Crimson King said:
They were climbing the tallest skyscraper in the city.
According to wikipedia, a skyscraper starts at 150 meters, so I'm using that since I don't know how tall that one is.
Although I seem to remember reading that the center building was 50 stories tall, I can't recall where I got that number from, so I can't prove it.
So instead I took the liberty of finding a good CG that showed the majority of the building and counted the floors that were visible, marking them with red dots. I counted 31 visible floors, but I'm fairly certain that there are around 3-5 more near the ground level being obscured by the buildings and trees in the foreground—however, I can't prove that either.
Using the
criteria listed on this page and
the linked calculator, I can estimate the average height of a tall builting based on the number of floors it has. Given that the Shinto Center Building is an office building and has 31 confirmed floors, the average height should be at least
138.645 meters, and with the maximum 5 additional possible floors the average height would increase to 159.12 meters.
For the lower limit, I'll use the Hyatt Hotel, which used to be the tallest building in Fuyuki prior to its destruction during the events of Fate/Zero. The Hyatt Hotel's top floor is the 32nd, meaning that it likely had an average height of
108.603333 meters. The Center Building should at least this tall. This is roughly equivalent to an office building with a height of 23.7 floors.
Finally, for a upper limit, I'll use "50 stories" I mentioned earlier, despite the lack of evidence for it. A 50-story tall office building would have an average height of
216.45 meters. Why not? As upper limits go, it's not an unreasonable one.
A method I will use to establish some credibility for these height estimations is with this passage:
I run up the stairs full speed.
I don't know how long it's been since Saber left me.
I don't think it's been ten minutes yet, but that's still too long.
The "Empire State Building Run-Up" race involves climbing 86 floors of the eponymous building, a total of 1576 steps. This means there are an average of 18 steps/flight. It's reasonable to assume that the number of steps per flight would be similar in the Center Building. The average of the three times for this race is about 11:00, which is 2.3878787 steps/second.
23.7*18/2.3878787 = 2:59
31*18/2.3878787 = 3:54
36*18/2.3878787 = 4:31
50*18/2.3878787 = 6:17
So, it is possible to run up the stairs of the Center Building in well under 10 minutes given the height values here.
...All that's left to do is the actual calculation.
Lower Limit: 108.603333/(1/120) = 13032.4 m/s or
Mach 38.3
Confirmed: 138.645/(1/120) = 16637.4 m/s or
Mach 48.89
Unconfirmed: 159.12/(1/120) = 19094.4 m/s or
Mach 56.11
Upper Limit: 216.45/(1/120) = 25974 m/s or
Mach 76.33
So, the answer should lie somewhere between those numbers.
