So, it’s been a disturbingly long time since my last Fermi problem, and as previously discussed, I’ve always loved Seto Kaiba. For those not in the know, original series Yu-Gi-Oh released a movie called Dark Side of Dimensions. The plot is heavily Kaiba-focused as he uses his Elon-like power, technology and money to recreate the Millenium Puzzle. Kaiba’s untouchable status is shown in one pivotal scene wherein he is shown riding a personal elevator into space.
When I was done outright simping for the daring entrepreneur upon first watching this scene, my rational brain turned on. I began to wonder how much that elevator must’ve cost. Enter the itch and I felt an insatiable urge drag my fingernails along the rash. And I damn near scratched down to the bone on this one…
Math Time
But before we can get to any financial estimates, assumptions need to be made (my favorite part of Fermi problems!). The satellite that Kaiba boards in the movie is not quite zero-gravity, as Kaiba is shown walking normally, thus I’ll be assuming that the satellite is at an altitude of 370 kilometers above sea level. Why this height? This is close to the orbit of satellites in micro-gravity that are still habitable.
Next, we need to establish the measurements of the elevator itself. Kaiba is described in the Yu-Gi-Oh wiki as being 186 centimeters tall. Thus, using Kaiba’s height as a measuring stick, we’ll need to calculate the circumference of the elevator. I’ll be assuming a uniform circumference throughout the height of the elevator, and assuming that the frontal shot of the elevator is the front-half of the cylinder (as shown by the shading at its edges).
The half-circumference of the elevator is 1488 cm, thus giving the elevator a circumference of 2976 cm. Knowing the circumference is important because we can now determine the radius of the cylinder, which will be crucial for several following calculations. Using the formula Circumference=2*π*radius, we can easily calculate that the radius of Kaiba’s elevator is 473.89 cm. From a spatial standpoint, Kaiba’s elevator has a pretty small foot print.
Using the known radius and the assumed height of 370 km, we can now calculate the volume of the cylindrical elevator. Using Volume= π*radius2*height, we can deduce that the volume of the cylinder is only 0.026 cubic kilometers. Knowing the volume of the elevator is crucial because it will rely on the same concept as Elon’s Hyperloop.
For the unenlightened, Elon Musk released a white paper detailing an alternate to high-speed rail which involved using a sealed mag-lev train car inside a vacuum tunnel. This design eliminates both friction and air-resistance, which as any physicist can tell you slows objects down considerably. Kaiba’s elevator only needing to vacuum out less than 0.03 cubic kilometers of air is actually pretty feasible, assuming an airtight seal. This is less air than the interior of Madison Square Garden. A single jet engine is capable of doing that to an enclosed (read: air-tight) space.
Knowing radius and height also allows us to easily calculate the surface area of the elevator. This is absolutely vital since we’ll need to know how much material to order for the construction. For cylinders, Surface Area=2*π*radius*height. Pluggin’n’chuggin the formula gets us a result of just over 11 square kilometers of material. This is nearly twenty-two times the surface area of the world’s tallest skyscraper. This’ll come in handy for material costs.
Money Talks
To say that the Hyperloop is expensive would be an understatement. Currently, it costs roughly $121 million per mile, based off of the real-world observations that we have. Multiply that out per the height of the elevator, and we’d have a price tag of nearly $27.83 billion for the project. Assuming Kaiba’s fictional net worth matches that of real-world Elon’s, then this is an affordable expense. However, I don’t think that is the true answer; I think the space elevator would be even cheaper than that.
For starters, much of the expense was incurred by buying land rights. However, Kaiba’s elevator won’t have this problem. As shown by the movie, Kaiba’s elevator is launched from an ocean platform. Assuming that this elevator is off of the east coast of Japan in international waters (because this is anime, after all) the cost of acquiring rights would be negligible.
Construction-grade steel typically runs about $20 per square foot. Multiplying that by the surface area of the cylindrical behemoth of an elevator shaft would put the cost of steel alone at $2.78 billion. Tacking on an extra 20% would put the cost at around $3.336 billion.
Clearly, an elevator to space is going to have a lot of material, thus I’m going to err on the side of the $3.336 billion number. And since material costs are typically about 40% of the budget, assume that would put the number around $8.3 billion for the construction of the cylinder. I’m going to assume that the 40% for labor costs is built in, since Japan is a nation with strong labor laws. Basically, I’m assuming no Kafala system. Oops, did I say that out loud?
However, there are other costs, such as Point A and Point B. What do I mean? The sea-base and the satellite itself. The sea base would not need to be so extravagant, given the small (though admittedly heavy) footprint of the elevator. Besides that, it would need to be earthquake and tsunami proof, as that part of the world is prone to such weather events. But besides the vacuum pump of the elevator, it would really just need to house what’s essentially an office (as depicted in the early part of the scene).
The international waters just outside of Japan’s exclusive economic zone likely are not ultra-deep, thus I’ll shoot for the low-range of $400 million. After all, not a lot of special equipment will be needed, and it’s not like KaibaCorp needs to reach the Mariana’s Trench for a foundation.
The satellite itself wouldn’t be too expensive, relatively speaking. While the satellite is shown to be more spacious than the typical satellite, it doesn’t have that much in the way of specialized equipment outside of a conveyor belt (His Highness will not walk!), the robotic arms, and the talking AI. Throw in some recycled breathable air, and the standard of $400 million seems to be a safe bet. Thus, the price tag runs up to a cool $9.1 billion.
Truthfully, this checks out. The train between Stockholm and Helsinki cost $64 million per mile. Multiplying that by the height of the elevator leaves a price tag of $14.7 billion. The Scandinavian train line even had the advantage of building underwater, thus still skirting the whole issue of land rights that plague the Hyperloop. Therefore, while my estimate is a bit low, it’s at least in the ballpark of reality.
Results
The movie depicts Kaiba’s elevator reaching the satellite in 27 seconds (if you’re being literal). I’m not going to use that since it would involve the pod moving several times faster than the rosiest-and-unconfirmed claims of Hyperloop enthusiasts . Thus, I’ll be assuming that the elevator would move at the verified speed of actual hyperloop test tracks (roughly 108 mph). That would mean that Kaiba’s elevator would take him to the satellite in roughly 2 hours and 7 minutes.
Time is money and most CEO’s don’t have two hours to spend waiting inside an elevator (even if it is to literal fucking space). With that said, it would be a much more pleasant ride from a gravitational standpoint.
Even if the near 1000 km/h hyperloop speeds become attainable, there would be no need for any such negation of gravity fields inside of the elevator (whatever the fuck that means?). The G-forces would be intense, but definitely survivable. Doubly so since Kaiba is a military-age male rocking a cheese-grater of a core. Thus, there would be no need for KaibaCorp to spend on whatever contraption at sea level that made the “gravitation field stable”.
Limitations and Rounding Errors
The true wild card would be the infrastructure required to build into space. Truthfully, I have no idea how to calculate that, since there is little real-world comparison to judge it against. But then again, that’s what makes this a Fermi problem; it is inherently unknowable. Though, I could very easily be future-countered if some real-world megalomaniac actually decides to try something like this.
I admit, I’m not an architect, construction worker, or structural engineer. Thus, I’ll admit my ignorance when it comes to structural design and logistics such as scaffolding and on-the-job safety equipment costs (see above, not running the Kafala here). Maybe these expenses are covered in the 15% of the $8.3 billion for the elevator ($124.5 million, in case you were wondering). But then again, this could easily be an area of cost overrun. Who the hell knows for sure, amirite?
As for negligible costs, we’ll start with Kaiba’s pod. The pod of the elevator (that is, where Kaiba sits) would need to be air-tight and feature some sort of mechanism to recycle and filter breathable-quality air. However, this is a standard feature on literally every commercial aircraft, thus this will not be a major technological hurdle for Kaiba to overcome.
Then, there’s the vacuum system. As mentioned earlier, a single jet engine could quite easily provide the vacuum needed for the Hyperloop elevator to work as intended. Given that these only run into the low double-digit of millions, that isn’t even scratching the surface for the price of the elevator. Not a bad deal, if you think about it.
And now I’ll leave you with some words from the wise philosopher LittleKuriboh…
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