A PROHIBITED AREA P56 ENTRY BY AN ACR ON DEP FROM DCA.

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DEPARTING DCA RWY 1 IN IMC; WE FAILED TO INTERCEPT THE 328 DEG RADIAL; AND APPARENTLY VIOLATED PROHIBITED AIRSPACE. THE DEP HAD BEEN BRIEFED AS PUBLISHED AND THE VOR AND RADIAL WERE SET INTO THE NAV. WE INCORRECTLY SET RWY HDG RATHER THAN AN INTERCEPT HDG AND HAD THE BANK LIMIT SET AT 15 DEGS RATHER THAN 25 DEGS; WHICH WOULD HAVE BEEN MORE PRUDENT. THE FO WAS AT THE CTLS; AND AFTER LIFTOFF; I DISTR MYSELF RESETTING THE PACKS; WHICH HAD BEEN SELECTED OFF FOR TKOF. INITIAL CONTACT WITH DEP WAS DELAYED; BECAUSE AN INCORRECT FREQ HAVING BEEN SET IN THE RADIO CTL HEAD HAD ADDED TO THE DISTR. AFTER AN UNSUCCESSFUL ATTEMPT TO CONTACT DEP; THE PROPER FREQ WAS FOUND AND SET. I NOTED THE RADIAL HAD NOT BEEN INTERCEPTED WHEN THE FO CALLED FOR THE 1000 FT CLEANUP PROCS. AN INTERCEPT TURN WAS THEN COMMENCED; BUT WAS SLOWED BY THE SHALLOW BANK ANGLE STILL SET INTO THE FLT DIRECTOR AND THE INITIAL INTERCEPT HDG WAS TOO SHALLOW. DURING THE TURN; CONTACT WITH DEP WAS ESTABLISHED AND I INFORMED THEM WE WERE TURNING TO INTERCEPT WITH THE INITIAL CALL. DEP ASKED ME TO CALL THEM AFTER LNDG; BUT MADE NO FURTHER COMMENTS. I HAD FLOWN THIS DEP ONCE BEFORE EARLIER IN THE MONTH WITHOUT PROB AND SHOULD HAVE HAD IT PLANNED BETTER THIS TIME. IT WAS THE FO'S FIRST TIME TO FLY THIS IMC DEP AND HAD SELECTED VOR INTERCEPT MODE AFTER LIFTOFF THINKING THE VOR WOULD CAPTURE AND COMMAND THE TURN TO INTERCEPT. I FAILED TO NOTE THE ERROR IN A TIMELY FASHION. WE WERE MET BY SECRET SVC AGENTS AND INFORMED OF THE AIRSPACE VIOLATION. SUPPLEMENTAL INFO FROM ACN 569482: THIS WAS MY THIRD TIME INTO DCA AND THE FIRST TIME I'VE FLOWN THIS DEP IN IMC. DURING THE TAXI OUT; THE CAPT FULLY BRIEFED ME ON THE NOISE ABATEMENT/P56 AVOIDANCE DEP PROC RWY 1; INCLUDING IMC DEP. WE BOTH RECOGNIZED THE IMC DEP WAS REQUIRED. INSTS WERE SET FOR THE DCA R-328. I HAD SET UP IN THE ARC POS AND WX MODE IN MY EFIS DISPLAY. THE CAPT HAD MAP AND TERRAIN SELECTED. IMC IMMEDIATELY AFTER TKOF. RIGHT AFTER GEAR RETRACTION; I SELECTED VOR/LOC ON THE DFGS. I NOTICED AN INITIAL ROLL TOWARD THE L AND VOR IN THE TARP DISPLAY. I TURNED MY ATTN TO CLEAN UP AND SPD CTLS. INITIAL LEVELOFF WAS TO BE AT 5000 FT MSL. RIGHT AFTER CLB; PWR WAS SELECTED (1000 FT AGL); THE CAPT DIRECTED ME TO TURN L. IT WAS AT THAT TIME I REALIZED THE FLT DIRECTOR BARS WERE NOT INTERCEPTING THE RADIAL; BUT WERE; IN FACT; CONTINUING ON THE RWY HDG. THE CAPT PROMPTED AN INITIAL HDG OF 310 DEGS. WE WERE STILL IN 15 DEGS OF BANK ON THE FLT DIRECTOR. AT THE SAME TIME; THE CAPT WAS BUSY RECONFIGURING OUR ACFT FOR ICING CONDITIONS. DUE TO OUR WT; WE HAD ELECTED TO MAKE A MAX PWR; BLEED OFF TKOF. ADDITIONALLY; THE CAPT WAS MAKING REQUIRED RADIO CALLS. ON HIS THIRD ATTEMPT TO CONTACT DEP CTL; DCA DEP ASKED IF WE WERE ON AN INTERCEPT HDG FOR THE 328 DEG RADIAL. THE CAPT REPLIED WE WERE; BUT THEN DIRECTED ME TO TURN FURTHER L TO APPROX 300 DEGS TO INTERCEPT. AFTER COMPLETING THE DEP; ATC NOTIFIED THE CAPT TO CALL THEM WHEN WE ARRIVED AT DFW. UPON ARR; WE WERE MET AND INTERVIEWED BY THE SECRET SVC. AT THAT TIME; WE WERE INFORMED THAT WE HAD FLOWN INTO THE PROHIBITED AIRSPACE. AFTER A THOROUGH DEBRIEF AND INVESTIGATION; WE WERE RELEASED. THE CAPT HAS CONTACTED THE FAA AS DIRECTED. OBSERVATION: LACKING A SPECIFIC DEP HDG IN THE PROC; I SHOULD HAVE SELECTED AND BRIEFED AT LEAST AN INITIAL HDG OF 320 DEGS AND THEN ADJUST AS REQUIRED. I DID NOT BRIEF MY CAPT ON THE TECHNIQUE I PLANNED FOR THE DEP. ADDITIONALLY; I MISINTERPED THE LOCATION OF THE VOR WITH RESPECT TO THE FIELD AND INCORRECTLY THOUGHT I COULD ARM THE VOR ON THE FLT DIRECTOR TO ENSURE A PROPER INTERCEPT. IN FACT; I WAS ALREADY PAST THE RADIAL; WHEN I HAD SELECTED VOR.