Updated throughput graph

Changes include:
-Slider limits updated to new in game limits
-Optimized functions to make using the graph feel just a bit smoother
-Added more descriptions for velocity and friends
-Moved everything to make things topologically sorted, meaning the definition of a ...

Hmmmm.... I think I'll like this change.

For low demand fluids (lubricant for example), I think builds using the two systems would end up nearly identical. The difference is only noticeable for high demand fluids. When throughput isn't enough in the old system, you have to split the build into ...

I think it'd be funny if some of the ruins have to be demolished with explosives before you can place miners on them.

Yet another graph!
Here's what's different:

I learned how to make an actual approximation function for the inverse of stop point displacement. This didn't change the results of the graph at all, but is once again what I spent most of my time on.

I changed the train displacement over time formula ...

Graph number 5, 5 times the math, 50 times the effort, 5% more accurate.


I must confess, the previous graph was horribly, terribly wrong. My mistake was calculating throughput using the distance between two trains at a single point in time, which can vary over time, as I mentioned before. What I ...

Once you all are done over-engineering the solution, something on page 1 will be updated with the answer so others don't need to read through the whole thing, right? :mrgreen: :lol:


I can add a link to my newest graph to my first post, but I think the last part of my throughput calculation is ...

New graph 2, Remastered edition

-Updated Velocity and friends to be a tiny bit more accurate
-Changed v_max to show the right unit
-Added a formula for S_0 that looks to give a good starting point for Newton's method for all vanilla configurations.
-Added functions for average speed and distance ...

New graph 2, Electric Boogaloo

New graph, new model, this time including acceleration.

Velocity formula comes from something I did a while ago, I messed around with regressions to find a good formula for train velocity until I got something that was suspiciously perfect. I later looked up ...

New graph with more bells and whistles.

Added settings for reversed locomotives, artillery wagons (because why not), fuel bonuses, drag, and switches for m/s to km/h or trains per minute to wagons per 10 seconds.

Max throughput calculation now accounts for top speed due to drag or the speed ...

On a straight track with constant signal spacing,
with identical trains as close to each other as can be (train -> braking distance -> signal block length -> train),
and assuming trains move at a constant speed,
this graph on desmos should show how throughput varies with speed.


Train throughput ...

I can't wait to see what kind of horrors I'll be able to create in 2.0!

With deciders having infinite conditions, is it possible to make a computer out of one decider combinator connected to itself?
...ah, I'm getting too excited, you can't tie different outputs to different conditions can you? It ...

Getting the numbers for thrust and drag requires its own set of measurements and calculations that I'm not going to get into here.


I think you did it the hard way with measurements, but it may be possible to do using the fact that locomotive have 600 kw energy consumption which is 600 kg m2 s ...

TL DR : i was not able to reproduce the 10 ticks difference you mention


1-18 coal powered train:
Total mass: 20000 kilograms

Total friction: 34200 Newtons = 19 rolling stock * 1800 Newtons per rolling stock

Total braking force:
-No research bonus: 264600 Newtons = friction + 36000 Newtons ...

So... trains start braking 1 meter before a rail signal, effectively adding ~1 meter to the braking distance and changing stop time accordingly.

The good news is: This doesn't happen when a train is stopping at a train stop.

The bad news is: Now there's a ~10 tick difference between calculated and ...

Milo_Thatch wrote: Sat Oct 07, 2023 4:44 pm I made new measurements that are a lot more precise.

If you subtract 10 ticks from all your game time measurements, the friction model is the most precise across the board. I'm not saying the numbers are wrong, I see this as another clue for how to change the friction model.

Including friction perfectly accounts for the difference (1800 Newtons per rolling stock, or 0.5 after converting seconds to ticks).


To be fair, i'm not understanding all the method that leads you to this conlusion.


I made two braking distance measurements. For each measurement, I ...

I've re-traced my steps and cleaned up my spaghetti code. This is how I figured out that friction counts towards braking force.


Braking distance meter.jpg


I improved on knightelite's design for measuring braking distance by taking advantage of diagonal tracks having an irrational (square ...

TL;DR
FIX_TRAIN_UNIT_PLS.png

What?

This topic of utmost importance deserves my strongest argument: Your own math.

From the locomotive wiki page:

The speed of an accelerating, fully fueled, train is calculated every tick by the game with the following formula:

train_speed = max(0, abs ...

At first it seem line an horizontal line, with some variation due to roundings as my measurement were done ingame with the truncated speed value.

But on the right part of the graphs, there are several ticks during which the speed between 2 tick decreased less than all the previous tick. Meaning ...

As you can see, we can forget about air resistance and friction.

...

I made 7 measurements (gamespeed=0.05) for different train length (1:0, 1:4, 1:8, 2:8) and varying braking research (1 or 7), starting at 298km/h (nuclear fuel).
Between the game and my program, all results were within 10 ...