these last couple years or so I've become interested in the engineering and history of rail transport: this has to do in part with local political and historical considerations, but also with the fact that they're just cool. This has brought me to the reflection that, in conworlding, we rarely pay attention to supply chains and the technologies utilized for production and moving around of goods and raw materials. Turns out rail transport, in the most lato sensu of having wagons that move around on some sort of rail <as opposed to moving around on a flat surface>, is just fantastically old technology, five thousand years ago or something like that. Of course, in principle, a conworld might as well never have developped it: the ancient civilizations of the american continent, while well aware of the concept of the wheel, don't seem to have found much use for the wagon: this is possibly to do with the local geography, possibly with their not having domesticated burly beasts of burden. Nevertheless they managed to achieve all of the classical "milestones" of civilization, such as writing and monumental architecture and all the rest of it, if that's the sort of thing one were to care about. Still, wagons are useful things to move stuff around on. this is intuitive enough.
Slightly less intuitive, though, is rails: ¿what's the deal with rails? like... I don't know, call me american or product of the de-trainification of my native country, but growing up I was always confused about trains: sure, they looked nice, but why did they run on *rails*? isn't it impractical that you can't run on roads? isn't it annoying to not be able to steer? who wants to roll over steel, anyway? don't you get problems with very low traction? You see, it's a natural, logical progression.
You need to transport 100 kilos of fruit: it's going to rot here, but back home mom can make it all into jam and, thus, make it stay edible for a long time. say you have a wagon all made out of wood<or whatever other similarly useful material, like seashells or rocks or horn or whatever you want that's hard and plentiful enough to be fit for purpose>: you pull it across a fairly flat field an things are good. it's much easier to pull the fruit on the wagon that to chuck them on your shoulder: for one thing, you *can't* carry 100 kilos on your back, but the wagon can. It's work, but it's doable. But the next day it rains, and the wagon is no longer working: or, rather, it does work, but it sinks into the mud so much that all the effort you're putting into pulling the thing is being wasted on scramblingh the mud around instead of, you know, getting mum her fruits. this gives you the basic intuition that informs rail transport: the concept of rolling resistence.
Seee in principle, if you had a very rigid wheel and a very rigid road, a very smooth and lubricated bearing on which your wagon rests, and so on, it would be very easy to move things around. Now that the road has become soft and plastic moving the wagon is night impossible. this principle is useful to have in mind: the stiffer the whole thing is, the easier pulling the wagon is going to be: this of course, as you found out with the mud, includes the rolling surface but it also includes the wheels themselves: just like the road deforms under the weights of the wheels, the wheels also deform under the weigth of whatever they bear, sandwitched as they are between your wagon and the ground, and that deformation also requires energy. You can make things better for yourself by stiffening up your wheels: making them, you know, out of something stiff, like wood, and put spokes on it so that it'll bend as little as possible. and maybe even put a nice layer of something even harder, like iron, around the wheel to protect it from stuff and make the wheel last longer. stiff wheels are just ace! they make life so much easier, but still, it's no good for your wheels to be stiff if your roads are all soggy and wet and soft.
The natural solution to this problem is to make a road of as hard and smooth a material as you can. you need to find a material that is at once very smooth and very hard, that doesn't deform under pressure and that can bear the punishment of, well, people and horses and wagons walking all over it.
One choice is rammed earth: we call this a dirt road and, honestly, it's not amazing but it works, you know, fine: it's much more pleasant to walk on it than to make your way through underbrush and thorny berry bushes and the like. Still, it gets muddy with rain and if people don't walk over it, keeping the earth rammed, then things will grow on it and it'll eventually become, well, a part of the forest or field or shrubland or whatever natural environment you happen to live in. But what if we cook the earth? well, yes! this works, it's called bricks. bricks are somewhat brittle and they break, but brick roads do, in fact, exist. how about stone? yes! stone does work and stone paved roads are, in fact, the gold standard of road paving quality throghout history: the romans, the tawantinsuyu, chinese, everyone who was a big an powerful empire made stone paved roads. paved roads are just ace.
Okay so the emperor built a very hard, very smooth stone road and you're about to move your cart over it to the next village, where mum lives. Well you see there's a problem with hard, smooth roads, and that problem is grip: you never had to worry, on your dirt paths, about your wagon slipping around and going where you didn't want it to go, did you? you actually had to work hard to make it go anywhere: but now, as the rolling resistance is lower and lower your wagon just slips everywhere. especially when it rains! this is horrible! oh, how will we get mum her fruits?
If your supply chain is not that important or high-volume, that is to say, if it's only from time to time you need to get a little bit of fruit to mum, then you leave well enough alone: the road is not perfectly smooth, it's just mostly smooth: and that's better, honestly, cause then the wheels have enough friction and resistence and so on that your wagon doesn't fly away from you. but what if it's a veeery high volume, very important road where everyday, all day, people need to be moving goods? for example the way from a port to a city or something?
turns out the mere act of using a road a lot makes it a better road for wagons, because the wheels wear it down and wear it down until there are grooves. granted, for this to happen a few things have to be true: the wagons need to have the same separation between the axles, and also there has to be a definite optimal path along it: but where a groove starts to form people immediately realize that life's a lot easier for them if they just put their wheels into the groove: not only is the surface inside the groove smoother than the rest of the road, they also don't need to worry about steering the wagon: the groove takes care of that. grooves are just ace.
So how can we leverage this principle in order to move freight around cheaply and easily? we don't want to have to build an entire stone paved road, that's too expensive. what if we need to move stuff over yonder, but we don't want to have to wait for the emperor to build a stone road, or for wagons to carve grooves? Okay, so this far we have concave grooves and convex wheels, right? it's the edges of the grooves that keep our wagons on the path we want.
These sorts of paths, called wagonways, have the immense advantage of being as heavy as a person or horse can pull. you simply cannot pull this off on a road wagon, because it needs to be able to stop, go, turn around, it needs some degree of agility: not rail vehicles, though: as long as they can be coerced into stopping at all they can be driven around, moving stuff. also they're predictable, so you're never wondering if it'll hit you or not: you're either in its groove, in which case it will, or you're not on its grooven, in which case you're safe. But in order to have a these excellent grooveways, we need to have a lot of paved road and then have people carve the grooves over millenia and... what if we only wanted the grooves though?
build grooves, of course. take a log and carve a grooven onto it as thick as your wheels. boom, you have a lot of the advanges of the groove in a stone path without the stone path. a much cheaper wagonway, with most of the advantages of a wagonway! but okay, okay, hear me out: what if we turn it around: what if we make convex grooves and concave wheels? okay, you can't have a convex groove, but lt's call it something else: instead of grooves into a path, we make, out of some hard and cheap material like wood, just a big thing for wheels to roll on top of, a bit higher than the ground and, instead of having a veeeery long groove, you build an anti-groove onto your wheel. the wheel keeps itself on track as it slides and rolls over these rails because of this anti-groove. a portable groove which keeps your wheel on track. how do we call this anti-groove and convex wheel arrangement? maybe the antigroove we call a rail, or an edge rail, and the self-guiding part of the wheel we call a flange.
what if you want something even better? you could make the path out of metal, now, couldn't you? like... it's too expensive to build an entire path out of metal, but if you just make two rails an lay the wheels on top of the rails, then it might not be as expensive... and if we have an industrial revolution and bessemer steel and blablabla, then even better! in reality, this all evolved rather messily: wooden rail systems were diverse, and sometimes they'd have grooved rails and flangeless wheels, sometimes rails and flanged wheels, maybe two flanges per wheel, maybe one flange per wheel, maybe only the left wheels have flanges and the right ones are free, to absorb any imperfections in the track layout. maybe the wheel doesn't have a flange but it's circularly concave so it can better roll onto the cheaper sort of rail there is: a barely de-branched log. Maybe instead of a flange your left wheel is higher on one edge than the other, so it wants to go to the right, and your right wheel is reversely uneven so it wants to go to the left, and then you don't have to worry about expensive flanges... maybe you put a flange just in case, though, for extra safety: even after the introduction of metal rails and wheels people would still put the flange on the track, sometimes, instead of on the wheel: instead of building complete grooves, people would sometimes just build an iron plate with one flange, and then for the other rail, another plate with just one flange on the other side: this way, you spend less material of flanges and you still don't derail. And from here we're in recognizeable territory: if you have an engine that can produce force you can put it on one of the wagons, and let it pull other wagons, which is amazing because now the whole thing moves without having to pull it. and then, well, you have a train.
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on future posts, ramblings about how planetary parameters such as gravity, atmospheric density, and the availability of materials might affect the viability and development of rail transport: can you have trains without fossil fuels? how thick does the air need to be for you to have sail trains? how much earlier -or later- in the technological development of a society could you have trains? that kind of thing.
conworlding, planetary science and trains
Re: conworlding, planetary science and trains
that was quite informative, and I enjoyed reading it; thank you for taking the time to think of & write all that.Torco wrote: ↑Mon Jun 19, 2023 3:40 pmSo how can we leverage this principle in order to move freight around cheaply and easily? we don't want to have to build an entire stone paved road, that's too expensive. what if we need to move stuff over yonder, but we don't want to have to wait for the emperor to build a stone road, or for wagons to carve grooves? Okay, so this far we have concave grooves and convex wheels, right? it's the edges of the grooves that keep our wagons on the path we want.
very much looking forwards to more in this series.
Re: conworlding, planetary science and trains
If I remember, the steel-on-steel interaction of train wheels on rails also produces less friction and wear on the wheels and rails than rubber-on-asphalt interactions for tires and roads. Maybe wood-on-wood interaction works the same way, being less frictious and damaging to the wheels and rails than a wooden wheel on a (stone) road.
Re: conworlding, planetary science and trains
Very interesting.
I'm looking forward to it!Torco wrote: ↑Mon Jun 19, 2023 3:40 pm
on future posts, ramblings about how planetary parameters such as gravity, atmospheric density, and the availability of materials might affect the viability and development of rail transport: can you have trains without fossil fuels? how thick does the air need to be for you to have sail trains? how much earlier -or later- in the technological development of a society could you have trains? that kind of thing.
Re: conworlding, planetary science and trains
Glad you guys liked it.
Wooden rails, I don't know: don't fully trust me on this but i often work with wood as an amateur carpenter and from intuition I get the feeling that any rail system that functions by wood-on-wood action is going to require very frequent replacement of both the rails and the wheels. thing is, wood is cheap, it literally grows on trees
Stone would be almost totally undamaged by wooden wheels. At first glance, I think the wooden wheels would suffer more rolling on wood than on stone, but flanges (either on the rails or on the wheels) would likely change this equation, since they're adding another contact surface.
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So for thousands and thousands of years (and I am here being literal: wagonways and rail in general is as old as writing, possibly older) wagonways and other rail arangements were used, mostly locally, to make it easier to move stuff around: mostly powered by horses and burly men and women. The first external power sources for rail vehicles, as far as I know, were employed to make funiculars move. Wagonways work best on level ground, but you know when you *really* would like to just put in fruits in the cart and forget about the whole thing? on slopes. A funicular is just a rail cart attached to a rope, such that somebody else is pulling on the rope so that the cart climbs along the railway. funiculars often work in pairs, such that one wagon goes up as the other one goes down because... yeah, otherwise you have to pull up the entire weight of the car, and that's hard. indeed i think if it doesn't have two carts it's not called a funicular, but an incline elevator or something. the point is that for thousands and thousands of years rail vehicles existed, and they were pulled by people, horses, donkeys, oxen etcetera. But what if you had a cart that had a big thing on top of it that exerted force upon the wheels? and what if that thing exerted so much force that you could move not just that cart, but like a bunch of carts behind it? this is what a train is. locomotives (also called engines sometimes) make trains possible.
To begin with, let's assume our conpeople will be using steam engines much like the ones 1800s europeans employed (for an excellent disquisition on the viability of steam engines deeper in the past than the 1700s, bradrn has an excellent blog post). At any rate, let us explore, briefly, the basics of steam locomotives.
In very basic terms, a steam loco consists of a wagon part, a hot bit, a place for water to boil using the heat of the hot part, and a bunch of mechanical elements that translate the steam power into the rotational movement we need to make the wheels go brr. let us call these parts as follows: we'll call the hot bit the firebox because it's, well, a box with fire inside of it. the firebox is going to generally be made out of metal (though in principle, any material that can keep its mechanical properties at high temperature works), and it's going to have a grate on the bottom: this is for two reasons: first, so that the air can get in and stoke the fire and, second, so that the ashes (or indeed the fire itself) can be dropped down. the bit where water is boiled using th heat of the firebox is called the boiler, for obvious reasons. the boiler in normal engines is a large tube filled to about three quarters up with water, the empty part being filled with air and, as the water gets hot, with steam. But the boiler is not just a bottle, oh, no, no sir: what we want is maximum heat exchange between the fire in the box and the water in the boiler and if we just put the fire next to the boiler and relied on the conductivity of the iron walls of the whole thing our engine would be kind of shit: rather, what you do is you put a bunch of little pipes running from the firebox through the water in the boiler and out to the external world: in this manner, what you get is air rising from the atmosphere into the firebox, doing a combustion, and the hot exhaust gases being piped through relatively thin pipes that heat the water and finally exiting the system through a chimney thing. these pipes are called flutes, and run through the entire length of the boiler: this is *one* of the reasons why as locomotives became more and more powerful they also became longer and longer: each meter of length in the boiler is = (2 x pi x the radius of the flute x however many flutes you have) more square meters of heat exchange surface. the inside of a firebox ends up looking like this.
Also, the flutes don't go directly to the outside: they output to a chamber where smoke is mixed with steam in order to push it out stronger, which makes the draft on the fire stronger, which makes the fire stronger: steamy exhaust is also a lot safer (not that anything about steam locos is inherently all that safe, mind you) because they don't have embers etcetera. So, in summary: fire hot, hot air from fire go through inside of flutes, flutes get very hot. outside of flutes is in water, which gets hot. water is contained in a big pipe, the boiler, where steam pressure builds up. pressurized steam outputs through pipes and valves and so on into a cylinder, where it pushes against a plate, where it pushes against rods, where it pushes against levers and so on and so on: ultimately all the pushing and pulling moves one or more wheels around, and boom, the locomotive moves.
But it is, of course, all a lot more complicated than this: for one thing, locos tend to have two cylinders, sometimes more, and they have something called a reverser that sort of controls, in a gearbox kind of way, how much speed / torque the cylinder applies to the wheels. the pistons themselves have a complicated design so that they extract energy from the steam both ways, and valves and so on. regulator valves control how much steam goes from the boiler to the piston, for when you don't want to move (or when you want to coast). operating a firebox itself is a whole thing, since you want the fire to be homogeneous and therefore you need to shovel wood or coal rather precisely. there's safety valves to release steam when the inner pressure of the boiler is above a certain threshold, since otherwise you'll explode, there's bogies the wheels sometimes sit on top of for reasons, there's brakes, it's a whole thing. let's say, however, that this explanation is enough. so how would steam locos, and rail transport in general, work on different worlds?
rolling resistence
Okay, so the whole point of rail transport is to make it easier to pull carts along a path. how easy, exactly, is it ? a simplified answer is the rolling resistance coefficient, or C. c is something like how many kilos of horizontal force do you have to exert in order to move something forward (or, rather, to keep it moving at a constant speed) per unit of weight of the thing you're moving. I am not american, so it's kilos all the way here baby. a car moving around on sand (or our wagon moving around on mud) will have a value of C of around 1/3: this means that we need to apply 1/3 of a kilo of force per kilo of weight in order to move the thing around. So if I need to move 100 kilos of fruit to mum's house, I'll have to pull with 30 kilos of force all the way. that's not horrible, but it's pretty bad honestly. Our wooden wagon moving on a stone paved road is much nicer, at something like 1/30: thus, I need to apply only 3 kilos of force to move my ruit. a car, say a regular hatchback, has a C of around 1/100: it takes something like 10 or 20 kilos of force to keep it moving, it being about 1,3 tons plus whatever I put on it (honestly try it, push a car down a road: it's suprisingly possible for a human being to do it, even if it's rather tiring). Even the worst rail system, let's say a dirty and uneven railway with dirt, muck, little pebbles, a lot of curves and whatever is going to be even beter, at 1/200 or so: only half a kilo of force to pull mum's fruit. proper railroads clock in anywhere from 1/350to 1/1000. In general, you want C to be as close to zero as possible: C goes smaller the better your track is, the rounder your round things are, the stiffer your stiff bits are, and it goes bigger the more curves you have, the rougher your rail joints are, etcetera etcetera.
of course, this force is constant force: if your C*weight (let's call it your pulling force) is 10 kilos, then you'll need to be exerting, all the way up until mom's house, as much force as 10 kilos exert on the scale, at least: there are other sources of drag for any vehicle, incluing air drag, curves, accelerating and decelerating, the wind, and the bits where the track makes you go uphill, amongst others, and we'll look at them later.
Now of course, you'll notice this whole time we've been talking about weight, not mass. weight is gravity times mass and, for this reason, the effects of gravity on rolling resistence are linear. Let us take an imaginary 100 ton train bearing another 100 tons of cargo (this number is imaginary and convenient, but also not unrealistic: there exist 30 ton locos which are able to produce something like 30 kilowatts of power, plus the weight of a bunch of wagons). in principle, just thinking about rolling resistence, our 200 tons will need something like 400 kilos of force in order to be pulled (C=1/500). 400 kilos of force is about 4kn, which means we need something like 4 kilowatts of power (5 hp) in order to keep our train moving: we have that power, and 26 more kilowatts to spare (which we'll need in order to defeat air drag, to accelerate our train, tackle any inclines we get, etcetera etcetera), and so our train can go and we can bring mum her fruit.
What if we live in a different planet? for example, if gravity is twice as much as on earth the same train and cargo will weigh not 200 tons but 400, but this doesn't make the locomotive any stronger. besides making inclines harder to tackle (which is already a big problem), it'll take 800 kilos of force, 8kn, 10 hp, to keep the thing rolling. as a not, when I say 800 kilos of force, I mean 800 kilos on earth: it'll be the same 400 kilos on this bigger planet because, well, 8kn is the amount of force 400 kilos do exert under twice earth gravity, but we're here talking about absolute force. 10hp is still not *that* bad, to be honest, our train can still pull itself, but it can't, for example, pull 1000 tons, whereas on earth it can actually do so.
On the other hand, what if we run a train on mars? as an approximation, let's say mars has 1/3 earth gravity (in reality it's more like 3/8ths, but that's harder math): this means our train, which masses 200 tons, weighs 66 tons: thus you need 130 earth-kilos of force, 1,2kn, 1,5 horsepower, to keep our train rolling.
(small note: i'm using newtons here as short for newtons per meter per second). this is all napkin math, but you get the idea: 1/3 as much gravity means 1/3 as much effort to keep the train rolling.
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of course in reality it's harder to keep a train rolling faster than it is to keep it rolling slower because there are more sources of drag than rolling resistence: there is air resistence, for example, which does scale with velocity, and there is also the limiting factor of braking distance and acceleration: if it takes you 100 kilometers to come to a stop, or to achieve 1 kilometer per hour, then you might as well not start. or halve your train and move it around in two trips, etcetera. there is the elasticity of the train, which is a real thing btw, as well as the weight distribution and a billion other factors: but long story short, the rolling resistance of a rail vehicle, or ineed I suppose any wheeled vehicle, scales linearly with the surface gravity of the planet it's rolling on. What does this mean?
Well, fuck if I know, exactly: on first look, it means that trains on low-gravity worlds can be operated on the cheap, whereas trains on high-gravity worlds are more expensive: after all, it's cheaper to run a small loco and more expensive to run a big loco: this is for a great many reasons. componding this napkin math about rolling resistence is the very important fact that wear and tear also scale with gravity, so that rails will either be cheaper for a given weight: railways are built to a certain spec, of course, and part of that spec is how much weight a section of track can take: if you have less gravity, you can build cheaper, thinner rails and still move as many tons of freight, because those tons weigh fewer newtons: alternatively, the same rail will last longer, because it's, again, bearing fewer newtons. Additionally, climbing inclines becomes even easier, necessitating less spare power in your loco to move across a given distance: I haven't done the math here, but I suspect that this effect is not going to be linear because two distinct things are helping you climb an incline if you're a train on mars: on the one hand, climbing the gravitational well is cheaper: i.e. you need less energy to make a kilo of train be one meter higher. but, on the other hand, a lot of how trains climb inclines is by expending their inertia: and inertia has nothing to do with gravity! so that one kilo of freight has the same inertia even though it weighs fewer newtons: this means that a train has the same amount of energy reserves, so to speak, to climb small inclines (let's say small here means "small enough that you don't need to increase power in order to climb the incline) while the freight is both easier to move forwards and easier to move up.
then again, low gravity worlds have their own challenges for train operation related to this very invariance of inertia: you see you pay a price for the low coefficient of rolling resistence on a train, and that price is adhesion. In principle, an infinitely stiff rail where an infinitely stiff wheel is rolling should, if they're perfectly shaped (flat and round, respectively), not have any friction between them: this is nice if you want to keep going, but it's extremely dangerous if you want to stop (or start, anyway). its only because one or the two of them deform that wheels adhere to roads, and they only deform under the influence of gravity so the less gravity, the less adhesion you get between wheel and track. I haven't done the math for this, either, but it seems to me at this point that, ultimately, a train is going to be more like a train under low gravity, more like a car under high gravity: what I mean by this is that trains, as compared to cars, are a) more inertial, so less maneouverable and b) more efficient, as in less force needed to move the same amount of freight (at the cost of that maneouverability). Ultimately, there's going to be a point where the gravity is so low that trains can't work: if you try to run a train on, say, an asteroid then sure, you'll get essentially no rolling resistence, but why do you need the tracks? you might as well give your wagon a good kick and it'll float, in a nice ballistic trajectory, until it lands on the other side of the asteroid (or floats off into interplanetary space, i guess, if you kick too hard). denizens of mars-like worlds however have a few choices available to them: one is making wheels our of softer materials, such as bronze: thus making their trains more car-like.
both very true, and indeed you incurr less wear and tear for the very same rason you incurr less rolling drag: because stell, or iron, or even wood, are rather stiff materials, when compared to, you know, rubber. it's, ultimately, the same principle than with the mud: you're effectively deeply "damaging" the "rails" you're running on, if you try to drive for example a car over a mud road: I once drove a pickup over a muddy field and it was devastating: the mud was just flying all over the place, bits of root and probably worms and so on were getting moved here and there. the damage is just a value-laden term for, well, plastic deformation: that's the secret of rail, ultimately: to minimize plastic deformation of both the wheels and the rolling surface. rubber wheels survive the stresses of rolling through two different means: having a material that can survive a lot of plastic deformation (rubber, which bends but doesn't break) and having a lot of the stiffness being provided by compressed air, which it doesn't matter how much it deforms because, well, it's air.If I remember, the steel-on-steel interaction of train wheels on rails also produces less friction and wear on the wheels and rails than rubber-on-asphalt interactions for tires and roads. Maybe wood-on-wood interaction works the same way, being less frictious and damaging to the wheels and rails than a wooden wheel on a (stone) road.
Wooden rails, I don't know: don't fully trust me on this but i often work with wood as an amateur carpenter and from intuition I get the feeling that any rail system that functions by wood-on-wood action is going to require very frequent replacement of both the rails and the wheels. thing is, wood is cheap, it literally grows on trees
Stone would be almost totally undamaged by wooden wheels. At first glance, I think the wooden wheels would suffer more rolling on wood than on stone, but flanges (either on the rails or on the wheels) would likely change this equation, since they're adding another contact surface. ____________________
So for thousands and thousands of years (and I am here being literal: wagonways and rail in general is as old as writing, possibly older) wagonways and other rail arangements were used, mostly locally, to make it easier to move stuff around: mostly powered by horses and burly men and women. The first external power sources for rail vehicles, as far as I know, were employed to make funiculars move. Wagonways work best on level ground, but you know when you *really* would like to just put in fruits in the cart and forget about the whole thing? on slopes. A funicular is just a rail cart attached to a rope, such that somebody else is pulling on the rope so that the cart climbs along the railway. funiculars often work in pairs, such that one wagon goes up as the other one goes down because... yeah, otherwise you have to pull up the entire weight of the car, and that's hard. indeed i think if it doesn't have two carts it's not called a funicular, but an incline elevator or something. the point is that for thousands and thousands of years rail vehicles existed, and they were pulled by people, horses, donkeys, oxen etcetera. But what if you had a cart that had a big thing on top of it that exerted force upon the wheels? and what if that thing exerted so much force that you could move not just that cart, but like a bunch of carts behind it? this is what a train is. locomotives (also called engines sometimes) make trains possible.
To begin with, let's assume our conpeople will be using steam engines much like the ones 1800s europeans employed (for an excellent disquisition on the viability of steam engines deeper in the past than the 1700s, bradrn has an excellent blog post). At any rate, let us explore, briefly, the basics of steam locomotives.
In very basic terms, a steam loco consists of a wagon part, a hot bit, a place for water to boil using the heat of the hot part, and a bunch of mechanical elements that translate the steam power into the rotational movement we need to make the wheels go brr. let us call these parts as follows: we'll call the hot bit the firebox because it's, well, a box with fire inside of it. the firebox is going to generally be made out of metal (though in principle, any material that can keep its mechanical properties at high temperature works), and it's going to have a grate on the bottom: this is for two reasons: first, so that the air can get in and stoke the fire and, second, so that the ashes (or indeed the fire itself) can be dropped down. the bit where water is boiled using th heat of the firebox is called the boiler, for obvious reasons. the boiler in normal engines is a large tube filled to about three quarters up with water, the empty part being filled with air and, as the water gets hot, with steam. But the boiler is not just a bottle, oh, no, no sir: what we want is maximum heat exchange between the fire in the box and the water in the boiler and if we just put the fire next to the boiler and relied on the conductivity of the iron walls of the whole thing our engine would be kind of shit: rather, what you do is you put a bunch of little pipes running from the firebox through the water in the boiler and out to the external world: in this manner, what you get is air rising from the atmosphere into the firebox, doing a combustion, and the hot exhaust gases being piped through relatively thin pipes that heat the water and finally exiting the system through a chimney thing. these pipes are called flutes, and run through the entire length of the boiler: this is *one* of the reasons why as locomotives became more and more powerful they also became longer and longer: each meter of length in the boiler is = (2 x pi x the radius of the flute x however many flutes you have) more square meters of heat exchange surface. the inside of a firebox ends up looking like this.
- inside.gif (72.14 KiB) Viewed 843 times
But it is, of course, all a lot more complicated than this: for one thing, locos tend to have two cylinders, sometimes more, and they have something called a reverser that sort of controls, in a gearbox kind of way, how much speed / torque the cylinder applies to the wheels. the pistons themselves have a complicated design so that they extract energy from the steam both ways, and valves and so on. regulator valves control how much steam goes from the boiler to the piston, for when you don't want to move (or when you want to coast). operating a firebox itself is a whole thing, since you want the fire to be homogeneous and therefore you need to shovel wood or coal rather precisely. there's safety valves to release steam when the inner pressure of the boiler is above a certain threshold, since otherwise you'll explode, there's bogies the wheels sometimes sit on top of for reasons, there's brakes, it's a whole thing. let's say, however, that this explanation is enough. so how would steam locos, and rail transport in general, work on different worlds?
rolling resistence
Okay, so the whole point of rail transport is to make it easier to pull carts along a path. how easy, exactly, is it ? a simplified answer is the rolling resistance coefficient, or C. c is something like how many kilos of horizontal force do you have to exert in order to move something forward (or, rather, to keep it moving at a constant speed) per unit of weight of the thing you're moving. I am not american, so it's kilos all the way here baby. a car moving around on sand (or our wagon moving around on mud) will have a value of C of around 1/3: this means that we need to apply 1/3 of a kilo of force per kilo of weight in order to move the thing around. So if I need to move 100 kilos of fruit to mum's house, I'll have to pull with 30 kilos of force all the way. that's not horrible, but it's pretty bad honestly. Our wooden wagon moving on a stone paved road is much nicer, at something like 1/30: thus, I need to apply only 3 kilos of force to move my ruit. a car, say a regular hatchback, has a C of around 1/100: it takes something like 10 or 20 kilos of force to keep it moving, it being about 1,3 tons plus whatever I put on it (honestly try it, push a car down a road: it's suprisingly possible for a human being to do it, even if it's rather tiring). Even the worst rail system, let's say a dirty and uneven railway with dirt, muck, little pebbles, a lot of curves and whatever is going to be even beter, at 1/200 or so: only half a kilo of force to pull mum's fruit. proper railroads clock in anywhere from 1/350to 1/1000. In general, you want C to be as close to zero as possible: C goes smaller the better your track is, the rounder your round things are, the stiffer your stiff bits are, and it goes bigger the more curves you have, the rougher your rail joints are, etcetera etcetera.
of course, this force is constant force: if your C*weight (let's call it your pulling force) is 10 kilos, then you'll need to be exerting, all the way up until mom's house, as much force as 10 kilos exert on the scale, at least: there are other sources of drag for any vehicle, incluing air drag, curves, accelerating and decelerating, the wind, and the bits where the track makes you go uphill, amongst others, and we'll look at them later.
Now of course, you'll notice this whole time we've been talking about weight, not mass. weight is gravity times mass and, for this reason, the effects of gravity on rolling resistence are linear. Let us take an imaginary 100 ton train bearing another 100 tons of cargo (this number is imaginary and convenient, but also not unrealistic: there exist 30 ton locos which are able to produce something like 30 kilowatts of power, plus the weight of a bunch of wagons). in principle, just thinking about rolling resistence, our 200 tons will need something like 400 kilos of force in order to be pulled (C=1/500). 400 kilos of force is about 4kn, which means we need something like 4 kilowatts of power (5 hp) in order to keep our train moving: we have that power, and 26 more kilowatts to spare (which we'll need in order to defeat air drag, to accelerate our train, tackle any inclines we get, etcetera etcetera), and so our train can go and we can bring mum her fruit.
What if we live in a different planet? for example, if gravity is twice as much as on earth the same train and cargo will weigh not 200 tons but 400, but this doesn't make the locomotive any stronger. besides making inclines harder to tackle (which is already a big problem), it'll take 800 kilos of force, 8kn, 10 hp, to keep the thing rolling. as a not, when I say 800 kilos of force, I mean 800 kilos on earth: it'll be the same 400 kilos on this bigger planet because, well, 8kn is the amount of force 400 kilos do exert under twice earth gravity, but we're here talking about absolute force. 10hp is still not *that* bad, to be honest, our train can still pull itself, but it can't, for example, pull 1000 tons, whereas on earth it can actually do so.
On the other hand, what if we run a train on mars? as an approximation, let's say mars has 1/3 earth gravity (in reality it's more like 3/8ths, but that's harder math): this means our train, which masses 200 tons, weighs 66 tons: thus you need 130 earth-kilos of force, 1,2kn, 1,5 horsepower, to keep our train rolling.
(small note: i'm using newtons here as short for newtons per meter per second). this is all napkin math, but you get the idea: 1/3 as much gravity means 1/3 as much effort to keep the train rolling.
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of course in reality it's harder to keep a train rolling faster than it is to keep it rolling slower because there are more sources of drag than rolling resistence: there is air resistence, for example, which does scale with velocity, and there is also the limiting factor of braking distance and acceleration: if it takes you 100 kilometers to come to a stop, or to achieve 1 kilometer per hour, then you might as well not start. or halve your train and move it around in two trips, etcetera. there is the elasticity of the train, which is a real thing btw, as well as the weight distribution and a billion other factors: but long story short, the rolling resistance of a rail vehicle, or ineed I suppose any wheeled vehicle, scales linearly with the surface gravity of the planet it's rolling on. What does this mean?
Well, fuck if I know, exactly: on first look, it means that trains on low-gravity worlds can be operated on the cheap, whereas trains on high-gravity worlds are more expensive: after all, it's cheaper to run a small loco and more expensive to run a big loco: this is for a great many reasons. componding this napkin math about rolling resistence is the very important fact that wear and tear also scale with gravity, so that rails will either be cheaper for a given weight: railways are built to a certain spec, of course, and part of that spec is how much weight a section of track can take: if you have less gravity, you can build cheaper, thinner rails and still move as many tons of freight, because those tons weigh fewer newtons: alternatively, the same rail will last longer, because it's, again, bearing fewer newtons. Additionally, climbing inclines becomes even easier, necessitating less spare power in your loco to move across a given distance: I haven't done the math here, but I suspect that this effect is not going to be linear because two distinct things are helping you climb an incline if you're a train on mars: on the one hand, climbing the gravitational well is cheaper: i.e. you need less energy to make a kilo of train be one meter higher. but, on the other hand, a lot of how trains climb inclines is by expending their inertia: and inertia has nothing to do with gravity! so that one kilo of freight has the same inertia even though it weighs fewer newtons: this means that a train has the same amount of energy reserves, so to speak, to climb small inclines (let's say small here means "small enough that you don't need to increase power in order to climb the incline) while the freight is both easier to move forwards and easier to move up.
then again, low gravity worlds have their own challenges for train operation related to this very invariance of inertia: you see you pay a price for the low coefficient of rolling resistence on a train, and that price is adhesion. In principle, an infinitely stiff rail where an infinitely stiff wheel is rolling should, if they're perfectly shaped (flat and round, respectively), not have any friction between them: this is nice if you want to keep going, but it's extremely dangerous if you want to stop (or start, anyway). its only because one or the two of them deform that wheels adhere to roads, and they only deform under the influence of gravity so the less gravity, the less adhesion you get between wheel and track. I haven't done the math for this, either, but it seems to me at this point that, ultimately, a train is going to be more like a train under low gravity, more like a car under high gravity: what I mean by this is that trains, as compared to cars, are a) more inertial, so less maneouverable and b) more efficient, as in less force needed to move the same amount of freight (at the cost of that maneouverability). Ultimately, there's going to be a point where the gravity is so low that trains can't work: if you try to run a train on, say, an asteroid then sure, you'll get essentially no rolling resistence, but why do you need the tracks? you might as well give your wagon a good kick and it'll float, in a nice ballistic trajectory, until it lands on the other side of the asteroid (or floats off into interplanetary space, i guess, if you kick too hard). denizens of mars-like worlds however have a few choices available to them: one is making wheels our of softer materials, such as bronze: thus making their trains more car-like.
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rotting bones
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Re: conworlding, planetary science and trains
so, in summary, rolling resistance scales linearly with gravity, so that if you have 0.5 G you can, with the same power, pull twice as much freight. Also, the less gravity you have, the easier it is to climb inclines, also linearly. let's look at another fun physics concept: traction.
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friction was our enemy when we were considering rolling resistence, but it is, in fact, also our friend. this is because, at least normally, a rail vehicle moves because some or all of the wheels are made to roll while they're resting against the rail: thus, it is the steel-against-steel friction that is going to be turning all of the energy our vehicle is going to produce into energy, and the thing is that it can only do so in proportion to how much friction there is. A thing that actually happens to rail vehicles, especially steam locos (which, for reasons, produce just astonishingly high amounts of torque compared to their power), is that the wheels can actually roll with more force than they can impart unto the rails and then just slip and roll in place, causing all kinds of bad things. In general trains have low amounts of traction when compared to trucks or cars, and traction is such an important factor in train operations that most trains actually have the in-built capacity to sprinkle a little ordinary sand onto the rails to increase the friction between wheels and rails, which I just find adorable tbh.
like... inside of this enormous, heavy, highly technologically advanced, ultra-efficient machine with a huge diesel engine, electric motors, fluid couplings, air brakes and all sorts of ultra-powerful, super expensive, industrial machinery... right besides the lever that's deciding how many megajoules of energy will be made to run through the windings of an alternator so powerful it could literally light up an entire town... there's a small 'pour a bit of sand' button, too.
Okay, friction. the maximum amount of force a wheel can exert against a road (railroad or any other kind of road) is going to be given by the equation F = k * W, where F is the max amount of force which can be exerted, W is the weight that is resting upon that particular wheel, and k is some coefficient. this means that you would, ceteris paribus, probably want as many wheels of your vehicle to be powered as possible, since the sum of the weight borne by all of your wheels is going to be, well, the weight of your train, and you're not going to get any more weight than that. (okay, actually you could get more: you could 'artificially' increase W by adding an aileron to your vehicle designed to increase downforce, as racecars do. no one does this in earthbound trains, as far as I know, but they do have a small 'pour sand' button). In principle you can do this, and actually some modern rail vehicles do have all of their wheels powered: this is only done, as far as I know, with electricity in very fast and performant passenger trains: electric engines are small and so you can put one in each wheel, connect the whole train with wires, and boom, maximum acceleration. The same by the way applies to brakes. Of course if you fail to start no one dies, if you fail to stop they do, thus all-wagons braking is much more common that all-wagons propulsion.
The normal coefficient of friction for railroads is, in general, around 0.4: as always, this will change depending on conditions: rain makes it smaller, and that adorable little 'pour some sand on the rails' button makes it bigger. how does this affect our fantastical train that can travel between hypothetical conworlds?
reviewing, our train was 200 tons, 100 of train and 100 of freight and our 30 ton locomotive was able to produce 30kilowatts of power. in order to figure out just how much traction it can exert (and this is more complicated, but lt's stick to this simpler model) we need to know how many wheels the loco has.
locomotive wheel arrangements are like an entire subfield of human endeavour: simply put, it's a tradeoff between rail loading, cornering ability, and traction. On the one hand you have the simplest loco: four whels <fewer and it falls down>, all powered. this, in steam enthusiast, is called a 0-4-0. these have the distinct advantage of having, basically, as much tractive power as possible for any given mass, but they're less stable on the tracks. you could have, in principle, as many wheels as you want: crazy things like a 4-10-2 exist. this means four leading unpowered wheels, 10 powered wheels (probably strung together with a big iron, though other methods exist), and 2 trailing wheels also unpowered: because in steam powered wheels are bigger, this can be drawn, as an icon of the profile of the wheels, like ooOOOOOoo.
small aside: why *do* locomotives have as many wheels as they do? because, mostly, of two reasons: axle loading/traction and stability at speed. if your locomotive weighs 30 tons and it has 4 wheels, then each wheel (assuming a central center of gravity, rare but bear with me) is going to bear 7,5 tons. because of the above equation, where maximum traction is weight on the wheel times a coefficient, the more weight rests on a wheel, the stronger acceleration (or braking) that wheel can impart on the vehicle, but the downside is twofold: on the one hand, these wheels are subject to various dynamic forces, including the piston pulling and pushing onto it at different times, but also the inherent stability of a heavy thing rolling over relatively thin rails: this means that fewer wheels are less stable, especially at speed, on the rails. The other problem is that rails can bear a limited amount of weight before they're unsafe. one way to represent the amount of weight railways can bear is the axle loading, in tons. our 30 ton four-wheeler would have 15 tons per axle (because it has two axles). This is enough to break some of the weaker railways, but most would be okay: 20 tons axle loading is a decent amount, and I think the strongest railway in the world in this sense can bear 40 tons per axle. This magnitude should, in principle, not be affected by gravity too much since it has to do, for the most part, with the size of the rails and with the quality of the infrastructure the rails are resting on (you know, the wooden thingies and the gravel the wooden thingies rests on).
Right, so knowing all of this let's look at our two conworlds of different gravity and how our train may do.
7,5 (tons per wheel) times 0.4(our friction) is 3 tons of force: that's the maximum force our wheels can exert: how about on the heavy world with 2 times gravity? 30 tons weight 60 tons here, so it's 15 tons per wheel (30 per axle), so 6 tons of force maximum. on the lighter conworld, the mars-sized one, our locomotive massing 30 tons is only going to weight 10: this means that each axle bears 5 tons, 2,5 per wheel: all else being equal, the wheels are going to be able to exert a force of 2500*0.4 = 1 ton. (my tons are 1 thousand kilos). this means 12 tons total on earth (to defeat 400 kilos of rolling resistence), 24 tons total on 2G world (to defeat 800 kilos), and 4 tons total on our mars analogue (to defeat, what was it, 130?): if you check the above thread, all of these numbers are way above what we need to defeat rolling resistence, and I think this gives one a good feeling of just how fantastically efficient trains are: in any world our small loco can pull much more than its own mass in freight. Thus far, the relationships are all linear, but we've still hit our first actual problem: our reference train works on earth and it works on mars, but it doesn't work on the land of 2 gravities: it breaks our railway (actual axle loading, 30 per axle, is rather on the high end of what modern railroads can support without breaking).
So 2G land needs either a lighter locomotive (and 30 tons isn't even heavy) or we need moar wheels. If our loco was the same 30 tons in mass (which weigh 60 tons) but used... oh, let's say a 4-4-2 design (four unpowered wheels, four powered ones or 'drivers' and 2 more wheels for good measure, or ooOOo ), then each wheel (again lets imagine all wheels bear equal weight, this is never the case but whatever) bears 1/10th of the loco, or 6 tons, 12 per axle. that's a reasonable load to put on a wheel, our rails will survive this time: but each of the wheels is now getting less weight: 6*0.4=2.4 tons of force per wheel, for a grand total of almost 10 tons maximum pull force of the whole loco. while our rails don't break, we're going to need almost a full 10% of our maximum tractive force (10 tons) to defeat the rolling resistence of even this tiny train (see earlier post, it was 800 kilos on the 2G world). And that's not even taking into account the fact that, you know, wheels are heavy! moving our loco from 4 to 10 wheels is definitely going to increase its mass, and it's going to have to be even more heavy if we want it to not break under twice earth gravity. And let's not even consider inclines (which are twice as dificult to tackle on 2G world) and, interestingly, curves.
What? no one said railway engineering was easy! yes, curves, as a general rule, make trains harder to pull. this should be intuitive but, if it isn't, consider what's happening in a curve: at time t you're pulling in a direction, but the track is taking that energy and, through being rigid, making the vehicle go in a slightly different direction. people who drive experience this: you're coasting with your foot pressing with some force on the gas, you take a curve and all of a sudden your car slows down. just how hard are curves? okay, the actual calculations are probably supercomputer-level, but a general rule of thumb the soviets used is much simpler: 700/R kilos per ton (of rolling resistance) where R is the radius of the curve in meters. What's the radius of a curve? take a circle, and cut off a chunk: doesn't matter if the chunk is half a circle or a tiny chunk of the circle, they're both going to be exactly as curvy, for our purposes. if you want to turn around in a curve that's got a radius of 700 meters, then if you start going north the point where you're pointing south is going to be a kilometer and a half away.
For trains, a curve with a radius of 50 meters is considered tight but not too tight. 700/50 is 14 kilos per ton, so... YIKES! 5600 tons of rolling resistance from taking a curve alone! (14 kilos per ton times 400) I honestly don't know if that number (700 in the 700/R) would be affected by gravity, other than there being more tons, so best case scenario, for our 2G conworld, this is a 5 tons of resistence for a full half of the maximum amount of traction our wheels can exert. without even considering our engine (which, and i'll spare you the napkin math, can only produce something like 3 tons of force) means that, alas, our reference is, well, going to have a bad time of it.
By contrast, our mars train is going to be able to exert 4 tons of adhesive force onto the tracks, but the same curve is going to cost it the same 14kilos per ton: it weighs something like 60 tons, so it'll have to exert something like one ton of force to take that curve out of the 4 tons of total tractive force possible and out of the 3 tons of actual engine power: it can probably manage.
_________
friction was our enemy when we were considering rolling resistence, but it is, in fact, also our friend. this is because, at least normally, a rail vehicle moves because some or all of the wheels are made to roll while they're resting against the rail: thus, it is the steel-against-steel friction that is going to be turning all of the energy our vehicle is going to produce into energy, and the thing is that it can only do so in proportion to how much friction there is. A thing that actually happens to rail vehicles, especially steam locos (which, for reasons, produce just astonishingly high amounts of torque compared to their power), is that the wheels can actually roll with more force than they can impart unto the rails and then just slip and roll in place, causing all kinds of bad things. In general trains have low amounts of traction when compared to trucks or cars, and traction is such an important factor in train operations that most trains actually have the in-built capacity to sprinkle a little ordinary sand onto the rails to increase the friction between wheels and rails, which I just find adorable tbh.
like... inside of this enormous, heavy, highly technologically advanced, ultra-efficient machine with a huge diesel engine, electric motors, fluid couplings, air brakes and all sorts of ultra-powerful, super expensive, industrial machinery... right besides the lever that's deciding how many megajoules of energy will be made to run through the windings of an alternator so powerful it could literally light up an entire town... there's a small 'pour a bit of sand' button, too.
Okay, friction. the maximum amount of force a wheel can exert against a road (railroad or any other kind of road) is going to be given by the equation F = k * W, where F is the max amount of force which can be exerted, W is the weight that is resting upon that particular wheel, and k is some coefficient. this means that you would, ceteris paribus, probably want as many wheels of your vehicle to be powered as possible, since the sum of the weight borne by all of your wheels is going to be, well, the weight of your train, and you're not going to get any more weight than that. (okay, actually you could get more: you could 'artificially' increase W by adding an aileron to your vehicle designed to increase downforce, as racecars do. no one does this in earthbound trains, as far as I know, but they do have a small 'pour sand' button). In principle you can do this, and actually some modern rail vehicles do have all of their wheels powered: this is only done, as far as I know, with electricity in very fast and performant passenger trains: electric engines are small and so you can put one in each wheel, connect the whole train with wires, and boom, maximum acceleration. The same by the way applies to brakes. Of course if you fail to start no one dies, if you fail to stop they do, thus all-wagons braking is much more common that all-wagons propulsion.
The normal coefficient of friction for railroads is, in general, around 0.4: as always, this will change depending on conditions: rain makes it smaller, and that adorable little 'pour some sand on the rails' button makes it bigger. how does this affect our fantastical train that can travel between hypothetical conworlds?
reviewing, our train was 200 tons, 100 of train and 100 of freight and our 30 ton locomotive was able to produce 30kilowatts of power. in order to figure out just how much traction it can exert (and this is more complicated, but lt's stick to this simpler model) we need to know how many wheels the loco has.
locomotive wheel arrangements are like an entire subfield of human endeavour: simply put, it's a tradeoff between rail loading, cornering ability, and traction. On the one hand you have the simplest loco: four whels <fewer and it falls down>, all powered. this, in steam enthusiast, is called a 0-4-0. these have the distinct advantage of having, basically, as much tractive power as possible for any given mass, but they're less stable on the tracks. you could have, in principle, as many wheels as you want: crazy things like a 4-10-2 exist. this means four leading unpowered wheels, 10 powered wheels (probably strung together with a big iron, though other methods exist), and 2 trailing wheels also unpowered: because in steam powered wheels are bigger, this can be drawn, as an icon of the profile of the wheels, like ooOOOOOoo.
small aside: why *do* locomotives have as many wheels as they do? because, mostly, of two reasons: axle loading/traction and stability at speed. if your locomotive weighs 30 tons and it has 4 wheels, then each wheel (assuming a central center of gravity, rare but bear with me) is going to bear 7,5 tons. because of the above equation, where maximum traction is weight on the wheel times a coefficient, the more weight rests on a wheel, the stronger acceleration (or braking) that wheel can impart on the vehicle, but the downside is twofold: on the one hand, these wheels are subject to various dynamic forces, including the piston pulling and pushing onto it at different times, but also the inherent stability of a heavy thing rolling over relatively thin rails: this means that fewer wheels are less stable, especially at speed, on the rails. The other problem is that rails can bear a limited amount of weight before they're unsafe. one way to represent the amount of weight railways can bear is the axle loading, in tons. our 30 ton four-wheeler would have 15 tons per axle (because it has two axles). This is enough to break some of the weaker railways, but most would be okay: 20 tons axle loading is a decent amount, and I think the strongest railway in the world in this sense can bear 40 tons per axle. This magnitude should, in principle, not be affected by gravity too much since it has to do, for the most part, with the size of the rails and with the quality of the infrastructure the rails are resting on (you know, the wooden thingies and the gravel the wooden thingies rests on).
Right, so knowing all of this let's look at our two conworlds of different gravity and how our train may do.
7,5 (tons per wheel) times 0.4(our friction) is 3 tons of force: that's the maximum force our wheels can exert: how about on the heavy world with 2 times gravity? 30 tons weight 60 tons here, so it's 15 tons per wheel (30 per axle), so 6 tons of force maximum. on the lighter conworld, the mars-sized one, our locomotive massing 30 tons is only going to weight 10: this means that each axle bears 5 tons, 2,5 per wheel: all else being equal, the wheels are going to be able to exert a force of 2500*0.4 = 1 ton. (my tons are 1 thousand kilos). this means 12 tons total on earth (to defeat 400 kilos of rolling resistence), 24 tons total on 2G world (to defeat 800 kilos), and 4 tons total on our mars analogue (to defeat, what was it, 130?): if you check the above thread, all of these numbers are way above what we need to defeat rolling resistence, and I think this gives one a good feeling of just how fantastically efficient trains are: in any world our small loco can pull much more than its own mass in freight. Thus far, the relationships are all linear, but we've still hit our first actual problem: our reference train works on earth and it works on mars, but it doesn't work on the land of 2 gravities: it breaks our railway (actual axle loading, 30 per axle, is rather on the high end of what modern railroads can support without breaking).
So 2G land needs either a lighter locomotive (and 30 tons isn't even heavy) or we need moar wheels. If our loco was the same 30 tons in mass (which weigh 60 tons) but used... oh, let's say a 4-4-2 design (four unpowered wheels, four powered ones or 'drivers' and 2 more wheels for good measure, or ooOOo ), then each wheel (again lets imagine all wheels bear equal weight, this is never the case but whatever) bears 1/10th of the loco, or 6 tons, 12 per axle. that's a reasonable load to put on a wheel, our rails will survive this time: but each of the wheels is now getting less weight: 6*0.4=2.4 tons of force per wheel, for a grand total of almost 10 tons maximum pull force of the whole loco. while our rails don't break, we're going to need almost a full 10% of our maximum tractive force (10 tons) to defeat the rolling resistence of even this tiny train (see earlier post, it was 800 kilos on the 2G world). And that's not even taking into account the fact that, you know, wheels are heavy! moving our loco from 4 to 10 wheels is definitely going to increase its mass, and it's going to have to be even more heavy if we want it to not break under twice earth gravity. And let's not even consider inclines (which are twice as dificult to tackle on 2G world) and, interestingly, curves.
What? no one said railway engineering was easy! yes, curves, as a general rule, make trains harder to pull. this should be intuitive but, if it isn't, consider what's happening in a curve: at time t you're pulling in a direction, but the track is taking that energy and, through being rigid, making the vehicle go in a slightly different direction. people who drive experience this: you're coasting with your foot pressing with some force on the gas, you take a curve and all of a sudden your car slows down. just how hard are curves? okay, the actual calculations are probably supercomputer-level, but a general rule of thumb the soviets used is much simpler: 700/R kilos per ton (of rolling resistance) where R is the radius of the curve in meters. What's the radius of a curve? take a circle, and cut off a chunk: doesn't matter if the chunk is half a circle or a tiny chunk of the circle, they're both going to be exactly as curvy, for our purposes. if you want to turn around in a curve that's got a radius of 700 meters, then if you start going north the point where you're pointing south is going to be a kilometer and a half away.
For trains, a curve with a radius of 50 meters is considered tight but not too tight. 700/50 is 14 kilos per ton, so... YIKES! 5600 tons of rolling resistance from taking a curve alone! (14 kilos per ton times 400) I honestly don't know if that number (700 in the 700/R) would be affected by gravity, other than there being more tons, so best case scenario, for our 2G conworld, this is a 5 tons of resistence for a full half of the maximum amount of traction our wheels can exert. without even considering our engine (which, and i'll spare you the napkin math, can only produce something like 3 tons of force) means that, alas, our reference is, well, going to have a bad time of it.
By contrast, our mars train is going to be able to exert 4 tons of adhesive force onto the tracks, but the same curve is going to cost it the same 14kilos per ton: it weighs something like 60 tons, so it'll have to exert something like one ton of force to take that curve out of the 4 tons of total tractive force possible and out of the 3 tons of actual engine power: it can probably manage.
Re: conworlding, planetary science and trains
Does this mean that trains cannot work on a world with 2G of gravity? not by any means! for one thing, there's more incentive for trains in such a world: everything is twice as heavy, and so people would be willing to invest more resources (pay more in a market economy, for example) in anything that makes moving things and people easier: still one must consider alternatives: boats, for example, are not meaningfully more expensive to run on such a world than they are in ours: the resistance is increased, yes, but water is rather hard to compress and under 2G it would not, I think, be all that denser: even on earth big boats are amongst the cheapest, if not the cheapest way to move bulk goods. It is possible, however, to build extensive networks of cannals for the purpose of both irrigation and logistics (one folk hero of the chinese supposedly did just that back in antiquity), and at some point, as gravity increases, a linear metre of artificial river becomes cheaper than a linear metre of railway to build and operate. I would expect people in higher gravity worlds to rely more on boats, less on trains, but trains are still viable for less mass intensive applications: notably, passenger services, light rail and trams, and the transportation of expensive goods. A particularly good idea for passengers in such a world would be using not big trains but small railcars. a railcar is like a bus, but on rails. steam railcars are known to be as light as 10 tons, which makes even small engines adequate, and with 1880s technology could move 30 or 40 people at a respectable 50 kilometers per hour.
Still, passenger trains are almost always an outgrowth, historically, of freight trains, and very often in the real world passengers are not the thing that keeps railways profitable: freight is. "no trains in my high gravity conworld" is a prefectly good conclusion to reach, but if one wants them, keep in mind that they would likely have to be lighter rail, they'd be much more expensive, and they would probably have more wheels than comparable trains on earth (and trains already have a bunch of wheels on earth, especially modern ones). notably, wagons would have to be either smaller or equipped with more bogies (a bogie is the thingie where the wheels are) in order to keep axle loadings low, and on would see bigger locomotives pulling on smaller trains. On the flipside, trains under higher gravity have shorter braking distances, making them somewhat safer.
On the other hand, we have the mars analogue situation of 1/3 of a gravity: our reference train (100t train, 100t freight, 30kw of engine, 0-4-0) runs fine here, but it is nearing the limits of its capacity: though operation is easier on the engine (because it all weighs less), the wheels are less able to exert force on the tracks. This is problematic, as it means we can't add more wagons and make it a 300, 400, 500 tons train: the engine could manage, but the wheels would end up slipping. The simplest solution to this problem is to make the locomotive heavier: more fuel and more water, a taller locomotive, a bigger boiler, etcetera: in general we try to make vehicles lighter, but there's always a useful thing you can add to a vehicle to make it better. Big tanks of water, for example, will make your locomotive able to go further without needing a refill, as will a bigger fuel tank (whichever your fuel is). A bigger cab (the cab is the bit with the people in it) makes it easier to work the locomotive, and if you made the car really big you could have a crew sleeping while another crew works the machine, allowing for more continuous operation, etcetera.
Still, passenger trains are almost always an outgrowth, historically, of freight trains, and very often in the real world passengers are not the thing that keeps railways profitable: freight is. "no trains in my high gravity conworld" is a prefectly good conclusion to reach, but if one wants them, keep in mind that they would likely have to be lighter rail, they'd be much more expensive, and they would probably have more wheels than comparable trains on earth (and trains already have a bunch of wheels on earth, especially modern ones). notably, wagons would have to be either smaller or equipped with more bogies (a bogie is the thingie where the wheels are) in order to keep axle loadings low, and on would see bigger locomotives pulling on smaller trains. On the flipside, trains under higher gravity have shorter braking distances, making them somewhat safer.
On the other hand, we have the mars analogue situation of 1/3 of a gravity: our reference train (100t train, 100t freight, 30kw of engine, 0-4-0) runs fine here, but it is nearing the limits of its capacity: though operation is easier on the engine (because it all weighs less), the wheels are less able to exert force on the tracks. This is problematic, as it means we can't add more wagons and make it a 300, 400, 500 tons train: the engine could manage, but the wheels would end up slipping. The simplest solution to this problem is to make the locomotive heavier: more fuel and more water, a taller locomotive, a bigger boiler, etcetera: in general we try to make vehicles lighter, but there's always a useful thing you can add to a vehicle to make it better. Big tanks of water, for example, will make your locomotive able to go further without needing a refill, as will a bigger fuel tank (whichever your fuel is). A bigger cab (the cab is the bit with the people in it) makes it easier to work the locomotive, and if you made the car really big you could have a crew sleeping while another crew works the machine, allowing for more continuous operation, etcetera.