Could steam engine fuel costs be measured in time rather than by distance?

[Matthew]

This is not a proposal or request for changing anything about Simutrans; it's a theoretical question about transport simulations, described in terms of Simutrans because that's what we all know here. That's why it's in the Randomness Lounge.§

The answer may be very obvious to those of you from engineering or physics backgrounds, or who have operated steam locomotives, but I studied humanities & social sciences, so it's very possible that I have overlooked a critical factor.

In Simutrans, vehicles typically incur maintenance on a per-km basis. That makes sense for many things. Any vehicle with tyres will wear them away more when it's moving than when it's stationary. Vehicles that use block brakes won't wear them at all when stationary. They further they move, they more likely they are to wear away the brakes. We can imagine corner cases like a train running from one side of a U-shaped valley to another that never needs to brake, but in practice a linear increase in maintenance costs per km makes sense for wear-and-tear.

However, my interest here is focused on fuel costs. For diesel, electric, and petrol vehicles, per-km also makes obvious sense. Whenever you are moving, you are using fuel; in the case of a single DC electric locomotive on a flat electrified line I would guess it is an almost perfectly linear relationship between distance and electricity consumption after the initial acceleration, right? I'd guess that an electric locomotive in a temperate climate wouldn't need to draw any power if it isn't moving (excluding the "hotel load" elements for cab lighting, dashboard instruments, etc.). If internal combustion vehicles come to a stop, whether that's because of an unexpected red signal or because it's time for a tea break at their destination, fuel consumption will drop dramatically. In the former case, the driver will probably leave the engine idling, but the fuel consumption is still likely to be far lower than when actually moving (a search online suggests about 25% for a car engine compared to travelling at ~100km/h, though it's obviously going to vary hugely). In the latter case, all these types of engines can just be switched off, so fuel consumption drops to zero. After you've had your cup of tea, you switch the engine on and again and it works just as well as before. There might be a small loss of efficiency for internal combustion engines in cold climates, but that's going to be a small factor, and perhaps there might even be some gain in efficiency in hot climates, because less of the fuel is being consumed by cooling systems when you start back up.

But for steam engines, the principle that you burn fuel while moving still holds. But the costs are going to be very different when you are stationary, in both the scenarios discussed above. When the footplate crew go for a cup of tea, the water in the boiler is cooling down and the fire is slowly dying down. If the locomotive has further duties, it will need to raise steam again and that won't happen instantly. Let's say that the fireman normally adds five shovels of coal a minute to keep the fire at an optimum level. When he comes back from his tea break, if he wants the loco to move soon, he might have to add ~seven shovels/minute to get the fire to hotter level that will the boiler steaming fast (though I think locomotive fire building is tricky and this won't always be optimal). If he's not in a hurry, he could just use the normal five shovels/minute to get there at a slower pace, but it will take longer to get to the required water temperature, so it's possible the coal consumption could actually be higher. I don't know which method is actually more fuel-efficient (presumably depends on variables like the boiler size and pressure that are going to vary between locomotives??), but the point here is that the longer the tea break, the more fuel you are going to need afterwards to get full power again.

If a steam train is stopped at a red signal, it needs to be ready to go at a moment's notice. You can't just switch the fire in a steam locomotive off and on again. It's going to carry on burning coal and the driver can safely allow some of that to convert into a higher boiler pressure. My guess is that for a short stop, you might get a small reduction in fuel costs, because the stoker stops shovelling, and when the train moves again, the driver lets the steam pressure fall back to its normal level. But for a longer stop, the stoker is going to keep on shovelling coal to keep the fire hot and the water boiling. It may not be quite our hypothetical five shovels/minutes, but the longer the locomotive is stationary, the more the driver is just going to be using her escape valve to let off steam while wasting just as much fuel as if her train was moving. Is the amount of coal required for that closer to four shovels/minute than one? I don't know, but presumably this question was settled long ago.

So in practice, I am wondering whether steam locomotives still need more or less as much fuel when they're stationary as when they're moving (I admit the phrase "more or less" is doing a lot of work there, but that's true of almost every factor Simutrans simulates). And if that's true, then theoretically wouldn't steam fuel costs be more accurately simulated on a per-tick rather than per-km basis? Again, I am not asking anyone to implement this (fuel costs for volunteer coders are very high!    ), but it does help to explain some of the decisions that steam railways took (e.g. clock-face timetabling was less common then, to keep locomotives working once the water had been heated).

§ When I was looking for an appropriate place, for a split second the the Steam board seemed the obvious place.... 

[prissi]

The fire in steam engines often burned all night when they were used the next day (although very low, with no one stoking it).

Heating water from 20 to 120° (depending on steam pressure) takes quite some time (high heat capacity of water). A stationary engine will not need much steam (more if it is in front of a train and if it had an electric generator or steam-powered brakes and steam heating lines).

The extra energy to make steam is released quickly. As soon a the pressure drops, more water is going over the boiling point (because that drops too with lower pressure). Only then heat is taken out of the system. Keeping the water hot enough does not need much steam. Thus, when an engine has to stop suddenly, they could even drop some fire on the track to quickly reduce the temperature and it will still stop with blowing off the steam until the temperature drops.

The fireman will only start to raise a fire shortly before departure be from then on he gets very busy.

In terms of Simutrans, you have monthly maintenance cost, which include also the personnel on stationary engines. (I read somewhere that a typical freight train engineer is driving distance in Germany on average less than three hours a day and otherwise is waiting/paperwork/etc. That engineer still will be paid monthly.)

[Matthew]

Thank you for taking the time to explain this, Prissi. Getting an answer from a professional physicist is better than I expected! I have been pondering what you said.

The fire in steam engines often burned all night when they were used the next day (although very low, with no one stoking it).

Heating water from 20 to 120° (depending on steam pressure) takes quite some time (high heat capacity of water).

Yes, that seems to be the critical point compared to internal combustion engines.

A stationary engine will not need much steam (more if it is in front of a train and if it had an electric generator or steam-powered brakes and steam heating lines).

The extra energy to make steam is released quickly. As soon a the pressure drops, more water is going over the boiling point (because that drops too with lower pressure). Only then heat is taken out of the system. Keeping the water hot enough does not need much steam. Thus, when an engine has to stop suddenly, they could even drop some fire on the track to quickly reduce the temperature and it will still stop with blowing off the steam until the temperature drops.

I never thought of dropping fire onto the track; I guess that's the steam engine equivalent of turning a diesel engine off. But that compounds the 'problem' in my OP: the more heat that is lost from the fire while stationary, the more coal will be consumed when the train is ready to move.

In terms of Simutrans, you have monthly maintenance cost, which include also the personnel on stationary engines. (I read somewhere that a typical freight train engineer is driving distance in Germany on average less than three hours a day and otherwise is waiting/paperwork/etc. That engineer still will be paid monthly.)

Yes, that accounts for part of the cost, and you are totally right that it is an entirely time-based element. pak128.Britain-Ex calculates fuel costs entirely in the per-km element so I didn't think about including fuel in the monthly amount.

[jamespetts]

I should note that the fuel consumption figures that I have managed to obtain for steam locomotives all tend to be based on weight of coal consumed per unit of distance, which is how coal consumption was typically measured. The amount of coal required to keep a fire hot enough to produce steam to run was considerably in excess of that required to keep the boiler hot enough to remain in steam when stationary. Obviously, some coal would be burnt when stationary, just like some diesel is used by diesel engines when idling.

[prissi]

There were quite some diesel engines in the 60ies, which were never turned off as ignition was a 1-2 h procedure. The German BR V60 hat 150 kg of coke for firing up the engine! (Until 1987 all engines were converted to oil preheater.)  https://en.wikipedia.org/wiki/DB_Class_V_60

And again, keeping a warm engine warm could be done by an overnight fire. So at 16h the stoker drove the engine to the shed and set the night fire. (Nothing spectacular, but one can see this sometimes on turntable pictures.) At 6:00 in the morning, he raised the fire, and the engine could leave with the train 30 minutes later. At least, that was what I had read on operation on small branch lines in Germany when there was still steam. Might change with engine size, of course.

What I had also heard of getting cold engines up to running (like on heritage lines), the times were rather measured in hours. That would not have been practical at all.

[jamespetts]

There were quite some diesel engines in the 60ies, which were never turned off as ignition was a 1-2 h procedure. The German BR V60 hat 150 kg of coke for firing up the engine! (Until 1987 all engines were converted to oil preheater.)  https://en.wikipedia.org/wiki/DB_Class_V_60

And again, keeping a warm engine warm could be done by an overnight fire. So at 16h the stoker drove the engine to the shed and set the night fire. (Nothing spectacular, but one can see this sometimes on turntable pictures.) At 6:00 in the morning, he raised the fire, and the engine could leave with the train 30 minutes later. At least, that was what I had read on operation on small branch lines in Germany when there was still steam. Might change with engine size, of course.

What I had also heard of getting cold engines up to running (like on heritage lines), the times were rather measured in hours. That would not have been practical at all.

My grandfather worked in a steelworks during the Second World War, and one of his jobs was to light the fire in the very small 0-4-0 industrial shunting engine that they would have there - that would take circa 3 hours to get into steam. I believe that larger locomotives take 5-10 hours to get into steam from cold (which would have needed to have happened regularly, as they would have to be washed out every week or two, which was a process lasting several days and needed to be done with the engine cold).