GLF5 CREW AVOIDED A TSTM CELL BY TURNING AWAY. THEY TRIED TO COORD THE TURN WITH ATC. TFC VOLUME AND FREQ CONGESTION PREVENTED THIS.

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ON MAY/SUN/02 AT AROUND XA15; WE WERE ON CLBOUT OUT OF MDW. THERE WAS CONTINUOUS MODERATE TURB ON DEP AS WELL AS CUMULONIMBUS TO THE W OF CHICAGO AND HVY TFC. WE WERE ON AN ASSIGNED HDG OF 270 DEGS; FL240. THIS HDG WAS DRIVING US DIRECTLY INTO A FAIRLY MENACING CELL. WE MADE 4 XMISSIONS REQUESTING A 240 DEG HDG. ON THE 4TH; THERE WERE VARIOUS XMISSIONS AT THE SAME TIMED THE CAPT FOR THIS TRIP WAS IN THE R-HAND SEAT HANDLING THE RADIOS. WE HEARD WHAT APPEARED TO SOUND LIKE ROGER TO OUR CALL SIGN AND HDG. WE TURNED TO 240 DEGS. THERE WAS A PERIOD OF 15-20 SECONDS WHERE NO XMISSIONS FROM ATC WERE HEARD; THEN ATC GAVE US A 180 DEG HDG. WE NEVER RECEIVED ANY TCASII ALERTS -- RA OR TA. THE CLOSEST TFC WE OBSERVED WAS PRIOR TO TURNING TO 180 DEG HDG. IT WAS AT OUR 2 O'CLOCK POS; 1300 FT ABOVE; OUTSIDE THE 5 NM RING. I AM MAKING THIS RPT ON MAY/THU/02. I WOULD HAVE MADE IT EARLIER; HOWEVER; THERE WERE NO INDICATIONS FROM EITHER ATC OR ANY OTHER AUTHS THAT THERE WAS A PROB UNTIL TODAY. SUPPLEMENTAL INFO FROM ACN 546251: WE WERE DEPARTING CHICAGO AREA ENRTE TO PHX. THERE WAS LOTS OF CONVECTIVE ACTIVITY IN THE AREA; AND WE WERE EXPERIENCING CONSTANT MODERATE TURB WITH SOME JOLTS 'BEYOND MODERATE.' RADAR WAS PAINTING NUMEROUS RETURNS. WE WERE ON A 270 DEG ASSIGNED HDG; REQUESTED AND RECEIVED A 240 DEG HDG. SHORTLY THEREAFTER; IT WAS APPARENT THAT WE NEEDED TO TURN BACK R TO 270 DEGS DUE TO WX TO AVOID A CELL. THE FREQ HAD BECOME VERY BUSY AND AT LEAST 3 CALLS BY US TO TURN BACK TO 270 DEGS WERE NOT ANSWERED. ON THE 4TH CALL; THE PF AND I BOTH HEARD OR THOUGHT WE HEARD THE CTLR ACKNOWLEDGE OUR CALL AND WE RESUMED A 270 DEG HDG. SHORTLY AFTER; THE CTLR; OBVIOUSLY AGITATED; CALLED ASKING FOR OUR HDG. WE GAVE IT TO HIM AND HE RESPONDED 'NEGATIVE; NEGATIVE; YOU'RE SUPPOSED TO BE ON A 240 DEG HDG; TURN R NOW TO 180 DEGS.' AT THIS POINT WE COULD JUST CLR THE CELL WE HAD TURNED TO AVOID AND WE TURNED IMMEDIATELY. DURING THE TURN; WE SAW THE OTHER ACFT ON TCASII AT THE 5 MI RING. AT NO TIME DID WE GET A TA OR RA. WE THEN SPOTTED THE OTHER ACFT VISUALLY AS WE TURNED AWAY TO THE 180 DEG HDG. I BELIEVE THE PROB WAS CAUSED BY NUMEROUS ACFT TRYING TO AVOID SOME SIGNIFICANT WX. THE HIGH PLT/CTLR WORKLOAD; NUMEROUS UNANSWERED RADIO CALLS (MISSED COMS) RADIO XMISSIONS BEING 'STEPPED ON' BY OTHER ACFT; AND POSSIBLY ANOTHER ACFT ON FREQ WITH SOME SIMILARITY IN HIS CALL SIGN. PERHAPS IF THE CTLR HAD BROADCAST AN 'ALL ACFT STAND BY' IT WOULD HAVE CLRED THE FREQ. IN OUR CASE; THE WX; THE TURB; AND THE ABSOLUTE NEED TO AVOID PENETRATING A TSTM WERE CONTRIBUTORS.