Date: 201903
Local time of day: 1201-1800
Location: ZZZ.Airport, US
Light: Daylight
Aircraft: Commercial Fixed Wing
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Other Go-Around
Airspace: Class C ZZZ
ATC / advisory: Tower ZZZ
Second aircraft: Commercial Fixed Wing
Reporter organization: Air Carrier
Reporter function: Pilot Flying; Captain
Reporter qualification: Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Human factors: Situational Awareness; Communication Breakdown
Second reporter function: First Officer; Pilot Not Flying
Anomaly: ATC Issue All Types; Conflict NMAC; Deviation / Discrepancy - Procedural Published Material / Policy
Detector: Automation Aircraft TA; Person Flight Crew
When detected: In-flight
Result: Air Traffic Control Issued New Clearance; Flight Crew Took Evasive Action
Contributing factors: Procedure; Weather; Human Factors
Primary problem: Human Factors

Narrative: As we were on short final to Runway 22L at ZZZ; about 300' from touchdown; we were told to go around by ZZZ Tower. There was another Company aircraft that had been cleared for takeoff; but had taken the runway very slowly; for some reason they did not start their takeoff roll immediately. We did our normal go-around procedure and flew runway heading as instructed. At about 1000' AGL we got a TCAS (Traffic Collision Avoidance System) alert 'Traffic; Traffic.' We looked out our front window; and to our astonishment we saw a [another] aircraft slightly above 100'-200' and less than 1/4 mile. It could have been as little as a few hundred feet in front. It was so close I could see his flap retractions. We leveled off at 1000' to allow him to climb out and get some altitude separation. We did not get an RA (Resolution Advisory) probably because it is inhibited below 1000' RA. The Tower did not say anything to either aircraft and I'm not sure they were aware of our close proximity. They told us to contact Departure Control and we were given an immediate turn to the south for another RNP (Required Navigation Performance) approach and landing. My F/O (First Officer) and I discussed this at length at the gate and we were in agreement that we were given a fly runway heading clearance. Apparently the aircraft that we went around for had finally started his takeoff roll as we were doing our go-around. If he would have started his takeoff roll about one or two seconds later; it could have ended in disaster as he couldn't see me and I couldn't see him; and with both aircraft TCAS RA inhibited.For runway heading clearances on go-around for aircraft on the runway takeoff clearances should be canceled.


Second narrative: On RNAV Y 22L turned into a visual. We were cleared to land with an aircraft lined up and waiting on the same runway. They were cleared to take off; but were slow in doing so; at about 300' we are instructed to 'go around; fly runway heading; climb and maintain 3000'.' We went around; and below us [another aircraft] was rotating and climbing out of our field of view. At about 1000' the same aircraft appeared in front of us; same altitude and less than a mile; very close. TCAS (Traffic Collision Avoidance System) only produced a 'Traffic; Traffic' Alert but no Resolution Advisory; probably because of the low altitude and proximity to the airport. Our first vector turn came from Departure. I seem to remember Tower or Departure telling our traffic to initiate their turn but I'm not sure at what point that occurred. It was the closest I've ever been to another aircraft while airborne in years of flying.A better clearance would have been to 'Go around; turn heading XXX; maintain 3000'' or 'Go around; fly the missed approach as published' which has a turn to the south before 1000'AGL. These suggestions are not aimed to tell controllers how to do their job but rather to highlight what would be easier for us in the flight deck. Also; I know that controllers are encouraged or forbidden to issue instructions below 1000' AGL. Although a good policy; I strongly believe in a case like this; both departing and arriving crews would be quite happy to receive and comply with a simple instruction like 'Immediate left turn heading XXX'; no need to reply. It is a busy time but far less so than when trying to recover from a mid-air collision.


Synopsis: ZZZ Tower Controller and air carrier Flight Crew reported a near mid-air collision during go-around with a departing aircraft on the same runway.