Date: 201407
Local time of day: 0601-1200
Location: ZZZ.Airport, US
Flight conditions: VMC
Weather elements / visibility: 20
Light: Daylight
Aircraft: Small Aircraft; Low Wing; 1 Eng; Fixed Gear
Operator: Personal
Operating under: Part 91
Flight plan: IFR
Mission: Personal
Flight phase: Initial Climb
Airspace: Class D ZZZ
ATC / advisory: TRACON ZZZ; Tower ZZZ
Aircraft component: Air Conditioning Distribution System
Component problem: Malfunctioning
Reporter organization: Personal
Reporter function: Pilot Flying
Reporter qualification: Flight Crew Private; Flight Crew Instrument
Human factors: Situational Awareness; Troubleshooting; Distraction; Confusion; Communication Breakdown
Anomaly: Aircraft Equipment Problem Less Severe; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT
Detector: Automation Aircraft Terrain Warning; Person Flight Crew
When detected: In-flight
Result: Flight Crew Took Evasive Action; Flight Crew Became Reoriented
Contributing factors: Aircraft; Human Factors; Environment - Non Weather Related
Primary problem: Human Factors

Narrative: I departed on ZZZ Runway XXL about midday. I climbed quickly past 600 feet making a steep climbing left turn but should have turned right. During this turn Tower handed me off to Approach. As was changing frequencies my Terrain Warning System activated loudly repeating 'PULL UP' and I immediately discovered I had turned in the wrong direction and quickly took corrective actions to increase climb and avoid obstacles and traffic. We are taught to 'fly the airplane first' and since I had already turned to the southeast I quickly made the decision to continue the turn to my assigned heading of 350 degrees and climb to the assigned 2;000 feet. I decided not to correct back to the right due to the close proximity of traffic and the Class B airspace. During this corrective action there was never any conflict with any other aircraft or obstacles and I was able to stay close to the airport traffic Class D airspace. After correcting I contacted Approach when leveling at 2;000 feet at a heading of 350 degrees. I deviated by turning in the wrong direction when taking off. A number of distractions before takeoff I believe contributed to my confusion on the direction of turn. When on the ramp after starting the engine; I discovered that my air conditioning had malfunctioned and before calling Ground I took an extended time while warming up the engine to try to troubleshoot this system. Due to the extremely hot day and the extended time running the engine without any cooling it became almost unbearably hot in the cabin. This was complicated since on this type plane you can't open doors or windows with the engine running. When contacting Ground for my IFR clearance and taxi instructions the moisture from extreme sweating was contributing I believe to a clear hearing issue with my head phones. I also believe that when I readback the turn instruction of 350 degrees to the Tower Controller I only repeated the heading but didn't repeat the direction of turn. I did change head phones just prior to taking off. Since I was less than a minute out in a turn to the left when the Tower handed me off to Approach with excellent visibility I believe the Tower should have clearly seen the incorrect left turn.




Synopsis: A pilot became distracted troubleshooting an aircraft malfunctioning on a hot day while receiving the ZZZ Runway XXL clearance and then on takeoff turned southeast activating their Terrain Warning.