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Don't know if you were serious or not. But I found some info on that yesterday. Apparently super serious bicycle racers do this. (He) Unfortunately Helium is a very small (Atomic number 2, mass 4) atom and it is monoatomic. This means that it can easily leak out of the tire. For the bike racer it doesn't matter becuase of the short duration of the race. For a car it would be ridiculous. If you are thinking about weight savings see below.
For kicks I did some quick math. I will assume that the tire is a constant volume system. Use the ideal gas law and some constants for the different gasses. Foe a P215 50 R16, the approximate volume for air is 150L Under 2.5bar pressure at 50C, 150L of N2 weighs 0.2438 lbs 150L of air weighs 0.2525 lbs. That is a difference of less than a hundreth of a pound per tire, for a net savings (4 tires) of 0.035 lbs. or about 0.56 oz. (less than a wheel balance weight) I bet four of those big green valve caps are more than that.
If you wanted to fill the tires with helium the helium would weight about .0348 pounds for a weight savings of 0.2177 pounds per tire, or 0.8708 pounds for the entire vehicle. Not worth it to me... Take a shit and you will reduce the weight more.
I also searched the GMR library for info about filling tires with nitrogen. I did not find much there was one SAE paper (SAE-AME-970808-003) But it was published by the compant that makes the nitrogen charging machinery. I asked the librarian for a copy and I will read it later. It seems like more of a press release than a technical paper. The Abstract from the paper is below:
Abstract:
The ECO Air Products Co has announced the introduction of TireLIFE, a system for inflating vehicle tires with nitrogen. The company said its testing of nitrogen-inflated tires has confirmed a 25% to 30% increase in tire mileage. The company's system involves equipment which supplies low cost nitrogen by using a new type of generator. The NitraFill design provides totally automatic, on-demand operation. The product will initially be marketed to fleet maintenance facilities; later to tire stores, service stations, quick lubes, and other automotive service centers. The new system removes moisture and oxygen, eliminating rubber oxidation, a major destructive element affecting tire life and safety.
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