AN NMAC OCCURRED WHEN A DEP AND A MISSED APCH OCCUPIED THE SAME AIRSPACE SIMULTANEOUSLY. THE TWO PROCS HAVE A BUILT-IN CONFLICT WHEN A MISSED APCH IS EXECUTED AND DEP EITHER PROCEEDS OR IMMEDIATELY FOLLOWS THE MISSED APCH.

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AFTER LIFT-OFF FROM JFK RWY 04L; WHILE IN CLBING R TURN TO 5000 FT; 100 DEG HDG; WE HEARD AN ACR Y B757 ON FREQ CALL MISSED APCH ON RWY 04R. SHORTLY THEREAFTER; WHILE AT APPROX 1000 FT AGL; WE RECEIVED TCASII RA 'MONITOR VERT SPD;' FOLLOWED VERY SHORTLY BY 'DSND.' WE STARTED A PUSHOVER TO COMPLY WITH TCASII AND INFORMED ATC; THEY ISSUED INSTRUCTIONS TO LEVEL AT 1500 FT ABOUT THE TIME OUR CLB WAS PEAKING AT 1700 FT. MY FO HAD OTHER ACFT IN SIGHT AS THEY PASSED OVERHEAD ABOUT THIS TIME; HE ESTIMATED THE VERT SEPARATION AS 300-500 FT; ACR Y ESTIMATED 200 FT. TCASII GAVE 'CLR OF CONFLICT;' SHORTLY AFTER XING. THE DEP AND MISSED APCH PROCS FOR JFK RWY 04R AND 04L ARE A SET-UP FOR THIS TO HAPPEN AND I HAD BEEN THINKING ABOUT THIS AS WE TAXIED OUT. WHEN ACR Y CALLED MISSED APCH; MY IMMEDIATE COMMENT TO MY FO WAS THAT THIS WOULD BE A PROB AND TO LOOK FOR THE OTHER ACFT. THE TCASII WARNING FOLLOWED IMMEDIATELY. IN MY OPINION; DEPS; AT LEAST IN IMC CONDITIONS; SHOULD MAINTAIN RWY HDG FOR SOME MINIMAL SPECIFIED DISTANCE OR UNTIL A CERTAIN SPECIFIED ALT; EVEN IF QUITE LOW; TO GIVE ATC A MOMENT TO REACT IN THE EVENT OF A SIMULTANEOUS MISSED APCH. SUPPLEMENTAL INFO FROM ACN 338299: AT APPROX XA09 AN AIRBUS (ACR X) WAS CLRED FOR TKOF ON RWY 4L. ACR X ACKNOWLEDGED THE TKOF CLRNC AND ADVISED 'ROLLING.' SHORTLY AFTER THIS AN ACR Y B757 ON APCH TO RWY 4R ADVISED HE WAS ABORTING THE APCH AND GOING AROUND. ACR Y WAS AT THE OM; 2.1 MI FROM THE RWY; AT THIS TIME. ACR Y WAS INSTRUCTED TO TURN R TO A HDG OF 130 DEGS AND A CLB TO 2000 FT TO ENSURE SEPARATION WITH THE RWY 4L DEP. THE DATA BLOCK AND RADAR TARGET OF ACR Y THEN DROPPED OFF THE BRITE RADAR DUE TO PROXIMITY TO THE FIELD. AT APPROX XA11; TARGETS APPEARED ABOUT A MI OFF THE DEP END OF RWY 4R; ACR Y INDICATING 2000 FT AND ACR X INDICATING 1300 FT ABOUT A MI FROM ACR Y. ACR X WAS INSTRUCTED TO STOP HIS CLB AND TURN L TO 040 DEGS. ACR X SUBSEQUENTLY CONTINUED ON TO HIS DEST AND ACR Y LANDED ON RWY 4R A FEW MINS LATER. THIS INCIDENT COULD HAVE BEEN AVOIDED HAD THE ACFT GIVEN A TIMELY COMPLIANCE TO INSTRUCTIONS. REVIEW OF TAPES AND THE RADAR DUMP SHOWED ACR X DID NOT BEGIN HIS DEP ROLL UNTIL 1 MIN AND 15 SECS AFTER HE ADVISED HE WAS ROLLING. ACR Y DID NOT BEGIN HIS TURN TO 130 DEGS UNTIL APPROX THE DEP END OF RWY 4R; ABOUT 3.5 MI BEYOND THE POINT WHERE HE WAS INSTRUCTED TO TURN. NEITHER ACFT ADVISED THAT THEY WERE UNABLE OR UNWILLING TO EXECUTE THEIR CLRED INSTRUCTIONS AT THE TIME THEY ACKNOWLEDGED THEM. THIS PROVED CRITICAL DUE TO RADAR LIMITATIONS IN THE VICINITY OF THE FIELD AND THE POOR VISIBILITY AND LOW CEILINGS EXISTING AT THE TIME. THE CTL TOWER WAS LESS VIGILANT THAN IT COULD HAVE BEEN DUE TO THE LIGHT TFC AND APPEARANCE THAT ACTIONS TAKEN HAD RESOLVED ANY APPARENT CONFLICT. THIS SIT CAN BE AVOIDED IN THE FUTURE BY CHANGING THE JFK RWY 4L SID AND AIRSPACE. ALL RWY 4L DEPS MUST CROSS THE RWY 4R MISSED APCH COURSE. TO AVOID THIS; THE DEP MUST BE SENT ON A RWY HDG WHICH WILL PUT THEM INTO LGA AIRSPACE NE OF THE FIELD. MORE AIRSPACE MUST BE GIVEN TO JFK FOR THIS RWY CONFIGN AND THE SID SHOULD REQUIRE A MORE NORTHERLY HDG OFF OF RWY 4L INSTEAD OF TURNING R TO 100 DEGS.