Narrative:

The copilot and I planned a repositioning flight with no passenger under far part 91 from the uncontrolled airport. After a preflight; we taxied out to runway while monitoring the CTAF frequency for the airport. The winds were fairly calm but favoring runway xy. We observed and heard an airplane landing on runway xy. As we approached the runway holding point; we heard three aircraft inbound for landing at the airport. Two of the aircraft announced they would land on runway yx which was the opposite direction of our departure.I asked the copilot to switch to the number 2 radio and pick up our takeoff clearance from clearance delivery while I monitored the CTAF to keep track of the inbound aircraft. I was not listening to the takeoff clearance given to the copilot which was 'climb on runway heading to 3;000 feet.'he switched back over and asked if I was ready; to which I replied; 'ready'. I thought we had enough time to takeoff from runway xy before the other aircraft were in the pattern. The copilot briefed me that the clearance was climb to 3;000 and turn on course which would be approximately 120 degrees. As we entered the runway; we heard aircraft Y announce on CTAF that he was 10 miles out and inbound for runway yx. In my mind; this made sense with what I thought was our clearance to turn on course of 120 degrees which would take us away from the incoming aircraft Y.after takeoff; I started a right turn to 120 degrees while climbing. At approximately 2000 feet; the copilot called nashville approach and stated; 'aircraft X is climbing thru 2000 for 3000 heading zero (pause) one zero.' at this point we were probably on a heading of 100 degrees (not 010 as stated). I immediately ask the copilot to correct this error. The controller came back and asked us to turn 'immediately to a heading of 360 and we had been given the clearance to stay on runway heading and climb to 3000. I immediately turned the aircraft to the heading and the copilot rechecked his written notes to show that the clearance was to fly runway heading and not turn on course as I did.a few minutes later we were notified that we had a possible pilot deviation and I needed to call upon landing. We acknowledged and continued the flight.upon landing; I called and gave all information requested. In my opinion; the problem was caused by a busy uncontrolled airport with traffic landing on opposing runways. I; as the pilot in command (PIC); should have monitored the 'all important' takeoff clearance so that we could double check each other for mistakes. As a procedure going forward; both pilots will monitor ATC and obtain the clearance together and then cross check each other for mistakes.

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Original NASA ASRS Text

Title: Air carrier flight crew reported not being able to comply with an ATC clearance with the stipulation that clearance void if not airborne in five minutes. The departure from an uncontrolled airport with high traffic and landing aircraft from the opposite direction; caused a distraction in departure; resulting in miscommunication between the flight crew.

Narrative: The copilot and I planned a repositioning flight with no passenger under FAR part 91 from the uncontrolled airport. After a preflight; we taxied out to Runway while monitoring the CTAF frequency for the airport. The winds were fairly calm but favoring runway XY. We observed and heard an airplane landing on runway XY. As we approached the runway holding point; we heard three aircraft inbound for landing at the airport. Two of the aircraft announced they would land on runway YX which was the opposite direction of our departure.I asked the copilot to switch to the number 2 radio and pick up our takeoff clearance from Clearance Delivery while I monitored the CTAF to keep track of the inbound aircraft. I was not listening to the takeoff clearance given to the copilot which was 'climb on runway heading to 3;000 feet.'He switched back over and asked if I was ready; to which I replied; 'ready'. I thought we had enough time to takeoff from runway XY before the other aircraft were in the pattern. The copilot briefed me that the clearance was climb to 3;000 and turn on course which would be approximately 120 degrees. As we entered the runway; we heard Aircraft Y announce on CTAF that he was 10 miles out and inbound for runway YX. In my mind; this made sense with what I thought was our clearance to turn on course of 120 degrees which would take us away from the incoming Aircraft Y.After takeoff; I started a right turn to 120 degrees while climbing. At approximately 2000 feet; the copilot called Nashville Approach and stated; 'Aircraft X is climbing thru 2000 for 3000 heading zero (pause) one zero.' At this point we were probably on a heading of 100 degrees (not 010 as stated). I immediately ask the copilot to correct this error. The controller came back and asked us to turn 'immediately to a heading of 360 and we had been given the clearance to stay on runway heading and climb to 3000. I immediately turned the aircraft to the heading and the copilot rechecked his written notes to show that the clearance was to fly runway heading and not turn on course as I did.A few minutes later we were notified that we had a possible pilot deviation and I needed to call upon landing. We acknowledged and continued the flight.Upon landing; I called and gave all information requested. In my opinion; the problem was caused by a busy uncontrolled airport with traffic landing on opposing runways. I; as the Pilot in Command (PIC); should have monitored the 'all important' takeoff clearance so that we could double check each other for mistakes. As a procedure going forward; both pilots will monitor ATC and obtain the clearance together and then cross check each other for mistakes.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.