LJ55 CREW HAD TRACK DEV IN TPA CLASS E AIRSPACE.

Narrative

THIS WAS THE THIRD LEG OF A 4 LEG TRIP; ALL WITHIN THE STATE OF FLORIDA. THIS LEG WAS BTWN NAPLES; FL; AND TAMPA; FL -- A FLT OF LESS THAN 30 MINS. THE FLC CONSISTED OF 2 ATP AND TYPE RATED PLTS IN THE LR55. THE PNF WAS RELATIVELY NEW TO THE LR55; BUT HAS NUMEROUS HRS IN A LEAR 36; 35 AND 31. DURING ARR INTO THE TPA ARPT ON THE BRDGE 5 ARR; THE PNF PROGRAMMED OUR FMS FOR THE ARR. USUALLY I RE-VERIFY THAT THE FMS HAS BEEN PROGRAMMED CORRECTLY; BUT TODAY I DID NOT. I FELT THAT THE PNF WAS EXPERIENCED ENOUGH WITH THE FMS TO DO THIS TASK CORRECTLY. SOON AFTER BEGINNING THE ARR OVER BRDGE INTXN; THE ACFT MADE A TURN WHICH APPEARED TO BE THE RIGHT DIRECTION FOR THE ARR; BUT APPARENTLY IT WAS NOT. A FEW MINS LATER; APCH CAME ON AND ASKED US IF WE WERE ON THE ARR. TO WHICH WE REPLIED 'YES.' HE STATED THAT HE DID NOT SHOW US ON THE ARR AND GAVE US A VECTOR TO 290 DEGS AND VECTORS TO FINAL AND WE LANDED WITHOUT INCIDENT. THIS OCCURRED BECAUSE OF A FEW MAIN REASONS: 1) OVERDEPENDENCE ON THE ACCURACY OF THE FMS. 2) FAILURE OF THE CREW TO VERIFY THAT THE FMS HAD THE PROPER ARR AND/OR FIXES PROGRAMMED IN. 3) FAILURE OF THE CREW TO HAVE THE 'PAPER' COMMERCIAL CHART OUT IN PLAIN VIEW TO FOLLOW ALONG WITH; THUS ELIMINATING THE POSSIBILITY THAT THE FMS FLIES THE WRONG PROC. 4) FAILURE OF THE CREW TO PROPERLY TUNE AND FOLLOW THE FLT'S PROGRESS BY USING GND BASED VOR NAV. IN TODAY'S 'HIGH TECH' AVIONICS WORLD; WE; AS PLTS; ARE BECOMING OVERDEPENDENT ON ALL THE GIZMOS AND ARE FORGETTING THE OLD ART OF FLYING. IT IS IMPERATIVE THAT TODAY'S CREW BACK UP FMS INFO WITH VORS AND PAPER METHODS TO ASSURE THAT THE FMS WILL BE DOING WHAT YOU HAVE PROGRAMMED IT TO DO. NOTE: THERE WERE NO KNOWN CONFLICTS CREATED BY THIS DEV FROM THE ARR PROC.