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Summary of Feat: In S2 CH318, Three Rankers (Prowler, H-14, and Water Jelly) stop the Hell Train, and SIU later states this in a Blogpost (here)

[Frog may have a lower ranking than Yuri, but is still a High Ranker

It’s pretty evident from how Frog managed to stop the train alone,

while three Rankers had to collaborate together to stop it.]

In other words, if the energy of the Hell Train is calculated, then a high-end figure for the AP of normal Rankers can be gotten.

ON THE HELL TRAIN'S SIZE:

Unfortunately trying to get a solid scale of the Hell Train is... rather difficult, on account of it being a 3D modeled object appearing in several arcs and drawn over across several years. The Cars of the Hell Train have appeared in every size scale-able, from being slightly larger than the wingspan of the Bong Bong, to dwarfing the Namehunt Station. Seriously. Daniel said that it was several times larger than the Archimedes when you add all the cars together in S2 CH134, but that doesn't help with scaling, and Daniel's also a chronic liar and an utter troll.

Using character heights when they appear in front of the door gets dimensions of dozens to a couple hundred meters across, but then scaling them to structures inside the Train make the outside dimensions too small for them to fit. Way too small.

The only time we're given a concrete metric to work with is in S2 CH 161, where we see what the Hell Train looks like from a height of 15 kilometers, where the unnamed Khun-guy is. As such, the size of the Hell Train and other derivative calculations will be calculated from that moment.

GETTING DIMENSIONS FOR SIZE AND SPEED:

REFERENCE IMAGES: here

SCAN ONE:

Distance to Train: 15km

Height of Panel: 877 pixels

Length of Train: 120 pixels

  • Angsizing for Length: 2 * tan(70/2) * 15 * 120/877 = 2.874284079

A single car of the Hell Train is 2.874 kilometers long

SCAN TWO:

Boxcar Length (2.87km): 256 pixels

Boxcar Height: 95 pixels

  • 2.874284079 / 256 * 95 = 1.066628857

Boxcar Height: ~1 km (1.066628857km)

Wooden Horse Height: 662 pixels

  • 2.874284079 / 256 * 662 = 7.432718986

Wooden Horse Height: 7.432718986 km

SCAN THREE:

Boxcar Height (1.066628857km): 158 pixels

Boxcar Width (157 pixels):

  • 1.066628857 / 158 * 157 = 1.059878041

Boxcar Width: ~1 km (1.059878041km)

Panel Height: 920 pixels

Wooden Horse Height(7.432718986 km): 138 pixels

  • Angsizing to get the distance: 7.432718986km * 920/(138 * 2 * tan(70/2) = 35.38340935

Linear Distance to Wooden Horse: 35.38340935 km

Except that the Hell Train approaches from the front of the Station (you can see the Wooden Horse's "Head" pointing towards the Train), but the panels of the Hell Train when stopped in the station show it passing through width-ways (it goes through the "Body" of the Horse, with the Head positioned perpendicular to the Hell Train), meaning the Hell Train had to have turned 90 degrees at some point in order to enter the Station. Modeling it's path from the reference point as a half-circle in order to do the rotation, means the actual length of the path it took to reach the Station was

  • 35.38340935/2 * Pi = 55.58012944 kilometers long

TIME FRAME: The next panel after the reference Panel used for Angsizing the distance to the Station, Poe gives an announcement that the train is going to stop in just a moment. This announcement happens simultaneously over all the other dialogue that occurs in the Train, which is useful because there's a lot of talking. Right after he finishes it cuts to Boro and Sachi talking, and then they get cut off by the Train arriving, as seen with reference images- here.

[This is an announcement to the regulars on the Train. The train will be arriving at the Wooden Horse Station on the 37th Floor in a moment. I repeat, this Train will be arriving at the Wooden Horse Station on the 37th Floor in a moment. Those who are getting off the train please be prepared to exit. I repeat; those who are getting off the train- please be prepared!

I see. He said that he'd bring Roen back to life, huh? Daniel that kid, I was wondering what would have happened to make Aka come and look for me all of a sudden but. Now I get the idea of what's going on. It's a good thing that I happened to be around here thanks to this "Emily." Isn't that Emily? Are you using it too? Yeah, it was useful to find the ticket. What's that message? This message was sent this morning. For a few days, similar messages were sent. For a couple of days!? Damn it, what are they up to this time? What do you mean? You see! This device called "Emily" is, in fact-](THUMP)

Running this through a syllable counter and then using the speed someone can talk at to get the timeframe gets-

Number of Syllables: 236

Average Person Speaks 4 - 5 syllables per second (source):

  • 236 / 4 = 59
  • 236 / 5 = 47.2

Time elapsed between Angsized Shot and the Train Arriving: 59 - 47.2 seconds

SPEED OF TRAIN:

Divide Distance by Time:

55.58012944 / 59 = 0.9420360922 km/s = 942.0360922 m/s = Mach 2.74646091 [ACCEPTED]

55.58012944 / 47.2 = 1.177545115 km/s = 1177.545115 m/s = Mach 3.433076138

The Hell Train can move at 942.0360922 - 1177.545115 m/s.

[SEE: "EDIT ON HELL TRAIN'S SPEED"]

VOLUME OF TRAIN: 1.059878041 km * 1.066628857 km * 2.874284079 km = 3.249368101 cubic kilometers / 3,249,368,101 cubic meters

MASS OF TRAIN CAR:

The Volume of a 60' Boxcar can be used to get the scaling factor between it and a car of the Hell Train. (Volume Source here)

  • Volume of a 60' Boxcar: 5,830 - 7,633 cubic feet or 165.0872 - 216.14249 cubic meters

Scaling to Volume:

  • 3249368101 / 165.0872 = 19,682,737.98
  • 3249368101 / 216.14249 = 15,033,453.63

One Hell Train Car has 19,682,737.98 - 15,033,453.63 times the volume of a standard 60' boxcar.

Using the mass of an empty and half-full 60' standard Boxcar (source) as a base to apply the scale to (since the amount of "stuff" in the Train varies), we can get the high and low ends for the mass of one Hell-Train car. (The average carrying capacity of a 60' boxcar is 100 American tons (not tonnes), or 200,000 lbs. Half is 100,000lbs)

  • Weight of a 60' Empty Boxcar: 63000 lbs or 28,576.319 kg or 28.576319 tonnes
  • Weight of a 60' Half Full Boxcar: 63000 + 100,000 lbs or 74,842.741 kg, or 74.842741 tonnes

Scaling the Mass: (Empty Boxcar)

  • 19682737.98 * 28.576319 tonnes = 562,460,199.3 tonnes
  • 15033453.63 * 28.576319 tonnes = 429,600,766.6 tonnes

Scaling the Mass: (Half Full Boxcar):

  • 19682737.98 * 74.842741 tonnes = 1,473,110,060 tonnes
  • 15033453.63 * 74.842741 tonnes = 1,125,144,880 tonnes [ACCEPTED]

And then to get the mass of the whole train, we multiply by the number of cars. The Hell Train has at least 20 cars; as seen at the start of S2 CH260, meaning;

Empty:

  • 562,460,199.3 * 20 = 11.249204 billion tonnes
  • 429,600,766.6 * 20 = 8.59201533 billion tonnes

Half Full:

  • 1,473,110,060 * 20 = 29,462,201,200 billion tonnes
  • 1,125,144,880 * 20 = 22,502,897,600 billion tonnes

And then finally, using the Kinetic Energy formula the mass and speed can be physics'd to see how much energy the Hell Train has in motion, and thus how much energy it would require to stop the thing. Using the two speed ranges and four different masses, we get 8 different answers.

- 942.0360922 m/s (Empty)

(11.249204 trillion kg/2) * 942.0360922^(2) = 4.99145E+18 J or 1192.99 Megatons

(8.59201533 trillion kg/2) * 942.0360922^(2) = 3.81241E+18 J or 911.19 Megatons

- 1177.545115 m/s (Empty)

(11.249204 trillion kg/2) * 1177.545115^(2) = 7.79914E+18 J or 1864.04 Megatons

(8.59201533 trillion kg/2) * 1177.545115^(2) = 5.9569E+18 J or 1423.73 Megatons

- 942.0360922 m/s (Half Full)

(29.4622012 trillion kg/2) * 942.0360922^(2) = 1.30729E+19 J or 3124.5 Megatons

(22.5028976 trillion kg/2) * 942.0360922^(2) = 9.9849E+18 J or 2386.45 Megatons [ACCEPTED]

- 1177.545115 m/s (Half Full)

(29.4622012 trillion kg/2) * 1177.545115^(2) = 2.04263E+19 J or 4882 Megatons

(22.5028976 trillion kg/2) * 1177.545115^(2) = 1.56014E+19 J or 3728.8 Megatons

[SEE: "EDIT ON HELL TRAIN'S SIZE"]

CONCLUSION:

Before I summarize, keep in mind that the numbers listed below are the bare minimum values, as;

1. The full length of the Hell Train is never shown; this calc just uses the most we've seen which is 20 cars, meaning it could be way more massive. For example, a freight train can typically pull up to 200 cars. If the Hell Train was similar, then the KE would be 10 times the above results. Additionally, the place where the Dallar Show takes place is in the "74th Motor Sector", implying there's at least 73 other motor sectors. Unfortunately this could not be used to help determine the number of cars, as it's unknown how many Motor Sectors are in 1 Car. (If it's less than 4 then there's more than 20 Cars.)

-and

2. The speed of the Hell Train used in this calc was when it was stopping at the Wooden Horse Station, meaning it was slowing down.

Now then, the average velocity gotten from a timeframe where an object slows down to halt, is only half the initial velocity, as Average Velocity = (Initial Velocity + Final Velocity) / 2, and when the final velocity is 0, the calc will be some proportion of 1 = (2 + 0) / 2. This means that the Hell Train can on average travel twice as fast as in the scene where it stops at the Last Station. Since velocity is squared in the KE formula, even going twice as fast would quadruple the above results. Not only that, but the Hell Train wasn't just travelling at average speed in the Feat Scene, as when it was chugging towards Dorian Frog; and later Prowler, H-14, and Water Jelly; it was actually going at Max Speed, meaning it was going even faster. The only reason I didn't bring this up during the calc is because only realized this days after I was done, and I'm too lazy to redo the math.

- With these two points in mind, I strongly advocate that (should this calc be accepted) the High-End calc for the AP should be used. Now then, onto the actual results!

Full Range of AP: 911.19 - 1,192.99 - 1,423.73 - 1,864.04 - 2,386.45 [ACCEPTED] - 3,124.5 - 3,728.8 - 4,882 Megatons

The amount of force it'd take to stop the Hell Train has a low-to-high end of 911.19 Megatons - 4.882 Gigatons; making the feat 7-A to 6-C, making the high-end AP for an individual standard Ranker 7-A to High 7-A.

[EDIT ON 3/29/21: The Hell Train's Size]

So, turns out that there is a shot that has what should be the full length of the Hell Train in it, and it's this tiny one (here) with Evan above the dock that the Hell Train is supposed to go into along with the Last Station, that Water Jelly just closed off, and uh... it's a smidge longer than 20 cars.

  • Length of 8 Boxcars: 40 pixels
  • Length of Last Station + Dock Tube: 663 pixels long
  • 8 / 40 * 663 = ~132 Boxcars (Removed fraction because you can't have a fraction of a boxcar)

Multiplying the new number of cars by the accepted mass of a Boxcar gets...

  • 1,125,144,880 * 132 = 148.519124 billion tonnes

And plugging the mass into the KE formula after converting to kilograms, and using the accepted speed gets...

  • 148.519124 trillion kg/2 * 942.0360922^(2) = 6.59003116E+19 J

The KE of the full Hell Train has an output of ~15.75 Gigatons, making the feat 6-C, or Island level.

[EDIT ON 9/5/21: The Hell Train's Speed]

Alright so, after rereading Last Station for the trillionth time, I realized that there were definitely ways to calculate the Hell Train's speed as it was approaching the Station, instead of using its speed in a previous arc which was a bit sketchy. Reference pictures (here)

DISTANCE FROM FRONT OF TRAIN APPROACHING THE PLANE OF OBSERVERS:

  • Length of Train (2.87 km): 186 pixels
  • Front of Train to Observers (eyeballed due to angle): 211 pixels
  • 2.874284079 km / 186 * 211 = 3.260612584 km

DISTANCE FROM FRONT OF TRAIN PASSED THE PLANE OF OBSERVERS:

  • Length of Train (2.87 km): 230 pixels
  • Front of Train Passed Observers: 273 pixels
  • 2.874284079 km / 230 * 273 = 3.411650233 km

TOTAL DISTANCE + SPEED + KINETIC ENERGY:

  • 3,260.612584 meters + 3,411.650233 meters = 6672.262817 meters
  • 6672.262817 / Standard Across Panel Timeframe (5 seconds) = 1334.452563 m/s
  • 148.519124 trillion kg (Full size of Train)/2 * 1334.452563^2 = 1.32238728e+20 joules

The Total KE of the Hell Train is 31.60581457 Gigatons, or Island level.

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