SMA ON TRAINING FLT HAS NMAC WITH ANOTHER SMA.

Narrative

I WAS FLYING WITH A HOOD ON. MY R-SEATER WAS A LICENSED INST PLT ACTING AS SAFETY PLT. WE HAD JUST COMPLETED OUR THIRD APCH (VFR; LOC RWY 36) TO FALSE RIVER. ALL 3 APCHS WERE SET UP VIA RADAR VECTORS FROM BATON ROUGE APCH CTL. AT THE MARKER INBOUND; APCH ADVISED OF TFC N OF THE ARPT AT 3300 FT; THEN APPROVED A FREQ CHANGE TO ADVISORY. AFTER SWITCHING I BROADCAST OUR POS AND INTENTIONS. THE OTHER ACFT RESPONDED HE WAS N AT 3500 FT AND HAD US IN SIGHT. ON THE MISSED APCH; I CLBED NBOUND AND THEN TURNED TO 270 DEGS PER BTR APCH'S MISSED APCH INSTRUCTIONS. I CALLED THE OTHER ACFT WHO ADVISED HE WAS NOW S OF THE ARPT HEADED EBOUND AT 3300 FT. I THEN CHANGED FREQ TO BTR APCH AND ADVISED WE WOULD LIKE TO HEAD BACK TO BATON ROUGE FOR A LOC BACK COURSE APCH TO RWY 4L. THIS WAS APPROVED AND THE CTLR ISSUED A VECTOR FOR A HDG OF 150. HE ALSO ADVISED OF TFC AT 12 TO 1230 O'CLOCK; 4 MI EBOUND AT 3300 FT. WE RESPONDED HE WAS NOT IN SIGHT. WE WERE THEN AT 2000 FT AND FIGURED WE WERE WELL BEHIND AND BELOW THE OTHER ACFT WHO WAS PROBABLY HEADED BACK TO BTR AS WELL. I THEN INITIATED A SHALLOW CLB INTENDING TO CLB TO 2800 FT; WHICH IS THE PROC TURN ALT FOR THE LOC 4L APCH TO BTR. A FEW SECONDS LATER; I HEARD MY SAFETY PLT UTTER A LOUD EXCLAMATION -- HE CLAIMS HE SAID 'DIVE L' BUT THE WORDS DIDN'T REGISTER WITH ME. I QUICKLY LIFTED THE HOOD AND OBSERVED AN SMA SLIGHTLY ABOVE AND SLIGHTLY TO THE R OF US; ALMOST HEAD-ON. WE WERE AT APPROX 2500 FT. I RECALL REALIZING IMMEDIATELY THAT WE WERE NOT GOING TO COLLIDE; ALTHOUGH I HAD NO TIME TO REACT ANYWAY; SINCE HE WAS ONLY A COUPLE OF HUNDRED FT IN FRONT OF US AND HEADED THE OPPOSITE DIRECTION. CONTRIBUTING TO THIS INCIDENT WAS THE FACT THAT THE BTR CTLR WAS VERY BUSY VECTORING TFC AROUND BUILDING TSTMS NEAR THE BTR ARPT; AND HIS RESPONSIBILITY TO US WAS ADVISORY ONLY. THE STUDENT PLT IN THE SMA; WE LEARNED LATER; WAS INDEED HEADED FOR BTR AND HAD CHANGED TO APCH FREQ; ONLY TO HEAR ABOUT THE TSTMS IN THE AREA. HE THEN ELECTED TO RETURN TO FALSE RIVER AND WAS DSNDING TOWARD THE PATTERN WHEN THE NEAR MISS OCCURRED. HE DID NOT SEE US AT ALL. MORAL: KEEP YOU EYES OPEN AND IN MOTION. USE THE RADIO IF IN ANY DOUBT ABOUT ANOTHER ACFT IN THE VICINITY. QUERY THE CTLR; BROADCAST YOUR POS AND INTENTIONS. DON'T ASSUME SOMEBODY ELSE'S INTENTIONS.