CLOSE PROX 2 GA-SMA ACFT IN TRAFFIC PATTERN AT PLM.

Narrative

I WAS INVOLVED IN A NMAC WHILE ON FINAL APCH TO RWY 24 AT PYM. I WAS CONDUCTING A PLT CHK FLT WITH A PVT PLT WISHING TO HAVE RENTAL PRIVILEGES AT THE FBO/FLT SCHOOL WHERE I AM A PART TIME CFI. I CAN ONLY ASSUME I WAS INVOLVED IN A MIDAIR NEAR MISS BECAUSE I NEVER HAD THE OTHER ACFT IN SIGHT. BUT; I ASSUME IT DID HAPPEN BASED ON THE STATEMENT OF THE PLT OF THE OTHER ACFT. WHILE TAXIING TO THE ACTIVE RWY I ATTEMPTED TO CONFIRM WITH THE PLYMOUTH UNICOM THAT THE ACFT RADIO WAS OPERATING PROPERLY. I NEVER RECEIVED A RESPONSE FROM THEM TO MY REQUEST FOR A RADIO CHK. I ASSUMED THE ACFT RADIO WAS NOT TRANSMITTING BUT DECIDED TO CONTINUE THE FLT SINCE USE OF A RADIO IS NOT REQUIRED AT UNCTLED ARPTS. TO HELP PLTS SEE US BETTER; I TURNED ON THE ACFT'S NAV; STROBE AND LNDG LIGHTS AND LEFT THEM ON THROUGHOUT THE FLT. ALSO; I DID BROADCAST MY POS ANYWAY WHILE OPERATING IN THE TFC PATTERN. DURING THE THIRD LNDG WE TURNED; AND AFTER BEING ESTABLISHED ON A BASE LEG I HEARD THE PLT OF AN SMA Y BROADCAST HE WAS ALSO ON BASE. I BEGAN TO LOOK FOR HIM. ONCE MY ACFT WAS ON FINAL; A FEW SECS LATER; I HEARD HIM BROADCAST THAT HE WAS GOING AROUND. AT THIS POINT I STILL DID NOT SEE SMA Y AND PROCEEDED WITH THE LNDG. ONCE ON THE RAMP AND AFTER HE SHUT DOWN; HE CAME OVER TO ME AND EXPLAINED HOW CLOSE WE HAD COME. HE ALSO TOLD ME THAT I SHOT OUT FROM UNDER HIM. SINCE WE WERE BOTH FLYING LOW WINGED ACFT; I CAN ONLY COME UP WITH ONE EXPLANATION. IF I WAS UNDER AND BEHIND HIM; I WOULD HAVE HAD TO SEE HIM. MY EXPLANATION IS THAT WE WERE ALREADY ON FINAL AND PROCEEDING TOWARD THE RWY AT ABOUT 70 KTS; THE FINAL APCH SPD OF SMA Y IS 63 KTS. THE SMA X WITH AN APCH SPD RECOMMENDED BY ACFT MFTR IS 75 KTS; WAS TURNING BASE TO FINAL. OUR SPD TOWARD THE RWY WOULD CERTAINLY SEEM LIKE WE OVERTOOK THE ACFT; BUT AT THAT TIME WE WOULD HAVE BEEN TRAVELING IN DIFFERENT DIRECTIONS. FORTUNATELY NO ACCIDENT OCCURRED. SINCE MY ACFT WAS UNDER THE SMA Y AND ON FINAL WE HAD THE RIGHT OF WAY. THE PLT OF THE SMA Y RPTED A NMAC RPT WITH THE NE FSDO OFFICE. SINCE I WAS IN THE RIGHT SEAT; THE BASE TO FINAL TURN WOULD HAVE POSITIONED THE ROOF OF THE SMA X TO BLOCK ANY TFC ABOVE US. OUR APCH SPDS WERE APPROX 70 KTS OR LOWER; SINCE I INSIST ON THIS WITH STUDENTS AND WAS PAYING PARTICULAR ATTN TO HOW THE PVT PLT I WAS CHKING WAS HANDLING THE ACFT. ALL 3 TIMES WE FLEW THE TFC PATTERN PROPER ALTS; TURNS; ETC; WERE MADE