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particularly the fact that there was a patch availible:
"For several years now, Airbus has offered its customers a special safety program - called "Buss" -- at a cost of €300,000 per aircraft. If the airspeed indicator fails, this software shows pilots the angle at which they must point the plane.
Up to now, Air France has chosen not to invest in this optional extra for its fleet."
To this day, the relevant licensing bodies still only test pitot tubes down to temperatures of minus 40 degrees Celsius (minus 40 degrees Fahrenheit) and an altitude of about 9,000 meters (30,000 feet). These completely antiquated specifications date back to 1947 -- before the introduction of jet planes.
So part of the problem was they didn't have enough fuel to move around the storms. Couldn't they have descended to a lower altitude so the ice would melt?