A J41 PIC SUFFERS A LOSS OF TKOF AND CLB PERFORMANCE AND A HEADING DEV WHEN THE ACFT IS ROTATED TOO EARLY ON A ZERO FLAP TKOF WHEN DEPARTING DCA; DC.

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UPON COMPLETION OF THE WT AND BAL; WE DETERMINED OUR RAMP WT AS 24053 LBS (MAX RAMP WT IS 24110 LBS). THE WINDS WERE FAVORING RWY 1 FOR DEP. OUR PERFORMANCE DETERMINED THAT WE WOULD NEED TO PERFORM A FLAP 0 DEG TKOF; NOT AN ABNORMAL PROC; BUT DEFINITELY OUT OF THE ORDINARY. ON TAXI OUT; THE FO BUGGED THE SPDS FOR A FLAP 9 DEG TKOF; NOT A FLAP 0 DEG TKOF; I COMPLETELY MISSED THIS. FOR FLAP 9 DEGS; V1/VR IS 117 KTS; V2 IS 121 KTS. FOR FLAP 0 DEG; V1/VR IS 126 KTS; V2 IS 130 KTS. THE TAXI WAS SHORT; AND WE WAITED A MIN OR TWO TO BURN FUEL TO BE AT THE MAX TKOF WT (24000 LBS). IT WAS MY LEG TO FLY; THE DEP OUT OF DCA CALLED FOR A R TURN TO A 090 DEG HDG TO AVOID THE PROHIBITED AIRSPACE TO THE NE OF THE ARPT. AT 117 KTS; THE FO CALLED 'V1; ROTATE;' I BEGAN ROTATING AND SOON REALIZED THAT SOMETHING WASN'T RIGHT. I SLIGHTLY LOWERED THE NOSE TO ALLOW THE ACFT TO ACCELERATE; AND WHILE DOING THIS BEGAN A SHALLOW BANK TO THE R TO AVOID THE PROHIBITED AREA. ONCE THE AIRSPD INCREASED; THE ACFT FLEW NORMALLY; AND WE AVOIDED THE PROHIBITED AREA BY MAYBE A 1/2 MI AT THE CLOSEST POINT. BY THIS TIME; I HAD BEEN FLYING FOR 5 STRAIGHT DAYS; 2 OF THESE DAYS IN POOR WX; AND WAS AT 28 HRS OF FLYING IN THE LAST 7 DAYS. THE PREVIOUS NIGHT; WE HAD ABOUT 17 HRS OF REST. ALTHOUGH THIS EVENT ENDED SUCCESSFULLY; IT COULD HAVE VERY EASILY NOT BEEN SO SUCCESSFUL. I REMEMBER MENTIONING TO THE FO THAT I WAS READY TO BE FINISHED WITH THE TRIP. ALTHOUGH I HAD A VERY LONG OVERNIGHT THE NIGHT BEFORE; I WAS STILL TIRED; AND FOUND MYSELF NOT THINKING AS CLRLY AS I NEEDED. FIRST; IT WOULD HAVE BEEN VERY EASY; AND WOULD HAVE HAD NO PROB JUST REQUESTING A L TURN AFTER DEP INSTEAD OF THE HARD R THAT THE TURBOPROPS NORMALLY RECEIVE. I HAVE ASKED FOR IT BEFORE AND WAS NEVER EVEN QUESTIONED ABOUT IT. AT MAX GROSS WT; THIS IS WHAT WE SHOULD HAVE DONE. SECONDLY; OUR TAXI CHK REQUIRES BOTH CREW MEMBERS TO VERIFY THE TKOF SPDS; AND ACFT CONFIGN. WHILE WE RAN THE TAXI CHKLIST; WE FOUND THE FO HAD SET THE TKOF CONFIGN WARNING SYS (TOCWS) FLAP SWITCH TO A FLAP 9 DEGS; NOT A FLAP 0 DEG TKOF; ALTHOUGH THE FLAPS WERE ACTUALLY SET TO ZERO. THIS TOO SHOULD HAVE RANG A BELL THAT MAYBE WE WOULD TAKE A LOOK AT THINGS BEFORE WE DEPARTED. AGAIN IT DIDN'T. WE DIDN'T REALIZE THAT THE INCORRECT SPDS WERE BUGGED UNTIL WE WERE WELL ON OUR WAY. IN MANY WAYS I WAS LEGAL TO TAKE THAT FLT. I HAD PLENTY OF REST THE NIGHT BEFORE; WE HAD AN EARLY SHOW THAT MORNING; NOT TERRIBLY EARLY. I WAS ONLY SCHEDULED FOR ABOUT 4 HRS OF FLYING THAT DAY; AND WAS CLOSE; BUT STILL UNDER 30 HRS IN 7 DAYS. I DIDN'T REALLY EVEN FEEL TOO TIRED TO BE TAKING THAT FLT; BUT IT SURPRISED ME HOW EASILY I JUST BECAME COMPLACENT. I HAD FLOWN WITH THIS FO ON PREVIOUS TRIPS; AND FOUND HIM TO BE VERY COMPETENT. HE HAD JUST STARTED FLYING THE PREVIOUS DAY TO THIS. I FOUND MYSELF PUTTING A LOT OF TRUST IN HIM. HAD WE HAD AN ENG FAILURE ON TKOF; IT COULD HAVE BEEN DRAMATICALLY DIFFERENT. WE EITHER WOULD HAVE NOT BEEN ABLE TO CLB; OR WE WOULD HAVE HAD A GOOD VIEW OF THE CAPITOL; AS WE WOULD HAVE PROBABLY FLOWN OVER IT AT ABOUT 500 FT. EITHER WAY; THE SIT WAS NOT GOOD.