Furious 7 Etihad Towers stunt: can it be done?
First it was Tom Cruise, inducing vertigo in cinema audiences around the world by dangling precariously from the upper reaches of the Burj Khalifa in the 2011 blockbuster Mission Impossible blockbuster Ghost Protocol.
Now it’s the turn of Hollywood action hero Vin Diesel to exploit the high-rise landscape of the UAE, in a spectacular teaser scene from the hotly anticipated seventh instalment in the Fast & Furious franchise, which has its world premiere next week.
Interest in Furious 7 in the UAE, triggered when the stars of the film arrived in Abu Dhabi for six days of filming last April, has reached fever pitch since the release of the film’s first trailer, which makes clear that the UAE has another big location hit on its hands.
The Fast & Furious franchise is known for its preference for real stunts rather than computer-generated imagery, but one scene in the trailer blends the two techniques, to stunning effect.
The premise, deduced from a 27-second sequence in the two-minute 50-seconds trailer is this: Diesel’s character Dominic Toretto finds himself behind the wheel of a powerful sports car on about the 45th floor of the tallest of the five buildings in the Etihad Towers complex in Abu Dhabi.
Why? Who knows? Maybe he didn’t trust the valet parking. After all, the car is a Lykan HyperSport, the first supercar to hail from the Middle East and, with diamonds in its headlights as standard, priced at US$3 million (Dh11m).
But whatever the improbable reason, there he is, and the movie’s villain, Deckard Shaw, played by Jason Statham, is hot on his heels, on foot but toting a rocket-propelled grenade.
Well, what is an action hero to do?
Of course, Toretto could just reverse over Shaw, but where’s the fun in that? Instead, he floors the accelerator and sends the car hurtling through the glass side of the building.
To certain death on the street below? Oh please.
In a split second, Toretto has obviously calculated that he stands a better than fair chance of powering his car across the gap between the two buildings – and, thanks to the magic of Hollywood physics, pulls off the jump in spectacular fashion.
On the far side, the car punches through another glass wall, lands in a packed art gallery and skittles sideways through what appears to be a detachment of China’s famed (and priceless) Terracotta Army.
Spinning out of control to the far side of the building, it demolishes one more glass wall before finally tumbling to the street below.
Diesel manages to bail out just in time and seems to have come through the whole episode remarkably unscathed. The Terracotta troops, less so.
So, phew. And don’t try this at home.
But, you know, if you did happen to have the world’s rarest and most expensive supercar (only seven Hypersports will be made) and two glass-clad skyscrapers to play around with, could you pull it off?
The answer boils down to a fairly simple maths problem, says Phil Chaffe, a mathematician who works for the UK-based charity Mathematics in Education and Industry, which supports the learning and teaching of maths in schools and universities.
The maths behind the stunt: click here for the full findings
In fact, Chaffe, the maths lead for Warwick University’s International Postgraduate Certificate in Education qualification, was recently in Abu Dhabi training teachers, and “so I was immediately interested” in the problem.
Not, he says, that he would attempt the leap himself. “I would trust the calculations, but not my driving ability.”
The problem, he says, “can be solved with a very simple mathematical model that strips away a lot of the unnecessary detail, such as getting through the glass”.
Ah, yes, we’ll get back to that oh-so-easily shattered glass shortly.
But for now, says Chaffe, let’s start with some convenient assumptions – that both the glass and the air offer zero resistance, that the wall of the target tower is exactly 50 metres away and that the car can hit 100 kph by the time it leaves the first building.
And, as the Lykan HyperSport, powered by a Porsche 3.7-litre Boxer unit, is capable of 385 kph and can accelerate from zero to 100 kph in a mere 2.8 seconds, that, at least, is a reasonable assumption.
“What we do is imagine the car to be a particle,” says Chaffe.
A diamond-encrusted particle, obviously.
That, he says, “means there will be no air resistance to worry about. Once the car has left the first building there will be no rolling resistance either, so we can imagine it to be like a ball thrown horizontally”.
The motion of the car then has to be considered in two directions – horizontal and vertical. Because mathematicians like their velocity in metres per second, first we have to convert the speed by dividing 100kph by 3.6. Rounding up a smidgeon, this gives us a horizontal velocity of 27.8 metres per second.
Dividing the distance (50 metres) by the velocity (27.8) tells us that Vin Diesel and his awfully expensive car will be in flight for just 1.8 seconds.
So how far will the car drop in that time – or, to put it another way, can it possibly reach the other tower?
Surprisingly, yes, it can.
Here’s where a spot of Newtonian physics comes in handy – to be precise, the formula s=ut+½at².
Don’t panic, Vin. In this equation, s is the distance dropped, u is the initial vertical velocity (zero, in this case, as at the beginning of the jump all the movement is horizontal), a is the acceleration due to gravity and t is the time of flight.
The only component of this formula we are missing, therefore, is the downward acceleration.
At this point, says Chaffe, it helps to know that the “commonly used approximation for acceleration due to gravitation on Earth” is 9.8 metres per second squared (think back to physics classes and Galileo chucking stuff off the tower of Pisa).
In short, this means the car will increase its downward velocity by 9.8 metres per second every second.
Run the equation – s=0x1.8+½x9.8x1.8² – and out pops the vertical drop: 15.9 metres – or, assuming a standard floor-to-floor height of a mixed-use skyscraper of 3.5 metres, about four and a half floors.
But would the glass interfere much with our calculations?
It’s a short question, but one that leads Chaffe into a long series of baffling calculations, employing, he insists, “only” the mechanics covered in A-level maths and physics, and factors including the weight of the Lykan (1,380kg), its rate of acceleration and the maximum load capacity of a 5cm-thick sheet of laminated glass (54,000 Newtons, since you ask).
We could repeat the impressive maths here, but then this would become less of an article and more of a degree course.
The bottom line, Chaffe concludes, is that the glass would “slow the car by only about 0.1 metres per second”.
All of which adds up to the conclusion that, all things being equal, Vin Diesel might actually expect to pull off such a stunt in real life, without the safety net of CGI.
Unfortunately, though, in real life all things aren’t equal.
The good news, says Chaffe, is that even if one applies “some nifty fluid dynamics” to factor in air resistance – which he then does – there would be “very little change to the result … a slight increase in time of flight, of a few hundredths of a second, and a slightly bigger drop, only a matter of centimetres”.
The real problem, he says, would be the landing, which would prove a tough call for a car made from lightweight carbon fibre.
Touchdown would, he says, “be more nose-first than in the trailer and make a real mess of the car, and probably the driver”.
To be precise, as the car comes in to land with a horizontal velocity of 27.8 m/s and a vertical velocity of 17.64 m/s, it would touch down at 118.5km/h, at an angle of 32 degrees.
And that, as Chaffe notes, “is quite a speed to be hitting a solid surface. The suspension would probably leave the car through its hood”.
His final verdict?
“I’m still pretty confident that the car would get through the glass easily and without much slowing. I still wouldn’t try it.”
To give the last word to one of the characters in the film: “This right here takes crazy to a whole ’nother level.”