End of Alicization Kirito's Speed

Notice of Invalidity

As we have gotten exact numbers for the distance between Admina and Cardina, this calculation I was instructed to do based on incredibly vague reference numbers is no longer valid. Do not use this for any kind of sourcing and kindly refer to the new calculation.

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Goal of the Calculation

To determine the speed of End of Alicization, as well as Star King Kirito, by scaling him to the Abyssal Horror, as well as the Mechadragon jets and regular dragonjet transport vehicles

Important Disclaimers:

• This is the complete version of this entry. Unless further changes are recommended upon review, it has been finalized.

• I have used "End of Alicization Kirito" as the title, as all of memories (and thus experiences) of Kirito during his 200 year time in Underworld are no longer accessible to him. In addition to this, during the 200 years (and when he actually did become Star King), Kirito had a direct connection to the Main Visualizer, the source of Incarnation, which gave him a much higher Incarnation potential than usual as a result. This connection was unlocked by Takeru Higa to aid his recovery process. No longer having this connection on his subsequent dives (including the dive in Volume 18, Prologue III which is the topic of this calculation), a distinction between "End of Alicization" and "Star King" Kirito have to be made, to avoid being misled by possible achievements during the 200 year period.
  • tl;dr: Star King during 200 years > End of Alicization Kirito

Calculation:

Speed = Distance / Time

We have no explicit mention of a speed, thus it needs to be calculated based on the formula. For that, we need to pinpoint Distance and Time variables.

Distance

The volumetric size of Underworld is currently unknown to make any reasonable references for the distance for the travels, however we currently know that it consists of Solus (the Sun) and two planets orbiting it (Admina and Cardina).

The current maximum size of the Underworld is one sun and two planets orbiting it. -Reki Kawahara

Beyond the scope of the orbit of these planets, nothing exists and it is "the same starry sky we see in open world games" per Reki Kawahara, a typical Skybox. Thus there is no "interstellar travel" in Underworld, and the use of the term in Sword Art Online Light Novels comes from a simple terminology shift, as rather than referring to planets as "planets", Underworlders refer to them as "Companion Star" as well as "Companion Planet", while explicitly making it clear they are habited planets rotating around Solus (the Sun). As Cardina and Admina are internally referred to as "Stars", their travel terminology reflects this shift as "interstellar" travel as well, despite not being interstellar in real world terms without the shift.

And it was a whole three-hour journey [from Cardina] to reach the companion star of Admina. -Stica Schtrinen, Volume 18, Prologue III

We also do know the two planets Cardina and Admina are closer to each other than Earth and Mars are, which gives a clear distance range to work with at the moment, with the exact distance measurements promised to arrive in Sword Art Online Volume 26.

The specific distance should be revealed in SAO volume 26, but it is much, much closer than Earth and Mars. -Reki Kawahara

For the purposes of this calculation, to avoid arbitrary decisions on the distance, "much, much" statement, that cannot be reasonably quantified, will be ignored until the exact distance is revealed in the next volume, and the calculation will thus be based on the "closer than Earth and Mars" statement alone and thus as the next closest reference, distance between Earth and Venus will be used.

To avoid further arbitrary picks, there will be high-, mid- and lowball calculations.

For the highball calculation, the maximum distances of the planets will be used.

For the midball calculation, the average distances of the planets will be used.

For the lowball calculation, the minimum distances of the planets will be used.

Distances are rounded to nearest 10 million measurement for the ease of simplicity.

For Distance we have:

Highball: Maximum Distance to Venus = 260 million km

Midball: Average Distance of Earth to Venus = (Minimum Distance to Venus + Maximum Distance to Venus) / 2 = (40 million km + 260 million km) / 2 = 150 million km

Lowball: Minimum Distance to Venus = 40 million km

Time

We have 2 statements of how long it takes to get from one planet to the other for 2 different vehicle types. Mechadragon Jets and Dragon Jets (transport vehicles).

For Mechadragon Jets:

The rules of the Underworld Space Force were absolute, but even their drill instructor couldn’t see them out beyond the atmosphere. And it was a whole three-hour journey to reach the companion star of Admina. That meant there was room for a little error. -Narrator from the perspective of Stica Shrinen, Volume 18, Prologue III

For Dragonjet transport vehicles:

旅客機がカルディナからアドミナまで飛ぶのにかかる時間はおよそ六時間です。つまり理論的には一日に二往復することも可能なのですが、一月半前までは一週間に一回しか飛べませんでした。-Eolyne Herlentz, Volume 25, Part 10

Exact Translation by the current SAO Fan Translator, Gsimenas of the SAO Wikia:

It takes approximately six hours for a passenger craft to fly from Cardina to Admina. Meaning that from a perspective of logic, it should be possible to make two round-trips per day, but we only used to make one trip per week until that day 1.5 months ago. -Eolyne Herlentz, Volume 25, Part 10

For Time we have:

Mechadragon Jet: 3 hours

Dragon Jet: 6 hours

Speed

Now that we have a measure of distance, as well as time, we can actually calculate the speed of the vehicles. For the purposes of simplicity, the calculation ignores the loss of time through take off, acceleration, deceleration and landing.

Speed = Distance / Time

Highball

Maximum Distance of Venus / Time

Mechadragon: 260 million km / 3 hours = 86.666.700 km/h = 24.074.083,33 m/s

Dragon Jet: 260 million km / 6 hours = 43.333.300 km/h = 12.037.027,78 m/s

Midball

Average Distance of Venus / Time

Mechadragon: 150 million km / 3 hours = 50.000.000 km/h = 13.888.888,89 m/s

Dragon Jet: 150 million km / 6 hours = 25.000.000 km/h = 6.944.444,44 m/s

Lowball

Minimum Distance of Venus / Time

Mechadragon: 40 million km / 3 hours = 13.333.300 km/h = 3.703.694,44 m/s

Dragon Jet: 40 million km / 6 hours = 6.666.670 km/h = 1.851.852,78 m/s

How does this tie to Kirito himself?

First off, let's start with our introduction of the Abyssal Horror, as it is a potential relevant piece of information. According to one of the best Integrity Pilots of Cardina Space Force, Stica Schtrinen states that her Mechadragon should be able to run away from the Abyssal Dragon and the reason it is unable to during their encounter is because Abyssal Horror is draining Spatial Resources in the vicinity that all types of dragon crafts need for their propulsion systems, thus resulting in a far cry from their actual maximum speed.

She put on maximum acceleration, praying. The eternal-heat elements screamed and roared.

But the speedometer’s needle came to a stop five whole pips short of its maximum value. The Abyssal Horror was taking resources from such a vast range that the resource-collection tanks in the dragoncraft’s wings couldn’t reach their maximum potential.

The rear view on the auxiliary vision board made it clear that the spacebeast’s black form was much larger than before. She could even see its writhing tentacled appendages already. -Stica Schtrinen, Volume 18, Prologue III

Despite putting her thrusters to maximum, as the thrusters were not being fed the required amount of Spatial Resources due to the Abyssal Horror draining them, otherwise it would be able to out-speed and get away from the grasps of the mythical beast.

So, in terms of a neutral case where the Mechadragon is not afflicted by an additional handicap;

Speed of a Mechadragon > Speed of the Abyssal Horror

And now, we come to Kirito himself. The flight of Kirito is achieved through the same foundational Sacred Arts usage as the Dragon Jet vehicles, albeit it is less refined. The speed is achieved through the propulsion of elements generated around the users' body.

At the moment, I had wind elements forming a protective barrier around Asuna and me, and I was also popping those wind elements in succession from behind to propel us like a jet engine. -Kirito, Volume 18

Kirito is not stating that he is moving at the speed of a fighter jet, but rather explaining his methodology of his flight, propulsion. All Dragon Jet vehicle types utilize the same concept for propulsion, however they are actually designed to maximize the efficiency of the propulsion by physically narrowing the outgoing exhaust to condense the pressure to achieve higher thrust, whereas Kirito is only relying on the elements exploding on their own. This is the first evidence that Kirito's flight speed is much slower than that of Mechadragons, as well as Dragon Jet transport vehicles.

Secondly, Star King Kirito has his own Mechadragon for travel, his X'rphan Mark 13, which is faster than a transport vehicle, but appears to be not as fast as the Integrity Pilot Mechadragons.

「えーと……いまさらこんなこと言って申し訳ないけど、今回も俺とアスナとアリスは夕方の五時までしかアンダーワールドにいられないんだ。戻ってこられるのはたぶん、明日の朝になると思う。あと六時間じゃ、とてもアドミナまでは行けないよな……？」

「うーん……」　エオラインはちらりとカセドラルの上部を見上げてから答えた。 「出発する時間とゼーファン十三型の性能にもよるけど、移動だけなら間に合うと思うよ」

「ま、マジで……？」-A chat between Eolyne and Kirito, Volume 25, Part 11

Exact Translation by the current SAO Fan Translator, Gsimenas of the SAO Wikia:

"Ehm... this might not be the best time to bring this up, but Asuna, Alice, and I can only stay in Underworld till five o'clock in the evening this time. We're probably only going to be able to return tomorrow morning, I think. It totally doesn't sound like we can go all the way to Admina within just six hours, right...?"

"Hmm..." Eolyne took a fleeting glimpse at the top of the Cathedral, before answering me. "It does depend on when exactly we depart, and the capabilities of the X'rphan Mk. XIII, but just moving from place to place shouldn't be a problem."

"F-for real...?"-A chat between Eolyne and Kirito, Volume 25, Part 11

Within 6 hours, "just getting to Admina" is not necessarily a problem with X'rphan, but anything more is clearly out of their reach.

The fact that Kirito has his own Dragon Jet vehicle rather than flying everywhere himself is yet another indication that he is simply slower than a Dragon Jet, at least slower than his own personal X'rphan Mark 13, which has the potential to reach to Admina from Cardina within the remaining 6 hours, but leave no time for the crew to have any investigations when they reach Admina. This showcases that X'rphan is barely faster than a Dragon Jet transport vehicle.

And the final indication that Kirito's flight is outright slower is that never in the entire conversation it is recommended to Kirito that he should simply fly there himself. The conversation takes place at a time of distress in Underworld and time is of utmost value as the Commander of the Integrity Pilots, Eolyne Herlentz suspects that the populace of Admina are preparing for a revolt against Cardina. They are trying to get Kirito to reach Admina as quickly as possible for investigation, but his best options are consistently stated to be Dragon Jet vehicles and never his personal flight. If his personal flight was faster than these options, the clear recommendation would be to send him flying without a vehicle at all.

While Kirito is less powerful in this instance than his Star King version was during the 200 years due to having connected directly into the Main Visualizer, for suggestions of the Integrity Pilot Commander Eolyne Herlentz, this information is irrelevant. Eolyne has not been provided with the information that Kirito no longer is connected to the Main Visualizer and is making his recommendations based on the feats of Star King in Underworld.

Conclusions

In consideration of the sources stated above, the flight speed scaling of all our variables are as follows:

Mechadragon Jets > Abyssal Horror >? Kirito's X'rphan Mark 13 > Dragon Jet transport vehicle > Star King Kirito

As Kirito finds himself in the lowest flight speed in the entire chain, we have no reference for a lowest point, so the conclusion of this calculation yields to an "at most, it is as fast as the next lowest". The next lowest speed belongs to a Dragon Jet transport vehicle, which yields the following speeds:

Highball, using the maximum distance of Venus to Earth: 43.333.300 km/h = 12.037.027,78 m/s = Sub-Relativistic

Midball, using the average distance of Venus to Earth: 25.000.000 km/h = 6.944.444,44 m/s = Sub-Relativistic

Lowball, using the closest distance of Venus to Earth: 6.666.670 km/h = 1.851.852,78 m/s = Massively Hypersonic+

According to the data we have available;

• Per the highball and midball calculations, Star King Kirito's speed cannot be more than Sub-Relativistic.
• Per the lowball calculation, Star King Kirito's speed cannot be higher than Massively Hypersonic+.
• These state what is still potentially possible but do not state what his current speed actually is. As we do not have any specific feats by Kirito to put into a calculation, his speed remains unknown, with the potential of being as high as, but no more than what is stated above.