CARJ HAS TRACK DEV ON KENNEDY DEP; CANARSIE CLB WHEN FLT CREW INTERVENES WITH AUTOFLT CTLED DEP THAT APPEARS TO BE TURNING PREMATURELY.

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ON CLB FROM JFK ON THE KENNEDY 9 DEP/CANARSIE CLB; WE WERE ESTABLISHED DIRECT TO CRI AS PUBLISHED. AUTOPLT WAS ENGAGED; SET DIRECT TO CRI; ON FMS. A FEW MI PRIOR TO THE VOR; THE ACFT TURNED HARD TO THE L AND ESTABLISHED A STANDARD RATE TURN. IT APPEARED TO ME TO BE TURNING AWAY FROM THE DEP TRACK; SO I IMMEDIATELY WENT TO THE HDG MODE AND TURNED THE AIRPLANE BACK DIRECT TO THE VOR (THE PROC WAS DIRECT TO VOR AFTER TKOF). WE RE-ESTABLISHED DIRECT TO VOR BUT WERE VERY CLOSE TO IT AND NEEDED TO MAKE L TURN TO THE OUTBOUND RADIAL (176 DEGS) ALMOST IMMEDIATELY; SO I STARTED AN IMMEDIATE L TURN FOR THE OUTBOUND COURSE. BUT WE PASSED OVER THE VOR AND WENT SLIGHTLY WIDE ON THE TURN (TO THE W) IN THE L TURN THE WHOLE TIME. CTLR QUESTIONED US REGARDING WHAT CLB WE WERE FLYING. WE TOLD HIM AND HE GAVE US A TURN AND HDG; THEN HANDED US OFF. I'M NOT SURE WHY THE AIRPLANE BEGAN THE L TURN INITIALLY. IT'S POSSIBLE THAT IT WAS ACTUALLY TURNING TO INTERCEPT THE OUTBOUND COURSE BUT IT TURNED QUICKLY; TURNED EARLIER (IN MY PERCEPTION) THAN IT SHOULD AND IT KEPT TURNING. I'M VERY VIGILANT ON THESE DEPS (ESPECIALLY THIS ONE) AND THINK I WAS TOO WIRED TO EXPECT A PROB. AS A RESULT; I RAPIDLY CORRECTED BACK TO THE VOR. BUT; DUE TO THE SHORT DISTANCES ON THIS DEP; WE ENDED UP SLIGHTLY WIDE. 1 THING ABOUT THIS PROC: THE AIRPLANE BEHIND US APPARENTLY HAD THE SAME PROB. I HAVE HEARD NUMEROUS PLTS SAY THEY HAD PROBS ON THIS; AND HAVE HEARD CTLRS SAY THIS HAPPENS ALL THE TIME.