PA24 STUDENT AND INSTRUCTOR PRACTICING POWER OFF LANDING FORGET TO LOWER THE LANDING GEAR AND LAND GEAR UP.

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I WAS THE INSTRUCTOR ON A LCL TRAINING FLT. THIS WAS THE THIRD LESSON FOR MY STUDENT TO GET A CHKOUT IN THIS MAKE AND MODEL ACFT. HE IS A PVT SEL PLT AND CURRENT AND LEGAL IN COMPLEX ACFT; JUST NEEDED A CHKOUT IN THIS MODEL. THIS WAS AN OLDER ACFT AND HAD NO USEFUL CHKLIST. WE HAD BEEN BUILDING A CHKLIST FOR ALL PHASES OF FLT OVER THE PREVIOUS LESSONS. THIS FLT WE DID AIRWORK; PWR ON AND OFF STALLS AND WERE ALMOST OVER THE ARPT WHEN I SIMULATED A COMPLETE ENG FAILURE BY PULLING THE PWR TO IDLE. WE HAD BRIEFED THIS WOULD HAPPEN. I BEGAN READING 'ENG FAILURE AT ALT' CHKLIST WHICH HE HAD WRITTEN PREVIOUSLY. I WAS READING; DOING LOTS OF COACHING AND MAKING SMALL NOTES ON IT. WE ESTABLISHED BEST GLIDE AND TRIMMED. LOCATED LNDG SITE. TRIED RESTART (SWITCH TANKS; FUEL PUMP ON; MIXTURE RICH; CARB HEAT; MAG SWITCH; PRIMER; ETC). COVERED 'SQUAWK AND TALK' AND DISCUSSED PLANNING THE APCH (CLOSE IN BASE AND FINAL); WENT INTO SECURING THE ACFT FOR TOUCHDOWN. FOR REASONS I CANNOT EXPLAIN I WAS SO BUSY USING THE CHKLIST AND MAKING MENTAL NOTES ABOUT MODIFICATIONS; AND COACHING HIS TURNS AND GLIDING TARGET 1/3 DOWN THE RWY THAT I NEVER PUT THE LNDG GEAR DOWN OR DID THE CHK ON SHORT FINAL TO VERIFY ITS POS. HE MADE A SMOOTH TOUCHDOWN RIGHT ON THE CTRLINE WITH THE GEAR UP! IT WAS SO SMOOTH AND STRAIGHT THAT NEITHER WINGTIP TOUCHED NOR DID THE FLAPS. WE BENT THE PROP AND SCRAPED A 2 FOOT BY 3 FOOT SQUARE ON THE BELLY. LESSON AND COMMENTS: I SHOULD NOT HAVE BEEN MAKING NOTES AND FOCUSED ON ANY CHKLIST ONCE I WAS BELOW 1000 FT AGL. I MUST PUT IT AWAY AND LOOK AT THE 'BIG PICTURE' AND THE TASK AT HAND AND USE THE RELIABLE 'GUMPSSS' CHKLIST (WHICH HAS WORKED FOR ME FOR 23 YRS OF INSTRUCTING) IN PREPARATION FOR ANY LNDG. WE HAD MINS EARLIER BEEN DOING PWR OFF STALLS WHERE THE GEAR WARNING HORN WAS SOUNDING. IT WAS WEAK TO ME BUT I REMEMBER HEARING IT; HE HAS A NOISE CANCELING HEADSET AND SAID HE HAD NEVER HEARD IT. I NEVER HEARD IT DURING THE ENG OUT SIMULATION. I WONDER IF I HAD MENTALLY BLOCKED IT OUT DUE TO IGNORING IT DURING PREVIOUS STALL SERIES. SUPPLEMENTAL INFO FROM ACN 761068: DURING A TRAINING FLT; WE WERE PRACTICING EMER ENG-OUT PROCS. WE SET UP FOR A LNDG ON A PAVED RWY; WHILE GOING THROUGH OUR NEWLY FORMULATED EMER CHKLIST. OUR ATTN WAS DIVERTED WHILE CONCENTRATING ON THE APCH; ADJUSTING FOR A XWIND; ETC. NEITHER OF US HEARD THE WARNING HORN (POSSIBLY DUE TO NOISE CANCELING HEADSET) AND IT DID NOT REGISTER WITH EITHER OF US THAT THE GEAR WAS NOT DOWN UNTIL WE WERE IN THE FLARE. THIS ACFT HAS NO MANUFACTURER'S CHKLISTS. WE WERE DEVELOPING MANY CHKLISTS OVER THIS AND PREVIOUS LESSONS. DURING OUR ENG-OUT PRACTICE; INSTRUCTOR WAS READING/MODIFYING ENG-OUT CHKLIST. WE WERE BOTH INVOLVED IN MUCH DISCUSSION CONCERNING ALL PROCS. THIS MAY HAVE LED TO FAILURE TO VERIFY GEAR DOWN.