How many wagons to an engine? How to define the optimum power to weight ratio.

[mail]

In all train games that I have been playing, there is always a decision to be made which engine to use and how many wagons to put behind it.

I am not really happy with the try and error method. It is time-consuming and not how I want to play the game. Transport Fever is actually amazingly programmed in terms of the physics, so real life methods can be used for decision making in the game, at least certainly this one will get me the right decisions:

The solution to getting it right the first time is not that hard - in theory - as it all comes down to the power to weight ratio, quoting English Wikipedia here, in case you are not familiar: "Power-to-weight ratio (PWR) (also called specific power, or power-to-mass ratio) is a calculation commonly applied to engines and mobile power sources to enable the comparison of one unit or design to another."

So, you take the power (e.g. 400kW) and divide it through the mass (e.g. 200 tons) and there you have it,
PWR is 2 kiloWatts per ton (kW/t). Bigger number means that you have better acceleration, top speed, grade climb ability etc.

Now, all you need is the required PWR and you can configure your train in game accordingly.

So, I set up a huge excel file, containing all available engines, wagons, cargo and the relevant data and it tells me many things really quickly, e.g.:
For a desired PWR, I am shown how many of the selected wagons and cargo I can put behind each engine.
For an actual configuration it shows me the exact PWR as well as the length of the train.

Where I am struggling is to define the desired PWR.
It depends largely on the top-speed of the train and the actual route that you want to run the train on.
E.g. early trains with 40 km/h top speed are doing well with about 1 kW/t. Once trains can go 100 km/h, anything lower than 2,3 kW/t seems useless and the biggest issue is how to predict the influence of track grades.

So, here are my questions:
1. I have read somewhere that there is a spreadsheet here for download with data concerning top-speed on grades. Does anyone know where I can find it?
2. In case, you have a similar approach: Could you advise on how you use PWR? What do you use for what sort of track and top-speed?
3. Is there maybe a simpler approach that works well enough? And by well enough, I mean that I can rely on it without double-checking the result and without consistently overpowering my trains. (I have noticed that the detail tab of train will tell you how well you powered your train with ratings "excellent", "good", "mediocre" and "poor". Maybe that could be used, if I knew how. For me the range of "mediocre" seems so big that it is not really helpful.)
4. Is there a helpful discussion about this somewhere already? I couldn't seem to find it.

Thanks for any helpful answers in advance,
Kaeptn_Massaka

P S: The a.m. excel file is definitely not in a condition to be shared and due to the required effort it would take, will never be. There is a mix of languages, any number of unexplained abbreviations and data tagged with the same name that isn't the same data. For me, it doesn't matter, because I know what I mean and how it works and how I have to work with it.
Having said that, if someone wants to see it, I don't want to be the guy that asks questions and doesn't show what he needs the answers for.
So, if requested, I can upload it, but this should not become the discussion topic.

[mail]

tl/dr:
What power to weight ratio works for trains going at 100, 120 or 160 km/h on flat, medium and steep slopes?

[Didz]

I've seen an excel spreadsheet that does this but it was really complicated.
https://docs.google.com/spreadsheets/d/1FW5R8aq3E88py-sTObi5s-w8U1z_li8Q9Mzp1ZQ9iPU/edit#gid=326947738

The only spreadsheet I created was one that accurately displayed my companies annual profit by ignoring capital investments.

[Vimpster]

Originally posted by mail:

tl/dr:
What power to weight ratio works for trains going at 100, 120 or 160 km/h on flat, medium and steep slopes?

There are so many variables to account for and the answers would be largely subjective. However I would add that distance is an important factor too. The shorter the line the less efficient it becomes to be spending money on trains that are pulling wagons that can do 120 if the train never even gets close to 120 at any point along the way because of how short the line is.

There is also the changing weight to consider. An empty cargo train vs. a fully loaded cargo train. Do you aim to split the difference in terms of performance or do you tailor it for when it is at it's heaviest state?

There is also the power vs tractive effort factor to consider. Since they are so closely related it becomes a question of just how many units of power is a single unit of tractive effort worth. The tractive effort helps acceleration at slower speeds and raises the minimum speed on slopes, but more power helps acceleration at higher speeds, and allows for higher speeds to be reached.

These are interesting questions you ask, but I just don't know that there is any real solid answers to them.

[mail]

Originally posted by Didz:

I've seen an excel spreadsheet that does this but it was really complicated.
https://docs.google.com/spreadsheets/d/1FW5R8aq3E88py-sTObi5s-w8U1z_li8Q9Mzp1ZQ9iPU/edit#gid=326947738

The only spreadsheet I created was one that accurately displayed my companies annual profit by ignoring capital investments.

Uh, that is quite awesome. Even at first glance, he is doing similar things to what I am doing.
And he seems to have slopes included. Nice! Thanks a lot!.

[mail]

Originally posted by Vimpster:

Originally posted by mail:

tl/dr:
What power to weight ratio works for trains going at 100, 120 or 160 km/h on flat, medium and steep slopes?

There are so many variables to account for and the answers would be largely subjective. However I would add that distance is an important factor too. The shorter the line the less efficient it becomes to be spending money on trains that are pulling wagons that can do 120 if the train never even gets close to 120 at any point along the way because of how short the line is.

There is also the changing weight to consider. An empty cargo train vs. a fully loaded cargo train. Do you aim to split the difference in terms of performance or do you tailor it for when it is at it's heaviest state?

There is also the power vs tractive effort factor to consider. Since they are so closely related it becomes a question of just how many units of power is a single unit of tractive effort worth. The tractive effort helps acceleration at slower speeds and raises the minimum speed on slopes, but more power helps acceleration at higher speeds, and allows for higher speeds to be reached.

These are interesting questions you ask, but I just don't know that there is any real solid answers to them.

It is true, distance is very important, too.
I have actually started a second file, where I am trying to calculate the whole system: acceleration, time and speed. It requires numerical solvation of integral equations, however, and therefore the results will never match what has been done in the game. Also, if the developpers haven't made it very simple and actually take into account friction, then it can't be done, because friction data is not available in the game. (Real vehicles at high speed use most of their power against friction, road vehicles especially air resistance. So there is less and less power available (excess power) to accelerate. Top speed is reached when the maximum power equals all friction resistance.)

I will look into that, there is a discussion about that linked in the spreadsheet that Didz provided.

empty vs. full:
Currently, I am looking at the course of the line and if it is empty uphill, I would rather look at that then care about downhill full. I can put how many full or empty wagons the train consists of. In the table, where I can see how many wagons a train can pull at desired PWR, I only have full state column for now. But I have included up to three engines of one kind, so I will quickly see, e.g. if it is better to use "3 Atlantic" or one "Milwaukee".

Regarding tractive effort, I have read the opposite somewhere. They wrote that the game does not care about tractive effort on slopes only for acceleration limitation up to the speed that I have labeled "vTrac" in my files. Now, if this is not true, then PWR sure doesn't mean as much as I thought it would.
You can easily figure out this speed for an engine and it is not depending on what you put behind the engine.
It is power of the engine, divided by the tractive effort. As they are both given in kilo, you don't have to adjust for units. Multiply the result with 3,6, which will convert your m/s to km/h.
I ususally generally stay away from engines with high "vTrac".
I haven't even put them in my file so far.
Take the 4-4-2 Hiawatha: 77,5 km/h.
No, thank you.
I have double-checked the running cost of some engines with the power and they were very similar, so I am working on the assumption that I pay dollars per kW per year.
I really don't want to pay for power that I don't have and low speed acceleration is really important anyhow. In terms of travel time going slow is almost like not going, so a decent speed should be reached very quickly.

You are probably right, there is not a real solid answer.
You can accelerate very slow and make a profit and really fast and make a profit.
To figure out the optimum requires a lot of calculation and a rule of thumb would probably very much depend on how people want to see their trains moving.

Thx for your answer.
I see you are having a lot of similiar thoughts as I have on it and it also made me realize that I really need to find out the full meaning of tractive effort.

[Vimpster]

My simplistic description of how the tractive effort works was based on what I remember the developer posting about it years ago. It is possible I am not remembering correctly, or the game changed after the fact, or the developer was just wrong about how it works.

I just did some testing in TpF2. I assume they didn't change the physical workings between the two games. My results were disappointing. I saw no difference whatsoever between a train with 115kn vs one with 229kn of tractive effort, weight and power being identical.

My test had a roughly 1km stretch of flat before starting a maximum grade climb to the top of a small mountain. Each train had 1000kw power and weighed 497t. To make the weight match since the locomotives were slightly different weights, I had to use a few different wagons on the end, making the train with 229kn tractive effort 27meters longer. Which also means 27 meters less run up on the flat section. The 115 tractive effort train reached 52km/h before starting to decline in speed because of the slope at the base of the mountain. The higher tractive effort train reached the same spot at 51km/h. Both trains slowed down to 27km/h before reaching the top.

So, despite one train having twice the tractive effort, it was the lower tractive effort train that was a bit shorter that had the very slight advantage due to having a slightly longer run up.

Also, at no point did either train get speed limited due to any curves.

So maybe the tractive effort stat is effectively meaningless. It certainly proved to be in my test.

[mail]

I understand that you are calling your sentence on the meaning of tractive effort simplistic, but it is the simplification that the developer has informed you about. IRL the tractive effort changes on a slope. In game it doesn't. That is what you could interpret from his statement.
And then, you have covered its full meaning for how it would affect vehicle behaviour in the game.

So, you went ahead and tested it in TpF2. I agree with your assumption that the game physics is the same. I read that somewhere. Results of your tests therefore should definitely be applicable to TpF1.

That is a very good test you did there. Somehow, it didn't occur to me that I could test it and I believe it would have taken me way more time to do it. So I am really thankful you have done that.

Let's check it out:
I am gonna use "vTrac" again for lack of better terminology and refer to your trains as "weak" and "strong".
So, your weak train has a vTrac of 31,3 km/h. That is actually still a pretty solid vTrac.
Strong train vTrac: 18,8 km/h. That is around the level of e.g the "Mikado" or the EMD GP 9 and definitely a value that leads me to believe its purpose IRL was to pull cargo trains.
Nevertheless, the difference is only 12,5 km/h between the values and given how fast trains accelerate from a stop in the game, I would assume that the difference it makes for those 12,5 km/h where it actually makes a difference, could hardly be noticed.

Length:
Weak train is shorter by 27 meters, giving it 27 meters more acceleration distance on a 1 km stretch of track. 51 km/h is 14,17 m/s, so that translates to 1,9 seconds additional time for acceleration. (I need to remark that this is a simplification.)

Power to Weight:
2,01 kW/t for both trains. That is a low value for fast trains so very good in order to do this test.

When estimating as an engineer, one method is to assume linear relationships or constant values, even though in reality they are not. This should work well here, because of the low PWR and the short difference in distance traveled to slope.
So, engineering estimate for difference in speed to hill, using longer train as reference:
At 51 km/h= 14,17 m/s the power of 1000 kW leads to a pulling force of 71 kN.
With the mass of 497 tons this translates to 0,142 m/s*s acceleration.
With the estimated 1,9 seconds above, the speed difference is therefore 0,27 m/s = 0,97 km/h.

51+0,97 = 51,97, which is 52.
So, your explanation of difference in speed can be fully and even astonishingly precisely backed up with the physics.
(On the assumption that the game does not have any driving resistances, though. This estimate works on the assumption that all power can be used for acceleration.)

You didn't mention where they slowed down to 27 km/h, but I assume it was almost in the same spot, otherwise you would have mentioned it.

One more thing that could be done with the numbers that you have provided:

We can use the physical relations to calculate the slope angle.
If the calculation shows the slope angle that you have used in the game, that would prove there are no driving resistances in the game.

I haven't done that in a while, so I need to sit down with a piece of paper and now it is lunch time as well.

For now, your test has proven that the tractive effort does not affect speed on slope.
To test if tractive effort has an impact of acceleration from a stop, it will be necessary to take an engine with a real bad vTrac vs a real good one, so that differences could actually be observed. I have been thinking about doing this test for a while, because for my judgement trains early acceleration seems way to high. I haven been doubting full implementation of tractive effort for acceleration purposes for a while now.

Thanks a lot and I will write again, when I have calculated the slope from the vehicle and speed figures.

[Huperspace]

https://www.youtube.com/watch?v=GcPR1FJoX58
tractive Effort is the max Force a train can use for accel.
1000kW / 115kN = 8.7m/s -> linear accel. of (115kN/497t =) 0.23m/s^2 (v/s) until 31.32km/h then the normal P=F*v, F=m*a relation (without any resistance)
1000kW / 229kN = 4.36m/s -> linear accel of (229kN/497t =) 0.46m/s^2 (v/s) until 15.7km/h (without any resistance)
9sec diff until 15.7km/h + ca. ((8.7-4.36)/0.46/2=) 4.5sec (linearised) diff until 31.32km/h then they accel. the same thats about 50m (40m = 1x train station modul) difference
mean power/weight is significant more important.
tractive effort only for stop&go trains (metro, etc: 500-1km until next stop)

you already have the "power rating", poor is enough for flat, medicore for 1. steep, good for 2. steep. (rule of thumb for maximum profit)

[mail]

Thank you Huperspace,

after I wrote last post I started on the slope angle calculation, but was interrupted and very busy since then. But I will hopefully get it done Sunday at the latest and then also have some time to look into detail at your post. The last part of your calculation (where you linearised) I couldn't graps right now.

I love that you have given a rule of thumb.

[mail]

So, I finally got around to the slope angle calculation and put a lot of thought and effort into it.
I had hoped to get either 10 degrees or 10 per cent as slope angle.
Depending on source (unfortunately there is no manual for the game for reference) the maximum angle in game is either 10 per cent or 10 degrees.

I calculated the slope angle to be 1,57 degrees = 2,73%.

So, this doesn't really make a lot of sense.
I would have expected the developers to condense topography, for real life height differences that matter for construction are actually so small that any construction site is always measured first and any design work starts based on the according plan. It doesn't make sense to start with a water gutter on one side and no one can really tell, if that is actually the lower side. If you cannot relate, maybe you have experienced this while driving: You thought you were going down or up a hill and as a matter of fact it was the opposite and even pretty much so. You could only tell by how your car reacted to your input on accelerator or brakes. Our eyes just cannot do that job.

So, to condense or compress the topography in a sense that everything is steeper than in reality is actually necessary for a construction game, if players are supposed to build something on basis of what they are able to see. This has numerous implications regarding game vs reality, the biggest ones being:
You need to allow players to build steeper than possible IRL.
If you want to apply physics, you need to factor in your compresssion, i.e. to define how your world should relate to reality. One would expect this to be linear (for physical reasons) and a whole-number (for reasons of how humans usually work, when doing modeling).

This is where the disappointment kicks in.
Dividing 10 by 2,73 and 1,57 results in 3,66 and 6,36 respectively.
If it had been a pretty precise 4, one could have worked on the assumption of that for further thoughts, but this seems just some random numbers, not a factor for modeling purposes.

So to conclude:
If assumed that the test of Vimpster is representative for how the game is programmed, then the following could be concluded:
- Tractive effort has not been implemented in the game.
- Real life physics could be applied to explain speed differences in the flat.
- Speed on slope solely depends on PWR.
- Slope physics do not transfer to real life, there is an unknown factor that has to be accounted for.
- There seem to be no driving resistances in the game.

This leaves me with two main questions and I am not sure, if I will look for the answer of them:
1. Why do they show us "tractive effort" in the game? It seems to be misleading only.
2. What are the game mechanics for slopes?
3. Are there and if there are what game mechanics are there to reduce top speed in the flat?

Thx for your input.
I think I will not put some further thought in it for a while.

I will put the main string of thoughts and calculations in a second post.

[mail]

Slope angle base line and calculations:
From analysis of the test results, it can be assumed with a high certainty that the tractive effort does not impact vehicle behaviour on slopes.
If the game is simplified furthermore to not inlcude any driving resistances, but stays true to real physics the speed in the equilibrium of forces is solely dependent on the PWR and the slope angle.
Train of thought slope angle:
So, if the calculation of slope angle matched the slope angle in the test in game, it would prove the following:
- There are no driving resistances in the game.
- Hill climbing is implemented according to real life physics with the known simplification that tractive effort is disregarded.

So, with a PWR of 2,01 kW/t or the weight of 497 tons and the power of 1000 kW, what is the slope that would lead to a speed of 27 km/h = 7,5 m/s?

2,01 kW/t = 2,01 W/kg = 2,01 Nm/(kg*s)
is the PWR that would lift any given mass by 2,01/9,81 m/s = 0,205 m/s
This would be the speed of a vehicle moving straight upwards.
Given above assumption there is no other work to be done with the power other than "loading" the vehicle with elevation energy, so the sought-after slope angle is the angle at which the speed of 7,5 m/s translates to a 0,205 m/s elevation.
Geometric relations:
Sought after angle position leads to right-angled triangle with an opposite leg of 0,205 and a hypotenuse of 7,5.
Applying trigonometric function:
sine of slope angle is 0,205/7,5
slope angle is arc sine of 0,205/7,5 = arc sine (0,02733)
Slope angle = 1,56628 degrees = 2,734 %

This seems way too small. Depending on source slopes in game are 5 and 10 either degree or per cent.
Checking forces for that angle and speed.
497 tons = 497.000 kg will cause a downhill force FA equal to mass multiplied with g and the sine of slope angle:
FA = 497.000 kg * 9,81 m/s * sin(1,56628) = 133.265 N = 133,265 kN
At 27 km/h = 7,5 m/s pull forces of trains in test are:
F= P/v = 1.000.000 W/7,5 m/s /// unit check: [kgm2s3 / m/s = kgm/s2 = N] ok
= 133.333 N = 133,333 kN
So this checks out. Also note that this is a higher value than tractive effort of weak train. So, there is visual and mathematical proof to the fact that tractive effort is not used to simulate train on slope in game.
However,
this was supposed to be the maximum track angle in game and it is neither 10 per cent nor 10 degrees, which I hoped to be the result. Neither is it an obvious fraction of 10. It is roughly one fourth of 10 per cent, but not close enough really to assume that the developers have introduced the factor 4 from this test.

[mail]

tl;dr:
Calculated slope angle following real physics is 1,56 degrees or 2,73%.
That is very disappointing and leads to more questions than answers.

If I haven't messed up, the behaviour of vehicles on slopes in game can not be explained with physics. There has to be some additional factor, table or array that is unknown or it just done with completely physics unrelated rules.

[mail]

OMG!!!!!

I have just found out that there is a tool tip when you leave your mouse pointer on the actual value of powerrating, e.g. over "mediocre".

It shows for flat, medium and steep, top speed, acceleration time and acceleration distance of the train.
So you can actually configure a train in the depot and know exactly how it will behave!

Did you guys know this?
Does it work?
I think I can work my way back to the game physics from that and then come up with the spreadsheet that I was trying to do.

[Vimpster]

Originally posted by mail:

Did you guys know this?
Does it work?
I think I can work my way back to the game physics from that and then come up with the spreadsheet that I was trying to do.

Yeah. I couldn't actually remember if it was in this game since I haven't played it in a while, but I knew it was in the second game. It shows you those stats when configuring the train and then also shows it in the vehicle details tab. However in the configuration screen it shows it based on being empty and in the detail tab it shows it based on it's current weight I think. It ends up being different in any case.

[mail]

Originally posted by Vimpster:

Yeah. I couldn't actually remember if it was in this game since I haven't played it in a while, but I knew it was in the second game. It shows you those stats when configuring the train and then also shows it in the vehicle details tab. However in the configuration screen it shows it based on being empty and in the detail tab it shows it based on it's current weight I think. It ends up being different in any case.

Thanks a lot Vimpster!
These values are only shown in the vehicle details tab in TpF1, and when you hover over the power rating "value", but I noticed that the "power rating" could change, e.g. from "mediocre" to "poor". Wasn't sure on what basis though.
Yeah, you might not remember or you might never have known for TpF1, because they hide them so well in TpF1. I might have never found them, if I hadn't read about it today. I really hover over a lot in every game and application, and probably even did over that spot before, but it seems they take longer to open than other tool tips as well.

But, really glad I know where they are now and you say they are good.
And empty for configuration and later based on current load. Well for TpF1 it always means current then, because there is only one place to see them.

You have helped me out a lot.
Thank you!