EMB120 FLC PERFORMS AN EVASIVE ACTION TO MISS 2 C140'S FLYING OPPOSITE DIRECTION. FLC MISJUDGED THEIR ACFT'S PERFORMANCE CAPABILITIES AND THE RATE OF CLOSURE.

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CLBING OUT OF CRW ON VECTORS TO OUR FIRST FIX WE WERE ADVISED BY ATC ABOUT A FLT OF SEVERAL C140'S. A PAIR OF THEM IN FORMATION; APPEARED ON OUR TCASI AT A RANGE OF 5- 6 MI. AT FIRST; IT LOOKED LIKE WE WOULD BE ABLE TO CLB AND PASS THROUGH THEIR ALT WITH NO CONFLICT. SOON; WE REALIZED THAT THIS WAS INCORRECT. AT 1200 FT HORIZ AND 200 FT VERT WE LEVELED THE ACFT AND TURNED L TO AVOID A POSSIBLE COLLISION. THE CTLR ASKED IF WE HAD TURNED L. THE CAPT RESPONDED AFFIRMATIVE TO THE QUESTION. THE CTLR REPLIED 'THAT'S FINE; BUT I'D LIKE TO KNOW ABOUT IT.' THE CAPT SAID THE MANEUVER WAS UNEXPECTED AND HE DIDN'T HAVE TIME TO RPT THE TURN; BUT HE APOLOGIZED FOR BEING UNABLE TO ADVISE THE CTLR. I BELIEVE THE CONFLICT RESULTED FROM OVERESTIMATING OUR CLB PERFORMANCE AND UNDERESTIMATING OUR CLOSURE RATE. I SHOULD HAVE SLOWED OUR RATE OF CLB DOWN OR LEVELED OFF. ALSO; LOOKING TO THE R AT 2 SMALL ACFT; I COULDN'T SEE THE TCASI. I COULDN'T SEE THEIR DIRECTION OF FLT UNTIL THE LAST FEW SECONDS BEFORE OUR TURN TO THE L. SUPPLEMENTAL INFO FROM ACN 380281: IN RETROSPECT; I BELIEVE THE CONFLICT RESULTED FROM MY UNDERESTIMATING OUR RATE OF CLOSURE. IF I HAD IT TO DO OVER; I WOULD HAVE LEVELED OFF EARLIER AND NOT NEEDED THE TURN OFF COURSE. I MIGHT ALSO HAVE OVERESTIMATED OUR CLB PERFORMANCE. A CONTRIBUTING FACTOR TO THIS INCIDENT MAY HAVE BEEN A FALSE SENSE OF SECURITY PROVIDED BY THE TCASI. WITHOUT IT; I DOUBT THAT I WOULD HAVE EVEN ATTEMPTED TO OUT CLB THE TFC.