Skyhawk 172/Cutlass 172
Flight Crew Private; Flight Crew Instrument
Flight Crew Total 230; Flight Crew Type 160
Aircraft Equipment Problem Critical
Air Traffic Control Provided Assistance; Flight Crew Returned To Departure Airport; Flight Crew Landed in Emergency Condition; General Flight Cancelled / Delayed; General Maintenance Action
Aircraft
Me and a Flight Instructor were planning on taking Aircraft X; a Cessna 172S; to go practice some commercial maneuvers in the southeast practice boxes I was the PIC for this flight. ZZZ was the departure airport. After start-up; we taxied to the north run-up with no issues. A run-up was completed with no issues or negative signs; and the 'Before take-off' checklist was completed and a takeoff briefing was completed.  We were cleared for take-off XXL and 'fly straight out'. A short field take-off was performed for this particular take off. Adequate RPMs were present and all engine gauges were in the green. the take-off was performed and on the climb out the flaps were raised. at about 700-800 AGL (just about over A16) the RPMs dropped about 400RPMs for about 4 seconds and the nose began to pitch down. Adequate RPMS returned after about 4 seconds and we kept the climb going. I Immediately called 'Aircraft X mayday mayday we're getting some engine roughness were going for Runway XY' and began turning to the east to make a left downwind for Runway XY. ATC did a wonderful job of helping us handle this emergency/clearing traffic off the runway. We were cleared to land Runway XY quickly. We landed the aircraft safely and cleared the runway with no further issues. A squawk was written up for the incident and the plane was grounded so that Maintenance could investigate.
On initial climb out from Runway XXL at ZZZ with a commercial student.  At approximately 800 feet AGL we had a significant engine hesitation. Student [advised ATC] immediately turned left to enter a downwind to Runway XY.  We landed without further issue on Runway XY and the engine did not fully quit.  Grounded the airplane.
C172 flight crew reported engine power loss on takeoff; resulting in an air turnback.