INSTRUCTOR AND NEW STUDENT PLT LOSE CTL OF ACFT AFTER LNDG AT 1G1 AND SKID OFF THE RWY TO THE R INTO A SNOW BANK.

Narrative

DSNDING INTO ELYRIA ARPT (1G1) (USING RWY 9); WE MADE A NORMAL APCH AND LNDG; LNDG IN THE CTRLINE RIGHT AFTER THE NUMBERS. I EXPECTED TO USE ALL OF THE RWY FOR LNDG; BEING I WAS WITH A BRAND NEW STUDENT AND WANTED TO BE GRACEFUL. THE STUDENT WAS ALLOWED TO FOLLOW THROUGH WITH THE CTLS; TO 'FEEL' THE LNDG. WHILE ON THE DSCNT; I PREPARED THE STUDENT. I TOLD HIM ONCE THE MAIN WHEELS TOUCH DOWN; WE CAN BEGIN TO APPLY THE BRAKES ( BEING I ONLY HAD USES OF THE PARKING BRAKES). BEFORE I HAD A CHANCE TO TAKE HIM THROUGH IT; THE MAIN WHEELS HIT AND THE BRAKES WERE APPLIED WITH DIFFERENTIAL BRAKING. THE R WAS APPLIED FIRST. IT SEEMS LIKE A NORMAL REACTION FOR A BRAND NEW STUDENT TO BRAKE FULL R (FROM AUTOMOBILE EXPERIENCES.) I STATED IT WAS MY PLANE; HOWEVER; WITH THE R MAIN GEAR LOCKED UP; WE WERE SKIDDING TO THE R OVER PATCHY THIN SNOW AND ICE. PUTTING MY FULL BODY WT INTO THE L RUDDER IN ATTEMPT TO RECOVER DID NOTHING. WITHIN SECONDS FROM TOUCHING DOWN; WE WERE IN THE SNOW BANK. I ESTIMATE ABOUT 50-75 FT. I DID THE BEST I COULD DO TO PREVENT FURTHER DAMAGE OR INJURY TO MY STUDENT AND THE ACFT. WE BOTH WALKED AWAY FROM THE ACFT. HE SAID HE HAD NO HEALTH PROBS AFTER THE INCIDENT; HOWEVER; I HAVE MODERATE NECK AND BACK PAIN. THE R SIDE HIT FIRST. THANKFULLY; I GOT THE BRUNT OF IT INSTEAD OF MY STUDENT.