FLC OF A B727 TURNED THE WRONG WAY AFTER TKOF ON AN IFR DEP.

Narrative

THE PROB WAS AN ATC CLRNC DEV. THE CLRNC WAS TO DEPART RWY 5R AND TURN L TO 300 DEG HDG. WE INITIATED A R TURN TO 300 DEGS. IN OUR BEFORE TKOF BRIEFING WE DISCUSSED THAT IT WAS TO BE A R TURN TO 300 DEGS WHEN WE CHKED WITH DETROIT DEP THE CTLR SAID IT SHOULD BE A L TURN. WE DECIDED SINCE WE WERE ALREADY HALFWAY THROUGH THE R TURN THAT THERE WOULD BE A SMALLER AIRSPACE INVERSION IF WE CONTINUED THE TURN AND NOTIFIED THE CTLR OF OUR INTENT. HE ASKED THAT IT BE AS TIGHT AS POSSIBLE. ON THE TWR TAPE WE HAD REPEATED THE CLRNC PROPERLY AS A L TURN BUT BECAME SURE THAT IT WAS A R TURN AS WE TAXIED INTO POS. BOTH CAPT AND FO AGREED IT WAS A R TURN SO WE DID NOT CONFIRM WITH TWR A SECOND TIME AS IS OUR PROC. THERE WAS NOT A CONFLICT WITH OTHER TFC. FACTORS AFFECTING OUR JUDGEMENT AND DECISION MAKING ARE RELATED TO FATIGUE. THIS INCIDENT OCCURRED AT XA20 AM LCL TIME AND CREW HAD BEEN ON DUTY SINCE XB30 AM. IT WAS ALSO THE FIRST 'DUTY' DAY OF A NIGHT SCHEDULE AFTER THE CREW HAD BEEN ON DAYS OFF AND OBSERVING NORMAL SLEEP HABITS AT NIGHT. BY THIS TIME IN THE MORNING THE CREW HAD BEEN AWAKE FOR OVER 20 HRS. OF NOTE ALSO IS THAT THE FIRST DEP THAT NIGHT HAD BEEN MOVED TO 1 HR PRIOR TO THE SCHEDULED DEP TIME DEPRIVING THE CREW OF 1 HR OF EXPECTED SLEEP TIME AFTER COMMUTING TO WORK. THIS KIND OF FATIGUE IS COMMON ON THE FIRST ROTATION OF A NIGHT SCHEDULE. IT IS IMPORTANT FOR CREW MEMBERS TO GET SOME SLEEP BEFORE OR DURING THIS PERIOD. THIS ALSO SHOWS THE IMPORTANCE OF WRITING DOWN ALL CLRNCS.