FLC OF A PIPER 28 TRAINING FLT MISUNDERSTOOD THE TWR CTLR DURING LNDG PRACTICE AND MADE A 'TOUCH AND GO' RATHER THAN A FULL STOP CAUSING THE CTLR TO ASK THEM TO LEAVE HIS AIRSPACE.

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ON OCT/SAT/97; I WAS A FLT INSTRUCTOR ON A VFR FLT FROM BUTLER; PA (BTP; UNCTLED); TO BEAVER COUNTY; PA (BVI; CLASS D). BEFORE ENTERING CLASS D AIRSPACE WE LISTENED TO ATIS AND CALLED THE TWR WITH OUR LOCATION. THEY TOLD US TO PROCEED INBOUND AND RPT OVER THE BEAVER RIVER (4 NM E OF ARPT). WE RPTED OVER THE RIVER WITH A REQUEST FOR TOUCH AND GOES. THEY TOLD US TO ENTER A L DOWNWIND FOR RWY 10. TURNING ONTO THE L BASE LEG; WE WERE 'CLRED FOR TOUCH AND GO.' WE MIGHT HAVE ACTUALLY BEEN 'CLRED TO LAND;' BUT I PERCEIVED 'CLRED FOR TOUCH AND GO' WAS GIVEN. AFTER TOUCHDOWN; THE STUDENT ADVANCED FULL PWR. RIGHT BEFORE LIFT-OFF WE WERE TOLD TO 'TURN L AS SOON AS POSSIBLE.' I TOOK THIS AS A REQUEST TO START THE XWIND LEG AS SOON AS POSSIBLE. WE TOOK OFF; AND MADE THE L TURN WHEN WE HEARD 'CHEROKEE; STATE INTENTIONS.' THE STUDENT WANTED ONE MORE TOUCH AND GO. THE TWR THEN INSTRUCTED US TO GET CLR OF HIS AIRSPACE TO THE N AND THAT THEY WILL FIND OUT MY ADDRESS. AT THAT TIME I KNEW SOMETHING WENT WRONG. I THOUGHT WE MAY HAVE ENTERED THE WRONG DOWNWIND. I APOLOGIZED TO THE TWR IF WE ACTUALLY DID ENTER THE WRONG DOWNWIND (PERHAPS HE SAID R DOWNWIND INSTEAD OF L DOWNWIND). HE TOLD ME IF I WANT TO BE A PROFESSIONAL PLT I NEED TO TELL THE TWR OF MY INTENTIONS; BUT HE SAID NOTHING OF A POSSIBLE WRONG DOWNWIND. THE REST OF THE FLT WE WONDERED IF WE ENTERED THE WRONG DOWNWIND. AFTER WE GOT BACK TO BUTLER; I CONSIDERED THE POSSIBILITY THAT HE GAVE US A CLRNC TO LAND INSTEAD OF A TOUCH AND GO CLRNC. THAT WOULD EXPLAIN THE 'TURN L AS SOON AS POSSIBLE' INSTRUCTION AFTER WE TOUCHED DOWN; BECAUSE ALL OF THE RWY EXITS ARE A L TURN FROM RWY 10. BUT I STILL WAS NOT SURE. I TRIED TO CALL THE TWR AFTER WE LANDED; BUT THE PHONE NUMBER TO THE TWR WAS DISCONNECTED AND NO LONGER AVAILABLE. A THIRD POSSIBILITY WAS THE CTLR'S ANNOYANCE WITH MY STUDENT'S RADIO PHRASEOLOGY. THIS WAS MY VERY FIRST FLT AS AN INSTRUCTOR; AND MY FIRST FLT INTO BEAVER; PA. THE STUDENT WAS GETTING READY FOR HIS PVT PLT CHK RIDE AND HAD PREVIOUSLY WORKED WITH ANOTHER INSTRUCTOR. HE TOLD ME HE HAD BEEN TO BEAVER MANY TIMES; SO I LET HIM DO ALL THE RADIO WORK UNTIL WE WERE TOLD TO LEAVE BEAVER'S AIRSPACE; EVEN THOUGH HE APPARENTLY DID NOT KNOW THE PHRASEOLOGY TO USE WHEN TALKING TO A TWR. HOWEVER; I LET HIM CONTINUE TO DO THE TALKING SINCE HE WAS GETTING READY FOR HIS CHK RIDE. BECAUSE THIS WAS MY FIRST FLT AS A CFI AND I WAS UNFAMILIAR WITH THE AREA; I HAD A LOT ON MY MIND. BECAUSE BEAVER TWR DOES NOT MAKE ITSELF AVAILABLE OVER THE TELEPHONE; I STILL AM NOT REALLY SURE WHAT WENT WRONG.