CRJ200 CREW ROUSES THE IRE OF AN N90 CTLR DURING THE KENNEDY ONE CRI CLB.

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WE DEPARTED JFK ON THE KENNEDY ONE DEP; CANARSIE CLB OFF RWY 31L. WE TURNED AT 400 FT TO GO DIRECT CRI VOR. I HAD THE 039 DEG RADIAL DIALED IN ON GREEN DATA PRIOR TO DEP. AS WE APCHED CRI; THE AUTOPLT WAS ENGAGED AND THE ACFT BEGAN TO TURN TO THE R. UNSURE OF WHY THE ACFT WAS TURNING; I PUT THE AUTOPLT IN HDG MODE AND MADE A TURN TO THE L TO GET BACK DIRECT CRI. I THEN NOTICED WE WERE CLOSE TO THE VOR AND THE NEEDLE WAS SWINGING AND AS WE APCHED WE WERE ABOUT TO PASS OVER THE VOR. ABOUT THIS TIME THE ATC DEP CTLR TELLS US TO TURN TO A HDG OF 060 DEGS; A L-HAND TURN. HE THEN VERIFIES IF WE ARE ON THE CANARSIE CLB AND WE SAY AFFIRMATIVE. HE INSTRUCTS US TO TURN IMMEDIATELY TO 060 DEGS WHILE WE WERE ALREADY IN THE TURN. HE TELLS US THAT WE REALLY NEED TO READ THE DEP CAREFULLY TO FOLLOW IT; WHICH WE THOUGHT WE WERE DOING. HE DIDN'T TELL US WHAT WE DID WRONG IF ANYTHING. AFTER DISCUSSING THE DEP WITH THE FO; WE CONCLUDED THAT WE MUST HAVE PASSED THE 039 DEG RADIAL WHILE FLYING DIRECT TO CRI; BUT WE CAN'T BE SURE SINCE WE WEREN'T TOLD WHAT THE PROB WAS BY ATC. IT HAD BEEN A LONG DAY AND THE CREW HAD ENDURED BAD WX AND AN EXTENSIVE; UNNECESSARY GND DELAY PRIOR TO THIS LEG. THE CREW HAD NOT EATEN A MEAL IN THE PREVIOUS 11 HRS. WE WERE HUNGRY AND TIRED. WITH ONLY A 35 MIN FLT TO OUR OVERNIGHT; WE CHOSE TO SKIP TRYING TO GET SOMETHING TO EAT AT JFK; THINKING RESTAURANTS WOULD PROBABLY BE CLOSED ON A SUNDAY NIGHT ANYWAY. IN RETROSPECT; KNOWING IT USUALLY TAKES A LONG TIME TO GET OUT OF JFK; WE SHOULD HAVE TAKEN SOME TIME TO SEE WHAT WE COULD HAVE GOTTEN TO EAT; IN ORDER TO KEEP OUR BODIES AND BRAINS FUNCTIONING PROPERLY.