PA34 SENECA PLT HAS A TXWY EXCURSION AND IMPACTS AN EMBANKMENT.

Narrative

THE STUDENT (L SEAT) IS A PVT STUDENT OF MINE WHO IS PREPARING TO SOLO IN A PIPER WARRIOR. ON THIS PARTICULAR DAY IT WAS MORE CONVENIENT FOR US TO TAKE THE SENECA (OUR TRAINING TWIN) TO VISIT FAMILY AND WE DECIDED TO TRAIN ON THE WAY. ENG START WAS COMPLETED AND TAXI WAS INITIATED TO RWY. THE ACFT WAS ON TXWY A; A DOWNHILL TXWY; AND I ADVISED THE STUDENT TO SLOW HIS TAXI SPD. THE BRAKES WERE APPLIED AND THE ACFT BEGAN TO VEER RIGHT AND HEAD TOWARDS A GRASS EMBANKMENT. I (INSTRUCTOR) TOLD THE STUDENT TO APPLY L PEDAL AND BRAKE TO SLOW DOWN WHILE I REACHED FOR THE R THROTTLE AND TRIED TO REMEDY THE SITUATION. I WAS UNSUCCESSFUL. WHEN IT WAS CLR THAT THE ACFT WAS GOING TO DEPART THE TXWY; I PULLED BOTH MIXTURES TO IDLE CUT-OFF. IT WAS TOO LATE; HOWEVER; TO PREVENT THE R PROP FROM STRIKING A PIECE OF THE EMBANKMENT. THE ACFT CAME TO REST WITH THE NOSEWHEEL ON THE EMBANKMENT. NO DAMAGE TO THE ACFT WAS DONE; HOWEVER; THE STATUS OF THE R ENG IS UNCLR PENDING DECISIONS FROM MECH ON WHETHER TEARDOWN IS NECESSARY. THE PROP IS NOT VISIBLY DAMAGED OR BENT EITHER. A SIMILAR EVENT HAPPENED TO ME IN AN ARROW NOT LONG AGO AND BOTH OF THESE ACFT HAVE ONE THING IN COMMON -- NO BRAKES ON THE R SIDE (SIDE I WAS ON). I BELIEVE THIS EVENT WOULD NOT HAVE OCCURRED IF I HAD BRAKES ON MY SIDE. THE STUDENT RPTED THAT HE FELT LIKE THEY WEREN'T WORKING; BUT THIS IS NOT THE CASE. THE BRAKES WERE WORKING FINE; THE STUDENT LOST CTL AND BECAME FRIGHTENED PUSHING ON THE BRAKES HARDER AND A SITUATION DEVELOPED THAT I FEEL WAS UNRECOVERABLE.