FLC FLEW WRONG SID AFTER TKOF. NO MENTION WAS MADE BY THE TWR OR DEP CTLR TO FLC CONCERNING THE DEV. RPTR SAW DEPARTING ACFT AND THEN REALIZED THEY WERE ON THE WRONG SID. APPARENT LOSS OF SEPARATION; BUT ATC WAS UNCONCERNED.

Narrative

DFW TO OKC. ATC GAVE US THE JACKY 2 DEP (FLY HDG 270 DEGS ON DEP). BEFORE TAXI; CAPT ASKED ME; TRI GATE 3 IS THE DEP? AND WITHOUT LOOKING AT THE CLRNC I COPIED; I SAID YES. BOTH ARE VALID DEPS WHEN TAKING OFF NBOUND AT DFW TO OKC. TRI GATE 3 TURNS R TO 030 DEGS ON DEP. ATC GND TOLD US TO TAXI TO RWY 36R. THIS SHOULD HAVE BEEN THE FIRST CLUE THAT WE HAD THE WRONG DEP IN MIND. THE CAPT HAD APPROX 190 HRS AS CAPT AND ABOUT THE SAME AMOUNT FLYING OUT OF DFW. I HAD 8 MONTHS FLYING OUT OF DFW; APPROX 500 HRS. I THOUGHT THAT SINCE IT WAS A SLOW PERIOD AT DFW; THEY WERE USING THIS DEP BECAUSE IT IS ONE USED TO DEPART FOR OKC. AFTER TKOF AT 400 FT; WE TURNED 030 DEGS INTO RWYS 35L/C. TWR SAID NOTHING ON RADIO. I AM STILL THINKING ATC KNOWS WHAT THEY ARE DOING BUT I STILL AM CLRING OUR FLT PATH TO THE R. THERE ARE NO DEPS FROM RWY 35L AND THE FREQ IS QUIET. AS WE CROSS THE DEP END OF RWY 35L (HDG 030 DEGS) I SEE A B767 BEGIN HIS TKOF ROLL. AT THIS TIME WE LEVEL AT 2000 FT MSL; BEGIN ACCELERATING TO 250 KTS; AND CONTACT THE TRI GATE 3 DEP CTL FREQ. WHEN I CHK IN WITH ATC; THEY SOUND SURPRISED AND THIS IS MY FIRST INDICATION WE GOOFED. I IMMEDIATELY CHK THE TCASII AND THE B767 IS 2 - 2 1/2 NM BEHIND US ON TCASII. AT THIS TIME WE HAVE ACCELERATED TO 230 KIAS AND I FIGURE WE WON'T HAVE A SEPARATION CONFLICT. THE CTLR ACCEPTS US AND COORDINATES THE HDOF TO ZFW. BEFORE LEAVING THE FREQ I ASK HIM IF WE HAD A 'DEAL' AND HE LAUGHS AND SAYS NO; AND CONTACT ZFW BLAH; BLAH; BLAH FREQ. THE REST OF THE FLT WAS UNEVENTFUL. I FEEL 3 FACTORS CONTRIBUTED TO THIS MISTAKE: 1) MOST IMPORTANTLY; THIS TRI GATE 3 SID IS MADE TO HAVE FLTS FROM THE W RWYS TURN INTO THE E RWYS AT DFW. THIS TIME I MADE THE ERROR BUT SOMETIMES THE GND CTLR GIVES YOU THE WRONG DEP RWY. I KNOW THIS HAS HAPPENED BEFORE BUT THE RESULT IS THE SAME -- WE TURN INTO DEPARTING TFC. 2) WE WERE SCHEDULED FOR 9 HRS 35 MINS REST; BUT WE GOT 6 HRS SLEEP. WRONG HOTEL LISTED IN THE BID PACKET (WE HAVE 2 IN HOU LONG AND SHORT LAYOVER). WAITED 15 MINS FOR VAN THAT WASN'T COMING. AFTER SEVERAL PHONE CALLS; GOT TO HOTEL 30 MINS LATE. ENTIRE CREW WENT OUT TO EAT BECAUSE WE HADN'T EATEN SINCE XA00 AM THAT MORNING. CAPT HAD TROUBLE GETTING TO SLEEP; SO HE HAD LESS THAN 6 HRS. WE ALL WOKE UP 90 MINS PRIOR TO DEP TO EAT THE FREE BREAKFAST IN THE HOTEL. BOTTOM LINE: I WAS MORE TIRED THAN NORMAL. I KNOW THE CAPT WAS EXTREMELY TIRED BECAUSE HE TOLD ME HE WAS. 3) BOTH PLTS HAD FLOWN FOR YRS OUT OF ORD BUT WERE BOTH FAIRLY NEW TO DFW. WE ARE BOTH GETTING USED TO THE LACK OF STANDARDIZATION OF THE OPS (ATC) AT DFW. SOMETIMES THE TWR DOESN'T EVEN KNOW WHAT GND CTL FREQS ARE BEING USED WHERE. THE CTLRS ACT LIKE THE SYS WORKS JUST FINE BUT COMPARED TO ORD THE WAY THE OP IS LAID OUT THEY DON'T HAVE A CLUE HOW THEY PALE IN COMPARISON. IT'S NOT THE CTLRS' FAULT -- IT IS THE WAY THE FLOW OF TFC IS COMPOSED; DESIGNED; AND IMPLEMENTED. THE SID THAT ALLOWS W SIDE TFC TO TURN INTO THE E SHOULD BE CHANGED. WE ARE HUMAN BEINGS THAT MAKE MISTAKES WHEN WE ARE TIRED. IF WE ARE GOING TO SHOOT OURSELVES IN THE FOOT; THE LEAST WE CAN DO IS TAKE THE BULLETS OUT OF THE GUN. I KNOW A CAPT WHO DID THIS SAME THING 2 YRS AGO AND I THOUGHT I WOULD NEVER DO THIS -- AND HERE I DO IT 2 YRS LATER. I STILL CAN'T BELIEVE I MADE THIS MISTAKE.