C172 ON TRAINING FLT EXPERIENCED ENG FAILURE REQUIRING OFF FIELD LNDG; CAUSAL FACTORS REPORTED AS UNKNOWN.

Narrative

FLT WAS A TRAINING MISSION FOR A STUDENT PLT WORKING TOWARDS THEIR PVT PLT CERTIFICATE. WE WERE GOING TO DO GND REF MANEUVERS AND FOUND A GOOD GND REF AREA. ON THE WAY TOWARDS THE AREA; MY STUDENT DSNDED FROM 1500 FT TO 800 FT. WE HAD PREVIOUSLY DISCUSSED THAT WE WANTED TO DO THE MANEUVER (S-TURNS) AT 1000 FT. AS MY STUDENT STARTED CLBING; HE NOTICED THE ENG RUNNING ROUGH. I ASSUMED CTLS OF THE ACFT AND HAD THE STUDENT BACK ME UP WITH EMER CHKLISTS. BEING THAT WE DID NOT HAVE MUCH ALT UNTIL TOUCHDOWN; WE DID THE ENG RESTART CHKLIST ONCE TO NO SUCCESS. I THEN SQUAWKED 7700 ON THE XPONDER AND TOLD TWR THAT OUR ENG WAS DEAD AND WERE MAKING AN EMER LNDG. WE THEN UTILIZED THE EMER LNDG WITH NO ENG CHKLIST AS MUCH AS WE HAD TIME FOR. WE SUCCESSFULLY LANDED ON THE SIDE OF A LONG LEVEE AND BOTH MYSELF (THE INSTRUCTOR) AND THE STUDENT WERE ABLE TO WALK AWAY WITHOUT INJURY. WE HAD THE PLANE TOPPED OFF WITH FUEL BEFORE THE FLT; 56 GALLONS IS FULL TANKS IN A C172S. THE PREFLT AND PRE-TKOF CHKLISTS WERE COMPLETED SUCCESSFULLY. WE WERE ABOUT 10-15 MINS INTO THE FLT. ONE ITEM WE WERE NOT ABLE TO ACCOMPLISH ON THE ENG RESTART CHKLIST WAS THE ELECTRIC FUEL PUMP ON. IN THE HEAT OF THE MOMENT; WE FAILED TO COMPLETE THAT ITEM. THE PLANE HAD AN ENG OVERHAUL 10 HRS PREVIOUS TO THIS FLT. I DO NOT KNOW WHAT CAUSED THE ENG TO SPUTTER AND DIE AS THE FUEL SELECTOR WAS ON BOTH; FUEL SHUTOFF VALVE WAS OFF; MIXTURE WAS IN AND MAGNETOS WERE ON BOTH.