FK10 CREW AVOIDED PENETRATING A TSTM IN C90 CLASS B AIRSPACE.

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ON DEP WE WERE GIVEN A 090 DEG HDG WHICH WOULD HAVE TAKEN US INTO A TSTM CELL E OF THE FIELD. THIS CELL WAS PAINTING ON RADAR. WE ASKED FOR A L TURN TO AVOID THE CELL AND WERE TOLD NOT TO CONTINUE 090 DEGS AND GO TO DEP CTL. WE CAME WITHIN 3-5 MI OF THE CELL AND TURNED R TO 140 DEGS TO AVOID IT AND INFORMED DEP CTL OF OUR HDG. WE PROBABLY SHOULD HAVE TRIED TO COORDINATE A HDG WITH TWR PRIOR TO TKOF ROLL. NO TCASII ALERTS WERE RECEIVED. SUPPLEMENTAL INFO FROM ACN 481425: CLRED FOR TKOF AND INSTRUCTED TO FLY A 090 DEG HDG AFTER TKOF. WE ADVISED TWR AFTER LIFTOFF THAT WE WOULD NEED A HDG OF 060 DEGS TO AVOID WX (TSTM CELL SHOWING ON RADAR AND FROM COCKPIT). TWR ADVISED HE COULD NOT ASSIGN A 060 DEG HDG AND FOR US TO REMAIN ON A 090 DEG HDG AND CONTACT DEP CTL. WE SWITCHED TO DEP AND ADVISED THEM THAT WE WERE TURNING TO A 140 DEG HDG AND WOULD ADVISE WHEN WE COULD TURN BACK TO A 090 DEG HDG. WE REMAINED VFR UNTIL WE WERE ESTABLISHED ON THE 140 DEG HDG. WE NEVER RECEIVED A TCASII ALERT NOR SAW ANY ACFT CLOSE (1-2 MI) TO OUR POS. THIS OCCURRENCE WOULD HAVE BEEN LESS CONFUSING IF WE HAD COORDINATED A HDG FOR WX BEFORE WE STARTED OUR TKOF ROLL.