Light Transport
Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument
Situational Awareness; Fatigue; Confusion; Communication Breakdown
ATC Issue All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy
Air Traffic Control Issued New Clearance; Flight Crew Requested ATC Assistance / Clarification; Flight Crew Became Reoriented
Human Factors; Procedure
Official duty time started at XA:00 EST. It was now XK:00 EST and I was PIC (Pilot in Command) sitting number one at the hold short line awaiting takeoff clearance. I'd been there a few minutes. Tower said that TRACON was so busy they weren't picking up the phone (to issue takeoff clearances to Tower). When Clearance finally came through; we left the ground at XK:12 EST. We flew the RNAV Departure and were headed 280 degrees at 2;000 feet MSL when switched to Departure Control frequency. Departure frequency was saturated with the single voice of the Controller giving rapid-fire instructions to multiple aircraft at the speed of an auctioneer (without the sing-song). One aircraft made a check in call and was answered with a broadcast of words to the effect: 'Nobody talk. We're busy here. Mine is the only voice on the radio. I'll get to you.'We were given a series of incremental climbs and heading changes until we were eventually heading 310 degrees and climbing to 8;000 feet. Each altitude and heading change was verbalized on the intercom by both the Pilot Flying (me) and Pilot Monitoring. Departure Control made the following call: '[Callsign]; give me right three sixty.' I swung the heading control knob around to the right for 100 or more degrees and the Pilot Monitoring verbalized taking over control of the heading control knob while I attended to other control and mode inputs. After about 180 degrees of turn; TRACON queried if we were in a turn; we said yes; that we were accomplishing a right three sixty as directed. 'I wanted North; um; [Callsign] go direct (first fix on our route of flight).' There was no further conversation with Departure Control except frequency change to next controller down the line.Both myself and the Pilot Monitoring had absolutely no doubt that we were being given an in-place turn to facilitate some spacing issue that Departure needed to make happen. Task saturation on the part of the Controller and his use of the term 'right three sixty' vice 'right three six zero' led us to misunderstand his intended instruction. His command to stay off the radio precluded an opportunity to catch this error at inception. Verbalizing individual digits; in this case 'three six zero;' confirms that the number is a heading call.
A Light Transport pilot reported ATC used non-standard phraseology which led to the crew executing a right 360 degree turn instead of turning to a heading of 360.