IAI1124/1124A Westwind
Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 105; Flight Crew Total 2850; Flight Crew Type 325
Communication Breakdown; Situational Awareness; Time Pressure
Aircraft Equipment Problem Less Severe; Conflict Airborne Conflict; Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Clearance
Flight Crew Took Evasive Action
Airport; Human Factors
Takeoff clearance was given with a turn after takeoff. Before reaching 500 ft. AGL; an RA (Resolution Advisory) was received in the aircraft for another aircraft directly ahead so the turn was started early. Neither the Tower nor the Departure Controller mentioned the airplane directly in our path. Then upon reaching 9;000 ft. assigned; another RA was received for a plane at 9;000 ft. and less than two miles off the left of the plane. At that moment I was not sure whether the plane was coming toward our airplane or not.I disconnected the autopilot and initiated a climb and turn away from the direction and altitude of the RA alert and at a greater bank angle than the autopilot would perform. In doing so; I exceeded the assigned altitude by 1;000 ft. and then once I was clear of the other aircraft I descended back to 9;000 ft. on the heading assigned. The airspace was very busy and the Controller was handling several aircraft. He stated that I deviated from his assigned altitude. I explained I had an RA.I reacted aggressively to the second RA because the first RA was so unexpected just after takeoff and while being transferred from Tower to departure. If I had not been climbing faster and turning I would have quickly overtaken the small piston plane that was directly in front of us. Once that happened; when the RA went off again and I couldn't see the other plane and didn't know where it was coming from or going except that it was exactly at our assigned altitude and within the inner ring (our TCAS was set on 10 mile range) on the TCAS; I took more drastic action than might have been necessary as it turned out.The Controller was convinced there was no other traffic in our area and said as much; but we were not warned about either of those two airplanes. So he must have been seeing something different than what we were seeing inside the airplane.
WW24 Pilot reported taking evasive action responding to two Resolution Advisories after takeoff.