UNAUTH PENETRATION OF P56 PROHIBITED AREA BY AN MD88 IN A TURN OFF RWY 1 DEP AT DCA; DC.

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WE DEPARTED FROM DCA ON MAR/WED/04; IN THE LATE AFTERNOON USING RWY 1. WE WERE HVY; AND SHORTLY AFTER TKOF; I BEGAN A TURN TOWARD THE RIVER/DEP RADIAL; USING APPROX 10-15 DEGS OF BANK. WHEN WE SWITCHED TO DEP FREQ; THE CTLR DIRECTED US TO TURN IMMEDIATELY TO AVOID RESTR AIRSPACE. WE WERE IN A TURN AT THE TIME OF THE CTLR'S CALL AND IN IMC CONDITIONS. I IMMEDIATELY INCREASED THE BANK ANGLE TO 30 DEGS OF BANK AND CONTINUED THE TURN USING 30 DEGS OF BANK; THE CTLR RESTATED A CALL FOR US TO TURN; AND I KEPT THE BANK OF 30 DEGS UNTIL I HAD ESTABLISHED AN INTERCEPT HDG FOR THE DEP RADIAL. WE INTERCEPTED THE RADIAL AND CONTINUED OUR CLB OUT. THE FOLLOWING DAY; FAA INFORMED US WE HAD ENTERED RESTR AIRSPACE. I WAS SURPRISED BY THE INITIAL CALL FROM ATC TO TURN IMMEDIATELY. THE ONLY REASON I CAN THINK OF; WHICH WOULD CAUSE THIS SIT WOULD BE NOT ENOUGH BANK OR INADEQUATE INTERCEPT HDG TO PREVENT GOING INTO RESTR AIRSPACE. OBVIOUSLY; IF EITHER (OR BOTH) OF THESE WERE THE CAUSE; THE CORRECTIVE ACTION WOULD BE STEEPER BANK AND LARGER INTERCEPT HDG.