STUDENT RECEIVING MULTI ENG FLT INSTRUCTION. DOING TOUCH AND GO LNDGS IN LIGHT TO MODERATE TURB. STUDENT WAS HIGH AND FAST ON APCH. STUDENT REDUCED PWR AND LOWERED NOSE. THIS RESULTED IN LOW AND SLOW PROFILE. INSTRUCTOR TOOK OVER; APPLIED PWR RAPIDLY. ENGS DID NOT RESPOND TO RAPID THROTTLE MOVEMENT. ACFT HAD HARD LNDG SHORT OF RWY; THEN WENT OFF R SIDE OF RWY. ACFT WAS DAMAGED.

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AFTER DOING 4 TOUCH-AND-GOES AT F28 ARPT; MADE L TFC FOR A FINAL TOUCH-AND-GO ON RWY 17. THE WINDS AT THE TIME WERE VARIABLE AT 5-10 KTS (APPROX) WITH LIGHT TO MODERATE TURB AT LOW ALT. STUDENT WAS AT THE CTLS. WE WERE HIGH AND SLIGHTLY FAST. STUDENT PITCHED DOWN AND REDUCED PWR. WITHIN THE LAST 200 FT; I FELT A STRONG SINK FROM A DOWNDRAFT. I IMMEDIATELY PUSHED STUDENT'S HAND OFF THE THROTTLES AND PUSHED THEM FULL FORWARD. THE ENGS COUGHED AND HESITATED AT FIRST BUT WE WERE GENERATING PWR BY THE TIME THE MAIN GEAR CONTACTED THE GRASS APPROX 3 METERS BEFORE THE END OF THE RWY. THE ACFT BALLOONED AND I RETARDED THE THROTTLES TO MAKE A LNDG ON THE HARD SURFACE OF THE RWY. I RETAINED CTL OF THE ACFT AND LANDED SLIGHTLY L WING LOW FOR WIND CORRECTION. AS THE R SIDE CAME DOWN; IT CONTINUED TO DROP MORE THAN USUAL. I AT FIRST THOUGHT IT WAS A FLAT TIRE AND WAS SURPRISED BECAUSE THE LNDG DIDN'T FEEL HARD ENOUGH TO BURST THE TIRE. I BROUGHT THE MIXTURE BACK ON THE ENGS TO AVOID A PROP STRIKE ON THE GND. HOWEVER; THE R SIDE CONTINUED TO DROP AND DIG INTO THE RWY. I USED FULL L RUDDER AND AILERON UNTIL THE SPD WAS SO SLOW THAT THERE WAS NO REMAINING RUDDER NOR AILERON EFFECTIVENESS AND THE ACFT SLOWLY WENT OFF THE R SIDE OF THE RWY INTO THE GRASS. WE EVACED THE ACFT AND ARPT PERSONNEL WERE AT THE SCENE IMMEDIATELY.