A 2T BIPLANE CFI AND STUDENT GND LOOPED AT TOA; CA.

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AFTER INSTRUCTIONAL FLT WITH AN 80+ YR OLD STUDENT IN THE AFT SEAT OF THE BIPLANE; I NEEDED TO MAKE 3 FULL STOP LNDGS TO SATISFY FUTURE CURRENCY NEEDS AS THE OLD GENTLEMAN WHO OWNED THE ACFT FLEW WITH LARGE TIME GAPS BTWN FLTS. ON THE THIRD LNDG -- NORMAL WITH A SLIGHT L XWIND; I TOUCHED DOWN ON CTRLINE AND WAITED TO APPLY FULL BACKSTICK TO TRACK THE TAILWHEEL. WITH THE ACFT SLOWING WITH FULL BACKSTICK; IT STARTED A SLIGHT TURN TO THE L WHICH INCREASED RAPIDLY. I HAVE A LOT OF TAIL DRAGGER EXPERIENCE; BUT I COULDN'T GET ENOUGH R RUDDER TO COUNTERACT THE SUDDENLY INCREASING L TURN; SO I WENT WITH THE TURN AND EXITED THE RWY ON THE L SIDE TO KEEP FROM DRAGGING THE R WINGTIP. WE WERE IN THE GRASS BORDERING THE RWY AND I KEPT THE TURN GOING TILL WE DID A 360 DEGS AND WERE BACK ON THE RWY. I THINK THE STUDENT IN THE BACK INADVERTENTLY HIT THE L HEEL BRAKE (HE DID IT BEFORE ON TKOF) WHICH PUT THE ACFT ON A VEERING PATH BEYOND CTL. HE DIDN'T ADMIT IT; BUT LATER SAID HE HAD PROBS WITH THE RUDDER/HEEL BRAKE CTLS AND HIS 'BIG FEET.' NO DAMAGE TO THE ACFT OR RWY/GRASS; JUST MY PRIDE.