the outside of your 10x8 footprint. Is it actually crossing over functional tracks near the middle of the back 10'7" side (so clearance between lower railhead and underside of the bridge supporting the upper track must be sufficient to permit your tallest equipment to pass under)? ...or do the lower rails pass off the edge of the layout to "suggest" to viewers that trains travel to distant cities but in reality the rails end in a mirror or behind buildings/trees (so equipment on the lower track wouldn't ever need to actually fit under the bridge)?

    If you don't have to clear tall equipment, could you reduce the elevation of the upper track (and thus reduce the grade)?

    Let's assume you have a twice-around HO track plan (=folded figure 8 with upper half folded over the lower half, and the upper track passing over the lower track near the middle of the back 10'7" side), and you need to have 4 inches between railheads where the upper tracks cross the lower tracks. Tracks in the middle of the front side could be set at 2 inches elevation, the lower track on the back side could be at 0 inches elevation, and the upper track could be at 4 inches elevation. Even with vertical easements transitioning into and out of the grades, you would have 8 feet to rise or fall along the sides...which would roughly translate into a 2 percent grade.

    Concerns about drag on curves making a 2% grade seem more like a +3% grade could be addressed by starting the grade transitions near the middle of the front and back sides, but not achieve a full 2% grade until after the curves.

    Vertical easements might necessitate reducing the length of your straight and level upper track across the back side of the plan from 10 feet to 6 or 7 feet, but that would still leave an impressive viaduct.
  14. COverton

    COverton TrainBoard Member

    I have had three layouts. I finally relented on my third and have kept my steepest grades to 2.4%. My helix is an honest-to-goodness 2.2%, the standard grade set by the Cumberland & Wheeling Railroad way back in the middle of the 19th Century, and subsequently adopted as the Federal standard grade by Congress. My second layout was supposed to be below 3%, but I goofed on my too-generous transitions and it ended up closer to 3.4%. I regretted that outcome bitterly, lemme tell ya. My nice BLI 4-8-4 locos could barely haul four Walthers heavyweights up that grade, and a couple of them spun a bit, making the odd loud groan as their metal tires ground down the rails and their coatings.

    There is a way to reduce your grade, but it means that your railroad should be a loop if it is smaller, and shaped like a figure 8. The part rising over the bottom track needs only to rise at 2%, but the tracks under it also need to drop toward it at 2%. As soon as the overpass is taken, the nether track begins a gradual rise to 'ground level' again.
  15. ScrewySqrl

    ScrewySqrl TrainBoard Member

    I'm assuming you are in HO scale.

    are you worried more about appearance or hauling capacity of your engines?

    On an old door layout in N scale, a single Life-Like SW9/1200 was able to haul 10 cars up a 2% grade and around 9-3/4" turns (the curves were 'transitioned' with a single 19" curve first) and worked just fine. The almost over-under figure 8 train set is a 3-4% curve. Most trains can handle a 2% grade, even around a curve, fairly well.

    If you're worried more about prototype, remember, there is a prototype for EVERYTHING, including steep grades and heavy curves.

    Check out Agony Point on the Darjeeling Himalayan Railway sometime. a loop over its own track in a 69-foot radius curve!
  16. JimInMichigan

    JimInMichigan TrainBoard Member

    Trying to get the most out of my layout space, I gave up on the grades and am now working on a flat layout. Thanx guys.
  17. MarkInLA

    MarkInLA Permanently dispatched

    ​Hey ! Here's an idea..Now that it's flat you could put a Christmas tree in the middle in December ...
  18. ppuinn

    ppuinn Staff Member

    Jim, Don't give up yet!!!

    You've clearly indicated some features that you want in your track plan:
    1. a maximum footprint of 10'7" x 8'
    2. changes in elevation
    3. a removable bridge that is level in the front of the layout
    4. a long bridge or elevated section across the back of the layout

    You probably don't want a 4 foot reach into the center of the layout, so can we assume the removable bridge would be to provide access into the center of an around-the-room track plan?

    What scale are you working in? The options Crandell and I proposed could work for HO, but if you are working in a larger scale, there may not be enough length for a 2% grade to let O or G scale trains pass over themselves.
  19. BigJake

    BigJake TrainBoard Member

    I found this old thread referring to the compounding effect of curves on the steepness of inclines, with respect to the ability to pull a train up such a curved incline.

    In the above quote, Cuyama referred to an HO rule of thumb from John Allen that adds additional percent grade in the amount of 32/R to the incline to allow for the effects of the additional friction.

    I assume this is scale dependent (the slippage of one wheel on an axle relative to the other is proportional to the physical distance between rails and the radius of the turn,) and that for N scale, it should be scaled by 88/160, or 17.6/R.

    Any comments?
  20. acptulsa

    acptulsa TrainBoard Member

    I don't think it's scale dependent, at least not completely. Had to think about that one. Grade is measured in percentage, and is not scale dependent. No law of physics is scale dependent.

    It isn't so much friction. You can't find a magical point where the centrifugal force is shoving equipment out while the drag of the grade is pulling it in, canceling each other out. Fact is, it takes energy to change an object's direction. That's a law of physics, and you can't break it. Yes, friction usually enters into it where wheels are involved, but even if keep the rail flat and grease it, a train will lose momentum in a curve.

    A three percent grade is just as steep whether the track is 160:1 or 87:1 or 1:1, and the number/R shouldn't change, on the surface of it. But then, N scale trains have less mass than HO, O, real, or most things in life. The number may be less than 32/R just because of reduced mass. This is a rule of thumb, and has to involve mass, which is related to 3D volume, which acts more like the cube of length. So you may be looking at a different number. It may not be as simple as 87.5/160 X 32=17.5

    In fact, I'm sure it's not. HO cubed/N cubed is 0.16. That's close to the weight difference between models of similar prototypes. But you can't convert cubic mass in a fraction over linear radii and get a number that works. In short, mass enters into 32/R somehow. So applying a ratio based only on linear length is using only apples to modify a formula that mixes apples and oranges. It won't taste the same.

    I suspect that number may be lower for N, but it would take experimentation to find it. At least, I can think of no other way. The 32/R rule of thumb was found by experiment.

    Do remember this is a rule of thumb. It's got to be scale dependent. It's also dependent on conventional practice, meaning it only works in a narrow range. If you take that ratio, that thing which doesn't deserve the label of "formula", too seriously, then you believe using 40" radius curves results in a lower effective grade than straight track. Don't take it too literally.
    Last edited: Mar 25, 2021

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