The Breakdown: Bourne Edition

As far as meaty physics goes, The Bourne Ultimatum is a standout among action flicks. Compared with other pillars of the genre, like Mission Impossible and XXX, Bourne sustains some impressive dramatic excitement without succumbing to the patently ridiculous.

It's not hard to suspend disbelief during the movie's dizzying quick cuts, but Jason Bourne's Superman-like physical capabilities are a little suspect. He has astonishing reaction reflexes, infinite physical stamina, and the ability to withstand an amazing quantity of forceful blows, impacts and collisions without sustaining much more than a few scratches and an intermittently gimpy leg—pretty unlikely stuff, even for an elite assassin.

But we're not here to criticize the improbable. Why else do we go to action movies, after all? That said, there is one interesting physics moment that I feel obligated to point out: a motorcycle chase scene in which Bourne tries to prevent a CIA assassin from snuffing out the closest thing he has to a romantic interest. While taking a short cut, Bourne jumps his motorcycle over what appears to be a six-foot concrete wall. Fans of XXX may not bat an eye—Vin Diesel's grasshopper-esque, unassisted leaps over a 30-foot fence, a guard tower and a house, all without the assistance of a ramp of any kind, make Bourne's paltry six-footer look like a bunny hop. Nevertheless, it's worth taking a look at the numbers. Just how much force must he be capable of exerting on the ground to get him over the wall?

First, a little kinematics. Assuming he leaps just high enough to make it over, he'll have zero vertical velocity at the top of his trajectory. We can then calculate the initial speed with which he must have left the ground:

V² - V₀² =  2aΔy,

where V is the vertical velocity at the top (zero), V₀ is the vertical velocity upon launch, a is the acceleration due to gravity and Δy is about six feet, or two meters. Solving for V₀ we get:

V = (2(9.8m/s²)(2m))^1/2 = 6.3 m/s.

Now let’s consider that a typical jump involves about 0.2 seconds of contact time with the ground. From this we can calculate Bourne’s upward acceleration when he pushes off:

a = Δv/Δt = 6.3 m/s/0.2 s = 32 m/s².

Applying Newton's Second Law we can now estimate how much force he will have to apply to do this. (And don’t forget Newton's Third Law: However hard he pushes down into the ground, the ground will push back up with an equal force.)

F_net =  F_push – mg = ma,

where F_push is the force the ground exerts upward on Jason and his relatively small motorcycle and mg is their combined weight. Let's assume that his futuristic bike is super-light at 100 kg, and he himself is a trim but solid 80 kg.

F_push = mg + ma = 180kg (9.8m/s²) + 180kg (32m/s²) = 7600 N . . . or 1,700 lbs!

Not even the winner of the World's Strongest Man contest has muscles capable of exerting a force of almost a ton. Think about it this way: To accomplish this stunt, Bourne must not only be capable of jumping six feet straight up, he has to be able to do it while holding onto a 200-pound motorcycle. Now imagine how strong Vin Diesel had to be in XXX to leap at least five times as high. This prompts the question: Why all the death-defying? With hops like that, Jason Bourne should consider a more easygoing (and lucrative) career in the NBA.—Adam Weiner

Comments

[Hector]

Is this the scene where he used the sidewalk curb to help get him up there? If it is, then you're over-simplifying the problem. He doesn't generate all of the force with his legs, he uses the motorcycle's power to do most of it. He bumps the front wheel up in the air using the curb, and then releases a burst of power from the rear wheel, using the curb to help re-direct the thrust vertically. Watch "trials" bike competitions and you'll see similar feats performed many times throughout every ride.

[Mike]

I've seen the film twice and not only does the bike launch off the curb as Hector states, but you can also clearly see that the section of the curb that Bourne hits has been shaped like a ramp. There was certainly no CG involved.

[Adam Weiner]

You guys may be right. Normally when I review movie physics I do it off of the DVD with plenty of opportunity to replay scenes and review the details. I didn't remember seeing a ramp when I watched the scene in the theater, but from what you say apparantly there was. If so then clearly the jump could be possible. In that case apply the physical analysis to the sublimely ridiculous jumps in "XXX" for contrast.

[Jake P]

good work on the physics...im enjoying my course in it this year...

[joeschmoe]

do a math analysis of bourne movie 1 where he uses the fat guy to cushion his fall and fall 3-4 flights onto hard marble, and survives without a broken bone.....would he survive without breaking bones in reality?

[mike d.]

Is that movie any good? If so on a 1-10 scale where would it stand (1 being the worst and 10 being the best movie you have ever seen).

[Priya]

this movie is definetly a 10. but you HAVE TO watch the first two before you see this one. the whole story is just incredible.

[Adam Weiner]

Joe-I haven't seen the first movie yet, but the short answer to your question on whether Bourne can have his fall broken by "the fat guy" without being hurt is - extremely unlikely! What breaks bones and causes injury due to impacts or other sudden motions is the magnitude of force applied in changing your velocity - in this case slowing you to a stop. The less time it takes for a given change in velocity the greater your acceleration, and therefore the the greater the force that has to act on you. (F= ma) Impact times during collisions with hard objects are generally very short, generally a few hundredths of a second. Falling into a pad like a pole vaulter greatly increases the time it takes to come to a stop, and therefore reduces the force proportionally. However using a person as a pad, even a "hefty" one, will not likely reduce the acceleration time all that much. Even a very padded body is not as soft as you might think. The likelyhood of just surviving is low, not to mention walking away without a serious injury.

[ssalty48]

Normally I don't watch many spy movies made after Goldfinger, but I did see the Bourne Identity. I only saw the first movie. On Pay Per View. I'd rate it a 5 (one which I'll probably rent or buy on PPV one day, as long as I see the second one first...or actually second). Anyway: I got a D in Physics -- but at least I passed. Still, I realize the calculations were only about 'vertical' acceleration, but what about horizontal acceleration? And, that said, how thick were the soles of his spy shoes to stand even the nanosecond it took to help launch him?

[peterwjj]

i disagree with your conclusion that bourne needed 2 tons of leg push to hop his cycle over a six foot wall. rear tire compression, when lifting the front of the bike with a yank back and balance of body weight shift, causes the rear tire to flatten out then spring back to normal shape. the spring back is timed with the leg push in order to maximize lift and the spinning rear tire also impacts the wall on the way up providing additional lift at the sacrifice of some forward momentum but if timed right and body weight is thrown forward

[Peter G.]

Yeah, this was sloppy. Advanced trials-bike riders can do stuff like that routinely. Bourne wasn't on a trials bike, but the curb was slightly rigged, so there's no reason to doubt it's possible.

You can see more of this sort of thing here, a YouTube video I found by searching for "trials". A few similar vertical-wall attacks can be found around 45 seconds in.

http://www.youtube.com/watch?v=_zPNQAZMVOA

Also, you're completely wrong to say "Not even the winner of the World's Strongest Man contest has muscles capable of exerting a force of almost a ton." In fact, the World's Strongest Man competition often involves such forces. I can leg-press a ton myself, though only for short extensions. (Famously, even Pat Robertson has made the same claim. :-) A professional weight lifter can exceed a ton even for a full-extension leg press.

Now, would anyone be able to apply a ton of force over an 0.2-second interval? That's probably impossible just on the basis that it would have to take place over a distance of several feet, and nobody's legs are that long.

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[Ray Best]

If you want to see a phenominal display of physics in action, go to a world round observed trials competition.Top ranked riders routinely climb 8 foot vertical walls, and many more jaw dropping feats.

[Trials pro]

The tires were Michellin X11 trials tires. Best sticky traction tires used by trials riders worldwide. I can vault and climb, and I'm just an average skills rider. No real science breakdown here, just a stuntman with trials skills. I can even bunny hop over a fat man.

[Bob "Motorcycle Lift" James]

Great post! I especially found it interesting when you began discussing the physics of the movie. The movie has awesome special effects, with little reality, thats hollywood for ya.

[Retro Jordan]

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Jason Charles Bourne, born David Webb, is a fictional character in the novels of Robert Ludlum and subsequent film adaptations. He first appeared in the novel The Bourne Identity (1980). This novel was first adapted for television in 1988, and then adapted to the film, which is very loosely based on the novels, in 2002 under a title of the same name.
The Bourne Identity (2002)
The Bourne Supremacy (2004).
The Bourne Ultimatum (20007)
These American Spy movies are directed by Paul Greengrass
The fourth movie, The Bourne Legacy, is scheduled for release in July 2012.