Train's Speed, Power and Max. Tractive Effort

[Core Xii]

This is actually kind of strange, I searched on the wiki as well as the forums, but couldn't find any info regarding these.

A train's speed is self-explanatory.

How does an engine's power affect its movement? To my understanding, the weight of the train directly scales its speed based on the engine's power, but to what extent? Can the weight of the train totally cap its speed? And is there any way to acquire the information how powerful an engine is required for a certain load? (like a calculation, perhaps?)

What about max. tractive effort? As I understand it, this determines the train's rate of acceleration proportional to its weight.

And how does all this fit with multi-headed trains?

[Thief^]

Power is related to the speed and the weight, tractive effort is almost entirely to the weight.
A high power train can go really fast, but if it doesn't have much tractive effort it's not going to be pulling heavy stuff, even slowly.

I think.

[Badger]

Speed is the top speed that can be attained.

Power is related to the amount of weight that can be moved. Something with low power will struggle with big loads, whereas something with more power will find it easier.

Tractive effort is a measure of how well the power figure is applied to the track, acceleration I s'pose. Low tractive effort will mean that even something with a high power figure will struggle to get up to speed.
A heavy freight engine would want high power and high tractive effort.
A shunting engine will have low ratings.

[PikkaBird]

Tractive effort is a measure of how well the power figure is applied to the track, acceleration I s'pose. Low tractive effort will mean that even something with a high power figure will struggle to get up to speed.
A heavy freight engine would want high power and high tractive effort.

In practice, tractive effort and top speed are a tradeoff. Think of the gears in a car: the engine is always putting out the same amount of power, but by selecting gears you can either get high traction and low speed, or low traction and high speed, or somewhere in between. In real life (and in NARS2 ) many diesel engines were available with different gearings, allowing the same model to be used for freight drags (low geared) or express trains (high geared).

[Badger]

In practice, tractive effort and top speed are a tradeoff. Think of the gears in a car: the engine is always putting out the same amount of power, but by selecting gears you can either get high traction and low speed, or low traction and high speed, or somewhere in between.

Yeah, that too!

[michael blunck]

[What is "Train's Speed, Power and Max. Tractive Effort"?]

I´ve explained it here, incl all the mathematics.

regards
Michael

[Core Xii]

Great. Now, how can one know how much power is required to pull a certain load? (other than... eh, getting "the feel" for it)

[DaleStan]

If the train gets up to speed fast enough, you have enough of both power and TE. If it doesn't, then you need more of one or the other.

[Core Xii]

That's not really an acceptable solution. Are you telling me I'm supposed to try out every single engine before I even know if they can pull the cargo?

[DaleStan]

No, you're supposed to use a little thought, and not try engines labeled "Express passenger" for mile-long coal rakes.

Also, you're supposed to realize that, if the 300 kN / 3000 HP engine isn't strong enough, the 200 kN / 2000 HP engine is unlikely to be strong enough.

Furthermore, if you really want to know, MB's pointed you at the equations. Simulate the physics yourself.

[Core Xii]

It's too complicated. So in other words, there really is no other way but to just go on instinct. Kind of makes it insanely difficult to attempt to play the game as a game per se rather than just a sandbox.

[planetmaker]

It's too complicated. So in other words, there really is no other way but to just go on instinct. Kind of makes it insanely difficult to attempt to play the game as a game per se rather than just a sandbox.

If my understanding is correct: basically the HP is an indicator on how much an engine can pull (and given the weight of the train also determines the max velocity, if not limited by the engine max velocity). The tractive effort on how fast it can accelerate.

[michael blunck]

Now, how can one know how much power is required to pull a certain load?

That´s easy.

Let´s assume you have a 800 ton train which needs to reach a speed of 60 km/h on a 30 ‰ incline.

To move one ton on level track (e.g., µ = 0.35) you´ll need a force of 35 Newton. For grades you´ll need another 10 Newton per mil.

Now, let´s calculate:

800 (tons) * 35 N = 28,000 N
800 (tons) * 30 (‰) * 10 N = 240,000 N
sum = 28,000 N + 240,000 N = 268 kN

1) You´ll need a locomotive with a tractive effort of min 268 kN.


Now, for the power needed:

P = F * v, i.e.

P = 268 kN * 60 km/h = 268 kN * 16.66 m/s = 4466 kW

2) You´ll need a locomotive with a power of min 4466 kW.

HTH
regards
Michael

[Core Xii]

Thank you, that's more like it!

Now how does multiple heads affect this? Does it double the power or traction?

[DaleStan]

If my understanding is correct: basically the HP is an indicator on how much an engine can pull (and given the weight of the train also determines the max velocity, if not limited by the engine max velocity). The tractive effort on how fast it can accelerate.

Yes and no. Max TE limits low-speed force output -- at low speeds, a high power train is quite capable of spinning its wheels if it tries to deliver too much power to its wheels. It must, therefore, limit the power to something that keeps the force provided by the wheels below the max TE.
Power limits high-speed force output; producing a given force requires a power output proportional to the current speed.

The values of power and TE determine where the speed switches from "low-speed" to "high-speed".

In this image, Max TE is the portion of the greenish force-output graph that is horizontal at 100. Max TE remains constant throughout the engine's entire speed range.
Where the path turns hyperbolic, the limiting factor switches from max TE to max power output. When limited by power, the maximum force an engine can produce is inversely proportional to its speed.
The overall effect is that output force of an engine is never greater than either power/speed or max TE.

The engine pictured there has a power drop near 70 that most TTD engines (being ideal engines) do not experience. Some callbacks may enable more realistic engine performance.

Does [multiple heads] double the power or traction?

Yes.

[Core Xii]

Does [multiple heads] double the power or traction?

Yes.

So which one? Or both?

[michael blunck]

Just adding to Dale´s post.


Since ages, the DB Set Donotreadme has some information about tractive effort:

Tractive effort and choice of locomotives

What´s "tractive effort"?

"Tractive effort" is the force that a locomotive can apply to pull a train. It´s a function of power and speed:

(1) TE = P / v

However, TE is limited by "adhesion" which is a measure of the resistance of friction to slippage, in this case between the powered wheel´s surface and the rail.

I.e. the max force that a locomotive can generate in order to pull a train is limited by its weight and the amount of adhesion that it can maintain without wheel slippage: once the wheels start to slip the pulling force is lost.

(2) TE_max = W adh * µ

where µ = 0.20 ... 0.33, depending on the condition of the steel surfaces (roughness, moisture, ...).

The attached diagram shows tractive effort vs. speed for the BR101 electric engine. The blue line is tractive force according to friction, the black hyperbola is the tractive force according to motor power (Eq. 1) and the red line is the max speed.

tractive_effort.png (4.08 KiB) Viewed 18981 times

Thus, for motion, only area 3 will be usable: Area 1 is beyond max friction, which results in wheel slippage, for area 2 the tractive effort is too low. If it wasn´t, wheels would slip, too. In area 4 wheels wouldn´t slip at all but the tractive effort is too low, either. And area 5 is inaccessible because it´s beyond max speed. Anyway, notice that TE at max speed is only a third of TE_max.

Does [multiple heads] double the power or traction?

Yes.

So which one? Or both?

Yes, o/c both.

HTH
regards
Michael

[LoWang]

I really think this should be in the manual. I would maybe write it there if I was sure that I understand it
So is it right that if I put another engine to my train, than it's acceleration will double (because the TE will be doubled) if total power is high enough not to be a limitation?

[SirXavius]

I'd like to address the same question in actual (though hypothetical) gameplay terms....

I need to decide which train to buy. I anticipate heavy output from the source station. There is a train for sale that has 1000 HP and 200 "kN" (whatever that is) and one for 2000 and 100. I guess i need to buy the more powerful train, but let's see....what cars are available?.....

Now i have a choice of cars to carry the materiel. The short car weighs 18t and can carry 22t of materiel. The long car weighs 22t and can carry 33. I can buy 6 short cars, which will end up weighing 108t empty and 240t full. Or i can buy 4 long cars carrying the same amount, but weighing 88t empty and 220t full.

The question is, does the total weight of the cars (plus the engine?) count against the horsepower or the tractive effort (the kN)? Do i subtract the total train weight from the HP to determine how much i have "left" before the train is unable to reach top speed? Do i only need to consider tractive effort if i'm going uphill? STARTING uphill?

[LoWang]

What about some kind of formula? I guess realistic acceleration calculations can be quite complex, but at least some part of it could be mentioned in the wiki or manual! Unfortunatelly there is nothing about tractive effort nor realistic acceleration :-\ I found something here I checked the sourcecode and found the function, but it is not very clear to me :-\

edit: I found this (at the bottom), but it seems to be old and not counting with tractive effort. Can this be the same as it is in now OpenTTD?