Another very telling Sunday. Instead of digging through the maths, I looked for reasons not to do it.
Part 1: Quick remarks triggered Eduard's excellent source1) It cites Wood: Principles of Locomotive Operation, 1925. The 1915 edition of this can be downloaded
here. I recommend it to all who feel locked out by all the discussion of Igel and other Germans. It's the US parallel and comparing it to Igel subtopic by subtopic would be a great project for anyone seeking a degree in history of technology or something like that.
2) Since the trigger to this quest here is a rather early design, I feel that it is important to take the historical context of each engine into consideration when trying to define its parameters of performance.
At the risk of looking ridiculous, let me fake an introduction to steam engine history so you know what I mean by shifting limitations.
The constant background is that for 150 years, people wanted more and more performance from engines. First engines had to justify their price against horses that could almost do the same unless traffic was really heavy. Last designs tried to show that they can do what Diesel engines do.
- First, internal friction plus balancing the rotating parts was an issue, so they preferred uncoupled designs.
- When they got that settled, they moved to 2, latter three coupled axles, even for fast running engines.
- Without clever arrangements for sideways shift of coupled axles and an understanding how to build that so the engine does not derail at higher speed, they could not go much farther that 3 coupled axles.
- Before the introduction of vacuum or air brakes, no one needed fast running engines that could carry a heavy train.
- High boiler pressure has always been a great thing but steel was not durable enough for quite a while.
- Superheated steam was known to be more efficient, but supply of suitable grease was a serious limiting factor.
- Compound engines were a great success for static engines and ships, but whether they paid off financially (counting in maintenance effort) in railway engines was debated quite to the end of their history.
- Maximum axle load was limited by the company's will to invest in better trackwork.
- Almost all engines were designed as improvements of an existing one. Changing as few parts as necessary meant substantial savings in maintenance but it sometimes reduced the degree of harmony among all the parts of an engine, thereby reducing the benefit from an improvement in some parts.
- Countless economical, political, geographical and social constraints hindered (and only sometimes promoted) progress.
- When they got all that settled, they found that gas dynamics and some other complex stuff matters in the most advanced engines. They only focussed on those, since there was the money.
- In the majority of cases, the reduction of maintenance cost was the one thing the operators cared the most. So staff were told not to take the engine to its limits in many ways (maximum pressure, pressure changes, steam production, sanding. And staff were not always motivated to take it to its limits in some other ways or to listen to the authorities (taking care of the firebed, building up steam for a prompt departure even if it is not sure whether signals will clear, sanding).
Looking at older engines, we are left at our own devices. They were defined by some of the limits on the above list and finding out which is the cornerstone of defining their performance.
This does not mean that dealing with the scientific findings at the end of the steam era is irrelevant. But without knowing the limiting factors, details of steam flow may not bear as much as those factors.
Some fun facts from good old Austria, to illustrate the above:
Military authorities demanded that all engines had an axle load of no more than 14 tons so in case of war, they could freely use them throughout the empire. Though this never had much bearing, even during WW I, saving every kg you could save was a distinct feature of Austrian engines almost into WW II.
This greatly increased maintenance cost as all this saving lead to various parts that wore quicker than desired.
They even left out some springs that would center the leading running axle, accepting the associated drop in maximum space, or else the load on that axle would have been to high.
During WW I, there was a shortage of high-temperature grease from the US, so they added a contraption that sprayed water into the superheated steam to cool it down again so the mediocre grease would not ruin the valves and cylinder. It was more feasible than taking out the superheater, I read.
One of the factories in Vienna had rather short traversers between their halls. They opted against taking down a significant part of them and produced engines that were not as long as they ought have been instead.
Austrian engines generally fired local lignite but those in the farthest south (that is now Italy and Slovenia) fired English coal that was shipped to Triest.
One of the railway lines was bought by French who brought in some French engine designs.
One company, facing rocky terrain, took a page from the Americans while the other copied the English. That was about the one thing they did right, if they changed idols, results would not have been as good.
The reports from trips to America in the 1840ies count with the earliest detailed descriptions of American railways that still exist.
https://archive.org/details/diebaltimoreohi00gheggooghttps://archive.org/details/dieinnerncommun00kleigoogOops, off topic now. But fun to read, if you love old-fashioned German and old stuff in general.
Part 2: How to take this to RW/TS2016?For me, it all starts with the train that the engine pulls. What you observe in the end is whether the engine succeeds in what you expect it to do. So all the performance is relative to the train and if the train is not set up properly, then setting up the engine properly alone does not lead to success.
There are lots of reports describing which engine pulled which train on which gradient at which speed. Of course, there are just as many remarks on how realistic these official "duty tables" were, some engineers outperformed them while others failed due to bad weather and other reasons without their influence.
I admit to being a bit grumpy about RW physics and I lost interest when half a decade ago I found that I could not find out whether loading a wagon during a scenario effectively changed the train mass due to the broken wheelslip.
Under the influence of the good people here I went back and unriddled a few things that I put aside until now. This was greatly helped by stock that I knew was set up with care (i.e., the one that came with the 50ies Riviera route).
The aim of the undertaking is to see how precisely you can depict the waggons & coaches. This degree of precision forms the baseline for any work on engines, for me.
To see the relative importance of each factor contributing to the TE needed, let's go back to my old-time, Continental perspective, just to compare the size of factors.
Rolling friction ... 3 (or about 2.4 in later years)
Gradient ... 10 for a 1 in 100 grade, 5 for 1 in 200, 25 on a mountain route at 1 in 40
Air drag ... v²/2500 as an example, which gives 0.64 for 40 km/h = 25 mph, but 4 for 100 km/h = 62 mph
Curve resistance ... 650 / (radius in m - 30) for tight curves giving 3.8 for a 200 m curve.
The sum of this is multiplied by the train weight. A loaded freight train weighs about three times as much as an empty one.
So on a level track, resistance is composed of 3 + 1 to 4 for air drag + 1 for a wide curve.
On a 1 in 100 grade, 10 is added to that, and air drag will become less of a factor as speed will go down.
On a mountain climb, you get 3 + 25 + 1 + 4 (25 permille, tight curves).
This means that the relative importance of each of these factors depends on the route you are looking at. Only mass matters all the time.
So how much off can we be in the simulation, for each of these influence factors?
Rolling frictionThe documentation on RollingFrictionCoefficient says it is multiplied with gravity and mass. So this is the old factor as in my old books - funny given that kg/metric ton is not exactly British.
I peeked into the files of a few new items of rolling stock to repent for talking about the 2007 default stock for too long.
[EK] BR Centenary 3rd Class 0.0015
[EK] Collett "Sunshine" Third - BR Blood & Custard 0.00087
same vor all Mk1 for all I see
[EK] 3Plank 0.001
same with canvas and for other plank count; same for van and bloater.
old Mk2: 0.00082 as in the documentation.
The numbers in the documentation where they quote Railway Magazine give 3.4 lbs/ton on my scrible pad, which would be 1.52 kg per metric ton, or 0.00152 kg per kg of mass. This ties in exactly with the 0.0015 found.
It does not tie in with the 0.0024 I would consider the lower end, by 60%. Now these Mk2/3 coaches must have roller bearings, so I cut out complaints here, but for the 4-wheeled wagons that certainly had none.
GradientThe good news is that most people use DEM data so the total climb in a real mountain will be as precise as you would care for. The bad news is that the DEM data is less precise as people may think and thus trick route builders in some local deviations that might cause wrong gradients. But by and large, I observe that the gradient profiles people find in books are no more precise that what people produce if they use a small portion of care. This is subjective, of course, but I need to plug in an unanimously positive note here.
Air dragDocumentation on DragCoefficient mentions halving that and multiplying it with air densitiy, which is 1 for all I care. Wikipedia says it is 1.225 at sea level and it depends on a ton of factors that RW certainly does not model, though it could: altitude, temperature, humidity.
However, it does not mention mass (nor gravity), so it must be a constant only multiplied by the squared speed.
Looking at the quote from Railway Magazine, I guess air drag at 0.00166 lbs/ton, which would be a factor of 0.00074 if you convert it to kg (force) per metric ton.
Multiplying that with some 32 tons would give 0.024. But that would be for velocity in mph. If velocity is in m/s, then my factor must be 5,06 as high. And I ought to multiply 9.81 to go from kg to N. But the docu does not mention that. Anyway, I end up at 1.19 then.
How does that tie in with the same files? Not at all.
[EK] BR Centenary 3rd Class 7.2
[EK] Collett "Sunshine" Third - BR Blood & Custard 1.5
same vor all Mk1 for all I see
[EK] GW Standard Van 2.04
[EK] Fish Van - Bloater 1.5
[EK] 3Plank 1.75
same with Canvas
[EK] 5Plank 1.2
[EK] 7Plank 1.5
Some stuff from the time when the docu was written:
Mk2 Second BR Blue 2.76 - true to the documentation !
5 and 7-plank had the same figures back then as now.
Going back to Igel, I find factors for the squared speed. I converted them to N for speed in m/s.
Frank: 0.038 to 0.056 depending on train length (longer trains are more favourable, of course).
Hütte: 0.032.
For a balance, I checked Wood mentioned above. He gives 0.001 lbf per ton for velocity in mph for the first coach, 0.0001 for an intermediate one and 0.00026 for the last. That would be 0.148 for the first and 0.0148 for intermediate ones. A 10 coach train should then see an average factor of 0.027 for each coach.
So if we multiply 0.03 by 30 (which is the lower end of the mass range for coaches), we get 0.9.
If we multiply 0.05 (which is near the upper end of Frank) with 33 (which is given for Mk1 and Collet in the .bin files), then we get 1.65.
So the 1.5 seen in the majority of the newer stock is close to the forumlas I picked. 7.2 will be a typo and 2,76 will go unexplained for the rest of the product lifetime, though we could theorise that multiplying it by 0.5 and air density as suggested in the documentation, one gets 1.69 which is a valid figure. Did the game do that back when it was new?
There are many formulas in literature that contain a linear factor on speed. You need to compromise when you map those and the linear factor is not exactly scientifically justified but rather pragmatic, which is why I did not mention them.
For vans, Frank quotes 0.052. The bloater's mass is given at 12 which results in 0.6. This is a fraction of the 1.5 set in the file, but using the same figure as for a coach is not implausible.
The standard van's 2.04 is even higher. Frank would say 0,37 if you would ask him but that is based on the mass of just 6.48 in the .bin file which is far out even for an empty one. Minimum tare of a GWR wagon I know is 7.1, and the German vans Frank tried were certainly more 10 tons empty, and most likely they were not empty.
Knowing that the models converned never ran too fast, I would not obsess over them as much as over the coaches.
For open goods wagons, there is a marked distinction between empty and loaded. Loaded ones have an air drag that is slightly higher than coaches and vans. Empties have horrible aerodynamics.
For empty open goods wagons, Frank's factor is 0.24.
For loaded ones, it he quotes 0.041.
Hütte gives 0.18 for empties and 0.029 for loaded ones.
Mass and (loading) capacity are:
3Plank: 4.8 and 8
5Plank: 5 and 10
7Plank: 5.2 and 12
So for the empty ones, Frank would suggest, if he knew RW, 1.152, 1.2, 1.248.
Loaded: 0.52, 0.62, 0.71.
Hütte would suggest 2/3 and 3/4 of that.
(In case someone cares, Hütte must be the journal "Die Hütte"; I skipped copying the page with the references back then when photocopies cost money.)
So, refocussing on the original of idea of finding out how much precision we get, we can say the following:
Not considering the mass, in contrast to historic literature, is a good move in RW. For all sorts of covered vehicles, you can enter a factor that gives N if multiplied with the squared speed in m/s. The current stock suits the assumption that this is right.
For open stock, you would need distinct models for loaded and unloaded versions if you care about air drag. I have no clue whether the game physics consider the loading state. If the total train mass does not add capacity to mass, then you necessarily need two different models or your train mass is 1/3 of what it ought to be. So air drag is a small issue then.
Also consider that these things fell appart before you reach any speed where air drag becomes noticeable. There are a few modern hoppers that run fast and are not covered, but who has precise air drag figures for those anyway?
Curve resistance0/10 is all you can say. You can go and excuse this by stating that modern stock goes through curves easily but no one will ever claim that curves have no cost. You could say that there is a hidden formula, but I want to see it before I cheer. More likely they simply dropped it.
There are a few positive thought on this that could be made up:
Clever designers of the original route sometimes reduced the gradient in curves to keep the TE required constant. If the person modelling the route does not know this, they will lay a constant gradient that will approach the TE required in the original.
Where the track is curved most of the time, without any straights, it often is inclined, too. In such a case, the gradient requires much TE and the curve resistance is just 10 or 20% of that. Routes that not as steep often have wider curves, too.
If there is a sharp bend between straights, it only affects part of the train.
In addition to the formular by Röckl which is the most commonly used one, there is one by Frank that takes the wheelbase into account.
wheelbase / radius * (180 - 1000 * wheelbase / radius)
For 200 m radius and bogeys of 2 m wheelbase, that only gives 1,7. This sounds much nicer, but applies only to coaches with bogeys.
For freight trains, the 1000 are replaced by 2000, most likely to cater for the reduced speed (and thus reduced issues in curves). Entering UK wagons of but 9 ft wheelbase, you get 2.1. But the wagons Frank sampled will have had an average wheelbase of around 4 m or so. For 3.5, 4.0 and 4.5 m, you get resistance factors of 2.5, 2.8 and 3.0, respectively.
This is still below the 3.8 that Röckl estimates. To arrive at that using Frank's formula, you need a wheelbase of 5 m for a 4-wheeled coach or 7 m for a 4-wheeled van. These are not unrealistic, around 8 m were en vogue for some time. Though these had axles that moved freely and adjusted themselves to curves.
MassI have a few drawings. It is clear that there were many things going by the same names, so the figures I found need not be the figures the modeller was looking at.
Goods wagons, found in .bin vs. found in GWR drawings:
3Plank: 4.8 and 8 ... nothing found
5Plank: 5 and 10 ... 5.7 - 6 and 10
7Plank: 5.2 and 12 ... 6.2 for a 5-plank, 12 ton china clay wagon
Van: 6.48 and 12 ... 7.3 and 12
Bloater: 12 and 10 ...8.6 and 6 (smaller, for meat); 8 and 10 (bananas);
No fish found on this harddisk. With all the ice, 12 tons are not unbelievable for me.
In general, I would increase the tare by some 10-20% in the stock I sampled.
No info on coaches that I could grab fast.
SummarySo how much precision do we get on the train side of things?
Rolling friction should be 0.0024 or more, found values range from 0.001 and less to 0.0015. I.e., I would almost double these figures if I were to fix all these files.
Gradients look very good to me, by which I mean that deviations between sources are as big as deviations between the model and the source used. But this clearly is a sweeping statement that cannot be true for all routes out there. And it can only refer to routes that are laid out with care by someone who knows of the importance of gradients.
Drag coefficient can be set correctly if your gold standard does not use a linear term in the formula. The coaches I checked looked mostly fine. For open wagons, you need two models if you care about the difference in air drag. For vans and wagons, I would suggest values that differ by under 50%. This would have small effect at realistic speed.
Curve resistance is simply missing. This causes an error of 50% when shunting, but only for those few wagons that are on curved track), and around 10% for an up gradient with tight curves, largely depending on the route.
Mass. You need different models for loaded closed vehicles (tankers, vans).
It needs to be found out under which circumstances the game handles the train load correctly (loading during the scenario, coupling during the scenario). If loading fails, duplicate models with different mass could provide a partial solution.
I would modify the tare by up to 20% if I were to edit all these files.
So of five factors, I see deviations between 10 and 50 % in three of them and they mostly add up: half the rolling friction, no curve resistance, sometimes reduced mass.
Much of that can be fixed, but the idea here is to point out under which circumstances your carefully tuned engine will be used. Of course, you can supply a set of equaly well tuned wagons with it, but you need to take that into consideration.
All that said, I must certify that the situation of the default stock I looked at is worlds from what was pretty normal in MSTS days.
(Edit: fixed Frank's figures on curve friction.)