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The captain and his co-pilot on the packed 325-seat Airbus A330 had decided to take turns in having 20-minute naps during the journey on August 13.
But less than two hours after take-off, both were reportedly asleep, leaving the plane cruising on autopilot with no-one to take control in the event of an emergency.
They admitted what had happened to the Civil Aviation Authority (CAA), blaming longer shifts over the peak holiday season, which left them unable to get more than five hours’ sleep in the preceding 36.
The watchdog has declined to name the airline concerned for fear of deterring other pilots from reporting problems.
It confirmed the carrier was UK-based but would not say where the plane had departed from or where it was heading.
David Learmount, an air safety expert, told The Sun : “The plane is capable of cruising on autopilot, but if there’s an emergency there would be no one to take the controls.
“The pilots need to be alert. But the greatest danger is they wake up and do something as a knee-jerk reaction while still suffering sleep inertia.”
A CAA spokesman said: “We take fatigue-related incidents extremely seriously.”
The British Airline Pilots Association has warned that proposed changes to flying rules being voted on by MEPs next month would lead to pilots working up to seven starts in a row and being awake for 22 hours if standby hours are taken into account.
Last month a survey of more than 2,000 adults commissioned by the association suggested that nine out of 10 would be worried about being in an aircraft flown by a pilot who has been awake for 22 hours.