Medium Large Transport; Low Wing; 2 Turbojet Eng
Flight Crew Air Transport Pilot (ATP)
Workload; Situational Awareness; Human-Machine Interface; Distraction; Communication Breakdown; Confusion
Airspace Violation All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy
Air Traffic Control Issued Advisory / Alert; Flight Crew Became Reoriented; Flight Crew Took Evasive Action; Flight Crew Returned To Clearance
Airport; Weather; Human Factors; Chart Or Publication; Airspace Structure
The physical location of DCA presents challenges to departures and arrivals because of its proximity to Prohibited airspace and the requirement to operate extremely close to P56. Departing with a tailwind is never ideal and this increase in ground speed reduced the time available to the crew to identify and react to a deviation from the published departure route. Also; the boundaries of P-56 are NOT clearly depicted on the Lido chart for the JDUBB 1 RNAV. They are blocked by the course 332 to ADAXE. Although P-56A is depicted on multiple charts; several of the charts show the south western boundary in different locations. Please reference Lido charts: JDUBB 1 RNAV; CCI 02 (LOF); P56 Avoidance NAP; and Prohibited Area P56/Noise Abatement.I was the captain of flight from DCA.  During our departure briefing at the gate; we specifically noted that the winds were 170 at 6; and traffic was departing runway 1. Although the winds favored runway 19; we acknowledged that they were within our limits for a tailwind takeoff on runway 1. We also noted that Wind Shear Advisories were in effect; and we followed required procedure using a 'No Flex'; max thrust takeoff. We also briefed the special single engine procedure and the location of P-56. Given the visual conditions of visibility 10 SM; FEW 020 and SCT 160; our method of compliance was visual reference and we briefed 'to stay over the river; and at no time cross east of the river.'Taxi out was normal and we were issued a takeoff clearance from runway 1. At 400 feet AGL; the FO was the pilot flying and incorrectly called for Heading Mode. I was the pilot monitoring and responded correctly with 'NAV Mode' and selected NAV Mode on the flight control panel. The two lights adjacent to the NAV mode button illuminated. I referenced my PFD and noticed that the airplane was still in heading mode and that NAV Mode was not armed. Our ground speed was higher than normal due to the tailwind and we were rapidly approaching the departure course. Again; I reached up and selected NAV Mode; with the same result. I referenced our location on the MFD and we were exactly over the intended departure course however we were still following the flight director incorrectly on runway heading. I said; 'Turn left' and shouted 'IMMEDIATELY!' The FO banked into a left turn. I observed the river from the captain side window and we were directly over the river and clear of P-56. I spun the heading bug directly to the first fix; ADAXE; and we proceeded toward ADAXE. Upon reaching ADAXE; we incorrectly overflew it and I insisted the FO turn right to rejoin the departure. He turned right; and I said; 'You have to follow the white needle' (Specifically referencing our FMS/GPS navigation). He responded; 'I don't have a white needle.' He then reached down and turned the Nav Selector Knob to FMS 2 which gave him proper FMS/GPS navigation. We were able to engage the autopilot at this point and complete the remainder of the JDUBB1 departure. I missed the hand off to departure control; and tower asked me again to call them; which I did. Before the hand off to center; the departure controller gave me a phone number to call because of a possible entry into P-56.
Air carrier Captain reported possible entry into P-56 while departing DCA Runway 1.