AN SMT PLT FAILED TO MONITOR HIS HDG GYRO PROPERLY.

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KING AIR 200TG DEPARTED RWY 02 AT MUNCIE ON AN IFR FLT PLAN TO EVANSVILLE. CLRNC WAS 'CLRED AS FILED; CLB MAINTAIN 3000 FT EXPECT 14000 FT IN 10 MIN. DEPT CTL FREQ 120.65.' CLRED FOR TKOF RWY 02 AND TWR SAID 'CLB AND MAINTAIN 3000 L TURN ON COURSE.' WX WAS 400 OVCST; 4 MI WITH FOG. TOOK OFF; STARTED L TURN TO 230 DEGS AND TWR SAID 'CONTACT DEP CTL' AS I WAS DOING SO; I ENTERED THE OVCST AND CONTACTED INDIANAPOLIS DEP CTL AND RECEIVED 'FLY HDG 240 MAINTAIN 3000 FT.' I TURNED L TO 240 DEG AND DEP SAID 'I SAID 270 DEGS.' AND I TOLD HIM THAT HE SAID 240 DEGS. HE THEN SAID 'FLY 270 DEGS.' I TURNED ACFT TO 270 DEGS. DURING THIS TIME THE DIRECTIONAL GYRO SPUN AND I WAS ACTUALLY ON A 90 HDG. BY THE TIME I HAD THE DIRECTIONAL GYRO UNDER CTL AND RESET TO 90 DEGS SO I COULD TURN L TO 270 DEGS; DEP CTL ADVISED ME OF MY HDG AND HAD TO VECTOR ANOTHER ACFT COMING INTO MUNCIE. I TURNED L TO 270 DEGS AS ADVISED BY ATC. DIRECTIONAL GYRO WAS NOW WORKING PROPERLY AND I CONTINUED THE FLT TO EVANSVILLE; IF THERE WAS NO RADAR SVC AT MUNCIE; THERE COULD HAVE BEEN A MIDAIR IN IMC CONDITIONS; OR IF IT WAS CTLED BY GRISSOM APCH CTL; WHICH IT USED TO BE; AND I HAVE BEEN ADVISED BY INDIANAPOLIS ATC THAT THE FAA IS GOING TO TRY TO GIVE IT BACK TO GRISSOM. AND IF THIS HAPPENS AND ANOTHER ACFT HAS THE SAME OR DIFFERENT PROB AS I DID; THE ENDING RESULT COULD BE WORSE; BECAUSE THE RADAR COVERAGE THAT WE HAD BEFORE WITH GRISSOM WAS NOT VERY GOOD.