CAPT OF SF34 STRIKES TFC VOLUME CONE ON RAMP WITH PROP DURING INITIAL TAXI FOLLOWING RELEASE FROM GUIDANCE BY MARSHALLER.

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I LOOKED OVER TO MY L AT THE MARSHAL AND GOT A SALUTE CLRING ME TO LEAVE THE RAMP. WE WERE PARKED IN THE CLOSEST SPOT NEXT TO THE TERMINAL BUILDING AND THERE WERE NO OTHER ACFT ON THE RAMP AT THAT TIME. I LOOKED TO THE R AND ASKED THE FO IF THE AREA WAS CLR. SHE RESPONDED THAT IT WAS CLR. I STARTED TO MOVE THE ACFT TO THE R TOWARD TXWY B. I DID NOT SEE A TFC CONE THAT WAS LEFT BY SAN RAMP AGENTS AS IT WAS HIDDEN BY THE GLARE SHIELD. AS WE STARTED TO FINISH THE TURN HEADING TOWARD TXWY B; POST EVENT INSPECTION DISCLOSED THE L PROP STUCK A TFC CONE. I WAS LOOKING FORWARD AND DID NOT SEE THE IMPACT. THE SOUND OF THE IMPACT WAS THE FIRST INDICATION OF A PROB. I BROUGHT THE ACFT TO AN IMMEDIATE STOP AND LOOKED OUT MY L SIDE WINDOW. I SHUT THE ENG DOWN. I ASKED THE FO TO TAKE CTL OF THE ACFT WHILE I WENT OUTSIDE TO INSPECT THE DAMAGE. WHEN I DETERMINED THAT THE FLT WOULD BE DELAYED UNTIL MAINT COULD INSPECT THE PROP; I RETURNED TO THE COCKPIT AND TAXIED THE ACFT TO A REMOTE PARKING SPOT ON THE RAMP. INSPECTION OF THE PROP INDICATED IT HAD STRUCK A TFC ONE. WE CONTACTED DISPATCH AND MAINT VIA THE TELEX AND MADE AN APPROPRIATE AML ENTRY. CAUSES: 1) TFC CONE SITUATED IN THE MIDDLE OF THE RAMP AREA. 2) ABSENCE OF PAINTED LINES FOR TAXI RTES AND PARKING LOCATIONS. 3) FAILURE TO TAXI FORWARD BEFORE STARTING THE R TURN AND FOLLOW USUAL TAXI RTE. 4) FAILURE OF THE FO TO PROPERLY CHK THE AREA WAS CLR; INSTEAD OF FOCUSING ON A NEW DEP PROC. 5) FO'S UNFAMILIARITY WITH NEW ARPT AND RTE. REMEDIES: 1) REMOVAL OF TFC CONES FROM THE RAMP AREA UNLESS THEY ARE BEING USED IN THE IMMEDIATE VICINITY OF PARKED ACFT. 2) TAXI LINES AND DESIGNATED PARKING AREAS NEED TO BE PERMANENTLY PAINTED ON THE RAMP. 3) I SHOULD HAVE PROVIDED A PREFLT BRIEFING TO THE FO COVERING THE DEP PROC PRIOR TO STARTING THE TAXI.