Learjet 45
Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 100; Flight Crew Total 18500; Flight Crew Type 1500
Conflict Airborne Conflict; Deviation - Altitude Excursion From Assigned Altitude; Inflight Event / Encounter CFTT / CFIT
Flight Crew FLC complied w / Automation / Advisory; Flight Crew Took Evasive Action
Aircraft
Departing from ADS we were cleared for takeoff from RWY 15 and given a turn to heading 090. Our initial altitude clearance was 2000 feet. ADS is directly below the 2000 feet overhang to the DFW Class B airspace. A single-engine Cirrus was cleared to enter a downwind for runway 15 by the tower. We were warned of the Cirrus by tower as we began the turn. Once on a heading of 090 and approaching 2000 feet; we received a TCAS TA then almost immediate RA to descend. I saw the aircraft; however the pilot flying decided to descend just in case I had the wrong plane in sight. In the meantime while following the RA our GPWS gave us a 'Don't Sink!' command. We were VMC and knew the terrain fairly well. However; we couldn't be sure that there wasn't a tower or unknown object which was not easily visible. We advised ATC of the RA after being switched to Fort Worth Departure by the tower. There was not time to advise ADS tower of the RA. Ultimately; it became apparent that if this had been in a lower visibility environment; things might have been even more interesting.
LR45 Captain reported that while departing ADS and descending in compliance with a TCAS RA they received a 'Don't Sink!' message from the GPWS.