The Rumbling's Math (or lack thereof)- Part II
The Time Factor
Finally, there is the question of time. We don’t have an exact timeline of the events between Eren waking up the Wall Titans and the Battle of Heaven and Earth, but we do have the speed:
If the rumbling covers 600 km in half a day, that’s 1,200 km per 24 hours – 50 km/h (for details on horse speed, you can check my essay Distances in AoT). That’s also about the fastest a real ship can go, so I’ll assume their speet is the same both on land and in water.
Unlike normal titans, wall titans do not go dormant at night, so they advance 24/7 (ch. 126). It makes sense, too, since, if they’d stopped at night, people could simply surround them towards the already trampled areas, saving a lot of lives, and the combat planes could gun down a good number of them as well—as long as they stayed out of reach of the rock-hurling titans sprouting on Eren’s back.
Since the manga does feature a nice map of Paradis and Marley, we can try to calculate how long it would take for the Rumbling to get to Fort Salta.
Some notes on how I worked the map:
Wall Maria has a diameter of 960 km. From atop the 50 m walls, the line of horizon lies 25 km far. Paradisians ignore the existence of the ocean, so the nearest coastline must be at least 25 km away from the wall (realistically, a bit more, since certain atmospheric conditions can make visible things that are usually below the line of horizon, but let’s keep things simple and say 25). Therefore, the island of Paradis would be 960+25+25= 1,100 km of minimal width.
Please note that, although the island of Paradis is based on the island of Madagascar, the diameter of Wall Maria alone (960 km) is over 1.5 times the width of the actual island of Madagascar (580 km).
The island width in my (printed, as It’s easier for me to do this stuff with actual ruler and pencil) map is 7 mm, so all measures are calculated upon this scale of 7 mm = 1,100 km.
Before all the titans cross the strait into Marley, they need to assemble. They can’t just emerge from the walls and start walking, or else they’d destroy Paradis first, the very land the Rumbling is supposed to protect. So they’re likely walking in a more or less single line along the path the now torn walls leave (more like a trench, since the bottom 10 m of every titan are underground forming the wall’s foundations) until reaching the sea, from where they swim to the coast of Marley. This line, for the titans in the further edge of wall Maria, would be just over 1,500 km, so 1,500 ÷ 50 = 30; it would take them one day and six hours just to clear the walls and gather on the coast to start their march onto Marley—which, incredibly, ch. 126 pretty much confirms.
It’s worth noting that, in contrast to the impossibly fast horses of the Utgard castle siege, this time Connie and Falco are shown to spend the night on their way to Ragako.
Mind you, even when trying to minimize destruction within the island, the titans in walls Sina and Rose still have to breach the distance between those walls and wall Maria, so there will be a non-negligible strip of scorched earth between the three walls—as the manga itself acknowledges in ch. 125.
We know the Rumbling does not cross the sea from the port where the Scouts board the Azumabito ship, as it shows no signs of titans having passed. The port seems to be in a straight line south of Shiganshina, which is not the closest point to Marley. The closest point to Marley is nearer to the Yarkell-Krolva-Quinta axis, and general consensus is that Liberio is near this point.
Now this is where things get murky, or Yams forgets all about math again. Here’s the map I printed, with the distances calculated based on the (minimum) Paradis island witdh of 1,100 km = 7 mm on paper.
https://i.postimg.cc/ZRM2nXSX/image08.jp
And those distances are HUGE. Plus, Liberio, Odiha and Fort Salta—the three key locations of the Rumbling and the Battle of Heaven and Earth, are in a triangle, not a line. And at 50 km/h, the time it takes to get from one to the other is also remarkably long:
Scale: mm km Time to reach at 50 km/h
Paradis width 7 1.100,00 (in decimal) (in hrs:min) (in days)
Paradis-Marley 6 942,86 18,9 18:54 0 d 18 h 54 m
Paradis-Ft Salta 99 15.557,14 311,1 311:06 12 d 23 h 6 m
Odiha-Ft Salta 75 11.785,71 235,7 235:42 9 d 19 h 42 m
Paradis-Odiha 42 6.600,00 132,0 132:00 5 d 12 h
For context, the 11.785 km from Odiha to Fort Salta is only a bit more than the current SCL-CDG flights between Santiago, Chile and Paris, France (11,666 km). That’s how far those 2 are. Hold on to that commercial aviation reference.
In this sense, the only way to destroy those three as seen in canon would be a curved trajectory: cross the sea and turn towards Odiha, flattening Liberio in the process; turn left again in Odiha towards Fort Salta. This would reduce a bit the time needed to connect all 3 places, though not significatively. Another possibility is that Eren’s splitting the titans in two or more columns in order to target more densely-populated areas and strategic bases first (like the base in the north of Marley that Yelena points at right before Ft Salta and never gets mentioned again), but then again, this would leave large swathes of land untouched, serving as refuge for everyone smart enough, and close to the rumbling’s border enough, to escape sideways, unlike Rickon Stark in GOT, but nothing in canon suggests that.
Also, let me remind you again that the titans’ column is made of several ranks, so its total width is much less that if we just lined up all the titans side by side. Here are the ranks width projected onto the previous map at scale; remember that the advancing column has between 3 and >6 ranks, so the actual width of the whole thing is probably between the 4- and 5-rank values, if not less (the rank width are the brown “rows” in the image).
Ranks Titans/rank Rank width in km
1 358.600 8.965 (Discarded)
2 179.300 4.483 (Discarded)
3 119.533 2.988 (true in some sections)
4 89.650 2.241 (true in some sections)
5 71.720 1.793 (true in some sections)
>6 <59.767 <1.494 (true in Odiha and Fort Salta columns)
Next we have the Alliance. We aren’t told how long it takes them to reach Odiha from Paradis on the Azumabito ship. Their route must be slower than the titans, though, as only super-fast modern ferries can reach 50 km/h, so it would take them no less than a week to get there. They arrive just before the titans, though, who, by my calculations, would need only five and a half days to get there straight from Paradis, so this supports the theory that the Rumbling would not advance in a straight line. Or that Yams just didn’t do the math, which should surprise absolutely no one at this point.
However: the Alliance escapes Odiha by flying boat (plane) just as the titans are arriving. But by the time they spot the Founder and Fort Salta, they are behind the mass of Titans. This supports the two-column theory, as the only way for the titans (50 km/h) to have such advantage against a plane (~300 km/h) is to have a very generous start, that is, heading for Fort Salta straight from Liberio coast, without deviating to Odiha first.
The glaring problem with this part, though, is one that, if you’re lucky enough to have taken more than two or three plane trips in your life, probably already realised: there’s no way in hell that that tiny plane, which isn’t even fully fuelled, can cover the distance between Odiha and Fort Salta.
The flying boat appears to be based on the Kawanishi H8K, a Japanese WW2 flying boat. At a length of 29 m, it was smaller and had less fuel capacity than the Airbus A318 of today. Its cruise speed was 296 km/h. At that speed, it would take over a day and a half to get from Odiha to Fort Salta.
Time to reach at cruise speed
Cruise speed Distance in decimal hrs:min in days
296.0 km/h 11,785.7 km 39,8 39:48 1 d 15 h 48 m
The above number is net time, that is, if the plane didn’t stop at all. But a plane that size only has a 5,000-7,000 km range—with a full tank. Only big long-haul airliners like the Boeing 747, Airbus A330 and up can travel more than 10,000 km without refuelling. If the plane did pit-stops, it could work but, the thing is, where on the Titan-flattened earth is Azumabito’s flying boat going to land and refuel?
If the Rumbling advances in two or more columns, there might be available non-destroyed airstrips along the road to stop, but if that’d be the case, it’s a huge thing, more than worthy of showing up in canon, isn't it? Yet they make it look like a short flight.
80 % of humanity, dead
Actually, I’ve no problem with this number. Some people tend to conflate 80 % of the world’s population with 80 % of the world’s surface, but this is wrong. People are not distributed evenly across our world and neither would they be in AoT’s world. There’s no shortage of maps available on the internet showing population density. as a sample, this one showing 25, 50 and 75 % of our world’s population:
So no, Eren needn’t to trample everything to kill everyone.
If anything, what bugs me about the 80 % is that neither Eren not ANYONE at that point can possibly know what percentage of humanity perishes in the Rumbling. This is because the actual extent of the damage and body count can't be known until weeks, if not months, after the Rumbling stops: they don't have internet or satellite phones, radio towers would be out, so data assessment and communication would take time. Also, because the power of the titans ceases to exist after Eren’s death, he couldn’t possibly remember this info from the future Attack titan (it's a closed time loop, so they can't see things in paths from after the time loop). One more oversight from Isayama, who has proven time and again to be shit with numbers. He could have just said Eren wiped out "most of humanity", with Armin confirming the number in the epilogue, but no, he just had to pull more random numbers out of his ass. The only way Eren could have known what percentage of humanity he’d kill would be for him to thoroughly study the available population data and chart the route of the Rumbling accordingly, but this is Eren we’re talking about. He may go as far as to target the cities with the bigger font size on the map, but you know he won’t ever crunch the numbers.
I find it interesting, too, that no one seems to care about all the other things destroys. Save for a brief mention by Willy Tybur in ch. 100 (and I think Hange also mentions something in passing at some point, will add if I find it).
Final musings
I have no conclusion for this rant more than that the geography and maths of the Rumbling make no more sense than the geography and maths of the walls, that is, little to none at all. The TL:DR of this is that there aren’t enough titans to cause the level of destruction the manga shows in as little time as the manga suggests, and that the timing of the alliance flight and pursuit is all over the place.
There are two questions that remain a mystery and could provide an answer to the incongruencies of the Rumbling. Unfortunately, canon says nothing for or against this, so strictly speaking, they are more headcanon meant to explain the gaps in the manga rather than an informed interpretation of canonical events.
The first question is whether Eren’s founder is capable of creating more titans than the ones existing within the walls. As we’ve seen, the roughly 400k titans we have are too few to cause that level of destruction in just a few days. Being able to create more titans could allow to reach the necessary number to destroy the whole continent within a week. However, if Eren were able to create titans out of thin air, it’d make no sense to awake the wall titans in the first place, spreading terror on Paradis before crossing the sea. Just make a gazillion titans appear on the coast of Liberio and go.
The second question is how much control Eren actually has on the wall titans, and how far reaching that control is. Does he have to be within a certain distance of the titans to order them to march? Do they sense humans the way mindless titans do so you just tell them “go” and they’ll find their way to the next densely populated spot? Can Eren order one titan 2,000 km away to walk or stop? Or do the orders pass from close-by titans to far-flung titans like a network? Can he control them individually?
Though Reiner says in Ch. 124 that “the founding titan is able to control all titans and subjects of Ymir as it sees fit” the answer to that question seems to be he can’t or, if he can, he can’t control more than one individual titan simultaneously. We can see evidence of this a few panels later, when Armin notes the mindless titans born of Zeke’s scream have started eating Eldians (looks like Eren forgot to tell those what to do), as well as the panels in later chapters where we see titans tripping and falling. Do those become stragglers, following the rumbling from way behind? Or strays, walking aimlessly in random directions?
Are they still bumping into the White Cliffs of Dover?












