Train of Thought

I'm a simple man. I like physics, I like Attack On Titan. I see trains smashing into giant naked monsters, I cheer. But how practical would a steam train be at running into a titan?

That's what we're about to find out, kids. Buckle up.

Trains are a heavy thing. Even the smaller steam locomotives had over 100 metric tons of mass and could reach the crazy mass of 200.
That's crazy. That's nearly the mass of 3 average-sized houses.
They were historically made mostly out of cast iron and steel, with small parts of bronze, copper and brass.
Okay, that's good and all, here's the CRAZY part:
In the AoT universe, say they build a train out of stainless steel. It would way MORE than an average train, not less! This is because stainless steel is about 8 tons per cubic meter, while cast iron at most only 7.8, and can go as low as 6.8!

Let's assume that the different material will give the average train an extra 5% on the weight, turning our rough 170 tons of train into a 178.5, which we will round to a 180.
What about speed?
That's a tricky thing, because based on the type of train, the difference could be tremendous. Trains carrying coal could go as slow as 30 mph, while fast passenger trains could hit a 90mph. I'm assuming that the AoT train would be a freight train (Carrying supplies), which on historical data give it about 50mph, or about 80.5 kilometers per hour.
As physicists, though, we care for the meter per second, which is 22.352.

Sweet. That's the train. Let's look into titans and collisions now!

Titans, in general, are mysterious, so we're going to have to pull a lot of assumptions now.
We know titans are lighter than they seem, but how much is still uncertain. However, recent anime events have shed some light on the matter, and can help us narrow it down.

===Spoilerish territory===
Person X weighs 95KG, is well trained, and can lift a 2/3-meter class titan all on his own.
Average males can carry/squat about 60kg. Let's say that X is powerful enough to carry his own weight. This means that AT MOST (Though probably smaller), a 2.5 meter class can weigh 95kg.
Most humans, for comparison, who are taller or even remotely close to 2 meters of height are well over 100kg. Person X is 192cm tall, a bit short of 2m.
This, VERY roughly, puts titans at about 80-66% the weight of humans. For our sake, let's go with 70%.
Okay. Now, titans in height go anywhere from 2 to 15 meters on average. Weight is based on 3 dimensions, so increasing the height by X times increases the weight by X^3 times. This puts 15m class titans, who are about 6 or 7 times the height of the titan we discussed earlier, at a MUCH bigger weight.
95[kg]* 6.5^3 = 25265.5[kg].
That's over 25 tons. Holy shit.

For our scenario, let's have a train going at max speed and hitting a 15m titan. What happens?

On one side, we have a 180 ton machine with the speed of 20 meters per second. On the other side, a stationary 25 ton monster.
I'll save you all the calculating, because it's a bit complex. The result is that the train is slowed down by about 25% to 15.12 meters per second, while the titan is hit with 36 mega-netwons of kinetic energy.
This makes the titan fly forward at about 35.12 meter per seconds, or 126 kilometers per hour.

That titan's goddamn toast.

Still, recurring collision would slow down the train significantly. If the train gets into a field of titans, it could prove problematic.

So that's it. Want to complain about my rough estimates? Go right ahead, I welcome it

Alan.

Before I say anything else, I need to say this one thing.

You're fucking amazing. Marvelous job, my friend, marvelous.



For one thing, I'm not really going to complain about any of the estimates. Reason for that being they're fully understandable and mostly were for our sake. You seem more than just used to work with much more complicated numbers on a daily basis.


The only thing I'm going to comment on is the fact that you consider the mass of the locomotive, but the speed of an actual freight train. Given the reason the train is slower than a passenger train is the fact the passenger one has less weight to pull, I think that either the speed should be higher (in case you calculate for the free locomotive), or the mass hitting (in case you're calculating for a full train).

(both of them being even worse news for the titans)

I don't know how the fact wagons are linked together is going to affect anything, though. Maybe it does indeed mean only the locomotive weight matters, and you just forgot to mention it? And, in that case, how badly would the shock of the impact be on the wagons? (given it's a sudden drop of 5 meters per second, and their inertia is going to carry them against the linking bits; is the number significant enough to take into account?)



Also, if you'd be to add a triangular plow-like object in front of the train, how much would it mitigate the speed loss? (and would it rip the titan apart?) I assume that depends on the angle as well as the titan's body density and resistance to impact, or the likewise. If you need any more specific data to be able to calculate that one, please just tell me and I'll see what I can gather.
(for one thing, we know blades wielded by humans can cut through a titan's nape, but that an axe swung down on their neck won't do almost anything; no idea what that says about them, though)

Alas, this is where my sub-par English comes into play.
I was using the terms 'locomotive' and 'train' interchangeably. This has led to some embarrassingly stupid mistakes, for which I apologize.

According to actual railroaders, full trains can weigh anywhere from 3000 tons to 10000 tons, with rails cars weighing about 30 tons empty and closer to 150 while loaded.
In general, this raises the mass in our calculation. A lot.
Say we're talking about a train carrying mostly construction supplies, with some space for soldiers and cannons (Each weighing roughly 1.5 tons, historically).
Whatever. Let's just say that this badboy will weigh 5000 tons. More than enough for all of the things needed to be carried.
This changes the calculation, a lot. The train would barely be affected by impact with a 25-ton titan (a drop in less than one kilometer per hour in speed), while the titan will be wrecked by the huge force of the impact. Like, doesn't stand a chance.

My calculation was very rough, ignoring friction and handling the train as a single body. I'll try to answer the cart-question now. As far as I can tell, the train shouldn't be too affected by a crash like this. Because it is so long, and if the links are built with impact in mind, it will act sort of like a giant metallic spring, spreading the impact slowly and effectively over the body of the train. It shouldn't be much of a problem.

A plow won't even be necessary. The colossal amount of kinetic energy packed into a train going at this speed would make a titan explode, as in completely tear it open. As long as the shell of the locomotive is built sturdy and hard, it can take the titan's collision.
The plow, under NO CIRCUMSTANCE, should be built to pierce through titans - any design putting a point at its end to pierce through a titan would be faulty, put too much pressure on a single point, and result in the front of the train getting wrecked.
The train's best chance is to have a large, wide-aread slope that takes up as much area as possible and has the lowest angle. This means that the impact would be spread over the most area possible, and that there would be more 'material' blocking the impact per point on the front of the train. Tanks are also built with these slopes in mind, to make piercing shots less effective.
Steam locomotives have a height of about 4.5 meters, as far as I could find.
Giving the train a slope that's 9 meters long in front of it and about as wide as it is high (4.5 meters) will give the slope a surface area of 40.5 square meters. Stainless steel can handle stress in hundreds of KSI (Kilopounds per square inch). Converting the train's weight to pounds puts it at about 1e+7, which is a lot. Still converting our 40.5 square meters to square inch gives us 62775.13 square inch. Dividing the pounds by the square inch gives us a ratio of 159.29, which is a lot of stress, but less than stainless steel at room temperature can handle.
The TL;DR is that trains could destroy titans with or without plows, but crazy big plows are required to protect the train from harm.