How steep is too step for your inclines?

Here’s a thorny issue that comes up quite a lot in my inbox.

A big thanks to Bruce for this one. His last post is here.


Some time ago, I sent a graphic with explanation on selecting the minimum radius for two parallel sets of rails. Some appreciative comments were added.

I have noted that in several viewer responses that there may be some difficulty determining rail length for various %slopes.

I thought perhaps that some users might have an easier solution by using a graph. Therefore, I am providing the following with example of usage.

Rise and Run

%slope (percent slope) is determined by using the formula

RISE X 100 = %slope

The graph is graduated in UNITs. One unit may be any length measure base.

This would be determined by the measure the user decides to use; mm (millimeters), cm (centimeters) or inches.

Of course one could use Yards, Miles, Light Years or any other.

On the graph are lines representing typical %slopes plotted for determining either RISE or RUN.

Or, knowing the RISE and RUN, the %slope may be found.

Assume the user is into HO scale. Then on both the vertical (RISE) and horizontal (RUN), the Unit 1, 2, 50, 100, etc, might be labeled as cm (centimeters).

First one must determine the minimum height to be used for clearances of one track over or under another.

Select the tallest Locomotive or Car and measure its height in the cm.

Add additional measure for assurance of clearance.

I.e., tallest item might be 5.0 cm.

Then add to this using this measure, the height of roadbed and rails; 0.5 cm is assumed for example.

Then 5.5 cm would represent the minimum amount of RISE to be used with the desired %slope to determine the amount of RUN required.

Now one can determine whether he has enough real estate to accomplish the desired %slope.

Example referring to the accompanying graph.

Note that the RISE graph values range from 0 – 2.0 and the RUN values range from 0 – 100 UNITs.

Note also that the graph is linear for both RISE and RUN.

Minimum clearance height of 5.5 cm. This value is then equal to 1 UNIT on both RISE and RUN.

Example #1: Determine amount of RISE for given RUN and any %slope.

Select the desired RUN based of available real estate.

Assume RUN available to be 440 cm.

440 cm divided by 5.5 cm equals 80 UNITs.

Assume maximum clearance RISE allowed to be 11 cm or 2 UNITs.

Then search RISE value for each crossing value on the %slope values vertical to the 80 cm RUN value.

For this example, the 1.5 %slope provides a 1.2 UNIT RISE for the 80 UNIT RUN., or 5.5 X 1.2 = 6.6 cm minimum.

Also, using the 80 UNITs RUN, find the %slope value using the 11 cm RISE line. The crossing is found to be the 2.5 %slope line. One might consider this to be the steepest grade for his train to successfully climb with a desired number of cars coupled.

Example #2, the 3 %slope is desired for the 80 UNIT RUN. Find the required RISE (height) for this %slope.

The graph is linear; thus, the 3 %slope RISE would equal 2 X 1.5% RISE = 2.4 UNIT RISE or 2.4 UNITs X 5.5 cm = 13.2 cm.

Example #2: Determine amount of RUN for given RISE and SLOPE.

Assume RISE = 1.2 UNITs and SLOPE = 2%.

Search the 1.2 UNIT RISE value horizontal to the intersection of the 2% SLOPE line.

The RUN would be down from this intersect to the value of 60 UNITs.

The amount real estate required would be 60 UNIT RUN X 5.5 cm = 330 cm.

In like manner, one could determine %sLOPE by locating the intersect of the given RISE versus the given RUN.

Of course not all measurements will coincide with any graph interest, but the use can then eyeball the desired value between any two intersects.

Al, I certainly hope this is of value to your viewers. I certainly, enjoy all the posts and comments. I also have gained some insight from many of the posts as I continue my future layout. I have a lot of work ahead. Many comments have assisted to reduce some of the work load.


(Image is clickable)

A huge thanks to Bruce. What a clever lot you all are.

And if you like this tip, don’t forget the Beginner’s Guide is jam packed with more just like it.

That’s all this time folks.

Please do keep ’em coming.



PS Have you had a look at the new ebay cheat sheet yet?

30 Responses to How steep is too step for your inclines?

  1. Rob says:

    Just as important as the percentage slope is the transition curve at top and bottom of the rise. This needs to be as smooth as possible else you risk lifting a wheel set as you enter or crest the gradient.

  2. Roy Forbes says:

    Gosh! That looks complicated. Does it have to be?

  3. Bob Compton says:

    Thanks Bruce, I am still in the planning stage and wonder what is the optimal %slope that trains will operate smoothly? I will be modelling in HO and plan on a early 50s era. (Mostly steam)
    Also don’t forget the thickness of the overhead bridge/structure when calculating rise.
    Bob in BC

  4. Don Ripper says:

    No it doesn’t have to be. Use one of the track design packages. I use SCARM which constantly calculates the rise as you lay the track on your screen.

  5. Paul Braddock says:

    That’s a brilliant system for incline calculation, mine was a little more basic, I used the really old Triang incline piers and doubled the distance, adding extra piers with a shim underneath to give me a more gradual slope, as I have an outdoor line this is fairly critical as the slightest damp and loco’s will slip (inclines are supposed to be a no! no! in the garden)
    I do have a couple of quick videos if they’re of interest.

  6. BOB LANDESS says:

    the question on inclines was not fully answered … the maximum incline should not exceed 4% … and ideally a 2% incline would be best if you adequate space for the longer run required …

  7. Douglas Nicholls says:

    HO may do a little better than N, and locos with traction tires do better than those without. Generally speaking, you want to model in the same grades as occur in real life. On U.S. Mainlines, Sherman Hill is recognized as the steepest at around 1.7%, letting you push to 2.

    On my first layout, I did a bit of research and found there were 5% grades on some mountain railroads and assumed my equipment could handle 3%. Not with any cars attached!

    Also, if you’re running vintage equipment, some doesn’t have traction tires and some locomotives (Atlas in N Scale is poorest in my experience) have few driving wheels. The Atlas equipment I’ve acquired struggles with anything over 0%.

  8. Bruce says:

    I apologize for not having included a caution concerning the gradual change in rail slope at the beginning and end of the transitions. That, as noted by the first comment, is of upmost importance and MUST be taken into account.

    Also, Bob mentioned that the overhead bed and rail thickness should also be included.

    Also, my computer uses spell check and I had to edit this a couple of times. One error is still visible. About 2/3 way down the following:
    “Then search RISE value for each crossing value on the %slope values vertical to the 80 cm RUN value.” This should have been 80 units RUN value.

    Thank you for the kind comments
    Bruce SC USA

  9. Rod Mackay says:

    Gosh that seems a lot of calculation, Sure, start by seeing what’s the tallest thing you’ve got to get over, and see how long you have to make the climb in, but then you can just set up some plain track propped on a bit of timber raised to the same height one end over the same length and see what your engines will pull up the slope. Revise the plan or the train lengths until happy. Bingo! More fun anyway.

    Don’t forget, if you haven’t got room to climb high enough, maybe you could lower the track under the bridge a smidge. The poster at 12:00 is absolutely right about needing a bit of transition top and bottom, we had one loco on my son’s railway where the pony truck shorted out under the cab floor when coming onto the grade, sorted out with milling a little floor away and lining the recesses with thin plasticard. Also, remember it’s harder to pull a train round a curve, don’t assume your loco will pull as much on a curve as on a straight.

  10. Chris Fishburn says:

    I would generally think in N scale that to elevate by 1 inch would take 1 foot although the curve at the bottom & top would of this elevation would be very gradual, perhaps the 1st & last foot would only elevate half an inch !

  11. Roland Aldridge says:

    Some additional points from hard experience: you can get more “run” by curving the track, but the curve adds more friction so the beneficial effect is pretty much lost. If you put a magnet on the bottom of your loco, and lay the track on a steel plate, the increased adhesion will help it haul more up the hill. But it will also pick up all the lost screws and track pins and anthing else magnetic!
    A little 0-6-0 tank loco can pull one or maybe two coaches up a 4% grade. The little Adams Radial can only manage one.
    You better figure on only pulling the fancy brass track cleaner down the grade! To get it up takes two heavy little American style tanks. Two 0-6-0 PT locos won’t do it.
    But it gives you a reason to use a banker engine to help get trains up the hill, which is fun once or twice, if not much fun on a continuous basis!

  12. Don Jennings says:

    Hey guys another way to measure incline is to take 100 inches – which is just over eight feet – ((12 times 8 equals 96 )) and go up one inch ==is a one percent rise.
    In fifty inches you rise up two inches, you have a two percent grade
    In fifty inches (just over four feet) you go up three inches = you would have a six percent grade ( or rise) = ((that is getting real steep )) and you probably do not need that incline. No HO or N scale Locomotive will ride that STEEP unless it is a cog railway.
    To shorten one measure, you double the other measure

  13. Don Jennings says:

    Another way of thinking is to have you pull an empty wagon up a hill. Usually there is no problem.
    Now at the bottom of the hill again, place a load of cinder blocks in the wagon, and go up the same hill. Either you need help pulling the load (I.E. a friend to help you or another locomotive to pull the cars) OR YOU CAN LESSEN THE LOAD UNTIL YOU CAN GO UP THE HILL. That is called doubling the hill with half the load first and then getting the remainder and going up the hill again.

  14. This made something I previously understood very confusing.

  15. Rob McCrain says:

    If you want to run just about anything up your grades, stick to 2%. If you are willing to reduce the length of your trains go 3%, but in the end you’ll probably regret it. Model trains especially steam locomotives cannot climb 3% with much load at all. I use the foam inclines for perfect climbs, but even then, it must be perfectly flat when you lay your foam inclines because irregularities will be telegraphed up through the foam to the track bed. The bump created could be a 5% incline and your trains will stall. Rob McCrain Farland Howe

  16. Great info for everyone!!
    keep em runnin fellas
    stjohn in long beach calif

  17. David Wright says:

    I don’t mean to be picky, but if 1″ rise in 100″ = 1 %, 2″ rise in 50″ does not equal 2%” rather it equals 4%. The real slope for 2% would be 2″ rise in 100″ of run. The constant is 100″. In 50″ to rise 2 % would be 1/2″. David

  18. Sam Stockley says:

    Brilliant work. Just one major discovery I made on inclines – The maximum incline your loco’s will pull is considerably less if the track is not completely straight. I had a slow S bend on one of my inclines and the wheels slipped on just about every loco when pulling several carriages. After much deliberation, I realised that it was due to the fact that as the driving wheels are on a solid axle, when they go around a curve one wheel (or both) has to slip so reducing the grip. As soon as I changed my layout and straightened the track on the incline the loco’s all went up with no problems.

  19. Bob Carlson says:

    Bruce, your graph as the simplest way to illustrate per cent grade. However, check your graph. The 3% line is slightly higher than it should be. At 50 units run it should intersect the 1,5 inch rise line. As shown it intersects the 1.6 rise line.

  20. Philip Gray says:

    Great discussion, I have been struggling with my steam locos making a 2.5-3% grade on my layout. Needed to double head to pull a string of cars.
    Now I know that this is not unusual. from now on I will leave one of two cars back at the yard. Thanks for the discussion, Phil G.

  21. Hi guys, I love to read about what you are doing. Thanks a bunch. For me , i run my rails flat. All my stuff is currently in boxes , but if i ever resurrect it. It will be two tiers, each one running flat. I have some beautiful o guage stock. generally ,the biggest, heaviest , most elaborate and longest unit ( like an ALCO PA with 2 power units and 4 Sreamliner cars run on a large oval/ rectangle (or such ), out or around the perimeter. . i set it to run continuously and about at one speed. The other units 2 or 3, run on the second tier platform of some irregular shape. These intertwine , in and out avoiding scenes of interest. That’s where the ACTION is. ie Passenger stations road crossings, signals ,sidings, etc. Can’t you just imagine the layout?
    OH what fun IT is. Enjoy with me. Regards to U all, Bill

  22. Bruce says:

    Re 6:29 PM. You are correct about the 3% line. The line is incorrect, but I believe the noted rise values on that line are correct.
    One can easily Copt the graph and print for filing.
    Thank you for you correction.

  23. Cary Price says:

    I put in the gravel track bed for my outdoor G scale layout last summer. I took my 4 foot level and added a 1.2″ spacer block to one end (48″ X .025 = 1.2″). This is for a 2.5% grade. For my 2 foot level it was 0.6″ (24 X .025 = 0.6″). As long as the level showed the bubble in the center then I was holding a 2.5% grade. I suppose you can be more exact on an indoor layout but this seemed to work well outdoors. I plan to use this same method when I start putting down track this summer.
    Cary in KY

  24. chuck henry says:

    I just keep the angle under 2% for short trains on mains Only mining, logging or coal yard dumping get steep. Radius change, is not my preferred choice at incline point changes.

  25. Dale Popula says:

    All the talk is about climbing a vertical grade. What about the decent down? How do you handle the clank-clank of run-in of the cars coming down grade?
    The person that referred to the curves leading into and out of a grade. It is not a transition curve it is a vertical curve. I guess you can use the term transition in model railroading same as easement is used instead of spiral for leading into and out of horizontal circular curves. My father first ran into the vertical curve problem building my first Lionel layout in ‘50-1. He was an excellent electrician, but not a civil engineer. One thing he did develop was the electronics to run two Lionel trains on the same track at different speeds. Today I believe it is called DCC. The problem he had was size. Back then the transistor was not available and vacuum tubes were far too big. He could not fit the system into my dummy F3 A&B units.
    I would like to hear some input on the run-in.

  26. Carl in Kansas says:

    Question: If I rise at 2:30 am and I have a 32′ run to the bathroom, will my old engine be strong enough to make the trip successfully?

    Carl in Kansas

  27. I’ve just added a quick clip of test run onto YouTube of the incline I have, as you can see I like Triang quite a bit, loads of work to be done on the railway in general once the weather gets better!

  28. Malcolm Hodgson says:

    How steep is too steep? I think that was the question.
    Lovely graph. Great because it works both in metric and imperial units or as pointed out SI units or banana lengths if you want.

    The answer to the question “what is the ideal slope?” is of course 0% but even then as pointed out the wheels slip on tight curves with heavy trains or longer train lengths. So even 0% doesn’t allow infinitely long trains. Everything has it’s limit. (even my wife’s patience……apparently!)

    Decide what your maximum train length is going to be. Get some track on a plank and try getting it to run up ever increasing slopes till it stalls or slips. That is now your maximum RUN and RISE.

    You must of course bear in mind that your bearings in your stock will age and create more friction and your track will get dirtier with time and so if you conduct the same experiment with the same track and stock 12 months later you may find that it will not achieve the present maximum.

    So to avoid disappointment, play it conservatively, maybe half the maximum to allow for degradation over time. If you are struggling with the problem of how to get over track B with track A in a short distance whilst hauling up 20 wagons and feel that luck and finger crossing has become part of the equation, it is probably not your best idea to date. Have a go at going back to the drawing board for another idea.

  29. Robert Rolfe says:

    Carl in Kansas, you nailed it, everything wears out, including us, get over it and have fun, hell you will properly change it anyway .
    NV BOB

  30. Ben Taul says:

    the simplest why I seen is in degrees 1 ‘ of incline = 1″ rise every 12″ so for every foot of track run it 1″ rise 24″ =2’ rise 36″= 3’rise etc

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