Date: 202006
Local time of day: 0601-1200
Location: ZZZ.Airport, US
Flight conditions: VMC
Light: Daylight
Aircraft: Skyhawk 172/Cutlass 172
Operator: Corporate
Operating under: Part 91
Flight plan: None
Mission: Training
Flight phase: Takeoff / Launch
Airspace: Class G ZZZ
ATC / advisory: CTAF ZZZ
Second aircraft: Skyhawk 172/Cutlass 172
Reporter organization: Corporate
Reporter function: Instructor
Reporter qualification: Flight Crew Multiengine; Flight Crew Commercial; Flight Crew Flight Instructor; Flight Crew Instrument
Human factors: Training / Qualification; Communication Breakdown; Situational Awareness
Anomaly: Conflict NMAC
Detector: Person Flight Crew
When detected: In-flight
Result: Flight Crew Took Evasive Action
Contributing factors: Procedure; Aircraft; Human Factors
Primary problem: Human Factors

Narrative: My private pilot student and I were practicing takeoff and landings with full-stop taxi backs each time. We had just announced on the CTAF frequency that we were departing on Runway X to remain in the pattern (this was our 6th takeoff on Runway X; and we had been in the traffic pattern for some time; the whole time using Runway X. There were also 1-2 other aircraft in the pattern at various times that were also using Runway X with us; without any issues.) As the student was rotating to lift-off; we heard another aircraft announce on the CTAF frequency that he was departing Runway XY. I immediately made a second call that we were taking off on Runway X and rotating at that moment; unsure if the other aircraft had heard our prior transmission. I was preparing to instruct my student to abort the takeoff; however; after a quick evaluation I made the determination that we would not have enough remaining runway distance to bring the aircraft to a safe stop. Soon after takeoff and as we approached 400 feet AGL; my student yelled out; 'Oh my God; there he is!' I immediately announced 'my controls;' took control of the flight controls; and aggressively banked to the left while pitching up; away from the aircraft. As I did so; I noticed the other aircraft directly in front of us; passing from our left to right. I estimated the other aircraft was within 100 feet of our altitude and 500-600 feet horizontally from our aircraft. I continued to fly the aircraft due north away from the airport; and safely began climbing us towards 2;500 feet. As we left I made an announcement on CTAF that we were departing the area to the Northeast; at that time; the other aircraft made a transmission; saying 'ZZZ traffic; sorry about that last one.'I believe the other pilot's disregard of our transmission (whether due to missing it or consciously disregarding it) was a key contributing factor to this incident. Upon reviewing the incident with my student and using it as a teachable moment; we discussed the importance of being vigilant at non-towered airports; making sure we listen to other aircraft transmissions; and never deciding to takeoff if another aircraft has already announced they were taking off on a cross runway. I also discussed had this occurred again; instead of simply making a second announcement I could have specifically asked the other aircraft to verify that they had heard our transmission.




Synopsis: Instructor Pilot reported a NMAC on departure with another aircraft departing a different runway.