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WASHINGTON — Air traffic controllers’ work schedules often lead to chronic fatigue, making them less alert and endangering the safety of the national air traffic system, according to a study the government has kept secret for nearly four years.

Federal Aviation Administration officials have declined to furnish a copy of the report despite repeated requests and a Freedom of Information Act request by The Associated Press. However, The AP was able to obtain a draft of the final report dated Dec. 1, 2011.

The impetus for the study was a recommendation by the National Transportation Safety Board to the FAA and the National Air Traffic Controllers Association to revise controller schedules to provide rest periods that are long enough “to obtain sufficient restorative sleep.”

The study found that nearly two in 10 controllers had committed significant errors in the previous year — such as bringing planes too close together — and more than half attributed the errors to fatigue. One-third of controllers said they perceived fatigue to be a “high” or “extreme” safety risk. More than six in 10 controllers indicated that in the previous year they had fallen asleep or experienced a lapse of attention while driving to or from midnight shifts, which typically begin about 10 p.m. and end around 6 a.m.

Overall, controllers whose activity was monitored closely by scientists averaged 5.8 hours of sleep per day over the course of a work week. They averaged only 3.1 hours before midnight shifts and 5.4 hours before early-morning shifts.

The most tiring schedules required controllers to work five straight midnight shifts, or to work six days a week several weeks in a row, often with at least one midnight shift per week. The human body’s circadian rhythms make sleeping during daylight hours before a midnight shift especially difficult.

The study is composed of a survey of 3,268 controllers about their work schedules and sleep habits, and a field study that monitored the sleep and the mental alertness of more than 200 controllers at 30 air traffic facilities.

NASA produced the study at the FAA’s request.

J.D. Harrington, a NASA spokesman, also declined to release the study, saying in an e-mail that because the FAA requested it, “they own the rights to decide its release.”

In the field study, researchers concentrated on controllers who worked a schedule known as the “rattler” in which controllers squeeze five eight-hour shifts into four 24-hour periods by cutting the turnaround time between shifts to as little as eight hours. Some controllers like the schedule because it gives them a 3-day weekend.

Controllers participating in the study wore a wrist device that recorded when they were asleep. They also kept logs of their sleep and were administered alertness tests several times per work shift.

The study makes 17 recommendations to the FAA, including that the agency discontinue mandatory six-day schedules “as soon as possible.”