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Track types

Started by fam621, January 14, 2019, 06:42:36 PM

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fam621

Quote from: SuperTimo on October 22, 2018, 10:32:54 AM
From my understanding from my work, differential speed limits are usually related to signalling (although there are other cases such as tilting trains on the WCML and some structures). Generally they exist to allow a stock type to use a line for which the signalling has not been designed, or to get a bit more of an advantage out of rolling stock which has better performance than the current system. My experience of working on projects with multiple signalling systems is that differential speeds tend to be far more common in areas with 4 aspect signalling than 2 aspect or absolute block signalling.

Traditionally a line's signalling is designed with the braking distance of the slowest braking rolling stock in mind, which usually will be freight. However on busy commuter lines, such as the Brighton Mainline (BML) freight is relatively rare and designing the signalling to accommodate freight would comprise the headway of the line for little to no benefit. Therefore to enable freight to use the route a differential speed limit is created (BML uses the 2/3rds rule which states that freight trains are permitted at 2/3rd of the linespeed except where a specific differential speed limit applies). This speed limit will be calculated such that the slowest braking speed for any permitted freight consist will allow it to stop within 1 or two signalling sections (depending on the number of aspects that signalling system uses).

The opposite can also be true. In some cases a train may have a slightly better braking characteristics then the rolling stock that the signalling was designed for. As such certain stock types (usually multiple units or HSTs) can be permitted at a speed limit higher than line speed (normally only 10 - 15 Mph higher) in order to achieve slightly improved journey times. Such speed profiles were commonly introduced by BR in the 1980s when HSTs and Sprinter DMUs began operating on lines previously worked by loco hauled trains. In this case it was not economical to upgrade the signalling for the new rolling stock, but journey time improvements could be made by increasing the speed limits for the new stock to operate within the existing system.


This picture shows an example of a differential speed profile with a higher speed for DMUs (albeit with a non-standard sign)

It is possible that some features of the Permanent Way will require a differential speed profile, however from my experience this is not usually due to track curvature and more to do with weak structures. Freight trains exert considerable dynamic loads when travelling at high speeds and as such may be slowed to reduce the wear on certain structures on a route.


For example this extract from the National Electronic Sectional Appendix (this is available publicly by the way) shows the famous Morpeth curve at the top of diagram where the speed limit changes from 110 Mph to 50 Mph. Despite this being one of the sharpest corners on a mainline in the UK there is no differential speed limit as the signalling system can accommodate freight trains at line-speed.

From an in game perspective a lot of this should be represented by the signalling modelled in the game, however a useful feature could be to allow the player to chose a line-speed for a section of line. Often when express trains arrive into termni in cities it could be useful to restrict them to the speed of local trains to prevent them catching up too quickly and therefore constantly stopping and starting when they catch up with a slower train, the same can be true of freight trains when they are behind a stopping service, a lower speed limit for freight could reduce the need for them need to stop completely.

Taking this quote from another topic which I started a couple months ago. I've been looking at this reply that James got from SuperTimo and I found this very interesting. Because, I directly think that like higher permissive speed limit tracks should be a feature on Simutrans Extended and that weight/tilt restricted tracks should feature in-game to give people an option of running loco-hauled passenger or freight trains without the need to use track with a higher max, speed.

Vladki

OK, let me sum up what do we already have in simutrans:

Signals have speed limit that should be relevant to their visibility (e.g. dwarf, classic, cab signals).
Every way/track has a speed limit, and axle load limit; bridges also total weight limit. You can change the behavior in simuconf.tab:
# This setting allows the way in which weight limits are enforced to be customised.
# The meanings of each setting are as follows:
# 0: weight limits are ignored entirely.
# 1: then vehicles can travel over roads, rails, tunnels and bridges for which they are too heavy, but only at greatly reduced speed.
# 2: Vehicles cannot travel over ways for which they are overweight at all.
# 3: Vehciles cannot travel over ways for which they are more than 10% overweight at all, and will travel on ways for which they are up to 10% overweight at a greatly reduced speed.
#
# To revert to the behaviour of Simutrans-Standard, set enforce_weight_limits=0

enforce_weight_limits=3

Although I don't know what exactly is the "greatly reduced speed".
And we have tilting trains, that can pass curves 30% faster faster.

And what is in real world (Czech railways).
There are different speed limits for:
1. tilting trains - higher speed in corners (cca 35%)
2. 6 axle engines (Co'Co' or 3-3) - lower speed in corners (due to higher wear)
3. selected non tilting trains - slightly higher speed in corners (cca 10%) - perhaps those with better brakes and suspension, multiple units, with possible exceptions for given track,
4. cargo trains - lower speed limit only on some places, specially mentioned in track info.

Example here: https://cs.m.wikipedia.org/wiki/Soubor:Rychlostniky_Chocen.JPG
The basic speed limit is 80, some engines can go 85 (#3), 6-axle engines 70 (#2), and tilting trains 100 km/h (#1, the tilting speed sign is further back at the signal)

Out of those, we have #1 already implemented. #2 and #3 could be made as generalization of #1. Instead of binary value (tilting or not), could be a % that says how much faster or slower this train can go through corners.
#4 is imho for places where train weight matters like old bridges that do not match the axle load of the rest of the track. This is possible with setting enforce_weight_limits=1.
So far none of these are relevant to signalling - only to track geometry (curves), axle load, and train characteristics.

For signalling there is one important value: braking distance. It is a distance at which train should be able to halt. It of course depends on speed, and is defined:
400 m for speeds < 60 km/h
700 m for speed 60 - 100 km/h
1000 m for speed 100 - 120 km/h
1000 m for speed 120 - 160 km/h with cab-signalling
(higer speed is not allowed in CZ)
All distant signals and 3-aspect signals are built at this distance from next signal. If a train is not capable to break at this distance, it must reduce its speed accordingly. This is partially done in simutrans too. If you put the distant signal too close to the main signal (or not at all), trains will start braking earlier even if the signal is clear. Moreover, trains without cab signalling are limited to 120 km/h. So it seems that the 1 km distance is not enough for higher speeds, and cab-signalling gives you one more block (1 km) to brake. Of course trains do not have to start braking immediately after passing caution signal. The driver has to know how much he needs with given train. (That is also implemented in simutrans). 4-aspect signalling was used to increase capacity by using blocks shorter than braking distance (cca 1970-2010), now it is used only in stations, when you need shorter blocks due to track layout. Again 4-aspect signaling works well in simutrans.

So I think simutrans-extended has all this covered quite well. What exactly are you missing?

fam621

I am just trying to explain how like there are tracks which is limited for certain trains (i.e. on the Chiltern mainline) where past High Wycombe, there is 1 55/85mph limit the 55mph limit applying to freight trains and the 85mph limit applying to passenger trains (including those loco-hauled). So, in simple terms. I'm asking for a bit of track variation within the game as like there are also lines which have speed limits for heavier trains (i.e the Middlesbrough line) where there are speed limits which apply to the class 185s which are slower due to there weight and faster speed limits which apply to sprinter trains.

Vladki

As I said above, would not that be the case for enforce_weight_limits=1 or 3 ?
In that you can let overweight (freight) train on cheap track, but it will go slowly...

fam621

Yeah, thats the issue you see and I want to run loco hauled pass. trains but with the weight restrictions it seems impossible as they will run slowly.

ACarlotti

Quote from: mammothim2906 on January 18, 2019, 09:42:09 PMwhere past High Wycombe, there is 1 55/85mph limit the 55mph limit applying to freight trains and the 85mph limit applying to passenger trains (including those loco-hauled)
The 55/85 differential limit is due to different braking rates - the line mostly uses 3-aspect signalling which wouldn't allow (many) freight trains enough time to stop safely after encountering a yellow 'caution' signal. That line also has some locations where the speed limit differs for variants of the same class of DMU, depending on whether it has end gangway doors or not, due to door restricting visibility of signals in certain locations.

The way that Simutrans (Extended) handles this sort of speed restriction is different to how it is handled in reality. Firstly, Simutrans estimates the braking rate of a train and uses that to work out how fast it can go through a signal. This is a much more precise restriction than in reality, and allows each train to effectively have a different speed limit. Secondly, the speed limits in reality are generally chosen to be speeds at which trains can drive continuously without having to slow down until a restrictive signal aspect is seen. On the other hand, in Simutrans trains will quite happily run faster than this between signals, but will then brake on approach to signals until the driver can see that it has a clear aspect, at which point they will accelerate again. This behaviour is probably easier to program an use, but woudn't be applied in reality because it would have a significant detrimental effect on energy consumption.

Quote from: mammothim2906 on January 18, 2019, 09:42:09 PM(i.e the Middlesbrough line) where there are speed limits which apply to the class 185s which are slower due to there weight and faster speed limits which apply to sprinter trains.
As far as I can see (looking at the Sectional Appendix) there aren't currently higher permitted speed limited for sprinter trains on the Northallerton-Middlesborough line, despite what Wikipedia suggests. However, they do exist elsewhere, and the principle is still relevant. Perhaps what you want is a gradual reduction in speed limit for trains with an axle weight higher than that normally permitted - maybe something like 50% higher weight leading to a 40% reduction in speed limit, with anything exceeding this prohibited altogether. (I've just plucked those numbers out of thin air - better numbers would be required if such a feature were to be implemented.) 

fam621

Quote from: ACarlotti on January 19, 2019, 01:50:44 PM
The 55/85 differential limit is due to different braking rates - the line mostly uses 3-aspect signalling which wouldn't allow (many) freight trains enough time to stop safely after encountering a yellow 'caution' signal. That line also has some locations where the speed limit differs for variants of the same class of DMU, depending on whether it has end gangway doors or not, due to door restricting visibility of signals in certain locations.

The way that Simutrans (Extended) handles this sort of speed restriction is different to how it is handled in reality. Firstly, Simutrans estimates the braking rate of a train and uses that to work out how fast it can go through a signal. This is a much more precise restriction than in reality, and allows each train to effectively have a different speed limit. Secondly, the speed limits in reality are generally chosen to be speeds at which trains can drive continuously without having to slow down until a restrictive signal aspect is seen. On the other hand, in Simutrans trains will quite happily run faster than this between signals, but will then brake on approach to signals until the driver can see that it has a clear aspect, at which point they will accelerate again. This behaviour is probably easier to program an use, but woudn't be applied in reality because it would have a significant detrimental effect on energy consumption.
As far as I can see (looking at the Sectional Appendix) there aren't currently higher permitted speed limited for sprinter trains on the Northallerton-Middlesborough line, despite what Wikipedia suggests. However, they do exist elsewhere, and the principle is still relevant. Perhaps what you want is a gradual reduction in speed limit for trains with an axle weight higher than that normally permitted - maybe something like 50% higher weight leading to a 40% reduction in speed limit, with anything exceeding this prohibited altogether. (I've just plucked those numbers out of thin air - better numbers would be required if such a feature were to be implemented.)

Oops, I think I made a mistake with what line it was. It was the Scarborough line btw.

fam621

And just for some reference, this is where I kind of got what I kind of want in-game from: https://www.youtube.com/watch?v=Z7K43e5uwKc

Vladki

That is quite long video. What part is interesting?

As said before, if the limit is due to braking, then that means that the blocks are too short, and simutrans will already make the trains run slower (break earlier than at the signal). And that should force you to fix the signalling - either use 4-aspects, or make longer blocks. Also in real world, when train is assembled, its weight and braking capabilities must be calculated and compared with the tracks requirements - steepness of downhill parts and block length (or distance of distant signals), and the top speed might be limited if necessary. That is done by simutrans automatically, as if the driver always knows where the main signal is and know when to start braking.

This is interesting topic and made me study more about railways. In CZ freight trains are generally limited to 100 km/h - this can be enforced in the dat file for wagons. Only some can go 120 km/h when loaded, some others can go 120 km/h only empty. Every freight wagon has a table stating how much you can load it (at 100 or 120 km/h) in order not to go over the allowed axle load for given class of track.     A = 16 t/axle; B = 18 t/axle; C = 20 t/axle;  This makes it quite complicated. Part of that would be nice to have in simutrans. If the track (or road in general) to the destination is weak to support fully loaded vehicles, load them only partially so that they can pass. That would be nice addition to enforce_weight limits.

Also tracks support different axle loads at different speeds. As the freight trains are limited to 100 km/h, the weight limits usually apply to this speed. Passenger trains are usually lighter (and break faster) so they may go faster.  For example, Concrete sleepers B03 (252 kg) with rails S49 (49 kg/m) support 22.5 t/axle at 120 km/h but only 18 t/axle at 160 km/h. It might be nice to be able to specify set of weight/speed parameters for single way type.

To sum it up I think we could have these improvements:

- more pairs of weight/speed limits for each way
- instead of tilting 0/1, have a % how faster or slower can given train go in curves than "normal train"
- allow vehicles to load only partially in order to use weaker ways

However I do not see these as really fundamental problem.

fam621

Quote from: Vladki on January 19, 2019, 09:28:38 PM
That is quite long video. What part is interesting?

As said before, if the limit is due to braking, then that means that the blocks are too short, and simutrans will already make the trains run slower (break earlier than at the signal). And that should force you to fix the signalling - either use 4-aspects, or make longer blocks. Also in real world, when train is assembled, its weight and braking capabilities must be calculated and compared with the tracks requirements - steepness of downhill parts and block length (or distance of distant signals), and the top speed might be limited if necessary. That is done by simutrans automatically, as if the driver always knows where the main signal is and know when to start braking.

This is interesting topic and made me study more about railways. In CZ freight trains are generally limited to 100 km/h - this can be enforced in the dat file for wagons. Only some can go 120 km/h when loaded, some others can go 120 km/h only empty. Every freight wagon has a table stating how much you can load it (at 100 or 120 km/h) in order not to go over the allowed axle load for given class of track.     A = 16 t/axle; B = 18 t/axle; C = 20 t/axle;  This makes it quite complicated. Part of that would be nice to have in simutrans. If the track (or road in general) to the destination is weak to support fully loaded vehicles, load them only partially so that they can pass. That would be nice addition to enforce_weight limits.

Also tracks support different axle loads at different speeds. As the freight trains are limited to 100 km/h, the weight limits usually apply to this speed. Passenger trains are usually lighter (and break faster) so they may go faster.  For example, Concrete sleepers B03 (252 kg) with rails S49 (49 kg/m) support 22.5 t/axle at 120 km/h but only 18 t/axle at 160 km/h. It might be nice to be able to specify set of weight/speed parameters for single way type.

To sum it up I think we could have these improvements:

- more pairs of weight/speed limits for each way
- instead of tilting 0/1, have a % how faster or slower can given train go in curves than "normal train"
- allow vehicles to load only partially in order to use weaker ways

However I do not see these as really fundamental problem.

I mean ideally, I want there to be a feature where you as the player can set the speed limit of that line (track) so that in certain places. You can set the speed limit to a lower speed limit for certain places (i.e. terminus stations). But, I do understand where you are coming from.

jamespetts

Thank you for your feedback.

It is not clear what advantage that there would be to a player in setting a speed limit on a piece of railway line: a player always has an incentive to allow trains to travel as fast as possible. In reality, people who run railways set speed limits because, without them, the trains might crash because they cannot stop for signals in time, derail on corners or at least the passengers might be thrown around inside the trains travelling too fast around corners; however, we do not simulate any of those things in Simutrans, so the speed limits need to be imposed automatically to simulate what sensible people running a railway would do in reality to ensure safe operation.

The imposition of speed limits by players is a different topic to the issue of differential speed limits which I believe is where this topic began. Differential speed limits, as I understand it, are used where different types of rolling stock have different characteristics which allow them to travel safely at a higher speed over certain stretches of line, such as the ability of tilting trains to take corners more quickly or the ability of trains with better brakes to stop in time for signals spaced more closely together.

In Simutrans-Extended these attributes are simulated, not by a fixed speed limit imposed on a section of track, but by a dynamically calculated speed limit for corners and dynamically calculated braking distances for signals. This gives the closest conformity to the modelling of the economic effect of various features of railway operation (such as signal spacing, curve radii, tilting mechanisms, braking capabilities and so forth) with the minimum of complexity both to code and to interact with for the player. The thing to remember is that the speed limit for a particular type of track is not intended to be a representation of the line speed limit of an actual piece of railway line: it is intended only to be a representation of the fastest line speed limit that that type of track will allow. The actual line speeds are calculated dynamically taking into account all relevant features.

Remember, the goal of Simutrans-Extended is to be an economic simulation, not a computerised model railway. Operational details that have minimal economic impact and which would be complicated to simulate (e.g. the fact that, in reality, speed limits are calculated by engineers when the line is constructed rather than calculated dynamically by each passing train) are generally not represented.
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fam621

Thinking about all of this now, I was more thinking of being able to set speed limits, for it to be that like you can set low speed limits (i.e. 25mph (40km/h) on the approach to terminus stations and higher speeds (i.e. 125mph (200km/h)) on fast lines as such as opposed to making every single track being able to handle heavy locomotives.

jamespetts

Quote from: thegamer7893 on April 18, 2019, 04:19:50 PM
Thinking about all of this now, I was more thinking of being able to set speed limits, for it to be that like you can set low speed limits (i.e. 25mph (40km/h) on the approach to terminus stations and higher speeds (i.e. 125mph (200km/h)) on fast lines as such as opposed to making every single track being able to handle heavy locomotives.

Do you simply mean to suggest that there ought to be lower cost track with a lower speed limit but high weight limit available?
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fam621

Quote from: jamespetts on April 18, 2019, 04:28:00 PM
Do you simply mean to suggest that there ought to be lower cost track with a lower speed limit but high weight limit available?

Yes, in more simpler and in more thoughtful terms. I was originally focusing on making every track being able to handle heavy trains.

jamespetts

Quote from: thegamer7893 on April 18, 2019, 05:32:23 PM
Yes, in more simpler and in more thoughtful terms. I was originally focusing on making every track being able to handle heavy trains.

That might be worthwhile - do you have any data relating to low speed track capable of carrying heavier rolling stock?
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fam621

Quote from: jamespetts on April 18, 2019, 05:44:48 PM
That might be worthwhile - do you have any data relating to low speed track capable of carrying heavier rolling stock?

In terms of data, I have looked up such data, but could not find any proper info. to suggest this, but however in terms of lines which carry heavy rolling stock the GOBLIN and the North London Line carries heavy freight as well as the West London Line with the latter line having a max. speed of 60mph (97km/h). Although should a type be made, I would personally make the line have a max speed of 70mph (112km/h) to allow for better timings for passenger trains.

jamespetts

Quote from: thegamer7893 on April 18, 2019, 07:08:24 PM
In terms of data, I have looked up such data, but could not find any proper info. to suggest this, but however in terms of lines which carry heavy rolling stock the GOBLIN and the North London Line carries heavy freight as well as the West London Line with the latter line having a max. speed of 60mph (97km/h). Although should a type be made, I would personally make the line have a max speed of 70mph (112km/h) to allow for better timings for passenger trains.

Do we know whether the GOBLIN's restrictions are due to the quality of track itself or the curvature of the route?
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ACarlotti

Quote from: jamespetts on April 18, 2019, 08:20:51 PMDo we know whether the GOBLIN's restrictions are due to the quality of track itself or the curvature of the route?
Or a third possibility - due to the signal spacing and different braking rates.

jamespetts

Quote from: ACarlotti on April 18, 2019, 08:29:52 PM
Or a third possibility - due to the signal spacing and different braking rates.

Yes, indeed. Does anyone have any data on the relationship between the track itself and speed limits, controlling for such other factors?
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fam621

Both of those points do really interlink with eachover as I've travelled on the line and the track quality in areas isn't the best and the line has quite alot of curves which makes it for a curvy ride.

jamespetts

Quote from: thegamer7893 on April 18, 2019, 08:35:05 PM
Both of those points do really interlink with eachover as I've travelled on the line and the track quality in areas isn't the best and the line has quite alot of curves which makes it for a curvy ride.

Do you or does anyone else have any data on the relationship between the track itself and speed limits (data, that is, as opposed to a general impression, as I cannot get figures from a general impression)?
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fam621

Quote from: jamespetts on April 18, 2019, 08:42:14 PM
Do you or does anyone else have any data on the relationship between the track itself and speed limits (data, that is, as opposed to a general impression, as I cannot get figures from a general impression)?

Unfortunally after researching for a while for any data online, no. No data is available James.

Ranran(retired)

Is the amount of track endurance reduction of the current Extend based on the fact that the amount of track breakage of the track is proportional to the fourth power of the axles weight and the second power of the vehicle speed?

Currently, we have to lay high standard tracks in order to purchase heavy axles locomotive in the depot.
In the real world the yard and depot, we often see old rails with low standards being used for a long time without replacement.
It may make sense to reduce track wear and cost by intentionally limiting the maximum speed in such places.
ひめしという日本人が開発者達の助言を無視して自分好みの機能をextendedに"強引に"実装し、
コードをぐちゃぐちゃにしてメンテナンスを困難にし(とりわけ道路と建物関連)、
挙句にバグを大量に埋め込み、それを知らんぷりして放置し(隠居するなどと言って)別のところに逃げ隠れて自分のフォーク(OTRP)は開発を続けている
その事実と彼の無責任さに日本人プレイヤーは目を向けるべき。らんらんはそれでやる気をなくした(´・ω・`)
他人の振り見て我が振り直せ。ひめしのようにならないために、らんらんが生み出したバグや問題は自分で修正しなくちゃね(´・ω・`)

jamespetts

Quote from: Ranran on April 19, 2019, 10:42:43 PM
Is the amount of track endurance reduction of the current Extend based on the fact that the amount of track breakage of the track is proportional to the fourth power of the axles weight and the second power of the vehicle speed?

Currently, we have to lay high standard tracks in order to purchase heavy axles locomotive in the depot.
In the real world the yard and depot, we often see old rails with low standards being used for a long time without replacement.
It may make sense to reduce track wear and cost by intentionally limiting the maximum speed in such places.

Wear for roads is based on the fourth power law, but my research at the time that I implemented this feature (circa 2014) suggested that this did not apply to rail, so this uses I believe the second rather than the fourth power of axle loading. The speed at which the vehicles travel over the rail is not taken into account and to do so would require a substantial rewrite, which is not currently a priority. My research at the time did not suggest that the speed was so important that it needed to be modelled - do you have data to suggest otherwise?
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fam621

Quote from: Ranran on April 19, 2019, 10:42:43 PM
Is the amount of track endurance reduction of the current Extend based on the fact that the amount of track breakage of the track is proportional to the fourth power of the axles weight and the second power of the vehicle speed?

Currently, we have to lay high standard tracks in order to purchase heavy axles locomotive in the depot.
In the real world the yard and depot, we often see old rails with low standards being used for a long time without replacement.
It may make sense to reduce track wear and cost by intentionally limiting the maximum speed in such places.

In may cases, this is true as old track can get used for up to 50+ years without been replaced. But as James has mentioned, data is needed to suggest otherwise.

Ranran(retired)

First of all, I apologize for the fact that this topic has a lot of technical content so the English translation may be inaccurate. (´・ω・`)


This is an article published by the largest railway company in Japan. (Operates around the metropolitan area of Japan with a former national railway)
https://www.jreast.co.jp/development/tech/pdf_17/Tech-17-13-18.pdf

The second page of this article shows the percentage of rail replacement reasons, showing 45% damage, 18% fatigue, and 16% wear.
And it is stated that the representative of the damage is "shelling".
"Fatigue" is described as being calculated by passing tonnage.
"Wear" is described as a major factor in curve sections and bifurcations.



If you look at "shelling" that is represented by damage, you can see that this is likely to occur at high speeds.
It is stated that this problem did not occur when the train was at low speed.

https://bunken.rtri.or.jp/PDF/cdroms1/0004/2011/0004005490.pdf
In this document, it is described that in Japan, shelling has become prominent since 1973, nine years after the Japanese high-speed railway Shinkansen was opened.
The speed at the opening of the Shinkansen was 210 km/h and the conventional line was 120 km/h.


It is written that shelling is called squat in England.
http://hosenwiki.com/index.php?title=%E3%82%B7%E3%82%A7%E3%83%AA%E3%83%B3%E3%82%B0
And according to the contents written here, it is written that there is a doubled tonnage difference until shelling occurs on the Shinkansen and the conventional line.
Quoteシェリングの発生の仕組みはまだ解明されていないのだが、発生時期については、たとえば新幹線の場合、累積の通過トン数が1.5億トン程度になると、その発生確率は急増することが分かっている。在来線の場合は、追跡通過トン数が3.0億トン程度になると発生する。
(The current railways in Japan are approximately 270-320 km/h for Shinkansen, and 100-120 km/h for conventional lines.)

https://www.ias.ac.in/article/fulltext/sadh/009/04/0345-0369
I found the following description from above English documentation.
QuoteThe frequency of occurrence of these defects and their severity depend upon speed, curvature and axle load experienced by the track.


The fact that the amount of destruction of the orbit is proportional to twice the speed can be found here.
http://jtqsw192.nobody.jp/DOC/diary/dry0246.htm

Quote「自然に学んだ500系新幹線電車」
時速300キロの軌跡(7)  ,
元 西日本旅客鉄道kk   ,
総合企画本部技術開発室長
 同  試験実施部長
中津 英治氏 執筆
 (鉄道ジャーナル誌2010/06号p88右~)
 500系新幹線の車体の横板と床材に、このアルミハニカムパネルが使われている。これらも含む実践により500系電車は、車体重量が40トンという軽量化に成功した。この軽量化の意味するところは実に大きい。軌道に優しいのである。概括的に言うと線路、道路などの破壊量は車両速度の2乗に比例し、車両の軸重の4乗に比例する(米国アッショーテスト)。鋼体でできていた0系新幹線の重量は60トンあり軸重に換算して15トンであった。500系の軸重は10トンである。速度は時速200キロの0系に比べ時速300キロとなった。
The source of the information seems to be a magazine with descriptions by people involved in the development of the Shinkansen running at 300 km/h in Japan.
ひめしという日本人が開発者達の助言を無視して自分好みの機能をextendedに"強引に"実装し、
コードをぐちゃぐちゃにしてメンテナンスを困難にし(とりわけ道路と建物関連)、
挙句にバグを大量に埋め込み、それを知らんぷりして放置し(隠居するなどと言って)別のところに逃げ隠れて自分のフォーク(OTRP)は開発を続けている
その事実と彼の無責任さに日本人プレイヤーは目を向けるべき。らんらんはそれでやる気をなくした(´・ω・`)
他人の振り見て我が振り直せ。ひめしのようにならないために、らんらんが生み出したバグや問題は自分で修正しなくちゃね(´・ω・`)

jamespetts

That is interesting - thank you.

Simulating the effect of speed on wear would require a major rewrite, and, for my own work at least, that is not the priority currently, as there are many other more balance critical features that are of higher priority.

If this were to be done, what would be needed would be a formula, based on real world data, that takes as its input the combined axle loading of the vehicle expressed as a wear factor (as currently represented in the pakset) and modifies that wear factor on the way surface (not just for railways, but for all types of way, in a manner that is accurate for each type of way) based on the current speed of the vehicle. In other words, what is needed is a system that can be abstracted and applied to all vehicles on all waytypes at all times in history with a single algorithm. It would also be necessary to find a way of communicating this effect to users clearly and accurately.

Incidentally, I am having trouble downloading the PDF (although I am not sure whether this is in English or not).
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Ranran(retired)

QuoteWear for roads is based on the fourth power law, but my research at the time that I implemented this feature (circa 2014) suggested that this did not apply to rail, so this uses I believe the second rather than the fourth power of axle loading.
I suppose that the second is to the rail and the fourth is to the track(including sleepers and ballasts).
We need to consider the fact that we are replacing sleepers and ballasts, not only rail. Therefore, the same calculation formula is used for the road and the track.
Of course, their replacement period is different from the rails, but it is not necessary to distinguish them.
The ballast replacement cycle is said to be about 30 years in the Japanese Shinkansen, which is longer than that of the rails.
However, ballast maintenance takes place much more often than rail replacement. Add ballast and harden it.
After all, they are averaged and considered abstractly, just like roads.
Quote線路、道路などの破壊量は車両速度の2乗に比例し、車両の軸重の4乗に比例する(米国アッショーテスト)
米国アッショーテスト - This is likely to point to "American Association of State Highway and Transportation Officials's test".
And the article says that that formula was demonstrated in comparative experiments of 200 km/h and 300 km/h travel on the Shinkansen. (0 Series vs 500 Series)

I think you may need to compare with the reason you decide to be proportional to the second power of axles.
But if you do not need to distinguish the tracks, it only simplifies the code.

QuoteSimulating the effect of speed on wear would require a major rewrite, and, for my own work at least, that is not the priority currently, as there are many other more balance critical features that are of higher priority.
In Japan, we used to forecast the renewal time of the orbit by axle weight and passing tonnage.
However, they realized that the forecasting method was incorrect due to the fact that they degrade faster than expected when the trains are running at high speed.

If, as in reality, endurance decreases with speed, players will be able to reduce endurance consumption anywhere by using speed limit signs. It will also not be unduly reduced in durability for vehicles with lower maximum speeds.

I thought about preparing a low speed and durable track as a plan until it is implemented, but I think that it will not work well because it can not be overwritten with a track with lower durability. (´・ω・`)


QuoteIncidentally, I am having trouble downloading the PDF (although I am not sure whether this is in English or not).
One of them was difficult to download. It could be read when it was reloaded several times. But except for one written English, it is all Japanese documents.
ひめしという日本人が開発者達の助言を無視して自分好みの機能をextendedに"強引に"実装し、
コードをぐちゃぐちゃにしてメンテナンスを困難にし(とりわけ道路と建物関連)、
挙句にバグを大量に埋め込み、それを知らんぷりして放置し(隠居するなどと言って)別のところに逃げ隠れて自分のフォーク(OTRP)は開発を続けている
その事実と彼の無責任さに日本人プレイヤーは目を向けるべき。らんらんはそれでやる気をなくした(´・ω・`)
他人の振り見て我が振り直せ。ひめしのようにならないために、らんらんが生み出したバグや問題は自分で修正しなくちゃね(´・ω・`)

jamespetts

Thank you for your thoughts. I cannot now remember in detail the reason that I chose the second power law; I do not recall any of my research indicating a significance in the difference between rail and ballast/sleepers for the relationship between weight and wear; certainly in the UK, rail and sleepers are almost always replaced at the same time, and the ballast is usually replaced at the same time as the track, too (although sometimes track is reballasted without being replaced: but that is intended to be simulated as part of routine maintenance).

It would take quite a long time for me to go back to the archives from 2014 and piece together how I worked out the relationship between weight and wear. You might be able to find some posts in the forum discussing this if you look back far enough. As indicated, simulating this would need a specific data based formula, which I have yet to find (if there is one in one of the documents to which you have linked, I have not been able to download it and cannot read Japanese), and also a lot of time not only to rewrite the code but also to rebalance the pakset based on the new system.

Incidentally, I should note that it is possible to downgrade ways in Simutrans (both Standard and Extended) by holding CTRL while dragging the lower specification of way. It is in principle possible simply to implement track with a lower maximum speed and lower maintenance costs as TheGamer originally suggested, but I would need some data showing how much lower a maximum speed results in how much lower maintenance, at least approximately, in order to be able to do this.
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Ranran(retired)

#29
Thank you for the explanation.

Quotecertainly in the UK, rail and sleepers are almost always replaced at the same time, and the ballast is usually replaced at the same time as the track
At least in Japan, there is almost no case to replace them at the same time except when upgrading orbits. Because they have completely different wear rates. And, in the case of sleeper, the replacement cycle is long especially in the case of concrete, and there is a difference such as a short replacement cycle near the joint. It is not necessary to replace things that are not exhausted, and replacing them simultaneously is not always efficient. And now it is possible to replace only the error part by scanning the track condition.
In any case, there is no meaning to distinguish it in the game, and it is only necessary to average.


QuoteAs indicated, simulating this would need a specific data based formula, which I have yet to find (if there is one in one of the documents to which you have linked, I have not been able to download it and cannot read Japanese),
Quote線路、道路などの破壊量は車両速度の2乗に比例し、車両の軸重の4乗に比例する(米国アッショーテスト)
Translate this to the following formula:
Amount of destruction such as track, road = Σ(V^2 * Axles^4)
The second half is based on this:
https://en.wikipedia.org/wiki/AASHO_Road_Test
And it is shown by the example of the Japanese high-speed railway - Shinkansen that this applies to not only roads but also railways.
As mentioned above, high-speed driving made the deterioration of the track remarkable as seen in shelling.

However, the original AASHO_Road_Test has no description about speed. Certainly, if road take the damage of speed squared on the road, the German Autobahn will receive considerable damage, so it can not be denied that it may differ from the track.
The only fact is that the above formula has been proven in Japan's high-speed railways.

Quote
https://bunken.rtri.or.jp/PDF/cdroms1/0004/2011/0004005490.pdf
In this document, it is described that in Japan, shelling has become prominent since 1973, nine years after the Japanese high-speed railway Shinkansen was opened.
The speed at the opening of the Shinkansen was 210 km/h and the conventional line was 120 km/h.
I think that pdf you say can not download is probably this. This is only the episode that the Shinkansen encountered an unexpected track deterioration problem due to shelling after nine years of operation. But I think you can find literature on shelling and speed in English literature.  ;)



QuoteIncidentally, I should note that it is possible to downgrade ways in Simutrans (both Standard and Extended) by holding CTRL while dragging the lower specification of way.
Yes, I know that feature before and I think I talked about it on the mothball road topic.

Here's why I thought I was not good:
The problem is that in addition to its function not being accurate(not simulate actual speed), there are many points that are unfriendly to the player.
Overwriting is bothersome, and it's unclear why it can't be done. Especially Extended checks not only speed but also durability.
When thinking about that point, I think it would be better to issue a warning message like overwriting a station.
And it distinguishes two cases where the speed decreases and the durability decreases.
Also, it makes things inconvenient if you can not distinguish the appearance of the track. If it makes a distinction, the effort of the pakset author will increase.
However, these may not be necessary under specifications where speed accurately affects endurance. In that case, I think the effort to implement this is so wasteful.
ひめしという日本人が開発者達の助言を無視して自分好みの機能をextendedに"強引に"実装し、
コードをぐちゃぐちゃにしてメンテナンスを困難にし(とりわけ道路と建物関連)、
挙句にバグを大量に埋め込み、それを知らんぷりして放置し(隠居するなどと言って)別のところに逃げ隠れて自分のフォーク(OTRP)は開発を続けている
その事実と彼の無責任さに日本人プレイヤーは目を向けるべき。らんらんはそれでやる気をなくした(´・ω・`)
他人の振り見て我が振り直せ。ひめしのようにならないために、らんらんが生み出したバグや問題は自分で修正しなくちゃね(´・ω・`)

jamespetts

This is an extremely complex topic, which covers several issues, many of those with several sub-issues:

(1) whether it is necessary to add speed to the way wear formula, and, if so:
  (a) whether that should be confined to:
    (i) certain waytypes only; and/or
    (ii) speeds above a certain base level only (given that the problem was first noticed on high speed track, do we know whether a train travelling at 20km/h wears the track significantly less than one travelling at 40km/h?); and
  (b) exactly what that formula (or those formulae) need to be (for each waytype, if applicable);
(2) whether any additional data representing a way's susceptibility to speed as opposed to weight would need to be added to the ways' .dat files to simulate this accurately;
(3) to what extent that this mechanic can be simulated by simply having waytypes with a lower maximum speed and greater durability without changing the wear algorithm, and, if so:
  (a) whether the UI for downgrading a way needs to change; and
  (b) if so, to precisely what it needs to change; and
(4) if a formula (with or without additional data per waytype) be used, precisely how to communicate this formula to players.

Anything involving actually writing a new algorithm for way wear would involve a very significant amount of work (both in code and pakset), and is not something that I am likely to be able to do soon (as in, within the next few years).

As to the formula itself, I am not very familiar with mathematical notation, so I am trying to understand Σ(V^2 * Axles^4). I understand that the Σ is a summation operator, but since what follows is a single formula with a single product, it is not clear what is being summed - do you simply mean that this should be summed for each vehicle in a convoy? As for V, I assume that this is speed, but in what units should this be represented? As for "axles", is this axle load, or axle count, axle load per axle multiplied by axle count, or something else? Certainly, from the research that I recall, having a load of (say) 10t on one axle gives significantly more wear than two axles each with a load of 5t, so presumably this formula cannot mean to treat "axles" simply as gross axle loading? Or do you mean that, per axle, the second power of the speed (in km/h? m/s?) multiplied by the fourth power of the weight bearing upon that axle is the load upon the way? If so, does this apply universally, or only when the speed is above a certain threshold? Does this apply equally to roads, monorails, maglevs and trams? These are all things that we would need to know in order to implement this system in the game and have it balance properly.

I have spent a considerable time searching for, but have not been able to find, a discussion about the way wear feature when it was first implemented (2014/early 2015). I do recall that I had researched in detail the position, and had initially applied the fourth power law to all types of way, but found that I could not get sensible results with the fourth power law for rail, so had to revert to the second power law. I cannot now recall the details of this (and cannot now find any record of it being discussed), but what I believe that I found was that the railways would need to be renewed much sooner with the fourth power law than they would in reality under at least some conditions. What we now have does seem to give a fairly accurate and reasonable service life of railway line (do look on the Bridgewater-Brunel server to get an idea of how long that rails are lasting compared with the intensity of their use).

As to the proposed UI changes, may I ask in detail how you imagine that these might work? Again, I am not likely to have time to code these myself for some time, but it might be that you are able to assist with this. I am not adverse to an improvement in the UI for downgrading ways in principle, although I should prefer to avoid confirmation dialogues if possible, as this interrupts the player and their absence is a long-standing deliberate design feature of Simutrans.
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jamespetts

This discussion has reminded me of some research that I unearthed some years ago relating to the introduction of the High Speed Train in the UK, and about which I posted in 2013 here.

The relevant part is as follows:

Quote
...the additional speed caused the cars to lurch noticeably on encountering minor misalignments of the track. Thus, a major leap in the maintenance of track and the parameters of acceptable track geometry were required. Since track maintenance was historic:ally labor-intensive, the higher standards have led BR to introduce continuous welded rail (CWR), found extensively (ultimately ubiquitously) on high-speed lines, and to introduce new very sophisticated equipment to detect track wear and to replace manual labor in maintenance
activity. The network relays roughly 600 miles of track per year, and on the high-speed lines the new track is laid on concrete ties, now more closely spaced than hithertofore, and n a greater depth of ballast (Nock, 1980: 33-39).

By 1979, BRh ad largely completed the installation of CWRw ith heavy rail comparable to that used elsewhere in Europe (60 kg rail per meter/ll5 lbs a yard) and had made a lot of progress with ballasting and tamping machines to adjust misaligned track 0R J, December 1979: 42-44). BR also developed its own track recording car in 1977 (IRJ, March 1977: 29).

As a result of that research, Pak128.Britain-Ex does have a higher cost for the "high speed" track allowing more than 160km/h running.

For reference, the UK's "High Speed Train", originally branded the "Inter-City 125" travelled at up to 125mph, or 200km/h. This is, I understand, a very similar speed to the original Shinkansen, which, if I recall correctly, travelled at up to 130mph (or 208km/h).

The extract above (and the fact that the Japanese engineers working on the Shinkansen only realised that extra maintenance was needed for high speed lines after the Shinkansen had been running for some time) suggests that there may well be a threshold below which the speed of the vehicle makes only a very limited amount of difference to the wear caused by passing weight, although this is not entirely clear.

Nonetheless, it does in principle seem feasible to model this phenomenon by having more expensive track for high speed running. What is not yet clear from any data that I can find is the extent to which track for especially low speed running can be maintained and/or built at less cost than track for moderate speed running (quite aside from the other characteristics of the line that limit line speed, such as curves and signal placement). It is also not immediately clear how useful that such track would be - it might be useful, for example, for branch lines serving only freight of a type (e.g. bulk freight) where speed is of little importance, or for track leading to depots.

As stated, reworking the code to allow for full dynamic impact of speed on track wear would require more resources (both in pakset and code) than I currently have available and also more data (to determine how to code it, how to calibrate it in the pakset and whether this is worthwhile) than is currently available, but the lesser expedient (and what, I think, the OP was interested in having) may well be worthwhile if we can find some data on this sort of line (the weight of the track, the axle load limit, the speed limit and the relative maintenance cost, even approximately).
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Vladki

I agree that this is very complex issue. When I was looking for czech rails specifications, I found a lot of information - even materials from czech technical university - but I did not find definitive answer. What you have to consider is:
- rail types - most important is their weight in kg/m. Now the heaviest in use is 60 kg/m for main lines, and then 49 kg/m for less frequent tracks (local lines, sidings,...)
- sleeper types - wood/concrete and different weights. Wooden are not used now (due to lack of suitable wood). Concrete sleepers in use are 252 kg (only for 49 kg/m rails) and 304 kg (for both rail types)
- depth of ballast, precision of construction and maintenance. (Unfortunately I have not found more info about these).

In the information I found was that the lighter rail with lighter sleepers can be used at 120 km/h and 22.5 t/axle; or at 160 km/h and 18 t/axle
The heavier sleepers, can be used (probably with both rail types?) - at 160 km/h and 25 t/axle; or 220 km/h and 22.5 t/axle, or 300 km/h and 18 t/axle
If the lighter rail really can be used for high speed track, that would mean that the lighter rail is just less durable. But I doubt it can be (and most probably is not) used for tracks over 120 km/h. And there are no high speed tracks (>160 km/h) in CZ, except for the test ring. And according to czech rail map, there is no track for 25/t axle either. Some parts of main lines are made to high speed standards (to test the durability), but they do not use sleepers + ballast but a fixed concrete rail bed https://en.wikipedia.org/wiki/Ballastless_track

Anyway you see that the same rails and same sleepers still give several options of speed and axle load combo. However for practical reasons I think the railways have for each track only one pair of specs (speed + axle load). So the difference must be in ballast, precision and maintenance. Also in one article about speeding up czech railways I read that the tracks are often capable of slightly higher speeds (10%), especially for passenger trains, but at higher maintenance costs. On the other hand even a many years abandoned track might be still passable, if you clear the trees and go very slow (drive by sight).

Also the rail itself is very durable, and is often reused (maybe after some fixes). Outer rails in corners are worn out faster than inner rails, so they may be swapped before scrapping. Also old rails from main lines can be re-used at sidings, etc... But that is a bit off topic - it just could be used to reduce the cost of complete removal of rails (IIRC now it is the same as the cost to build it?)

Ranran(retired)

Quote(i) certain waytypes only
I think the current discussion is about railways. In the first place, the 4th power theory is for paved road, and if you think about it, you will see contradictions on the entire road. For example, damage to a bridge uses a completely different formula (12th power) and requires more maintenance. What data do you have for damage to none paved (such as dirt and gravel) roads?


Quote(2) whether any additional data representing a way's susceptibility to speed as opposed to weight would need to be added to the ways' .dat files to simulate this accurately;
I don't think it needs to add anything. Speed affects, and the influence of axle load on the railway is even stronger. Overall, the durability reduction amount at high speed is increased, and at low speed, the durability reduction amount is adjusted to be decreased.


Quote(3) to what extent that this mechanic can be simulated by simply having waytypes with a lower maximum speed and greater durability without changing the wear algorithm, and, if so:
  (a) whether the UI for downgrading a way needs to change; and
  (b) if so, to precisely what it needs to change; and
You will be able to simulate more correctly the fact that high speed trains require a lot of cost to maintain. However, the original aim is that those with slow actual speeds do not unduly reduce durability.


Quote(4) if a formula (with or without additional data per waytype) be used, precisely how to communicate this formula to players.
Isn't it an existing "way wear factor"? (Or a new one that is substituted for it)


Quotedo you simply mean that this should be summed for each vehicle in a convoy?
I quoted it from the sentence of the person who was explaining the formula, but it seems to be a constant for converting to the wear index. When used in code, it is the same as having to multiply by a constant to adjust the durability to reduce.
Regarding units:
The important thing here is that it is proportional to the square of velocity and the fourth power of the axis weight. Even if they are m/s or km/h, they are finally adjustable by a constant.


QuoteDoes this apply equally to roads, monorails, maglevs and trams? These are all things that we would need to know in order to implement this system in the game and have it balance properly.
As said above, I think that the fourth power theory itself currently used can not be applied to all roads. This is mainly used to estimate by car owners how much they damaged the road and use it as an excuse to take taxes and tolls, but it is not a real figure. There will be no problems in that example.


QuoteAs to the proposed UI changes, may I ask in detail how you imagine that these might work?
The player is warned of the reason why the overwrite can not be performed. like
"It can not be overwritten as durability decreases. If you want to overwrite forcibly, please execute while holding ctrl key."
If the player is informed that durability will be reduced, you can interrupt it before performing the overwrite, but if nothing is informed you may overwrite it without knowing it. It is his responsibility if he knows and did it.
And this warning message tells the fact that holding ctrl can overwrite lower orbits.
I think that there is no problem if only the maximum speed is reduced. However, players may be puzzled if due to durability.


About that formula,
I thought that it was an open fact, as I saw everywhere that the orbit wears out in proportion to the fourth power of the axle and the second power of the speed. So I asked about that first in this thread.
All of them are traced back to the source of the 200km / h and 300km / h comparative demonstration articles I showed above.
That is to compare the amount of track breakage of series 500 with 15t axles weight at a maximum speed of 200 km/h and series 500 with 10t axles weight at a maximum speed of 300 km/h.
(10^4*300^2)/(15^4*200^2)=0.44444
According to the above formula from the data, they seem to say that the Series 500 has succeeded in reducing the consumption of the track to less than half.
It is said that the Shinkansen had a hard time in maintenance work because it destroyed the track than originally expected.
It should be noted that the 15t axle weight is lighter than many Japanese steam locomotives before the arrival of the Shinkansen.
And Shinkansen used a different reinforced rail than usual. It was a 50T rail, but was later replaced by a 60kg rail.
So what do you think was the cause of damage to Shinkansen tracks more than with conventional locomotives? It is said that it has made maintenance work hard for a long time.

Yes, if you use the axles weight ^ 2 calculation, you get the same result as that calculation.
10^2 / 15^2 = 0.44444
However, does the passing speed of the vehicle not really affect the track?
The shelling example listed above denies it. Look at an example of a long-standing side line and the yard.
Yes, this is a very complex issue.
http://hosenwiki.com/index.php?title=%E3%82%B7%E3%82%A7%E3%83%AA%E3%83%B3%E3%82%B0
The fact that shelling has an impact on speed is documented everywhere. However, the details are not completely understood.

The train speed was raised from 120 km/h to 210 km/h by the Shinkansen in Japan.
If it is proportional to the square of velocity,
210^2/120^2=3.0625
The decrease in endurance is expected to increase threefold.
I think this represents a reasonable number.

What is the meaning of track durability in simutrans extended? Rail durability? Or durability of rail + ballast + sleeper? I thought that was the latter.
As mentioned earlier, the wear rates of rail, ballast and sleeper are different and the exchange cycles are also different. Therefore, much of the literature is only about the wear of each, and there is little to be said about their totals. The only thing that is found, and that is currently spoken of as a fact, is the V ^ 2 * Axles ^ 4 formula.
I thought that wear was proportional to the square might be wear of the rail, but I could not find such an article.



about balancing issue:
Quoteit might be useful, for example, for branch lines serving only freight of a type (e.g. bulk freight) where speed is of little importance, or for track leading to depots.
Yes, this is the part I care most about.

In the real world, sidelines and tracks around depots are not updated frequently. Maintenance is also not considered important. You will often find that the old low standards rails are used for a long time there.
Because it is not a track for the main route. The train never pass at high speed on it.
https://ja.wikipedia.org/wiki/%E7%B7%9A%E8%B7%AF%E7%AD%89%E7%B4%9A
In Japan's rules, the rules for tracks used in such places are very loose.

Pakset(Britain-Ex) balancing issue:
track:Maximum speed, maintenance and allowable axles weight are proportional. That means, if you choose a vehicle with a high axle weight, you have to choose a track with high top speed and high maintenance costs.
train:there are 95km/h freight wagons with 22t axle weight, 120km/h freight wagons with 26t axle weight, and 100km/h steam locomotives with 20t axle weight

To give a concrete example, please start the game in 1971. At that time, there are only wagons that can carry bulk goods with a axles weight of 22t. There are only wagons that can carry oil with axles weights 21t and 22t.
The only track it can pass is for the most expensive high-speed railways. This means that all the ore and oil transport line must be expensive tracks for high speed railways.
Was the real world really so? Did those wagons actually damage the track like a high-speed train on a high-grade track? Were those wagons which for ore and oil operated only on high-speed track in the UK? Also the yard and side line and pull-in line?


I understand that it is hard to implement a mechanism in which the speed of the vehicle affects the trajectory. The speed of the vehicle passing over the tiles is not always constant.
ひめしという日本人が開発者達の助言を無視して自分好みの機能をextendedに"強引に"実装し、
コードをぐちゃぐちゃにしてメンテナンスを困難にし(とりわけ道路と建物関連)、
挙句にバグを大量に埋め込み、それを知らんぷりして放置し(隠居するなどと言って)別のところに逃げ隠れて自分のフォーク(OTRP)は開発を続けている
その事実と彼の無責任さに日本人プレイヤーは目を向けるべき。らんらんはそれでやる気をなくした(´・ω・`)
他人の振り見て我が振り直せ。ひめしのようにならないために、らんらんが生み出したバグや問題は自分で修正しなくちゃね(´・ω・`)

fam621

I'll be brutally honest, all of this does take some reading and much understanding but if its gonna take long pieces of information to be able to have a heavy load low speed track well so be it.