What could origami possibly have to do with automotive airbags? Quite a lot, it turns out.
Automobile airbags are the result of some incredible engineering. In a high-speed crash, the occupants of the car can be hurled into the side, dash, or windshield. But in an airbag-equipped car, in the instant after a crash is detected, the onboard electronics detonate a small explosive charge that inflates the airbag, providing enough cushioning to protect the occupant from impact with something less yielding than the inflated bag. Fatality and serious injury rates have plummeted since the widespread installation of airbags in cars.
However, an airbag has a challenging job to do. It must fully inflate in a few milliseconds and be firm enough to stop a rapidly-accelerating body, but must do so while still providing cushioning. Hitting a brick-hard rigidly-inflated airbag could do as much damage as no airbag at all, and airbags must work for a wide range of body sizes, from children to large adults, over a wide range of automobile speeds and varying impact angles. Automotive designers must find one airbag design that works for a wide range of conditions.
This all means that airbag design is quite a precise science, involving a great deal of both experiment and computer simulation. The latter is especially important; if you’re designing airbags for Mercedes-Benz, you don’t want to crash too many automobiles if you don’t have to. So computer simulation is critical to airbag design. Most simulation uses a combination of techniques with forbidding-sounding names: nonequilibrium thermodynamics (to simulate the detonation of the explosive charge and expansion of the gases) and finite element analysis (to simulate the inflation of the airbag).
In finite element analysis, one divides up the surface of the airbag into many tiny triangles, and then calculates the position and orientation of each triangle as the airbag inflates, taking into account things like the stretchiness of the material, the expansion and cooling of the inflating gases, the shape of the airbag, external forces exerted upon it, and so forth. Simulating an inflating airbag is an extremely complex process, and the companies that specialize in it — companies like EASi Engineering GmbH — must be experts in computational geometry, physics, engineering, and thermodynamics.
The shape of the airbag is critical; spherical, oblong, or even donut-shaped airbags all provide different amounts and distributions of cushioning, so a big part of the study of airbags includes characterizing how well different shapes work. Of course, all airbag simulations start with the airbag folded up into a small packet and tucked into the (simulated) steering wheel or dashboard. So a simulation of an inflated airbag needs to start with a simulation of a folded-up airbag.
And that’s where the problem arises. While flattening an airbag in real life is fairly easy to do – you just squash all the air out of it — simulating the flattening process is quite a challenge. In order to flatten an airbag in simulation, you need to first treat it as a rigid object (as if it were made out of cardboard), then find creases that flatten it, then fold it up into a small packet; all before your simulation can ever start.
That’s how the problem was described to me by Rainer Hoffmann, manager of the airbag team at EASi Engineering, a German company that specializes in computer-aided engineering. That’s also where the origami comes in. It turns out that the problem of finding the creases to flatten an airbag from a 3-D polyhedron to a flat shape is not that far from finding the creases that turn a flat sheet of paper into another flat shape, and the latter is the fundamental challenge faced by all origami designers.
And it’s one that I’d already developed several computer algorithms for. Within a branch of computational origami that I call “tree theory,” the problem arises where one needs to flatten a set of polygons so that their edges remain aligned to one another. In origami, the polygons are all part of a single square of paper, but they could as easily be the polyhedral facets of an inflated airbag. The algorithm, called the “universal molecule”, turned out to be directly applicable to the airbag problem, providing the solution for how to flatten a large class of shapes in simulation.
EASi incorporated the universal molecule algorithm into their simulation code and have used it for several simulations; you can observe one such simulation at the top of this page;. The application of origami to airbag simulation continues to be an active field of study, and research in this topic is ongoing.
For further information, see:
- Hoffmann, R., et al. "A Finite Element Approach to Occupant Simulation: The PAM-CRASH Airbag Model", SAE-Paper 890754, International Congress and Exposition, Detroit, Michigan, 1989 (also SAE Transactions 1989)
- Gärtner, Torsten; Eriksson, Magnus; Fältström, Jonas; EASi GmbH, Advanced Technologies for the Simulation of Folded Airbags, 2nd European LS-DYNA Conference, Gothenburg, Sweden, June 1999
Animation courtesy of EASi Engineering GmbH.
For more general information about airbags, see The Airbag Center.