SMA INSTRUCTOR AND TRAINEE HAD NMAC IN THE PATTERN AT HPN.

Narrative

I WAS WITH A STUDENT DOING TOUCH AND GOES IN CLOSED TFC. ON THE DOWNWIND FOR OUR THIRD TOUCH AND GO; TWR ASKED US TO FALL IN BEHIND THE CESSNA OFF OUR R FRONT. I LOOKED FOR TFC BUT HE WAS INITIALLY BLOCKED BY THE R WINDSHIELD PILLAR OF OUR ACFT. I MOVED MY HEAD TO LOOK AROUND THE PILLAR AND SAW AN ACFT (CESSNA 172) ENTERING THE 45 DEG MID-FIELD L DOWNWIND ON A COLLISION COURSE WITH US. I ROLLED SHARPLY TO THE R AND DSNDED TO AVOID HIM AND THEN I TURNED BACK TO THE L TO FOLLOW HIM. ALL OF THIS TOOK ROUGHLY 10 SECONDS. CONTRIBUTING FACTORS WERE: MY CONCENTRATION ON MY STUDENT'S PROCS AND THE LNDG CHKLIST IN ADDITION TO SCANNING THE BASE AND FINAL FOR TFC POINTED OUT BY THE TWR DISTRACTED ME FROM SCANNING FOR TFC ENTERING THE DOWNWIND. THE OTHER ACFT PLT MAY HAVE BEEN SIMILARLY DISTRACTED. THE TWR WAS VERY BUSY AND MIGHT HAVE BEEN DISTRACTED ALSO; HOWEVER; WHEN HE DID POINT OUT THE TFC HE SAID NOTHING OF THE UNUSUALLY CLOSE PROX. IN MY OPINION; THE TWR ALLOWED HIMSELF TO BECOME OVERWHELMED. MAYBE THERE WERE TOO MANY ACFT IN CLOSED TFC; OR MAYBE HE JUST SQUEEZED EVERYONE IN TOO CLOSE. EITHER WAY BOTH ACFT FAILED TO SEE AND AVOID AND THE TWR FAILED TO SAFELY SPACE TFC IN THE PATTERN. IN HIGH TFC AREAS DURING TIMES OF INCREASED WORKLOAD IN THE COCKPIT; IT IS EASY TO BECOME DISTRACTED AND GET BEHIND. THIS GOES EQUALLY FOR TWR CTLRS WHO SOMETIMES BITE OFF MORE THAN THEY CAN CHEW. PLTS MUST MAINTAIN THEIR SCAN FOR TFC AND NOT GET LOST INSIDE THE COCKPIT. TWR CTLRS MUST DO THEIR BEST TO KEEP TFC SEPARATED IN THE TFC PATTERN.