Skyhawk 172/Cutlass 172
Flight Crew Commercial; Flight Crew Flight Instructor; Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 200; Flight Crew Total 1000; Flight Crew Type 500
Situational Awareness; Communication Breakdown
Conflict NMAC
Flight Crew Took Evasive Action
Human Factors
I was instructing on a training flight; and departed from ZZZ; while climbing out and making a crosswind departure to the east. The student was flying while I was making radio calls. Upon reaching approximately 2;300 feet MSL; I caught a plane performing a steep left turn bank towards us. I took flight controls from the student and descended around 500 feet approximately 1;000 feet AGL to avoid the other traffic. I made radio calls on CTAF at the local airport and the other aircraft was not on frequency. I proceeded to warn an aircraft behind us on CTAF performing a low approach with a departure to the east as well about an aircraft performing unpredictable maneuvers on the departure end at a low altitude. Once on the ground we were able to review the flight data and track logs of the other aircraft. My assumption is the other aircraft was unaware of their proximity to the airport and performing steep turns. Another contributing factor could have been the difference in altimeter settings between the two local airports and change from departure of approximately .11 in/hg. The maneuvers were being performed outside the local practice area box. Panel mounted ADS-B-In could have assisted with our situational awareness of the aircraft location. We had a portable receiver but did not have an tablet out as we were practicing crosswind landings so we had no traffic advisory until after corrective action. Once corrective action was taken; and tablet was consulted; we still had traffic above and turning towards us from the opposite side. We maintained a low altitude until well clear of the aircraft. Which leads me to believe he was unaware of us and their proximity to other aircraft and airport.
Flight Instructor reported an NMAC occurred nearby the departure airport when another aircraft maneuvered directly into their flight path requiring evasive action. The other aircraft was not on CTAF and appeared to not be aware of their proximity to the airport.