MOONEY M20 PLT MAKES WRONG RWY TKOF AFTER BEING CLRED FOR TKOF DUE TO UNFAMILIARITY WITH ARPT AND FOLLOWING ANOTHER ACFT THAT HAD JUST TAKEN OFF.

Narrative

UNFAMILIAR WITH ARPT; REQUESTED PROGRESSIVE TAXI TO RUN-UP AREA FOR DEP. HELD SHORT OF RWY FOR RUN-UP WHILE ANOTHER ACFT DEPARTED L TO R. CLRED TO DEPART RWY 8; I FOLLOWED THE TAXI LINE TO CTR OF RWY VIA R TURN/CURVE; AND DEPARTED. DEP WAS FROM MIDPOINT OF RWY 17R. DISCUSSED WITH CTLR AFTERWARD AND HE INDICATED THAT SINCE THERE WAS NO OTHER TFC; HE ALLOWED ME TO DEPART RATHER THAN TERMINATE MY ROLLOUT. THAT WAS NICE TO KNOW HE WAS ON TOP OF IT. CONTRIBUTING FACTORS AND HUMAN PERFORMANCE CONSIDERATIONS: THIS INCIDENT WAS 100% PLT ERROR (MINE). FATIGUE WAS THE OVERRIDING FACTOR. UNFAMILIARITY WITH THE ARPT RESULTING IN RELIANCE ON PROGRESSIVE TAXI INSTRUCTIONS MEANT I WAS AT THE RUN-UP AREA WITHOUT KNOWLEDGE OF THE ARPT LAYOUT; NOT REALIZING THE RWY LAYOUT. FATIGUE WITH THE ACFT DEPARTING BEFORE ME L TO R GAVE ME THE MENTAL IMAGE THAT I WOULD DEPART TO THE R HENCE THE R TURN ONTO RWY. INACTIONS: LEARNING ARPT LAYOUT AND FOLLOWING SIGNS (I TOOK AN AVIATION SAFETY SEMINAR ON ARPT SIGNS WITHIN THE YR SO NO EXCUSES). NOT XCHKING DIRECTIONAL GYROSCOPE (HEADING) PRIOR TO DEP (WOULD HAVE SHOWN 170 DEGS). DID I MENTION FATIGUE AS I WAS 3 HRS INTO A 5 HR FLT; WITH NO AUTOPLT.