Attack on Titan’s finale begins with the dramatic release of an army of colossal titans to “trample every inch of the world.” Moving past the arguments for and against it in the show, this raises 2 questions that have fascinated me.
Starting at Paradis Island:
1. What would be the optimal strategy to step on every inch of the world?
2. Following that strategy how long would it take with X Titans?
Part 1: Optimal Traversal
Let’s start to break this problem down with baby steps (er… well… giant steps).
I’m going to assume a few things:
- What some fans have speculated is this takes place on the same map as we have and that Paradis Island is what we call Madagascar.
- Mombasa Harbour in Kenya is where Eren first makes landfall.
- Titan’s feet are flat rectangles with no arches or rounded heels that need to be filled in to truly step on every inch.
- Using the reference below, Titan feet are:
- 6 meters wide.
- Going from a US size 6 shoe that has a medium width of approximately 3.5 inches and a length of 9.2 inches. Then retaining that 3.5:9.2 width-to-length ratio would give about a 16-meter length, but I’ll round up to 18 for easier grid traversal.
- Between a Titan’s feet, there is a 4-meter gap, but a Titan can walk in such a way that there will not be a gap.
- Titans move unimpeded by structures and geography.
- Collasal Titan speed does not reduce at night like the smaller Titans.
- Titan bodies are magic. They ignore the square-cube law and increase in air/water resistance. Their movement speed scales with the square root of the length (as some biomechanical movements do) from an average 1.75-meter tall man to 60-meter Titan. The scale is sqrt(60*1.75) = 5.85
Titan Speed:
A journey of a thousand miles begins with a single step
First things first, we need to know how fast a Titan walks and swims.
The swim speed of the average man is 3.3-5.6mph we’ll take the middle. So 4.5mph = 7.25 km/h * 5.85 scale = 42 km/h Titan swim speed.
Next, the walking speed of the average man is 3mph = 4.83 km/h * 5.85 = 28 km/h Titan max walk speed.
To see if this is accurate to the lore is a little difficult. We get this information:
“Over the course of four days after first setting foot on the continental mainland, the Rumbling brought about the complete destruction of the northern continent of Marley… Approximately 80% of all human life on the planet was ended.”
We don’t know the population distribution of the world but in 4 days of walking the Titans could go 2688km. That would cover a large part of Africa, but not “complete destruction.”
If we wanted “complete destruction” of Africa in 4 days the Titans would need to go about 6400km. Which would require them to move at 67km/h. That would be a speed of about 11.5mph or a 5.22-mile time if we scaled down. The Titans certainly aren’t sprinting in the show. *Sigh*… a show with 60-meter-tall magic humanoids isn’t 100% realistic. Well, what can you do? We’ll move just forward with a swim speed of 42 km/h and a 28 km/h walk.
Stride Lengths:
The final piece of information we need is about stride lengths. I am going to assume at max speed a step length (from one heel to the other) of 2x the length of the foot as that is what mine is. That makes the stride length (same heal to heal) 4x the length. With 3-foot lengths between footsteps.
Now things get interesting. Remember our goal is to “trample every inch.” If a Titan’s foot passes above some ground before coming down that space between has not been trampled. In the example above there are 6 pieces of ground that have been passed over. At a step length of 2L after the first step, there will be 1 space between footsteps and 3 thereafter. If we bring the step length to 1L we get this on the left and at what we’ll call 0L we get the right.
So 2L has 25% coverage, 1L is 50% and 0L is 100%. I’m going to assert that there is a cost to increasing the coverage and that is a speed reduction. How much of a reduction? I couldn’t find a good resource for this so let’s do some science ourselves! I set up a test that is 180 inches long. My feet are about 10 inches so I split up the distance into 10-inch steps and followed each of the patterns above recording the total time it took.
| Step Type | Average Time (seconds) | Increase | Final Titan Speed Scaled | Days to travel 3500km |
| 2L | 7 | 1 (base) | 28km/h | 5.2 |
| 1L | 10 | 1.42 | 19.7km/h | 7.4 |
| 0L | 15.5 | 2.2 | 12.7km/h | 11.5 |
We have everything we need to start planning out how to move our Titans around. Stick around for part 2 where we will begin developing traversal strategies at the micro level before finishing with the macro level.