COMMUTER ACR OPERATED BY FLC WHEN KNOWN TO BE OUT OF LIMITS FOR ACFT'S WT AND BAL. TAIL STRIKE ON LNDG.

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FLT WAS INITIALLY DELAYED OUT OF IAD DUE TO LATE BAGS. WITH THE CABIN COMPLETELY FULL AND FORWARD CARGO COMPARTMENT AT MAX WT WITH AFT CARGO CONTAINING THE REST OF THE LOAD; THE CTR OF GRAVITY WAS COMPLETELY AFT OF THE LEGAL LIMIT. DURING ROTATION; THE ACFT PITCHED UP EASILY; BUT CORRECTLY FOR THE CTR OF GRAVITY; HOWEVER NOSE DOWN TRIM WAS REQUIRED FOR THE CLB. NO EVENTS NOTED DURING CRUISE. THE APCH WAS THE VOR TO RWY 13L WHICH INVOLVES FOLLOWING A SERIES OF SEQUENCE FLASHERS ON THE APCH. INITIAL CONTACT WITH THE TWR; WE WERE TOLD TO CONTINUE. AT THIS TIME WE WERE IN COMPLETE LNDG CONFIGN; AND ON APCH SPD. KENNEDY TWR HAD AIRPLANES LNDG ON RWYS 13L AND 22L WHILE DEPARTING RWY 13R. DURING OUR APCH; KENNEDY TWR WAS SWITCHING THE DEP LINE UP TO ANOTHER FREQ. AROUND 500 FT MSL; THE TWR STILL HAS NOT CLRED US TO LAND AND HAD A B747 GAR ON RWY 22L. AT THIS TIME I AM PLANNING TO LAND BUT PREPARING FOR A GAR MYSELF. AS I BEGAN THE ROUND-OUT FOR FLARING THE TWR FINALLY CLRED US TO LAND. I REDUCED THE PWR AND THE TAIL OF THE ACFT SANK SO I INTRODUCED PWR TO ARREST THE SINKING BUT WE STILL IMPACTED; UNKNOWING TO THE CREW WE HAD SCRAPED THE TAIL. ONCE DISCOVERED; APPROPRIATE COMPANY PROCS WERE FOLLOWED. INITIALLY I HAD PLANNED TO CARRY EXTRA PWR FOR THE AFT CTR OF GRAVITY LNDG; BUT IN THE MIDST OF THE TWR NOT CLRING US TO LAND UNTIL THE LAST SECOND; THINKING OF A GAR; XING DEPARTING TFC IN THE EVENT OF THE BALKED LNDG; AND A XWIND; THE EVENTS CAUSED ME TO LAPSE OF THE NEEDED PWR. I BELIEVE THAT THE TWR SHOULD CLR US TO LAND NO LESS THAN 1/4 MI FROM TOUCHDOWN. THIS WOULD REDUCE SOME OF THE MENTAL WORKLOAD.