C172 INSTRUCTOR; INST RATING TRAINEE; ENTERED CLASS D AIRSPACE WITHOUT CLRNC WHEN THEY MISTAKENLY BELIEVED THAT THEY HAD BEEN HANDED OFF TO THE TWR FROM APCH CTLR WHEN DSNDING ON A LOC BACK COURSE APCH.

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MY STUDENT AND I WERE CONDUCTING AN INST TRAINING FLT IN NIGHT VFR CONDITIONS IN THE VICINITY OF MARTINSBURG; WV. WE WERE HEADED TOWARDS THE GERRA INTXN ON A SW HDG AT 3900 FT. I CALLED UP DULLES APCH. I SAID SOMETHING LIKE 'DULLES APCH; ACFT X AT 3900 FT OVER MARTINSBURG; WE WOULD LIKE TO DO THE LOC BACK COURSE INTO MARTINSBURG.' THE CTLR REPLIED 'ACFT X; THAT IS APPROVED; MAINTAIN VFR.' UPON INTERSECTING THE LOC BACK COURSE; WE HEADED OUTBOUND ON THE LOC FRONT COURSE TO GERRA AND DID A PROC TURN AS REQUIRED. WE INTERCEPTED THE LOC BACK COURSE; AND STARTED A DSCNT AS CALLED FOR ON THE APCH PLATE. WHEN REACHING GERRA; I EXPECTED THE DULLES CTLR TO HAND US OFF TO THE TWR; BUT WHEN THAT DID NOT HAPPEN I ASSUMED DULLES LOST RADIO CONTACT WITH US (HAS HAPPENED TO ME BEFORE) AND TUNED IN THE MARTINSBURG TWR ON COM #2 WHILE STILL LISTENING TO DULLES ON COM #1. I RECALL SAYING 'MARTINSBURG; TWR; CESSNA ACFT X IS GERRA INBOUND ON THE LOC BACK COURSE RWY 8.' THE TWR CTLR REPLIED SOMETHING LIKE 'CESSNA X; FLY A HDG OF N AND EXIT THE CLASS D AIRSPACE; YOU'VE GOT C130 TFC INBOUND.' I TURNED TO N AND STARTED A CLB. THE TWR CTLR ASKED FOR OUR TAIL NUMBER; WHICH I GAVE HIM. I LEVELED OFF AT 3500 FT AND WHEN I WAS ABEAM THE NUMBERS FOR RWY 8; I SAW THE LIGHTS OF A LARGE AIRPLANE ON A 1 MI FINAL WELL BELOW ME. THE LARGE AIRPLANE DID A TOUCH-AND-GO OR LOW APCH AND TURNED S AND CLBED (STILL BELOW US). I TOLD THE CTLR THAT WE WERE TALKING TO DULLES APCH. THE CTLR REPLIED THAT DULLES DID NOT TELL HIM ABOUT US. THE CTLR ASKED FOR OUR INTENTIONS AND ALT AND I TOLD HIM THAT WE WOULD LIKE TO DO A PRACTICE ILS OR LOC APCH AND THAT WE WERE AT 3500 FT. HE SUGGESTED WE CONTACT DULLES APCH FOR THE APCH; BUT AT THAT POINT I WAS CONFUSED ENOUGH THAT I THOUGHT IT BETTER TO CALL IT A DAY AND HEAD HOME. IN RETROSPECT; I REALIZE THAT THE DULLES CTLR NEVER GAVE US A SQUAWK CODE AND NEVER SAID 'RADAR CONTACT.' THEREFORE; IN RETROSPECT; HE WAS NOT HANDLING US; BUT AT THE TIME I MISUNDERSTOOD THE WORDS 'THAT IS APPROVED; MAINTAIN VFR.' WHAT WAS 'APPROVED?' THE PRACTICE APCH? WAS HE GOING TO COORD OUR APCH WITH MARTINSBURG TWR? I NOW REALIZE HE WAS NOT INTENDING TO NOTIFY MARTINSBURG TWR. NEXT TIME; IF I DO NOT RECEIVE A SQUAWK CODE; I WILL BE SURE TO CONTACT MARTINSBURG TWR WHILE WELL CLR OF THEIR AIRSPACE. ONCE HOME; I CALLED DULLES APCH AND SPOKE TO THE CTLR ON DUTY. I NOW UNDERSTAND WHAT I DID WRONG.