Train Engine Acceleration

[akuenzi]

I've been experimenting with RRT2's engines trying to learn how far (in terms of numbers of map cells) each one will travel per month or year on a particular grade carrying a particular weight. Naturally there are numerous iterations of this, and it's been fun, but I'm wondering if someone here that is far smarter than me (which shouldn't be very difficult :)) would know how to calculate an acceleration curve, one that is expressed in terms of mph by distance. This would greatly shorten the amount of time it takes to research this.

Here is a typical string of data I can get out of the game. I don't remember which engine this is, but here it is:

Cells Speed (mph)

------ ----------------

0........................0

1........................4

2........................7

3........................8

4........................9

5.......................10

6.......................11

7.......................11

8.......................12

9.......................12

10.....................13

11.....................13

12.....................13

13.....................13

14.....................13

15.....................14

At the 15th cell the train has reached its maximum speed of 14 mph. I know technically the chart should be mph based on elapsed time, but it�s nearly impossible to get this data from the game. Even the data above isn't perfect, and likely only rounded figures at best. A time factor could be interpolated using some of the acceleration formulas that are out there. However, knowing this still wouldn't solve the question as to how to calculate this basic curve. Given the number of cells on the left (x), what equation comes up with speed in mph (y) on the right?

The curve is going to change based on weight pulled, the grade of the track, and the type of engine involved, but if I knew the formula, these other pieces would likely fall into place more easily.

So, is there a math genius lurking somewhere on this board that can put this in simple terms that even I might be able to understand? Calculus is almost twenty years into the past for me, and I never took Physics.

[jeffryfisher]

I'm not sure that there's enough information there, since we don't have a conversion from "miles" into cells.

For constant acceleration:

d = at² / 2

v = at

But you need consistent units before you can compare the two.

[akuenzi]

I'm not sure that there's enough information there, since we don't have a conversion from "miles" into cells.

I agree -- that does seem to complicate the problem. However, from everything I've seen, it doesn't matter what the scale is, the train speed is going to be the same. If it's a map of North America, the scale might be 5-6 miles per cell. If it's a little map of some 20 square mile region, it might be less than 1 mile per cell. Either way, the game data is going to say that after X cells, the speed is XX mph. So, I approached this by simply looking at distance as 'numbers of cells,' kind of leaving it generic rather than in terms of miles, since we don't know the scale for which the game was designed... or do we? Does anybody know what 1 map cell is supposed to represent? Maybe I should try to convert the speed from miles-per-hour to cells-per-hour.

I have seen the formulas you gave and have played around with them using data I've taken from the game. I do think the time can be interpolated using them, as well as the rate of acceleration. However, if I'm calculating things properly, it doesn't appear to yield a constant rate of acceleration, so I'm back to the same problem of trying to determine the formula for a curve.

I've looked a number of places online, and there seems to be some very complicated formulas for locomotive acceleration and tractive effort, and a number of other things I only marginally understand, as well as some high powered mathematics to boot (integral calculus). I suppose in the case of RRT2 it's a matter of simply trying to guess the formula the game maker used.

[jeffryfisher]

In game terms, "cells per hour" becomes "cells per month". If it's possible to run a train at constant speed for an entire year, then we can get a more precise conversion rate.

The game does have engine parameters for both "acceleration" and "traction". I'm still not sure what traction does. I would really like to see the source code on that one.

One hint I have is that a powerful late engine like the T1 was able to spin its wheels when starting from a standstill. Engineers had to be careful with the throttle at low speeds. However, at higher speed, the engine could pump out more of its power without exceeding tractive effort. That's the physics of power versus force.

[akuenzi]

The game does have engine parameters for both "acceleration" and "traction". I'm still not sure what traction does. I would really like to see the source code on that one.

That's interesting -- I'd seen the parameters for 'acceleration,' but I must have missed the one on traction.  I thought the other parameter was 'reliability.'  Hopefully I'm not asking about something that has been sitting in front of my face this whole time, but where do you find the information on 'traction?'

[jeffryfisher]

I think Hawk & Badger has engine data files. Links exist in other threads around here somewhere.

[Hawk]

I think Hawk & Badger has engine data files.

The loco data files are on the same page as your map building guide Aden.  ;)

http://hawkdawg.com/rrt/rrt2/rrt2.htm

[akuenzi]

Thanks, Hawk.  I looked there, but the files don't appear to say anything about traction.  :(  Well, maybe someone else knows where this might be.

[jeffryfisher]

I guess it's time to upload what I've gleaned from the EXE file. See the modding RT2 thread.

[akuenzi]

That's an interesting file you uploaded, Jeff. Thanks for sharing it! It contains information on the trains that is similar to some of the information in the file on Hawk's site, which is a 'locomotive table' dated 4-25-99. This table has three columns in there that are confusing to me, and I was curious if anyone on this board knows what they mean. If you download the file, you'll see these columns over to the right. I put in the values for the top engine, the 'mighty' Trevithick for conversation purposes:

2% Drop 4

Acceleration 50

Fuel Cost 321

Does anyone know what '2% drop' means or where this term came from? Jeff had this same term in his spreadsheet, but he told me that it didn't come from the game. He got this term from the spreadsheet on Hawk's site. I can understand that the term relates to how the engine behaves when the grade increases, but what is the genesis of the term? Is this really what these numbers are supposed to represent? If so, it probably has clues to what I'm trying to figure out with train acceleration. And does anyone know what '4' means, if it is in fact related to how the engine works when the grade changes? In the same spreadsheet, I noticed that the 3-Truck Shay has a value of '50' in this category. The Shay seems able to pull mountains and still maintain its speed well on the steeper grades. I guess we can infer that the higher the number, the better the engine performs on the grade with any given weight. But does anyone know how to quantify this?

What does 'Acceleration' mean? The Trevithick has a rate of '50,' and later the Maglev has a value of '7.' So, I guess we can infer that the lower the number, the quicker is an engine's get-up-and-go, or the faster it can reach its maximum speed. Does anyone know how to quantify how quickly that happens with these rates? Probably more clues with what I'm trying to figure out in calculating acceleration rates if only I was smart enough to be able to back into the data with these. :)

And then there is the 'fuel cost' column. This column seems curious, because it is different from the information the game gives. What does '321' mean in the case of the Trevithick? It can't be a cost per month, else the total fuel cost for the year would be $3,852 ($321 x 12) versus the game amount of $3,844. Maybe that example is too close -- a better one might be the DeWitt Clinton. The spreadsheet has a fuel cost of 250 ($3,000 annually if this is in monthly dollars) while the game says it's $7,676. Any guesses as to how this number works?

[jeffryfisher]

I know that an engine will burn less fuel when it's waiting versus when it's moving, so the formula is probably complex, depending on both time and distance.

If it had been up to me, I would simply have burned some number of fuel units each time the engine entered a new cell. Maybe the game also burns a number of fuel units each time the engine increases speed, and that number may depend on total train weight. That could make it expensive to stop and start heavy trains. Climbing grades might be costly too.