A RUSHED E145 FLT CREW INCORRECTLY INTERP DCA DEP CLRNC RESULTING IN P56 AIRSPACE VIOLATION.

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MY CREW AND I WERE LATE ARRIVING INTO DCA FROM OUR SCHEDULED DEADHEAD FLTS. WE THEN WAITED EVEN LONGER FOR OUR ACFT TO ARRIVE. AND WHEN IT FINALLY DID; WE WERE SEVERAL HRS BEHIND SCHEDULE AND FELT PRETTY RUSHED. WE BEGAN OUR PREFLT DUTIES; AND WHILE I WAS GOING INSIDE TO CALL DISPATCH FOR THE DCA 'CODE WORD;' THE FO COPIED THE CLRNC TO CMH. HE UNDERSTOOD HIS CLRNC TO BE 'CLRED TO CMH; NW SECTOR; RADAR VECTORS; J149 AS FILED.' AND WHEN I RETURNED TO THE ACFT; THAT IS THE CLRNC WE DISCUSSED. SHORTLY THEREAFTER; WE DISCUSSED AND SET UP THE FMS AND NAVS FOR DEP. WHILE TAXIING OUT; WE WERE FEELING 'HURRIED' AND 'ROUGHED UP' AS WE DEALT WITH THE NIGHT MVFR. WHILE PULLING OUT OF THE SPOT; THE ACFT HAD SLID ON SOME ICE; AND I FOCUSED INTENTLY ON THE TAXI BECAUSE OF THIS; AND ALSO BECAUSE OF THE LIMITED EXPERIENCE THAT MY FO AND I HAD WITH DCA. BECAUSE OF THESE CHALLENGING CIRCUMSTANCES; I WAITED TO DO THE TAXI CHKLIST AND TKOF BRIEFING UNTIL WE HAD CROSSED RWY 4/22 AND WERE HOLDING SHORT OF RWY 1. AT THIS POINT; I GAVE THE STANDARD BRIEFING FOR TKOF; AND I FLIPPED THE COMPANY COMMERCIAL ARPT DIAGRAM PAGE OVER SO THAT THE 'OBSTACLE DEP' PROC WOULD BE VISIBLE ON TKOF. I THEN DISCUSSED THESE PROCS ALONG WITH ALL THE OTHER BRIEFING ITEMS. BUT AT MOST OF THE ARPTS WE FLY INTO; WE RECEIVE OUR 'RADAR VECTORS' PORTION OF THE DEP DIRECTLY FROM TWR OR THE FIRST DEP CTLR. IN ERROR; THIS IS WHAT THE FO AND I WERE EXPECTING WHEN WE TAXIED OUT TO 'POS AND HOLD.' AS I TAXIED ONTO THE RWY; WE WERE GIVEN OUR CLRNC FOR TKOF; BUT I WAS PREOCCUPIED WITH RUNNING THE LINE-UP CHKLIST AND MOVING THE ACFT; AND DID NOT HEAR THE TWR CTLR'S FULL INSTRUCTIONS. I DID HEAR THE FO RESPOND WITH 'CLRED FOR TKOF' AND I WAS SURE AT THIS POINT THAT I HEARD HIM SAY 'RWY HDG.' I'VE THOUGHT ABOUT THIS MOMENT A MILLION TIMES NOW LOOKING BACK; AND IT DOESN'T SEEM TO GET ANY CLRER. BUT AT THE TIME; I WAS QUITE POSITIVE THAT I HAD HEARD THE FO SAY THAT -- NOT TO THE TWR CTLR PERHAPS; BUT AT LEAST TO ME. I KNOW FOR SURE THAT AT THAT POINT I WAS EXPECTING ANY VECTORS TO BE IN A MUCH MORE NW DIRECTION; SO I REPEATED THE WORDS 'RWY HDG;' SO THAT THE FO COULD VERIFY; WHICH HE DID. THE FO; IN TURN; SEEMED TO HAVE DEFAULTED TO A 'RWY HDG' FRAME OF MIND IN THE ABSENCE OF A DEPARTING VECTOR. THIS WAS AN ERROR OF DCA INEXPERIENCE MADE WORSE BY MY OWN ATTEMPT TO CONFIRM THE CLRNC. UP TO THIS POINT; I HAD NEVER FLOWN A SINGLE DEP OUT OF DCA IN MY 5 YRS WITH OUR COMPANY. THE FO ALSO HAD LITTLE OR NO EXPERIENCE THERE; BUT HAS OTHERWISE PROVEN HIMSELF TO BE A DISCIPLINED; PROFICIENT; AND ABOVE-AVERAGE FO -- ONE THAT I CAN DEFINITELY CALL TRUSTWORTHY. SO IT WAS AT THIS TIME THAT I THOUGHT 'RWY HDG' WAS AGREED UPON; AND EVEN VERIFIED. I BELIEVED THAT WE MIGHT GET OUR NECESSARY L TURN; AWAY FROM THE PROHIBITED AREA; IMMEDIATELY AFTER TKOF; OR; AT THE LATEST; WHEN WE REACHED ACCELERATION ALT AND ARE TYPICALLY HANDED TO THE FIRST DEP CTLR. THIS WOULD HAVE ALLOWED JUST ENOUGH TIME TO RECEIVE A MORE APPROPRIATE VECTOR; BUT NOT A LOT. I BEGAN TO THINK THAT THIS WAS HOW THE CTLRS MAINTAINED POSITIVE CTL OVER DEPARTING TFC TO THE N. AFTER CHKING IN WITH DEP IN A TIMELY FASHION WITH THE WORDS 'RWY HDG;' THE POTOMAC CTLR SIMPLY ISSUED A CLB TO 17000 FT. I KNEW THEN THAT SOMETHING WAS VERY WRONG; AND I TOLD THE FO TO CONFIRM 'RWY HDG' AGAIN WITH ATC; WHICH HE QUICKLY DID. IN THE MEANTIME; I HAD ALREADY SPUN THE HDG BUG; AND WAS TURNING L TO CAPTURE THE 328 DEG RADIAL; WHICH HAD BEEN SET EARLIER IN MY NAV RADIOS. NEXT; I HEARD THE CTLR RESPOND WITH AN IMMEDIATE TURN TO A HDG OF 270 DEGS. I COULD NOT TURN ANY FASTER THAN I ALREADY WAS; SO I INCREASED MY CLB RATE TO SLOW MY LATERAL MOVEMENT UNTIL ESTABLISHED ON THE 270 DEG HDG. I VACATED THE AREA AS FAST AS HUMANLY POSSIBLE. UPON LNDG IN CMH; I CALLED THE POTOMAC OPS MGR REGARDING THE 'POSSIBLE PLTDEV.' HE INFORMED ME THAT I HAD VIOLATED THE PROHIBITED AIRSPACE WHILE IN THE HARD TURN. WE CONTINUED OUR FLTS NORMALLY TO OUR 2 OTHER DESTS. I CAN PROMISE THAT THERE WAS NO VIOLATION OF STERILE COCKPIT. IF ANYTHING; I FELT A LITTLE TOO JOB-ORIENTED AND ANXIOUS TO GET THINGS UNDERWAY. THE NEXT MORNING; I CALLED POTOMAC QUALITY ASSURANCE. HE COMMENTED THAT WE HAD DONE A GOOD JOB OF GETTING OUT OF P-56 QUICKLY; MADE POSSIBLE BECAUSE OF OUR IMMEDIATE QUERY TO ATC. HE ALSO APOLOGIZED THAT THE CTLR HAD NOT CAUGHT OUR 'RWY HDG' STATEMENT UPON CHK-IN. LOOKING BACK; THIS WAS CLRLY A CASE OF FALSE EXPECTATIONS AND MISCOM BTWN MYSELF AND THE FO; AND BTWN THE CREW AND ATC. IT'S EASY TO SEE NOW THE 'CHAIN OF EVENTS' OFTEN SPOKEN OF. AND THIS EVENT IS SOMETHING THAT I FREELY ADMIT TO AND APOLOGIZE FOR. AT ALL TIMES; THE FO AND I THOUGHT WE WERE FOLLOWING THE CORRECT COURSE OF ACTION; AND THAT WE HAD USED THE NECESSARY SAFEGUARDS TO VERIFY OUR INFO. AS THE CAPT AND PF; I ACCEPT FULL RESPONSIBILITY FOR WHAT HAPPENED. CERTAINLY; THE AIRLINE HAS GONE TO GREAT LENGTHS TO MAKE THE DCA PROCS RUN AS SMOOTHLY AS POSSIBLE. NO DOUBT; ALMOST EVERY PLT IN THE NATION KNOWS OF THIS PROHIBITED AREA. I THOUGHT I HAD VERIFIED AND UNDERSTOOD THE DEP CLRNC; BUT IT SOMEHOW SLIPPED THROUGH A SYS OF CHKS AND BALS. AS A RECOMMENDATION; I HIGHLY SUGGEST THAT DCA TWR CTL ADD THE WORDS 'FLY THE 328 DEG RADIAL' TO EACH AND EVERY TKOF CLRNC FOR RWY 1. SOMETHING THIS SIMPLE COULD PREVENT THE NEXT PLT FROM MAKING MY MISTAKE AGAIN. SUPPLEMENTAL INFO FROM ACN 602651: THE FLT WAS RUNNING ALMOST 3 HRS LATE DUE TO AREA WX AND I FELT SLIGHTLY RUSHED AND OVERLY RESPONSIBLE FOR ENSURING THE FLT DID NOT ENCOUNTER ANY MORE DELAYS OF ANY KIND. I UNDERSTOOD THE CLRNC TO MEAN WE WERE CLRED OUT THE ARPT'S NW SECTOR VIA RADAR VECTORS TO OUR ASSIGNED AIRWAY. I DID NOT HAVE MY DCA DEP PROCS OUT SINCE I WAS CONVINCED WE'D BE RECEIVING RADAR VECTORS SUPERSEDING THE DEP PROC. I DO NOT RECALL AT WHICH POINT THE CAPT BECAME CONVINCED; AS I WAS; THAT WE WERE TO RECEIVE RADAR VECTORS IN LIEU OF THE DEP PROC. I DO NOT RECALL IF I READ BACK THE TKOF CLRNC ADDING 'RWY HDG' TO THE TAIL-END OF MY XMISSION. I QUERIED POTOMAC FOR HDG WITH THE CAPT'S CONCURRENCE. IT IS CLR TO ME THAT THIS INCIDENT'S PRIMARY CONTRIBUTING FACTORS INCLUDE OUR OBVIOUS MISUNDERSTANDING OF THE IFR ROUTING CLRNC ACCOMPANIED BY OUR LACK OF COMPLETE FAMILIARIZATION WITH DCA ARPT DEP PROCS; RESULTING IN OUR FAILURE TO ADHERE TO SAID PROCS.