PVT PLT OF AN SMA SEL ACFT INADVERTENTLY PENETRATED CLASS B AND D AIRSPACE.

Narrative

I MAY HAVE FLOWN (INADVERTENTLY) INTO CLASS B (HOU) WITHOUT CLRNC AND/OR CLASS D (EFD) WITHOUT 2-WAY COM WITH TWR; AFTER FLYING OVER CLOVER FIELD (T02). I WAS DEMONSTRATING RNAV OP TO A PAX AND CONTINUED TO HEAD N TOWARD CLASS B INNER RING AND TEMPORARILY LOST POS AWARENESS. CONTRIBUTING TO MY LOSS OF POS AWARENESS WAS A DIRECTIONAL GYRO WITH A LARGE PRECESSION (INDICATING 60 DEGS N OF HDG). I THOUGHT I WAS HDG E TO STAY OUT OF CLASS B AND D AIRSPACE BUT I WAS FLYING DIRECTLY TOWARD THEM. IN ADDITION; I DELAYED MY TURN E BECAUSE I WAS DEMONSTRATING RNAV. WHEN I REALIZED MY POS/ERROR; I MADE AN IMMEDIATE TURN TO A SE COMPASS HDG AND PROCEEDED TO MY BASE ARPT WITHOUT FURTHER INCIDENT. I BELIEVE THE REAL CAUSE OF THE INCIDENT WAS MY FAILURE TO KEEP CORRECTING THE DIRECTIONAL GYRO PRECESSION (EXCESSIVE OR NOT). CONTRIBUTING WAS MY FAILURE TO MAINTAIN POS AWARENESS. IF I HAD MAINTAINED EITHER OF THESE; I BELIEVE THIS INCIDENT WOULD NOT HAVE HAPPENED. THIS 'CLOSE' CALL REINFORCED WHAT I'VE READ IN FLT TRAINING AND AVIATION SAFETY THAT THE MOST VULNERABLE TIME FOR A PVT PLT IS BTWN 100 AND 200 HRS OF FLT TIME. SINCE THIS INCIDENT; I HAVE DISCUSSED THE SIT WITH MY INSTRUCTOR AND OTHER PLTS. I WAS VERY UPSET THAT I ALLOWED THIS TO HAPPEN. THIS COULD HAVE TURNED OUT WORSE THAN IT DID BEING THAT HOU IS ONE OF THE BUSIEST ARPTS IN THE UNITED STATES. I AM DETERMINED TO MAKE SURE THIS DOESN'T HAPPEN AGAIN BY ALWAYS MAINTAINING POS AWARENESS. IN ADDITION; I PLAN TO SET UP SOME DUAL INSTRUCTION TO REVIEW MY HABITS/INST SCAN AND FOR SOME HOOD TIME TO CORRECT DEFICIENCIES I MAY HAVE.