The Hogwarts Express: How long? · 8:25am Apr 15th, 2020
A question that just came up in my writing: How long are each of the passenger coaches used on the Hogwarts Express, and how many do they carry?
Oh yes: Spoiler alert for a paragraph or two of an asofyet unwritten chapter of On the Implications of Parallel Worlds.
This will be fairly important, as in the above named story, the Hogwarts Express needs to move about 12,536 students in one trip. How many cars will they need, and how long will the train be? How many additional locomotives will they need to tack on to the front? For simplicity's sake, I'm ignoring any problems that might arise from putting all the locomotives at the front of an excessively long train. Wizards could probably counter them fairly easily anyways, with a wave of their magic wands.
For those not mathematically inclined, be warned. Just like with my wand deliberations, this is going to be a long and mathematical worldbuilding exercise so I can be satisfied that the numbers some character or another spouts at Platform Nine and Three Quarters are accurate. Despite that being the only time these numbers will ever be used.
For those that are mathematically inclined, it is simple algebra. The above warning is for those unfortunate souls who get headaches from what I (and, probably, you) would think of as simple math problems. I've known a few, personally.
So then, shall we get started?
First off, we know that Hogwarts has exactly 40 students in Harry's year. This wasn't stated in any of the books, but in supplemental material- Rowling even had names hashed out for each and every one of those 40 students, a couple of which never appeared in the series. These students were distributed perfectly between the houses and genders- 5 girls and 5 boys per house. Thus, as much as I've heard Rowling cited 'about a thousand' as total Hogwarts attendance, that is evidently false: Hogwarts attendance is clearly exactly 280 each year, being 40 students times 7 years.
This is further supported by the movie, as in the movie, the Hogwarts Express was shown to have 4-5 passenger coaches attached to it. These numbers offer 50-75 students per car...
Given the type of cars they were, "compartment cars", and the fact that these passenger cars were/are usually 60 to 70 feet long, we can begin estimating. Right off, that 50 students per car sounds about right- but that's just like a hundred thousand wands sounded "about right" for Ollivanders' salesfloor that only turned out to hold 30k or so.
Thus, to estimating.
The first thing about these cars is that their floorplan is not exactly what you would expect. The compartments are against one side of the car, and the passage against the far wall of the car- it is not like an 'open' coach car, or an airplane, that would have the passage down the middle. Note that it is possible to build a compartment car with slightly greater overall capacity by putting the corridor down the middle and compartments on both sides, but that this reduces compartment sizes to much smaller than they evidently were in canon. As such, the passage must curve back in around the compartments at either end of the car, to hit the centerline for the transfer area between cars. Oh, and since the train is known to depart at 11 AM and arrive after dark shortly after the longest day of the year, the train can be expected to be in motion for a minimum of seven continuous hours, nevermind that steam locomotives require regular maintenance and oiling every hundred miles or so... and you thought six or ten thousand miles was frequent for your car's oil change. We can pretend the wizards handwaived that maintenance requirement with their magic wands.
Thus, since eight hours is a mighty long time to expect an eleven-year-old to go without using the bathroom, these cars simply must have bathrooms on them as well. One would work, but I want to say there would be two, just to be safe. Conveniently, there's a little void on the floor plan at either end of the car, opposite the main passage, that is not occupied by a compartment- those two corners of the car... and the spaces in them that would be big enough for an airplane-style bathroom each, or perhaps a little larger. Thus, the bathrooms need not be included in our floor plan estimates.
So, since we know the compartments each contain two bench-style seats facing each other, with a window at one end and a doorway into the passage at the other, we can guess at capacity. Since most railcars would have an interior dimension of about 10' across, we can allocate 6' of that width to those benches, creating comfortable space for 4 people per bench- and it leaves 4' for suitable passages outside. Each compartment will have those two seats facing each other, and presumably some space between them. Assume they're fairly normal-sized seats, like you might find in the back of an SUV or something, and they'll be about two feet long- including the seatback and the seat base. Put two or three feet between the seats, and you have enough room to move around; I'll make that three, so it's an acceptable passage for people to walk through. Thus, each compartment is 7' long, and can comfortably fit a maximum of 8 passengers.
Now, back to the overall car floorplan. Since our compartment size gives us a 4' passage, we need to carve that passage out to the doors on either end of the car. I expect the passage segments at the ends, snaking up to the doors, would be thinner- say, 3', as a compromise between spaciousness and passenger density. The bathrooms would then be in spaces of about 3'x3'- you'll never manage that with an elongated bowl toilet with a sizable tank, but with special equipment, you shouldn't have any trouble at all building a bathroom in that space. So, passages account for 6' of the car's overall length.
Now, every railcar has a coupler on either end. On these passenger coaches, especially for a school train, the coupler won't be readily visible as you pass between cars- there will be some kind of passage hanging over it, making a full walkway between the two cars... and making it actually difficult to fall down to the tracks between the cars. Since these cars won't need to turn very sharply, they need not have much space set aside for coupler leeway- call it 1' per coupler, so 2' of the car's overall length.
Thus, we have only 8' of the car's length accounted for... and the only thing we're missing is the compartments, at 7' a piece. With a common length of 60 to 70 feet long, we can compute... If it has 8 compartments on these measurements, it would be 64 feet long. 9 compartments would make it 71 feet long. Both of these numbers can be "smashed" to 60 and 70 respectively, by using 2'6" gaps between seats in the compartments for the former, and 2'10 2/3" gaps between compartment seats in the latter, both acceptable measurements. The 60-foot car would have a capacity of 64 passengers, and the 70-foot a capacity of 72 passengers.
I think I'll use the 60-foot variant, for no better reason than that it offers (slightly) greater passenger density per train length. So, in order to carry 280 passengers with 64-passenger cars, they would need a minimum of 4 3/8 cars.
The fraction is important because, judging by what appears in the books, the average compartment will have between two and six passengers in it... so, the train is conceivably about half full. Double the length, we get 8 3/4 cars- effectively, 9 cars. Thus, we know the movie doesn't have enough cars, at 4- or 5, in Half Blood Prince.
With an average fill of 32 passengers apiece (assuming 50% fill), OtIoPW's Hogwarts Express will require 392 cars... which will have an overall length of 23,505 feet, or 4.5mi/7.2km.
This then begs the question, assuming that "magic" is the answer for how the students will get down the full length of the train without issue: How many locomotives do they need?
Presumably, since they only had a month, the wizards would have done a bit of panicking and snagged basically whatever locomotives they could that could help pull the train without doing too much damage to the muggle railroad industry... which means, in this day and age, they likely got diesel-electric freight locomotives. Which is good news for them, because those things have a ton of pulling power, compared to most steam or passenger locomotives.
As I recall, the world record longest train was 8 miles long, and had 8 diesel-electric locomotives evenly spaced, and this one will be 4.5 miles long.... So, call it 4 diesel-electric heavy-haulers, plus the Hogwarts Express locomotive, to pull this monster of a Hogwarts Express train... and slap on a Big Boy for good measure, why not?
... So, very long.
Edit: I made a mistake on the number of cars the "canon" Hogwarts Express would have to have to serve the known number of students. Fixed it.
If wizards have spells that can make a car light enough to fly, and are lazy enough to make everyday objects like luggage feather light/ levitate beside you, it would be safe enough to assume they've charmed the carriages. If only to lighten the load and reduce fuel consumption of the train, and the work required to shovel coal.
Also, let's not forget expansion charms that could likely increase the amount of seating compartments per train car. Because I don't think wizards would be smart enough to keep too many spare cars for an unforeseen 'population boom' of magical students.
5242912
Expansion charms only go so far, though... at a certain point, it starts becoming easier to (quickly) acquire fresh cars. After all, using expansion charms to increase the compartment number would require reconstruction of the entire interior of the car, which then could not be returned to muggle service, and acquisition of a fresh car is just a few memory charms away- and the resultant car could be returned to muggle service once it finished its job for the day. I imagine they'd do that, while they worked on building/acquiring/whatever more proper, long-term coaches. And something you'll notice about all those flying car/luggage/etc things: The momentum remains unchanged... and that's what the extra locomotives are required to overcome, mostly.
Plus, magically reducing the weight of a long train = BAD THING. The tension from the couplers around corners could case artificially lightened cars to roll. (It does that with models, if you've got a long enough train, because the cars aren't heavy enough and the corners too sharp...)
Personally, they'd be more likely to charm the shovel to stock the firebox automagically, or to charm the boiler to heat up faster and more efficiently, thence reducing fuel requirement. For any freshly acquired diesel-electrics... they wouldn't know enough about them to do any augmentations like that, so the things' massive range would come in quite handy.
If the job is too complicated, they might elect to skip the train this year and simply use mass quantities of portkeys like they did for the World Cup. that would give them enough time to figure out something for the train, and would also let them avoid trying to move 12,536 children through King's Cross station.
Because that's the sort of thing that gets noticed.
5242987
Or like they apparently did in the ancient past... that wasn't safe, regulated, or whatever else, and was the reason they started the train.
This kind of calculation would give wizards a headache. But since they already have Undetectable Extension charm and Featherweight charm, these over-populate/weight issues should not be an issue, no?
5243374
...
The featherweight charm does not remove momentum, which would be one of the reasons using it on something like a piece of rolling stock is deadly dangerous. There's a reason they're as heavy as they are, and it's not just that the floor of the car is made of concrete!
And the Expansion Charm (because it's not "undetectable", it's "we can't detect it with our current spells", and it's really no different from a "detectable" expansion charm) only works for interiors. If they wanted each compartment to hold fifty students, they could do that. Might have to magically reinforce the suspension and tracks to handle the weight, but they could do that...
Then what? They could swap those 'compartment' cars for regular 'coach' cars and about double individual car capacities. In order to make a suitable Compartment Car (like we see in the books/movies) with an expansion charm, they would have to remove all of the compartments, expand the overall interior of the car, then add the compartments back in in greater numbers. Which is a lot of construction and deconstruction work, even for wizards... it's easier for them to just go acquire another car. The train can handle it- and if they're worried, they can always apply reinforcement spells to the couplers. Bonus, an unexpanded car is NOT a violation for the Misuse of Muggle Artifacts Office to deal with, as it's completely unmodified, except maybe the color or decorations! Thus, if the wizards suddenly have no use for it, they can simply return it to muggle service, who needs to store the thing!
All in all, yes, it would give them a headache. However, unlike me, they can step into the car, count the seats, and multiply by their desired fill ratio (which is apparently around 50%) to get individual car effective capacities- they don't have to worry about how big what part of the floor plan is, they can just count one, two, three. Then, if they divide the total number of students by the individual car effective capacity, that will give them the number of cars they need. You'll notice that most of my conjecture/math/etc was figuring out how many a single car could hold, then the car counts for the train were easy...
Worst case scenario, they don't bother with the math, and be like "This train has enough cars for 288 students. This extra car we could attach has space for 32 students. We have more than 288 students to put in the train. Add the car. This train now has enough cars for 288+32=320 students. This extra car we could attach has space for 32 students..." ... And so on. 383 times.
For locomotive counts, they'd simply be like "Apply power. Does train accelerate fast enough (Y/N)? If yes, Done. Otherwise, Attach locomotive and repeat."
The locomotives, on the other hoof, would be marginally modified from the get-go, to synchronize their controls from one set, probably in the lead locomotive... Yeah, they're unaware that the diesel-electrics provide such a function on their own already. And any locomotive they planned to keep would be modified, like the Hogwarts Express, to run on magic instead of steam... The diesel electrics would probably still burn diesel for quite a while, because they don't understand how it works well enough to make it burn magic instead... which would, coincidentally, make the Hogwarts Express dementor-resistant, as they only darken perception and consume magic, they don't actually erase light... or pressure in an engine cylinder... or electricity. Making muggle tech dementor-resistant, and wizardized-tech vulnerable to such, though the latter would never need fuel or maintenance.
5243416
When I think of the application of those two charms, I always refer to Newt Scamander's portable zoo/house luggage. If the momentum still affects the thing inside, won't all the creatures/furnitures be all over the places every time he open it?
5243519
I often consider things like that to have more spells on them, such that they’re not “expanded” so much as “pocket dimension”... which has its own set of stability problems, making them totally unsuited for anything with very large or multiple entrances. Because otherwise, expansion/featherweight charms would be OP, and they’re not even characters...
You do realize that if you have them using muggle engines, and book three (4?) has dementors show up, ** and the train keeps going because the muggle engines are too dumb to stop**, then some wizards will take notice, and there will be a massive improvement in "resistant" devices coming out a year or two after that.
Just imagine what kind of fortune the Weasleys can make with improved quality "magical" devices that just won't stop no matter what sort of cancellation spells are used.
5244619
Yep. There'd also be a lot of "Wait, don't muggle devices stop working with any magic nearby?" wonderings... when the muggle machines simply ignore all the magic and keep on going...
Pretty sure it was book 3, yes, Prisoner of Azkaban. 4 was Goblet of Fire.
I thought it was electronics that died; something about magic vs transistors in some fandom. Makes me wonder about vacuum tubes, which got the same effect through different means
5245086
In my headcanon, it's electromagnetic interference generated by the amount of magic in the air. Since early portable electronics were all wireless-based, it makes perfect sense that the signal would have been destroyed by it... and the wizards, caught up in their superiority complex as they are (completely canon, wizards in general think they're better than muggles), saw that it wasn't working, and made a somewhat logical conclusion that it was the electricity part that didn't work... because they could make magic-driven ones without much difficulty, and they would work near magic.
Heavy interference like this would be enough to destroy almost any wireless signal, and also damage some unprotected electronics... Specifically some, basically all electronics nowadays are given at least basic shielding against that sort of thing, allowing them to resist it without issue. Except, of course, no WiFi...
That said, yes, in canon, it's apparently electricity itself that dies... which, as around 1/3 of the sub-atomic particles in the universe qualify as "electricity" (do not quote me on that), I'm inclined to believe that- especially since that issue was only referred to in character dialogue- it's a case where "common knowledge" and, of course, Hogwarts: A History were wrong... by reason of misperception and/or overgeneralization.
Yeah, the idea that a basic force of nature like electricity will somehow not work and yet you don't fall apart into a pile of atoms and molecules doesn't make sense.
If static electricity from washing different fabrics together still works, then there is a way to manage voltage difference to drive a force that can push electrons.
Saying that electronic devices fail because shielding problems, for 1992, makes sense. I actually don't remember when the shielded CMOS revolution took over and replaced the old LS non-shielded chips, but it wasn't that far before 1992. So 1980's equipment might have failed, and no one bothered checking to see that the newest stuff from intel was now working properly.
But yea, making it a case of unshielded electronics dying from radiation effects of magic -- that's actually pretty darn close to the whole "LS chips are subject to state alteration by background radiation, which is causing computers to make errors" reality.
So, something that makes this interfere with some radio wave frequency -- which just happen to be where we have computer radios -- as well as radiation affecting unshielded electronics, would do a wonderful job of replicating the canon effects, with a somewhat realistic effect, and more importantly, *military* grade equipment would use different radio frequencies, and have better EM shielding, and would still work. Which gets back to that fandom wonder of "the statue of secrecy is actually broken".
Wait, fandom? It's canon that the head of britain's government is informed, and there's probably knowledge of this in the intelligence people. So yea, fits, fits nicely.