Google's executives have been getting cheap flights for their private planes due to a "misunderstanding" that led Google to buy fuel from from the US space agency Nasa at cut prices, according to a report from Nasa's inspector general.

Now the company may have to compensate Nasa, after the report from Nasa's top lawyer noted that the arrangement had "engendered a sense of unfairness and a perception of favouritism", and recommended it explore "possible options to remedy this situation".

Since 2007, Nasa's Ames Research Centre, the administration's home in Silicon Valley, has been leasing space in one of its aircraft hangers to H211, a private company which manages the planes owned and leased by Google execs Larry Page, Sergey Brin, and Eric Schmidt - comprising a Boeing 757 and 767, three Gulfstream 5 private jets and a Dassult alpha jet (classified by aircraft books as a "light attack jet").

The company bought the Dassult jet in 2008 specifically so that it could fulfil the terms of its lease at Ames.

Under the deal, H211 allows the Dassult jet to be borrowed by Nasa for no charge to conduct scientific research. But the company fuels all its planes for both private and Nasa-related flights with aviation fuel provided by the US Department of Defence (DoD).

Flight rate

While the DoD charges a higher rate to non-DOD entities such as Nasa and its contractors, that rate still excludes state and local taxes and other fees that H211 would have paid at local airports. The fuel was supplied for between $3.05 and $3.81 per gallon, compared to $7.01 and $7.44 per gallon at "retail" prices on the airport in 2012.

The report finds that: "A misunderstanding between Ames and DLA-Energy personnel rather than intentional misconduct led to H211 enjoying the discounted fuel rate for flights that had no NASA-related mission." The only "victims", it says, are the state of California and local government which "may have lost tax revenue" from the fuel purchases, and any commercial supplier which missed out on profit from the fuel sales.

"While this arrangement did not cause a loss to Nasa or DLA-Energy, it resulted in considerable savings for H211. Specifically, we calculated that since inception of its lease H211 paid approximately $3.3m to $5.3m less for fuel supplied by DLA-Energy than it would have paid to buy fuel at market rates."

Since September 2013, H211 has been paying a market rate for fuel it purchases for private flights. The difference goes to the US Treasury.

Since 2009, the report says, the Alpha jet has flown more than 200 flights to collect climate data at no cost to Nasa - though the plane costs $4,500 per hour to fly according to H211, compared to costs for Nasa planes ranging between $1.800 and $6,500 per hour. The value of the "free" flights provided to Nasa totals $668,000 based on H211's pricing, the report says.

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