A CLBING; DEPARTING S80 PIC HAS A PROB WHEN THE DEP CTLR REPEATEDLY ISSUES A HDG AND CLB CLRNC THAT WILL STEER THEM INTO A TSTM SW OF BWI. IF CLRNC NOT ACCEPTED THE FLT WILL PENETRATE THE P56 PROHIBITED AREA IN DCA. CAPT ELECTS TO PENETRATE P56.

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LOCATION: BWI 230 DEG RADIAL; 20 DME. WAS CLBING OUT OF BWI; ASSIGNED A HDG OF 230 DEGS WITH CLRNC TO CLB TO; I BELIEVE; 17000 FT. WHEN HANDED OFF TO DCA DEP; NEW VECTOR OF 270 DEGS WAS ISSUED WITH CLB CLRNC TO FL230. WE TOLD DCA DEP THAT THERE WAS SEVERE TSTMS TO THE W AND SW AND THE OVERHANG WAS DIRECTLY ABOVE US AND THAT WE WERE UNABLE TO TURN TO A HDG OF 270 DEGS AND CLB RAPIDLY TO FL230. HIS RESPONSE WAS 'OK; JUST FLY HDG 270 DEGS; AND I NEED A GOOD RATE OF CLB TO FL230.' WE TOLD HIM AGAIN WE WERE UNABLE TO CLB TO FL230 AND THAT WE NEEDED TO FLY PRESENT HDG FOR ABOUT ANOTHER 10 MI OR SO. HIS RESPONSE WAS AGAIN THE SAME. WE FINALLY DECIDED TO CONTINUE A SLOW CLB ABOUT 1000 FPM AND MAINTAINED OUR HDG OF ABOUT SSW TO AVOID LEVEL 6 TSTMS. CTLR MENTIONED THAT WE COULD NOT TURN ANY FURTHER L BECAUSE OF P56 PROHIBITED AREA AND HE COULDN'T HAND US OFF TO ZDC UNTIL WE CLBED TO FL230. HE THEN GAVE US ANOTHER TURN INTO THE WX AND WE AGAIN TOLD HIM WE WERE UNABLE TO TURN INTO THAT WX. HE WAS SILENT FOR A COUPLE OF MINS THEN ASKED IF WE COULD TURN TO THE W. THIS TIME WE WERE PAST THE BIGGEST CELL AND TURNED TO THE W AND CONTINUED A GOOD RATE OF CLB TO FL230. HE THEN HANDED US OFF TO ZDC AND WE WERE GIVEN CLRNC TO CONTINUE OUR CLB AND INTERCEPT OUR FILE RTE. SUPPLEMENTAL INFO FROM ACN 407061: AS ALL OF THIS WAS GOING ON; WE WERE ALSO DEALING WITH AN ABNORMAL PROC OF A L HIGH TEMP PACK LIGHT. WE WERE HELD ON THE GND IN BWI FOR 1 HR FOR WX TO THE W AND WHEN WE WERE RELEASED; THE SPACING WAS 25 MI IN TRAIL. WE WERE THE FIRST DEP OUT OF BWI AFTER THEY RELEASED ACFT WBOUND.