Incline and curves question

JimInMichigan Oct 1, 2014

  1. James Fitch

    James Fitch TrainBoard Member

    Some of this below has already been stated:

    "Grade equivalent is the drag (expressed as a grade) that a train sees from going through a curve. There is actually a complicated formula to figure this out, however there is also an easy rule of thumb for HO. Basically 32/radius of the curve= grade equivalent. So a train going through a LEVEL 24" radius curve will experience a drag equivalent to a 32/24 = 1.33 degree grade. So if a 24" radius helix produces an actual 2.65% grade (~2.5%) then the train will experience an almost 4% grade.

    There is a lengthy discussion at MRH forums that also might be good to read.
  2. BigJake

    BigJake TrainBoard Member

    The original (HO scale) formula was 32/R, and is added to the percent grade to provide an "effective" percent grade. As R approaches infinity (i.e. a straight line), the quantity 32/R (or any other constant over R) approaches zero, thus this formula would never predict that the effective grade would be less than the actual slope grade.

    The additional friction in a curve is based on the wheel slippage to compensate for the unequal distance traveled by opposite-side wheels fixed on the same axle. The amount of slippage is proportional to both the radius AND the physical (not scale) distance between the rails. This slippage in a curve is also compounded by the reduced tractive effort of the locomotive's wheels which also start slipping.

    The mass effect on the friction is also linear, but you are correct in that the mass itself is not linear with scale, it is cubic (3rd order). If anything, the reduced (beyond linear, to cubic) mass of the smaller scale would produce a more favorable (smaller) additive to pure slope.

    Suffice it to say that 32/R is pessimistic at scales smaller than HO. How much exactly? Who knows, but it is at least first-order linear with scale, and likely higher order due to the cubic order of mass with scale. At any rate, 17.5/R is a safe amount to add to the percent grade to estimate a workable grade in N scale, and is certainly safer than adding nothing.

    I had an N scale layout that had one grade on a sharper curve, and the opposite grade on a broader curve. Trains that could easily make the lap in one direction, failed to make it in the opposite direction (corresponding to uphill on the more sharply curved slope.) So, I know there is an additional effect of curvature on top of ordinary grade, and am just trying to adapt a rule of thumb for HO to N scale to predict that effect.
    gjslsffan and acptulsa like this.
  3. BigJake

    BigJake TrainBoard Member

    One more aspect to curves is that the slippage of at least one wheel on every axle (including locomotives') reduces the pulling force of the locomotive, while increasing the drag from the unpowered railcars. It would be interesting to experiment with curved grades that transition to a straight (same) grade at the top, by testing how many cars on the curved grade can be pulled by the locomotive, when it is on the straight grade at the top (and therefore not slipping itself), vs on the curved grade with the cars whose wheels are slipping/dragging due to the curve.

    Also, weight on a straight grade is not drag. Drag (from friction) increases with speed, whereas weight does not. Both exert a restraining force on a locomotive pulling a train up-hill, but they change across circumstances differently.
  4. SDVike

    SDVike TrainBoard Member

    While I feel kinda smart that I actually understand what you just said , I like using this calculator for it’s simplicity.

    I was hoping the modeling software I used factored curves into its grade calculator. Using this calculator It doesn’t. My 6” rise over 242” results in a grade of 2.48%. With the 24” curves, my effective grade is 3.81%. It makes me wonder if I need to reduce the grade on the curves and increase it on the straightaways.

    Sent from my iPhone using Tapatalk
    Last edited: Mar 31, 2021
    BigJake likes this.
  5. SDVike

    SDVike TrainBoard Member

    Interestingly, if you use the exact same parameters between N & HO, N scale has a lower effective grade. I think it’s due to the narrower wheels having less slippage as BigJake describes. However, how often do N Scale layouts have 24” curves.

    Sent from my iPhone using Tapatalk
  6. BigJake

    BigJake TrainBoard Member

    Yeah, that's the gotcha (but one of the things I really like about N scale compared to HO). If you model N in a space for HO, you've got it made! But most of us either don't have space for HO to begin with, or decide "Wow! Look how much more I can do in my available space in N than in HO!"

    My layout space of choice (or not) is a 36x80 HCD, so an average radius of 17" for a 180 degree turn is the best I can do. I try to "ease" my Unitrack curves by using longer radius pieces at the beginning/end of the curve, and shorter radii in the middle of the curve, leaving only a short space where the trains display at (or drag) their worst.

    On the other hand, that available space means I'm not running very long trains either, unless I just want to see an absurdly long train (with a "40-mule-team" on point) chasing its tail for the heck of it (after all, IT IS MY RAILROAD!)

    And even when I do run such a tail-chaser, less than half of it is on the incline, while the other half is still on the flat, if not on the decline!
  7. jdetray

    jdetray TrainBoard Member

    I'm sorry to be so late to this thread. My website has some info about grades on curves. Included are the formulas for HO and N-scale (which are different for each scale), as well as online calculators for HO and N-scale that determine the effective grade if you enter the rise, run, and curve radius:

    Railroad Boy's Grade Calculators

    - Jeff
    BigJake, Shortround and Sumner like this.
  8. Shortround

    Shortround TrainBoard Member

    Thanks for the link to the calculators.
  9. RailMix

    RailMix TrainBoard Member

    Personally, I'm just a tad bit gun shy about math for something like this. There are way too many variables involved to build something based on theory and then try to figure out why it doesn't work, so on the advice of other members here, I built a little test bed and ran some experiments. Here are the results I came up with. I decided that given the size of the planned layout and train lengths I wanted, I was OK with the results:

    Grade Pull Test | - The Internet's Original
    Last edited: Apr 29, 2021

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