A LESS THAN STANDARD RATE OF TURN CAUSES ATC DEP CTLR TO REMIND ACR CREW NOT TO STRAY INTO P56 ON DEP FROM DCA; VA.

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AFTER TKOF; OUR COMPANY PROC CALLS FOR A TURN AT 400 FT MSL TO JOIN DCA 341 DEG RADIAL AND AT 2.7 DME FROM DCA; TURN L TO JOIN DCA 328 DEG RADIAL. AT 2.7 DME I WAS FOLLOWING THE FLT DIRECTOR WHICH WAS LATER FOUND TO BE AT 15 DEGS OF BANK INSTEAD OF NORMAL 25 DEGS OF BANK. I WAS SLOW IN THE TURN AND WAS PROMPTED BY ATC TO REMAIN OVER THE POTOMAC RIVER AND AWAY FROM P56. I ESTIMATE WE WERE LESS THAN 1 MI FROM THE PROHIBITED AREA; BUT DID NOT ENTER IT. THE CAPT TOOK CTL OF THE AIRPLANE AND INCREASED THE BANK TO THE L. WE QUERIED ATC AND NO PROB WAS RPTED TO US FROM THE ATC FACILITY. A MORE THOROUGH PREFLT OF THE MCP SHOULD HELP PREVENT THIS FROM OCCURRING IN THE FUTURE. SUPPLEMENTAL INFO FROM ACN 490650: BANK AND INDICATOR SET TO 15 DEGS (SHOULD HAVE BEEN 30 DEGS) ON PREFLT. FO FOLLOWING COMMAND BARS. CAPT; HEADS DOWN PUSHING BUTTONS; DID NOT NOTICE SHALLOW BANK (15 DEGS). INSTRUCTED FO TO INCREASE BANK L. SLOW (FO) TO RESPOND. CAPT TOOK CTL OF ACFT FOR MAC L BANK ALLOWED TO CORRECT TO COURSE.