A C150 TAILWHEEL CONVERSION CONDUCTING LNDG TRAINING DEPARTED THE RWY AT HFD AND STRUCK A TXWY LIGHT.

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I WAS TEACHING LNDGS IN A C150 TAIL DRAGGER CONVERSION TO A STUDENT PLT ON RWY 20 AT HFD. THE RPTED WIND WAS FROM 260 DEGS AT 10 KTS. THE STUDENT PLT WAS FLYING. AS THE AIRPLANE TOUCHED DOWN IT VEERED TO THE R; I CALLED FOR FULL PWR AND L RUDDER. THE STUDENT WAS SLOW IN RESPONDING SO I PUSHED FULL L RUDDER AND AGAIN CALLED FOR FULL PWR. THE STUDENT ADDED FULL PWR JUST AS THE AIRPLANE WENT ONTO THE GRASS. THE AIRPLANE REMAINED UNDER CTL AND IT WAS MY INTENTION TO HAVE THE STUDENT TAKE OFF FROM THE GRASS. I WAS CONCERNED THAT REDUCING PWR WOULD REDUCE OUR CTL OVER THE AIRPLANE AND THAT IT MIGHT VEER INTO THE VASI LIGHTS OR TAXI LIGHTS; WHICH WERE CLOSE BY. HOWEVER; THE STUDENT PULLED THE PWR OFF AGAIN; SO I AGAIN CALLED FOR FULL PWR. JUST AS THE AIRPLANE WAS LIFTING OFF; THE R FRONT TIRE STRUCK SOMETHING ON THE GND; AND I SAW A PIECE OF DEBRIS FLY OUT FROM IN FRONT OF THE R TIRE. THERE WAS NOT ENOUGH AREA IN FRONT OF US TO LAND; SO I CHOSE TO CONTINUE AROUND THE PATTERN AND MAKE A FULL STOP LNDG. AFTER THE LNDG; I CALLED THE CTL TWR TO RPT THAT WE HAD STRUCK AN OBJECT DURING THE TKOF. I RPTED THAT I BELIEVED IT WAS A TAXI LIGHT. DURING THE POSTFLT INSPECTION OF THE AIRPLANE WE DISCOVERED DAMAGE TO THE HORIZ STABILIZER. I BELIEVE THAT IF I HAD APPLIED PWR THE INSTANT THE AIRPLANE STARTED TO VEER OFF THE RWY; THE AIRPLANE WOULD NOT HAVE LEFT THE RWY. IF AFTER DEPARTING THE RWY IF I HAD HELD CONTINUOUS FULL PWR; I BELIEVE THAT WE WOULD HAVE TAKEN OFF BEFORE REACHING THE TAXI LIGHT.