TXWY EXCURSION DURING LOSS OF ACFT CTL BY A C172 INSTRUCTOR PLT WITH 2 FIRST TIME FLT STUDENTS AT SAN; CA.

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I WAS TO FLY A TRIAL INTRODUCTORY FLT FOR 2 POTENTIAL FLT STUDENTS ON A VFR DAY. I HAD DECIDED TO TAKE THE PAIR ON A COASTLINE FLT AND INTRODUCE SOME BASIC MANEUVERS. WE SPENT AN HR OR SO ON THE GND TALKING ABOUT THEIR GOALS AND INTRODUCING SOME BASIC FLT PRINCIPLES. FOLLOWING A DEMONSTRATION PREFLT; WE BOARDED THE ACFT AND BEGAN OUR JOURNEY. I STARTED THE ACFT AND TAXIED OUT OF THE HANGAR ENVIRONMENT TO AN OPEN TXWY. WE HAD DISCUSSED TAXIING AND USE OF THE RUDDER STEERING AND TOE BRAKES PRIOR TO DEP AND I ALLOWED THE STUDENT TO CONTINUE THE TAXI TO OUR RUN-UP DEST. E CONTINUED OUR TAXI PARALLEL TO OUR TKOF RWY AND APCHED A 90 DEG TURN THAT WOULD HEAD US TOWARD OUR RWY. APCHING THE TURN; I NOTICED THE STUDENT WAS TAXIING TOO FAST FOR THE IMPENDING TXWY WHEREBY I SUGGESTED WE SLOW THE ACFT DOWN. A NUMBER OF CONTRIBUTING FACTORS FOUND THE ACFT CONTINUING OFF OUR TXWY AND OFF THE TXWY ENVIRONMENT. A DOWN SLOPING TXWY; A 13 KT DIRECT TAILWIND AND AN INEXPERIENCED STUDENT SHOULD HAVE GEARED ME INTO EXTRA CAUTION AS WE APCHED THE TURN. UNFORTUNATELY; COMPLACENCY AND A LACK OF COM ON MY PART SAW TO IT THAT WE ENDED UP IN THE WEEDS. MY INSTRUCTION REQUESTING THE STUDENT TO 'SLOW THE ACFT DOWN' WAS ASSUMING THE STUDENT KNEW THE EXACT CTL INPUTS. UNFORTUNATELY; A FIRST DAY STUDENT DOESN'T HAVE THE INSIGHT TO REACT ACCORDINGLY. ALTHOUGH I NEVER SAW IT OCCUR; I'M FAIRLY CERTAIN HE INADVERTENTLY ADDED PWR AS WE PICKED UP SPD APCHING THE TURN. I ATTEMPTED TO BRAKE AND PULL PWR (WHICH DID LITTLE OR NOTHING) TO THE ACFT NOW XING OVER THE TXWY END AND ONTO A DIRT AND GRAVEL PATH. DECISION TIME PROMPTLY KICKED IN -- DO I ATTEMPT TO TURN L AND HIT A MAJOR ARPT MARKING SIGN? DO I TURN R AND RUN INTO A DITCH? OR DO I CONTINUE STRAIGHT AHEAD AND TAKE ON THE WEEDS? I CHOSE THE LATTER OF THE 3 AND CAME TO A STOP 10-15 OFF OF THE TXWY. LESSON LEARNED: NEVER ASSUME AN INEXPERIENCED STUDENT WILL UNDERSTAND AN INSTRUCTION -- COM TEAMED WITH FULL SUPERVISION IS PARAMOUNT FOR A SAFE FLT. GIVE CONSIDERATION TO VARIABLES AFFECTING TAXI SPDS; INCLUDING DOWN SLOPING TXWY AND STRONG TAILWINDS. NEVER DELAY TAKING THE AIRPLANE TO AVOID A DANGEROUS SIT.