CRJ200 CREW TURNS EARLY ON THE KENNEDY 1 CANARSIE CLIMB TO THE DISPLEASURE OF AN N90 CONTROLLER.

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ON DEP FROM JFK WE WERE ASSIGNED THE JFK 1 WITH THE CRI CLB. IT WAS THE FO'S LEG AND HE GAVE ME A DETAILED BRIEFING; POINTING OUT THE DISCUSSION FROM GND SCHOOL ABOUT TURNING E OF THE 039 DEG RADIAL. HE SET UP HIS RADIOS FOR THE 176 DEG RADIAL OFF CRI AND I PUT THE 039 DEGS AND 176 DEG RADIALS OFF CRI IN THE FIX PAGE OF THE FMS FOR REF. THE WINDS IN JFK WERE 280 DEGS AT 17 KTS GUSTING 23 KTS. AFTER TKOF AT 400 FT THE FO BEGAN THE TURN TOWARDS CRI AND I BEGAN DOING THE CLB CHKLIST. THE CLB WAS QUITE BUMPY WITH MODERATE TURB. THE FO WAS MAKING THE TURN A LITTLE EARLY TO AVOID OVERSHOOTING THE 039 DEG RADIAL; BUT WITH THE STRONG WIND; WE UNDERSHOT THE VOR. AS WE WERE HEADING TOWARDS THE 176 DEG RADIAL; DEP ASKED OUR HDG AND QUESTIONED WHY WE TURNED SO EARLY. WE SAID THAT WE WERE IN THE TURN TO INTERCEPT THE 176 DEG RADIAL. DEP TOLD US WE TURNED TOO EARLY AND TO TURN TO 060 DEGS AND CLB TO 6000 FT. AS THE FO WAS CONTINUING THE TURN AND CLB; I WAS SETTING THE HDG BUG AND ALT SELECTOR. ATC WAS INFORMING US THAT TURNING EARLY WAS AS BAD AS LATE AND THAT ACR HAS HAD ISSUES WITH THIS SID AND WE SHOULD REALLY READ THE SID BEFORE TKOF. DURING THAT TIME; THE FO HAD ASKED FOR HDG MODE AND THE AUTOPLT. I THOUGHT I HAD ENGAGED THE AUTOPLT; BUT WAS DISTR BY A SINGLE CHIME CAUTION MESSAGE. THE AUTOPLT DIDN'T ENGAGE AND THE ACFT CLBED THROUGH 6000 FT BY ABOUT 400 FT. THE FO RECAPTURED THE ALT AND THE AUTOPLT WAS RE-ENGAGED. THE CTLR THEN GAVE US A HIGHER ALT AND TOLD US NOT TO WORRY ABOUT THE UNDERSHOOT AND SWITCHED US TO ANOTHER FREQ. I BELIEVE PART OF THE PROB WAS THE EMPHASIS OF OVERSHOOTING THE 039 DEG RADIAL. THE ACFT WAS LIGHT; SO WE ROTATED EARLIER (LENGTH WISE) THAN NORMAL; SO WE WERE FURTHER FROM CRI ALREADY AND THE STRONG WINDS ALSO HELPED KEEP US AWAY FROM THE 039 DEG RADIAL. WITH THE LIGHT ACFT WE WERE CLBING AT OVER 3000 FPM WHICH MAKES THE LEVELOFF COME THAT MUCH QUICKER. THE ALT PROB WAS A COMBINATION OF FACTORS. WE WERE ALREADY DISTR FROM ATC TALKING ABOUT THE PROBS WITH THE SID. THE AUTOPLT DIDN'T ENGAGE AS PLANNED; THE TURB AND ALSO THE CAUTION LIGHT AND SINGLE CHIME BECAME A DISTR. I SHOULD HAVE PAID MORE ATTN TO THE ACFT TRACK DURING THE INITIAL PART OF THE CLB AND WAITED ON THE CHKLIST UNTIL WE WERE ESTABLISHED.