Honestly, running the 306 laps till the tender runs out could very well prove to be an interesting endurance challenge. 24 Hours of Le Mans but for steam locomotives and their crews.
I have a question and the question is can you show how they might have loaded things like tank cars back when they were for creating the railroad and then Holly load tanker today that would be super interesting
That would be quite the challenge of endurance because you have to keep not only the water, fire and coal in check, but the pressure under control as well.
Now down by the station early in the morning there’s a whole lot of people line and they got a ticket on the train to yesterday it’s going to leave on time take on some water at the needleton tank and the struggle up a 2 5 grade and by time you get your hight pass the snow shed slide you had a ride on the silver ton. Here comes the silverton up from Durango here comes the silverton shoveling coal here comes the silverton up from the mountain see the smoke and hear the whistle blow 🚂🚋🚋🚋🚋🚋🚋🚂
I love how counter intuitive it is that the harder you work a steam locomotive, the more efficient it is. Unlike an internal combustion where the efficiency goes down the more you load it
That is only true in some cases. In this example the 491 is nowhere near its optimum performance level while 20 is working hard. It is like comparing a little 4-cylinder internal combustion engine to a V-8. Naturally the smaller engine uses less fuel.
Isn't a internal combustion engine more efficient at high load but low rpm? An ICE will indeed use more fuel at full throttle but will also produce more power. The gain in useful power will result in a lower amount of fuel per kWh produced. It's at least the case for petrol engines if I remember correctly because of the pumping losses induced by the throttle body. Maybe is it not the same for diesels because they run lean at low loads.
think of the superheater like a turbocharger. in a turbocharged ICE if you never get into the throttle/rpm enough to spool up the turbo, you never get the power and efficiency gains.
With the larger diesels common in trucks, container frame generators ect efficiency actually increases all the way to 100% load (the engine is still lean even at this point)... but its pretty flat from 65-70% upwards, and falls steeply below that. So the number one reason for excess fuel consumption is oversized engines. With the otto (spark ignited) cycles things are a little different, as in non-aircraft installations these engines almost always run slightly fuel rich (in large part for emissions reasons and the catalytic converter during low loads, where aircraft will often be lean). With typical modern compression ratio's its normal to require to retard ignition timing and/or enrich fuel mix further at high throttles to avoid pre-detionaiton (aka "knock", in this case "soft knock" which is where you have some pockets of fuel burning because of heat/pressure ahead of the main flame front, disruption smoothness of combustion, not "hard knock" where the fuel will be ignited before/without the spark plug firing at all). Soaking everything in excess hydrocarbons delays knock a LOT, but its also terrible for fuel economy, so for very small engines peak economy can be as low as 35-40% throttle and ~1/3rd redline RPM, but as engines grow larger or more optimized for high duty cycles these numbers grow, with something like a spark ignited school bus motor most efficient at maybe 70-80% throttle and 50-60% max RPM. That said in a vehicle you'll normally use less fuel per distance working the engine a lot less than ideal efficiency, because increasing speed increases drag far more dramatically than the extra idle fuel consumption for taking more time... which leads to the common misconception that car engines are economical at much lower loads than is actually the case, engines will tend to have good economy up to around their peak torque.. for a mustang GT thats 4,250rpm, its just also making a lot of power at that RPM which your mostly going to waste as brake heat at the next corner.
@malolavoue4717 I think another set of factors to consider is the powerbands of the motor and their relationship to load, fuel trim, and spark. I don't have any engineering expertise, but it seems that when the engine is working lighter but towards the powerbands (torque specifically) my cars seems to run better mileage. The only relatable thing I can think of is coming off the valve on a steam engine once you're rolling and coming up in speed to "trim" the amount of steam and everything else being used since the excess power is being wasted if not actually hindering performance.
I'd donate ten million, or give them the deed to the land behind the museum, just to see that. Then again, I'd also pay to have the entire layout reconfigured for dual gauge, so they can run more locos and rolling stock. Alas, I have neither.
We have a fun oddity at my railroad that our big 2-8-0 have to use more regulator and cutoff than our smaller 2-6-4T when pulling the same load. On paper the bigger engine have about 12.5% more tractive efforts.
"Railroad till you puke, baby!" That is definitely a Hyceism! Thanks for looking into this sorta thing; it seems to be the sorta thing that railroads and their employees thought about during the steam days and how the steam locomotives were designed and run. I do know that every railroad had to have "custom" steam power
I suppose this is also why steam locomotives were much more built specifically for a job seeing as a hardworking smaller locomotives are more efficient then a large do it all
Awesome subject and video Hyce! When I was firing the N&W 611 running the main during the 2015-2017 years, she would average 1 ton of coal and 2,000 gallons of water every 10 miles. But there are seemingly endless variables- average speed, wet or dry weather, outside temps, quality of coal, skill of fireman and engineer, etc.
The Peppercorn A1 class Pacific “Tornado” over in the UK, according to Top Gear (UK) Season 13 Episode 1, can burn 33 pounds of coal per mile at 75MPH.
Thanks for the metric conversions, makes things easier for a lot of us outside of the US. (Owning a US car I'm pretty used to inches and stuff, but never got the "feel" for fahrenheit degrees). Small hint on converting and using measurements in general by using a saying: 87.4199% of all measured numbers are suggesting an accuracy that can't be justified by the way those numbers were gathered. Meaning that for a three digit number you don't need to provide decimals anymore if you aren't into space missions or nuclear science. ;).
The only defense for F I can offer is that the degrees are smaller and therefore more accurate. For high temps just double the C to get the F. For low temps, multiply by 1.8 (or 2 if you're as lazy as me) and add 32. We hate it too.
@@alext8828 That's always the argument, but it's really meaningless. If I measure in tenths of a degree C, now my unit is smaller, and therefore "more accurate". So then you measure in tenths of a degree F, then I measure in hundredths of a degree C, etc.
TBF 491's boiler derate also hurts her efficiency as it makes it harder for her to hit superheat. I'd love to see you all fix that and bring her up to full spec for a K-37 again. But that's a "next overhaul problem" last I checked.
It would be interesting too see a comparison of Coal burners to Oil Burners. Specifically in Narrow Gauge. At OCSR we average about 10 gallons of oil per mile with our superheated 2-6-2 McCloud 25, which is roughly 70Lbs of oil per mile and Standard Gauge. compared to your 130Lbs of coal per mile on a narrow gauge 2-8-2. Would be interesting too see a comparison between the 491 and say a similar sized oil burner at Durango. also I just like oil burners more than rock burners. All Hail the Carbon Soup.
I would assume boiler size plays a part in this too. 491 has to heat a lot more volume of water than 20 does, and as you mentioned if 491 was truly working as close to tonnage as 20 was during the event it may be equally as efficient in coal/ton.
Mark this analytical video was fabulous! Among so many things to ponder, your video made me think about the square footage of the fireboxes. I was rather blown away by the size of 491 at 52sf. Having to fling coal over that much space is quite an operation. Makes me realize the kind of skill you must develop to stoke them. It also reinforces what you’ve told us in your earlier tutorials about setting up a fire in the firebox and developing a scooping technique. Loved seeing the superheater and all those tubes. So interesting to learn that Peaches doesn’t get a hard enough workout to superheat. Finally, great point about choosing the proper engine for the needed job. Visiting the roundhouse must have been like going shopping. Again Professor many thanks for this nerdy deep dive. Nerd out as much as you want we learn so much from these details. As always cheers to you!
@@Hyce777 I think it would be easier to measure using percentage of the tender at full (100%) and compare it to used water (100% minus airspace percent) then convert percentage to gallons/pounds.
on the furka pass i fire 600+800 HP compound engines, using about 700-800kg per day. that's 17km over the pass and back, engine weight being 36/45T and load between 55-70t it's a height difference on one side of 660m, the other side 810m. in that time i evaporate about 10 cubic meters of water. the maximum gradient is 11.8% in translated for the 3 countries worldwide that don't understand: coal consumption: 1500/1760 pounds Distance 21 miles loco weight 80'000/99'000 pounds train weight 121'000/154'000 pounds climbed height in a day: 4'822 ft water consumed: 2640 Gallons here's a video of a whole pass crossing: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-Hopge6rm3Ys.htmlsi=9h6raer8Wew1ZRcc
And I worked as a fireman on the Durango and Silverton narrow gauge railroad. I was always told that on a normal day we would shovel 5 to 6 tons of coal for the trip there and back. Which makes sense since the bunker held 8 tons and by the time the day was over about 3/4 was gone. It was a lot of work, but was sure fun!
Very interesting, well it’s historical facts that we need to continue to pass on to the next generation. Fascinating yes I walk near a steam locomotive my 5 year old self comes out lol these machines are awesome to see and hear.
Well interesting topic, but sadly no table for compare...would be nice to know the HP of each engine and the load...stats. Since some years I am a deckhand on a steam tug in Hamburg, named TIGER. Tiger: 17 m long, 40 tonnes water displacement. Compound HP (8bar)/LP (5-6bar) = 250 (at 110 RPM) Horses average, Marine Boiler, one furnace, 9000 Liter (12 bar) Tiger was built 1910, in service until 1966 at the port of Hamburg. Now we make cruises at the weekend. To get from cold to 12 bar, we need approx 12 houres and use 300-400 kg of anthrazite (from Brasil or Poland). On average we use 80-90 kg anthrazite per hour steaming through the harbour. The bunker capacity is around 7000-8000 kg. I know, you cant give exactly consumption per hour because its depends on how hard the engine is used, its like driving your car and pushing the excellerator... A video of Tiger: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-hlmg-70Loxc.html
i'm kind of astonished how the efficiency works out per pound of coal used to move a pound of load. You tell that to the pig headed execs at some of these railroads and I bet they'd switch to steam tomorrow. :P just don't bring up maintenance
HYCE love your videos. I worked on a 55ton Climax in WV for 20 years. We started with a 4 car train 153 ton running 11 mile round trip. We burned 500 lbs of coal per trip depending on the fireman. The firemen that lifted safety valves and made a lot if smoke could burn as much as 650 lbs. In the old days they would have deen fired for wasting fuel and water costing there company money.
1:55 I knew that locomotives were heavy and all, but for perspective: Number 20 at full weight is roughly the Maximum TakeOff Weight (MTOW, or how heavy a plane can get before it is literally to heavy to get off the ground) of an Airbus A220-100 (135k vs 139k pounds.) 491 on the other hand, is about the MTOW of a Boeing 767-200 (307k vs 315k pounds.)
Yea? The weight of the Number 20 is easily within reason for a 24 meter Scandinavian Lorry and wagon. (box truck+ trailer) 64.000kg. Even in most of Europe 40.000 - 50.000kg is just normal. Aircrafts are just stupid and a waste. It is bad enough derailing/running into a ditch or sinking! Aircrafts are all of that and worse! Even trains with there horrendous brake distances are better then a falling barely in control thing that is a aircraft. Anyways Number 20 seems reasonable in size and weight. 70.000kg - 80.000kg - 90.000kg? No big sweat. I mean 90.000kg is extreme overload for something built for a total weight of 64.000kg or at best 74.000kg. XD But possible to transport on decent roads even with standard equipment. Just asking for trouble but yea. 139.000kg? Now that is just insane! And it is a narrow gauge loco! 140.000kg is heavy enough to be a road transport nightmare even with good conditions, right special transport equipment and good roads! Like a Abrams tank is just 62.000kg or something! Even if a road can hold 2 trucks hauling 2 Abrams meeting each outer going either directions at the same time? It still would be 160.000kg+ on a single direction of the road. It starts to be ridicules when you start to question if the road is going to take it. Let alone bridges and the equipment on said road! Or told to calm down as the road is meant to be able to handle tanks being shuffled around with one going to the front and one being rushed back to be repaired! It is funny then to be worried about 200kg of overload weight. Being fined for 200kg overload! When the road/bridges is not even close to hitting the limits! Sure feels silly having to worry that refueling would be enough truly impact much. When you are not going to try and take off into the sky or something ridicules. Why back in the days overloading underpowered machines was just a slap on the wrist. Even driving without license where just the braking point for the popo! Fun times. Different times. I'm sure the TakeOff weight limits are just a matter of trying a bit harder to get off the runway. But then what do I know! 200kg might be enough to run into a ditch instead of taking off. Anyways 61.000kg of iron meant to be able to last 200 years or more? Sounds good to me! Aircrafts are meant to be as light as possible. Even the cargo of a aircraft is normally just humans or whatever fits in the load limits and pockets of people with to much money and no time to wait on shipments by ground/water. Much of the weight of a aircraft is in fuel. While a steam loco is mostly brutal and ever lasting. Machines that sticks around and useful passed our own lifetime is far more impressive then some flying thing in the sky. It is quite sad when you are told that a engine or something is going to stick around being useful passed your own lifetime even when very young. Aircrafts? Well... Not so much.
The issue with things like "running hard" is it is relative to the engine. A big engine running not hard can be running more and burning through more fuel than a small engine running hard. I would expect that with the same load being pulled, the larger engine would need to burn more fuel, because it is moving more weight, because it includes the weight of itself.
Statistics are cool! Information I never considered, but you bet some division Vice President was all about that in the day. Last night, I was watching The Proper People's "Abandoned Steam Engine Brought Back to Life! - 1908 Industrial Time Capsule" about a stationary steam engine that was used to pump water for a Massachusetts town water supply. At one point, the logs for the engineer from 1890 came out, and he was figuring 1.5 pounds of coal to pump 1.5 gallons of water. It was a fascinating show.
A recommendation for your testing from a boiler inspector's grandson; if possible have the #491 pull #20 with the same number of cars as you orginal test to see if that extra weight aids in superheating. The best explanation for steam locomotives is high torque variable horsepower.
At least once, you guys need to do a special event where you just go for an entire weekend, fill the tender Saturday morning, put tonnage behind 20, and only stop to swap crews until it's empty some time Sunday.
Really enjoyed this. You kinda confirmed some back of the envelope estimates I had made concerning how much coal one of my model locomotives would use on a run (if it were real of course) to work in fuel, water, and ash stops in my operations. I don't have near your eperience or knowledge, but I really enjoy nerding out about steam locomotives. Thank you!
Next weekend I’m going to Chicago for the Fall Steam Festival at the IRM. Gonna do some downtown stuff too. Looking forward to seeing Shay 5 and Frisco 1630, that’s gonna be real neat.
491: I've got a big appetite and I'll eat a lot. Feed me enough if you want to get up the line. 😰 20: I'm not asking for too much, just enough to get me through the day. 😊
Very interesting video Mark! So if you guys had to guess, how long WOULD it take for 491's superheaters to charge up to their rated temps? Assuming ofc, you had the necessary tonnage for her to pull and work hard at the museum
I remember one time riding on the Durango silverton narrow gauge, while stopped I remember them saying it took about 6 or 8 tons of coal to get halfway
Love your videos. On top of your steam production efficiency in relation to fire temp, fire temp would also directly affect your fuel consumption efficiency. Fuel would be consumed more efficiently at a higher temperature.
Thanks for the deep dive, Mark! Seeing p-V-T diagrams in college is one thing, but seeing how you actually implement it on a water tube boiler makes it so much more real and understandable. Always here for the nerd out.
Just found your channel today! Gotta say I love it! Ive asked myself this question many times. Every time I see a picture of a large 8 coupled loco on something such as a local freight I wonder if its just as efficient as using a smaller loco since its obviously working at less than full capacity (if all variables add up).
If you worked 491 hard enough to get significant superheat, she would be much more efficient than 20. Superheating exists because it makes the engine so much more efficient by increasing the temperature of the working fluid, allowing for a higher Carnot efficiency.
its fascinating to me that the superheater basically means nothing when running on the museum because in service, many companies found that superheaters did reduce coal consumption in the range of 10-15% I wanna say, though I'd have to verify and re-check my sources as I read this years and years ago.
@@andrewreynolds4949 Thats just not something I thought about before but after hearing it, "oh wow that makes sense, I'm an idiot for not thinking about that" a bit like Hyce and Gearing in the last Derail valley episode
@@KPen3750 There's a lot of mechanical stuff on steam engines that's surprising like that. Every small piece you see is like "oh, that's what that's for"
The Museum needs to buy more land if possible and make a hill on it and name it super steam slope and you can take 491 on it and get her into superheat
I have fired countless trips up Mount Washington in New Hampshire on the Cog Railway. We shovel 2000 ponds of coal per trip. It's a three mile run and it is done in about 55 minutes of running time. It is not uncommon to make three trips per day.
This was actually pretty cool and it honestly doesnt surprise me on the results. You use the engine best fit for the job which is why a lot of railroads kept the fuel efficient but weaker 4-4-0 running on branch lines up until Doodlebugs came along. They were the right engine for the job and were cost friendly and thats only one example out of many. Now in terms of fuel economy i always wanted to know under ideal circumstances (flat track no wind, burning efficiently and unloaded what would the potential burn rate be say per mile or hour. I also wonder if much like a car going 55-60 mph is there a speed at which the engine is the most happiest in terms of fuel economy. Your video did great but ive always wondered just so i really get an idea on how often these beasts had to stop for fuel. Loved your video and as always i look forward to more.
please do a video on the porters steam loco the cook mogul the class 48 tank engine the Japanese class d51 nick name hero of the railways. how do gear trains work something on saddle bolier tank engines one talking about the different types of steam funnles and there uses, a short video on how a Armstrong turn table works the different types of cut offs/reversers/Johnson bar some are a big lever, some are a big valve wheel, and ive also seen some that are like rods, one exsample is train sim world 3 and im not sure where to find the other reverser but a video on the different models of these and different whisle models would be nice
I feel like the one thing you left out was parasitic loss, it takes more coal to heat the larger boiler and it will shed a larger total amount of heat to atmosphere
I'd be very interested in seeing this same experiment run on the C&TS comparing the K-27, K-36, and K-37 #492, once that's up & running. I've taken the school classes and fired there, and the experience gives a whole new level of respect for the folks who did & do this every day (I envy them!). Thank you for taking this deep dive, it was most interesting.
Love the nerdy tech talks! It would stand to reason that a steam engine needs to be working hard to get into its peak efficiency. If it’s not working hard it’s wasting coal to produce steam that is not require to maintain speed.
Interesting! The tiny steam locomotives (narrow gauge industrial/quarry locomotives, weigh less than 10 metric tons) at the Efteling theme park in the Netherlands are coal fired and they appear very economical. Each lap (about 3km i think) they get fired only a couple small scoops of coal. It surprised me. They're not run hard, there's no grade and the speed is very limited.
I liked this one. NOW, how much water do both engines use in the 3 miles and how far can they go with the water they have on board before they need to take on water.
You can make the same efficiency arguements for something like passenger automobiles. When pulling a trailer, obviously the big truck will be more energy efficient than a small car; but when getting groceries, the efficiency flips, with the small car proving the better value in transport distance. Just about everything in our world works just like that. Air mail for a single package would be just a complete waste, but when transporting a full cargo haul, the energy usage vs mass transported makes more sense for the aircraft.
I wonder how frequent stops and starts figured into this, like on railroads with commuter service like the Boston & Maine (which also had long-distance trains)?
as a live steamer, i tell people on average in an average 4 hour run day. i typically go thru between a bucket and bucket and a half. sometimes two. but that depends on how many cars im pulling mostly between 4 to 5 cars maximum, whether or not i put people in those cars. each car weighs 300 pound a piece and probably close to 500 pounds a piece with people in them. but at least no more than a bucket and a half a day. so im probably not going thru as much as you guys go thru at the musueum
So what I'm hearing is that 491 could go all the way from Skagway to Whitehorse (107 miles) and partway back, on a single tender of coal. Y'know, if the WP&Y actually reopened the line to Whitehorse. 20 could go Skagway to Whitehorse and almost all the way back, maybe all the way back if she drifted down from White Pass summit. That's some perspective. Incidently, Robert Athearn's book "The Denver and Rio Grande Western Railroad" has some numbers from the early days of the D&RG, back in the 1870's. Using coal sourced near Canon City, one ton would last 85.29 miles, or 23 lbs/mile. Meanwhile, one ton of coal used by the Kansas Pacific (and probably the D&RG originally) from Fort Scott lasted 39.87 miles, or 50lbs/mile. Admittedly, this is with tiny engines like the Montezuma pulling similarly tiny trains, but it's an interesting comparison on the different grades of coal as well.
Well, that depends entirely on grade. Who knows what the usage is otherwise... if the WP&Y is alternating 3.5% up and 4% down every half mile for that distance, yup! Lol. It is a neat comparison. I'd love to get more data points such that we can come up with a "this much coal per mile per ton of train per grade percentage point" number.
Fascinating! I always wondered, and now I don't have to. I always wondered as I see the looonnnggg trains out in the desert southwest here is which would be more efficient, say a 2 mile train, latest diesel locomotive , 4 each or the big boy by itself which should be no prob for the BB. Sometimes I count 6 or 7 diesel locomotives on the long ones. Cheers!
Those range estimates imply that either locomotive would be able to perform at most, a single trip on my local railway line (i.e. terminus to terminus in one direction). Would coal useage rates change if you're running the locomotives over longer distances without frequent stops like you might do at the museum between laps? Or maybe the Victorian Railways locomotives just had larger tenders back in the steam train days haha...
Range generally shrinks with stops. While loading/unloading you want to keep the pressure up because pulling away is when you need most effort, so you're burning fuel to replace heat losses while covering no distance. Also, until you get up to your cruising speed you're accelerating and that's the equivalent of a hill climb so you're making maximum effort for less than maximum speed. I've seen locos with two tenders. I don't know if one was coal and one water or if they were both normal and got swapped over during a stop mid-journey to extend range where there were no facilities en-route.
Love your series. They are are all very informative and hands on, but I just have one little nitpick. Your title should read: How much COAL does a steam LOCOMOTIVE burn. Sorry, I'm a retired engineer. 😁
Actually thar discussion at the end brings up a question. What do you think range on a flat grade would be hauling load? How many water refills before the coal runs out?
Very interesting analysis! 😊 About as scientific as you can get short of a laboratory analysis. I guess the comparison between #20 & #491 as you guys are using them for this short train might be likened to using a VW Beetle vs. a Lamborghini Countac to drive a few blocks at 20 - 30 MPH for a trip to the local grocery store. 😊
seems like as the engines reach max tonnage and are working their hardest, they just run into the thermal effiencecy of heating water with an open flame
I was thinking that, all else equal, the small one might be more efficient based purely on the fact that, in my very non-professional and limited experience, higher temps/pressures/temperature gradients tend to provide better efficiency. Including car engines; gasoline car engines typically produce power most efficiently around 80-90% load and ~1800 rpm (give or take a few hundred rpm). This is one of the big reasons smaller car engines, all else equal, are generally more efficient; they spend more time closer to higher loads to produce the same power. It's neat that it turned out that way, and I suspect the big engine might be even _more_ efficient at producing power near max output than the small engine is, in part because of the superheating tubes, but also because of scale. (Note; more efficient at producing power. That is, fuel used per amount of power produced.)
"Railroad 'till you puke, baby." But what if it _wasn't_ the same scenery? Those machines literally were not engineered to go around a half-mile scenic test track all day. Just imagine taking them a hundred some miles across the actual territory they were built for.
I remember reading in a book that in the early to mid 20th century the CNR Transcontinental passenger train would typically burn through 113,000 pounds of coal running between Toronto and Winnipeg, a distance of about 2000 Km. Does that figure sound about right? Edited to add: I ran the numbers and it works out to 90 pounds per mile, so well in the ballpark. How's that for some nerdy calculations?
If my calculations are correct, this means on your oval - 491 emits about 13.4 tons of CO2 per 100 km - 20 emits about 6.4 tons of CO2 per 100 km For comparison, a petrol car emits about 19 kg of CO2 per 100 km. According to a quick research, in the US there's an average of 1.5 passengers in a car. Going on with those numbers, the steam engine driven train is more efficient than a car … - with 491 at about 1060 passengers - with 20 at about 505 passengers I'll assume some 50 people per car? If I guess correctly that's about four times a cars emissions for 491 and twice a cars emissions for 20. And that's under terrible conditions, in normal operations back in the day it would probably be significantly more efficient; after all, the engines were constructed for a different use profile than running in a small circle, stopping every other mile, way below tonnage. Now add to this the fact that a coal burning steam engine is probably the least energy efficient way of putting power on the rail and you see how ridiculously efficient railways are compared to road traffic. Organisations running steam trains over here in Germany report having carbon emissions of comparable size to cars. Now remember a steam loco reaches an energy efficiency of about 10 % under good conditions (coal to traction), modern electric locos and railcars reach values of up to 90 % (overhead wire to traction).
Later on in the video you explain how you always wanted a locomotive fitting the task to reach peak efficiency. In non-electrified rail networks like the US's that's presumably true to this day. Electric works a little bit different, though … from my own experience I can tell that having two locomotives instead of one makes the train significantly more efficient. One factor is that you accelerate faster which in turn means you can keep to a lower speed (meaning less air resistance loss) to reach the destination in the same time; but that's a relatively small factor, though it increases the shorter the distance in question is. That would be true with steam or diesel as well. But the other factor is the big, decisive one: Having twice the motive power means having twice the recuperative brake force. Ideally that's enough to get the train down to a crawl all by itself, before you need the air for the last few km/h. In other words: More power means more recuperation of kinetic energy back into the electric network. A modern passenger train with a decent power to weight ratio can get up to some 30, 40 percent recuperation. Pretty insane, if you ask me.
Okay, here's some more insight into electric train running. I can't get into too much detail about what line and what vehicle and so on because getting too specific would go into economical secrets of the company. But on a certain line with a modern electric train and running in both directions (so topography roughly cancels out) I end up with a net electric power usage corresponding to roughly 80 l of petrol per 100 km. The occupancy varies throughout the week and the day, but we end up at about half a litre of petrol per passenger per 100 km. So even if the electricity was generated from fossil energy (which it doesn't - our company runs on 100 % solar, wind and water), it would be ridiculously efficient.
40 per car in our case, but only for 4 of the cars, the last car is specifically for crew. I'm not sure how much CO2 they actually put out, that'd be interesting to do a study on. Thank you for doing the math! :)
I wonder how this would equate into HO Scale models, maybe a way to program a decoder to measure coal/water usage as an added operating skillset. & The next time I'm out to the museum I should give you a shout hi. :)
For a US midsized loco (Pacific, Mikado, Hudson, Consolidation) figure 150 to 200lbs of coal a mile and 150 to 200gals of water if your layout has grades (most do) 2/3 or half that if the tracks are flat like in Nebraska or Florida.
