Tuesday, June 9, 2009

Unwanted, or, How Not To Run Down A Hall(minimal spoilers)

In the beginning of the movie Wanted, there is an epic scene where some nameless man in a business suit is trying to get a bullet identified. Just before he can get anymore information out of his contact, assassins on the building across the street open fire on the office, killing his contact, but missing him. He runs down the hall away from the office, seemingly to escape the gunfire. When he reaches the end of the hallway though, he turns around, gauges the distance, opens the elevator door to give him a longer acceleration distance and starts sprinting down the hallway with so much force he dents the wall of the elevator. Papers are flying and people around are being blown back by his wake. He smashes through the plate glass window in the office, flies across the gap between the buildings, shooting three of the assassins on the other roof, and then crashes into the next floor down. A very epic scene, but is it reasonable?

The first thing we need to determine are the approximate distances involved: how long was the hallway, what was the gap between the buildings, and how far did he drop. The length of the hallway can be determined using the distance between doors in the hall and then counting doors. We'll approximate the width of the office as being typical for an office, about 5 meters, and the elevator as being 2 meters wide, giving us a total acceleration distance of 21 meters. To determine the distance between the buildings, we'll use the top down view of his jump as a reference. There appears to be 8 lanes of traffic and 2 sidewalks between the window he starts from and the one he crashes into. Using the national highway standard for minimum lane width of 12 feet, and seeing that the sidewalk was somewhat wider than the lanes or about 15 feet, he would have to cover a gap of 126 feet, or about 38 meters. Using the height of 6 feet for the assassins you can approximate the distance down to the window he enters the building through. You find that he dropped around 6 meters. So he accelerated over 21 meters, burst through a plate glass window and cleared a 38 meter drop falling only 6 meters. That's quite the jump. Now we'll take a look at the physics.

First off, how fast would he have to be going to make the leap across the building gap? Since he fell 6 meters, using some basic kinematics and ignoring wind resistance, we get that he would have to cover the gap in 1.1 seconds in order to only drop 6 meters. Since the gap was 38 meters, that give us a speed of 34.5 meters per second, or 77 miles per hour! Needless to say, this is unreasonably fast for a person to run and still be called human. The bigger problem though, is what kind of energy would he have to burn to reach this speed? If we assume that he has a constant acceleration down the hall, we get that over the hall's length, he would have to be accelerating at 28.34 meters per second squared to have achieved his required speed by the time he hit the window, assuming the window didn't slow him down at all. To achieve this kind of acceleration the guy would have to be putting out 59 HP! To put this into some perspective, this would require that he metabolize just over 3.2 grams of sugar, using 2.7 litres of oxygen just in the ~1.2 second run down the hall! In other words, he's putting out about the same amount of power as a 1967 Volkswagen bug's peak horsepower. This may not seem like much, but this is also 44 times the peak power output generated by Lance Armstrong while riding in the Tour De France in 2007. You would exhaust your body's sugar reserves, on average, in less than 3 seconds with that kind of output. It just doesn't make sense.

Overall, I liked the scene, and I say you could keep it, but maybe put the buildings 15 meters apart instead of 38? At least that way you end up with numbers that a human being might possibly accomplish!


  1. I never saw Wanted. Spoiler alert! Is the sprint-jumping subject supposed to be a normal human?

  2. He is supposed to be a human, who, using a combination of a elevated heart rate(400 bpm) and lots of adrenaline, does seemingly superhuman acts.

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