Grade, Mass, Tractive Effort, and you.

A simple guide on how you can calculate the grade your locomotive can pull it's train up yourself.
Avoid having to wait for online calculators to update to new locomotives and rolling stock or stat adjustments and do it yourself.

Caution, this guide is encouraging you to do math.

The Equations

For those who just want to grab the equation, here you are. I even already transformed it for you.

Use the in-game imperial measurements for tractive effort and mass.

Give yourself some margin when putting the results to use, curves and track imperfections will have some (minor) impact.

How much choo to get up the hill?

If you know the grade of the hill and know the mass of your load (remember to include the mass of the cars when empty) this equation will tell you the tractive effort needed to get up the hill.

You will need to add the mass of your chosen locomotive/s to the mass of your load, they don't get up the hill for free.

How big can I make this train?

So you've got your locomotive/s and you've got your hill, but how much can you get up there in one go?

Plug and play with this equation, remember the answer will be in pounds.

For flat ground expect high numbers (millions of pounds), locomotives are really good with flat ground.

Should I re-lay this line?

Determining the grade an already known train can make it up can be very useful in planning, or re-planning, routes.

Maybe you can make it up in fewer trips if the hill was just a touch more gentle. Maybe you can make that slope steeper and still make it up, I'm sure you have your reasons.

Examples to get you started

[Rina Ravyn]

Unpopular opinion, i just take the weight of the loaded cars, hook em up to a loco, and then i unhook one car after another until the engine keeps going again.

Boom, thats your loadlimit for the gradient in question. No calculations required.

[Srednuas]

@enejvizintin I wouldn't say 'exact'.
They should be really close, but any corners will increase the friction.
Also you've got to consider the lines you lay will likely have some inconsistency.

I'd treat these as the maximum, and realistically you should be giving yourself some wiggle room under them.
Of course with a runup you can make it up slopes you wouldn't be able too from a standstill.

Track design add so many variables I didn't even try to cover them, a windy mountain track will be adding a lot of friction from the curves, that long straight flat section before the hill could let you get high enough speed to clear it when the same grade after a tight curve has you going slow so you have no chance of getting up it, etc.

[enejvizintin]

Just a quick question are the results that we get exact or roughly in the area?

[Srednuas]

@Woodman1225 if you find the calculations too daunting to do yourself you can always use one of the calculators others have posted or simply trial - and - error your runs in game.

[Woodman1225]

why this sh!t look my 7th grade algebra class

[tOhB_]

@Lord Srednuas I noticed this right after posting im really stupid lol, thanks for responding tho

[Srednuas]

@tOhB_ when you highlight a loaded car the loads properties are displayed up the top left of your screen. This includes the mass of the load.
There are other guides and calculators that include load mass, I have elected not too in order to future proof, and allow for partial loads. Any patches to the load mass or new resources my guide already covers without me needing to do anything.

[tOhB_]

how do you get the mass of the load? where do you see the weight of resources?

[Srednuas]

@bigbama819 What you have there is an order of operations error.
Maths has rules about the order in which to do operations because you can end up with some very different answers using different orders.

In the case you reference, you need to do the operation for the numerator (the top part of the fraction) and the denominator (the bottom part of the fraction) separately.

I show this in the next stage of the worked example, where the 34,420,000 numerator is over the 25 denominator.

What you have done is use 5 as the denominator, and added the 20 after the fact.

The correct way to express the equation in a single line is (2,000 x 17,210) ÷ (5 + 20 x 1)

The order of operations is to then solve the area inside the parentheses first.

[bigbama819]

Thank you for making this guide. I'm having a bit of conflicting calculations with what you're showing us on here. 2,000×17,210÷5+(20×1)= 6,884,020... where are you getting 34,420,000 from? Are you using 6,884,020÷2 ? If so that comes to 3,442,010. If you're not dividing the 6,884,020 by 2, then where is the 34,420,000 coming from?