STUDENT AND INSTRUCTOR EXPERIENCE RWY EXCURSION DURING REJECTED TKOF INITIATED BY STUDENT.

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THE STUDENT WAS PERFORMING THE PREFLT AS I WALKED OUT TO THE PLANE. I PLACED MY HEADSET AND CHARTS ON THE R WING ROOT AND BEGAN MY USUAL WALKAROUND OF THE ACFT. I FIRST CHKED THE FUEL LEVEL IN THE R WING BY VISUALLY LOOKING INTO THE TANK. THE LEVEL INDICATED GREATER THAN 3/4 FULL. I THEN WALKED TO THE NOSE COWLING TO CHK THE OIL. THE DIPSTICK INDICATED 6 QUARTS. I WAS THEN DISTR BY A PUDDLE OF OIL THAT HAD COLLECTED UNDERNEATH THE ENG COWLING. I QUESTIONED THE STUDENT; AND AFTER A BRIEF DISCUSSION OF WHAT IT MIGHT BE FROM; I WALKED INTO THE HANGAR TO GET A MECH TO TAKE A CLOSER LOOK. AFTER CLOSER EXAM IT WAS DETERMINED THE OIL WAS FROM ANOTHER ACFT THAT HAD LEAKED A LARGE AMOUNT OF OIL THE DAY PRIOR. AS THE MECH WALKED AWAY THE STUDENT WAS GETTING INTO THE PLANE AND I CONTINUED A WALKAROUND OF THE PLANE IN WHICH I DID A VISUAL SCAN OF THE ACFT AND TIE-DOWNS. I NEVER DID TOUCH THE LEFT FUEL CAP; ONLY VERIFIED THE LEVEL WITH THE STUDENT AND COCKPIT GAUGE. THE ACFT WAS READY FOR FLT. IT HAD BEEN DECIDED THAT THE FLT WOULD DEPART N TO COMPLETE THE DAY'S LESSON. ATIS INFO RPTED THE WINDS AS 'CALM' AND IT WAS DECIDED THAT RWY XX WOULD BE USED SINCE IT PROVIDED FOR A SHORTER TAXI AND MORE DIRECT DEP RTE. THE RWY IS 3000 FT AND HAD BEEN USED SEVERAL TIMES IN THE PAST FOR SUCH FLTS. THE RUN-UP WAS UNEVENTFUL AND THE TKOF BRIEFING FOLLOWED. THE STUDENT WAS TO PERFORM THE 'SHORT-FIELD' PROC OF HOLDING THE BRAKES AND APPLYING FULL PWR BEFORE BEGINNING THE TKOF ROLL. THE TKOF BEGAN AS USUAL. THE BRAKES WERE HELD AND FULL PWR WAS APPLIED. BOTH THE STUDENT AND I VERBALIZED 'NEEDLES NORMAL; GAUGES GREEN;' FOLLOWED BY MY INSTRUCTIONS TO 'RELEASE BRAKES.' THE AIRSPD BEGAN TO CLB AND THE STUDENT VERBALIZED 'AIRSPD ALIVE;' WHILE I CONFIRMED '40 KTS; AIRSPD ALIVE.' THE ACFT WAS ROLLING DOWN CTRLINE WITHOUT ANY INDICATION OF A PROB. I GLANCED AT THE AIRSPD INDICATOR; WHICH WAS NOW PASSING THROUGH 60 KTS; AND WAS SHORTLY EXPECTING THE STUDENT TO BEGIN ROTATION. WITHOUT ANY INDICATION OR WARNING; THE STUDENT ABRUPTLY MOVED THE THROTTLE TO IDLE AND VERY HEAVILY APPLIED THE BRAKES. THE ACFT BEGAN SKIDDING IMMEDIATELY. MY INITIAL REACTION WAS TO SAY 'WHAT ARE YOU DOING? GET OFF THE BRAKES; OFF THE BRAKES.' THE STUDENT CONTINUED TO APPLY THE BRAKES. WITHIN SECONDS OF THE REDUCTION IN PWR; THE ACFT BEGAN TO SWERVE FROM SIDE-TO-SIDE. AT THE FIRST INDICATION OF A DIRECTIONAL CTL PROB; I AGGRESSIVELY VERBALIZED; 'LET GO OF THE CTLS; MY AIRPLANE; MY AIRPLANE.' THE STUDENT APPEARED TO RELEASE THE YOKE; BUT AS I ATTEMPTED TO STEER AND REGAIN CTL; THE STUDENT CONTINUED TO APPLY PRESSURE ON THE RUDDER AND BRAKES. HE SEEMED TO FREEZE ON THE PEDALS AND WOULD NOT RELINQUISH CTL TO ME; THUS FORCING ME TO TRY TO OVERPOWER HIS PRESSURE. THE ACFT CONTINUED TO SKID AND WAS SHORTLY IN THE GRASS NEXT TO RWY XX/YY; WHERE WE CAME TO A COMPLETE STOP. AFTER STOPPING; THE TWR ASKED 'CAN YOU TAXI OUT OF THE GRASS OR DO YOU NEED A TOW?' I FIRST REPLIED 'WE WILL TRY AND TAXI OUT.' AFTER EVALUATING THE SITUATION; I ASKED FOR A TOW AND WE PROCEEDED TO SHUT DOWN THE ENG. AT LEAST TWICE THE STUDENT EXCLAIMED 'I'M SO SORRY; IT WAS MY FAULT!' WHEN QUESTIONED AS TO WHY HE HAD INITIATED A REJECTED TKOF; HE SAID 'THE FUEL CAP CAME OFF.' THIS WAS THE FIRST EXPLANATION I RECEIVED OF WHY HE HAD REDUCED THE PWR AND ATTEMPTED TO BRAKE. THE L FUEL CAP HAD INDEED COME UNDONE; BUT SEEMED TO POSE NO CRITICAL THREAT TO THE AIRWORTHINESS OF THE ACFT. WHEN I EXITED THE PLANE; I REALIZED THE L WING HAD STRUCK A RWY LIGHT; WHICH LEFT A SMALL CRACK IN THE LNDG LIGHT LENS AND SMALL MARK IMMEDIATELY NEXT TO THE LNDG LIGHT. THE ACFT MECHS MET US ALONG WITH THE ARPT EMPLOYEES. THE TIRE WAS REPLACED AND THE ACFT WAS TAXIED UNDER ITS OWN PWR BACK TO THE HANGAR. IN A WRITTEN RPT I RECEIVED FROM THE STUDENT HE MAKES THE STATEMENT '(THE INSTRUCTOR) AND I WERE TRYING TO REGAIN CTL OF THE AIRPLANE BY KEEPING THE RUDDER PEDALS NEUTRAL.' THIS FURTHER LEADS ME TO BELIEVE THAT IN THE FEW SECONDS FOLLOWING MY FORCEFUL STATEMENT 'LET GO OF THE CTLS; MY AIRPLANE; MY AIRPLANE;' THE STUDENT CONTINUED HIS ATTEMPT TO BRAKE AND STEER THE ACFT; AND NOT BEING FAMILIAR WITH THE HIGH SPD STEERING AND BRAKING CHARACTERISTICS OF THE ACFT; FURTHER HINDERED MY ATTEMPT TO PREVENT A LOSS OF DIRECTIONAL CTL. WHILE THE DISLODGED FUEL CAP WAS NOT A NORMAL SITUATION; IT WAS NOT; IN MY OPINION; A JUSTIFIED REASON TO REJECT A TKOF AT ROTATION SPD ON A 3000 FT RWY. I HAD CONSIDERED TO RE-APPLY FULL PWR AND CONTINUE THE TKOF ROLL; BUT THE PLANE HAD ALREADY BEGAN SKIDDING AND I FELT IT WOULD BE A BETTER DECISION TO ATTEMPT TO STOP THE ALREADY SLOWING PLANE; RATHER THAN FACE THE CONSEQUENCES OF STRIKING AN OBJECT OFF THE END OF THE RWY AT TKOF SPD. I BELIEVE MY RESPONSE DID PREVENT A POTENTIALLY SERIOUS ACCIDENT.