Date: 202109
Local time of day: 1201-1800
Location: ZZZ1.ARTCC, US
Flight conditions: VMC
Weather elements / visibility: 10
Light: Daylight
Aircraft: Skyhawk 172/Cutlass 172
Operator: FBO
Operating under: Part 91
Flight plan: None
Mission: Training
Flight phase: Landing
Airspace: Class G ZZZ1
ATC / advisory: UNICOM ZZZ
Second aircraft: Texan T6/Harvard (Antique)
Aircraft component: VHF
Component problem: Improperly Operated
Reporter organization: Personal
Reporter function: Pilot Flying
Reporter qualification: Flight Crew Private
Human factors: Communication Breakdown; Situational Awareness
Second reporter function: Instructor
Anomaly: Aircraft Equipment Problem Critical; Conflict NMAC; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy
Detector: Person Flight Crew
When detected: In-flight
Result: Flight Crew Executed Go Around / Missed Approach; Flight Crew Took Evasive Action
Contributing factors: Human Factors; Aircraft; Procedure
Primary problem: Procedure

Narrative: I was in my instrument flight lesson with my Instructor. We were doing the GPS XX approach at the ZZZ airport while self-announcing our position and did not hear anyone else on the CTAF frequency. As we are about .2 miles from the threshold of the XX Runway at ZZZ; tracking the GPS radial for landing on short final; my instructor immediately puts in full throttle. He then flies a climbing left turn to avoid the other aircraft while the T6 aircraft makes a climbing turn to the right. We have a quick conversation with the other aircraft where we note that we didn't hear the T6 aircraft's calls and would put in a report to NASA.


Second narrative: Me and My student were shooting a VFR GPS practice approach to Runway XX. We did a full procedure starting at ZZZZZ. We made traffic calls using distance instead of fixes so VFR traffic would know our position. (Example: ZZZ TRAFFIC Aircraft X IS 11 MILES NORTH OF THE FIELD SHOOTING THE GPS XX PRACTICE APPROACH TOUCH AND GO ZZZ). We made call outs at 11 miles (IAF); 5 miles (FAF); and short final (2-3 miles). When we were final approach fix inbound I noticed on my MFD of our G1000 an ADSB hit that was +23 above our altitude at FAF and east slightly north of the field heading northwest. I assumed the traffic was passing by as I had not heard call outs other than us for ZZZ and began to focus more on my student who was on his second ever approaches lesson and thus required a higher amount of monitoring and supervision than a student who was more experienced with approaches. On short final; maybe 10-20 seconds from touch down I glanced from the student to the MFD and noticed a MFD hit in yellow that was nearly on top of us and slightly behind at +100 ft. I looked back and to my left out a rearward window to see the engine slight belly of a T6 coming down on top of us. I immediately took control from the student and evasive action applying full power; flaps up and offset further down and to the left of the runway crossing the threshold about that time. The next time I saw the T6 was about 3-5 seconds later in a climbing right turn mid gear retraction. I called up and asked 'T6 IN ZZZ ARE YOU ON FREQUENCY?'. They replied that they had not heard us. We let them know we had not heard them either and would be filing a safety report with NASA. I think contributing factors to this was the T6 being a low wing and us being a high wind making visibility poor between both aircraft in close proximity. Further more me being task saturated with the student and assuming the aircraft was passing by ZZZ at FAF. Based on the tone of the T6 Instructors voice I got the impression that they were just as surprised to see us; leading me to believe they were also just ask task saturated teaching their student.


Synopsis: Flight Crew reported evasive action to avoid another aircraft that was not communicating their intentions correctly while landing.