Saturday, August 1, 2009

Summer School Lesson 1: Movie Physics

Before you try stunt-jumping your car over the nearest chasm, read up on the physics of why you're doomed to fail. This video puts some perspective on the action-movie high-speed car chase jump phenomenon. Notice how close this car comes to wrecking when launched off of a little two-foot-high ramp and moving at a relatively slow velocity.

Furthermore, the guys at popular science have done a rough estimate of the takeoff velocity. They approximate that the car lands about 10 meters from its takeoff point and is in the air for close to one second. Applying this information they can do a simple calculation to determine its horizontal component of velocity on takeoff:

vx = Δx/ t = 10 m/1s = 10 m/s

Using a little vector addition they can also determine the net velocity off the ramp based on the ramp angle. They'll leave this as an exercise for anyone so inclined (no pun intended), but because the take off angle is pretty small (we estimated 17 degrees) the net velocity is still only approximately 10.5 m/s or 23 mi/hr -- not really a high-speed stunt.

Fun, games and calculations aside, one of many problems any "would-be" stunt car driver is going to face on attempting a jump, is that the car is generally going to follow the standard parabolic trajectory of a projectile. Let's assume for the moment that the car has its center of mass relatively near its geometric center. In that case the upward angle of the car at any given height on its ascent should be the same as the downward angle at the same height during the descent. If, as is more likely, the car has its center of mass located towards the front half of the car, it will cause it to nose down even more steeply. In fact, in the video you can see the car landing at an alarmingly steep angle. They were lucky to pull that one out.

If you've ever seen an actual stunt jump then you know that they put ramps at both ends of the jump. That's for good reason. (They also have specially designed suspension systems.) Try sticking the landing when your car impacts the ground at an angle of 25 degrees below horizontal, at a speed of say 80 miles per hour. The hood is going to crumple and you're going to need rehab before the tires ever make contact. Seriously, don't try this at home!

So next time you're watching Gone in Sixty Seconds, Speed, The Fast and the Furious or any movie with some spectacular cinematic leaps, recall this little video and contemplate just how far the fantasy of the action film is divorced from any semblance of reality. (I'm not suggesting that you don't already know that, but this gives a pretty vivid demonstration of what kind of limitations we might be dealing with.)

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