Date: 202101
Local time of day: 1201-1800
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: Initial Climb
Airspace: Class C ZZZ
Reporter organization: Corporate
Reporter function: Instructor
Reporter qualification: Flight Crew Instrument; Flight Crew Flight Instructor; Flight Crew Commercial; Flight Crew Multiengine
Human factors: Situational Awareness; Distraction; Communication Breakdown; Workload
Anomaly: ATC Issue All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy
Detector: Person Air Traffic Control; Person Flight Crew
When detected: In-flight
Result: Air Traffic Control Issued New Clearance
Contributing factors: Human Factors
Primary problem: Human Factors

Narrative: With a pre-checkride PPL (Private Pilot License) student; we were discussing pre-takeoff briefings and engine out after takeoff procedures. For our flight that day; I decided it would be good practical experience to get the student thinking about emergency landing options after an engine failure on takeoff. I believed it would be beneficial to see in reality what the landing options would look like with engine loss shortly after takeoff.The student performed a normal takeoff. Shortly after handoff from Tower Controller to Departure Controller (estimated 550 [feet.] AGL); I reduced the throttle to idle and instructed the student to pitch for best glide. I asked the student where an attempted landing might be possible based on our altitude and glide. I then asked if a 180 degree turn back to the departure runway seemed possible. After asking these two questions; I pushed the throttle back to full power and resumed normal climb. We continued to discuss procedures for engine failure on takeoff.Shortly after this; I noticed that our heading had deviated from the assigned runway heading by about 40 degrees to the south. Before I was able to correct; the Departure Controller assigned us an on-course heading. A few minutes later; Departure Controller asked if we had experienced an issue or needed assistance. I did not think much of it at the time and responded that we didn't need assistance.I later learned (from a phone call from Tower Controller to the flight school) that the Tower Controller had heard the engine power reduction and had seen the turn; and assumed an engine failure. I am not fully aware of what was experienced on the Tower Controller's end; but it is clear that my decision to practice an engine out procedure on takeoff caused a distraction to the Tower Controller that may have ended up impacting safety.Additionally; the fact that I did not notice the aircraft had turned 40 degrees to the south indicates that practicing that maneuver caused me to become more distracted that I had realized; or expected to be.Remedy:-Notify or request to Tower/ATC of my intention to practice any sort of maneuvers/procedures that are out of the ordinary from what is expected.-Be more aware of the probability of distraction while practicing any sort of maneuver during a high workload phase of flight.-Consider making engine out on takeoff procedures a ground instruction maneuver rather than in-flight.Human performance/Judgement:Ultimately; I made a bad judgement call by practicing an unusual/unexpected maneuver in controlled airspace. I did not expect or anticipate any disruption to the tower procedures; but I should have been more aware and given more thought to how my maneuvers would affect ATC.




Synopsis: Flight Instructor reported a track heading deviation while demonstrating an engine out after takeoff with student.