PVT PLT OF A C172 TURNED TOO SOON AFTER TKOF FROM CDW RESULTING IN A DEV OF ARPT NOISE ABATEMENT PROCS.

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I TOOK OFF FROM CDW IN VFR CONDITIONS WITH INTENTION TO FLY TOWARDS ROBBINSVILLE VOR. AT RUN-UP PRIOR TO TKOF; I ADJUSTED MY DIRECTIONAL GYRO TO SYNCHRONIZE IT WITH MY COMPASS. IMMEDIATELY UPON TKOF; I PROCEEDED IN SAME HDG AS RWY ACCORDING TO MY DIRECTIONAL GYRO. TWR ASKED MY HDG. I THOUGHT TWR WANTED MY REQUESTED HDG; SO I INDICATED 210 DEGS -- THE DIRECTION OF ROBBINSVILLE VOR. TWR THEN INDICATED THAT I DEVIATED FROM NOISE ABATEMENT PROCS BY TURNING TOO EARLY. I ACKNOWLEDGED. I EVENTUALLY TURNED TO 210 DEG HDG TO ROBBINSVILLE (ACCORDING TO MY DIRECTIONAL GYRO). AFTER CHANGING FREQ TO NEW YORK APCH; I INDICATED ON MY INITIAL ANNOUNCEMENT THAT I WAS; I BELIEVE; W OF CDW. NEW YORK APCH INDICATED THAT THIS WAS INCORRECT AND I WAS IN FACT 8 MI W OF NWK. I THEN LEARNED THAT MY DIRECTIONAL GYRO WAS OUT OF SYNCHRONIZATION WITH MY COMPASS. I INFORMED NEW YORK APCH OF THIS; AND ADJUSTED MY DIRECTIONAL GYRO ACCORDINGLY. THEN IN ACCORDANCE WITH ATC INSTRUCTIONS; I ADJUSTED MY HDG. I AM NOT AWARE WHETHER I ACTUALLY ENTERED CLASS B AIRSPACE PRIOR TO ATC INFORMING OF MY ACTUAL LOCATION 8 MI W OF NWK. I BELIEVE MY POSSIBLE BREACH OF CLASS B AIRSPACE AND DEV FROM NOISE ABATEMENT PROCS AT CDW WERE IN LARGE PART DUE TO THE FAILURE OF THE DIRECTIONAL GYRO TO STAY CONSTANT WHEN ALTERING RPM FROM RUN-UP TO CLB PWR SETTINGS. A GPS WOULD HAVE BEEN HELPFUL TO AVOID THIS PROB; BUT THERE WAS NOT ONE ON BOARD AT THE TIME.