So is there any way on Earth the world's tallest building could be uprooted, transported through the air for 5,500 kilometres and dropped, intact, head first on an unsuspecting London, as seen in the trailer for Independence Day: Resurgence?
No, of course not but that has not stopped Phil Chaffe, The National's pet mathematician, running the numbers, just in case.
Last year Phil, central co-ordinator of the United Kingdom's Further Mathematics Support Programme, a charity dedicated to improving the teaching and learning of maths, took a close look at the physics behind an impressive stunt in the film Fast & Furious 7, filmed in Abu Dhabi.
In the sequence, Vin Diesel’s character Dominic Toretto drove a $3 million supercar out of the 45th-floor window of one of the buildings in the Etihad Towers complex and in through the plate glass of a neighbouring structure.
Just possible, calculated Phil. So we asked Phil if aliens, or anyone else, could really pull off the Burj Khalifa stunt in Independence Day: Resurgence.
Phil started by looking at the energy required to uproot the 500,000 tonne Burj Khalifa from the ground in one piece, along with its 150,000 tonnes of foundations.
“I’m going to avoid the fact that the Burj Khalifa is made up of loads of components joined together and consider it to be a solid object,” said Phil. “This avoids the problem of it simply disintegrating when the aliens try to lift it.”
That, of course, is where the whole scheme falls apart. But, in the style of Hollywood, you are asked to suspend your disbelief.
All kinds of complex forces come into play. In a nutshell, the building stands on 192 cylindrical concrete-and steel pillars, each of which has a diameter of 1.5 metres and extends 50m into the ground.
“So the lift has to overcome the weight of the building and its foundations and the friction of sliding the piles out of the ground,” said Phil.
Together with its foundations, the Burj Khalifa weighs in at 650,000,000 kilograms (expressed in the following calculation as 6,370,000,000 Newtons).
The aliens would be aided by a small amount of upthrust (271,433,605 N, since you ask) created by the pressure of the soil on the foundations, but this still leaves an enormous amount of friction to be overcome (3,619,114,737 N).
“So the lift would have to be 6370,000,000 + 3,619,114,737 – 271,433,605 = 9,717,681,132 N,” said Phil.
Anyone who has anything heavy they need lifting anywhere in the world knows there is only one answer: the Russian-built Mil Mi-26 helicopter, which can lift 56,500kg.
The bad news is that carrying off the Burj Khalifa would require the equivalent of 17,550 Mi-26s and – setting aside the logistical impossibility of arranging that many giant helicopters and their dangling steel cables over such a small target without a series of catastrophic collisions – no more than about 300 of the beasts exist.
But moving on …
Next, Phil calculated what it would take “for the aliens throwing the Burj Khalifa at London” like a ballistic missile. Though hard to determine accurately from the film clip, “it looks like the building comes down at something like a 70 degree angle, which means the angle of projection is also 70 degrees”.
Dialling in the distance from Downtown Dubai to the London Eye, where the projectile lands, as 5,479,816m, Phil was able to calculate the speed necessary to achieve such a feat.
What he came up with was 9,140 metres per second, which is “about Mach 27”, 27 times the speed of sound and, at a shade over 30,000 kilometres an hour, a little faster than the speed achieved by spacecraft on re-entry to the Earth’s atmosphere. Hence his conclusion: “It can’t have been thrown because it would simply end up going out into space. So, they must have carried it.”
The energy necessary to transport the building to London, overcoming air resistance all the way, would be beyond enormous – 398,920,909,609,000,000 joules, or 399 petajoules.
This is equivalent to the energy in more than 65 million barrels of oil – about three weeks production for the UAE.
Or, as Phil summarised: “They must really have energy to burn.”
Finally, Phil took a look at the potential destructive power of an object weighing 650m kilograms being dropped from about 2,000m and striking the ground at 198 metres per second.
“The effect would be equivalent to 2,300 tonnes of TNT, or between 1/400 and 1/500 of the energy of a one megaton atomic bomb,” he said.
Not, in other words, “the most efficient way to destroy London but it does look good”.
The aliens would have been better off using the energy they expended moving the Burj Khalifa “directly for destructive purposes”.
But good maths rarely converts to good box office.