FLT INSTRUCTION ACFT HAS AN NMAC AT UNCTLED ARPT.

Narrative

STUDENT AND I (CFI) WERE IN PATTERN DOING TOUCH-AND-GOES. INFORMED UNICOM (IT IS AN UNCTLED ARPT) THAT WE WOULD REMAIN IN PATTERN. THERE WAS 1 OTHER ACFT IN THE PATTERN AS WELL. THERE WAS A GND UNIT ON THE GND CALLING POS RPTS WHILE DRIVING AROUND THE ARPT. WHEN A CALL CAME OVER THAT WAS INAUDIBLE; I BELIEVED IT WAS THE GND UNIT; AS HE HAD BEEN MAKING CALLS (PROBABLY ABOUT 4) WHILE WE WERE FLYING THE PATTERN. WE HAD BEEN MAKING REGULAR POS RPTS TO KEEP TRACK OF THE OTHER TFC IN THE PATTERN. WHILE ON DOWNWIND FOR WHAT WOULD HAVE BEEN OUR 7TH LNDG; WE CALLED DOWNWIND. AT ABOUT THE TIME A BASE LEG WOULD BE STARTED; A SIMULATED ENG OUT WAS BEGUN BY ME. MY STUDENT BEGAN HIS PROCS WHILE I CHKED THE FINAL LEG FOR TFC. I DID NOT SEE ANY. MY STUDENT CONTINUED THE APCH; AND WHEN WE HAD THE RWY MADE; BEGAN A FORWARD SLIP TO LOSE ALT. AT ABOUT 60 FT AGL; I SAW A PLANE PASS UNDERNEATH US ON FINAL APCH. I IMMEDIATELY INITIATED A GAR AND WE LANDED WITHOUT FURTHER INCIDENT. ACTIONS THAT I FEEL WOULD HAVE MADE A DIFFERENCE BY MYSELF WOULD HAVE BEEN TO CALL FINAL; SIMULATED ENG FAILURE. I FEEL THAT THE OTHER PLT COULD HAVE MADE A DIFFERENCE BY MAKING MORE RADIO CALLS AND ENTERING THE PATTERN ON A 45 DEG TO EITHER UPWIND OR DOWNWIND. UPON LNDG; I CONTACTED UNICOM; WHO TOLD ME THAT THE ACFT HAD MADE A CALL THAT WAS BARELY AUDIBLE; AND THAT HE NEVER DECLARED HIMSELF IN THE PATTERN. I REALIZE THE RADIO CALLS ARE A COURTESY TO AN UNCTLED ARPT; BUT I FEEL THIS WOULD HAVE MADE A DIFFERENCE. ALSO; PERHAPS A BETTER SCAN BY ALL INVOLVED MAY HAVE MADE EVEN MORE OF A DIFFERENCE.