Film Facts 3b: Dying In Die Hard - Part 2

Hello, and welcome back to part two of our epic odyssey into the world of quantum immortality and action hero deaths. Last time, we looked at how many bullets it takes to chew up John McClane's fleshy carcass before he stops moving, and today we'll keep the festivities going by looking at more fun and interesting ways our favourite cop would have got himself eviscerated in a giant ball of fire and broken glass:

Explosions

There are two major explosions in Die Hard that John gets himself all up and feely with: the exploding lift shaft and the exploding helicopter/roof. I never really understood why the helicopter decided to blow up too so long after the roof; was it feeling left out?

"Hey, guys, wait up!"

With the lift shaft, we're looking at a big lump of C4 exploding in a enclosed space and then blasting at our protagonist's face; not a healthy atmosphere. In the movie, we can see that John uses one block of C4, which weighs in at 1.25lbs (570g); for comparison, here's a video of 450g of C4 exploding and XBox. So, as should come as a surprise to exactly no-one, Hollywood has not exactly been accurate in depicting the veracity of this explosion, which is going to make working out how dead John is much more difficult.

Due to Boyle's Law, as the volume of a space decreases, the pressure of the contents rises, so with lots of gas firing outwards with great aplomb in a teensy weensy shaft, there's going to be lots of energy with nowhere to go. This is the same reason why grenades work so well indoors (if you don't believe me, throw one into your neighbour's daughter's Wendy house). C4 is classed as a high-order explosive, which means it creates firstly a "blast wave" then a "blast wind" when it explodes. These are surprisingly the dangerous bits, with actual fire and shit not really doing much seeing as you're likely already dead by that point. The blast wave is the initial super-fast shockwave created by the aforementioned explosion of gases and causes nasty blast damage to pretty much any pressurised part of your body that might be exposed, including but not limited to your eyes, lungs, ear canal, GI system and brain. When the C4 goes off, John is standing like this:

This is the exact moment he would die.

Say bye bye to your now-ruptured eyeballs, burst tympanic membrane and jellied brain; maybe even a perforated bowel and blast lung injury to boot. You're dead. So fucking dead. It doesn't matter that the explosion is a good 13 stories (I counted the lights in the shaft) down, that shockwave will have hit John's face harder than getting teabagged by an Ent. He's now blind, deaf, unable to breath and suffering from head trauma which, if it doesn't kill him, will likely leave him with irreversible brain damage for the rest of his life. Also he might be shitting himself from the inside. This is not a good time to be John McClane.

A bus explosion in Jerusalem might shine some more light on exactly how likely John is to die before stumbling across one of our self-imposed checkpoints. The attack sadly led to the deaths of 6 (3 instantly and 3 in hospital) out of the 58 passengers, 29 of whom were hospitalised with a variety of the things John will also be suffering from. So with that in hand and regarding the fact that John has no immediate access to medical care (both because he's trapped in a building and because he lives in the US. Ooo, sick burn), we can assume that if he were any of those 32 critically injured or killed victims, he would not be making it out alive.

And we would all be robbed of a beautiful bromance.

Explosion number two comes later in the movie after the whole roof blows up (see above for likely outcomes) and John manages to avoid the helicopter explosion by jumping into a fountain. For that reason and because I don't want to spend a whole day looking for statistics on helicopter explosions, I'm going to call this a water landing. The mortality rate of water landings in a helicopter is around 25%, with 55% of those deaths being attributed to drowning. Seeing as by this point in the film John will have suffered at least a couple gunshot wounds, will be blind, concussed and have agonising back pain (see below), I'm going to include the drowning statistic into his overall chances of dying because at least some of the McClanes in our infinite universes will probably make the wise decision to embrace the sweet release of death before they can suffer any more.

*blub*

All in all, John is pretty unlikely to survive regardless of whether or not either explosion actually killed him, what with the various non-fatal injuries he'd be stacking up along the way, so an actual number of dead Johns is very difficult to come to. What we can be certain of, though, is that he would definitely wish he was.

Falling

Again, we've got two occasions when this happens: one in another lift shaft and the other immediately after the roof explodes when John ties a hose to himself and leaps off the building.

Never before has a subtitle track been so in sync.

In the jumping off the building situation, John will experience the same difficulties also completely ignored in The Dark Knight Rises, namely the force of gravity and the effect it has on the likelihood of spine-shattering injury when you use a rope with absolutely no elastic properties.

Bruce Willis, thanks to a terrifying website that records this sort of thing, weighs apparently 92kg. We'll be nice and assume that, back in his prime, he weighed closer to 80kg. The Fox Plaza building, where the film was shot, is 150m tall and has 35 floors, making each floor 4.28m high. In the film we can clearly see that John falls 3 floors (12.84m) and, at an acceleration of 9.8m/s^2, he will reach a velocity of 15.86m/s by the time he hits the rope. The sudden stop when the rope goes taut, assuming it has no elasticity, will therefore exert a force of F (in Newtons)=ma (where m=Bruce Willis in kg and a=-15.86m/s^2), leading to F=1268.8N. The average rib can require 3300N of force to crack and a femur will break around 4000N, so we're nowhere near close enough to break any major bones. The vertebrae of the spine, however, can only need as little as 1100N in order to break, particularly in "upright, fast falls in which the individual had a...very tense torso musculature and little damping in the spine"; like, say, when you jump off a building with a fire hose wrapped around your waist.

"If only Captain Hindsight were here to tell me this was a terrible idea."

Judging from where the rope is wrapped around him, the force could feasibly snap his upper lumbar vertebrae, potentially damaging the nerves within and leading to paraplegia. Approximately 3.3% of acute lumbar fractures result in paraplegia, so for once the odds are on John's side; he'll likely only be in crippling agony rather than completely paralysed. Silver linings. Of the rest of people will lower back pain (caused by makeshift abseiling or not), around 8.2% could have disabling back pain at some point. So overall, John will either become paralysed or unable to continue around 10% of the time, meaning he won't be able to reach the fountain in time and will be vaporised by the incoming helicopter-bomb. Tough luck.

Earlier in the movie, whilst being chased by Karl and [insert terrorist name here], John manages to escape by climbing into a vent shaft and crawling into one of the smaller vents that run into it. You might also remember that he was a massive fud and used his gun strap as a rope, which promptly broke, causing him to fall before catching onto one of the edges of the vent.

This.

If you ever thought that that looked sore, that's because it would have been. This situation uses pretty much the same maths we just did above, with some changes in the speeds and such. From the gif, you can see that the distance between each of the vents is about twice McClane's height. Our handy creepy website lets us know that that makes his fall around 9.15m. He grabs the ledge falling at 13.4m/s, which exerts a force of 1071N on his arms. Want to know how much force it takes to dislocate your shoulder? Pulling on an abducted arm like the one in that scene, it can take as little as 150N to dislocate. Granted, John is a strong, fit guy, so his muscle bulk will help, but even if we were to give him up to 500N before a dislocation, both his arms would be guaranteed to pop out of their sockets, resulting in immediate loss of grip and John plummeting to his death every single time.

Huh, it turns out that through a whole movie of gunfire, explosions, leaping off buildings and god knows what else, the most dangerous part was when the main character voluntarily threw himself down a ventilation shaft for the hell of it. In our infinite universes, it could be likely that one John would be able to hold on, or that his arms would be in just the right position to not give way, but for the most part the bottom of that shaft would be filling up with millions of identical bodies from parallel universes, John stuck for eternity in a never ending loop of death, just like that bit in the movie Triangle.

That was a weird movie.

And that's that, ladies and menfolk. I hope you've enjoyed looking back at a great movie and proving that it's actually completely impossible. These two posts took a lot of time and extremely poor research to put together so if you liked it, please do pass it on to any other fans of Die Hard or badly done maths. Just for general interest, there were a few added occasions that didn't make it into the final list due to time and space, but for completion's sake I thought I'd best bring them up: falling down stairs, getting repeatedly kicked in the head, broken glass lacerations, general blood loss, concussions and the biggest killer of all, smoking.

Cause when you smoke, you lose every time.