In May of 2011, the average price of gasoline neared $4.00 a gallon and remained over $3.50 for some time. This caused high prices at the pump, stifling the American economy. In response to this problem, ARPA-E launched the Methane Opportunities for Vehicular Energy or MOVE program to take advantage of America's abundant natural gas resources and infrastructure. One challenge facing natural gas vehicles is that the gas tanks are typically cylindrical. A cylinder does not fill all the available space due to losses in the corners. Space in a vehicle comes at a premium, and nobody was going to switch to natural gas if the trunk was eliminated from their vehicle. Grocery room comes at a premium.

ARPA-E contracted REL Inc. (technology division now spun off to Loukus Tech) to build a conformable natural gas tank that would allow for much higher packing density of natural gas in vehicles. During the ARPA contract, the government point of contact, Dr. Dane Boysen, happened upon the Schwarz-P surface at a math exploration event for children (as I recall). He suggested the P-surface to all companies working the contract as an inner structure to the tank.
Schwarz P Surface - Anders Sandberg
At the time, REL was pursuing a stacked cube design, where a bunch of cubes was being cast in a matrix, with a porthole between them to allow for gas exchange. This approach was favored because it was easy to manufacture, with a grid pattern and a single volume. The P surface was harder on CAD, harder to machine, and harder to fixture in a casting. A very persuasive reason would be needed to adopt such a challenging geometry.
Cube tank design
Unfortunately, a hole in a sheet under tension is a major stress riser, with a factor of 3 increase in stress! In the burst tank above, you can see how the cracks all run right to the holes.
Hole stress field (www.fracturemechanics.org/hole.html)

The P-surface allowed for a much lower stress design to be built, as it involves none of these fatal holes.

FEA run during ARPA-E MOVE program
Notice how there isn't any location that is far higher in stress than any other location. This uniform activation of the material allows for much higher performance. The huge improvement in stress state shown in this analysis motivated the adoption of the Schwarz P surface as the geometry, despite the challenges associated with the CAD, machining dies, and casting fixturing. The geometry, combined with plenty of engineering on manufacturing and processing, allowed REL to meet its ARPA-E MOVE pressure goals.

The price of a gallon of gas fell precipitously in late 2014, reaching $2.07 in February of 2015, in large part due to the hydraulic fracturing technology in oil drilling. At these new prices, it was difficult to see natural gas competing with oil, and interest in the project as an onboard vehicle solution waned. The technology is now being developed for static storage and as a heat exchanger. If you are interested in the tank, contact Loukus Tech.

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