Date: 201302
Local time of day: 1201-1800
Location: BKL.Airport, OH
Flight conditions: IMC
Light: Daylight
Aircraft: Beechjet 400
Operator: Air Taxi
Operating under: Part 135
Flight plan: IFR
Mission: Passenger
Flight phase: Climb
Airspace: Class B CLE
ATC / advisory: TRACON CLE
Aircraft component: Traffic Collision Avoidance System (TCAS)
Component problem: Malfunctioning
Reporter organization: Air Taxi
Reporter function: Captain; Pilot Flying
Reporter qualification: Flight Crew Air Transport Pilot (ATP)
Human factors: Situational Awareness
Second reporter function: Pilot Flying; First Officer
Anomaly: ATC Issue All Types; Aircraft Equipment Problem Less Severe; Conflict Airborne Conflict; Deviation - Altitude Overshoot; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance
Detector: Person Flight Crew
When detected: In-flight
Result: Flight Crew Took Evasive Action
Contributing factors: Aircraft; Procedure; Weather
Primary problem: Ambiguous

Narrative: After takeoff we were on an assigned heading of approximately 030 degrees; level at 2;000 feet and in IMC. The SIC was hand flying the aircraft at this time. Departure Controller then gave us a turn to 130 degrees and a climb to 3;000 feet. Shortly thereafter our Controller told us of traffic at our 2 o'clock position. We were in our turn and just beginning our climb to 3;000 feet. Our Controller then told us the traffic was at 2;400 feet. We spotted our traffic on TCAS at about twelve o'clock; within 1-2 miles; and 200 feet above us. Simultaneous to my telling the SIC to increase our rate of climb and turn; he had already added power and pitched up. He also increased his rate of turn and passed the 130 degrees assigned in order to go to the right of the traffic. Once above and clear of the traffic he began a rapid push over to stop his climb at 3;000 feet; but could only stop his climb at 3;400 feet without causing items to fly upwards. Our Controller then came up and said he showed us at 3;400 feet and told us to descend to 3;000 feet. I informed him that we had to climb rapidly to avoid traffic and that we were in the process of descending to 3;000 feet and turning back to a heading of 130 degrees. Our flight thereafter proceeded normally. Our passengers did comment on our rapid pull up; followed by our rapid push over. Upon landing we explained what had occurred and they were quite satisfied with our explanation. No injuries were suffered. I advised Maintenance Control that; given the situation; we were at a loss to understand why our TCAS system failed to give us a TA or an RA before we took action. If the Controller knew the traffic was at 2;400 feet and our TCAS system showed him 200 feet above while we were climbing and turning into him; why didn't we receive alerts? Maintenance had me collar and MEL the TCAS system and they were going to have it checked. I do not see how we could have anticipated nor prevented an Air Traffic Controller from turning and climbing our aircraft into traffic when that traffic was unknown to us before our turn and climb. I do recommend that during all takeoffs that the MFD range rings in the mapping mode be put into the lowest available range. That would limit the traffic shown to only aircraft that could potentially be in conflict with it.


Second narrative: [No substantive additional information was provided in the secondary narrative.]


Synopsis: A BE-400 flight crew in IMC; cleared to climb and given a turn vector; took evasive action to avoid pop-up traffic shown by TCAS as 200 feet above them and between one and two miles away. While doing so they exceeded their assigned heading and altitude. Their TCAS provided neither TA nor RA warnings.