C150 PLT AND INSTRUCTOR HAVE AN NMAC AT RYN.

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OUR ACFT WAS BEING PLTED BY A PVT PLT ON A RECURRENCY RIDE. WE ASKED FOR AND RECEIVED PERMISSION TO REMAIN IN THE PATTERN FOR TOUCH-AND-GOES. THERE WERE BTWN 6-7 ACFT IN THE PATTERN. THE L SEAT PLT WAS VERY AWARE OF HIS PATTERN SPACING; AND I HAVE OVER 50 YRS EXPERIENCE FLYING INTO CONGESTED ARPTS; AND ROUTINELY TEACH SAFE PATTERN SPACING. THE TWR CTLR WAS ATTEMPTING TO EFFECT BETTER PATTERN SPACING BY EXTENDING DOWNWIND LEG FOR MOST TFC. I BELIEVE IT WAS OUR SECOND PATTERN WHEN SHE TOLD US (AGAIN) TO EXTEND DOWNWIND; THIS TIME FOR A SENECA MAKING AN INST APCH ON A MODIFIED STRAIGHT-IN. WHEN THE SENECA PASSED UNDER OUR WING; ABOUT 2 MI OUT; WE BEGAN A BASE TURN. WE WERE STILL AT PATTERN ALT. THE CTLR IMMEDIATELY SHOUTED; 'ACFT X TURN BACK TO DOWNWIND; YOU HAVE INBOUND TFC IN FRONT OF YOU! I WILL CALL YOUR BASE.' WE INSTANTLY COMPLIED; THOUGH WE HAD HEARD NO OTHER TFC APCHING FROM THE W; NOR COULD WE SEE ANY. AFTER ABOUT 2 MORE MI; WITH NO CALL FROM THE TWR AND APPARENTLY NO CONFLICTING TFC; I CALLED THAT WE WERE TURNING BASE. WE HAD SEVERAL ACFT BEHIND US ON DOWNWIND; IMPATIENT TO TURN TO BASE. (MY SURMISE WAS THAT THE CTLR'S DEPTH PERCEPTION AT THE 2 MI DISTANCE DID NOT ALLOW HER TO PROPERLY JUDGE OUR SPACING; OR IT WAS THE C150 BEHIND US WHO ACTUALLY TURNED; AND SHE CONFUSED OUR NUMBERS.) ON OUR THIRD APCH; TWR AGAIN EXTENDED OUR DOWNWIND. SHE DID NOT CALL OUR BASE LEG; BUT CLRED US FOR TOUCH-AND-GO. WE WERE ABOUT 2 MI OUT AND FOLLOWING A CHEROKEE WITH AS TIGHT A SPACING AS WAS SAFE. ON DOWNWIND; WE HEARD THE CTLR ASK THE C150 BEHIND US IF THEY HAD US IN SIGHT; AND THE ANSWER WAS IN THE AFFIRMATIVE. SHE REPEATED THE QUESTION TO THE C150 ON BASE; AND THE ANSWER WAS AGAIN IN THE AFFIRMATIVE. I DID NOT HAVE THAT ACFT IN SIGHT; BUT WAS WATCHING SPACING WITH THE CHEROKEE AHEAD. THE CHEROKEE JUST LIFTED OFF AS WE CAME OVER THE RWY THRESHOLD AND BEGAN TO FLARE. IN THAT INSTANT; I HEARD THE CTLR SCREAM; 'ACFT Y; GO AROUND; GO AROUND!' A SHADOW PASSED OVER US AND THE C150 FILLED OUR WINDSCREEN; ABOUT 20 FT ABOVE US AND JUST BEGINNING TO FLARE. LUCKILY; HIS APCH HAD BEEN HIGHER AND FASTER THAN OURS; AS THE CALL FOR HIM TO GO AROUND CAME ALMOST TOO LATE. AT AN ESTIMATED ALT OF ABOUT 40 FT; ACFT Y FINALLY BEGAN A GAR. WE COMPLETED OUR TOUCH-AND-GO; MOSTLY TO MAINTAIN PATTERN SPACING; AS CHEROKEE WAS VERY CLOSE BEHIND US; AND ACFT Y NOW FAR ENOUGH AHEAD.