INSTRUCTOR PLT WITH SPI ON LNDG ROLLOUT SIGHTS A TWIN ENG ACFT ON LNDG ROLL ON INTERSECTING RWY. HARD BRAKING RESULTS IN THE TAIL WHEEL ACFT FLIPPING OVER.

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I WAS IN A PA20-125 WITH A STUDENT DOING TKOF AND LNDGS TO A FULL STOP. THE RWY WE WERE USING WAS RWY 36. WE HELD AT THE BEGINNING OF THE RWY TO LET A C152 DEPART RWY 10 AFTER JUST BACK-TAXIING. THE 2 RWYS INTERSECT. AS WE DEPARTED; WE KEPT THE C152 IN SIGHT AND WIDENED OUR PATTERN TO ACCOMMODATE THE C152 AND OBSERVE OTHER TFC AND THE C152. WHEN ON FINAL THE C152 WAS TAXIING BACK AFTER LNDG. THE C152 WAS ON A PARALLEL TXWY. WE THEN SAW HE WAS HOLDING SHORT OF OUR RWY. WE THEN TOUCHED DOWN AND WERE ROLLING PAST THE TREE LINE WHICH BLOCKED THE VIEW OF HALF OF RWY 10. I THEN SPOTTED A TWIN-ENG WHICH JUST LANDED ON RWY 10. A COLLISION COURSE WAS SET. WE THEN APPLIED MAX BRAKES. BRAKING TOOK PLACE 200-300 FT; UNTIL 10-15 FT BEFORE THE INTXN OF RWY 10 WHERE OUR PLANE WENT OVER ON ITS BACK. AS THE TAIL CAME UP I TOLD THE STUDENT TO WATCH THE BRAKES BUT HE CONTINUED. THE PROBABLE CAUSE OR FACTOR WAS A STRAIGHT-IN APCH OF THE TWIN WHICH DISRUPTED TFC FLOW. ALSO; THE TREE LINE WHICH BLOCKS THE VIEW FOR ABOUT 1200-1500 FT OF THE RWY. MAX BRAKING WAS NEEDED TO AVOID COLLISION. IN ORDER TO AVOID OVERBRAKING WAS HARD TO AVOID. A MORE CLR PROC WAS NEEDED PRIOR TO THE TRAINING LESSON. INTRODUCING SUCH SCENARIOS TO FUTURE STUDENTS WILL BE OF MUCH USE. THIS WAS AN UNCTLED FIELD AND ABNORMAL TFC PATTERNS WILL BE AN ISSUE. PERHAPS THE TWIN SHOULD HAVE BEEN SPOTTED ON A 1 OR 2 MI FINAL BUT THAT IS DEBATABLE. WE WERE EQUIPPED WITH NO RADIO BUT WERE CONSTANTLY LOOKING FOR TFC WHEN WE COULD. LUCKILY WE WERE NOT INJURED AND THE PLANE ONLY RECEIVED MINOR DAMAGE.